Finite Group Databasebeta

← #17206993

Subgroups — #17206993

Order 4352.

3146 conjugacy classes of subgroups.

The subgroup lattice has 1872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763392C211yesmaximal, characteristic, complemented
2#14537099C211yesmaximal, characteristic, complemented
3#14537085C211yesmaximal, characteristic, complemented
4#14537076C211yesmaximal, characteristic, complemented
5#14537066C211yesmaximal, characteristic, complemented
6#14534679C211yesmaximal, characteristic, complemented
7#14534668C211yesmaximal, characteristic, complemented
8#14534636C211yesmaximal, characteristic, complemented
9#14534621C211yesmaximal, characteristic, complemented
10#14533039C211yesmaximal, characteristic, complemented
11#14532904C211yesmaximal, characteristic, complemented
12#14532829C211yesmaximal, characteristic, complemented
13#14532715C211yesmaximal, characteristic, complemented
14#14532676C211yesmaximal, characteristic, complemented
15#14532670C211yesmaximal, characteristic, complemented
16#14532602C211yesmaximal, characteristic, complemented
17#14532528C211yesmaximal, characteristic, complemented
18#14532519C211yesmaximal, characteristic, complemented
19#14532445C211yesmaximal, characteristic, complemented
20#14532320C211yesmaximal, characteristic, complemented
21#14532314C211yesmaximal, characteristic, complemented
22#14532240C211yesmaximal, characteristic, complemented
23#14532158C211yesmaximal, characteristic, complemented
24#14532152C211yesmaximal, characteristic, complemented
25#14532094C211yesmaximal, characteristic, complemented
26#14531482C211yesmaximal, characteristic, complemented
27#14531438C211yesmaximal, characteristic, complemented
28#14531417C211yesmaximal, characteristic, complemented
29C4×#10587639C211yesmaximal, characteristic, complemented
30C2×#11762688C211yesmaximal, characteristic, complemented
31C22×C4×D4×C17C211yesmaximal, characteristic, complemented
32C23×C22⋊D17C2211yescharacteristic
33#11763392—28no—
34C2×#10587584C2211yescharacteristic, complemented
35C2×#10587562C2211yescharacteristic, complemented
36C2×#10587561C2211yescharacteristic, complemented
37C2×#10587571C2211yescharacteristic, complemented
38C2×#10587580C2211yescharacteristic, complemented
39C2×#10587615C2211yescharacteristic, complemented
40C2×#10587615C2211yescharacteristic, complemented
41C2×#10587610C2211yescharacteristic, complemented
42C2×#10587564C2211yescharacteristic, complemented
43C2×#10587616C2211yescharacteristic
44C2×#10587616C2211yescharacteristic
45C2×#10587616C2211yescharacteristic, complemented
46C2×#10587616C2211yescharacteristic, complemented
47C2×#10587570C2211yescharacteristic, complemented
48C2×#10587625C2211yescharacteristic
49C2×#10587625C2211yescharacteristic
50C2×#10587568C2211yescharacteristic, complemented
51C2×#10587639C2211yescharacteristic
52C2×#10587639C2211yescharacteristic
53C2×#10587639C2211yescharacteristic
54C2×#10587639C2211yescharacteristic, complemented
55C2×#10587623C2211yescharacteristic
56C2×#10587623C2211yescharacteristic
57C2×C4×C22⋊D17C2211yescharacteristic, complemented
58C2×C4×C22⋊D17C2211yescharacteristic, complemented
59C2×C4×C22⋊D17C2211yescharacteristic, complemented
60C22×C22⋊Dic17C2211yescharacteristic
61C22×#63227C2211yescharacteristic, complemented
62C22×#63227C2211yescharacteristic, complemented
63#11762748C2211yescharacteristic, complemented
64#11762747C2211yescharacteristic, complemented
65#11762745C2211yescharacteristic, complemented
66#11762744C2211yescharacteristic, complemented
67#11762742C2211yescharacteristic, complemented
68#11762737C2211yescharacteristic, complemented
69#11762735C2211yescharacteristic, complemented
70#11762735C2211yescharacteristic, complemented
71#11762732C2211yescharacteristic, complemented
72#11762732C2211yescharacteristic, complemented
73#11762732C2211yescharacteristic, complemented
74#11762731C2211yescharacteristic, complemented
75#11762726C2211yescharacteristic, complemented
76#11762725C2211yescharacteristic, complemented
77#11762725C2211yescharacteristic, complemented
78#11762725C2211yescharacteristic, complemented
79#11762724C2211yescharacteristic, complemented
80#11762724C2211yescharacteristic, complemented
81#11762724C2211yescharacteristic, complemented
82#11762723C2211yescharacteristic, complemented
83#11762723C2211yescharacteristic, complemented
84#11762721C2211yescharacteristic, complemented
85#11762721C2211yescharacteristic, complemented
86#11762718C2211yescharacteristic, complemented
87#11762718C2211yescharacteristic, complemented
88#11762718C2211yescharacteristic, complemented
89#11762717C2211yescharacteristic
90#11762717C2211yescharacteristic
91#11762717C2211yescharacteristic
92#11762717C2211yescharacteristic
93#11762717C2211yescharacteristic, complemented
94#11762717C2211yescharacteristic, complemented
95#11762715C2211yescharacteristic, complemented
96#11762711C2211yescharacteristic, complemented
97#11762709C2211yescharacteristic, complemented
98#11762709C2211yescharacteristic, complemented
99#11762702C2211yescharacteristic, complemented
100#11762702C2211yescharacteristic, complemented
101#11762700C2211yescharacteristic, complemented
102#11762700C2211yescharacteristic, complemented
103#11762700C2211yescharacteristic, complemented
104#11762700C2211yescharacteristic, complemented
105#11762700C2211yescharacteristic, complemented
106#11762700C2211yescharacteristic, complemented
107#11762700C2211yescharacteristic, complemented
108#11762699C2211yescharacteristic, complemented
109#11762699C2211yescharacteristic, complemented
110#11762697C2211yescharacteristic, complemented
111#11762695C2211yescharacteristic, complemented
112#11762695C2211yescharacteristic, complemented
113#11762693C2211yescharacteristic, complemented
114#11762693C2211yescharacteristic, complemented
115#11762693C2211yescharacteristic, complemented
116#11762690C2211yescharacteristic, complemented
117#11762689C2211yescharacteristic
118#11762689C2211yescharacteristic
119#11762689C2211yescharacteristic
120#11762689C2211yescharacteristic
121#11762688C2211yescharacteristic
122#11762688C2211yescharacteristic
123#11762688C2211yescharacteristic
