Finite Group Databasebeta

← #28350771

Subgroups — #28350771

Order 13696.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293375C212yesmaximal, complemented
2#20293368C212yesmaximal, complemented
3#20293340C211yesmaximal, characteristic, complemented
4#20293330C211yesmaximal, characteristic, complemented
5#20293301C212yesmaximal, complemented
6#20293299C211yesmaximal, characteristic, complemented
7#20293278C211yesmaximal, characteristic, complemented
8#20293269C212yesmaximal, complemented
9#20293268C211yesmaximal, characteristic, complemented
10#20293268C211yesmaximal, characteristic, complemented
11D4×D428C211yesmaximal, characteristic, complemented
12#20293249C211yesmaximal, characteristic, complemented
13#20293233C211yesmaximal, characteristic, complemented
14#20293233C212yesmaximal, complemented
15#20293216C212yesmaximal, complemented
16#20293207C211yesmaximal, characteristic, complemented
17#20293196C212yesmaximal, complemented
18#20293196C211yesmaximal, characteristic, complemented
19#20293188C212yesmaximal, complemented
20#20293140C211yesmaximal, characteristic, complemented
21#20293136C211yesmaximal, characteristic, complemented
22C2×#16812084C211yesmaximal, characteristic, complemented
23#552×C107C211yesmaximal, characteristic, complemented
24C2×#13133819C2211yescharacteristic, complemented
25C2×#13133819C2211yescharacteristic, complemented
26C2×#13133818C2211yescharacteristic, complemented
27C2×#13133818C2212yescomplemented
28C22×D428C2211yescharacteristic
29C22×D428C2212yescomplemented
30C22×D428C2211yescharacteristic, complemented
31C2×D4×D107C2212yes—
32C22×C4×D107C2211yescharacteristic, complemented
33#16812108C2211yescharacteristic, complemented
34#16812106C2212yescomplemented
35#16812106C2212yescomplemented
36#16812106C2211yescharacteristic, complemented
37#16812104C2212yescomplemented
38#16812103C2212yescomplemented
39#16812098C2211yescharacteristic, complemented
40#16812097C2212yescomplemented
41#16812097C2212yescomplemented
42#16812097C2212yescomplemented
43#16812095C2212yescomplemented
44#16812094C2211yescharacteristic, complemented
45#16812094C2212yescomplemented
46#16812094C2212yescomplemented
47#16812094C2212yescomplemented
48#16812094C2212yescomplemented
49#16812094C2212yescomplemented
50#16812094C2212yescomplemented
51#16812094C2212yescomplemented
52#16812094C2212yescomplemented
53#16812092C2212yescomplemented
54#16812091C2211yescharacteristic, complemented
55#16812087C2211yescharacteristic, complemented
56#16812087C2212yescomplemented
57#16812087C2212yescomplemented
58#16812087C2212yescomplemented
59#16812086C2211yescharacteristic, complemented
60#16812085C2211yescharacteristic, complemented
61#16812084C2211yescharacteristic
62#16812084C2211yescharacteristic
63#16812084C2211yescharacteristic, complemented
64#16812084C2212yescomplemented
65#16812084C2211yescharacteristic, complemented
66#16812084C2212yescomplemented
67#16812084C2211yescharacteristic, complemented
68#16812084C2212yescomplemented
69#16812084C2212yescomplemented
70#16812084C2212yescomplemented
