Finite Group Databasebeta

← #17241214

Subgroups — #17241214

Order 4352.

2620 conjugacy classes of subgroups.

The subgroup lattice has 1812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763318C211yesmaximal, characteristic, complemented
2#14537073C211yesmaximal, characteristic, complemented
3#14537063C211yesmaximal, characteristic, complemented
4#14535298C211yesmaximal, characteristic, complemented
5#14535289C211yesmaximal, characteristic, complemented
6#14535244C211yesmaximal, characteristic, complemented
7#14535214C211yesmaximal, characteristic, complemented
8#14535199C211yesmaximal, characteristic, complemented
9#14535103C211yesmaximal, characteristic, complemented
10#14535079C211yesmaximal, characteristic, complemented
11#14535074C211yesmaximal, characteristic, complemented
12#14535045C211yesmaximal, characteristic, complemented
13#14535044C211yesmaximal, characteristic, complemented
14#14535029C211yesmaximal, characteristic, complemented
15#14535020C211yesmaximal, characteristic, complemented
16#14535015C211yesmaximal, characteristic, complemented
17#14534997C211yesmaximal, characteristic, complemented
18#14534996C211yesmaximal, characteristic, complemented
19#14534987C211yesmaximal, characteristic, complemented
20#14534669C211yesmaximal, characteristic, complemented
21#14534623C211yesmaximal, characteristic, complemented
22#14534456C211yesmaximal, characteristic, complemented
23#14534398C211yesmaximal, characteristic, complemented
24#14534350C211yesmaximal, characteristic, complemented
25#14534344C211yesmaximal, characteristic, complemented
26#14533746C211yesmaximal, characteristic, complemented
27#14533685C211yesmaximal, characteristic, complemented
28#14532404C211yesmaximal, characteristic, complemented
29#14532396C211yesmaximal, characteristic, complemented
30#14531417C211yesmaximal, characteristic, complemented
31C2×C17×#540C211yesmaximal, characteristic, complemented
32C22×#63252C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34C2×#10587626C2211yescharacteristic
35C2×#10587622C2211yescharacteristic, complemented
36#11763318—28no—
37C2×#10587580C2211yescharacteristic
38C2×#10587569C2211yescharacteristic
39C2×#10587621C2211yescharacteristic
40C2×#10587582C2211yescharacteristic
41C2×#10587564C2211yescharacteristic
42C2×#10587616C2211yescharacteristic
43C2×#10587616C2211yescharacteristic
44C2×#10587570C2211yescharacteristic
45C2×#10587625C2211yescharacteristic
46C2×#10587625C2211yescharacteristic
47C2×#10587625C2211yescharacteristic
48C2×#10587625C2211yescharacteristic
49C2×#10587625C2211yescharacteristic, complemented
50C2×#10587624C2211yescharacteristic
51C2×#10587624C2211yescharacteristic
52C2×#10587568C2211yescharacteristic
53C2×#10587623C2211yescharacteristic
54C2×#10587623C2211yescharacteristic
55C2×#10587623C2211yescharacteristic
56C2×#10587623C2211yescharacteristic
57C2×C4×D68C2211yescharacteristic
58C2×C4×C22⋊D17C2211yescharacteristic
59C2×C4×C22⋊D17C2211yescharacteristic
60C2×#10587558C2211yescharacteristic
61#11762748C2211yescharacteristic, complemented
62#11762747C2211yescharacteristic, complemented
63#11762747C2211yescharacteristic, complemented
64#11762745C2211yescharacteristic, complemented
65#11762744C2211yescharacteristic
66#11762744C2211yescharacteristic, complemented
67#11762742C2211yescharacteristic, complemented
68#11762742C2211yescharacteristic, complemented
69#11762740C2211yescharacteristic, complemented
70#11762737C2211yescharacteristic
71#11762737C2211yescharacteristic, complemented
72#11762735C2211yescharacteristic
73#11762735C2211yescharacteristic
74#11762735C2211yescharacteristic, complemented
75#11762732C2211yescharacteristic, complemented
76#11762732C2211yescharacteristic, complemented
77#11762731C2211yescharacteristic
78#11762731C2211yescharacteristic, complemented
79#11762729C2211yescharacteristic, complemented
80#11762726C2211yescharacteristic
81#11762726C2211yescharacteristic
82#11762725C2211yescharacteristic
83#11762725C2211yescharacteristic, complemented
84#11762724C2211yescharacteristic
85#11762724C2211yescharacteristic
86#11762723C2211yescharacteristic
87#11762723C2211yescharacteristic
88#11762723C2211yescharacteristic
89#11762723C2211yescharacteristic, complemented
90#11762723C2211yescharacteristic, complemented
91#11762723C2211yescharacteristic, complemented
92#11762723C2211yescharacteristic, complemented
93#11762721C2211yescharacteristic, complemented
94#11762718C2211yescharacteristic
95#11762718C2211yescharacteristic
96#11762717C2211yescharacteristic
97#11762717C2211yescharacteristic
98#11762717C2211yescharacteristic
99#11762717C2211yescharacteristic
100#11762717C2211yescharacteristic
101#11762717C2211yescharacteristic
102#11762717C2211yescharacteristic
103#11762717C2211yescharacteristic
104#11762717C2211yescharacteristic
105#11762717C2211yescharacteristic, complemented
106#11762717C2211yescharacteristic, complemented
107#11762717C2211yescharacteristic, complemented
108#11762717C2211yescharacteristic, complemented
109#11762714C2211yescharacteristic, complemented
110#11762710C2211yescharacteristic
111#11762709C2211yescharacteristic
112#11762704C2211yescharacteristic, complemented
113#11762703C2211yescharacteristic, complemented
114#11762702C2211yescharacteristic
115#11762702C2211yescharacteristic
116#11762700C2211yescharacteristic
