Finite Group Databasebeta

← #15661933

Subgroups — #15661933

Order 2816.

7230 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082687C218yesmaximal, complemented
2#13082595C214yesmaximal, complemented
3#13082578C214yesmaximal, complemented
4#13082483C212yesmaximal, complemented
5#13082457C214yesmaximal, complemented
6#13082380C211yesmaximal, characteristic, complemented
7#13082337C212yesmaximal, complemented
8#13082315C214yesmaximal, complemented
9#13082261C212yesmaximal, complemented
10#13082237C214yesmaximal, complemented
11#13082227C214yesmaximal, complemented
12#13082182C218yesmaximal, complemented
13#13082050C212yesmaximal, complemented
14#13082028C214yesmaximal, complemented
15#13081913C212yesmaximal, complemented
16C2×#10623155C214yesmaximal, complemented
17#13081820C212yesmaximal, complemented
18C2×C4×#4341C211yesmaximal, characteristic, complemented
19C11×#3501C211yesmaximal, characteristic, complemented
20C2×#67037C2212yes—
21C22×#4341C2211yescharacteristic
22C11×#554C2218yescomplemented
23C11×#554C2214yescomplemented
24D4×Q8×C11C2214yescomplemented
25C11×#544C2212yescomplemented
26C11×#543C2214yescomplemented
27C11×#533C2212yescomplemented
28C2×C11×C22⋊Q8C2214yescomplemented
29C11×#518C2212yes—
30C2×C4×D4×C11C2211yescharacteristic
31#10623348C2218yescomplemented
32C2×#67000C2214yescomplemented
33C2×Q8×Dic11C2214yescomplemented
34C2×D4×Dic11C2211yescharacteristic
35C2×#66983C2214yes—
36C2×C4×C22⋊D11C2212yescomplemented
37C22×C4×Dic11C2212yescomplemented
38#10623265C2218yescomplemented
39#10623264C2218yescomplemented
40#10623263C2218yescomplemented
41#10623263C2214yescomplemented
42#10623261C2214yescomplemented
43#10623259C2212yescomplemented
44#10623259C2212yescomplemented
45#10623259C2218yescomplemented
46#10623256C2212yescomplemented
47#10623256C2212yescomplemented
48#10623228C2218yescomplemented
49#10623226C2218yescomplemented
50#10623225C2218yescomplemented
51#10623225C2218yescomplemented
52#10623222C2214yescomplemented
53#10623222C2214yescomplemented
54#10623222C2218yescomplemented
55#10623176C22116yescomplemented
56#10623176C2218yescomplemented
57#10623176C2218yescomplemented
58#10623175C22116yescomplemented
59#10623175C2218yescomplemented
60#10623173C22116yescomplemented
61#10623173C22116yescomplemented
62#10623173C2218yescomplemented
63#10623168C22116yescomplemented
64#10623168C22116yescomplemented
65#10623168C22116yescomplemented
66#10623161C2218yescomplemented
67#10623158C2214yescomplemented
68#10623158C2214yescomplemented
69#10623158C22116yescomplemented
70#10623155C2214yescomplemented
71#10623155C2218yescomplemented
72#10623155C2218yescomplemented
73#10623155C2218yescomplemented
74#10623155C2218yescomplemented
75#10623155C2218yescomplemented
76#10623155C2218yescomplemented
77#10623155C2218yescomplemented
78#10623155C2214yescomplemented
79#10623155C22116yescomplemented
80#10623116C2214yescomplemented
81#10623115C2218yescomplemented
82#10623111C2214yescomplemented
83#10623111C2214yescomplemented
84C4×#4343C2214yescomplemented
85C4×#4343C2214yescomplemented
86#10623101C2214yescomplemented
87#10623086C2214yescomplemented
88#10623086C2218yescomplemented
89#10623086C2218yescomplemented
90#10623085C2218yescomplemented
91#10623085C2218yescomplemented
92#10623085C2218yescomplemented
93D4×D44C2214yescomplemented
94#10623077C2218yescomplemented
95#10623076C2218yescomplemented
96C4×D4×D11C2218yescomplemented
