Finite Group Databasebeta

← #44564736

Subgroups — #44564736

Order 32128.

1150 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30632428C212yesmaximal, complemented
2#30632425C212yesmaximal, complemented
3#30632405C211yesmaximal, characteristic, complemented
4#30632390C211yesmaximal, characteristic, complemented
5#30632358C212yesmaximal, complemented
6#30632355C211yesmaximal, characteristic, complemented
7#30632338C211yesmaximal, characteristic, complemented
8#30632333C211yesmaximal, characteristic, complemented
9#30632332C211yesmaximal, characteristic, complemented
10#30632329C212yesmaximal, complemented
11#30632321C211yesmaximal, characteristic, complemented
12#30632303C212yesmaximal, complemented
13#30632273C212yesmaximal, complemented
14#30632270C212yesmaximal, complemented
15#30632268C211yesmaximal, characteristic, complemented
16#30632266C211yesmaximal, characteristic, complemented
17#30632256C211yesmaximal, characteristic, complemented
18#30632253C211yesmaximal, characteristic, complemented
19#30632253C212yesmaximal, complemented
20#30632234C211yesmaximal, characteristic, complemented
21#30632234C211yesmaximal, characteristic, complemented
22#30632222C211yesmaximal, characteristic, complemented
23#553×C251C211yesmaximal, characteristic, complemented
24C2×#16860810C2211yescharacteristic, complemented
25C2×#16860810C2211yescharacteristic, complemented
26C2×#16860810C2212yescomplemented
27C2×#16860810C2212yescomplemented
28C2×#16860810C2211yescharacteristic, complemented
29C2×#16860809C2211yescharacteristic, complemented
30C22×D1004C2211yescharacteristic
31C2×D4×D251C2212yes—
32C2×D4×D251C2211yescharacteristic
33#22548714C2211yescharacteristic, complemented
34#22548714C2211yescharacteristic, complemented
35#22548712C2212yescomplemented
36#22548711C2211yescharacteristic
37#22548711C2211yescharacteristic
38#22548711C2212yescomplemented
39#22548711C2212yescomplemented
40#22548710C2212yescomplemented
41#22548710C2212yescomplemented
42#22548709C2212yescomplemented
43#22548708C2212yescomplemented
44#22548703C2211yescharacteristic
45#22548703C2212yescomplemented
46#22548701C2212yes—
47#22548701C2212yescomplemented
48#22548701C2211yescharacteristic, complemented
49#22548701C2211yescharacteristic, complemented
50#22548701C2212yescomplemented
51#22548700C2212yescomplemented
52#22548700C2212yescomplemented
53#22548700C2212yescomplemented
54#22548700C2212yescomplemented
55#22548699C2212yescomplemented
56#22548698C2212yescomplemented
57#22548695C2211yescharacteristic, complemented
58#22548695C2212yescomplemented
59#22548695C2211yescharacteristic, complemented
60#22548694C2211yescharacteristic, complemented
61#22548693C2212yescomplemented
62#22548692C2212yescomplemented
63#22548690C2211yescharacteristic
64#22548690C2211yescharacteristic
65#22548690C2211yescharacteristic
66#22548690C2211yescharacteristic, complemented
67#22548690C2211yescharacteristic, complemented
68#22548690C2212yescomplemented
69#22548690C2211yescharacteristic, complemented