117#11762700C2211yescharacteristic
118#11762700C2211yescharacteristic, complemented
119#11762699C2211yescharacteristic
120#11762697C2211yescharacteristic, complemented
121#11762697C2211yescharacteristic, complemented
122#11762697C2211yescharacteristic, complemented
123#11762695C2211yescharacteristic, complemented
124#11762695C2211yescharacteristic, complemented
125#11762693C2211yescharacteristic, complemented
126#11762690C2211yescharacteristic, complemented
127#11762689C2211yescharacteristic
128#11762689C2211yescharacteristic
129#11762689C2211yescharacteristic
130#11762689C2211yescharacteristic
131#11762689C2211yescharacteristic, complemented
132#11762689C2211yescharacteristic, complemented
133#11762688C2211yescharacteristic
134#11762688C2211yescharacteristic
135#11762688C2211yescharacteristic
136#11762688C2211yescharacteristic
137#11762688C2211yescharacteristic, complemented
138#11762686C2211yescharacteristic
139#11762686C2211yescharacteristic, complemented
140#11762685C2211yescharacteristic
141#11762685C2211yescharacteristic
142#11762685C2211yescharacteristic
143#11762685C2211yescharacteristic
144#11762685C2211yescharacteristic
145#11762685C2211yescharacteristic
146#11762685C2211yescharacteristic
147#11762685C2211yescharacteristic
148#11762685C2211yescharacteristic, complemented
149#11762685C2211yescharacteristic, complemented
150#11762685C2211yescharacteristic, complemented
151#11762684C2211yescharacteristic, complemented
152#11762684C2211yescharacteristic, complemented
153#11762682C2211yescharacteristic, complemented
154#11762682C2211yescharacteristic, complemented
155#11762682C2211yescharacteristic, complemented
156#11762680C2211yescharacteristic
157#11762680C2211yescharacteristic
158#11762680C2211yescharacteristic
159#11762680C2211yescharacteristic
160#11762680C2211yescharacteristic, complemented
161#11762677C2211yescharacteristic, complemented
162#11762675C2211yescharacteristic, complemented
163#11762672C2211yescharacteristic
164#11762670C2211yescharacteristic
165#11762669C2211yescharacteristic
166#11762669C2211yescharacteristic, complemented
167#11762669C2211yescharacteristic, complemented
168#11762666C2211yescharacteristic
169#11762666C2211yescharacteristic
170#11762664C2211yescharacteristic
171C4×C22⋊Dic17C2211yescharacteristic, complemented
172C2×#10587502C2211yescharacteristic, complemented
173C17×#540—28no—
174C2×C17×#127C2211yescharacteristic
175C2×C17×#125C2211yescharacteristic, complemented
176C2×C17×#123C2211yescharacteristic
177C2×C17×#123C2211yescharacteristic
178C2×C17×#123C2211yescharacteristic, complemented
179C2×C17×#123C2211yescharacteristic, complemented
180C2×C17×#121C2211yescharacteristic
181C2×C17×#121C2211yescharacteristic
182C2×C17×#121C2211yescharacteristic
183C2×C17×#121C2211yescharacteristic, complemented
184C2×C17×#121C2211yescharacteristic, complemented
185C2×C17×#121C2211yescharacteristic, complemented
186C2×C4×D4×C17C2211yescharacteristic
187C2×C4×D4×C17C2211yescharacteristic, complemented
188C2×C17×#117C2211yescharacteristic, complemented
189C24×D17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C22×D4×C17C2311yescharacteristic
194C22×D4×C17C2311yescharacteristic
195C22×D4×C17C2311yescharacteristic
196C22×D4×C17C2311yescharacteristic
197C22×D4×C17C2311yescharacteristic
198C22×D4×C17C2311yescharacteristic
199C22×D4×C17C2311yescharacteristic
200C23×C4×C17C2311yescharacteristic
201C23×C4×C17C2311yescharacteristic
202C23×C4×C17C2311yescharacteristic
203C23×C4×C17C2311yescharacteristic
204C23×C4×C17C2311yescharacteristic
205C22×C22⋊D17C2311yescharacteristic
206C22×C22⋊D17C2311yescharacteristic
207C22×C22⋊D17C2311yescharacteristic
208C22×C22⋊D17C2311yescharacteristic
209C22×C22⋊D17C2311yescharacteristic
210C22×C22⋊D17C2311yescharacteristic
211C22×C22⋊D17C2311yescharacteristic
212C22×C22⋊D17C2311yescharacteristic
213C22×C22⋊D17C2311yescharacteristic
214C22×C22⋊D17C2311yescharacteristic
215C22×C22⋊D17C2311yescharacteristic
216C22×C22⋊D17C2311yescharacteristic
217C22×C22⋊D17C2311yescharacteristic
218C23×Dic17C2311yescharacteristic
219C23×Dic17C2311yescharacteristic
220C23×Dic17C2311yescharacteristic
221C2×#63252—24no—
222C2×#63252—42no—
223C2×#63252—42no—
224C22×D68C2311yescharacteristic
225C22×D68C2311yescharacteristic
226C22×C4×D17—24no—
227C22×C4×D17—42no—
228C22×C4×D17—42no—
229C22×C4×D17C2311yescharacteristic
230C22×C4×D17C2311yescharacteristic
231C22×C4×D17C2311yescharacteristic
232C22×C4×D17C2311yescharacteristic
233C22×C4×D17C2311yescharacteristic
234C22×Dic34C2311yescharacteristic
235C17×#127—24no—
236C17×#125—24no—
237C17×#123—24no—
238C17×#123—24no—
239C17×#123—24no—
240C17×#123—24no—
241C17×#121—24no—
242C17×#121—24no—
243C17×#121—24no—
244C17×#121—24no—
245C17×#121—24no—
246C17×#121—24no—
247C4×D4×C17—24no—
248C4×D4×C17D418yescomplemented
249C17×#117—24no—
250C2×C4⋊C4×C17C2311yescharacteristic
251C2×C4⋊C4×C17C2311yescharacteristic
252C2×C4⋊C4×C17C2311yescharacteristic
253C2×C4⋊C4×C17C2311yescharacteristic
254C2×C4⋊C4×C17C2311yescharacteristic
255C2×C4⋊C4×C17C2311yescharacteristic
256C2×C4⋊C4×C17C2311yescharacteristic
257C2×C4⋊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×C22⋊C4×C17C2311yescharacteristic
265C2×C22⋊C4×C17C2311yescharacteristic
266C2×C22⋊C4×C17C2311yescharacteristic
267C2×C22⋊C4×C17C2311yescharacteristic