124#11762688C2211yescharacteristic
125#11762688C2211yescharacteristic
126#11762688C2211yescharacteristic
127#11762688C2211yescharacteristic
128#11762688C2211yescharacteristic
129#11762688C2211yescharacteristic, complemented
130#11762688C2211yescharacteristic, complemented
131#11762688C2211yescharacteristic, complemented
132#11762688C2211yescharacteristic, complemented
133#11762688C2211yescharacteristic, complemented
134#11762688C2211yescharacteristic, complemented
135#11762688C2211yescharacteristic, complemented
136#11762688C2211yescharacteristic, complemented
137#11762688C2211yescharacteristic, complemented
138#11762688C2211yescharacteristic, complemented
139#11762688C2211yescharacteristic, complemented
140#11762688C2211yescharacteristic, complemented
141#11762688C2211yescharacteristic, complemented
142#11762688C2211yescharacteristic, complemented
143#11762686C2211yescharacteristic, complemented
144#11762685C2211yescharacteristic, complemented
145#11762684C2211yescharacteristic, complemented
146#11762684C2211yescharacteristic, complemented
147#11762682C2211yescharacteristic, complemented
148#11762682C2211yescharacteristic, complemented
149#11762682C2211yescharacteristic, complemented
150#11762682C2211yescharacteristic, complemented
151#11762682C2211yescharacteristic, complemented
152#11762682C2211yescharacteristic, complemented
153#11762682C2211yescharacteristic, complemented
154#11762682C2211yescharacteristic, complemented
155#11762681C2211yescharacteristic, complemented
156#11762680C2211yescharacteristic, complemented
157#11762677C2211yescharacteristic, complemented
158#11762675C2211yescharacteristic, complemented
159#11762672C2211yescharacteristic, complemented
160#11762672C2211yescharacteristic, complemented
161#11762669C2211yescharacteristic, complemented
162#11762669C2211yescharacteristic, complemented
163#11762669C2211yescharacteristic, complemented
164#11762667C2211yescharacteristic, complemented
165#11762665C2211yescharacteristic
166#11762665C2211yescharacteristic, complemented
167#11762664C2211yescharacteristic, complemented
168C4×C22⋊Dic17C2211yescharacteristic, complemented
169C4×C22⋊Dic17C2211yescharacteristic, complemented
170C4×C22⋊Dic17C2211yescharacteristic, complemented
171C2×#10587502C2211yescharacteristic, complemented
172C2×#10587502C2211yescharacteristic, complemented
173C23×D4×C17C2211yescharacteristic
174C24×C4×C17C2211yescharacteristic
175C24×C4×C17C2211yescharacteristic, complemented
176C2×C4×D4×C17—28no—
177C2×C4×D4×C17C2211yescharacteristic
178C2×C4×D4×C17C2211yescharacteristic
179C2×C4×D4×C17C2211yescharacteristic
180C2×C4×D4×C17C2211yescharacteristic
181C2×C4×D4×C17C2211yescharacteristic, complemented
182C2×C4×D4×C17C2211yescharacteristic, complemented
183C2×C4×D4×C17C2211yescharacteristic, complemented
184C2×C4×D4×C17C2211yescharacteristic, complemented
185C22×C4⋊C4×C17C2211yescharacteristic, complemented
186C22×C22⋊C4×C17C2211yescharacteristic
187C22×C22⋊C4×C17C2211yescharacteristic, complemented
188C22×C42×C17C2211yescharacteristic, complemented
189C25×C17C2311yescharacteristic
190C25×C17C2311yescharacteristic
191C24×D17C2311yescharacteristic
192C22×D4×C17—24no—
193C22×D4×C17—24no—
194C22×D4×C17—24no—
195C22×D4×C17C2311yescharacteristic
196C22×D4×C17C2311yescharacteristic
197C22×D4×C17C2311yescharacteristic
198C22×D4×C17C2311yescharacteristic
199C23×C4×C17—24no—
200C23×C4×C17—24no—
201C23×C4×C17—42no—
202C23×C4×C17—42no—
203C23×C4×C17—42no—
204C23×C4×C17—42no—
205C23×C4×C17C2311yescharacteristic
206C23×C4×C17C2311yescharacteristic
207C23×C4×C17C2311yescharacteristic
208C23×C4×C17C2311yescharacteristic
209C23×C4×C17C2311yescharacteristic
210C23×C4×C17C2311yescharacteristic
211C23×C4×C17C2311yescharacteristic
212C23×C4×C17C2311yescharacteristic
213C23×C4×C17C2311yescharacteristic
214C23×C4×C17C2311yescharacteristic
215C23×C4×C17C2311yescharacteristic
216C23×C4×C17C2311yescharacteristic
217C23×C4×C17C2311yescharacteristic
218C22×C22⋊D17—24no—
219C22×C22⋊D17—42no—
220C22×C22⋊D17—42no—
221C22×C22⋊D17C2311yescharacteristic
222C22×C22⋊D17C2311yescharacteristic
223C22×C22⋊D17C2311yescharacteristic
224C22×C22⋊D17C2311yescharacteristic
225C22×C22⋊D17C2311yescharacteristic
226C22×C22⋊D17C2311yescharacteristic
227C22×C22⋊D17C2311yescharacteristic
228C22×C22⋊D17C2311yescharacteristic
229C22×C22⋊D17C2311yescharacteristic
230C22×C22⋊D17C2311yescharacteristic
231C22×C22⋊D17C2311yescharacteristic
232C22×C22⋊D17C2311yescharacteristic
233C22×C22⋊D17C2311yescharacteristic
234C23×Dic17C2311yescharacteristic
235C23×Dic17C2311yescharacteristic
236C23×Dic17C2311yescharacteristic
237C22×D68C2311yescharacteristic
238C22×D68C2311yescharacteristic
239C22×C4×D17C2311yescharacteristic
240C22×Dic34C2311yescharacteristic
241C4×D4×C17—24no—
242C4×D4×C17—24no—
243C4×D4×C17—24no—
244C4×D4×C17—24no—
245C4×D4×C17—24no—
246C4×D4×C17—24no—
247C4×D4×C17—24no—
248C4×D4×C17D418yescomplemented
249C2×C4⋊C4×C17—24no—
250C2×C4⋊C4×C17C2311yescharacteristic
251C2×C4⋊C4×C17C2311yescharacteristic
252C2×C4⋊C4×C17C2311yescharacteristic
253C2×C4⋊C4×C17C2311yescharacteristic
254C2×C22⋊C4×C17—24no—
255C2×C22⋊C4×C17—24no—
256C2×C22⋊C4×C17C2311yescharacteristic
257C2×C22⋊C4×C17C2311yescharacteristic
258C2×C22⋊C4×C17C2311yescharacteristic
259C2×C22⋊C4×C17C2311yescharacteristic
260C2×C22⋊C4×C17C2311yescharacteristic
261C2×C22⋊C4×C17C2311yescharacteristic
262C2×C22⋊C4×C17C2311yescharacteristic
263C2×C22⋊C4×C17C2311yescharacteristic
264C2×C42×C17—24no—
265C2×C42×C17C2311yescharacteristic
266C2×C42×C17C2311yescharacteristic
267C2×C42×C17C2311yescharacteristic
268C2×C42×C17C2311yescharacteristic
269#10587639—24no—
270#10587639—42no—
271#10587639—42no—
272#10587639—42no—
273C2×C22⋊Dic17—42no—
274C2×C22⋊Dic17C2311yescharacteristic
275C2×C22⋊Dic17C2311yescharacteristic
276C2×C22⋊Dic17C2311yescharacteristic
277C2×C22⋊Dic17C2311yescharacteristic
278C2×C22⋊Dic17C2311yescharacteristic
279C2×C22⋊Dic17C2311yescharacteristic
280C2×C22⋊Dic17C2311yescharacteristic
281C2×C22⋊Dic17C2311yescharacteristic
282C2×C22⋊Dic17C2311yescharacteristic
283C2×C22⋊Dic17C2311yescharacteristic
284C2×C22⋊Dic17C2311yescharacteristic
285C2×C22⋊Dic17C2311yescharacteristic