70#22548690C2212yescomplemented
71#22548689C2211yescharacteristic
72#22548689C2212yescomplemented
73#22548689C2212yescomplemented
74#22548689C2212yescomplemented
75#22548688C2211yescharacteristic
76#22548688C2212yes—
77#22548688C2211yescharacteristic, complemented
78#22548688C2212yescomplemented
79#22548688C2212yescomplemented
80#22548688C2212yescomplemented
81#22548688C2212yescomplemented
82#22548687C2212yescomplemented
83#22548687C2212yescomplemented
84#22548686C2211yescharacteristic, complemented
85#22548686C2211yescharacteristic, complemented
86#22548686C2212yescomplemented
87#22548685C2212yes—
88#22548685C2212yescomplemented
89#22548685C2212yescomplemented
90#22548685C2212yescomplemented
91#22548685C2212yescomplemented
92#22548683C2212yes—
93#22548683C2212yescomplemented
94#22548683C2212yescomplemented
95C4×Dic502C2212yescomplemented
96#22548680C2211yescharacteristic, complemented
97C4×D1004C2211yescharacteristic, complemented
98C4×D1004C2211yescharacteristic, complemented
99#22548677C2211yescharacteristic
100#22548677C2212yescomplemented
101#22548677C2212yescomplemented
102C4×C22⋊D251C2211yescharacteristic
103C4×C22⋊D251C2212yescomplemented
104C4×C22⋊D251C2211yescharacteristic, complemented
105(C22⋊D251)⋊C4C2212yescomplemented
106#22548673C2212yescomplemented
107#22548673C2211yescharacteristic, complemented
108C4⋊C4×D251C2211yescharacteristic, complemented
109C2×(C2×D251)⋊C4C2212yescomplemented
110C22⋊C4×D251C2212yescomplemented
111C42×D251C2211yescharacteristic, complemented
112#126×C251C2212yescomplemented
113#125×C251C2211yescharacteristic, complemented
114#123×C251C2212yescomplemented
115#121×C251C2211yescharacteristic
116#121×C251C2211yescharacteristic, complemented
117#121×C251C2212yescomplemented
118C4×D4×C251C2211yescharacteristic, complemented
119C4×D4×C251C2211yescharacteristic, complemented
120C4×D4×C251C2212yescomplemented
121#117×C251C2211yescharacteristic, complemented
122C2×C4⋊C4×C251C2211yescharacteristic, complemented
123C23×D251C2312yes—
124C23×D251C2312yes—
125#16860810—42no—
126#16860810—42no—
127#16860810—42no—
128#16860810—44no—
129#16860810—44no—
130#16860809—42no—
131C2×Dic502C2311yescharacteristic
132C2×Dic502C2312yes—
133C2×Dic502C2311yescharacteristic
134C2×Dic502C2311yescharacteristic
135C2×D1004—42no—
136C2×D1004C2311yescharacteristic
137C2×D1004C2311yescharacteristic
138C2×D1004C2312yes—
139C2×D1004C2312yes—
140C2×D1004C2311yescharacteristic
141C2×D1004C2312yes—
142C2×D1004C2312yes—
143C2×D1004C2311yescharacteristic
144C2×D1004C2312yes—
145C2×D1004C2312yes—
146C2×D1004C2311yescharacteristic
147C2×C22⋊D251C2311yescharacteristic
148C2×C22⋊D251C2312yes—
149C2×C22⋊D251C2311yescharacteristic
150C2×C22⋊D251C2312yes—
151C2×C22⋊D251C2312yes—
152C2×C22⋊D251C2312yes—
153C2×C22⋊D251C2311yescharacteristic
154C2×C22⋊D251C2312yes—
155C2×C22⋊D251C2311yescharacteristic
156C2×C22⋊D251C2311yescharacteristic
157C2×C22⋊D251C2312yes—
158C2×C22⋊D251C2311yescharacteristic
159C2×C22⋊D251C2312yes—
160D4×D251—42no—
161D4×D251—44no—
