Finite Group Databasebeta

← #17202101

Subgroups — #17202101

Order 4352.

3014 conjugacy classes of subgroups.

The subgroup lattice has 1724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763343C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D17C211yesmaximal, characteristic, complemented
3#14533045C211yesmaximal, characteristic, complemented
4#14533030C211yesmaximal, characteristic, complemented
5#14532925C211yesmaximal, characteristic, complemented
6#14532910C211yesmaximal, characteristic, complemented
7#14532835C211yesmaximal, characteristic, complemented
8#14532820C211yesmaximal, characteristic, complemented
9#14532736C211yesmaximal, characteristic, complemented
10#14532721C211yesmaximal, characteristic, complemented
11#14532608C211yesmaximal, characteristic, complemented
12#14532534C211yesmaximal, characteristic, complemented
13#14532445C211yesmaximal, characteristic, complemented
14#14532335C211yesmaximal, characteristic, complemented
15#14532261C211yesmaximal, characteristic, complemented
16#14532180C211yesmaximal, characteristic, complemented
17#14532152C211yesmaximal, characteristic
18#14532111C211yesmaximal, characteristic, complemented
19#14532071C211yesmaximal, characteristic, complemented
20#14532045C211yesmaximal, characteristic, complemented
21#14532028C211yesmaximal, characteristic, complemented
22#14532028C211yesmaximal, characteristic, complemented
23C4×#10587564C211yesmaximal, characteristic, complemented
24C4×#10587615C211yesmaximal, characteristic, complemented
25C4×#10587616C211yesmaximal, characteristic, complemented
26C4×#10587568C211yesmaximal, characteristic, complemented
27C4×#10587639C211yesmaximal, characteristic, complemented
28#14531227C211yesmaximal, characteristic, complemented
29#14531223C211yesmaximal, characteristic, complemented
30#14531165C211yesmaximal, characteristic, complemented
31C2×C4×C22⋊C4×C17C211yesmaximal, characteristic, complemented
32C23×C22⋊D17C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34#11763343—28no—
35C2×#10587562C2211yescharacteristic, complemented
36C2×#10587562C2211yescharacteristic, complemented
37C2×#10587556C2211yescharacteristic, complemented
38C2×#10587561C2211yescharacteristic, complemented
39C2×#10587615C2211yescharacteristic
40C2×#10587615C2211yescharacteristic
41C2×#10587615C2211yescharacteristic, complemented
42C2×#10587610C2211yescharacteristic, complemented
43C2×#10587564C2211yescharacteristic
44C2×#10587616C2211yescharacteristic
45C2×#10587616C2211yescharacteristic
46C2×#10587568C2211yescharacteristic
47C2×#10587639C2211yescharacteristic
48C2×C4×Dic34C2211yescharacteristic, complemented
49C2×C4×D68C2211yescharacteristic, complemented
50C2×C4×D68C2211yescharacteristic, complemented
51C2×C4×C22⋊D17—28no—
52C2×C4×C22⋊D17C2211yescharacteristic
53C2×C4×C22⋊D17C2211yescharacteristic
54C2×C4×C22⋊D17C2211yescharacteristic
55C2×C4×C22⋊D17C2211yescharacteristic
56C2×C4×C22⋊D17C2211yescharacteristic
57C2×C4×C22⋊D17C2211yescharacteristic
58C2×C4×C22⋊D17C2211yescharacteristic
59C2×C4×C22⋊D17C2211yescharacteristic
60C2×C4×C22⋊D17C2211yescharacteristic
61C2×C4×C22⋊D17C2211yescharacteristic, complemented
62C2×C4×C22⋊D17C2211yescharacteristic, complemented
63C2×#10587558C2211yescharacteristic, complemented
64C2×#10587558C2211yescharacteristic, complemented
65C2×#10587558C2211yescharacteristic, complemented
66C22×#63225C2211yescharacteristic
67C22×C22⋊Dic17C2211yescharacteristic
68C22×#63227C2211yescharacteristic
69C22×C4×Dic17C2211yescharacteristic
70#11762751C2211yescharacteristic, complemented
71#11762750C2211yescharacteristic, complemented
72#11762750C2211yescharacteristic, complemented
73#11762745C2211yescharacteristic, complemented
74#11762743C2211yescharacteristic, complemented
75#11762743C2211yescharacteristic, complemented
76#11762743C2211yescharacteristic, complemented
77#11762738C2211yescharacteristic, complemented
78#11762738C2211yescharacteristic, complemented
79#11762738C2211yescharacteristic, complemented
80#11762738C2211yescharacteristic, complemented
81#11762737C2211yescharacteristic, complemented
82#11762737C2211yescharacteristic, complemented
83#11762736C2211yescharacteristic, complemented
84#11762733C2211yescharacteristic, complemented
85#11762733C2211yescharacteristic, complemented
86#11762732C2211yescharacteristic, complemented
87#11762732C2211yescharacteristic, complemented
88#11762727C2211yescharacteristic, complemented
89#11762727C2211yescharacteristic, complemented
90#11762725C2211yescharacteristic
91#11762725C2211yescharacteristic
92#11762724C2211yescharacteristic
93#11762724C2211yescharacteristic
94#11762724C2211yescharacteristic
95#11762724C2211yescharacteristic
96#11762724C2211yescharacteristic, complemented
97#11762724C2211yescharacteristic, complemented
98#11762722C2211yescharacteristic, complemented
99#11762721C2211yescharacteristic, complemented
100#11762718C2211yescharacteristic
101#11762718C2211yescharacteristic
102#11762713C2211yescharacteristic, complemented
103#11762711C2211yescharacteristic, complemented
104#11762707C2211yescharacteristic, complemented
105#11762706C2211yescharacteristic, complemented
106#11762700C2211yescharacteristic, complemented
107#11762700C2211yescharacteristic, complemented
108#11762700C2211yescharacteristic, complemented
109#11762700C2211yescharacteristic, complemented
110#11762700C2211yescharacteristic, complemented