286C2×C22⋊Dic17C2311yescharacteristic
287C2×C22⋊Dic17C2311yescharacteristic
288C2×C22⋊Dic17C2311yescharacteristic
289C2×C22⋊Dic17C2311yescharacteristic
290C2×C22⋊Dic17C2311yescharacteristic
291C2×C22⋊Dic17C2311yescharacteristic
292C2×C22⋊Dic17C2311yescharacteristic
293C2×C22⋊Dic17C2311yescharacteristic
294C2×C22⋊Dic17C2311yescharacteristic
295C2×C22⋊Dic17C2311yescharacteristic
296C2×C22⋊Dic17C2311yescharacteristic
297#10587625—24no—
298#10587625—24no—
299#10587623—24no—
300#10587623—24no—
301#10587616—24no—
302#10587616—42no—
303#10587616—42no—
304#10587616—42no—
305#10587615—24no—
306#10587615—42no—
307C4×C22⋊D17—24no—
308C4×C22⋊D17—42no—
309C4×C22⋊D17—42no—
310C2×#63227—24no—
311C2×#63227—42no—
312C2×#63227C2311yescharacteristic
313C2×#63227C2311yescharacteristic
314C2×#63227C2311yescharacteristic
315C2×#63227C2311yescharacteristic
316C2×#63227C2311yescharacteristic
317C2×#63227C2311yescharacteristic
318C2×#63227C2311yescharacteristic
319C2×#63227C2311yescharacteristic
320C2×#63227C2311yescharacteristic
321C2×#63227C2311yescharacteristic
322C2×#63227C2311yescharacteristic
323C2×#63227C2311yescharacteristic
324C2×#63227C2311yescharacteristic
325C2×#63227C2311yescharacteristic
326C2×#63227C2311yescharacteristic
327C2×#63227C2311yescharacteristic
328C2×#63227C2311yescharacteristic
329C2×#63227C2311yescharacteristic
330C2×#63227C2311yescharacteristic
331C2×#63227C2311yescharacteristic
332C2×#63227C2311yescharacteristic
333C2×#63227C2311yescharacteristic
334C2×#63227C2311yescharacteristic
335C2×#63227C2311yescharacteristic
336C2×#63227C2311yescharacteristic
337C2×C4⋊Dic17C2311yescharacteristic
338C2×C4⋊Dic17C2311yescharacteristic
339C2×C4⋊Dic17C2311yescharacteristic
340C2×C4⋊Dic17C2311yescharacteristic
341C2×C4⋊Dic17C2311yescharacteristic
342#10587610—42no—
343C2×#63225C2311yescharacteristic
344C2×#63225C2311yescharacteristic
345C2×#63225C2311yescharacteristic
346C2×#63225C2311yescharacteristic
347C2×#63225C2311yescharacteristic
348C2×#63225C2311yescharacteristic
349C2×#63225C2311yescharacteristic
350C2×#63225C2311yescharacteristic
351C2×#63225C2311yescharacteristic
352C2×#63225C2311yescharacteristic
353C2×#63225C2311yescharacteristic
354C2×C4×Dic17C2311yescharacteristic
355C2×C4×Dic17C2311yescharacteristic
356C2×C4×Dic17C2311yescharacteristic
357#10587584—24no—
358#10587580—24no—
359#10587571—24no—
360#10587570—24no—
361#10587568—24no—
362#10587564—24no—
363#10587562—24no—
364#10587561—24no—
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379#10587502C2311yescharacteristic
380#10587502C2311yescharacteristic
381#10587502C2311yescharacteristic
382#10587502C2311yescharacteristic
383#10587502C2311yescharacteristic
384#10587502C2311yescharacteristic
385#10587502C2311yescharacteristic
386#10587502C2311yescharacteristic
387#10587502C2311yescharacteristic
388#10587502C2311yescharacteristic
389#10587502C2311yescharacteristic
390#10587502C2311yescharacteristic
391#10587502C2311yescharacteristic
392#10587502C2311yescharacteristic
393#10587502C2311yescharacteristic
394#10587502C2311yescharacteristic
395#10587502C2311yescharacteristic
396#10587502C2311yescharacteristic
397C24×C17—22no—
398C24×C17—22no—
399C24×C17—22no—
400C24×C17—22no—
401C24×C17—22no—
402C24×C17—22no—
403C24×C17—22no—
404C24×C17—22no—
405C24×C17—22no—
406C24×C17—41no—
407C24×C17—41no—
408C24×C17—41no—
409C24×C17—41no—
410C24×C17#4114yes—
411C24×C17C2411yescharacteristic
412C24×C17C2411yescharacteristic
413C24×C17C2411yescharacteristic
414C24×C17C2411yescharacteristic
415C24×C17C2411yescharacteristic
416C23×D17—22no—
417C23×D17—22no—
418C23×D17—22no—
419C23×D17—41no—
420C23×D17—41no—
421C23×D17—41no—
422C23×D17—41no—
423C23×D17C2411yescharacteristic
424C23×D17C2411yescharacteristic
425C23×D17C2411yescharacteristic
426C2×D4×C17—232no—
427C2×D4×C17—22no—
428C2×D4×C17—22no—
429C2×D4×C17—22no—
430C2×D4×C17—22no—
431C2×D4×C17—22no—
432C2×D4×C17—22no—
433C2×D4×C17—22no—
434C2×D4×C17—22no—
435C2×D4×C17—22no—
436C2×D4×C17—22no—
437C2×D4×C17C2×D414yes—
438C2×D4×C17#4114yes—
439C22×C4×C17—22no—
440C22×C4×C17—22no—
441C22×C4×C17—22no—
442C22×C4×C17—22no—
443C22×C4×C17—22no—
444C22×C4×C17—22no—
445C22×C4×C17—22no—
446C22×C4×C17—22no—
447C22×C4×C17—22no—
448C22×C4×C17—22no—
449C22×C4×C17—22no—
450C22×C4×C17—22no—
451C22×C4×C17—22no—
452C22×C4×C17—22no—
453C22×C4×C17—22no—
454C22×C4×C17—22no—
455C22×C4×C17—22no—
456C22×C4×C17—22no—
457C22×C4×C17—22no—
458C22×C4×C17—22no—
459C22×C4×C17—22no—
460C22×C4×C17—22no—
461C22×C4×C17—41no—
462C22×C4×C17—41no—
463C22×C4×C17—41no—
464C22×C4×C17—41no—
465C22×C4×C17—41no—
466C22×C4×C17—41no—
467C22×C4×C17—41no—
468C22×C4×C17—41no—
469C22×C4×C17—41no—
470C22×C4×C17—41no—
471C22×C4×C17—41no—
472C22×C4×C17—41no—
473C22×C4×C17—41no—
474C22×C4×C17—41no—
475C22×C4×C17—41no—
476C22×C4×C17—416no—
477C22×C4×C17—416no—
478C22×C4×C17C2×D414yes—
479C22×C4×C17C2×D414yescomplemented
480C22×C4×C17C2411yescharacteristic
481C22×C4×C17C2411yescharacteristic
482C22×C4×C17C2411yescharacteristic
483C22×C4×C17C2411yescharacteristic
484C22×C4×C17C2411yescharacteristic
485C22×C4×C17C2411yescharacteristic
486C22×C4×C17C2411yescharacteristic
487C22×C4×C17C2411yescharacteristic
488C22×C4×C17C2411yescharacteristic
489C22×C4×C17C2411yescharacteristic
490C2×C22⋊D17—22no—
491C2×C22⋊D17—22no—
492C2×C22⋊D17—22no—
493C2×C22⋊D17—22no—
494C2×C22⋊D17—22no—
495C2×C22⋊D17—22no—
496C2×C22⋊D17—22no—
497C2×C22⋊D17—22no—
498C2×C22⋊D17—22no—
499C2×C22⋊D17—22no—
500C2×C22⋊D17—22no—
501C2×C22⋊D17—22no—
502C2×C22⋊D17—22no—
503C2×C22⋊D17—22no—
504C2×C22⋊D17—22no—
505C2×C22⋊D17—22no—
506C2×C22⋊D17—22no—
507C2×C22⋊D17—22no—
508C2×C22⋊D17—22no—
509C2×C22⋊D17—22no—
510C2×C22⋊D17—22no—
511C2×C22⋊D17—41no—
512C2×C22⋊D17—41no—
513C2×C22⋊D17—41no—
514C2×C22⋊D17—41no—
515C2×C22⋊D17—41no—
516C2×C22⋊D17—41no—
517C2×C22⋊D17—41no—
518C2×C22⋊D17—41no—
519C2×C22⋊D17—41no—
520C2×C22⋊D17—41no—
521C2×C22⋊D17—41no—
522C2×C22⋊D17—41no—
523C2×C22⋊D17—41no—
524C2×C22⋊D17—41no—
525C2×C22⋊D17—41no—
526C2×C22⋊D17—41no—
527C2×C22⋊D17—41no—
528C2×C22⋊D17—41no—
529C2×C22⋊D17—416no—
530C22×Dic17—22no—
531C22×Dic17—22no—
532C22×Dic17—22no—
533C22×Dic17—41no—
534C22×Dic17—41no—
535C22×Dic17—41no—