97C4×#4341C2214yescomplemented
98C4×#4341C2214yescomplemented
99C4×#4341C2218yescomplemented
100C4×#4341C2214yescomplemented
101C4×#4341C2214yescomplemented
102#10623057C2214yescomplemented
103#10623055C2214yescomplemented
104#10623054C2214yescomplemented
105#10623053C2214yescomplemented
106#10623045C22116yescomplemented
107#10623045C2218yescomplemented
108C2×#66951C2218yescomplemented
109#10623041C2212yes—
110C2×#66946C2214yescomplemented
111C2×#66945C2218yescomplemented
112C2×#66945C2211yescharacteristic, complemented
113C2×#66943C2214yescomplemented
114C2×#66940C2211yescharacteristic, complemented
115#10623024C2214yes—
116#10623024C2218yescomplemented
117C2×#66939C2218yescomplemented
118#10623017C2218yescomplemented
119C2×(C22⋊D11)⋊C4C2218yescomplemented
120C2×(C22⋊D11)⋊C4C2212yescomplemented
121C2×#66930C2212yescomplemented
122#10623008C2212yes—
123C2×C42×D11C2211yescharacteristic, complemented
124C2×C4×Dic22C2211yescharacteristic, complemented
125C22×Q8×C11C2314yes—
126C22×D4×C11C2311yescharacteristic
127C23×C4×C11C2312yes—
128C22×C22⋊D11C2318yes—
129C22×C22⋊D11C2312yes—
130C23×Dic11C2312yes—
131C23×Dic11C2312yes—
132C2×#4343C2314yes—
133C2×#4343C2314yes—
134#67037—216no—
135C2×#4341—28no—
136C2×#4341C2314yes—
137C2×#4341C2314yes—
138C2×#4341C2318yes—
139C2×D4×D11C2318yes—
140C2×#4339C2314yes—
141C22×D44C2314yes—
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2318yes—
146C22×Dic22C2311yescharacteristic
147C11×C4⋊Q8C2312yes—
148C11×C4⋊Q8C2312yes—
149C11×C4⋊Q8C2318yes—
150C11×#125C2314yes—
151C11×#125C2318yes—
152C11×C22⋊Q8C2314yes—
153C11×C22⋊Q8C2318yes—
154C11×C22⋊Q8C2318yes—
155C11×C22⋊Q8C2318yes—
156C11×C22⋊Q8C2314yes—
157C11×C22⋊Q8C23116yes—
158C11×C22⋊Q8C23116yes—
159C4×Q8×C11C2314yes—
160C4×Q8×C11C2314yes—
161C4×D4×C11C2314yes—
162C4×D4×C11C2314yes—
163C4×D4×C11C2318yes—
164C4×D4×C11C2318yes—
165C11×#117C2314yes—
166C2×C11×C4⋊C4C2311yescharacteristic
167C2×C11×C4⋊C4C2314yes—
168C2×C11×C4⋊C4C2318yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C11×C22⋊C4C2318yes—
171C2×C42×C11C2311yescharacteristic
172C2×C22⋊Dic11C2312yes—
173#67000C2314yes—
174#67000C2314yes—
175#67000C23116yes—
176#67000C2318yes—
177#67000C2318yes—
178#67000C2318yes—
179#66999C23116yes—
180#66999C2314yes—
181#66999C2314yes—
182#66999C23116yes—
183Q8×Dic11C2318yes—
184Q8×Dic11C2314yes—
185Q8×Dic11C2314yes—
186Q8×Dic11C2318yes—
187Q8×Dic11C2318yes—
188D4×Dic11C2314yes—
189D4×Dic11C2314yes—
190#66983C2314yes—
191#66983C2314yes—
192#66983C2318yes—
193#66983C23116yes—
194#66983C23116yes—
195#66983C2318yes—
196#66983C2318yes—
197C4×C22⋊D11C23116yes—
198C4×C22⋊D11C23116yes—
199C4×C22⋊D11C2318yes—
200C4×C22⋊D11C2318yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2318yes—
203C2×(C2×D11)⋊C4C2318yes—
204C2×(C2×D11)⋊C4C2318yes—
205C2×(C2×D11)⋊C4C2318yes—
206C2×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2318yes—
208C2×C4⋊Dic11C2318yes—
209C2×C4⋊Dic11C2314yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2318yes—
213C2×C4×Dic11C2312yes—
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2312yes—
219C2×C4×Dic11C2318yes—
220C2×C4×Dic11C2314yes—
221C2×C4×Dic11C2314yes—
222C2×C4×Dic11C2314yes—
223C2×C4×Dic11C2314yes—
224#66951C23116yes—
225#66951C23116yes—
226#66951C23116yes—
227#66951C23116yes—
228#66951C2318yes—
229#66951C23116yes—
230#66951C23116yes—
231#66951C2318yes—
232#66950C2314yes—
233#66950C2318yes—