162C22×Dic251C2312yes—
163C2×C4×D251C2311yescharacteristic
164C2×C4×D251C2312yes—
165C2×C4×D251C2311yescharacteristic
166C2×C4×D251C2311yescharacteristic
167C2×C4×D251C2311yescharacteristic
168C2×C4×D251C2312yes—
169C2×C4×D251C2312yes—
170C2×C4×D251C2312yes—
171C2×C4×D251C2311yescharacteristic
172C4⋊Dic251C2311yescharacteristic
173C4⋊Dic251C2312yes—
174C4⋊Dic251C2311yescharacteristic
175C4⋊Dic251C2312yes—
176Dic251⋊C4C2312yes—
177Dic251⋊C4C2311yescharacteristic
178Dic251⋊C4C2311yescharacteristic
179Dic251⋊C4C2312yes—
180Dic251⋊C4C2312yes—
181Dic251⋊C4C2312yes—
182C22⋊Dic251C2312yes—
183C22⋊Dic251C2311yescharacteristic
184C22⋊Dic251C2312yes—
185C22⋊Dic251C2311yescharacteristic
186(C2×D251)⋊C4C2312yes—
187(C2×D251)⋊C4C2312yes—
188(C2×D251)⋊C4C2311yescharacteristic
189(C2×D251)⋊C4C2312yes—
190(C2×D251)⋊C4C2312yes—
191(C2×D251)⋊C4C2312yes—
192(C2×D251)⋊C4C2312yes—
193(C2×D251)⋊C4C2312yes—
194(C2×D251)⋊C4C2312yes—
195(C2×D251)⋊C4C2311yescharacteristic
196(C2×D251)⋊C4C2312yes—
197(C2×D251)⋊C4C2311yescharacteristic
198(C2×D251)⋊C4C2312yes—
199(C2×D251)⋊C4C2311yescharacteristic
200(C2×D251)⋊C4C2312yes—
201(C2×D251)⋊C4C2312yes—
202(C2×D251)⋊C4C2312yes—
203C4×Dic251C2311yescharacteristic
204C4×Dic251C2311yescharacteristic
205C4×Dic251C2311yescharacteristic
206C4×Dic251C2312yes—
207C4×Dic251C2312yes—
208C2×D4×C251C2311yescharacteristic
209C2×D4×C251C2312yes—
210C2×D4×C251C2311yescharacteristic
211C2×D4×C251C2312yes—
212C22×C4×C251C2311yescharacteristic
213C22×C4×C251C2311yescharacteristic
214C22×C4×C251C2312yes—
215C22×C4×C251C2312yes—
216C4⋊C4×C251C2311yescharacteristic
217C4⋊C4×C251C2311yescharacteristic
218C4⋊C4×C251C2312yes—
219C4⋊C4×C251C2311yescharacteristic
220C4⋊C4×C251C2312yes—
221C4⋊C4×C251C2311yescharacteristic
222C4⋊C4×C251C2312yes—
223C22⋊C4×C251C2312yes—
224C22⋊C4×C251C2311yescharacteristic
225C22⋊C4×C251C2312yes—
226C22⋊C4×C251C2312yes—
227C22⋊C4×C251C2311yescharacteristic
228C22⋊C4×C251C2312yes—
229C42×C251C2312yes—
230C42×C251C2311yescharacteristic
231C22×D251—42no—
232C22×D251—42no—
233C22×D251—42no—
234C22×D251—42no—
235C22×D251—42no—
236C22×D251—42no—
237C22×D251C2411yescharacteristic
238C22×D251C2412yes—
239C22×D251C2412yes—
240C22×D251C2411yescharacteristic
241C22×D251C2411yescharacteristic
242Dic502—22no—
243Dic502—24no—
244Dic502—41no—
245Dic502—41no—
246D1004—22no—
247D1004—22no—
248D1004—42no—
249D1004—42no—
250D1004—41no—
251D1004—42no—
252D1004—42no—
253D1004—41no—
254D1004—41no—
255D1004—42no—
256D1004—42no—
257C22⋊D251—22no—
258C22⋊D251—24no—
259C22⋊D251—22no—
260C22⋊D251—42no—
261C22⋊D251—42no—
262C22⋊D251—42no—
263C22⋊D251—41no—
264C22⋊D251—41no—
265C22⋊D251—41no—
266C22⋊D251—41no—
267C22⋊D251—42no—
268C22⋊D251—42no—
269C22⋊D251—42no—
270C2×Dic251—42no—
271C2×Dic251C2411yescharacteristic
272C2×Dic251C2411yescharacteristic
273C2×Dic251C2411yescharacteristic
274C2×Dic251C2412yes—
275C2×Dic251C2412yes—
276C2×Dic251C2411yescharacteristic
277C2×Dic251C2411yescharacteristic
278C4×D251—22no—
279C4×D251—22no—
280C4×D251—22no—