111#11762700C2211yescharacteristic, complemented
112#11762698C2211yescharacteristic, complemented
113#11762698C2211yescharacteristic, complemented
114#11762696C2211yescharacteristic, complemented
115#11762693C2211yescharacteristic, complemented
116#11762693C2211yescharacteristic, complemented
117#11762693C2211yescharacteristic, complemented
118#11762693C2211yescharacteristic, complemented
119#11762692C2211yescharacteristic, complemented
120#11762691C2211yescharacteristic, complemented
121#11762691C2211yescharacteristic, complemented
122#11762688C2211yescharacteristic
123#11762688C2211yescharacteristic
124#11762688C2211yescharacteristic
125#11762688C2211yescharacteristic
126#11762688C2211yescharacteristic
127#11762688C2211yescharacteristic, complemented
128#11762688C2211yescharacteristic, complemented
129#11762688C2211yescharacteristic, complemented
130#11762687C2211yescharacteristic, complemented
131#11762687C2211yescharacteristic, complemented
132#11762686C2211yescharacteristic
133#11762686C2211yescharacteristic
134#11762686C2211yescharacteristic
135#11762684C2211yescharacteristic
136#11762684C2211yescharacteristic
137#11762683C2211yescharacteristic, complemented
138#11762683C2211yescharacteristic, complemented
139#11762682C2211yescharacteristic
140#11762682C2211yescharacteristic, complemented
141#11762682C2211yescharacteristic, complemented
142#11762682C2211yescharacteristic, complemented
143#11762682C2211yescharacteristic, complemented
144#11762682C2211yescharacteristic, complemented
145#11762681C2211yescharacteristic
146#11762681C2211yescharacteristic
147#11762681C2211yescharacteristic
148#11762672C2211yescharacteristic, complemented
149#11762671C2211yescharacteristic, complemented
150#11762671C2211yescharacteristic, complemented
151#11762669C2211yescharacteristic, complemented
152#11762668C2211yescharacteristic, complemented
153#11762668C2211yescharacteristic, complemented
154#11762667C2211yescharacteristic
155#11762667C2211yescharacteristic
156#11762667C2211yescharacteristic
157#11762665C2211yescharacteristic
158#11762664C2211yescharacteristic
159#11762664C2211yescharacteristic
160#11762664C2211yescharacteristic
161C4×#63225C2211yescharacteristic, complemented
162C4×#63225C2211yescharacteristic, complemented
163C4×#63225C2211yescharacteristic, complemented
164C4×C4⋊Dic17C2211yescharacteristic, complemented
165C4×#63227C2211yescharacteristic, complemented
166C4×#63227C2211yescharacteristic, complemented
167C4×#63227C2211yescharacteristic, complemented
168C4×#63227C2211yescharacteristic, complemented
169C4×#63227C2211yescharacteristic, complemented
170C4×C22⋊Dic17C2211yescharacteristic
171C4×C22⋊Dic17C2211yescharacteristic, complemented
172C4×C22⋊Dic17C2211yescharacteristic, complemented
173#11762655C2211yescharacteristic, complemented
174C24×C4×C17C2211yescharacteristic
175C22×C22⋊C4×C17C2211yescharacteristic
176C22×C22⋊C4×C17C2211yescharacteristic
177C22×C42×C17C2211yescharacteristic, complemented
178C22×C42×C17C2211yescharacteristic, complemented
179C4×C22⋊C4×C17C2211yescharacteristic
180C4×C22⋊C4×C17C2211yescharacteristic
181C4×C22⋊C4×C17C2211yescharacteristic
182C4×C22⋊C4×C17C2211yescharacteristic
183C4×C22⋊C4×C17C2211yescharacteristic, complemented
184C4×C22⋊C4×C17C2211yescharacteristic, complemented
185C4×C22⋊C4×C17C2211yescharacteristic, complemented
186C4×C22⋊C4×C17C2211yescharacteristic, complemented
187C2×C17×#95C2211yescharacteristic, complemented
188C2×C17×#95C2211yescharacteristic, complemented
189C25×C17C2311yescharacteristic
190C24×D17C2311yescharacteristic
191C23×C4×C17—24no—
192C23×C4×C17—24no—
193C23×C4×C17—42no—
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C23×C4×C17C2311yescharacteristic
197C23×C4×C17C2311yescharacteristic
198C23×C4×C17C2311yescharacteristic
199C23×C4×C17C2311yescharacteristic
200C23×C4×C17C2311yescharacteristic
201C23×C4×C17C2311yescharacteristic
202C23×C4×C17C2311yescharacteristic
203C23×C4×C17C2311yescharacteristic
204C22×C22⋊D17—24no—
205C22×C22⋊D17—24no—
206C22×C22⋊D17—24no—
207C22×C22⋊D17C2311yescharacteristic
208C22×C22⋊D17C2311yescharacteristic
209C22×C22⋊D17C2311yescharacteristic
210C22×C22⋊D17C2311yescharacteristic
211C22×C22⋊D17C2311yescharacteristic
212C22×C22⋊D17C2311yescharacteristic
213C22×C22⋊D17C2311yescharacteristic
214C23×Dic17C2311yescharacteristic
215C23×Dic17C2311yescharacteristic
216C23×Dic17C2311yescharacteristic
217C22×D68C2311yescharacteristic
218C22×D68C2311yescharacteristic
219C22×C4×D17—24no—
220C22×C4×D17—24no—
221C22×C4×D17—42no—
222C22×C4×D17C2311yescharacteristic
223C22×C4×D17C2311yescharacteristic
224C22×C4×D17C2311yescharacteristic
225C22×C4×D17C2311yescharacteristic
226C22×C4×D17C2311yescharacteristic
227C22×Dic34C2311yescharacteristic
228C2×C22⋊C4×C17—24no—
229C2×C22⋊C4×C17—24no—
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C42×C17—24no—
239C2×C42×C17—42no—
240C2×C42×C17C2311yescharacteristic
241C2×C42×C17C2311yescharacteristic
242C2×C42×C17C2311yescharacteristic
243C2×C42×C17C2311yescharacteristic
244C2×C42×C17C2311yescharacteristic
245C2×C42×C17C2311yescharacteristic
246C2×C42×C17C2311yescharacteristic
247C2×C42×C17C2311yescharacteristic
248#10587639—24no—
249C2×C22⋊Dic17—24no—
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262C2×C22⋊Dic17C2311yescharacteristic
263#10587616—24no—
264#10587616—24no—
265#10587615—24no—