536C22×Dic17—41no—
537C22×Dic17—41no—
538C22×Dic17—41no—
539C22×Dic17C2411yescharacteristic
540C22×Dic17C2411yescharacteristic
541C22×Dic17C2411yescharacteristic
542C22×Dic17C2411yescharacteristic
543C22×Dic17C2411yescharacteristic
544C22×Dic17C2411yescharacteristic
545C22×Dic17C2411yescharacteristic
546C22×Dic17C2411yescharacteristic
547C22×Dic17C2411yescharacteristic
548C22×Dic17C2411yescharacteristic
549C22×Dic17C2411yescharacteristic
550C22×Dic17C2411yescharacteristic
551C22×Dic17C2411yescharacteristic
552C2×D68—22no—
553C2×D68—22no—
554C2×D68—41no—
555C2×D68—41no—
556C2×D68—41no—
557C2×D68—41no—
558C2×C4×D17—22no—
559C2×C4×D17—41no—
560C2×C4×D17—41no—
561C2×Dic34—22no—
562C2×Dic34—41no—
563C2×Dic34—41no—
564C4⋊C4×C17—22no—
565C4⋊C4×C17—22no—
566C4⋊C4×C17—22no—
567C4⋊C4×C17C2×D414yescomplemented
568C22⋊C4×C17—22no—
569C22⋊C4×C17—22no—
570C22⋊C4×C17—22no—
571C22⋊C4×C17—22no—
572C22⋊C4×C17—22no—
573C22⋊C4×C17—22no—
574C22⋊C4×C17C2×D414yes—
575C22⋊C4×C17C2×D414yescomplemented
576C42×C17—22no—
577C42×C17—22no—
578C42×C17—22no—
579C42×C17C2×D414yescomplemented
580C22⋊Dic17—22no—
581C22⋊Dic17—22no—
582C22⋊Dic17—22no—
583C22⋊Dic17—22no—
584C22⋊Dic17—22no—
585C22⋊Dic17—22no—
586C22⋊Dic17—22no—
587C22⋊Dic17—22no—
588C22⋊Dic17—22no—
589C22⋊Dic17—22no—
590C22⋊Dic17—22no—
591C22⋊Dic17—41no—
592C22⋊Dic17—41no—
593C22⋊Dic17—41no—
594C22⋊Dic17—41no—
595C22⋊Dic17—41no—
596C22⋊Dic17—41no—
597C22⋊Dic17—41no—
598C22⋊Dic17—41no—
599C22⋊Dic17—41no—
600C22⋊Dic17—41no—
601C22⋊Dic17—41no—
602C22⋊Dic17—41no—
603#63227—22no—
604#63227—22no—
605#63227—22no—
606#63227—22no—
607#63227—22no—
608#63227—22no—
609#63227—22no—
610#63227—22no—
611#63227—22no—
612#63227—22no—
613#63227—22no—
614#63227—22no—
615#63227—22no—
616#63227—22no—
617#63227—22no—
618#63227—22no—
619#63227—41no—
620#63227—41no—
621#63227—41no—
622#63227—41no—
623#63227—41no—
624#63227—41no—
625#63227—41no—
626#63227—41no—
627#63227—41no—
628C4⋊Dic17—22no—
629C4⋊Dic17—41no—
630C4⋊Dic17—41no—
631C4⋊Dic17—41no—
632C4⋊Dic17—41no—
633#63225—22no—
634#63225—22no—
635#63225—22no—
636#63225—22no—
637#63225—22no—
638#63225—22no—
639#63225—41no—
640#63225—41no—
641#63225—41no—
642#63225—41no—
643#63225—41no—
644C4×Dic17—22no—
645C4×Dic17—41no—
646C4×Dic17—41no—
647#34990—171nomaximal, Sylow
648C23×C17—21no—
649C23×C17—21no—
650C23×C17—21no—
651C23×C17—21no—
652C23×C17—21no—
653C23×C17—21no—
654C23×C17—21no—
655C23×C17—21no—
656C23×C17—28no—
657C23×C17—28no—
658C23×C17—28no—
659C23×C17—21no—
660C23×C17—21no—
661C23×C17—21no—
662C23×C17—21no—
663C23×C17—21no—
664C23×C17—21no—
665C23×C17—21no—
666C23×C17—21no—
667C23×C17—21no—
668C23×C17—21no—
669C23×C17—21no—
670C23×C17—21no—
671C23×C17—21no—
672C23×C17—21no—
673C23×C17—21no—
674C23×C17—21no—
675C23×C17—21no—
676C23×C17—21no—
677C23×C17—44no—
678C23×C17—44no—
679C23×C17—44no—
680C23×C17—44no—
681C23×C17—44no—
682C23×C17—44no—
683C23×C17—44no—
684C23×C17—44no—
685C23×C17—44no—
686C23×C17—44no—
687C23×C17—44no—
688C23×C17C22×D412yes—
689C23×C17C22×D412yes—
690C23×C17C2×#4112yes—
691C23×C17C2×#4112yes—
692C23×C17C2×#4112yes—
693C23×C17C2×#4112yes—
694C23×C17C2×#4112yes—
695C23×C17H(5,𝔽2)12yes—
696C23×C17H(5,𝔽2)12yes—
697C23×C17C2511yescharacteristic
698C22×D17—21no—
699C22×D17—21no—
700C22×D17—21no—
701C22×D17—21no—
702C22×D17—21no—
703C22×D17—21no—
704C22×D17—21no—
705C22×D17—21no—
706C22×D17—21no—
707C22×D17—21no—
708C22×D17—21no—
709C22×D17—21no—
710C22×D17—21no—
711C22×D17—21no—
712C22×D17—21no—
713C22×D17—21no—
714C22×D17—21no—
715C22×D17—21no—
716C22×D17—21no—
717C22×D17—21no—
718C22×D17—21no—
719C22×D17—44no—
720C22×D17—44no—
721C22×D17—44no—
722C22×D17—82no—
723C22×D17—82no—
724C22×D17—82no—
725C22×D17—82no—
726D4×C17—28no—
727D4×C17—28no—
728D4×C17—28no—
729D4×C17—28no—
730C2×C4×C17—28no—
731C2×C4×C17—28no—
732C2×C4×C17—21no—
733C2×C4×C17—21no—
734C2×C4×C17—21no—
735C2×C4×C17—21no—
736C2×C4×C17—21no—
737C2×C4×C17—21no—
738C2×C4×C17—21no—
739C2×C4×C17—21no—
740C2×C4×C17—21no—
741C2×C4×C17—21no—
742C2×C4×C17—21no—
743C2×C4×C17—21no—
744C2×C4×C17—21no—
745C2×C4×C17—21no—
746C2×C4×C17—21no—
747C2×C4×C17—21no—
748C2×C4×C17—21no—
749C2×C4×C17—21no—
750C2×C4×C17—21no—
751C2×C4×C17—21no—
752C2×C4×C17—21no—
753C2×C4×C17—21no—
754C2×C4×C17—21no—
755C2×C4×C17—44no—
756C2×C4×C17—44no—
757C2×C4×C17—44no—
758C2×C4×C17—44no—
759C2×C4×C17—44no—
760C2×C4×C17—44no—
761C2×C4×C17—44no—
762C2×C4×C17—44no—
763C2×C4×C17—44no—
764C2×C4×C17—44no—
765C2×C4×C17—44no—
766C2×C4×C17C22×D412yes—
767C2×C4×C17C22×D412yes—
768C2×C4×C17C22×D412yes—
769C2×C4×C17C22×D412yes—
770C2×C4×C17C22×D412yes—
771C2×C4×C17C2×#4112yes—
772C2×C4×C17H(5,𝔽2)12yes—
773C22⋊D17—44no—
774C22⋊D17—44no—
775C22⋊D17—44no—
776C22⋊D17—44no—
777C22⋊D17—44no—
778C22⋊D17—44no—
779C22⋊D17—44no—
780C22⋊D17—82no—
781C22⋊D17—82no—
782C22⋊D17—82no—
783C22⋊D17—82no—
784C22⋊D17—82no—
785C22⋊D17—82no—
786C2×Dic17—21no—
787C2×Dic17—21no—
788C2×Dic17—21no—
789C2×Dic17—21no—
790C2×Dic17—21no—
791C2×Dic17—21no—
792C2×Dic17—21no—
793C2×Dic17—21no—
794C2×Dic17—21no—
795C2×Dic17—21no—
796C2×Dic17—21no—
797C2×Dic17—21no—
798C2×Dic17—21no—
799C2×Dic17—21no—
800C2×Dic17—21no—
801C2×Dic17—21no—
802C2×Dic17—21no—
803C2×Dic17—21no—
804C2×Dic17—21no—
805C2×Dic17—21no—
806C2×Dic17—21no—
807C2×Dic17—21no—
808C2×Dic17—21no—
809C2×Dic17—21no—
810C2×Dic17—21no—
811C2×Dic17—21no—
812C2×Dic17—21no—
813C2×Dic17—21no—
814C2×Dic17—21no—
815C2×Dic17—21no—
816C2×Dic17—21no—
817C2×Dic17—21no—
818C2×Dic17—21no—
819C2×Dic17—21no—
820C2×Dic17—21no—
821C2×Dic17—21no—
822C2×Dic17—21no—
823C2×Dic17—21no—
824C2×Dic17—21no—
825C2×Dic17—44no—
826C2×Dic17—82no—
827C2×Dic17—82no—
828D68—82no—
829D68—82no—
830C4×D17—82no—
831Dic34—82no—
832C2×#538—171no—
833C22×C4×D4D1711yescharacteristic, complemented
834#2852—171no—
835#2850—171no—
836#2849—171no—
837#2847—171no—
838#2636—171no—
839#2635—171no—
840#2631—171no—
841#2630—171no—
842#2481—171no—
843#2472—171no—
844#2467—171no—
845#2459—171no—
846#2456—171no—
847#2456—171no—
848#2450—171no—
849#2444—171no—
850#2443—171no—
851#2437—171no—
852#2424—171no—
853#2424—171no—
854#2418—171no—
855#2410—171no—
856#2410—171no—
857#2403—171no—
858#2325—171no—
859#2321—171no—
860#2318—171no—