234#66950C2318yes—
235#66950C2314yes—
236#66950C2318yes—
237#66948C2314yes—
238#66948C2314yes—
239#66948C2314yes—
240#66948C2314yes—
241#66948C2318yes—
242#66948C23116yes—
243#66947C23116yes—
244#66947C2318yes—
245#66947C23116yes—
246#66947C2318yes—
247#66947C23116yes—
248#66946C2314yes—
249#66946C2314yes—
250#66946C2314yes—
251#66946C2314yes—
252#66946C2318yes—
253#66946C2318yes—
254#66946C2318yes—
255#66946C2318yes—
256#66946C2318yes—
257#66945C23116yes—
258#66945C2314yes—
259#66945C2314yes—
260#66945C2318yes—
261#66945C2314yes—
262#66945C2314yes—
263#66945C23116yes—
264#66945C2318yes—
265#66945C23116yes—
266#66945C2318yes—
267C4⋊C4×D11C2318yes—
268#66943C2314yes—
269#66943C23116yes—
270#66943C2314yes—
271#66943C2318yes—
272#66943C2318yes—
273#66943C2318yes—
274#66943C23116yes—
275#66940C2314yes—
276#66940C2314yes—
277#66940C2314yes—
278#66940C2314yes—
279#66939C2318yes—
280#66939C23116yes—
281#66939C23116yes—
282#66939C23116yes—
283#66939C23116yes—
284#66939C23116yes—
285#66935C23116yes—
286#66935C2318yes—
287#66935C23116yes—
288(C22⋊D11)⋊C4C2318yes—
289(C22⋊D11)⋊C4C23116yes—
290(C22⋊D11)⋊C4C2318yes—
291(C22⋊D11)⋊C4C2318yes—
292(C22⋊D11)⋊C4C23116yes—
293(C22⋊D11)⋊C4C23116yes—
294(C22⋊D11)⋊C4C2318yes—
295C22⋊C4×D11C23116yes—
296#66930C2318yes—
297#66930C2318yes—
298#66930C23116yes—
299#66928C2314yes—
300#66928C2318yes—
301#66927C2312yes—
302C4×D44C2314yes—
303C4×D44C2318yes—
304C4×D44C2314yes—
305C4×D44C2318yes—
306C4×D44C2318yes—
307#66925C2318yes—
308C42×D11C2312yes—
309C42×D11C2312yes—
310C42×D11C2312yes—
311C42×D11C2312yes—
312C42×D11C2318yes—
313#66922C2312yes—
314#66922C2318yes—
315C4×Dic22C2314yes—
316C4×Dic22C2314yes—
317C4×Dic22C2318yes—
318#62781—111nomaximal, Sylow
319C24×C11C2412yes—
320C23×D11C2418yes—
321C23×D11C2411yescharacteristic
322C2×Q8×C11—48no—
323C2×Q8×C11C2414yes—
324C2×Q8×C11C2418yes—
325C2×Q8×C11C2414yes—
326C2×D4×C11#4118yescomplemented
327C2×D4×C11C2414yes—
328C22×C4×C11—44no—
329C22×C4×C11C2411yescharacteristic
330C22×C4×C11C2414yes—
331C22×C4×C11C2412yes—
332C22×C4×C11C2414yes—
333C22×C4×C11C2411yescharacteristic
334C22×C4×C11C2418yes—
335C22×C4×C11C2418yes—
336C22×C4×C11C2411yescharacteristic
337C2×C22⋊D11—28no—
338C2×C22⋊D11—232no—
339C2×C22⋊D11C2418yes—
340C2×C22⋊D11C2418yes—
341C2×C22⋊D11C24116yes—
342C22×Dic11—28no—
343C22×Dic11—44no—
344C22×Dic11C2414yes—
345C22×Dic11C2414yes—
346C22×Dic11C2418yes—
347C22×Dic11C2411yescharacteristic
348C22×Dic11C2414yes—
349C22×Dic11C2411yescharacteristic
350C22×Dic11C2412yes—
351C22×Dic11C2411yescharacteristic
352C22×Dic11C2412yes—
353C22×Dic11C2414yes—
354#4343—48no—
355#4343—48no—
356#4341—216no—
357#4341—216no—
358#4341—232no—
359D4×D11—232no—
360#4339—216no—
361C2×D44—48no—
362C2×D44C2414yes—
363C2×D44C2414yes—
364C2×D44C2414yes—
365C2×D44C2418yes—
366C2×D44C2418yes—
367C2×D44C2418yes—
368C2×C4×D11—24no—
369C2×C4×D11—42no—
370C2×C4×D11—42no—
371C2×C4×D11—416no—
372C2×C4×D11C2412yes—
373C2×C4×D11C2412yes—
374C2×C4×D11C2412yes—
375C2×C4×D11C2412yes—
376C2×C4×D11C2418yes—
377C2×C4×D11C2418yes—
378C2×C4×D11C2412yes—
379C2×C4×D11C2412yes—
380C2×C4×D11C2418yes—
381C2×C4×D11C24116yes—
382C2×Dic22—24no—
383C2×Dic22C2414yes—
384C2×Dic22C2414yes—
385C11×C4⋊C4C2414yes—
386C11×C4⋊C4C2414yes—
387C11×C4⋊C4C2414yes—
388C11×C4⋊C4C2414yes—
389C11×C4⋊C4C2418yes—
390C11×C4⋊C4C2418yes—
391C11×C4⋊C4C24116yes—
392C11×C4⋊C4C2414yes—
393C11×C4⋊C4C2418yes—