281C4×D251—24no—
282C4×D251—22no—
283C4×D251—41no—
284C4×D251—42no—
285C4×D251—42no—
286C4×D251—42no—
287C23×C251C2411yescharacteristic
288C23×C251C2412yes—
289C23×C251C2411yescharacteristic
290D4×C251—22no—
291D4×C251—41no—
292D4×C251—42no—
293D4×C251—42no—
294C2×C4×C251—22no—
295C2×C4×C251—22no—
296C2×C4×C251—42no—
297C2×C4×C251—42no—
298C2×C4×C251C2411yescharacteristic
299C2×C4×C251C2412yes—
300C2×C4×C251C2411yescharacteristic
301C2×C4×C251C2411yescharacteristic
302C2×C4×C251C2412yes—
303C2×C4×C251C2411yescharacteristic
304C2×C4×C251C2412yes—
305C2×C4×C251C2411yescharacteristic
306C22×C251—21no—
307C22×C251—21no—
308C22×C251—21no—
309C22×C251—22no—
310C22×C251—22no—
311C22×C251—21no—
312C22×C251—21no—
313C22×C251—22no—
314C22×C251—21no—
315C22×C251C2511yescharacteristic
316C2×D251—21no—
317C2×D251—21no—
318C2×D251—21no—
319C2×D251—22no—
320C2×D251—21no—
321C2×D251—21no—
322C2×D251—22no—
323C2×D251—22no—
324C2×D251—21no—
325C2×D251—22no—
326C2×D251—21no—
327C2×D251—22no—
328C2×D251—21no—
329C2×D251—21no—
330C2×D251—22no—
331C2×D251—84no—
332C2×D251—84no—
333C4×C251—21no—
334C4×C251—21no—
335C4×C251—21no—
336C4×C251—22no—
337C4×C251—22no—
338C4×C251—21no—
339C4×C251—22no—
340C4×C251H(5,𝔽2)12yes—
341Dic251—21no—
342Dic251—21no—
343Dic251—21no—
344Dic251—22no—
345Dic251—22no—
346Dic251—21no—
347Dic251H(5,𝔽2)12yes—
348C2×C251—41no—
349C2×C251—42no—
350C2×C251—41no—
351C2×C251C2×H(5,𝔽2)11yescharacteristic
352C2×C251C2×H(5,𝔽2)11yescharacteristic
353C2×C251#58511yescharacteristic
354D251—41no—
355D251—41no—
356D251—42no—
357D251—41no—
358D251—42no—
359C251#354611yescharacteristic, complemented, Sylow
360#3546—2511nomaximal, Sylow
361#560—2512no—
362#560—2512no—
363#556—2511no—
364#553—2511no—
365#553D25111yescharacteristic, complemented
366#550—2511no—
367#550—2512no—
368#547—2511no—
369#546—2512no—
370#546—2511no—
371#546—2511no—
372D42—2511no—
373#542—2512no—
374#538—2512no—
375#538—2512no—
376#537—2511no—
377#537—2511no—
378#535—2512no—
379#535—2511no—
380#535—2511no—
381#532—2511no—
382#532—2511no—
383#529—2511no—
384C2×#41—2511no—
385C2×#41—2511no—
386C2×#41—2511no—
387C2×#41—2512no—
388C2×#41—2512no—
389C2×#41—2511no—
390C22×D4—2511no—
391C22×D4—2512no—
392C22×D4—2511no—
393C4⋊Q8—2511no—
394C4⋊Q8—2511no—
395#127—2511no—
396#127—2511no—
397#127—2512no—
398#127—2512no—
399#127—2512no—
400#126—2512no—
401#126—2512no—
402#126—2512no—
403#126—2512no—
404#126C2×D25112yescomplemented
405#125C2×D25111yescharacteristic, complemented
406#124—2512no—
407#124—2511no—
408#124—2511no—
409#124—2512no—
410#124—2512no—
411#124—2511no—
412#124—2512no—
413#123—2512no—
414#123—2512no—
415#123—2512no—
416#123—2512no—
417#123—2512no—
418#123—2512no—
419#123C2×D25112yescomplemented
420C22⋊Q8—2511no—
421C22⋊Q8—2511no—
422C22⋊Q8—2512no—
423C22⋊Q8—2511no—
424C22⋊Q8—2512no—
425C22⋊Q8—2512no—
426#121—2511no—
427#121—2511no—
428#121—2512no—
429#121—2512no—
430#121—2512no—
431#121—2512no—
432#121—2511no—
433#121—2512no—
434#121—2512no—
435#121—2511no—
436#121—2511no—