71#16812084C2212yescomplemented
72#16812084C2211yescharacteristic, complemented
73#16812084C2212yescomplemented
74#16812084C2211yescharacteristic, complemented
75#16812084C2212yescomplemented
76#16812084C2212yescomplemented
77#16812084C2212yescomplemented
78#16812084C2212yescomplemented
79#16812083C2211yescharacteristic
80#16812083C2211yescharacteristic, complemented
81#16812082C2211yescharacteristic, complemented
82#16812082C2212yescomplemented
83#16812082C2212yescomplemented
84#16812082C2212yescomplemented
85#16812081C2211yescharacteristic
86#16812079C2212yes—
87#16812079C2211yescharacteristic, complemented
88#16812079C2212yescomplemented
89#16812079C2212yescomplemented
90#16812079C2212yescomplemented
91#16812079C2212yescomplemented
92#16812079C2212yescomplemented
93#16812079C2212yescomplemented
94#16812077C2211yescharacteristic
95C4×D428C2211yescharacteristic, complemented
96C4×D428C2212yescomplemented
97C4×D428C2211yescharacteristic, complemented
98#16812071C2212yescomplemented
99#16812071C2211yescharacteristic, complemented
100#16812071C2211yescharacteristic, complemented
101#16812071C2212yescomplemented
102C4×C22⋊D107C2211yescharacteristic, complemented
103C4×C22⋊D107C2211yescharacteristic, complemented
104(C22⋊D107)⋊C4C2212yescomplemented
105#16812067C2211yescharacteristic, complemented
106#16812066C2211yescharacteristic, complemented
107#16812066C2212yescomplemented
108C4⋊C4×D107C2211yescharacteristic, complemented
109C2×(C2×D107)⋊C4C2212yescomplemented
110C22⋊C4×D107C2212yescomplemented
111C22⋊C4×D107C2212yescomplemented
112#126×C107C2212yescomplemented
113#125×C107C2211yescharacteristic, complemented
114#125×C107C2212yescomplemented
115#123×C107C2212yes—
116C22⋊Q8×C107C2211yescharacteristic, complemented
117C22⋊Q8×C107C2211yescharacteristic, complemented
118C4×Q8×C107C2211yescharacteristic, complemented
119C4×D4×C107C2211yescharacteristic
120#117×C107C2212yescomplemented
121#117×C107C2211yescharacteristic, complemented
122C2×C4⋊C4×C107C2211yescharacteristic, complemented
123C23×D107C2312yes—
124C23×D107C2311yescharacteristic
125C23×D107C2312yes—
126#13133819—42no—
127#13133819—42no—
128#13133818—42no—
129#13133818—44no—
130C2×Dic214C2311yescharacteristic
131C2×Dic214C2312yes—
132C2×D428—42no—
133C2×D428—42no—
134C2×D428—44no—
135C2×D428C2311yescharacteristic
136C2×D428C2311yescharacteristic
137C2×D428C2311yescharacteristic
138C2×D428C2312yes—
139C2×D428C2312yes—
140C2×D428C2312yes—
141C2×D428C2311yescharacteristic
142C2×D428C2312yes—
143C2×D428C2312yes—
144C2×D428C2312yes—
145C2×D428C2312yes—
146C2×D428C2312yes—
147C2×D428C2312yes—
148C2×D428C2311yescharacteristic
149C2×D428C2312yes—
150C2×D428C2312yes—
151C2×D428C2312yes—
152C2×D428C2312yes—
153C2×C22⋊D107C2312yes—
154C2×C22⋊D107C2311yescharacteristic
155C2×C22⋊D107C2311yescharacteristic
156C2×C22⋊D107C2311yescharacteristic
157C2×C22⋊D107C2311yescharacteristic
158C2×C22⋊D107C2312yes—
159D4×D107—44no—
160C22×Dic107C2311yescharacteristic
161C2×C4×D107—42no—
162C2×C4×D107C2311yescharacteristic