266#10587615—24no—
267#10587615—24no—
268C4×C22⋊D17—24no—
269C4×C22⋊D17—24no—
270C4×C22⋊D17—24no—
271C4×C22⋊D17—24no—
272C4×C22⋊D17—24no—
273C4×C22⋊D17—24no—
274C4×C22⋊D17—24no—
275C4×C22⋊D17—24no—
276C4×C22⋊D17—24no—
277C4×C22⋊D17—42no—
278C4×C22⋊D17D418yescomplemented
279C2×#63227—24no—
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2311yescharacteristic
294C2×#63227C2311yescharacteristic
295C2×#63227C2311yescharacteristic
296C2×#63227C2311yescharacteristic
297C2×#63227C2311yescharacteristic
298C2×#63227C2311yescharacteristic
299C2×#63227C2311yescharacteristic
300C2×#63227C2311yescharacteristic
301C2×#63227C2311yescharacteristic
302C2×#63227C2311yescharacteristic
303C2×#63227C2311yescharacteristic
304C2×#63227C2311yescharacteristic
305C2×#63227C2311yescharacteristic
306C2×#63227C2311yescharacteristic
307C2×C4⋊Dic17C2311yescharacteristic
308C2×C4⋊Dic17C2311yescharacteristic
309C2×C4⋊Dic17C2311yescharacteristic
310C2×C4⋊Dic17C2311yescharacteristic
311C2×C4⋊Dic17C2311yescharacteristic
312#10587610—24no—
313C2×#63225—24no—
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×#63225C2311yescharacteristic
318C2×#63225C2311yescharacteristic
319C2×#63225C2311yescharacteristic
320C2×#63225C2311yescharacteristic
321C2×#63225C2311yescharacteristic
322C2×#63225C2311yescharacteristic
323C2×#63225C2311yescharacteristic
324C2×#63225C2311yescharacteristic
325C2×#63225C2311yescharacteristic
326C2×#63225C2311yescharacteristic
327C2×#63225C2311yescharacteristic
328C2×#63225C2311yescharacteristic
329C2×#63225C2311yescharacteristic
330C2×#63225C2311yescharacteristic
331C2×#63225C2311yescharacteristic
332C2×#63225C2311yescharacteristic
333C2×#63225C2311yescharacteristic
334C2×#63225C2311yescharacteristic
335C2×C4×Dic17—24no—
336C2×C4×Dic17C2311yescharacteristic
337C2×C4×Dic17C2311yescharacteristic
338C2×C4×Dic17C2311yescharacteristic
339C2×C4×Dic17C2311yescharacteristic
340C2×C4×Dic17C2311yescharacteristic
341C2×C4×Dic17C2311yescharacteristic
342C2×C4×Dic17C2311yescharacteristic
343#10587568—24no—
344#10587564—24no—
345#10587562—24no—
346#10587562—24no—
347#10587561—24no—
348C4×D68—24no—
349C4×D68—42no—
350#10587558—24no—
351#10587558—24no—
352#10587558—42no—
353#10587556—24no—
354C4×Dic34—24no—
355C17×#95C2311yescharacteristic
356C17×#95C2311yescharacteristic
357C17×#95C2311yescharacteristic
358C17×#95C2311yescharacteristic
359C17×#95C2311yescharacteristic
360C17×#95C2311yescharacteristic
361C17×#95C2311yescharacteristic
362C17×#95C2311yescharacteristic
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×C17—22no—
392C24×C17—22no—
393C24×C17—22no—
394C24×C17—22no—
395C24×C17—41no—
396C24×C17—41no—
397C24×C17#4114yes—
398C24×C17C2411yescharacteristic
399C24×C17C2411yescharacteristic
400C24×C17C2411yescharacteristic
401C23×D17—22no—
402C23×D17—22no—
403C23×D17—22no—
404C23×D17—22no—
405C23×D17—22no—
406C23×D17—41no—
407C23×D17—41no—
408C23×D17C2411yescharacteristic
409C23×D17C2411yescharacteristic
410C23×D17C2411yescharacteristic
411C22×C4×C17—22no—
412C22×C4×C17—22no—
413C22×C4×C17—22no—
414C22×C4×C17—22no—
415C22×C4×C17—22no—
416C22×C4×C17—22no—
417C22×C4×C17—22no—
418C22×C4×C17—22no—
419C22×C4×C17—22no—
420C22×C4×C17—22no—
421C22×C4×C17—22no—
422C22×C4×C17—22no—
423C22×C4×C17—22no—
424C22×C4×C17—22no—
425C22×C4×C17—22no—
426C22×C4×C17—22no—
427C22×C4×C17—22no—
428C22×C4×C17—22no—
429C22×C4×C17—22no—
430C22×C4×C17—22no—
431C22×C4×C17—22no—
432C22×C4×C17—41no—
433C22×C4×C17—41no—
434C22×C4×C17—41no—
435C22×C4×C17—41no—
436C22×C4×C17—41no—
437C22×C4×C17—41no—
438C22×C4×C17—41no—
439C22×C4×C17—416no—
440C22×C4×C17C2×D414yes—
441C22×C4×C17#4114yes—
442C22×C4×C17C2411yescharacteristic
443C22×C4×C17C2411yescharacteristic
444C22×C4×C17C2411yescharacteristic
445C22×C4×C17C2411yescharacteristic
446C22×C4×C17C2411yescharacteristic
447C22×C4×C17C2411yescharacteristic
448C22×C4×C17C2411yescharacteristic
449C22×C4×C17C2411yescharacteristic
450C22×C4×C17C2411yescharacteristic
451C22×C4×C17C2411yescharacteristic
452C22×C4×C17C2411yescharacteristic
453C22×C4×C17C2411yescharacteristic
454C2×C22⋊D17—232no—
455C2×C22⋊D17—22no—
456C2×C22⋊D17—22no—
457C2×C22⋊D17—22no—
458C2×C22⋊D17—22no—
459C2×C22⋊D17—22no—
460C2×C22⋊D17—22no—
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—41no—
473C2×C22⋊D17—41no—
474C2×C22⋊D17C2×D414yes—
475C2×C22⋊D17#4114yes—
476C22×Dic17—22no—
477C22×Dic17—22no—
478C22×Dic17—22no—
479C22×Dic17—22no—
480C22×Dic17—22no—
481C22×Dic17—22no—
482C22×Dic17—22no—
483C22×Dic17—41no—
484C22×Dic17—41no—
485C22×Dic17C2411yescharacteristic
486C22×Dic17C2411yescharacteristic
487C22×Dic17C2411yescharacteristic
488C22×Dic17C2411yescharacteristic
489C22×Dic17C2411yescharacteristic
490C22×Dic17C2411yescharacteristic
491C22×Dic17C2411yescharacteristic
492C22×Dic17C2411yescharacteristic
493C22×Dic17C2411yescharacteristic
494C22×Dic17C2411yescharacteristic
495C22×Dic17C2411yescharacteristic
496C22×Dic17C2411yescharacteristic
497C22×Dic17C2411yescharacteristic
498C2×D68—22no—
499C2×D68—22no—
500C2×D68—22no—
501C2×D68—22no—
502C2×D68—41no—
503C2×D68—41no—
504C2×C4×D17—22no—
505C2×C4×D17—22no—
506C2×C4×D17—22no—
507C2×C4×D17—22no—
508C2×C4×D17—22no—
509C2×C4×D17—22no—
510C2×C4×D17—22no—
511C2×C4×D17—22no—
512C2×C4×D17—22no—
513C2×C4×D17—22no—
514C2×C4×D17—22no—
515C2×C4×D17—22no—
516C2×C4×D17—416no—
517C2×C4×D17—41no—
518C2×C4×D17—41no—
519C2×C4×D17C2×D414yes—
520C2×Dic34—22no—