437#121—2511no—
438#121—2511no—
439#121—2511no—
440#121—2512no—
441#121—2511no—
442#121—2512no—
443#121—2511no—
444#121—2511no—
445#121—2512no—
446#121—2512no—
447#121—2512no—
448#121—2512no—
449#121—2512no—
450#121C2×D25111yescharacteristic
451#121C2×D25111yescharacteristic, complemented
452#121C2×D25112yescomplemented
453#120—2512no—
454#120—2512no—
455#120—2512no—
456#120—2512no—
457#120—2512no—
458#120—2512no—
459#120—2512no—
460#120—2512no—
461C4×Q8—2511no—
462C4×Q8—2512no—
463C4×D4—2512no—
464C4×D4—2511no—
465C4×D4—2511no—
466C4×D4—2511no—
467C4×D4—2512no—
468C4×D4—2512no—
469C4×D4—2512no—
470C4×D4—2511no—
471C4×D4—2511no—
472C4×D4C2×D25111yescharacteristic, complemented
473C4×D4C2×D25111yescharacteristic, complemented
474C4×D4C2×D25112yescomplemented
475#117—2512no—
476#117—2511no—
477#117C2×D25111yescharacteristic, complemented
478C2×C4⋊C4—2511no—
479C2×C4⋊C4C2×D25111yescharacteristic, complemented
480C2×C22⋊C4—2512no—
481C2×C22⋊C4—2512no—
482C2×C42—2511no—
483C24—2512no—
484C24—2512no—
485#41—10042no—
486#41—10042no—
487#41—10042no—
488#41—10044no—
489#41—10044no—
490#41—10042no—
491C2×Q8—2511no—
492C2×Q8—2511no—
493C2×Q8—2511no—
494C2×Q8—2512no—
495C2×D4—10042no—
496C2×D4—10042no—
497C2×D4—10044no—
498C2×D4—2512no—
499C2×D4—2511no—
500C2×D4—2512no—
501C2×D4—2511no—
502C2×D4—2511no—
503C2×D4—2512no—
504C2×D4—2512no—
505C2×D4—2512no—
506C2×D4—2512no—
507C2×D4—2511no—
508C2×D4—2511no—
509C2×D4—2512no—
510C2×D4—2511no—
511C2×D4—2511no—
512C2×D4—2512no—
513C2×D4—2512no—
514C2×D4—2511no—
515C2×D4—2512no—
516C2×D4—2512no—
517C2×D4—2512no—
518C2×D4—2512no—
519C2×D4—2511no—
520C2×D4—2511no—
521C2×D4—2511no—
522C2×D4C22×D25111yescharacteristic
523C2×D4C22×D25111yescharacteristic
524C2×D4C22×D25112yes—
525C2×D4C22×D25112yes—
526C22×C4—2512no—
527C22×C4—2511no—
528C22×C4—2512no—
529C22×C4—2512no—
530C22×C4—2512no—
531C22×C4—2511no—
532C22×C4—2511no—
533C22×C4—2511no—
534C22×C4—2512no—
535C22×C4—2511no—
536C22×C4C22×D25111yescharacteristic
537C22×C4C22×D25111yescharacteristic
538C22×C4C22×D25112yes—
539C22×C4C22×D25112yes—
540C4⋊C4—2511no—
541C4⋊C4—2512no—
542C4⋊C4—2512no—
543C4⋊C4—2511no—
544C4⋊C4—2511no—
545C4⋊C4—2512no—
546C4⋊C4—2512no—
547C4⋊C4—2512no—
548C4⋊C4—2511no—
549C4⋊C4—2512no—
550C4⋊C4C22×D25111yescharacteristic
551C4⋊C4C22×D25111yescharacteristic
552C4⋊C4C22×D25112yes—
553C4⋊C4C22×D25111yescharacteristic
554C4⋊C4C22×D25112yes—
555C4⋊C4C22×D25112yes—
556C4⋊C4C22×D25111yescharacteristic
557C22⋊C4—2512no—
558C22⋊C4—2511no—
559C22⋊C4—2512no—
560C22⋊C4—2511no—
561C22⋊C4—2512no—
562C22⋊C4—2511no—
563C22⋊C4—2512no—
564C22⋊C4—2512no—
565C22⋊C4—2512no—
566C22⋊C4—2512no—
567C22⋊C4—2512no—
568C22⋊C4—2512no—
569C22⋊C4—2511no—
570C22⋊C4—2511no—
571C22⋊C4—2512no—
572C22⋊C4—2512no—
573C22⋊C4—2512no—
574C22⋊C4—2512no—
575C22⋊C4—2512no—
576C22⋊C4—2512no—
577C22⋊C4—2511no—
578C22⋊C4C22×D25111yescharacteristic
579C22⋊C4C22×D25112yes—
580C22⋊C4C22×D25112yes—
581C22⋊C4C22×D25111yescharacteristic
582C22⋊C4C22×D25112yes—
583C22⋊C4C22×D25112yes—