163C2×C4×D107C2311yescharacteristic
164C2×C4×D107C2311yescharacteristic
165C2×C4×D107C2312yes—
166C2×C4×D107C2312yes—
167C2×C4×D107C2312yes—
168C2×C4×D107C2312yes—
169C2×C4×D107C2312yes—
170C2×C4×D107C2311yescharacteristic
171C2×C4×D107C2312yes—
172C2×C4×D107C2311yescharacteristic
173C4⋊Dic107C2311yescharacteristic
174C4⋊Dic107C2311yescharacteristic
175Dic107⋊C4C2312yes—
176Dic107⋊C4C2311yescharacteristic
177Dic107⋊C4C2311yescharacteristic
178Dic107⋊C4C2311yescharacteristic
179Dic107⋊C4C2312yes—
180Dic107⋊C4C2312yes—
181Dic107⋊C4C2311yescharacteristic
182C22⋊Dic107C2311yescharacteristic
183C22⋊Dic107C2311yescharacteristic
184(C2×D107)⋊C4C2312yes—
185(C2×D107)⋊C4C2312yes—
186(C2×D107)⋊C4C2312yes—
187(C2×D107)⋊C4C2312yes—
188(C2×D107)⋊C4C2312yes—
189(C2×D107)⋊C4C2312yes—
190(C2×D107)⋊C4C2312yes—
191(C2×D107)⋊C4C2311yescharacteristic
192(C2×D107)⋊C4C2312yes—
193(C2×D107)⋊C4C2311yescharacteristic
194(C2×D107)⋊C4C2312yes—
195(C2×D107)⋊C4C2312yes—
196(C2×D107)⋊C4C2311yescharacteristic
197(C2×D107)⋊C4C2311yescharacteristic
198(C2×D107)⋊C4C2311yescharacteristic
199(C2×D107)⋊C4C2312yes—
200(C2×D107)⋊C4C2312yes—
201(C2×D107)⋊C4C2312yes—
202(C2×D107)⋊C4C2312yes—
203(C2×D107)⋊C4C2311yescharacteristic
204(C2×D107)⋊C4C2312yes—
205(C2×D107)⋊C4C2312yes—
206C4×Dic107C2312yes—
207C4×Dic107C2311yescharacteristic
208C2×Q8×C107C2311yescharacteristic
209C2×D4×C107C2311yescharacteristic
210C22×C4×C107C2312yes—
211C22×C4×C107C2311yescharacteristic
212C22×C4×C107C2311yescharacteristic
213C4⋊C4×C107C2311yescharacteristic
214C4⋊C4×C107C2311yescharacteristic
215C4⋊C4×C107C2312yes—
216C4⋊C4×C107C2312yes—
217C4⋊C4×C107C2311yescharacteristic
218C4⋊C4×C107C2312yes—
219C4⋊C4×C107C2312yes—
220C4⋊C4×C107C2311yescharacteristic
221C4⋊C4×C107C2312yes—
222C4⋊C4×C107C2312yes—
223C22⋊C4×C107C2312yes—
224C22⋊C4×C107C2312yes—
225C22⋊C4×C107C2311yescharacteristic
226C22⋊C4×C107C2311yescharacteristic
227C22⋊C4×C107C2312yes—
228C42×C107C2311yescharacteristic
229C42×C107C2312yes—
230C42×C107C2312yes—
231C23×C107C2411yescharacteristic
232C23×C107C2411yescharacteristic
233C22×D107—22no—
234C22×D107—24no—
235C22×D107—41no—
236C22×D107—41no—
237C22×D107—42no—
238C22×D107—42no—
239C22×D107—42no—
240C22×D107—42no—
241C22×D107—42no—
242C22×D107C2412yes—
243C22×D107C2411yescharacteristic
244C22×D107C2411yescharacteristic
245C22×D107C2412yes—
246C22×D107C2412yes—
247C22×D107C2411yescharacteristic
248Q8×C107—22no—
249D4×C107—22no—
250C2×C4×C107—24no—
251C2×C4×C107—22no—
252C2×C4×C107—22no—
253C2×C4×C107C2411yescharacteristic
254C2×C4×C107C2411yescharacteristic
255C2×C4×C107C2412yes—
256C2×C4×C107C2412yes—
257C2×C4×C107C2412yes—
258C2×C4×C107C2411yescharacteristic
259C2×C4×C107C2412yes—
260C2×C4×C107C2411yescharacteristic
261C2×C4×C107C2411yescharacteristic
262C22⋊D107—24no—
263C22⋊D107—22no—
264C22⋊D107—42no—
265C22⋊D107—41no—
266C22⋊D107—41no—
267C22⋊D107—41no—
268C2×Dic107—41no—
269C2×Dic107C2411yescharacteristic
270C2×Dic107C2411yescharacteristic
271C2×Dic107C2411yescharacteristic
272C2×Dic107C2412yes—
273C2×Dic107C2411yescharacteristic