861C4×#120—171no—
862C2×#386—171no—
863C22×C17—22no—
864C22×C17—22no—
865C22×C17—22no—
866C22×C17—22no—
867C22×C17—22no—
868C22×C17—22no—
869C22×C17—22no—
870C22×C17—22no—
871C22×C17—22no—
872C22×C17—22no—
873C22×C17—22no—
874C22×C17—22no—
875C22×C17—22no—
876C22×C17—22no—
877C22×C17—22no—
878C22×C17—22no—
879C22×C17—22no—
880C22×C17—22no—
881C22×C17—22no—
882C22×C17—22no—
883C22×C17—22no—
884C22×C17—416no—
885C22×C17—416no—
886C22×C17—41no—
887C22×C17—41no—
888C22×C17—41no—
889C22×C17—41no—
890C22×C17—41no—
891C22×C17—41no—
892C22×C17—41no—
893C22×C17—41no—
894C22×C17—41no—
895C22×C17—41no—
896C22×C17—41no—
897C22×C17—41no—
898C22×C17#52514yes—
899C22×C17#53814yescomplemented
900C22×C17C23×D411yescharacteristic
901C22×C17C22×#4111yescharacteristic
902C22×C17C22×#4111yescharacteristic
903C22×C17C2×H(5,𝔽2)11yescharacteristic
904C22×C17C2×H(5,𝔽2)11yescharacteristic
905C22×C17C2×H(5,𝔽2)11yescharacteristic
906C22×C17#58511yescharacteristic
907C2×D17—41no—
908C2×D17—41no—
909C2×D17—41no—
910C2×D17—41no—
911C2×D17—41no—
912C2×D17—41no—
913C2×D17—41no—
914C2×D17—41no—
915C2×D17—41no—
916C2×D17—41no—
917C2×D17—41no—
918C2×D17—41no—
919C2×D17—41no—
920C2×D17—41no—
921C2×D17—41no—
922C2×D17—41no—
923C2×D17—41no—
924C2×D17—41no—
925C2×D17—41no—
926C2×D17—41no—
927C2×D17—41no—
928C2×D17—88no—
929C4×C17—22no—
930C4×C17—22no—
931C4×C17—22no—
932C4×C17—22no—
933C4×C17—22no—
934C4×C17—22no—
935C4×C17—22no—
936C4×C17—41no—
937C4×C17—41no—
938C4×C17—41no—
939Dic17—41no—
940Dic17—41no—
941Dic17—41no—
942Dic17—41no—
943Dic17—41no—
944Dic17—41no—
945Dic17—41no—
946Dic17—41no—
947Dic17—41no—
948Dic17—41no—
949Dic17—41no—
950Dic17—41no—
951Dic17—41no—
952C23×D4—171no—
953C23×D4C2×D1711yescharacteristic
954C24×C4C2×D1711yescharacteristic
955C24×C4C2×D1711yescharacteristic, complemented
956#538—348no—
957C2×#126—171no—
958C2×#126—171no—
959C2×#124—171no—
960C2×#124—171no—
961C2×#123—171no—
962C2×#123—171no—
963C2×#123—171no—
964C2×C22⋊Q8—171no—
965C2×C22⋊Q8—171no—
966C2×#121—171no—
967C2×#121—171no—
968C2×#121—171no—
969C2×#121—171no—
970C2×#121—171no—
971C2×#121—171no—
972C2×#121—171no—
973C2×#120—171no—
974C2×#120—171no—
975C2×#120—171no—
976C2×#120—171no—
977C2×#120—171no—
978C2×#120—171no—
979C2×#120—171no—
980C2×C4×D4—28no—
981C2×C4×D4—171no—
982C2×C4×D4—171no—
983C2×C4×D4—171no—
984C2×C4×D4C2×D1711yescharacteristic
985C2×C4×D4C2×D1711yescharacteristic
986C2×C4×D4C2×D1711yescharacteristic
987C2×C4×D4C2×D1711yescharacteristic
988C2×C4×D4C2×D1711yescharacteristic, complemented
989C2×C4×D4C2×D1711yescharacteristic, complemented
990C2×C4×D4C2×D1711yescharacteristic, complemented
991C2×C4×D4C2×D1711yescharacteristic, complemented
992C22×C4⋊C4C2×D1711yescharacteristic, complemented
993C22×C22⋊C4—171no—
994C22×C22⋊C4—171no—
995C22×C22⋊C4—171no—
996C22×C22⋊C4C2×D1711yescharacteristic
997C22×C22⋊C4C2×D1711yescharacteristic, complemented
998C22×C42C2×D1711yescharacteristic, complemented
999#400—171no—
1000#400—171no—
1001#399—171no—
1002#399—171no—
1003#398—171no—
1004#397—171no—
1005#397—171no—
1006#397—171no—
1007#396—171no—
1008#396—171no—
1009#396—171no—
1010#396—171no—
1011#394—171no—
1012#394—171no—
1013#394—171no—
1014#394—171no—
1015#394—171no—
1016#394—171no—
1017#394—171no—
1018#394—171no—
1019#394—171no—
1020#393—171no—
1021#393—171no—
1022#392—171no—
1023#392—171no—
1024#392—171no—
1025#392—171no—
1026#392—171no—
1027#392—171no—
1028#392—171no—
1029#392—171no—
1030#392—171no—
1031#391—171no—
1032#390—171no—
1033#390—171no—
1034#390—171no—
1035#388—171no—
1036#388—171no—
1037#388—171no—
1038#388—171no—
1039#388—171no—
1040#388—171no—
1041#388—171no—
1042#388—171no—
1043#388—171no—
1044#388—171no—
1045#388—171no—
1046#388—171no—
1047#387—171no—
1048#387—171no—
1049#387—171no—
1050#387—171no—
1051#387—171no—
1052#387—171no—
1053#386—171no—
1054#386—171no—
1055#386—171no—
1056#386—171no—
1057#386—171no—
1058#386—171no—
1059#386—171no—
1060#386—171no—
1061#386—171no—
1062#386—171no—
1063#386—171no—
1064#386—171no—
1065#386—171no—
1066#386—171no—
1067#386—171no—
1068#386—171no—
1069#386—171no—
1070#386—171no—
1071#386—171no—
1072#386—171no—
1073#386—171no—
1074#386—171no—
1075#386—171no—
1076#386—171no—
1077#386—171no—
1078#386—171no—
1079#386—171no—
1080#386—171no—
1081#385—171no—
1082#385—171no—
1083#385—171no—
1084#385—171no—
1085#385—171no—
1086#385—171no—
1087#385—171no—
1088#385—171no—
1089#385—171no—
1090#385—171no—
1091#385—171no—
1092#385—171no—
1093#383—171no—
1094#382—171no—
1095#381—171no—
1096#381—171no—
1097#380—171no—
1098#380—171no—
1099#380—171no—
1100#380—171no—
1101#379—171no—
1102#379—171no—
1103#379—171no—
1104C4×C22⋊C4—171no—
1105C4×C22⋊C4—171no—
1106C4×C22⋊C4—171no—
1107C2×#95—171no—
1108C2×#95—171no—
1109C2×C17—24no—
1110C2×C17—24no—
1111C2×C17—42no—
1112C2×C17—42no—
1113C2×C17—42no—
1114C2×C17C2×#52511yescharacteristic
1115C2×C17C2×#53811yescharacteristic
1116C2×C17#345911yescharacteristic
1117C2×C17#348411yescharacteristic
1118C2×C17#348811yescharacteristic
1119C2×C17#351311yescharacteristic
1120C2×C17#351911yescharacteristic
1121D17—81no—
1122D17—81no—
1123D17—81no—
1124C25—171no—
1125C25C22×D1711yescharacteristic
1126C25C22×D1711yescharacteristic
1127C22×Q8—171no—
1128C22×D4—24no—
1129C22×D4—24no—
1130C22×D4—24no—
1131C22×D4—171no—
1132C22×D4—171no—
1133C22×D4—171no—
1134C22×D4—171no—
1135C22×D4—171no—
1136C22×D4—171no—
1137C22×D4—171no—
1138C22×D4—171no—
1139C22×D4—171no—
1140C22×D4—171no—
1141C22×D4—171no—
1142C22×D4—171no—
1143C22×D4—171no—
1144C22×D4—171no—
1145C22×D4—171no—
1146C22×D4—344no—
1147C22×D4—682no—
1148C22×D4—682no—
1149C22×D4C22×D1711yescharacteristic
1150C22×D4C22×D1711yescharacteristic
1151C22×D4C22×D1711yescharacteristic
1152C22×D4C22×D1711yescharacteristic
1153C23×C4—24no—
1154C23×C4—24no—
1155C23×C4—42no—
1156C23×C4—42no—
1157C23×C4—42no—
1158C23×C4—42no—
1159C23×C4—171no—
1160C23×C4—171no—
1161C23×C4—171no—
1162C23×C4—171no—
1163C23×C4C22×D1711yescharacteristic
1164C23×C4C22×D1711yescharacteristic
1165C23×C4C22×D1711yescharacteristic
1166C23×C4C22×D1711yescharacteristic
1167C23×C4C22×D1711yescharacteristic
1168C23×C4C22×D1711yescharacteristic
1169C23×C4C22×D1711yescharacteristic