268C2×C42×C17C2311yescharacteristic
269C2×C42×C17C2311yescharacteristic
270C2×C22⋊Dic17C2311yescharacteristic
271C2×C22⋊Dic17C2311yescharacteristic
272C2×C22⋊Dic17C2311yescharacteristic
273C2×C22⋊Dic17C2311yescharacteristic
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
293#10587626—42no—
294#10587625—24no—
295#10587625—42no—
296#10587625—42no—
297#10587625—42no—
298#10587625—42no—
299#10587624—42no—
300#10587624—42no—
301#10587623—24no—
302#10587623—42no—
303#10587623—42no—
304#10587623—42no—
305#10587622—42no—
306#10587621—42no—
307#10587616—42no—
308#10587616—42no—
309C4×C22⋊D17—24no—
310C4×C22⋊D17—24no—
311C2×#63227C2311yescharacteristic
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×C4⋊Dic17C2311yescharacteristic
333C2×C4⋊Dic17C2311yescharacteristic
334C2×C4⋊Dic17C2311yescharacteristic
335C2×C4⋊Dic17C2311yescharacteristic
336C2×C4⋊Dic17C2311yescharacteristic
337C2×#63225C2311yescharacteristic
338C2×#63225C2311yescharacteristic
339C2×#63225C2311yescharacteristic
340C2×#63225C2311yescharacteristic
341C2×#63225C2311yescharacteristic
342C2×#63225C2311yescharacteristic
343C2×#63225C2311yescharacteristic
344C2×#63225C2311yescharacteristic
345C2×#63225C2311yescharacteristic
346C2×#63225C2311yescharacteristic
347C2×#63225C2311yescharacteristic
348C2×C4×Dic17C2311yescharacteristic
349C2×C4×Dic17C2311yescharacteristic
350C2×C4×Dic17C2311yescharacteristic
351#10587582—24no—
352#10587580—24no—
353#10587570—24no—
354#10587569—24no—
355#10587568—24no—
356#10587564—24no—
357C4×D68—24no—
358#10587558—24no—
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
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
391C24×C17C2411yescharacteristic
392C24×C17C2411yescharacteristic
393C24×C17C2411yescharacteristic
394C24×C17C2411yescharacteristic
395C24×C17C2411yescharacteristic
396C23×D17—22no—
397C23×D17—22no—
398C23×D17—22no—
399C23×D17—41no—
400C23×D17—41no—
401C23×D17—41no—
402C23×D17—41no—
403C23×D17C2411yescharacteristic
404C23×D17C2411yescharacteristic
405C23×D17C2411yescharacteristic
406C2×D4×C17—22no—
407C2×D4×C17—22no—
408C2×D4×C17—22no—
409C2×D4×C17—22no—
410C2×D4×C17—22no—
411C2×D4×C17—22no—
412C2×D4×C17—22no—
413C2×D4×C17—22no—
414C2×D4×C17—22no—
415C2×D4×C17—41no—
416C2×D4×C17—41no—
417C2×D4×C17—41no—
418C2×D4×C17—41no—
419C2×D4×C17—41no—
420C2×D4×C17—41no—
421C2×D4×C17—41no—
422C2×D4×C17—41no—
423C2×D4×C17—41no—
424C2×D4×C17—41no—
425C2×D4×C17—41no—
426C2×D4×C17—41no—
427C2×D4×C17—41no—
428C2×D4×C17—41no—
429C2×D4×C17—41no—
430C2×D4×C17—41no—
431C2×D4×C17—41no—
432C2×D4×C17—41no—
433C2×D4×C17—41no—
434C2×D4×C17—41no—
435C2×D4×C17C2×D414yes—
436C22×C4×C17—22no—
437C22×C4×C17—22no—
438C22×C4×C17—22no—
439C22×C4×C17—41no—
440C22×C4×C17—41no—
441C22×C4×C17—41no—
442C22×C4×C17—41no—
443C22×C4×C17—41no—
444C22×C4×C17—41no—
445C22×C4×C17—41no—
446C22×C4×C17—41no—
447C22×C4×C17—41no—
448C22×C4×C17—41no—
449C22×C4×C17C2×D414yes—
450C22×C4×C17C2×D414yes—
451C22×C4×C17C2411yescharacteristic
452C22×C4×C17C2411yescharacteristic
453C22×C4×C17C2411yescharacteristic
454C22×C4×C17C2411yescharacteristic
455C22×C4×C17C2411yescharacteristic
456C22×C4×C17C2411yescharacteristic
457C22×C4×C17C2411yescharacteristic
458C22×C4×C17C2411yescharacteristic
459C22×C4×C17C2411yescharacteristic
460C22×C4×C17C2411yescharacteristic
461C2×C22⋊D17—22no—
462C2×C22⋊D17—22no—
463C2×C22⋊D17—22no—
464C2×C22⋊D17—22no—
465C2×C22⋊D17—22no—
466C2×C22⋊D17—22no—
467C2×C22⋊D17—22no—
468C2×C22⋊D17—22no—
469C2×C22⋊D17—22no—
470C2×C22⋊D17—22no—
471C2×C22⋊D17—22no—
472C2×C22⋊D17—22no—
473C2×C22⋊D17—22no—
474C2×C22⋊D17—41no—
475C2×C22⋊D17—41no—
476C2×C22⋊D17—41no—
477C2×C22⋊D17—41no—
478C2×C22⋊D17—41no—
479C2×C22⋊D17—41no—
480C2×C22⋊D17—41no—
481C2×C22⋊D17—41no—
482C2×C22⋊D17—41no—
483C2×C22⋊D17—41no—
484C2×C22⋊D17—41no—
485C2×C22⋊D17—41no—
486C2×C22⋊D17—41no—
487C2×C22⋊D17—41no—
488C2×C22⋊D17—41no—
489C2×C22⋊D17—41no—
490C2×C22⋊D17—41no—
491C2×C22⋊D17—41no—
492C2×C22⋊D17—41no—
493C2×C22⋊D17—41no—
494C2×C22⋊D17—41no—
495C2×C22⋊D17—41no—
496C2×C22⋊D17—41no—
497C2×C22⋊D17—41no—
498C2×C22⋊D17—41no—
499C2×C22⋊D17—41no—
500C22×Dic17—22no—
501C22×Dic17—22no—
502C22×Dic17—41no—
503C22×Dic17—41no—
504C22×Dic17—41no—
505C22×Dic17—41no—
506C22×Dic17—41no—
507C22×Dic17—41no—
508C22×Dic17—41no—
509C22×Dic17C2411yescharacteristic
510C22×Dic17C2411yescharacteristic
511C22×Dic17C2411yescharacteristic
512C22×Dic17C2411yescharacteristic
513C22×Dic17C2411yescharacteristic
514C22×Dic17C2411yescharacteristic
515C22×Dic17C2411yescharacteristic
516C22×Dic17C2411yescharacteristic
517C22×Dic17C2411yescharacteristic
518C22×Dic17C2411yescharacteristic
519C22×Dic17C2411yescharacteristic
520C22×Dic17C2411yescharacteristic
521C22×Dic17C2411yescharacteristic
522#63252—416no—
523C2×D68—22no—
524C2×D68—22no—
525C2×D68—22no—
526C2×D68—22no—
527C2×D68—41no—
528C2×D68—41no—
529C2×C4×D17—22no—
530C2×C4×D17—22no—
531C2×C4×D17—22no—
532C2×C4×D17—22no—
533C2×C4×D17—22no—
534C2×C4×D17—22no—
535C2×C4×D17—22no—
536C2×C4×D17—22no—
537C2×C4×D17—22no—
538C2×C4×D17—416no—
539C2×C4×D17—41no—
540C2×C4×D17—41no—
541C2×C4×D17—41no—
542C2×C4×D17—41no—
543C2×C4×D17—41no—
544C2×C4×D17—41no—
545C2×Dic34—22no—
546C2×Dic34—22no—
547C2×Dic34—41no—
548C4⋊C4×C17—22no—
549C4⋊C4×C17—22no—
550C4⋊C4×C17—22no—
551C4⋊C4×C17—22no—
552C4⋊C4×C17—22no—
553C4⋊C4×C17—22no—