394C11×C22⋊C4C2418yes—
395C11×C22⋊C4C24116yes—
396C11×C22⋊C4C2418yes—
397C42×C11C2412yes—
398C42×C11C2412yes—
399C42×C11C2418yes—
400C22⋊Dic11C2418yes—
401(C2×D11)⋊C4C2418yes—
402(C2×D11)⋊C4C2418yes—
403(C2×D11)⋊C4C2418yes—
404(C2×D11)⋊C4C2418yes—
405(C2×D11)⋊C4C24116yes—
406(C2×D11)⋊C4C2418yes—
407(C2×D11)⋊C4C2418yes—
408(C2×D11)⋊C4C2418yes—
409(C2×D11)⋊C4C2418yes—
410(C2×D11)⋊C4C24116yes—
411(C2×D11)⋊C4C24116yes—
412(C2×D11)⋊C4C2418yes—
413(C2×D11)⋊C4C24116yes—
414C4⋊Dic11C2414yes—
415C4⋊Dic11C2414yes—
416C4⋊Dic11C2414yes—
417C4⋊Dic11C24116yes—
418C4⋊Dic11C24116yes—
419C4⋊Dic11C2418yes—
420C4⋊Dic11C2418yes—
421C4⋊Dic11C2418yes—
422Dic11⋊C4C2418yes—
423Dic11⋊C4C24116yes—
424Dic11⋊C4C2418yes—
425Dic11⋊C4C2418yes—
426Dic11⋊C4C2418yes—
427C4×Dic11C2414yes—
428C4×Dic11C2414yes—
429C4×Dic11C24116yes—
430C4×Dic11C2412yes—
431C4×Dic11C2412yes—
432C4×Dic11C2412yes—
433C4×Dic11C2412yes—
434C4×Dic11C2411yescharacteristic
435C4×Dic11C2411yescharacteristic
436C4×Dic11C2411yescharacteristic
437C4×Dic11C2411yescharacteristic
438C4×Dic11C2418yes—
439C4×Dic11C2418yes—
440C4×Dic11C2414yes—
441C4×Dic11C2414yes—
442C4×Dic11C2414yes—
443C4×Dic11C2414yes—
444#3521—118no—
445#3515—114no—
446#3514—114no—
447#3507—112no—
448#3505—114no—
449#3501D1111yescharacteristic, complemented
450#3496—111no—
451#3493—112no—
452#3491—114no—
453#3485—112no—
454#3482—114no—
455#3481—114no—
456#3475—118no—
457#3461—112no—
458#3459—114no—
459#3444—112no—
460C2×#529—114no—
461C4×H(5,𝔽2)—112no—
462C2×C4×#41—111no—
463C23×C11—42no—
464C23×C11—42no—
465C23×C11C2×#4118yes—
466C23×C11C2514yes—
467C23×C11C2511yescharacteristic
468C22×D11—22no—
469C22×D11—216no—
470C22×D11—41no—
471C22×D11—41no—
472C22×D11—48no—
473C22×D11—48no—
474C22×D11C2518yes—
475C22×D11C2512yes—
476Q8×C11—28no—
477Q8×C11—44no—
478Q8×C11—48no—
479D4×C11C2×#41116yes—
480C2×C4×C11—22no—
481C2×C4×C11—28no—
482C2×C4×C11—48no—
483C2×C4×C11—41no—
484C2×C4×C11—44no—
485C2×C4×C11—42no—
486C2×C4×C11—48no—
487C2×C4×C11C2×#4114yes—
488C2×C4×C11C2511yescharacteristic
489C2×C4×C11C2514yes—
490C2×C4×C11C2518yes—
491C2×C4×C11C2512yes—
492C2×C4×C11C2518yes—
493C2×C4×C11C2512yes—
494C2×C4×C11C2511yescharacteristic
495C22⋊D11—216no—
496C22⋊D11—232no—
497C22⋊D11—216no—
498C2×Dic11—24no—
499C2×Dic11—22no—
500C2×Dic11—28no—
501C2×Dic11—28no—
502C2×Dic11—216no—
503C2×Dic11—28no—
504C2×Dic11—22no—
505C2×Dic11—41no—
506C2×Dic11—42no—
507C2×Dic11—44no—
508C2×Dic11C2511yescharacteristic
509C2×Dic11C2512yes—
510C2×Dic11C2514yes—
511C2×Dic11C2511yescharacteristic
512C2×Dic11C2511yescharacteristic
513C2×Dic11C2518yes—
514C2×Dic11C2514yes—
515C2×Dic11C2511yescharacteristic
516D44—28no—
517D44—28no—
518D44—48no—
519D44—48no—
520D44—48no—
521D44—44no—
522C4×D11—24no—
523C4×D11—24no—
524C4×D11—216no—
525C4×D11—24no—
526C4×D11—216no—
527C4×D11—24no—
528C4×D11—42no—
529C4×D11—416no—
530C4×D11—42no—
531C4×D11—48no—
532Dic22—28no—
533Dic22—28no—
534C2×H(5,𝔽2)—112no—
535C22×#41—111no—
536#559—114no—
537#557—114no—
538#556—118no—
539#556—114no—
540#556—118no—
541#555—118no—
542#554—114no—
543#554C2×D1118yescomplemented
544#554C2×D1114yescomplemented
545#553—118no—
546#553—1116no—
547#553—118no—
548#552—118no—
549#552—118no—
550#552—1116no—
551#552—1116no—
552#552—118no—
553#551—1116no—
554#551—1116no—
555#551—1116no—
556D4×Q8C2×D1114yescomplemented
557#548—118no—
558#547—118no—
559#547—118no—
560#547—114no—
561#546—118no—
562#546—118no—