521C2×Dic34—22no—
522C2×Dic34—41no—
523C22⋊C4×C17—22no—
524C22⋊C4×C17—22no—
525C22⋊C4×C17—22no—
526C22⋊C4×C17—22no—
527C22⋊C4×C17—22no—
528C22⋊C4×C17—22no—
529C22⋊C4×C17—22no—
530C22⋊C4×C17#4114yes—
531C42×C17—22no—
532C42×C17—22no—
533C42×C17—22no—
534C42×C17—22no—
535C42×C17—22no—
536C42×C17—22no—
537C42×C17—41no—
538C42×C17—41no—
539C22⋊Dic17—22no—
540C22⋊Dic17—22no—
541C22⋊Dic17—22no—
542C22⋊Dic17—22no—
543C22⋊Dic17—22no—
544C22⋊Dic17—22no—
545C22⋊Dic17—22no—
546C22⋊Dic17—22no—
547C22⋊Dic17—22no—
548C22⋊Dic17—22no—
549C22⋊Dic17—41no—
550C22⋊Dic17—41no—
551C22⋊Dic17C2×D414yes—
552#63227—22no—
553#63227—22no—
554#63227—22no—
555#63227—22no—
556#63227—22no—
557#63227—22no—
558#63227—22no—
559#63227—22no—
560#63227—22no—
561#63227—22no—
562#63227—22no—
563#63227—22no—
564#63227—22no—
565#63227—22no—
566#63227—22no—
567#63227—22no—
568#63227—22no—
569#63227—41no—
570#63227—41no—
571#63227—41no—
572#63227—41no—
573#63227—41no—
574#63227—41no—
575#63227—41no—
576#63227—41no—
577#63227—41no—
578#63227C2×D414yes—
579C4⋊Dic17—22no—
580C4⋊Dic17—22no—
581C4⋊Dic17—22no—
582C4⋊Dic17—22no—
583C4⋊Dic17—41no—
584#63225—22no—
585#63225—22no—
586#63225—22no—
587#63225—22no—
588#63225—22no—
589#63225—22no—
590#63225—22no—
591#63225—22no—
592#63225—22no—
593#63225—22no—
594#63225—22no—
595#63225—22no—
596#63225—22no—
597#63225—22no—
598#63225—22no—
599#63225—41no—
600#63225—41no—
601#63225—41no—
602#63225—41no—
603#63225—41no—
604#63225C2×D414yes—
605C4×Dic17—22no—
606C4×Dic17—22no—
607C4×Dic17—22no—
608C4×Dic17—22no—
609C4×Dic17—22no—
610C4×Dic17—22no—
611C4×Dic17C2×D414yes—
612#34670—171nomaximal, Sylow
613C23×C17—21no—
614C23×C17—21no—
615C23×C17—21no—
616C23×C17—21no—
617C23×C17—21no—
618C23×C17—21no—
619C23×C17—21no—
620C23×C17—21no—
621C23×C17—28no—
622C23×C17—28no—
623C23×C17—21no—
624C23×C17—21no—
625C23×C17—21no—
626C23×C17—21no—
627C23×C17—21no—
628C23×C17—21no—
629C23×C17—44no—
630C23×C17—44no—
631C23×C17—44no—
632C23×C17—44no—
633C23×C17—44no—
634C23×C17C22×D412yes—
635C23×C17C2×#4112yes—
636C23×C17C2×#4112yes—
637C23×C17C2×#4112yes—
638C23×C17C2×#4112yes—
639C23×C17C2×#4112yes—
640C23×C17C2×#4112yes—
641C23×C17C2511yescharacteristic
642C22×D17—28no—
643C22×D17—21no—
644C22×D17—21no—
645C22×D17—21no—
646C22×D17—21no—
647C22×D17—21no—
648C22×D17—21no—
649C22×D17—21no—
650C22×D17—21no—
651C22×D17—21no—
652C22×D17—21no—
653C22×D17—21no—
654C22×D17—21no—
655C22×D17—21no—
656C22×D17—21no—
657C22×D17—21no—
658C22×D17—21no—
659C22×D17—21no—
660C22×D17—21no—
661C22×D17—21no—
662C22×D17—44no—
663C22×D17—44no—
664C22×D17—44no—
665C22×D17—44no—
666C22×D17—44no—
667C22×D17—44no—
668C22×D17C22×D412yes—
669C22×D17C2×#4112yes—
670C2×C4×C17—21no—
671C2×C4×C17—21no—
672C2×C4×C17—21no—
673C2×C4×C17—21no—
674C2×C4×C17—21no—
675C2×C4×C17—21no—
676C2×C4×C17—21no—
677C2×C4×C17—21no—
678C2×C4×C17—28no—
679C2×C4×C17—28no—
680C2×C4×C17—21no—
681C2×C4×C17—21no—
682C2×C4×C17—21no—
683C2×C4×C17—21no—
684C2×C4×C17—21no—
685C2×C4×C17—21no—
686C2×C4×C17—21no—
687C2×C4×C17—21no—
688C2×C4×C17—21no—
689C2×C4×C17—21no—
690C2×C4×C17—21no—
691C2×C4×C17—21no—
692C2×C4×C17—21no—
693C2×C4×C17—21no—
694C2×C4×C17—21no—
695C2×C4×C17—21no—
696C2×C4×C17—21no—
697C2×C4×C17—21no—
698C2×C4×C17—21no—
699C2×C4×C17—21no—
700C2×C4×C17—21no—
701C2×C4×C17—44no—
702C2×C4×C17—44no—
703C2×C4×C17—44no—
704C2×C4×C17—44no—
705C2×C4×C17—44no—
706C2×C4×C17—44no—
707C2×C4×C17—44no—
708C2×C4×C17—44no—
709C2×C4×C17C22×D412yes—
710C2×C4×C17C22×D412yes—
711C2×C4×C17C2×#4112yes—
712C2×C4×C17C2×#4112yes—
713C2×C4×C17C2×#4112yes—
714C2×C4×C17C2×#4112yes—
715C2×C4×C17H(5,𝔽2)12yes—
716C22⋊D17—28no—
717C22⋊D17—28no—
718C22⋊D17—28no—
719C22⋊D17—28no—
720C22⋊D17—44no—
721C22⋊D17—44no—
722C22⋊D17—44no—
723C2×Dic17—28no—
724C2×Dic17—21no—
725C2×Dic17—21no—
726C2×Dic17—21no—
727C2×Dic17—21no—
728C2×Dic17—21no—
729C2×Dic17—21no—
730C2×Dic17—21no—
731C2×Dic17—21no—
732C2×Dic17—21no—
733C2×Dic17—21no—
734C2×Dic17—21no—
735C2×Dic17—21no—
736C2×Dic17—21no—
737C2×Dic17—21no—
738C2×Dic17—21no—
739C2×Dic17—21no—
740C2×Dic17—21no—
741C2×Dic17—21no—
742C2×Dic17—21no—
743C2×Dic17—21no—
744C2×Dic17—21no—
745C2×Dic17—21no—
746C2×Dic17—21no—
747C2×Dic17—21no—
748C2×Dic17—21no—
749C2×Dic17—21no—
750C2×Dic17—21no—
751C2×Dic17—21no—
752C2×Dic17—21no—
753C2×Dic17—21no—
754C2×Dic17—21no—
755C2×Dic17—21no—
756C2×Dic17—21no—
757C2×Dic17—21no—
758C2×Dic17—21no—
759C2×Dic17—44no—
760C2×Dic17—44no—
761C2×Dic17C22×D412yes—
762C2×Dic17C22×D412yes—
763C2×Dic17C22×D412yes—
764C2×Dic17C2×#4112yes—
765D68—44no—
766D68—44no—
767C4×D17—28no—
768C4×D17—44no—
769C4×D17—44no—
770C4×D17—44no—
771C4×D17—44no—
772Dic34—44no—
773C2×#529—171no—
774C22×C4×D4—171no—
775#2481—171no—
776#2480—171no—
777#2473—171no—
778#2472—171no—
779#2467—171no—
780#2466—171no—
781#2460—171no—
782#2459—171no—
783#2450—171no—
784#2444—171no—
785#2437—171no—
786#2425—171no—
787#2419—171no—
788#2412—171no—
789#2410—171no—
790#2405—171no—
791#2398—171no—
792#2395—171no—
793#2392—171no—
794#2392—171no—
795C4×C22⋊Q8—171no—
796C4×#123—171no—
797C4×#121—171no—
798C4×#120—171no—
799C4×#120—171no—
800#2290—171no—
801#2290—171no—
802#2280—171no—
803C2×C4×C22⋊C4D1711yescharacteristic, complemented
804C22×C17—22no—
805C22×C17—22no—
806C22×C17—22no—
807C22×C17—22no—
808C22×C17—22no—
809C22×C17—22no—
810C22×C17—22no—
811C22×C17—22no—
812C22×C17—22no—
813C22×C17—22no—
814C22×C17—22no—
815C22×C17—22no—