554C4⋊C4×C17—22no—
555C4⋊C4×C17C2×D414yes—
556C22⋊C4×C17—22no—
557C22⋊C4×C17—22no—
558C22⋊C4×C17—22no—
559C22⋊C4×C17—22no—
560C22⋊C4×C17—22no—
561C22⋊C4×C17—22no—
562C22⋊C4×C17—22no—
563C22⋊C4×C17—22no—
564C22⋊C4×C17C2×D414yes—
565C22⋊C4×C17C2×D414yes—
566C42×C17—22no—
567C42×C17C2×D414yes—
568C22⋊Dic17—22no—
569C22⋊Dic17—22no—
570C22⋊Dic17—22no—
571C22⋊Dic17—22no—
572C22⋊Dic17—22no—
573C22⋊Dic17—41no—
574C22⋊Dic17—41no—
575C22⋊Dic17—41no—
576C22⋊Dic17—41no—
577C22⋊Dic17—41no—
578C22⋊Dic17—41no—
579C22⋊Dic17—41no—
580C22⋊Dic17—41no—
581C22⋊Dic17—41no—
582C22⋊Dic17—41no—
583C22⋊Dic17—41no—
584C22⋊Dic17—41no—
585C22⋊Dic17—41no—
586C22⋊Dic17—41no—
587C22⋊Dic17—41no—
588C22⋊Dic17—41no—
589C22⋊Dic17—41no—
590C22⋊Dic17—41no—
591#63227—22no—
592#63227—22no—
593#63227—22no—
594#63227—22no—
595#63227—22no—
596#63227—22no—
597#63227—22no—
598#63227—22no—
599#63227—22no—
600#63227—22no—
601#63227—41no—
602#63227—41no—
603#63227—41no—
604#63227—41no—
605#63227—41no—
606#63227—41no—
607#63227—41no—
608#63227—41no—
609#63227—41no—
610#63227—41no—
611#63227—41no—
612C4⋊Dic17—22no—
613C4⋊Dic17—41no—
614C4⋊Dic17—41no—
615C4⋊Dic17—41no—
616C4⋊Dic17—41no—
617#63225—22no—
618#63225—22no—
619#63225—22no—
620#63225—22no—
621#63225—22no—
622#63225—41no—
623#63225—41no—
624#63225—41no—
625#63225—41no—
626#63225—41no—
627#63225—41no—
628C4×Dic17—22no—
629C4×Dic17—41no—
630C4×Dic17—41no—
631#36713—171nomaximal, Sylow
632C23×C17—21no—
633C23×C17—21no—
634C23×C17—21no—
635C23×C17—21no—
636C23×C17—21no—
637C23×C17—21no—
638C23×C17—21no—
639C23×C17—21no—
640C23×C17—21no—
641C23×C17—21no—
642C23×C17—21no—
643C23×C17—21no—
644C23×C17—21no—
645C23×C17—21no—
646C23×C17—21no—
647C23×C17—21no—
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—21no—
657C23×C17—21no—
658C23×C17—21no—
659C23×C17—21no—
660C23×C17—21no—
661C23×C17—21no—
662C23×C17—21no—
663C23×C17—21no—
664C23×C17—21no—
665C23×C17C22×D412yes—
666C23×C17C22×D412yes—
667C23×C17C2511yescharacteristic
668C22×D17—21no—
669C22×D17—21no—
670C22×D17—21no—
671C22×D17—21no—
672C22×D17—21no—
673C22×D17—21no—
674C22×D17—21no—
675C22×D17—21no—
676C22×D17—21no—
677C22×D17—21no—
678C22×D17—21no—
679C22×D17—21no—
680C22×D17—21no—
681C22×D17—21no—
682C22×D17—21no—
683C22×D17—21no—
684C22×D17—21no—
685C22×D17—21no—
686C22×D17—21no—
687C22×D17—44no—
688C22×D17—44no—
689C22×D17—44no—
690C22×D17—44no—
691C22×D17—44no—
692C22×D17—44no—
693C22×D17—44no—
694C22×D17H(5,𝔽2)12yes—
695C22×D17H(5,𝔽2)12yes—
696D4×C17—44no—
697D4×C17—44no—
698D4×C17—82no—
699D4×C17—82no—
700D4×C17—82no—
701D4×C17—82no—
702D4×C17—82no—
703D4×C17—82no—
704D4×C17—82no—
705D4×C17—82no—
706C2×C4×C17—21no—
707C2×C4×C17—21no—
708C2×C4×C17—21no—
709C2×C4×C17—21no—
710C2×C4×C17—21no—
711C2×C4×C17—21no—
712C2×C4×C17—21no—
713C2×C4×C17—21no—
714C2×C4×C17—21no—
715C2×C4×C17—21no—
716C2×C4×C17—21no—
717C2×C4×C17—21no—
718C2×C4×C17—21no—
719C2×C4×C17—21no—
720C2×C4×C17—21no—
721C2×C4×C17—21no—
722C2×C4×C17—21no—
723C2×C4×C17—21no—
724C2×C4×C17—21no—
725C2×C4×C17—21no—
726C2×C4×C17—21no—
727C2×C4×C17—21no—
728C2×C4×C17—21no—
729C2×C4×C17—21no—
730C2×C4×C17—21no—
731C2×C4×C17—44no—
732C2×C4×C17—44no—
733C2×C4×C17—44no—
734C2×C4×C17—82no—
735C2×C4×C17—82no—
736C2×C4×C17C22×D412yes—
737C2×C4×C17C22×D412yes—
738C2×C4×C17C22×D412yes—
739C2×C4×C17C22×D412yes—
740C2×C4×C17C22×D412yes—
741C22⋊D17—44no—
742C22⋊D17—44no—
743C22⋊D17—44no—
744C22⋊D17—44no—
745C22⋊D17—82no—
746C22⋊D17—82no—
747C22⋊D17—82no—
748C22⋊D17—82no—
749C22⋊D17—82no—
750C22⋊D17—82no—
751C22⋊D17—82no—
752C22⋊D17—82no—
753C22⋊D17—82no—
754C2×Dic17—21no—
755C2×Dic17—21no—
756C2×Dic17—21no—
757C2×Dic17—21no—
758C2×Dic17—21no—
759C2×Dic17—21no—
760C2×Dic17—21no—
761C2×Dic17—21no—
762C2×Dic17—21no—
763C2×Dic17—21no—
764C2×Dic17—21no—
765C2×Dic17—21no—
766C2×Dic17—21no—
767C2×Dic17—21no—
768C2×Dic17—21no—
769C2×Dic17—21no—
770C2×Dic17—21no—
771C2×Dic17—21no—
772C2×Dic17—21no—
773C2×Dic17—21no—
774C2×Dic17—21no—
775C2×Dic17—21no—
776C2×Dic17—21no—
777C2×Dic17—21no—
778C2×Dic17—21no—
779C2×Dic17—21no—
780C2×Dic17—21no—
781C2×Dic17—21no—
782C2×Dic17—21no—
783C2×Dic17—21no—
784C2×Dic17—21no—
785C2×Dic17—21no—
786C2×Dic17—21no—
787C2×Dic17—21no—
788C2×Dic17—21no—
789C2×Dic17—21no—
790C2×Dic17—21no—
791C2×Dic17—21no—
792C2×Dic17—44no—
793C2×Dic17—82no—
794C2×Dic17—82no—
795C2×Dic17H(5,𝔽2)12yes—
796D68—44no—
797D68—44no—
798C4×D17—28no—
799C4×D17—44no—
800C4×D17—44no—
801C4×D17—44no—
802C4×D17—44no—
803Dic34—44no—
804C2×#540D1711yescharacteristic, complemented
805C2×#525—171no—
806#2849—171no—
807#2847—171no—
808#2694—171no—
809#2693—171no—
810#2690—171no—
811#2688—171no—
812#2687—171no—
813#2678—171no—
814#2676—171no—
815#2675—171no—
816#2673—171no—
817#2673—171no—
818#2672—171no—
819#2671—171no—
820#2671—171no—
821#2669—171no—
822#2669—171no—
823#2668—171no—
824#2635—171no—
825#2630—171no—
826#2609—171no—
827#2602—171no—
828#2598—171no—
829#2598—171no—
830#2543—171no—
831#2535—171no—
832#2431—171no—
833#2430—171no—
834#2318—171no—
835C22×C17—22no—
836C22×C17—22no—
837C22×C17—22no—
838C22×C17—22no—
839C22×C17—22no—
840C22×C17—22no—
841C22×C17—41no—
842C22×C17—41no—
843C22×C17—41no—
844C22×C17—41no—
845C22×C17—41no—
846C22×C17—41no—
847C22×C17—41no—
848C22×C17—41no—
849C22×C17—41no—
850C22×C17—41no—
851C22×C17—41no—
852C22×C17—41no—
853C22×C17—41no—
854C22×C17—41no—