563#546—118no—
564#546—118no—
565D42—114no—
566#544C2×D1112yescomplemented
567#543C2×D1114yescomplemented
568#542—118no—
569#541—118no—
570#539—118no—
571#539—1116no—
572#539—118no—
573#538—118no—
574#538—1116no—
575#537—112no—
576#536—114no—
577#534—114no—
578#534—118no—
579#533—112no—
580#533—112no—
581#533—118no—
582#533C2×D1112yescomplemented
583#532—112no—
584#532—112no—
585#532—112no—
586#529—114no—
587#529—114no—
588#529—118no—
589#529—114no—
590#529—118no—
591#529—118no—
592#529—118no—
593#529—118no—
594#529—118no—
595#529—118no—
596#529—118no—
597#529—114no—
598#529—1116no—
599#529—114no—
600#529—114no—
601C2×#126—118no—
602C2×#125—114no—
603C2×#124—114no—
604#525—114no—
605#525—114no—
606#525—1116no—
607#525—114no—
608C2×#123—118no—
609C2×C22⋊Q8C2×D1114yescomplemented
610C2×#121—114no—
611#520—118no—
612#520—114no—
613#518—118no—
614#518—118no—
615#518C2×D1112yes—
616C4×#41—114no—
617C4×#41—114no—
618C4×#41—114no—
619C4×#41—114no—
620C4×#41—114no—
621C4×#41—114no—
622C4×#41—118no—
623C4×#41—114no—
624C2×C4×Q8—114no—
625C2×C4×Q8—111no—
626C2×C4×Q8—111no—
627C2×C4×D4—111no—
628C2×C4×D4—112no—
629C2×C4×D4—118no—
630C2×C4×D4—114no—
631C2×C4×D4—112no—
632C2×C4×D4—118no—
633C2×C4×D4C2×D1111yescharacteristic
634C2×#117—111no—
635C2×#117—118no—
636C2×#117—112no—
637C22×C42—112no—
638C22×C42—111no—
639C22×C11—24no—
640C22×C11—21no—
641C22×C11—24no—
642C22×C11—21no—
643C22×C11—48no—
644C22×C11C22×#4112yes—
645C22×C11C22×#4118yes—
646C22×C11C2611yescharacteristic
647C2×D11—28no—
648C2×D11—22no—
649C2×D11—28no—
650C2×D11—28no—
651C2×D11—22no—
652C2×D11—22no—
653C2×D11—44no—
654C2×D11—816no—
655C4×C11—21no—
656C4×C11—24no—
657C4×C11—28no—
658C4×C11—28no—
659C4×C11—22no—
660C4×C11C22×#4114yes—
661C4×C11#58512yes—
662Dic11—24no—
663Dic11—28no—
664Dic11—21no—
665Dic11—21no—
666Dic11—22no—
667Dic11—24no—
668Dic11—21no—
669Dic11#58512yes—
670H(5,𝔽2)—2216no—
671C2×#41—114no—
672C2×#41—114no—
673C2×#41—114no—
674C2×#41—114no—
675C2×#41—118no—
676C2×#41—114no—
677C2×#41—228no—
678C22×Q8—111no—
679C22×Q8C22×D1114yes—
680C22×D4—112no—
681C22×D4—118no—
682C22×D4—118no—
683C22×D4—114no—
684C22×D4C22×D1111yescharacteristic
685C23×C4—112no—
686C23×C4—112no—
687C23×C4—111no—
688C23×C4—118no—
689C23×C4—111no—
690C23×C4—111no—
691C23×C4C22×D1112yes—
692C4⋊Q8—112no—
693C4⋊Q8—118no—
694C4⋊Q8C22×D1112yes—
695C4⋊Q8C22×D1112yes—
696C4⋊Q8C22×D1118yes—
697#127—112no—
698#126—118no—
699#126—1116no—
700#126—1116no—
701#126—1116no—
702#126—118no—
703#126—1116no—
704#126—1116no—
705#126—1116no—
706#125—114no—
707#125—118no—
708#125—118no—
709#125—118no—
710#125—114no—
711#125—1116no—
712#125—1116no—
713#125C22×D1114yes—
714#125C22×D1118yes—
715#124—114no—
716#124—118no—
717#124—118no—
718#124—118no—
719#124—114no—
720#124—1116no—
721#124—114no—
722#124—118no—
723#123—118no—
724#123—118no—
725#123—1116no—
726#123—1116no—
727#123—1116no—
728#123—118no—
729#123—1116no—
730#123—1116no—
731#123—1116no—
732#123—1116no—
733#123—1116no—
734C22⋊Q8—114no—
735C22⋊Q8—114no—
736C22⋊Q8—1116no—
737C22⋊Q8—1116no—
738C22⋊Q8—114no—
739C22⋊Q8—114no—
740C22⋊Q8—118no—
741C22⋊Q8—118no—
742C22⋊Q8—118no—
743C22⋊Q8C22×D1114yes—
744C22⋊Q8C22×D1118yes—
745C22⋊Q8C22×D1118yes—
746C22⋊Q8C22×D1118yes—
747C22⋊Q8C22×D1114yes—
748C22⋊Q8C22×D11116yes—
749C22⋊Q8C22×D11116yes—
750#121—114no—
751#121—118no—
752#121—118no—
753#121—118no—
754#121—114no—
755#121—1116no—
756#121—1116no—