816C22×C17—22no—
817C22×C17—22no—
818C22×C17—22no—
819C22×C17—416no—
820C22×C17—41no—
821C22×C17—41no—
822C22×C17—41no—
823C22×C17—41no—
824C22×C17#52514yes—
825C22×C17#52914yescomplemented
826C22×C17C23×D411yescharacteristic
827C22×C17C22×#4111yescharacteristic
828C22×C17C22×#4111yescharacteristic
829C22×C17C22×#4111yescharacteristic
830C22×C17C22×#4111yescharacteristic
831C22×C17C2×H(5,𝔽2)11yescharacteristic
832C22×C17#58511yescharacteristic
833C2×D17—22no—
834C2×D17—22no—
835C2×D17—22no—
836C2×D17—22no—
837C2×D17—22no—
838C2×D17—22no—
839C2×D17—416no—
840C2×D17—41no—
841C2×D17—41no—
842C2×D17—41no—
843C2×D17—41no—
844C2×D17—41no—
845C2×D17—41no—
846C2×D17—41no—
847C2×D17—41no—
848C2×D17—41no—
849C2×D17—41no—
850C2×D17—41no—
851C2×D17—41no—
852C2×D17—41no—
853C2×D17—41no—
854C2×D17—41no—
855C4×C17—22no—
856C4×C17—22no—
857C4×C17—22no—
858C4×C17—22no—
859C4×C17—41no—
860C4×C17—41no—
861C4×C17—41no—
862C4×C17—41no—
863C4×C17—41no—
864C4×C17—41no—
865C4×C17—41no—
866C4×C17#54614yes—
867Dic17—22no—
868Dic17—22no—
869Dic17—22no—
870Dic17—22no—
871Dic17—41no—
872Dic17—41no—
873Dic17—41no—
874Dic17—41no—
875Dic17—41no—
876Dic17—41no—
877Dic17—41no—
878Dic17—41no—
879Dic17—41no—
880C23×D4—171no—
881C24×C4—171no—
882C24×C4C2×D1711yescharacteristic
883#529—348no—
884C2×#126—171no—
885C2×#126—171no—
886C2×#125—171no—
887C2×#124—171no—
888C2×#123—171no—
889C2×#123—171no—
890C2×#123—171no—
891C2×C22⋊Q8—171no—
892C2×C22⋊Q8—171no—
893C2×#121—171no—
894C2×#121—171no—
895C2×#120—171no—
896C2×#120—171no—
897C2×C4×Q8—171no—
898C2×C4×D4—171no—
899C2×C4×D4—171no—
900C2×C4×D4—171no—
901C2×C4×D4—171no—
902C2×C4×D4—171no—
903C2×C4×D4—171no—
904C2×C4×D4—171no—
905C2×C4×D4—171no—
906C2×C4×D4—171no—
907C2×C4×D4—171no—
908C2×C4×D4—171no—
909C2×C4×D4—171no—
910C2×C4×D4—171no—
911C2×C4×D4—348no—
912C2×#117—171no—
913C2×#117—171no—
914C2×#117—171no—
915C22×C4⋊C4—171no—
916C22×C22⋊C4—171no—
917C22×C22⋊C4—171no—
918C22×C22⋊C4C2×D1711yescharacteristic
919C22×C22⋊C4C2×D1711yescharacteristic
920C22×C42—171no—
921C22×C42C2×D1711yescharacteristic, complemented
922C22×C42C2×D1711yescharacteristic, complemented
923#400—171no—
924#400—171no—
925#400—171no—
926#399—171no—
927#398—171no—
928#398—171no—
929#398—171no—
930#397—171no—
931#397—171no—
932#397—171no—
933#397—171no—
934#397—171no—
935#397—171no—
936#397—171no—
937#396—171no—
938#396—171no—
939#396—171no—
940#396—171no—
941#394—171no—
942#394—171no—
943#394—171no—
944#394—171no—
945#394—171no—
946#394—171no—
947#394—171no—
948#394—171no—
949#394—171no—
950#394—171no—
951#393—171no—
952#393—171no—
953#392—171no—
954#392—171no—
955#391—171no—
956#390—171no—
957#389—171no—
958#389—171no—
959#388—171no—
960#388—171no—
961#388—171no—
962#388—171no—
963#388—171no—
964#388—171no—
965#388—171no—
966#388—171no—
967#387—171no—
968#387—171no—
969#387—171no—
970#387—171no—
971#387—171no—
972#387—171no—
973#387—171no—
974#387—171no—
975#386—171no—
976#386—171no—
977#386—171no—
978#386—171no—
979#386—171no—
980#386—171no—
981#386—171no—
982#386—171no—
983#386—171no—
984#386—171no—
985#386—171no—
986#386—171no—
987#386—171no—
988#385—171no—
989#385—171no—
990#385—171no—
991#385—171no—
992#385—171no—
993#385—171no—
994#385—171no—
995#385—171no—
996#385—171no—
997#385—171no—
998#385—171no—
999#385—171no—
1000#385—171no—
1001#381—171no—
1002#381—171no—
1003#381—171no—
1004#380—171no—
1005#380—171no—
1006#380—171no—
1007#380—171no—
1008#380—171no—
1009#380—171no—
1010#379—171no—
1011#379—171no—
1012#379—171no—
1013#379—171no—
1014C4×C4⋊C4—171no—
1015C4×C4⋊C4—171no—
1016C4×C4⋊C4—171no—
1017C4×C4⋊C4—171no—
1018C4×C22⋊C4—171no—
1019C4×C22⋊C4—171no—
1020C4×C22⋊C4—171no—
1021C4×C22⋊C4—171no—
1022C4×C22⋊C4—171no—
1023C4×C22⋊C4—171no—
1024C4×C22⋊C4—171no—
1025C4×C22⋊C4—171no—
1026C4×C22⋊C4C2×D1711yescharacteristic
1027C4×C22⋊C4C2×D1711yescharacteristic
1028C4×C22⋊C4C2×D1711yescharacteristic
1029C4×C22⋊C4C2×D1711yescharacteristic
1030C4×C22⋊C4C2×D1711yescharacteristic, complemented
1031C4×C22⋊C4C2×D1711yescharacteristic, complemented
1032C4×C22⋊C4C2×D1711yescharacteristic, complemented
1033C4×C22⋊C4C2×D1711yescharacteristic, complemented
1034#376—171no—
1035C2×#95C2×D1711yescharacteristic, complemented
1036C2×#95C2×D1711yescharacteristic, complemented
1037C2×C17—24no—
1038C2×C17—24no—
1039C2×C17—42no—
1040C2×C17C2×#52511yescharacteristic
1041C2×C17C2×#52911yescharacteristic
1042C2×C17#345911yescharacteristic
1043C2×C17C2×#54611yescharacteristic
1044C2×C17D4×#4111yescharacteristic
1045C2×C17#347511yescharacteristic
1046C2×C17#348111yescharacteristic
1047D17—42no—
1048D17—42no—
1049D17—81no—
1050C25—171no—
1051C25C22×D1711yescharacteristic
1052C22×Q8—171no—
1053C22×D4—171no—
1054C22×D4—171no—
1055C22×D4—171no—
1056C22×D4—171no—
1057C22×D4—171no—
1058C22×D4—171no—
1059C22×D4—171no—
1060C22×D4—171no—
1061C22×D4—171no—
1062C22×D4—344no—
1063C22×D4—344no—
1064C22×D4—344no—
1065C23×C4—24no—
1066C23×C4—24no—
1067C23×C4—42no—
1068C23×C4—171no—
1069C23×C4—171no—
1070C23×C4—171no—
1071C23×C4—171no—
1072C23×C4—171no—
1073C23×C4—171no—
1074C23×C4—171no—
1075C23×C4—171no—
1076C23×C4—344no—
1077C23×C4—344no—
1078C23×C4—682no—
1079C23×C4C22×D1711yescharacteristic
1080C23×C4C22×D1711yescharacteristic
1081C23×C4C22×D1711yescharacteristic
1082C23×C4C22×D1711yescharacteristic
1083C23×C4C22×D1711yescharacteristic
1084C23×C4C22×D1711yescharacteristic