274C2×Dic107C2411yescharacteristic
275D428—22no—
276D428—22no—
277D428—22no—
278D428—42no—
279D428—42no—
280D428—42no—
281D428—42no—
282D428—42no—
283D428—42no—
284D428—42no—
285D428—42no—
286D428—42no—
287D428—42no—
288D428—41no—
289D428—41no—
290D428—42no—
291D428—42no—
292D428—42no—
293C4×D107—22no—
294C4×D107—22no—
295C4×D107—22no—
296C4×D107—41no—
297C4×D107—41no—
298C4×D107—42no—
299C4×D107—42no—
300C4×D107—42no—
301C4×D107—42no—
302C4×D107—42no—
303C4×D107—42no—
304Dic214—42no—
305Dic214—41no—
306C22×C107—21no—
307C22×C107—21no—
308C22×C107—21no—
309C22×C107—21no—
310C22×C107—21no—
311C22×C107H(5,𝔽2)12yes—
312C22×C107C2511yescharacteristic
313C2×D107—21no—
314C2×D107—21no—
315C2×D107—21no—
316C2×D107—21no—
317C2×D107—22no—
318C2×D107—22no—
319C2×D107—22no—
320C2×D107—22no—
321C2×D107—22no—
322C2×D107—21no—
323C2×D107—21no—
324C2×D107—22no—
325C2×D107—22no—
326C2×D107—21no—
327C2×D107—21no—
328C2×D107—22no—
329C2×D107—21no—
330C2×D107—22no—
331C2×D107—44no—
332C2×D107—84no—
333C2×D107—84no—
334C4×C107—22no—
335C4×C107—21no—
336C4×C107—22no—
337C4×C107—21no—
338C4×C107—21no—
339C4×C107—22no—
340C4×C107—22no—
341C4×C107—21no—
342C4×C107H(5,𝔽2)12yes—
343Dic107—21no—
344Dic107—21no—
345Dic107—21no—
346Dic107—22no—
347Dic107—21no—
348Dic107—21no—
349C2×C107—22no—
350C2×C107—41no—
351C2×C107C2×H(5,𝔽2)11yescharacteristic
352C2×C107C2×H(5,𝔽2)11yescharacteristic
353C2×C107#58511yescharacteristic
354D107—41no—
355D107—41no—
356D107—41no—
357D107—42no—
358D107—42no—
359D107—42no—
360#3542—1071nomaximal, Sylow
361C107#354211yescharacteristic, complemented, Sylow
362#562—1072no—
363#560—1072no—
364#555—1071no—
365#553—1071no—
366#552D10711yescharacteristic, complemented
367#551—1072no—
368#550—1071no—
369#547—1071no—
370#546—1072no—
371#546—1071no—
372#546—1071no—
373D42—1071no—
374#542—1071no—
375#540—1071no—
376#540—1072no—
377#538—1072no—
378#537—1071no—
379#535—1072no—
380#535—1071no—
381#534—1072no—
382#525—1071no—
383#525—1071no—
384C2×#121—1071no—
385C2×#41—1071no—
386C2×#41—1071no—
387C2×#41—1071no—
388C2×#41—1072no—
389C22×D4—1072no—
390C22×D4—1072no—
391C22×D4—1071no—
392C22×D4—1071no—
393C23×C4—1071no—
394C4⋊Q8—1071no—
395#127—1072no—
396#127—1072no—
397#127—1071no—
398#126—1072no—
399#126—1072no—
400#126C2×D10712yescomplemented
401#125C2×D10711yescharacteristic, complemented
402#125C2×D10712yescomplemented
403#124—1071no—
404#124—1072no—
405#124—1072no—
406#124—1072no—
407#124—1072no—
408#123—1072no—
409#123—1071no—
410#123—1072no—
411#123—1072no—
412#123—1072no—
413#123—1072no—
414#123—1072no—
415#123—1072no—
416#123—1072no—
417#123—1072no—
418#123—1071no—
419#123C2×D10712yes—
420C22⋊Q8—1071no—
421C22⋊Q8—1071no—
422C22⋊Q8—1072no—
423C22⋊Q8—1072no—
424C22⋊Q8—1072no—
425C22⋊Q8—1071no—
426C22⋊Q8C2×D10711yescharacteristic, complemented
427C22⋊Q8C2×D10711yescharacteristic, complemented
428#121—1071no—
429#121—1071no—
430#121—1071no—
431#121—1071no—
432#121—1071no—
433#121—1072no—
434#121—1071no—
435#121—1071no—
436#121—1072no—
437#121—1071no—
438#121—1072no—
439#121—1072no—