757#121—114no—
758#121—114no—
759#121—114no—
760#121—114no—
761#121—1116no—
762#121—118no—
763#120—118no—
764#120—1116no—
765#120—1116no—
766C4×Q8—114no—
767C4×Q8—118no—
768C4×Q8—118no—
769C4×Q8—118no—
770C4×Q8—114no—
771C4×Q8—114no—
772C4×Q8—114no—
773C4×Q8—114no—
774C4×Q8—114no—
775C4×Q8—114no—
776C4×Q8—114no—
777C4×Q8—118no—
778C4×Q8C22×D1114yes—
779C4×Q8C22×D1114yes—
780C4×D4—114no—
781C4×D4—114no—
782C4×D4—118no—
783C4×D4—118no—
784C4×D4—1116no—
785C4×D4—1116no—
786C4×D4—114no—
787C4×D4—114no—
788C4×D4—118no—
789C4×D4—118no—
790C4×D4—118no—
791C4×D4—114no—
792C4×D4—118no—
793C4×D4—118no—
794C4×D4—114no—
795C4×D4—1116no—
796C4×D4—118no—
797C4×D4—118no—
798C4×D4—118no—
799C4×D4—1116no—
800C4×D4—1116no—
801C4×D4—118no—
802C4×D4—118no—
803C4×D4—118no—
804C4×D4—118no—
805C4×D4—114no—
806C4×D4—114no—
807C4×D4C22×D1118yes—
808C4×D4C22×D1114yes—
809C4×D4C22×D1114yes—
810C4×D4C22×D1118yes—
811#117—118no—
812#117—114no—
813#117—114no—
814#117—1116no—
815#117—1116no—
816#117—1116no—
817#117—118no—
818#117—114no—
819#117—114no—
820#117—118no—
821#117—118no—
822#117—118no—
823#117—1116no—
824#117—118no—
825#117C22×D1114yes—
826C2×C4⋊C4—111no—
827C2×C4⋊C4—112no—
828C2×C4⋊C4—112no—
829C2×C4⋊C4—118no—
830C2×C4⋊C4—118no—
831C2×C4⋊C4—114no—
832C2×C4⋊C4—118no—
833C2×C4⋊C4—118no—
834C2×C4⋊C4C22×D1111yescharacteristic
835C2×C4⋊C4C22×D1118yes—
836C2×C4⋊C4C22×D1114yes—
837C2×C22⋊C4—112no—
838C2×C22⋊C4—112no—
839C2×C22⋊C4—118no—
840C2×C22⋊C4—118no—
841C2×C22⋊C4—118no—
842C2×C22⋊C4—118no—
843C2×C22⋊C4—1116no—
844C2×C22⋊C4C22×D1112yes—
845C2×C22⋊C4C22×D1118yes—
846C2×C42—114no—
847C2×C42—112no—
848C2×C42—111no—
849C2×C42—118no—
850C2×C42—111no—
851C2×C42—114no—
852C2×C42—112no—
853C2×C42—112no—
854C2×C42—114no—
855C2×C42—114no—
856C2×C42—111no—
857C2×C42—118no—
858C2×C42—112no—
859C2×C42—112no—
860C2×C42—112no—
861C2×C42—112no—
862C2×C42C22×D1111yescharacteristic
863C2×C11—22no—
864C2×C11—28no—
865C2×C11C23×#4111yescharacteristic
866C2×C11C2×#58511yescharacteristic
867C2×C11C2×#58511yescharacteristic
868D11—42no—
869D11—48no—
870C24—118no—
871C24—111no—
872C24C23×D1112yes—
873#41—2216no—
874#41—2216no—
875#41—2232no—
876#41—2216no—
877#41—448no—
878#41—448no—
879C2×Q8—48no—
880C2×Q8—114no—
881C2×Q8—114no—
882C2×Q8—224no—
883C2×Q8C23×D1114yes—
884C2×Q8C23×D1118yes—
885C2×Q8C23×D1114yes—
886C2×D4—118no—
887C2×D4—1116no—
888C2×D4—118no—
889C2×D4—114no—
890C2×D4—114no—
891C2×D4—114no—
892C2×D4—118no—
893C2×D4—118no—
894C2×D4—118no—
895C2×D4—228no—
896C2×D4—2232no—
897C2×D4—2232no—
898C2×D4—448no—
899C2×D4#434318yescomplemented
900C2×D4C23×D1114yes—
901C22×C4—44no—
902C22×C4—114no—
903C22×C4—111no—
904C22×C4—111no—
905C22×C4—114no—
906C22×C4—114no—
907C22×C4—112no—
908C22×C4—118no—
909C22×C4—114no—
910C22×C4—111no—
911C22×C4—112no—
912C22×C4—112no—
913C22×C4—112no—
914C22×C4—112no—
915C22×C4—112no—
916C22×C4—118no—
917C22×C4—118no—
918C22×C4—112no—
919C22×C4—112no—
920C22×C4—118no—
921C22×C4—1116no—
922C22×C4—228no—
923C22×C4—224no—
924C22×C4—442no—
925C22×C4—4416no—
926C22×C4—442no—
927C22×C4—444no—
928C22×C4C23×D1111yescharacteristic
929C22×C4C23×D1114yes—
930C22×C4C23×D1114yes—
931C22×C4C23×D1112yes—
932C22×C4C23×D1111yescharacteristic
933C22×C4C23×D1118yes—
934C22×C4C23×D1118yes—
935C22×C4C23×D1111yescharacteristic
936C4⋊C4—114no—
937C4⋊C4—118no—
938C4⋊C4—118no—
939C4⋊C4—1116no—
940C4⋊C4—114no—
941C4⋊C4—118no—
942C4⋊C4—118no—
943C4⋊C4—118no—