855C22×C17—41no—
856C22×C17—41no—
857C22×C17—41no—
858C22×C17—41no—
859C22×C17—41no—
860C22×C17—41no—
861C22×C17—41no—
862C22×C17—41no—
863C22×C17—41no—
864C22×C17—41no—
865C22×C17—41no—
866C22×C17—41no—
867C22×C17—41no—
868C22×C17—41no—
869C22×C17—41no—
870C22×C17C23×D411yescharacteristic
871C22×C17C2×H(5,𝔽2)11yescharacteristic
872C22×C17C2×H(5,𝔽2)11yescharacteristic
873C22×C17C2×H(5,𝔽2)11yescharacteristic
874C22×C17#58511yescharacteristic
875C22×C17#58511yescharacteristic
876C22×C17#58511yescharacteristic
877C2×D17—22no—
878C2×D17—22no—
879C2×D17—22no—
880C2×D17—22no—
881C2×D17—22no—
882C2×D17—22no—
883C2×D17—416no—
884C2×D17—41no—
885C2×D17—41no—
886C2×D17—41no—
887C2×D17—41no—
888C2×D17—41no—
889C2×D17—41no—
890C2×D17—41no—
891C2×D17—41no—
892C2×D17—41no—
893C2×D17—41no—
894C2×D17—41no—
895C2×D17—41no—
896C2×D17—41no—
897C2×D17—41no—
898C2×D17—41no—
899C4×C17—22no—
900C4×C17—22no—
901C4×C17—22no—
902C4×C17—22no—
903C4×C17—22no—
904C4×C17—41no—
905C4×C17—41no—
906C4×C17—41no—
907C4×C17—41no—
908C4×C17—41no—
909Dic17—22no—
910Dic17—41no—
911Dic17—41no—
912Dic17—41no—
913Dic17—41no—
914Dic17—41no—
915Dic17—41no—
916Dic17—41no—
917Dic17—41no—
918Dic17—41no—
919Dic17—41no—
920Dic17—41no—
921Dic17—41no—
922C22×#41—171no—
923C24×C4—171no—
924#540—28no—
925C2×#127—171no—
926C2×#127C2×D1711yescharacteristic
927C2×#125C2×D1711yescharacteristic, complemented
928C2×#124—171no—
929#525—348no—
930C2×#123—171no—
931C2×#123—171no—
932C2×#123—171no—
933C2×#123C2×D1711yescharacteristic
934C2×#123C2×D1711yescharacteristic
935C2×#123C2×D1711yescharacteristic, complemented
936C2×#123C2×D1711yescharacteristic, complemented
937C2×C22⋊Q8—171no—
938C2×C22⋊Q8—171no—
939C2×#121—171no—
940C2×#121—171no—
941C2×#121—171no—
942C2×#121—171no—
943C2×#121—171no—
944C2×#121—171no—
945C2×#121—171no—
946C2×#121—171no—
947C2×#121—171no—
948C2×#121—171no—
949C2×#121C2×D1711yescharacteristic
950C2×#121C2×D1711yescharacteristic
951C2×#121C2×D1711yescharacteristic
952C2×#121C2×D1711yescharacteristic, complemented
953C2×#121C2×D1711yescharacteristic, complemented
954C2×#121C2×D1711yescharacteristic, complemented
955C2×#120—171no—
956C2×#120—171no—
957C2×#120—171no—
958C2×#120—171no—
959C2×#120—171no—
960C2×C4×D4—171no—
961C2×C4×D4—171no—
962C2×C4×D4—171no—
963C2×C4×D4C2×D1711yescharacteristic
964C2×C4×D4C2×D1711yescharacteristic, complemented
965C2×#117—171no—
966C2×#117C2×D1711yescharacteristic, complemented
967#400—171no—
968#400—171no—
969#400—171no—
970#399—171no—
971#399—171no—
972#399—171no—
973#398—171no—
974#398—171no—
975#398—171no—
976#397—171no—
977#397—171no—
978#397—171no—
979#397—171no—
980#397—171no—
981#396—171no—
982#396—171no—
983#396—171no—
984#396—171no—
985#395—171no—
986#394—171no—
987#394—171no—
988#394—171no—
989#394—171no—
990#394—171no—
991#394—171no—
992#394—171no—
993#394—171no—
994#394—171no—
995#394—171no—
996#394—171no—
997#394—171no—
998#394—171no—
999#393—171no—
1000#392—171no—
1001#392—171no—
1002#392—171no—
1003#392—171no—
1004#392—171no—
1005#392—171no—
1006#392—171no—
1007#392—171no—
1008#392—171no—
1009#392—171no—
1010#392—171no—
1011#392—171no—
1012#392—171no—
1013#392—171no—
1014#392—171no—
1015#391—171no—
1016#390—171no—
1017#390—171no—
1018#389—171no—
1019#388—171no—
1020#388—171no—
1021#388—171no—
1022#388—171no—
1023#388—171no—
1024#388—171no—
1025#388—171no—
1026#388—171no—
1027#388—171no—
1028#388—171no—
1029#387—171no—
1030#387—171no—
1031#387—171no—
1032#387—171no—
1033#386—171no—
1034#386—171no—
1035#386—171no—
1036#386—171no—
1037#386—171no—
1038#386—171no—
1039#386—171no—
1040#386—171no—
1041#386—171no—
1042#386—171no—
1043#386—171no—
1044#386—171no—
1045#386—171no—
1046#386—171no—
1047#386—171no—
1048#386—171no—
1049#386—171no—
1050#386—171no—
1051#386—171no—
1052#386—171no—
1053#386—171no—
1054#386—171no—
1055#386—171no—
1056#386—171no—
1057#385—171no—
1058#385—171no—
1059#385—171no—
1060#385—171no—
1061#385—171no—
1062#385—171no—
1063#385—171no—
1064#385—171no—
1065#385—171no—
1066#385—171no—
1067#383—171no—
1068#382—171no—
1069#381—171no—
1070#381—171no—
1071#380—171no—
1072#380—171no—
1073#380—171no—
1074#380—171no—
1075#380—171no—
1076#379—171no—
1077C4×C22⋊C4—171no—
1078C2×#95—171no—
1079C2×C17—42no—
1080C2×C17—42no—
1081C2×C17—81no—
1082C2×C17—81no—
1083C2×C17—81no—
1084C2×C17#344911yescharacteristic
1085C2×C17#348411yescharacteristic
1086C2×C17#348811yescharacteristic
1087C2×C17#353311yescharacteristic
1088C2×C17#353411yescharacteristic
1089C2×C17#353911yescharacteristic
1090C2×C17#354211yescharacteristic
1091D17—42no—
1092D17—42no—
1093D17—81no—
1094C25—171no—
1095C2×#41—344no—
1096C2×#41—682no—
1097C2×#41—682no—
1098C22×Q8—171no—
1099C22×D4—171no—
1100C22×D4—171no—
1101C22×D4—171no—
1102C22×D4—171no—
1103C22×D4—171no—
1104C22×D4—171no—
1105C22×D4—171no—
1106C22×D4—171no—
1107C22×D4—171no—
1108C22×D4—171no—
1109C22×D4—171no—
1110C22×D4—171no—
1111C22×D4—171no—
1112C22×D4—171no—
1113C22×D4—171no—
1114C22×D4C22×D1711yescharacteristic
1115C22×D4C22×D1711yescharacteristic
1116C22×D4C22×D1711yescharacteristic
1117C22×D4C22×D1711yescharacteristic
1118C22×D4C22×D1711yescharacteristic
1119C22×D4C22×D1711yescharacteristic
1120C22×D4C22×D1711yescharacteristic
1121C22×D4C22×D1711yescharacteristic
1122C22×D4C22×D1711yescharacteristic
1123C22×D4C22×D1711yescharacteristic