1170C23×C4C22×D1711yescharacteristic
1171C23×C4C22×D1711yescharacteristic
1172C23×C4C22×D1711yescharacteristic
1173C23×C4C22×D1711yescharacteristic
1174C23×C4C22×D1711yescharacteristic
1175C23×C4C22×D1711yescharacteristic
1176#126—344no—
1177#126—344no—
1178#124—344no—
1179#124—344no—
1180#123—344no—
1181#123—344no—
1182#123—682no—
1183C22⋊Q8—344no—
1184C22⋊Q8—682no—
1185#121—344no—
1186#121—344no—
1187#121—344no—
1188#121—344no—
1189#121—682no—
1190#121—682no—
1191#121—682no—
1192#120—344no—
1193#120—344no—
1194#120—344no—
1195#120—344no—
1196#120—682no—
1197#120—682no—
1198#120—682no—
1199C4×D4—24no—
1200C4×D4—24no—
1201C4×D4—24no—
1202C4×D4—24no—
1203C4×D4—24no—
1204C4×D4—24no—
1205C4×D4—24no—
1206C4×D4—344no—
1207C4×D4—682no—
1208C4×D4—682no—
1209C4×D4C22⋊D1718yescomplemented
1210C2×C4⋊C4—24no—
1211C2×C4⋊C4—171no—
1212C2×C4⋊C4—171no—
1213C2×C4⋊C4—171no—
1214C2×C4⋊C4—171no—
1215C2×C4⋊C4—171no—
1216C2×C4⋊C4—171no—
1217C2×C4⋊C4—171no—
1218C2×C4⋊C4—171no—
1219C2×C4⋊C4—171no—
1220C2×C4⋊C4—171no—
1221C2×C4⋊C4—171no—
1222C2×C4⋊C4—171no—
1223C2×C4⋊C4—171no—
1224C2×C4⋊C4—171no—
1225C2×C4⋊C4—171no—
1226C2×C4⋊C4—171no—
1227C2×C4⋊C4C22×D1711yescharacteristic
1228C2×C4⋊C4C22×D1711yescharacteristic
1229C2×C4⋊C4C22×D1711yescharacteristic
1230C2×C4⋊C4C22×D1711yescharacteristic
1231C2×C22⋊C4—24no—
1232C2×C22⋊C4—24no—
1233C2×C22⋊C4—171no—
1234C2×C22⋊C4—171no—
1235C2×C22⋊C4—171no—
1236C2×C22⋊C4—171no—
1237C2×C22⋊C4—171no—
1238C2×C22⋊C4—171no—
1239C2×C22⋊C4—171no—
1240C2×C22⋊C4—171no—
1241C2×C22⋊C4—171no—
1242C2×C22⋊C4—171no—
1243C2×C22⋊C4—171no—
1244C2×C22⋊C4—171no—
1245C2×C22⋊C4—171no—
1246C2×C22⋊C4—171no—
1247C2×C22⋊C4—171no—
1248C2×C22⋊C4—171no—
1249C2×C22⋊C4—171no—
1250C2×C22⋊C4—171no—
1251C2×C22⋊C4—171no—
1252C2×C22⋊C4—171no—
1253C2×C22⋊C4—171no—
1254C2×C22⋊C4—171no—
1255C2×C22⋊C4—171no—
1256C2×C22⋊C4—171no—
1257C2×C22⋊C4—171no—
1258C2×C22⋊C4—171no—
1259C2×C22⋊C4—171no—
1260C2×C22⋊C4—171no—
1261C2×C22⋊C4—171no—
1262C2×C22⋊C4—171no—
1263C2×C22⋊C4—171no—
1264C2×C22⋊C4—171no—
1265C2×C22⋊C4—171no—
1266C2×C22⋊C4—171no—
1267C2×C22⋊C4—171no—
1268C2×C22⋊C4—171no—
1269C2×C22⋊C4—171no—
1270C2×C22⋊C4—171no—
1271C2×C22⋊C4—171no—
1272C2×C22⋊C4—171no—
1273C2×C22⋊C4—171no—
1274C2×C22⋊C4—171no—
1275C2×C22⋊C4—171no—
1276C2×C22⋊C4—171no—
1277C2×C22⋊C4—171no—
1278C2×C22⋊C4—171no—
1279C2×C22⋊C4—171no—
1280C2×C22⋊C4—171no—
1281C2×C22⋊C4—344no—
1282C2×C22⋊C4—682no—
1283C2×C22⋊C4—682no—
1284C2×C22⋊C4C22×D1711yescharacteristic
1285C2×C22⋊C4C22×D1711yescharacteristic
1286C2×C22⋊C4C22×D1711yescharacteristic
1287C2×C22⋊C4C22×D1711yescharacteristic
1288C2×C22⋊C4C22×D1711yescharacteristic
1289C2×C22⋊C4C22×D1711yescharacteristic
1290C2×C22⋊C4C22×D1711yescharacteristic
1291C2×C22⋊C4C22×D1711yescharacteristic
1292C2×C42—24no—
1293C2×C42—171no—
1294C2×C42—171no—
1295C2×C42—171no—
1296C2×C42C22×D1711yescharacteristic
1297C2×C42C22×D1711yescharacteristic
1298C2×C42C22×D1711yescharacteristic
1299C2×C42C22×D1711yescharacteristic
1300#95—171no—
1301#95—171no—
1302#95—171no—
1303#95—171no—
1304#95—171no—
1305#95—171no—
1306#95—171no—
1307#95—171no—
1308#95—171no—
1309#95—171no—
1310#95—171no—
1311#95—171no—
1312#95—171no—
1313#95—171no—
1314#95—171no—
1315#95—171no—
1316#95—171no—
1317#95—171no—
1318#95—171no—
1319#95—171no—
1320#95—171no—
1321#95—171no—
1322#95—171no—
1323#95—171no—
1324#95—171no—
1325#95—171no—
1326#95—171no—
1327#95—171no—
1328#95—171no—
1329#95—171no—
1330#95—171no—
1331#95—171no—
1332C17#3499011yescharacteristic, complemented, Sylow
1333C24—22no—
1334C24—22no—
1335C24—22no—
1336C24—22no—
1337C24—22no—
1338C24—22no—
1339C24—22no—
1340C24—22no—
1341C24—22no—
1342C24—41no—
1343C24—41no—
1344C24—41no—
1345C24—41no—
1346C24—171no—
1347C24—171no—
1348C24—171no—
1349C24—342no—
1350C24—342no—
1351C24—342no—
1352C24—681no—
1353C24—681no—
1354C24—681no—
1355C24—681no—
1356C24#6325214yes—
1357C24C23×D1711yescharacteristic
1358C24C23×D1711yescharacteristic
1359C24C23×D1711yescharacteristic
1360C24C23×D1711yescharacteristic
1361C24C23×D1711yescharacteristic
1362C2×Q8—342no—
1363C2×Q8—681no—
1364C2×Q8—681no—
1365C2×D4—232no—
1366C2×D4—22no—
1367C2×D4—22no—
1368C2×D4—22no—
1369C2×D4—22no—
1370C2×D4—22no—
1371C2×D4—22no—
1372C2×D4—22no—
1373C2×D4—22no—
1374C2×D4—22no—
1375C2×D4—22no—
1376C2×D4—342no—
1377C2×D4—342no—
1378C2×D4—342no—
1379C2×D4—342no—
1380C2×D4—342no—
1381C2×D4—342no—
1382C2×D4—342no—
1383C2×D4—342no—
1384C2×D4—342no—
1385C2×D4—342no—
1386C2×D4—342no—
1387C2×D4—342no—
1388C2×D4—342no—
1389C2×D4—342no—
1390C2×D4—342no—
1391C2×D4—342no—
1392C2×D4—342no—
1393C2×D4—342no—
1394C2×D4—342no—
1395C2×D4—342no—
1396C2×D4—342no—
1397C2×D4—342no—
1398C2×D4—342no—
1399C2×D4—681no—
1400C2×D4—681no—
1401C2×D4—681no—
1402C2×D4—681no—
1403C2×D4—681no—
1404C2×D4—681no—
1405C2×D4—681no—
1406C2×D4—681no—
1407C2×D4—681no—
1408C2×D4—681no—
1409C2×D4—681no—
1410C2×D4—681no—
1411C2×D4—681no—
1412C2×D4—681no—
1413C2×D4—681no—
1414C2×D4—681no—
1415C2×D4—681no—
1416C2×D4—681no—
1417C2×D4—681no—
1418C2×D4—681no—
1419C2×D4—681no—
1420C2×D4—681no—
1421C2×D4—6816no—
1422C2×D4#6325214yes—
1423C2×D4C2×C22⋊D1714yes—
1424C22×C4—22no—
1425C22×C4—22no—
1426C22×C4—22no—
1427C22×C4—22no—
1428C22×C4—22no—
1429C22×C4—22no—
1430C22×C4—22no—
1431C22×C4—22no—
1432C22×C4—22no—
1433C22×C4—22no—
1434C22×C4—22no—
1435C22×C4—22no—
1436C22×C4—22no—
1437C22×C4—22no—
1438C22×C4—22no—
1439C22×C4—22no—
1440C22×C4—22no—
1441C22×C4—22no—
1442C22×C4—22no—
1443C22×C4—22no—
1444C22×C4—22no—
1445C22×C4—22no—
1446C22×C4—41no—
1447C22×C4—41no—
1448C22×C4—41no—
1449C22×C4—41no—
1450C22×C4—41no—
1451C22×C4—41no—
1452C22×C4—41no—
1453C22×C4—41no—
1454C22×C4—41no—
1455C22×C4—41no—
1456C22×C4—41no—
1457C22×C4—41no—
1458C22×C4—41no—
1459C22×C4—41no—
1460C22×C4—41no—
1461C22×C4—416no—
1462C22×C4—416no—
1463C22×C4—171no—
1464C22×C4—171no—
1465C22×C4—171no—
1466C22×C4—171no—
1467C22×C4—171no—
1468C22×C4—171no—
1469C22×C4—171no—
1470C22×C4—171no—
1471C22×C4—171no—
1472C22×C4—171no—
1473C22×C4—171no—
1474C22×C4—171no—
1475C22×C4—171no—
1476C22×C4—342no—
1477C22×C4—342no—
1478C22×C4—342no—
1479C22×C4—342no—
1480C22×C4—681no—
1481C22×C4—681no—
1482C22×C4—681no—
1483C22×C4—681no—
1484C22×C4—681no—