944C4⋊C4—1116no—
945C4⋊C4—118no—
946C4⋊C4—1116no—
947C4⋊C4—118no—
948C4⋊C4—114no—
949C4⋊C4C23×D1114yes—
950C4⋊C4C23×D1118yes—
951C4⋊C4C23×D1114yes—
952C4⋊C4C23×D1114yes—
953C4⋊C4C23×D11116yes—
954C4⋊C4C23×D1118yes—
955C4⋊C4C23×D1114yes—
956C4⋊C4C23×D1114yes—
957C4⋊C4C23×D1118yes—
958C22⋊C4—118no—
959C22⋊C4—118no—
960C22⋊C4—118no—
961C22⋊C4—118no—
962C22⋊C4—118no—
963C22⋊C4—118no—
964C22⋊C4—1116no—
965C22⋊C4—118no—
966C22⋊C4—1116no—
967C22⋊C4—1116no—
968C22⋊C4—1116no—
969C22⋊C4—118no—
970C22⋊C4—118no—
971C22⋊C4—118no—
972C22⋊C4C23×D11116yes—
973C22⋊C4C23×D1118yes—
974C22⋊C4C23×D1118yes—
975C42—111no—
976C42—112no—
977C42—111no—
978C42—111no—
979C42—111no—
980C42—114no—
981C42—112no—
982C42—114no—
983C42—118no—
984C42—112no—
985C42—114no—
986C42—112no—
987C42—114no—
988C42—114no—
989C42—114no—
990C42—118no—
991C42—1116no—
992C42C23×D1112yes—
993C42C23×D1112yes—
994C42C23×D1118yes—
995C11#6278111yescharacteristic, complemented, Sylow
996C23—42no—
997C23—42no—
998C23—118no—
999C23—112no—
1000C23—222no—
1001C23—2216no—
1002C23—441no—
1003C23—441no—
1004C23—448no—
1005C23—448no—
1006C23C2×#434318yes—
1007C23C24×D1114yes—
1008C23C24×D1111yescharacteristic
1009Q8—28no—
1010Q8—48no—
1011Q8—44no—
1012Q8—228no—
1013Q8—228no—
1014D4—2232no—
1015D4—2216no—
1016D4—2216no—
1017D4—228no—
1018D4—228no—
1019D4—448no—
1020D4—448no—
1021D4—444no—
1022D4—448no—
1023D4C2×#4343116yes—
1024C2×C4—22no—
1025C2×C4—28no—
1026C2×C4—44no—
1027C2×C4—42no—
1028C2×C4—48no—
1029C2×C4—41no—
1030C2×C4—48no—
1031C2×C4—111no—
1032C2×C4—111no—
1033C2×C4—111no—
1034C2×C4—111no—
1035C2×C4—114no—
1036C2×C4—112no—
1037C2×C4—114no—
1038C2×C4—118no—
1039C2×C4—2216no—
1040C2×C4—224no—
1041C2×C4—228no—
1042C2×C4—222no—
1043C2×C4—222no—
1044C2×C4—224no—
1045C2×C4—228no—
1046C2×C4—228no—
1047C2×C4—2216no—
1048C2×C4—224no—
1049C2×C4—224no—
1050C2×C4—2216no—
1051C2×C4—224no—
1052C2×C4—4416no—
1053C2×C4—442no—
1054C2×C4—442no—
1055C2×C4—448no—
1056C2×C4—444no—
1057C2×C4—442no—
1058C2×C4—441no—
1059C2×C4C2×#434314yes—
1060C2×C4C24×D1111yescharacteristic
1061C2×C4C24×D1114yes—
1062C2×C4C24×D1118yes—
1063C2×C4C24×D1112yes—
1064C2×C4C24×D1118yes—
1065C2×C4C24×D1112yes—
1066C2×C4C24×D1111yescharacteristic
1067C22—24no—
1068C22—21no—
1069C22—24no—
1070C22—21no—
1071C22—48no—
1072C22—222no—
1073C22—228no—
1074C22—228no—
1075C22—222no—
1076C22—222no—
1077C22—228no—
1078C22—444no—
1079C22—8816no—
1080C22C22×#434318yes—
1081C22C22×#434312yes—
1082C22C25×D1111yescharacteristic
1083C4—28no—
1084C4—22no—
1085C4—21no—
1086C4—24no—
1087C4—28no—
1088C4—112no—
1089C4—221no—
1090C4—221no—
1091C4—228no—
1092C4—224no—
1093C4—224no—
1094C4—221no—
1095C4—222no—
1096C4C22×#434314yes—
1097C4#1062345512yes—
1098C2—22no—
1099C2—28no—
1100C2—442no—
1101C2—448no—
1102C2C23×#434311yescharacteristic
1103C2D11×#58511yescharacteristic
1104C2C2×#1062345511yescharacteristic
subgroupG/H
center, FrattiniC22C25×D11
commutator, socle, cosocleC22×C11C26
FittingC11×#3501C2
hypercenter#3501D11
hypocenterC11#62781
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13082687C2semidirect
2. #13082595C2semidirect
3. #13082578C2semidirect
4. #13082483C2semidirect
5. #13082457C2semidirect
6. #13082380C2semidirect
7. #13082337C2semidirect
8. #13082315C2semidirect
9. #13082261C2semidirect
10. #13082237C2semidirect
11. #13082227C2semidirect
12. #13082182C2semidirect
13. #13082050C2semidirect
14. #13082028C2semidirect