1124C23×C4—171no—
1125C23×C4—171no—
1126C23×C4—171no—
1127C23×C4—171no—
1128C23×C4—171no—
1129C23×C4—171no—
1130C23×C4—171no—
1131C23×C4—171no—
1132C23×C4—344no—
1133C23×C4—682no—
1134C23×C4—682no—
1135C23×C4C22×D1711yescharacteristic
1136C23×C4C22×D1711yescharacteristic
1137C23×C4C22×D1711yescharacteristic
1138C23×C4C22×D1711yescharacteristic
1139C23×C4C22×D1711yescharacteristic
1140#127—24no—
1141#127—682no—
1142#125—24no—
1143#124—682no—
1144#123—24no—
1145#123—24no—
1146#123—24no—
1147#123—24no—
1148#123—344no—
1149#123—344no—
1150#123—682no—
1151C22⋊Q8—344no—
1152C22⋊Q8—344no—
1153#121—24no—
1154#121—24no—
1155#121—24no—
1156#121—24no—
1157#121—24no—
1158#121—24no—
1159#121—344no—
1160#121—344no—
1161#121—682no—
1162#121—682no—
1163#121—682no—
1164#121—682no—
1165#121—682no—
1166#121—682no—
1167#121—682no—
1168#121—682no—
1169#120—344no—
1170#120—344no—
1171#120—682no—
1172#120—682no—
1173#120—682no—
1174C4×D4—24no—
1175C4×D4—344no—
1176C4×D4—344no—
1177C4×D4—344no—
1178C4×D4C22⋊D1718yescomplemented
1179#117—24no—
1180#117—344no—
1181C2×C4⋊C4—171no—
1182C2×C4⋊C4—171no—
1183C2×C4⋊C4—171no—
1184C2×C4⋊C4—171no—
1185C2×C4⋊C4—171no—
1186C2×C4⋊C4—171no—
1187C2×C4⋊C4—171no—
1188C2×C4⋊C4—171no—
1189C2×C4⋊C4—171no—
1190C2×C4⋊C4—171no—
1191C2×C4⋊C4—171no—
1192C2×C4⋊C4—171no—
1193C2×C4⋊C4—171no—
1194C2×C4⋊C4—171no—
1195C2×C4⋊C4—171no—
1196C2×C4⋊C4—171no—
1197C2×C4⋊C4C22×D1711yescharacteristic
1198C2×C4⋊C4C22×D1711yescharacteristic
1199C2×C4⋊C4C22×D1711yescharacteristic
1200C2×C4⋊C4C22×D1711yescharacteristic
1201C2×C4⋊C4C22×D1711yescharacteristic
1202C2×C4⋊C4C22×D1711yescharacteristic
1203C2×C4⋊C4C22×D1711yescharacteristic
1204C2×C4⋊C4C22×D1711yescharacteristic
1205C2×C22⋊C4—171no—
1206C2×C22⋊C4—171no—
1207C2×C22⋊C4—171no—
1208C2×C22⋊C4—171no—
1209C2×C22⋊C4—171no—
1210C2×C22⋊C4—171no—
1211C2×C22⋊C4—171no—
1212C2×C22⋊C4—171no—
1213C2×C22⋊C4—171no—
1214C2×C22⋊C4—171no—
1215C2×C22⋊C4—171no—
1216C2×C22⋊C4—171no—
1217C2×C22⋊C4—171no—
1218C2×C22⋊C4—171no—
1219C2×C22⋊C4—171no—
1220C2×C22⋊C4—171no—
1221C2×C22⋊C4—171no—
1222C2×C22⋊C4—171no—
1223C2×C22⋊C4—171no—
1224C2×C22⋊C4—171no—
1225C2×C22⋊C4—171no—
1226C2×C22⋊C4—171no—
1227C2×C22⋊C4—171no—
1228C2×C22⋊C4—171no—
1229C2×C22⋊C4—171no—
1230C2×C22⋊C4—171no—
1231C2×C22⋊C4—171no—
1232C2×C22⋊C4—171no—
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⋊C4C22×D1711yescharacteristic
1250C2×C22⋊C4C22×D1711yescharacteristic
1251C2×C22⋊C4C22×D1711yescharacteristic
1252C2×C22⋊C4C22×D1711yescharacteristic
1253C2×C22⋊C4C22×D1711yescharacteristic
1254C2×C22⋊C4C22×D1711yescharacteristic
1255C2×C22⋊C4C22×D1711yescharacteristic
1256C2×C22⋊C4C22×D1711yescharacteristic
1257C2×C22⋊C4C22×D1711yescharacteristic
1258C2×C22⋊C4C22×D1711yescharacteristic
1259C2×C42—171no—
1260C2×C42—171no—
1261C2×C42—171no—
1262C2×C42C22×D1711yescharacteristic
1263C2×C42C22×D1711yescharacteristic
1264#95—171no—
1265#95—171no—
1266#95—171no—
1267#95—171no—
1268#95—171no—
1269#95—171no—
1270#95—171no—
1271#95—171no—
1272#95—171no—
1273#95—171no—
1274#95—171no—
1275#95—171no—
1276#95—171no—
1277#95—171no—
1278#95—171no—
1279#95—171no—
1280#95—171no—
1281#95—171no—
1282#95—171no—
1283#95—171no—
1284#95—171no—
1285#95—171no—
1286#95—171no—
1287#95—171no—
1288#95—171no—
1289#95—171no—
1290#95—171no—
1291#95—171no—
1292#95—171no—
1293#95—171no—
1294#95—171no—
1295#95—171no—
1296C17#3671311yescharacteristic, complemented, Sylow
1297C24—171no—
1298C24—171no—
1299C24—171no—
1300C24—342no—
1301C24—342no—
1302C24—342no—
1303C24—681no—
1304C24—681no—
1305C24—681no—
1306C24—681no—
1307C24C23×D1711yescharacteristic
1308C24C23×D1711yescharacteristic
1309C24C23×D1711yescharacteristic
1310C24C23×D1711yescharacteristic
1311C24C23×D1711yescharacteristic
1312#41—6816no—
1313C2×Q8—342no—
1314C2×Q8—342no—
1315C2×Q8—681no—
1316C2×D4—22no—
1317C2×D4—22no—
1318C2×D4—22no—
1319C2×D4—22no—
1320C2×D4—22no—
1321C2×D4—22no—
1322C2×D4—22no—
1323C2×D4—22no—
1324C2×D4—22no—
1325C2×D4—41no—
1326C2×D4—41no—
1327C2×D4—41no—
1328C2×D4—41no—
1329C2×D4—41no—
1330C2×D4—41no—
1331C2×D4—41no—
1332C2×D4—41no—
1333C2×D4—41no—
1334C2×D4—41no—
1335C2×D4—41no—
1336C2×D4—41no—
1337C2×D4—41no—
1338C2×D4—41no—
1339C2×D4—41no—
1340C2×D4—41no—
1341C2×D4—41no—
1342C2×D4—41no—
1343C2×D4—41no—
1344C2×D4—41no—
1345C2×D4—342no—
1346C2×D4—342no—
1347C2×D4—342no—
1348C2×D4—342no—
1349C2×D4—342no—
1350C2×D4—342no—
1351C2×D4—342no—
1352C2×D4—342no—
1353C2×D4—342no—
1354C2×D4—342no—
1355C2×D4—342no—
1356C2×D4—342no—
1357C2×D4—342no—
1358C2×D4—342no—
1359C2×D4—342no—
1360C2×D4—342no—
1361C2×D4—342no—
1362C2×D4—681no—
1363C2×D4—681no—
1364C2×D4—681no—
1365C2×D4—681no—
1366C2×D4—681no—
1367C2×D4—681no—
1368C2×D4—681no—
1369C2×D4—681no—
1370C2×D4—681no—
1371C2×D4—681no—
1372C2×D4—681no—
1373C2×D4—681no—
1374C2×D4—681no—
1375C2×D4—681no—
1376C2×D4—681no—
1377C2×D4—681no—
1378C2×D4—681no—
1379C2×D4—681no—
1380C2×D4—681no—
1381C2×D4—681no—
1382C2×D4—681no—
1383C2×D4—681no—
1384C2×D4—681no—
1385C2×D4—681no—
1386C2×D4—681no—
1387C2×D4—681no—
1388C2×D4—681no—
1389C2×D4—681no—
1390C2×D4C2×C22⋊D1714yes—
1391C22×C4—22no—
1392C22×C4—22no—
1393C22×C4—22no—
1394C22×C4—41no—
1395C22×C4—41no—
1396C22×C4—41no—
1397C22×C4—41no—
1398C22×C4—41no—
1399C22×C4—41no—
1400C22×C4—41no—
1401C22×C4—41no—
1402C22×C4—41no—
1403C22×C4—41no—
1404C22×C4—171no—
1405C22×C4—171no—