1085C23×C4C22×D1711yescharacteristic
1086C23×C4C22×D1711yescharacteristic
1087C23×C4C22×D1711yescharacteristic
1088C23×C4C22×D1711yescharacteristic
1089#126—344no—
1090#126—344no—
1091#125—344no—
1092#124—344no—
1093#123—344no—
1094#123—344no—
1095#123—344no—
1096C22⋊Q8—344no—
1097C22⋊Q8—344no—
1098#121—344no—
1099#121—344no—
1100#120—344no—
1101#120—344no—
1102C4×Q8—344no—
1103C4×D4—178no—
1104C4×D4—344no—
1105C4×D4—344no—
1106C4×D4—344no—
1107C4×D4—344no—
1108C4×D4—344no—
1109C4×D4—344no—
1110C4×D4—344no—
1111C4×D4—344no—
1112C4×D4—344no—
1113C4×D4—344no—
1114C4×D4—682no—
1115C4×D4—682no—
1116#117—344no—
1117#117—344no—
1118#117—682no—
1119C2×C4⋊C4—171no—
1120C2×C4⋊C4—171no—
1121C2×C4⋊C4—171no—
1122C2×C4⋊C4—171no—
1123C2×C4⋊C4—171no—
1124C2×C4⋊C4—171no—
1125C2×C4⋊C4—171no—
1126C2×C4⋊C4—171no—
1127C2×C4⋊C4—171no—
1128C2×C4⋊C4—171no—
1129C2×C4⋊C4—171no—
1130C2×C4⋊C4—171no—
1131C2×C4⋊C4—171no—
1132C2×C4⋊C4—171no—
1133C2×C4⋊C4—171no—
1134C2×C4⋊C4—171no—
1135C2×C4⋊C4—171no—
1136C2×C4⋊C4—171no—
1137C2×C4⋊C4—171no—
1138C2×C4⋊C4—171no—
1139C2×C4⋊C4—171no—
1140C2×C4⋊C4—171no—
1141C2×C4⋊C4—171no—
1142C2×C4⋊C4—171no—
1143C2×C4⋊C4—171no—
1144C2×C4⋊C4—171no—
1145C2×C4⋊C4—344no—
1146C2×C22⋊C4—24no—
1147C2×C22⋊C4—24no—
1148C2×C22⋊C4—171no—
1149C2×C22⋊C4—171no—
1150C2×C22⋊C4—171no—
1151C2×C22⋊C4—171no—
1152C2×C22⋊C4—171no—
1153C2×C22⋊C4—171no—
1154C2×C22⋊C4—171no—
1155C2×C22⋊C4—171no—
1156C2×C22⋊C4—171no—
1157C2×C22⋊C4—171no—
1158C2×C22⋊C4—171no—
1159C2×C22⋊C4—171no—
1160C2×C22⋊C4—171no—
1161C2×C22⋊C4—171no—
1162C2×C22⋊C4—171no—
1163C2×C22⋊C4—171no—
1164C2×C22⋊C4—171no—
1165C2×C22⋊C4—171no—
1166C2×C22⋊C4—171no—
1167C2×C22⋊C4—171no—
1168C2×C22⋊C4—171no—
1169C2×C22⋊C4—171no—
1170C2×C22⋊C4—171no—
1171C2×C22⋊C4—171no—
1172C2×C22⋊C4—171no—
1173C2×C22⋊C4—171no—
1174C2×C22⋊C4—171no—
1175C2×C22⋊C4—171no—
1176C2×C22⋊C4—171no—
1177C2×C22⋊C4—171no—
1178C2×C22⋊C4—171no—
1179C2×C22⋊C4—171no—
1180C2×C22⋊C4—171no—
1181C2×C22⋊C4—171no—
1182C2×C22⋊C4—171no—
1183C2×C22⋊C4—171no—
1184C2×C22⋊C4—171no—
1185C2×C22⋊C4—171no—
1186C2×C22⋊C4—171no—
1187C2×C22⋊C4—171no—
1188C2×C22⋊C4—344no—
1189C2×C22⋊C4—344no—
1190C2×C22⋊C4C22×D1711yescharacteristic
1191C2×C22⋊C4C22×D1711yescharacteristic
1192C2×C22⋊C4C22×D1711yescharacteristic
1193C2×C22⋊C4C22×D1711yescharacteristic
1194C2×C22⋊C4C22×D1711yescharacteristic
1195C2×C22⋊C4C22×D1711yescharacteristic
1196C2×C22⋊C4C22×D1711yescharacteristic
1197C2×C22⋊C4C22×D1711yescharacteristic
1198C2×C42—24no—
1199C2×C42—42no—
1200C2×C42—171no—
1201C2×C42—171no—
1202C2×C42—171no—
1203C2×C42—171no—
1204C2×C42—171no—
1205C2×C42—171no—
1206C2×C42—171no—
1207C2×C42—344no—
1208C2×C42C22×D1711yescharacteristic
1209C2×C42C22×D1711yescharacteristic
1210C2×C42C22×D1711yescharacteristic
1211C2×C42C22×D1711yescharacteristic
1212C2×C42C22×D1711yescharacteristic
1213C2×C42C22×D1711yescharacteristic
1214C2×C42C22×D1711yescharacteristic
1215C2×C42C22×D1711yescharacteristic
1216#95—171no—
1217#95—171no—
1218#95—171no—
1219#95—171no—
1220#95—171no—
1221#95—171no—
1222#95—171no—
1223#95—171no—
1224#95—171no—
1225#95—171no—
1226#95—171no—
1227#95—171no—
1228#95—171no—
1229#95—171no—
1230#95—171no—
1231#95—171no—
1232#95—171no—
1233#95—171no—
1234#95—171no—
1235#95—171no—
1236#95—171no—
1237#95—171no—
1238#95—171no—
1239#95—171no—
1240#95—171no—
1241#95—171no—
1242#95—171no—
1243#95—171no—
1244#95C22×D1711yescharacteristic
1245#95C22×D1711yescharacteristic
1246#95C22×D1711yescharacteristic
1247#95C22×D1711yescharacteristic
1248#95C22×D1711yescharacteristic
1249#95C22×D1711yescharacteristic
1250#95C22×D1711yescharacteristic
1251#95C22×D1711yescharacteristic
1252C17#3467011yescharacteristic, complemented, Sylow
1253C24—22no—
1254C24—22no—
1255C24—22no—
1256C24—22no—
1257C24—41no—
1258C24—41no—
1259C24—171no—
1260C24—171no—
1261C24—171no—
1262C24—342no—
1263C24—342no—
1264C24—342no—
1265C24—342no—
1266C24—342no—
1267C24—681no—
1268C24—681no—
1269C24#6325214yes—
1270C24C23×D1711yescharacteristic
1271C24C23×D1711yescharacteristic
1272C24C23×D1711yescharacteristic
1273C2×Q8—342no—
1274C2×Q8—342no—
1275C2×Q8—681no—
1276C2×D4—174no—
1277C2×D4—174no—
1278C2×D4—342no—
1279C2×D4—342no—
1280C2×D4—342no—
1281C2×D4—342no—
1282C2×D4—342no—
1283C2×D4—342no—
1284C2×D4—3432no—
1285C2×D4—342no—
1286C2×D4—342no—
1287C2×D4—342no—
1288C2×D4—342no—
1289C2×D4—342no—
1290C2×D4—342no—
1291C2×D4—342no—
1292C2×D4—342no—
1293C2×D4—342no—
1294C2×D4—342no—
1295C2×D4—342no—
1296C2×D4—342no—
1297C2×D4—342no—
1298C2×D4—342no—
1299C2×D4—342no—
1300C2×D4—681no—
1301C2×D4—681no—
1302C2×D4—681no—
1303C2×D4—681no—
1304C22×C4—22no—
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—22no—
1311C22×C4—22no—
1312C22×C4—22no—
1313C22×C4—22no—
1314C22×C4—22no—
1315C22×C4—22no—
1316C22×C4—22no—
1317C22×C4—22no—
1318C22×C4—22no—
1319C22×C4—22no—
1320C22×C4—22no—
1321C22×C4—22no—
1322C22×C4—22no—
1323C22×C4—22no—
1324C22×C4—22no—
1325C22×C4—41no—
1326C22×C4—41no—
1327C22×C4—41no—
1328C22×C4—41no—
1329C22×C4—41no—
1330C22×C4—41no—
1331C22×C4—41no—
1332C22×C4—416no—
1333C22×C4—171no—
1334C22×C4—171no—
1335C22×C4—171no—
1336C22×C4—171no—
1337C22×C4—174no—
1338C22×C4—171no—
1339C22×C4—171no—
1340C22×C4—171no—
1341C22×C4—171no—
1342C22×C4—171no—
1343C22×C4—171no—
1344C22×C4—171no—
1345C22×C4—171no—
1346C22×C4—171no—
1347C22×C4—342no—
1348C22×C4—342no—
1349C22×C4—342no—
1350C22×C4—342no—
1351C22×C4—342no—
1352C22×C4—342no—
1353C22×C4—342no—