584C42—2511no—
585C42—2511no—
586C42—2511no—
587C42—2512no—
588C42—2512no—
589C42C22×D25111yescharacteristic
590C42C22×D25112yes—
591C23—10042no—
592C23—10042no—
593C23—10042no—
594C23—10042no—
595C23—10042no—
596C23—10042no—
597C23—2512no—
598C23—2511no—
599C23—2512no—
600C23—2511no—
601C23—2511no—
602C23C23×D25111yescharacteristic
603C23C23×D25112yes—
604C23C23×D25111yescharacteristic
605Q8—10041no—
606Q8—10041no—
607Q8—5024no—
608Q8—5022no—
609D4—22no—
610D4—42no—
611D4—41no—
612D4—42no—
613D4—10042no—
614D4—10042no—
615D4—10042no—
616D4—10042no—
617D4—10041no—
618D4—10041no—
619D4—10041no—
620D4—10042no—
621D4—10042no—
622D4—10042no—
623D4—10042no—
624D4—10042no—
625D4—10041no—
626D4—10042no—
627D4—10042no—
628D4—10041no—
629D4—10041no—
630D4—10041no—
631D4—10042no—
632D4—5022no—
633D4—5024no—
634D4—5022no—
635D4—5022no—
636D4—5022no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—10042no—
642C2×C4—10042no—
643C2×C4—10042no—
644C2×C4—10041no—
645C2×C4—10042no—
646C2×C4—5024no—
647C2×C4—5022no—
648C2×C4—5022no—
649C2×C4—5022no—
650C2×C4—5022no—
651C2×C4—2511no—
652C2×C4—2511no—
653C2×C4—2511no—
654C2×C4—2512no—
655C2×C4—2512no—
656C2×C4—2511no—
657C2×C4—2511no—
658C2×C4C23×D25112yes—
659C2×C4C23×D25111yescharacteristic
660C2×C4C23×D25111yescharacteristic
661C2×C4C23×D25111yescharacteristic
662C2×C4C23×D25112yes—
663C2×C4C23×D25111yescharacteristic
664C2×C4C23×D25112yes—
665C2×C4C23×D25111yescharacteristic
666C22—21no—
667C22—22no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—22no—
672C22—21no—
673C22—22no—
674C22—21no—
675C22—20084no—
676C22—20084no—
677C22—5021no—
678C22—5022no—
679C22—5021no—
680C22—5022no—
681C22—5021no—
682C22—5022no—
683C22—5021no—
684C22—5021no—
685C22—5021no—
686C22—5022no—
687C22—5021no—
688C22—5021no—
689C22—5022no—
690C22—5022no—
691C22—5021no—
692C22C24×D25111yescharacteristic
693C4—21no—
694C4—22no—
695C4—22no—
696C4—21no—
697C4—21no—
698C4—21no—
699C4—22no—
700C4—5022no—
701C4—5021no—
702C4—5022no—
703C4—5021no—
704C4—5021no—
705C4—5021no—
706C4—2512no—
707C4#2254876112yes—
708C2—41no—
709C2—42no—
710C2—41no—
711C2—10042no—
712C2—10041no—
713C2—10042no—
714C2—10041no—
715C2—10041no—
716C2H(5,𝔽2)×D25111yescharacteristic
717C2C2×#2254876111yescharacteristic
718C2#3063252311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D251
commutator, socle, cosocleC22×C251C25
Fitting#553×C251C2
hypercenter#553D251
hypocenterC251#3546
LCSG ▷ C22×C251 ▷ C251
UCSC1 ◁ C22 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #30632428C2semidirect
2. #30632425C2semidirect
3. #30632405C2semidirect
4. #30632390C2semidirect
5. #30632358C2semidirect
6. #30632355C2semidirect
7. #30632338C2semidirect
8. #30632333C2semidirect
9. #30632332C2semidirect
10. #30632329C2semidirect
11. #30632321C2semidirect
12. #30632303C2semidirect
13. #30632273C2semidirect
14. #30632270C2semidirect
15. #30632268C2semidirect
16. #30632266C2semidirect
17. #30632256C2semidirect
18. #30632253C2semidirect
19. #30632253C2semidirect