440#121—1072no—
441#121—1072no—
442#121—1071no—
443#121—1072no—
444#121—1071no—
445#121—1072no—
446#121—1072no—
447#121—1072no—
448#121—1072no—
449#121—1071no—
450#121—1072no—
451#121—1072no—
452#121—1072no—
453#120—1071no—
454#120—1072no—
455#120—1071no—
456#120—1072no—
457#120—1072no—
458#120—1072no—
459#120—1072no—
460#120—1072no—
461#120—1072no—
462C4×Q8C2×D10711yescharacteristic, complemented
463C4×D4—1071no—
464C4×D4—1071no—
465C4×D4—1072no—
466C4×D4—1071no—
467C4×D4—1072no—
468C4×D4—1071no—
469C4×D4—1072no—
470C4×D4—1071no—
471C4×D4—1072no—
472C4×D4—1071no—
473C4×D4C2×D10711yescharacteristic
474#117—1071no—
475#117—1071no—
476#117—1072no—
477#117C2×D10712yescomplemented
478#117C2×D10711yescharacteristic, complemented
479C2×C4⋊C4—1071no—
480C2×C4⋊C4C2×D10711yescharacteristic, complemented
481C2×C22⋊C4—1072no—
482C2×C22⋊C4—1072no—
483C2×C22⋊C4—1072no—
484C24—1072no—
485C24—1072no—
486C24—1071no—
487#41—4284no—
488#41—4282no—
489#41—4282no—
490#41—4282no—
491C2×Q8—1071no—
492C2×Q8—1072no—
493C2×Q8C22×D10711yescharacteristic
494C2×D4—1071no—
495C2×D4—1071no—
496C2×D4—1071no—
497C2×D4—1072no—
498C2×D4—1071no—
499C2×D4—1072no—
500C2×D4—1072no—
501C2×D4—1072no—
502C2×D4—1072no—
503C2×D4—1071no—
504C2×D4—1072no—
505C2×D4—1072no—
506C2×D4—1072no—
507C2×D4—1072no—
508C2×D4—1072no—
509C2×D4—1072no—
510C2×D4—1071no—
511C2×D4—1072no—
512C2×D4—1072no—
513C2×D4—1072no—
514C2×D4—1072no—
515C2×D4—1071no—
516C2×D4—1071no—
517C2×D4—1071no—
518C2×D4—4284no—
519C2×D4—4282no—
520C2×D4—4282no—
521C2×D4—4284no—
522C2×D4C22×D10711yescharacteristic
523C22×C4—1071no—
524C22×C4—1072no—
525C22×C4—1072no—
526C22×C4—1072no—
527C22×C4—1072no—
528C22×C4—1072no—
529C22×C4—1071no—
530C22×C4—1072no—
531C22×C4—1071no—
532C22×C4—1071no—
533C22×C4—1071no—
534C22×C4—1071no—
535C22×C4—4282no—
536C22×C4C22×D10712yes—
537C22×C4C22×D10711yescharacteristic
538C22×C4C22×D10711yescharacteristic
539C4⋊C4—1071no—
540C4⋊C4—1072no—
541C4⋊C4—1071no—
542C4⋊C4—1071no—
543C4⋊C4—1071no—
544C4⋊C4—1072no—
545C4⋊C4—1071no—
546C4⋊C4—1072no—
547C4⋊C4—1071no—
548C4⋊C4C22×D10711yescharacteristic
549C4⋊C4C22×D10711yescharacteristic
550C4⋊C4C22×D10712yes—
551C4⋊C4C22×D10711yescharacteristic
552C4⋊C4C22×D10712yes—
553C4⋊C4C22×D10712yes—
554C4⋊C4C22×D10712yes—
555C4⋊C4C22×D10712yes—
556C4⋊C4C22×D10711yescharacteristic
557C4⋊C4C22×D10712yes—
558C22⋊C4—1071no—
559C22⋊C4—1071no—
560C22⋊C4—1072no—
561C22⋊C4—1072no—
562C22⋊C4—1072no—
563C22⋊C4—1072no—
564C22⋊C4—1072no—
565C22⋊C4—1072no—
566C22⋊C4—1072no—
567C22⋊C4—1072no—
568C22⋊C4—1071no—
569C22⋊C4—1072no—
570C22⋊C4—1071no—
571C22⋊C4—1071no—
572C22⋊C4—1072no—
573C22⋊C4—1072no—
574C22⋊C4—1071no—
575C22⋊C4—1072no—
576C22⋊C4—1072no—
577C22⋊C4—1071no—
578C22⋊C4—1072no—
579C22⋊C4—1072no—
580C22⋊C4—1072no—
581C22⋊C4—1071no—
582C22⋊C4C22×D10712yes—
583C22⋊C4C22×D10712yes—
584C22⋊C4C22×D10711yescharacteristic
585C22⋊C4C22×D10712yes—
586C22⋊C4C22×D10711yescharacteristic
587C42—1072no—
588C42—1071no—
589C42C22×D10712yes—
590C42C22×D10711yescharacteristic
591C42C22×D10712yes—
592C23—1072no—
593C23—1071no—