1354C22×C4—342no—
1355C22×C4—342no—
1356C22×C4—342no—
1357C22×C4—342no—
1358C22×C4—342no—
1359C22×C4—342no—
1360C22×C4—342no—
1361C22×C4—342no—
1362C22×C4—342no—
1363C22×C4—342no—
1364C22×C4—342no—
1365C22×C4—342no—
1366C22×C4—681no—
1367C22×C4—681no—
1368C22×C4—6816no—
1369C22×C4—681no—
1370C22×C4—681no—
1371C22×C4#6325214yes—
1372C22×C4D4×D1714yes—
1373C22×C4C23×D1711yescharacteristic
1374C22×C4C23×D1711yescharacteristic
1375C22×C4C23×D1711yescharacteristic
1376C22×C4C23×D1711yescharacteristic
1377C22×C4C23×D1711yescharacteristic
1378C22×C4C23×D1711yescharacteristic
1379C22×C4C23×D1711yescharacteristic
1380C22×C4C23×D1711yescharacteristic
1381C22×C4C23×D1711yescharacteristic
1382C22×C4C23×D1711yescharacteristic
1383C22×C4C23×D1711yescharacteristic
1384C22×C4C23×D1711yescharacteristic
1385C4⋊C4—174no—
1386C4⋊C4—342no—
1387C4⋊C4—342no—
1388C4⋊C4—342no—
1389C4⋊C4—342no—
1390C4⋊C4—342no—
1391C4⋊C4—342no—
1392C4⋊C4—342no—
1393C4⋊C4—342no—
1394C4⋊C4—342no—
1395C4⋊C4—342no—
1396C4⋊C4—342no—
1397C4⋊C4—342no—
1398C4⋊C4—342no—
1399C4⋊C4—342no—
1400C4⋊C4—342no—
1401C4⋊C4—342no—
1402C4⋊C4—342no—
1403C4⋊C4—342no—
1404C4⋊C4—342no—
1405C4⋊C4—681no—
1406C4⋊C4—681no—
1407C4⋊C4—681no—
1408C4⋊C4—681no—
1409C4⋊C4—681no—
1410C4⋊C4—681no—
1411C22⋊C4—22no—
1412C22⋊C4—22no—
1413C22⋊C4—22no—
1414C22⋊C4—22no—
1415C22⋊C4—22no—
1416C22⋊C4—22no—
1417C22⋊C4—22no—
1418C22⋊C4—174no—
1419C22⋊C4—174no—
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—342no—
1429C22⋊C4—342no—
1430C22⋊C4—342no—
1431C22⋊C4—342no—
1432C22⋊C4—342no—
1433C22⋊C4—342no—
1434C22⋊C4—342no—
1435C22⋊C4—342no—
1436C22⋊C4—342no—
1437C22⋊C4—342no—
1438C22⋊C4—342no—
1439C22⋊C4—342no—
1440C22⋊C4—342no—
1441C22⋊C4—342no—
1442C22⋊C4—342no—
1443C22⋊C4—342no—
1444C22⋊C4—342no—
1445C22⋊C4—342no—
1446C22⋊C4—342no—
1447C22⋊C4—681no—
1448C22⋊C4—681no—
1449C22⋊C4—681no—
1450C22⋊C4—681no—
1451C22⋊C4—681no—
1452C22⋊C4—681no—
1453C22⋊C4—681no—
1454C22⋊C4—681no—
1455C22⋊C4—681no—
1456C22⋊C4—681no—
1457C22⋊C4—681no—
1458C22⋊C4#6325214yes—
1459C42—22no—
1460C42—22no—
1461C42—22no—
1462C42—22no—
1463C42—22no—
1464C42—22no—
1465C42—41no—
1466C42—41no—
1467C42—174no—
1468C42—342no—
1469C42—342no—
1470C42—342no—
1471C42—342no—
1472C42—342no—
1473C42—342no—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—28no—
1483C23—28no—
1484C23—21no—
1485C23—21no—
1486C23—21no—
1487C23—21no—
1488C23—21no—
1489C23—21no—
1490C23—44no—
1491C23—44no—
1492C23—44no—
1493C23—44no—
1494C23—44no—
1495C23—172no—
1496C23—172no—
1497C23—348no—
1498C23—341no—
1499C23—341no—
1500C23—341no—
1501C23—341no—
1502C23—341no—
1503C23—341no—
1504C23—341no—
1505C23—341no—
1506C23—341no—
1507C23—341no—
1508C23—341no—
1509C23—341no—
1510C23—341no—
1511C23—341no—
1512C23—341no—
1513C23—341no—
1514C23—341no—
1515C23—341no—
1516C23—341no—
1517C23—684no—
1518C23—684no—
1519C23—684no—
1520C23—684no—
1521C23—684no—
1522C23—684no—
1523C23C2×#6325212yes—
1524C23C2×#6325212yes—
1525C23C2×#6325212yes—
1526C23C2×#6325212yes—
1527C23C2×#6325212yes—
1528C23C2×D4×D1712yes—
1529C23#41×D1712yes—
1530C23C24×D1711yescharacteristic
1531Q8—684no—
1532D4—348no—
1533D4—348no—
1534D4—348no—
1535D4—348no—
1536D4—684no—
1537D4—684no—
1538D4—684no—
1539D4—684no—
1540D4—684no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—28no—
1550C2×C4—28no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—21no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—44no—
1573C2×C4—44no—
1574C2×C4—44no—
1575C2×C4—44no—
1576C2×C4—44no—
1577C2×C4—44no—
1578C2×C4—44no—
1579C2×C4—44no—
1580C2×C4—172no—
1581C2×C4—172no—
1582C2×C4—172no—
1583C2×C4—172no—
1584C2×C4—348no—
1585C2×C4—341no—
1586C2×C4—341no—
1587C2×C4—341no—
1588C2×C4—341no—
1589C2×C4—341no—
1590C2×C4—341no—
1591C2×C4—341no—
1592C2×C4—341no—
1593C2×C4—348no—
1594C2×C4—341no—
1595C2×C4—341no—
1596C2×C4—341no—
1597C2×C4—341no—
1598C2×C4—341no—
1599C2×C4—341no—
1600C2×C4—341no—
1601C2×C4—341no—
1602C2×C4—341no—
1603C2×C4—341no—
1604C2×C4—341no—
1605C2×C4—341no—
1606C2×C4—341no—
1607C2×C4—341no—
1608C2×C4—341no—
1609C2×C4—341no—
1610C2×C4—341no—
1611C2×C4—341no—
1612C2×C4—341no—
1613C2×C4—341no—
1614C2×C4—341no—
1615C2×C4—341no—
1616C2×C4—341no—
1617C2×C4—341no—
1618C2×C4—341no—
1619C2×C4—341no—
1620C2×C4—341no—
1621C2×C4—684no—
1622C2×C4—684no—
1623C2×C4—684no—
1624C2×C4—684no—
1625C2×C4—684no—
1626C2×C4—684no—
1627C2×C4C2×#6325212yes—
1628C2×C4C2×#6325212yes—
1629C2×C4C2×#6325212yes—
1630C2×C4C2×#6325212yes—
1631C2×C4C2×D4×D1712yes—
1632C2×C4C2×D4×D1712yes—
1633C2×C4#1058769112yes—
1634C22—22no—
1635C22—22no—
1636C22—22no—
1637C22—22no—
1638C22—22no—
1639C22—22no—
1640C22—22no—
1641C22—22no—
1642C22—22no—
1643C22—22no—
1644C22—22no—
1645C22—22no—
1646C22—22no—
1647C22—22no—
1648C22—22no—
1649C22—416no—
1650C22—41no—
1651C22—41no—
1652C22—41no—
1653C22—41no—
1654C22—342no—
1655C22—342no—
1656C22—342no—
1657C22—342no—
1658C22—342no—
1659C22—342no—
1660C22—6816no—
1661C22—681no—
1662C22—681no—
1663C22—681no—
1664C22—681no—
1665C22—681no—
1666C22—681no—
1667C22—681no—
1668C22—681no—
1669C22—681no—
1670C22—681no—
1671C22—681no—
1672C22—681no—
1673C22—681no—
1674C22—681no—
1675C22—681no—
1676C22#1176331814yes—
1677C22#1176334314yescomplemented
1678C22C22×D4×D1711yescharacteristic
1679C22C2×#41×D1711yescharacteristic
1680C22C22×#6325211yescharacteristic
1681C22C22×#6325211yescharacteristic
1682C22C22×#6325211yescharacteristic