1485C22×C4—681no—
1486C22×C4—681no—
1487C22×C4—681no—
1488C22×C4C2×C22⋊D1714yes—
1489C22×C4C2×C22⋊D1714yescomplemented
1490C22×C4C23×D1711yescharacteristic
1491C22×C4C23×D1711yescharacteristic
1492C22×C4C23×D1711yescharacteristic
1493C22×C4C23×D1711yescharacteristic
1494C22×C4C23×D1711yescharacteristic
1495C22×C4C23×D1711yescharacteristic
1496C22×C4C23×D1711yescharacteristic
1497C22×C4C23×D1711yescharacteristic
1498C22×C4C23×D1711yescharacteristic
1499C22×C4C23×D1711yescharacteristic
1500C4⋊C4—22no—
1501C4⋊C4—22no—
1502C4⋊C4—22no—
1503C4⋊C4—342no—
1504C4⋊C4—342no—
1505C4⋊C4—342no—
1506C4⋊C4—342no—
1507C4⋊C4—342no—
1508C4⋊C4—342no—
1509C4⋊C4—342no—
1510C4⋊C4—681no—
1511C4⋊C4—681no—
1512C4⋊C4—681no—
1513C4⋊C4—681no—
1514C4⋊C4—681no—
1515C4⋊C4—681no—
1516C4⋊C4—681no—
1517C4⋊C4—681no—
1518C4⋊C4—681no—
1519C4⋊C4C2×C22⋊D1714yescomplemented
1520C22⋊C4—22no—
1521C22⋊C4—22no—
1522C22⋊C4—22no—
1523C22⋊C4—22no—
1524C22⋊C4—22no—
1525C22⋊C4—22no—
1526C22⋊C4—342no—
1527C22⋊C4—342no—
1528C22⋊C4—342no—
1529C22⋊C4—342no—
1530C22⋊C4—342no—
1531C22⋊C4—342no—
1532C22⋊C4—342no—
1533C22⋊C4—342no—
1534C22⋊C4—342no—
1535C22⋊C4—342no—
1536C22⋊C4—342no—
1537C22⋊C4—342no—
1538C22⋊C4—342no—
1539C22⋊C4—342no—
1540C22⋊C4—342no—
1541C22⋊C4—342no—
1542C22⋊C4—342no—
1543C22⋊C4—342no—
1544C22⋊C4—342no—
1545C22⋊C4—342no—
1546C22⋊C4—342no—
1547C22⋊C4—342no—
1548C22⋊C4—342no—
1549C22⋊C4—342no—
1550C22⋊C4—342no—
1551C22⋊C4—342no—
1552C22⋊C4—342no—
1553C22⋊C4—681no—
1554C22⋊C4—681no—
1555C22⋊C4—681no—
1556C22⋊C4—681no—
1557C22⋊C4—681no—
1558C22⋊C4—681no—
1559C22⋊C4—681no—
1560C22⋊C4—681no—
1561C22⋊C4—681no—
1562C22⋊C4—681no—
1563C22⋊C4—681no—
1564C22⋊C4—681no—
1565C22⋊C4—681no—
1566C22⋊C4—681no—
1567C22⋊C4—681no—
1568C22⋊C4—681no—
1569C22⋊C4—681no—
1570C22⋊C4—681no—
1571C22⋊C4—681no—
1572C22⋊C4—681no—
1573C22⋊C4—681no—
1574C22⋊C4C2×C22⋊D1714yes—
1575C22⋊C4C2×C22⋊D1714yescomplemented
1576C42—22no—
1577C42—22no—
1578C42—22no—
1579C42—342no—
1580C42—681no—
1581C42—681no—
1582C42C2×C22⋊D1714yescomplemented
1583C23—21no—
1584C23—21no—
1585C23—21no—
1586C23—21no—
1587C23—21no—
1588C23—21no—
1589C23—21no—
1590C23—21no—
1591C23—28no—
1592C23—28no—
1593C23—21no—
1594C23—21no—
1595C23—21no—
1596C23—21no—
1597C23—21no—
1598C23—21no—
1599C23—21no—
1600C23—21no—
1601C23—21no—
1602C23—21no—
1603C23—21no—
1604C23—21no—
1605C23—21no—
1606C23—21no—
1607C23—21no—
1608C23—21no—
1609C23—21no—
1610C23—21no—
1611C23—28no—
1612C23—44no—
1613C23—44no—
1614C23—44no—
1615C23—44no—
1616C23—44no—
1617C23—44no—
1618C23—44no—
1619C23—44no—
1620C23—44no—
1621C23—44no—
1622C23—44no—
1623C23—341no—
1624C23—341no—
1625C23—341no—
1626C23—341no—
1627C23—341no—
1628C23—341no—
1629C23—341no—
1630C23—341no—
1631C23—341no—
1632C23—341no—
1633C23—341no—
1634C23—341no—
1635C23—341no—
1636C23—341no—
1637C23—341no—
1638C23—341no—
1639C23—341no—
1640C23—341no—
1641C23—341no—
1642C23—341no—
1643C23—341no—
1644C23—684no—
1645C23—684no—
1646C23—684no—
1647C23—1362no—
1648C23—1362no—
1649C23—1362no—
1650C23—1362no—
1651C23C2×#6325212yes—
1652C23C2×#6325212yes—
1653C23C2×#6325212yes—
1654C23C2×#6325212yes—
1655C23C2×#6325212yes—
1656C23#1058769112yes—
1657C23#1058769612yes—
1658C23C22×C22⋊D1712yes—
1659C23C22×C22⋊D1712yes—
1660C23C24×D1711yescharacteristic
1661Q8—1362no—
1662D4—28no—
1663D4—28no—
1664D4—28no—
1665D4—28no—
1666D4—684no—
1667D4—684no—
1668D4—684no—
1669D4—684no—
1670D4—684no—
1671D4—684no—
1672D4—684no—
1673D4—1362no—
1674D4—1362no—
1675D4—1362no—
1676D4—1362no—
1677D4—1362no—
1678D4—1362no—
1679D4—1362no—
1680D4—1362no—
1681C2×C4—28no—
1682C2×C4—28no—
1683C2×C4—21no—
1684C2×C4—21no—
1685C2×C4—21no—
1686C2×C4—21no—
1687C2×C4—21no—
1688C2×C4—21no—
1689C2×C4—21no—
1690C2×C4—21no—
1691C2×C4—21no—
1692C2×C4—21no—
1693C2×C4—21no—
1694C2×C4—21no—
1695C2×C4—21no—
1696C2×C4—21no—
1697C2×C4—21no—
1698C2×C4—21no—
1699C2×C4—21no—
1700C2×C4—21no—
1701C2×C4—21no—
1702C2×C4—21no—
1703C2×C4—21no—
1704C2×C4—21no—
1705C2×C4—21no—
1706C2×C4—44no—
1707C2×C4—44no—
1708C2×C4—44no—
1709C2×C4—44no—
1710C2×C4—44no—
1711C2×C4—44no—
1712C2×C4—44no—
1713C2×C4—44no—
1714C2×C4—44no—
1715C2×C4—44no—
1716C2×C4—44no—
1717C2×C4—341no—
1718C2×C4—341no—
1719C2×C4—341no—
1720C2×C4—341no—
1721C2×C4—341no—
1722C2×C4—341no—
1723C2×C4—341no—
1724C2×C4—341no—
1725C2×C4—341no—
1726C2×C4—341no—
1727C2×C4—341no—
1728C2×C4—341no—
1729C2×C4—341no—
1730C2×C4—341no—
1731C2×C4—341no—
1732C2×C4—341no—
1733C2×C4—341no—
1734C2×C4—341no—
1735C2×C4—341no—
1736C2×C4—341no—
1737C2×C4—341no—
1738C2×C4—341no—
1739C2×C4—341no—
1740C2×C4—341no—
1741C2×C4—341no—
1742C2×C4—341no—
1743C2×C4—341no—
1744C2×C4—341no—
1745C2×C4—341no—
1746C2×C4—341no—
1747C2×C4—341no—
1748C2×C4—341no—
1749C2×C4—341no—
1750C2×C4—341no—
1751C2×C4—341no—
1752C2×C4—341no—
1753C2×C4—341no—
1754C2×C4—341no—
1755C2×C4—341no—
1756C2×C4—684no—
1757C2×C4—1362no—
1758C2×C4—1362no—
1759C2×C4—1362no—
1760C2×C4C2×#6325212yes—
1761C2×C4#1058769112yes—
1762C2×C4C22×C22⋊D1712yes—
1763C2×C4C22×C22⋊D1712yes—
1764C2×C4C22×C22⋊D1712yes—
1765C2×C4C22×C22⋊D1712yes—
1766C2×C4C22×C22⋊D1712yes—
1767C22—22no—
1768C22—22no—
1769C22—22no—
1770C22—22no—
1771C22—22no—
1772C22—22no—
1773C22—22no—
1774C22—22no—
1775C22—22no—
1776C22—22no—
1777C22—22no—
1778C22—22no—
1779C22—22no—
1780C22—22no—
1781C22—22no—
1782C22—22no—
1783C22—22no—
1784C22—22no—
1785C22—22no—
1786C22—22no—
1787C22—22no—
1788C22—416no—
1789C22—416no—
1790C22—41no—
1791C22—41no—
1792C22—41no—
1793C22—41no—
1794C22—41no—
1795C22—41no—
1796C22—41no—
1797C22—41no—
1798C22—41no—
1799C22—41no—
1800C22—41no—
1801C22—41no—
1802C22—681no—
1803C22—681no—
1804C22—681no—
1805C22—681no—
1806C22—681no—
1807C22—681no—
1808C22—681no—
1809C22—681no—
1810C22—681no—
1811C22—681no—
1812C22—681no—
1813C22—681no—
1814C22—681no—
1815C22—681no—
1816C22—681no—
1817C22—681no—
1818C22—681no—
1819C22—681no—
1820C22—681no—
1821C22—681no—
1822C22—681no—
1823C22—1368no—
1824C22#1176332014yes—
1825C22#1176339214yescomplemented
1826C22C23×C22⋊D1711yescharacteristic
1827C22C22×#6325211yescharacteristic
1828C22C22×#6325211yescharacteristic
1829C22C2×#1058769111yescharacteristic
1830C22C2×#1058769111yescharacteristic
1831C22C2×#1058769611yescharacteristic