594C23—1071no—
595C23—1072no—
596C23—1072no—
597C23—1071no—
598C23—4282no—
599C23—4282no—
600C23—4282no—
601C23—4282no—
602C23—4282no—
603C23—4281no—
604C23—4281no—
605C23—2144no—
606C23—2142no—
607C23C23×D10711yescharacteristic
608C23C23×D10711yescharacteristic
609Q8—22no—
610Q8—4281no—
611Q8—4282no—
612D4—22no—
613D4—4282no—
614D4—4282no—
615D4—4282no—
616D4—4282no—
617D4—4282no—
618D4—4282no—
619D4—4282no—
620D4—4282no—
621D4—4281no—
622D4—4282no—
623D4—4282no—
624D4—4282no—
625D4—4282no—
626D4—4282no—
627D4—4281no—
628D4—4282no—
629D4—4281no—
630D4—4281no—
631D4—4281no—
632D4—2144no—
633D4—2142no—
634D4—2142no—
635D4—2142no—
636D4—2142no—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—1071no—
641C2×C4—1071no—
642C2×C4—1071no—
643C2×C4—1072no—
644C2×C4—1071no—
645C2×C4—1071no—
646C2×C4—4281no—
647C2×C4—4281no—
648C2×C4—4282no—
649C2×C4—4282no—
650C2×C4—4282no—
651C2×C4—4282no—
652C2×C4—4282no—
653C2×C4—4282no—
654C2×C4—4281no—
655C2×C4—2142no—
656C2×C4—2142no—
657C2×C4—2142no—
658C2×C4C23×D10712yes—
659C2×C4C23×D10711yescharacteristic
660C2×C4C23×D10711yescharacteristic
661C2×C4C23×D10712yes—
662C2×C4C23×D10712yes—
663C2×C4C23×D10711yescharacteristic
664C2×C4C23×D10712yes—
665C2×C4C23×D10711yescharacteristic
666C2×C4C23×D10711yescharacteristic
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—8564no—
673C22—8564no—
674C22—4284no—
675C22—2141no—
676C22—2141no—
677C22—2141no—
678C22—2142no—
679C22—2142no—
680C22—2142no—
681C22—2142no—
682C22—2141no—
683C22—2142no—
684C22—2141no—
685C22—2141no—
686C22—2142no—
687C22—2142no—
688C22—2141no—
689C22—2142no—
690C22—2141no—
691C22—2141no—
692C22—2142no—
693C22#1681215512yes—
694C22C24×D10711yescharacteristic
695C4—22no—
696C4—21no—
697C4—22no—
698C4—21no—
699C4—21no—
700C4—22no—
701C4—22no—
702C4—21no—
703C4—2141no—
704C4—2141no—
705C4—2141no—
706C4—2142no—
707C4—2141no—
708C4—2141no—
709C4#1681215512yes—
710C2—22no—
711C2—41no—
712C2—4282no—
713C2—4282no—
714C2—4282no—
715C2—4281no—
716C2—4281no—
717C2—4281no—
718C2C2×#1681215511yescharacteristic
719C2C2×#1681215511yescharacteristic
720C2#2029346411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D107
commutator, socle, cosocleC22×C107C25
Fitting#552×C107C2
hypercenter#552D107
hypocenterC107#3542
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ #552

Complements

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

NH ≅ G/Ntype
1. #20293375C2semidirect
2. #20293368C2semidirect
3. #20293340C2semidirect
4. #20293330C2semidirect
5. #20293301C2semidirect
6. #20293299C2semidirect
7. #20293278C2semidirect
8. #20293269C2semidirect
9. #20293268C2semidirect
10. #20293268C2semidirect
11. D4×D428C2semidirect
12. #20293249C2semidirect
13. #20293233C2semidirect
14. #20293233C2semidirect
15. #20293216C2semidirect
16. #20293207C2semidirect
17. #20293196C2semidirect
18. #20293196C2semidirect
19. #20293188C2semidirect
20. #20293140C2semidirect
21. #20293136C2semidirect
22. C2×#16812084C2semidirect
23. #552×C107C2semidirect
24. C2×#13133819C22semidirect
25. C2×#13133819C22semidirect