1406C22×C4—171no—
1407C22×C4—171no—
1408C22×C4—171no—
1409C22×C4—171no—
1410C22×C4—171no—
1411C22×C4—171no—
1412C22×C4—171no—
1413C22×C4—171no—
1414C22×C4—171no—
1415C22×C4—171no—
1416C22×C4—171no—
1417C22×C4—342no—
1418C22×C4—342no—
1419C22×C4—342no—
1420C22×C4—342no—
1421C22×C4—342no—
1422C22×C4—342no—
1423C22×C4—342no—
1424C22×C4—342no—
1425C22×C4—342no—
1426C22×C4—342no—
1427C22×C4—342no—
1428C22×C4—681no—
1429C22×C4—681no—
1430C22×C4—681no—
1431C22×C4—681no—
1432C22×C4—681no—
1433C22×C4—681no—
1434C22×C4—6816no—
1435C22×C4—681no—
1436C22×C4—681no—
1437C22×C4—681no—
1438C22×C4—681no—
1439C22×C4—681no—
1440C22×C4—681no—
1441C22×C4—681no—
1442C22×C4C2×C22⋊D1714yes—
1443C22×C4C2×C22⋊D1714yes—
1444C22×C4C23×D1711yescharacteristic
1445C22×C4C23×D1711yescharacteristic
1446C22×C4C23×D1711yescharacteristic
1447C22×C4C23×D1711yescharacteristic
1448C22×C4C23×D1711yescharacteristic
1449C22×C4C23×D1711yescharacteristic
1450C22×C4C23×D1711yescharacteristic
1451C22×C4C23×D1711yescharacteristic
1452C22×C4C23×D1711yescharacteristic
1453C22×C4C23×D1711yescharacteristic
1454C4⋊C4—22no—
1455C4⋊C4—22no—
1456C4⋊C4—22no—
1457C4⋊C4—22no—
1458C4⋊C4—22no—
1459C4⋊C4—22no—
1460C4⋊C4—22no—
1461C4⋊C4—342no—
1462C4⋊C4—342no—
1463C4⋊C4—342no—
1464C4⋊C4—342no—
1465C4⋊C4—342no—
1466C4⋊C4—342no—
1467C4⋊C4—681no—
1468C4⋊C4—681no—
1469C4⋊C4—681no—
1470C4⋊C4—681no—
1471C4⋊C4—681no—
1472C4⋊C4—681no—
1473C4⋊C4—681no—
1474C4⋊C4—681no—
1475C4⋊C4—681no—
1476C4⋊C4—681no—
1477C4⋊C4C2×C22⋊D1714yes—
1478C22⋊C4—22no—
1479C22⋊C4—22no—
1480C22⋊C4—22no—
1481C22⋊C4—22no—
1482C22⋊C4—22no—
1483C22⋊C4—22no—
1484C22⋊C4—22no—
1485C22⋊C4—22no—
1486C22⋊C4—342no—
1487C22⋊C4—342no—
1488C22⋊C4—342no—
1489C22⋊C4—342no—
1490C22⋊C4—342no—
1491C22⋊C4—342no—
1492C22⋊C4—342no—
1493C22⋊C4—342no—
1494C22⋊C4—342no—
1495C22⋊C4—342no—
1496C22⋊C4—342no—
1497C22⋊C4—342no—
1498C22⋊C4—342no—
1499C22⋊C4—342no—
1500C22⋊C4—342no—
1501C22⋊C4—681no—
1502C22⋊C4—681no—
1503C22⋊C4—681no—
1504C22⋊C4—681no—
1505C22⋊C4—681no—
1506C22⋊C4—681no—
1507C22⋊C4—681no—
1508C22⋊C4—681no—
1509C22⋊C4—681no—
1510C22⋊C4—681no—
1511C22⋊C4—681no—
1512C22⋊C4—681no—
1513C22⋊C4—681no—
1514C22⋊C4—681no—
1515C22⋊C4—681no—
1516C22⋊C4—681no—
1517C22⋊C4—681no—
1518C22⋊C4—681no—
1519C22⋊C4—681no—
1520C22⋊C4—681no—
1521C22⋊C4—681no—
1522C22⋊C4—681no—
1523C22⋊C4—681no—
1524C22⋊C4—681no—
1525C22⋊C4—681no—
1526C22⋊C4—681no—
1527C22⋊C4—681no—
1528C22⋊C4—681no—
1529C22⋊C4—681no—
1530C22⋊C4C2×C22⋊D1714yes—
1531C22⋊C4C2×C22⋊D1714yes—
1532C42—22no—
1533C42—342no—
1534C42—681no—
1535C42—681no—
1536C42C2×C22⋊D1714yes—
1537C23—21no—
1538C23—21no—
1539C23—21no—
1540C23—21no—
1541C23—21no—
1542C23—21no—
1543C23—21no—
1544C23—21no—
1545C23—21no—
1546C23—21no—
1547C23—21no—
1548C23—21no—
1549C23—21no—
1550C23—21no—
1551C23—21no—
1552C23—21no—
1553C23—21no—
1554C23—21no—
1555C23—21no—
1556C23—21no—
1557C23—21no—
1558C23—21no—
1559C23—21no—
1560C23—21no—
1561C23—21no—
1562C23—21no—
1563C23—21no—
1564C23—21no—
1565C23—21no—
1566C23—21no—
1567C23—21no—
1568C23—21no—
1569C23—21no—
1570C23—172no—
1571C23—172no—
1572C23—341no—
1573C23—341no—
1574C23—341no—
1575C23—341no—
1576C23—341no—
1577C23—341no—
1578C23—341no—
1579C23—341no—
1580C23—341no—
1581C23—341no—
1582C23—341no—
1583C23—341no—
1584C23—341no—
1585C23—341no—
1586C23—341no—
1587C23—341no—
1588C23—341no—
1589C23—341no—
1590C23—341no—
1591C23—684no—
1592C23—684no—
1593C23—684no—
1594C23—684no—
1595C23—684no—
1596C23—684no—
1597C23—684no—
1598C23C22×C22⋊D1712yes—
1599C23C22×C22⋊D1712yes—
1600C23C24×D1711yescharacteristic
1601Q8—684no—
1602D4—44no—
1603D4—44no—
1604D4—82no—
1605D4—82no—
1606D4—82no—
1607D4—82no—
1608D4—82no—
1609D4—82no—
1610D4—82no—
1611D4—82no—
1612D4—684no—
1613D4—684no—
1614D4—684no—
1615D4—684no—
1616D4—684no—
1617D4—684no—
1618D4—1362no—
1619D4—1362no—
1620D4—1362no—
1621D4—1362no—
1622D4—1362no—
1623D4—1362no—
1624D4—1362no—
1625D4—1362no—
1626D4—1362no—
1627C2×C4—21no—
1628C2×C4—21no—
1629C2×C4—21no—
1630C2×C4—21no—
1631C2×C4—21no—
1632C2×C4—21no—
1633C2×C4—21no—
1634C2×C4—21no—
1635C2×C4—21no—
1636C2×C4—21no—
1637C2×C4—21no—
1638C2×C4—21no—
1639C2×C4—21no—
1640C2×C4—21no—
1641C2×C4—21no—
1642C2×C4—21no—
1643C2×C4—21no—
1644C2×C4—21no—
1645C2×C4—21no—
1646C2×C4—21no—
1647C2×C4—21no—
1648C2×C4—21no—
1649C2×C4—21no—
1650C2×C4—21no—
1651C2×C4—21no—
1652C2×C4—44no—
1653C2×C4—44no—
1654C2×C4—44no—
1655C2×C4—82no—
1656C2×C4—82no—
1657C2×C4—172no—
1658C2×C4—348no—
1659C2×C4—341no—
1660C2×C4—341no—
1661C2×C4—341no—
1662C2×C4—341no—
1663C2×C4—341no—
1664C2×C4—341no—
1665C2×C4—341no—
1666C2×C4—341no—
1667C2×C4—341no—
1668C2×C4—341no—
1669C2×C4—341no—
1670C2×C4—341no—
1671C2×C4—341no—
1672C2×C4—341no—
1673C2×C4—341no—
1674C2×C4—341no—
1675C2×C4—341no—
1676C2×C4—341no—
1677C2×C4—341no—
1678C2×C4—341no—
1679C2×C4—341no—
1680C2×C4—341no—
1681C2×C4—341no—
1682C2×C4—341no—
1683C2×C4—341no—
1684C2×C4—341no—
1685C2×C4—341no—
1686C2×C4—341no—
1687C2×C4—341no—
1688C2×C4—341no—
1689C2×C4—341no—
1690C2×C4—341no—
1691C2×C4—341no—
1692C2×C4—341no—
1693C2×C4—341no—
1694C2×C4—341no—
1695C2×C4—341no—
1696C2×C4—341no—
1697C2×C4—684no—
1698C2×C4—684no—
1699C2×C4—684no—
1700C2×C4—684no—
1701C2×C4—684no—
1702C2×C4—1362no—
1703C2×C4—1362no—
1704C2×C4C22×C22⋊D1712yes—
1705C2×C4C22×C22⋊D1712yes—
1706C2×C4C22×C22⋊D1712yes—
1707C2×C4C22×C22⋊D1712yes—
1708C2×C4C22×C22⋊D1712yes—