1683C22C2×#1058769111yescharacteristic
1684C22#1176364511yescharacteristic
1685C4—22no—
1686C4—22no—
1687C4—22no—
1688C4—22no—
1689C4—41no—
1690C4—41no—
1691C4—41no—
1692C4—41no—
1693C4—41no—
1694C4—41no—
1695C4—41no—
1696C4—342no—
1697C4—342no—
1698C4—342no—
1699C4—342no—
1700C4—681no—
1701C4—681no—
1702C4—681no—
1703C4—681no—
1704C4—681no—
1705C4—681no—
1706C4—681no—
1707C4—681no—
1708C4—681no—
1709C4#1176344914yes—
1710C2—24no—
1711C2—24no—
1712C2—42no—
1713C2—682no—
1714C2—682no—
1715C2—1361no—
1716C2C2×#1176331811yescharacteristic
1717C2C2×#1176334311yescharacteristic
1718C2#1454219311yescharacteristic
1719C2C2×#1176344911yescharacteristic
1720C2D4×#6325211yescharacteristic
1721C2#1454233811yescharacteristic
1722C2#1454238811yescharacteristic
subgroupG/H
centerC22×C4C23×D17
commutator, socle, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C4×C22⋊C4×C17C2
prime radical#14532152C2
hypercenterC2×C4×C22⋊C4D17
hypocenterC17#34670
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11763343C2semidirect
2. C22×C4×C22⋊D17C2semidirect
3. #14533045C2semidirect
4. #14533030C2semidirect
5. #14532925C2semidirect
6. #14532910C2semidirect
7. #14532835C2semidirect
8. #14532820C2semidirect
9. #14532736C2semidirect
10. #14532721C2semidirect
11. #14532608C2semidirect
12. #14532534C2semidirect
13. #14532445C2semidirect
14. #14532335C2semidirect
15. #14532261C2semidirect
16. #14532180C2semidirect
18. #14532111C2semidirect
19. #14532071C2semidirect
20. #14532045C2semidirect
21. #14532028C2semidirect
22. #14532028C2semidirect
23. C4×#10587564C2semidirect
24. C4×#10587615C2semidirect
25. C4×#10587616C2semidirect
26. C4×#10587568C2semidirect
27. C4×#10587639C2semidirect
28. #14531227C2semidirect
29. #14531223C2semidirect
30. #14531165C2semidirect
31. C2×C4×C22⋊C4×C17C2semidirect
35. C2×#10587562C22semidirect
36. C2×#10587562C22semidirect
37. C2×#10587556C22semidirect
38. C2×#10587561C22semidirect
41. C2×#10587615C22semidirect
42. C2×#10587610C22semidirect
48. C2×C4×Dic34C22semidirect
49. C2×C4×D68C22semidirect
50. C2×C4×D68C22semidirect
61. C2×C4×C22⋊D17C22semidirect
62. C2×C4×C22⋊D17C22semidirect
63. C2×#10587558C22semidirect
64. C2×#10587558C22semidirect
65. C2×#10587558C22semidirect
70. #11762751C22semidirect
71. #11762750C22semidirect
72. #11762750C22semidirect
73. #11762745C22semidirect
74. #11762743C22semidirect
75. #11762743C22semidirect
76. #11762743C22semidirect
77. #11762738C22semidirect
78. #11762738C22semidirect
79. #11762738C22semidirect
80. #11762738C22semidirect
81. #11762737C22semidirect
82. #11762737C22semidirect
83. #11762736C22semidirect
84. #11762733C22semidirect
85. #11762733C22semidirect
86. #11762732C22semidirect
87. #11762732C22semidirect
88. #11762727C22semidirect
89. #11762727C22semidirect
96. #11762724C22semidirect
97. #11762724C22semidirect
98. #11762722C22semidirect
99. #11762721C22semidirect
102. #11762713C22semidirect
103. #11762711C22semidirect
104. #11762707C22semidirect
105. #11762706C22semidirect
106. #11762700C22semidirect
107. #11762700C22semidirect
108. #11762700C22semidirect
109. #11762700C22semidirect
110. #11762700C22semidirect
111. #11762700C22semidirect
112. #11762698C22semidirect
113. #11762698C22semidirect
114. #11762696C22semidirect
115. #11762693C22semidirect
116. #11762693C22semidirect
117. #11762693C22semidirect
118. #11762693C22semidirect
119. #11762692C22semidirect
120. #11762691C22semidirect
121. #11762691C22semidirect
127. #11762688C22semidirect
128. #11762688C22semidirect
129. #11762688C22semidirect
130. #11762687C22semidirect
131. #11762687C22semidirect
137. #11762683C22semidirect
138. #11762683C22semidirect
140. #11762682C22semidirect
141. #11762682C22semidirect
142. #11762682C22semidirect
143. #11762682C22semidirect
144. #11762682C22semidirect
148. #11762672C22semidirect
149. #11762671C22semidirect
150. #11762671C22semidirect
151. #11762669C22semidirect
152. #11762668C22semidirect
153. #11762668C22semidirect
161. C4×#63225C22semidirect
162. C4×#63225C22semidirect
163. C4×#63225C22semidirect
164. C4×C4⋊Dic17C22semidirect
165. C4×#63227C22semidirect
166. C4×#63227C22semidirect
167. C4×#63227C22semidirect
168. C4×#63227C22semidirect
169. C4×#63227C22semidirect
171. C4×C22⋊Dic17C22semidirect
172. C4×C22⋊Dic17C22semidirect
173. #11762655C22semidirect
177. C22×C42×C17C22semidirect
178. C22×C42×C17C22semidirect
183. C4×C22⋊C4×C17C22semidirect
184. C4×C22⋊C4×C17C22semidirect
185. C4×C22⋊C4×C17C22semidirect
186. C4×C22⋊C4×C17C22semidirect
187. C2×C17×#95C22semidirect
188. C2×C17×#95C22semidirect
278. C4×C22⋊D17D4semidirect
803. C2×C4×C22⋊C4D17semidirect
825. C22×C17#529semidirect
921. C22×C42C2×D17semidirect
922. C22×C42C2×D17semidirect
1030. C4×C22⋊C4C2×D17semidirect
1031. C4×C22⋊C4C2×D17semidirect
1032. C4×C22⋊C4C2×D17semidirect
1033. C4×C22⋊C4C2×D17semidirect
1035. C2×#95C2×D17semidirect
1036. C2×#95C2×D17semidirect
1252. C17#34670semidirect
1677. C22#11763343semidirect

Maximal subgroups

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

subgroupindex
C2×#117633432
C22×C4×C22⋊D172
#145330452
#145330302
#145329252
#145329102
#145328352
#145328202
#145327362
#145327212
#145326082
#145325342
#145324452
#145323352
#145322612
#145321802
#145321522
#145321112
#145320712
#145320452
#145320282
C4×#105875642
C4×#105876152
C4×#105876162
C4×#105875682
C4×#105876392
#145312272
#145312232
#145311652
C2×C4×C22⋊C4×C172
#3467017