1832C22#1176364511yescharacteristic
1833C4—22no—
1834C4—22no—
1835C4—22no—
1836C4—22no—
1837C4—22no—
1838C4—22no—
1839C4—22no—
1840C4—41no—
1841C4—41no—
1842C4—41no—
1843C4—681no—
1844C4—681no—
1845C4—681no—
1846C4—681no—
1847C4—681no—
1848C4—681no—
1849C4—681no—
1850C4—681no—
1851C4—681no—
1852C4—681no—
1853C4—681no—
1854C4—681no—
1855C4—681no—
1856C2—24no—
1857C2—24no—
1858C2—42no—
1859C2—42no—
1860C2—42no—
1861C2—1361no—
1862C2—1361no—
1863C2—1361no—
1864C2C2×#1176332011yescharacteristic
1865C2C2×#1176339211yescharacteristic
1866C2#1454219311yescharacteristic
1867C2#1454241911yescharacteristic
1868C2#1454245311yescharacteristic
1869C2#1454272411yescharacteristic
1870C2#1454281611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC22×C4×D4×C17C2
hypercenterC22×C4×D4D17
hypocenterC17#34990
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#11763392C2semidirect
2. #14537099C2semidirect
3. #14537085C2semidirect
4. #14537076C2semidirect
5. #14537066C2semidirect
6. #14534679C2semidirect
7. #14534668C2semidirect
8. #14534636C2semidirect
9. #14534621C2semidirect
10. #14533039C2semidirect
11. #14532904C2semidirect
12. #14532829C2semidirect
13. #14532715C2semidirect
14. #14532676C2semidirect
15. #14532670C2semidirect
16. #14532602C2semidirect
17. #14532528C2semidirect
18. #14532519C2semidirect
19. #14532445C2semidirect
20. #14532320C2semidirect
21. #14532314C2semidirect
22. #14532240C2semidirect
23. #14532158C2semidirect
24. #14532152C2semidirect
25. #14532094C2semidirect
26. #14531482C2semidirect
27. #14531438C2semidirect
28. #14531417C2semidirect
29. C4×#10587639C2semidirect
30. C2×#11762688C2semidirect
31. C22×C4×D4×C17C2semidirect
34. C2×#10587584C22semidirect
35. C2×#10587562C22semidirect
36. C2×#10587561C22semidirect
37. C2×#10587571C22semidirect
38. C2×#10587580C22semidirect
39. C2×#10587615C22semidirect
40. C2×#10587615C22semidirect
41. C2×#10587610C22semidirect
42. C2×#10587564C22semidirect
45. C2×#10587616C22semidirect
46. C2×#10587616C22semidirect
47. C2×#10587570C22semidirect
50. C2×#10587568C22semidirect
54. C2×#10587639C22semidirect
57. C2×C4×C22⋊D17C22semidirect
58. C2×C4×C22⋊D17C22semidirect
59. C2×C4×C22⋊D17C22semidirect
61. C22×#63227C22semidirect
62. C22×#63227C22semidirect
63. #11762748C22semidirect
64. #11762747C22semidirect
65. #11762745C22semidirect
66. #11762744C22semidirect
67. #11762742C22semidirect
68. #11762737C22semidirect
69. #11762735C22semidirect
70. #11762735C22semidirect
71. #11762732C22semidirect
72. #11762732C22semidirect
73. #11762732C22semidirect
74. #11762731C22semidirect
75. #11762726C22semidirect
76. #11762725C22semidirect
77. #11762725C22semidirect
78. #11762725C22semidirect
79. #11762724C22semidirect
80. #11762724C22semidirect
81. #11762724C22semidirect
82. #11762723C22semidirect
83. #11762723C22semidirect
84. #11762721C22semidirect
85. #11762721C22semidirect
86. #11762718C22semidirect
87. #11762718C22semidirect
88. #11762718C22semidirect
93. #11762717C22semidirect
94. #11762717C22semidirect
95. #11762715C22semidirect
96. #11762711C22semidirect
97. #11762709C22semidirect
98. #11762709C22semidirect
99. #11762702C22semidirect
100. #11762702C22semidirect
101. #11762700C22semidirect
102. #11762700C22semidirect
103. #11762700C22semidirect
104. #11762700C22semidirect
105. #11762700C22semidirect
106. #11762700C22semidirect
107. #11762700C22semidirect
108. #11762699C22semidirect
109. #11762699C22semidirect
110. #11762697C22semidirect
111. #11762695C22semidirect
112. #11762695C22semidirect
113. #11762693C22semidirect
114. #11762693C22semidirect
115. #11762693C22semidirect
116. #11762690C22semidirect
129. #11762688C22semidirect
130. #11762688C22semidirect
131. #11762688C22semidirect
132. #11762688C22semidirect
133. #11762688C22semidirect
134. #11762688C22semidirect
135. #11762688C22semidirect
136. #11762688C22semidirect
137. #11762688C22semidirect
138. #11762688C22semidirect
139. #11762688C22semidirect
140. #11762688C22semidirect
141. #11762688C22semidirect
142. #11762688C22semidirect
143. #11762686C22semidirect
144. #11762685C22semidirect
145. #11762684C22semidirect
146. #11762684C22semidirect
147. #11762682C22semidirect
148. #11762682C22semidirect
149. #11762682C22semidirect
150. #11762682C22semidirect
151. #11762682C22semidirect
152. #11762682C22semidirect
153. #11762682C22semidirect
154. #11762682C22semidirect
155. #11762681C22semidirect
156. #11762680C22semidirect
157. #11762677C22semidirect
158. #11762675C22semidirect
159. #11762672C22semidirect
160. #11762672C22semidirect
161. #11762669C22semidirect
162. #11762669C22semidirect
163. #11762669C22semidirect
164. #11762667C22semidirect
166. #11762665C22semidirect
167. #11762664C22semidirect
168. C4×C22⋊Dic17C22semidirect
169. C4×C22⋊Dic17C22semidirect
170. C4×C22⋊Dic17C22semidirect
171. C2×#10587502C22semidirect
172. C2×#10587502C22semidirect
175. C24×C4×C17C22semidirect
181. C2×C4×D4×C17C22semidirect
182. C2×C4×D4×C17C22semidirect
183. C2×C4×D4×C17C22semidirect
184. C2×C4×D4×C17C22semidirect
185. C22×C4⋊C4×C17C22semidirect
187. C22×C22⋊C4×C17C22semidirect
188. C22×C42×C17C22semidirect
248. C4×D4×C17D4semidirect
479. C22×C4×C17C2×D4semidirect
567. C4⋊C4×C17C2×D4semidirect
575. C22⋊C4×C17C2×D4semidirect
579. C42×C17C2×D4semidirect
833. C22×C4×D4D17semidirect
899. C22×C17#538semidirect
955. C24×C4C2×D17semidirect
988. C2×C4×D4C2×D17semidirect
989. C2×C4×D4C2×D17semidirect
990. C2×C4×D4C2×D17semidirect
991. C2×C4×D4C2×D17semidirect
992. C22×C4⋊C4C2×D17semidirect
997. C22×C22⋊C4C2×D17semidirect
998. C22×C42C2×D17semidirect
1209. C4×D4C22⋊D17semidirect
1332. C17#34990semidirect
1489. C22×C4C2×C22⋊D17semidirect
1519. C4⋊C4C2×C22⋊D17semidirect
1575. C22⋊C4C2×C22⋊D17semidirect
1582. C42C2×C22⋊D17semidirect
1825. C22#11763392semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117633922
#145370992
#145370852
#145370762
#145370662
#145346792
#145346682
#145346362
#145346212
#145330392
#145329042
#145328292
#145327152
#145326762
#145326702
#145326022
#145325282
#145325192
#145324452
#145323202
#145323142
#145322402
#145321582
#145321522
#145320942
#145314822
#145314382
#145314172
C4×#105876392
C2×#117626882
C22×C4×D4×C172
#3499017