26. C2×#13133818C22semidirect
27. C2×#13133818C22semidirect
29. C22×D428C22semidirect
30. C22×D428C22semidirect
32. C22×C4×D107C22semidirect
33. #16812108C22semidirect
34. #16812106C22semidirect
35. #16812106C22semidirect
36. #16812106C22semidirect
37. #16812104C22semidirect
38. #16812103C22semidirect
39. #16812098C22semidirect
40. #16812097C22semidirect
41. #16812097C22semidirect
42. #16812097C22semidirect
43. #16812095C22semidirect
44. #16812094C22semidirect
45. #16812094C22semidirect
46. #16812094C22semidirect
47. #16812094C22semidirect
48. #16812094C22semidirect
49. #16812094C22semidirect
50. #16812094C22semidirect
51. #16812094C22semidirect
52. #16812094C22semidirect
53. #16812092C22semidirect
54. #16812091C22semidirect
55. #16812087C22semidirect
56. #16812087C22semidirect
57. #16812087C22semidirect
58. #16812087C22semidirect
59. #16812086C22semidirect
60. #16812085C22semidirect
63. #16812084C22semidirect
64. #16812084C22semidirect
65. #16812084C22semidirect
66. #16812084C22semidirect
67. #16812084C22semidirect
68. #16812084C22semidirect
69. #16812084C22semidirect
70. #16812084C22semidirect
71. #16812084C22semidirect
72. #16812084C22semidirect
73. #16812084C22semidirect
74. #16812084C22semidirect
75. #16812084C22semidirect
76. #16812084C22semidirect
77. #16812084C22semidirect
78. #16812084C22semidirect
80. #16812083C22semidirect
81. #16812082C22semidirect
82. #16812082C22semidirect
83. #16812082C22semidirect
84. #16812082C22semidirect
87. #16812079C22semidirect
88. #16812079C22semidirect
89. #16812079C22semidirect
90. #16812079C22semidirect
91. #16812079C22semidirect
92. #16812079C22semidirect
93. #16812079C22semidirect
95. C4×D428C22semidirect
96. C4×D428C22semidirect
97. C4×D428C22semidirect
98. #16812071C22semidirect
99. #16812071C22semidirect
100. #16812071C22semidirect
101. #16812071C22semidirect
102. C4×C22⋊D107C22semidirect
103. C4×C22⋊D107C22semidirect
104. (C22⋊D107)⋊C4C22semidirect
105. #16812067C22semidirect
106. #16812066C22semidirect
107. #16812066C22semidirect
108. C4⋊C4×D107C22semidirect
109. C2×(C2×D107)⋊C4C22semidirect
110. C22⋊C4×D107C22semidirect
111. C22⋊C4×D107C22semidirect
112. #126×C107C22semidirect
113. #125×C107C22semidirect
114. #125×C107C22semidirect
116. C22⋊Q8×C107C22semidirect
117. C22⋊Q8×C107C22semidirect
118. C4×Q8×C107C22semidirect
120. #117×C107C22semidirect
121. #117×C107C22semidirect
122. C2×C4⋊C4×C107C22semidirect
361. C107#3542semidirect
366. #552D107semidirect
400. #126C2×D107semidirect
401. #125C2×D107semidirect
402. #125C2×D107semidirect
426. C22⋊Q8C2×D107semidirect
427. C22⋊Q8C2×D107semidirect
462. C4×Q8C2×D107semidirect
477. #117C2×D107semidirect
478. #117C2×D107semidirect
480. C2×C4⋊C4C2×D107semidirect

Maximal subgroups

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

subgroupindex
#202933752
#202933682
#202933402
#202933302
#202933012
#202932992
#202932782
#202932692
#202932682
D4×D4282
#202932492
#202932332
#202932162
#202932072
#202931962
#202931882
#202931402
#202931362
C2×#168120842
#552×C1072
#3542107