20. #30632234C2semidirect
21. #30632234C2semidirect
22. #30632222C2semidirect
23. #553×C251C2semidirect
24. C2×#16860810C22semidirect
25. C2×#16860810C22semidirect
26. C2×#16860810C22semidirect
27. C2×#16860810C22semidirect
28. C2×#16860810C22semidirect
29. C2×#16860809C22semidirect
33. #22548714C22semidirect
34. #22548714C22semidirect
35. #22548712C22semidirect
38. #22548711C22semidirect
39. #22548711C22semidirect
40. #22548710C22semidirect
41. #22548710C22semidirect
42. #22548709C22semidirect
43. #22548708C22semidirect
45. #22548703C22semidirect
47. #22548701C22semidirect
48. #22548701C22semidirect
49. #22548701C22semidirect
50. #22548701C22semidirect
51. #22548700C22semidirect
52. #22548700C22semidirect
53. #22548700C22semidirect
54. #22548700C22semidirect
55. #22548699C22semidirect
56. #22548698C22semidirect
57. #22548695C22semidirect
58. #22548695C22semidirect
59. #22548695C22semidirect
60. #22548694C22semidirect
61. #22548693C22semidirect
62. #22548692C22semidirect
66. #22548690C22semidirect
67. #22548690C22semidirect
68. #22548690C22semidirect
69. #22548690C22semidirect
70. #22548690C22semidirect
72. #22548689C22semidirect
73. #22548689C22semidirect
74. #22548689C22semidirect
77. #22548688C22semidirect
78. #22548688C22semidirect
79. #22548688C22semidirect
80. #22548688C22semidirect
81. #22548688C22semidirect
82. #22548687C22semidirect
83. #22548687C22semidirect
84. #22548686C22semidirect
85. #22548686C22semidirect
86. #22548686C22semidirect
88. #22548685C22semidirect
89. #22548685C22semidirect
90. #22548685C22semidirect
91. #22548685C22semidirect
93. #22548683C22semidirect
94. #22548683C22semidirect
95. C4×Dic502C22semidirect
96. #22548680C22semidirect
97. C4×D1004C22semidirect
98. C4×D1004C22semidirect
100. #22548677C22semidirect
101. #22548677C22semidirect
103. C4×C22⋊D251C22semidirect
104. C4×C22⋊D251C22semidirect
105. (C22⋊D251)⋊C4C22semidirect
106. #22548673C22semidirect
107. #22548673C22semidirect
108. C4⋊C4×D251C22semidirect
109. C2×(C2×D251)⋊C4C22semidirect
110. C22⋊C4×D251C22semidirect
111. C42×D251C22semidirect
112. #126×C251C22semidirect
113. #125×C251C22semidirect
114. #123×C251C22semidirect
116. #121×C251C22semidirect
117. #121×C251C22semidirect
118. C4×D4×C251C22semidirect
119. C4×D4×C251C22semidirect
120. C4×D4×C251C22semidirect
121. #117×C251C22semidirect
122. C2×C4⋊C4×C251C22semidirect
359. C251#3546semidirect
365. #553D251semidirect
404. #126C2×D251semidirect
405. #125C2×D251semidirect
419. #123C2×D251semidirect
451. #121C2×D251semidirect
452. #121C2×D251semidirect
472. C4×D4C2×D251semidirect
473. C4×D4C2×D251semidirect
474. C4×D4C2×D251semidirect
477. #117C2×D251semidirect
479. C2×C4⋊C4C2×D251semidirect

Maximal subgroups

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

subgroupindex
#306324282
#306324252
#306324052
#306323902
#306323582
#306323552
#306323382
#306323332
#306323322
#306323292
#306323212
#306323032
#306322732
#306322702
#306322682
#306322662
#306322562
#306322532
#306322342
#306322222
#553×C2512
#3546251