1709C22—22no—
1710C22—22no—
1711C22—22no—
1712C22—22no—
1713C22—22no—
1714C22—22no—
1715C22—41no—
1716C22—41no—
1717C22—41no—
1718C22—41no—
1719C22—41no—
1720C22—41no—
1721C22—41no—
1722C22—41no—
1723C22—41no—
1724C22—41no—
1725C22—41no—
1726C22—41no—
1727C22—41no—
1728C22—41no—
1729C22—41no—
1730C22—41no—
1731C22—41no—
1732C22—41no—
1733C22—41no—
1734C22—41no—
1735C22—41no—
1736C22—41no—
1737C22—41no—
1738C22—41no—
1739C22—41no—
1740C22—41no—
1741C22—41no—
1742C22—41no—
1743C22—41no—
1744C22—342no—
1745C22—342no—
1746C22—342no—
1747C22—342no—
1748C22—342no—
1749C22—342no—
1750C22—6816no—
1751C22—681no—
1752C22—681no—
1753C22—681no—
1754C22—681no—
1755C22—681no—
1756C22—681no—
1757C22—681no—
1758C22—681no—
1759C22—681no—
1760C22—681no—
1761C22—681no—
1762C22—681no—
1763C22—681no—
1764C22—681no—
1765C22—681no—
1766C22C23×C22⋊D1711yescharacteristic
1767C22H(5,𝔽2)×D1711yescharacteristic
1768C22H(5,𝔽2)×D1711yescharacteristic
1769C22H(5,𝔽2)×D1711yescharacteristic
1770C22#1176364411yescharacteristic
1771C22#1176364511yescharacteristic
1772C22#1176364511yescharacteristic
1773C4—22no—
1774C4—22no—
1775C4—22no—
1776C4—22no—
1777C4—22no—
1778C4—41no—
1779C4—41no—
1780C4—41no—
1781C4—41no—
1782C4—41no—
1783C4—342no—
1784C4—681no—
1785C4—681no—
1786C4—681no—
1787C4—681no—
1788C4—681no—
1789C4—681no—
1790C4—681no—
1791C4—681no—
1792C4—681no—
1793C4—681no—
1794C4—681no—
1795C4—681no—
1796C2—42no—
1797C2—42no—
1798C2—81no—
1799C2—81no—
1800C2—81no—
1801C2—682no—
1802C2—682no—
1803C2—1361no—
1804C2#1454211311yescharacteristic
1805C2#1454241511yescharacteristic
1806C2#1454244611yescharacteristic
1807C2#1454294411yescharacteristic
1808C2#1454296711yescharacteristic
1809C2#1454303611yescharacteristic
1810C2#1454309111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC2×C17×#540C2
hypercenterC2×#540D17
hypocenterC17#36713
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#11763318C2semidirect
2. #14537073C2semidirect
3. #14537063C2semidirect
4. #14535298C2semidirect
5. #14535289C2semidirect
6. #14535244C2semidirect
7. #14535214C2semidirect
8. #14535199C2semidirect
9. #14535103C2semidirect
10. #14535079C2semidirect
11. #14535074C2semidirect
12. #14535045C2semidirect
13. #14535044C2semidirect
14. #14535029C2semidirect
15. #14535020C2semidirect
16. #14535015C2semidirect
17. #14534997C2semidirect
18. #14534996C2semidirect
19. #14534987C2semidirect
20. #14534669C2semidirect
21. #14534623C2semidirect
22. #14534456C2semidirect
23. #14534398C2semidirect
24. #14534350C2semidirect
25. #14534344C2semidirect
26. #14533746C2semidirect
27. #14533685C2semidirect
28. #14532404C2semidirect
29. #14532396C2semidirect
30. #14531417C2semidirect
31. C2×C17×#540C2semidirect
35. C2×#10587622C22semidirect
49. C2×#10587625C22semidirect
61. #11762748C22semidirect
62. #11762747C22semidirect
63. #11762747C22semidirect
64. #11762745C22semidirect
66. #11762744C22semidirect
67. #11762742C22semidirect
68. #11762742C22semidirect
69. #11762740C22semidirect
71. #11762737C22semidirect
74. #11762735C22semidirect
75. #11762732C22semidirect
76. #11762732C22semidirect
78. #11762731C22semidirect
79. #11762729C22semidirect
83. #11762725C22semidirect
89. #11762723C22semidirect
90. #11762723C22semidirect
91. #11762723C22semidirect
92. #11762723C22semidirect
93. #11762721C22semidirect
105. #11762717C22semidirect
106. #11762717C22semidirect
107. #11762717C22semidirect
108. #11762717C22semidirect
109. #11762714C22semidirect
112. #11762704C22semidirect
113. #11762703C22semidirect
118. #11762700C22semidirect
120. #11762697C22semidirect
121. #11762697C22semidirect
122. #11762697C22semidirect
123. #11762695C22semidirect
124. #11762695C22semidirect
125. #11762693C22semidirect
126. #11762690C22semidirect
131. #11762689C22semidirect
132. #11762689C22semidirect
137. #11762688C22semidirect
139. #11762686C22semidirect
148. #11762685C22semidirect
149. #11762685C22semidirect
150. #11762685C22semidirect
151. #11762684C22semidirect
152. #11762684C22semidirect
153. #11762682C22semidirect
154. #11762682C22semidirect
155. #11762682C22semidirect
160. #11762680C22semidirect
161. #11762677C22semidirect
162. #11762675C22semidirect
166. #11762669C22semidirect
167. #11762669C22semidirect
171. C4×C22⋊Dic17C22semidirect
172. C2×#10587502C22semidirect
175. C2×C17×#125C22semidirect
178. C2×C17×#123C22semidirect
179. C2×C17×#123C22semidirect
183. C2×C17×#121C22semidirect
184. C2×C17×#121C22semidirect
185. C2×C17×#121C22semidirect
187. C2×C4×D4×C17C22semidirect
188. C2×C17×#117C22semidirect
248. C4×D4×C17D4semidirect
804. C2×#540D17semidirect
927. C2×#125C2×D17semidirect
935. C2×#123C2×D17semidirect
936. C2×#123C2×D17semidirect
952. C2×#121C2×D17semidirect
953. C2×#121C2×D17semidirect
954. C2×#121C2×D17semidirect
964. C2×C4×D4C2×D17semidirect
966. C2×#117C2×D17semidirect
1178. C4×D4C22⋊D17semidirect
1296. C17#36713semidirect

Maximal subgroups

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

subgroupindex
C2×#117633182
#145370732
#145370632
#145352982
#145352892
#145352442
#145352142
#145351992
#145351032
#145350792
#145350742
#145350452
#145350442
#145350292
#145350202
#145350152
#145349972
#145349962
#145349872
#145346692
#145346232
#145344562
#145343982
#145343502
#145343442
#145337462
#145336852
#145324042
#145323962
#145314172
C2×C17×#5402
#3671317