15. #13081913C2semidirect
16. C2×#10623155C2semidirect
17. #13081820C2semidirect
18. C2×C4×#4341C2semidirect
19. C11×#3501C2semidirect
22. C11×#554C22semidirect
23. C11×#554C22semidirect
24. D4×Q8×C11C22semidirect
25. C11×#544C22semidirect
26. C11×#543C22semidirect
27. C11×#533C22semidirect
28. C2×C11×C22⋊Q8C22semidirect
31. #10623348C22semidirect
32. C2×#67000C22semidirect
33. C2×Q8×Dic11C22semidirect
36. C2×C4×C22⋊D11C22semidirect
37. C22×C4×Dic11C22semidirect
38. #10623265C22semidirect
39. #10623264C22semidirect
40. #10623263C22semidirect
41. #10623263C22semidirect
42. #10623261C22semidirect
43. #10623259C22semidirect
44. #10623259C22semidirect
45. #10623259C22semidirect
46. #10623256C22semidirect
47. #10623256C22semidirect
48. #10623228C22semidirect
49. #10623226C22semidirect
50. #10623225C22semidirect
51. #10623225C22semidirect
52. #10623222C22semidirect
53. #10623222C22semidirect
54. #10623222C22semidirect
55. #10623176C22semidirect
56. #10623176C22semidirect
57. #10623176C22semidirect
58. #10623175C22semidirect
59. #10623175C22semidirect
60. #10623173C22semidirect
61. #10623173C22semidirect
62. #10623173C22semidirect
63. #10623168C22semidirect
64. #10623168C22semidirect
65. #10623168C22semidirect
66. #10623161C22semidirect
67. #10623158C22semidirect
68. #10623158C22semidirect
69. #10623158C22semidirect
70. #10623155C22semidirect
71. #10623155C22semidirect
72. #10623155C22semidirect
73. #10623155C22semidirect
74. #10623155C22semidirect
75. #10623155C22semidirect
76. #10623155C22semidirect
77. #10623155C22semidirect
78. #10623155C22semidirect
79. #10623155C22semidirect
80. #10623116C22semidirect
81. #10623115C22semidirect
82. #10623111C22semidirect
83. #10623111C22semidirect
84. C4×#4343C22semidirect
85. C4×#4343C22semidirect
86. #10623101C22semidirect
87. #10623086C22semidirect
88. #10623086C22semidirect
89. #10623086C22semidirect
90. #10623085C22semidirect
91. #10623085C22semidirect
92. #10623085C22semidirect
93. D4×D44C22semidirect
94. #10623077C22semidirect
95. #10623076C22semidirect
96. C4×D4×D11C22semidirect
97. C4×#4341C22semidirect
98. C4×#4341C22semidirect
99. C4×#4341C22semidirect
100. C4×#4341C22semidirect
101. C4×#4341C22semidirect
102. #10623057C22semidirect
103. #10623055C22semidirect
104. #10623054C22semidirect
105. #10623053C22semidirect
106. #10623045C22semidirect
107. #10623045C22semidirect
108. C2×#66951C22semidirect
110. C2×#66946C22semidirect
111. C2×#66945C22semidirect
112. C2×#66945C22semidirect
113. C2×#66943C22semidirect
114. C2×#66940C22semidirect
116. #10623024C22semidirect
117. C2×#66939C22semidirect
118. #10623017C22semidirect
119. C2×(C22⋊D11)⋊C4C22semidirect
120. C2×(C22⋊D11)⋊C4C22semidirect
121. C2×#66930C22semidirect
123. C2×C42×D11C22semidirect
124. C2×C4×Dic22C22semidirect
326. C2×D4×C11#41semidirect
449. #3501D11semidirect
543. #554C2×D11semidirect
544. #554C2×D11semidirect
556. D4×Q8C2×D11semidirect
566. #544C2×D11semidirect
567. #543C2×D11semidirect
582. #533C2×D11semidirect
609. C2×C22⋊Q8C2×D11semidirect
899. C2×D4#4343semidirect
995. C11#62781semidirect

Maximal subgroups

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

subgroupindex
#130826872
#130825952
#130825782
#130824832
#130824572
#130823802
#130823372
#130823152
#130822612
#130822372
#130822272
#130821822
#130820502
#130820282
#130819132
C2×#106231552
#130818202
C2×C4×#43412
C11×#35012
#6278111