Finite Group Databasebeta

← #15661924

Subgroups — #15661924

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#13082673C218yesmaximal, complemented
2#13082585C214yesmaximal, complemented
3#13082568C214yesmaximal, complemented
4#13082478C212yesmaximal, complemented
5#13082450C214yesmaximal, complemented
6#13082419C211yesmaximal, characteristic, complemented
7#13082335C212yesmaximal, complemented
8#13082313C214yesmaximal, complemented
9#13082256C212yesmaximal, complemented
10#13082228C214yesmaximal, complemented
11#13082217C214yesmaximal, complemented
12#13082167C218yesmaximal, complemented
13#13082044C212yesmaximal, complemented
14#13082022C214yesmaximal, complemented
15#13081911C212yesmaximal, complemented
16C2×#10623131C214yesmaximal, complemented
17H(5,𝔽2)×Dic11C212yesmaximal, complemented
18C2×C4×#4341C211yesmaximal, characteristic, complemented
19C11×#3496C211yesmaximal, characteristic, complemented
20C2×C11×H(5,𝔽2)C2212yes—
21C22×#4341C2211yescharacteristic
22C11×#547C2214yescomplemented
23C11×#546C2218yescomplemented
24D42×C11C2214yescomplemented
25C11×#537C2212yes—
26C11×#534C2214yes—
27C11×#532C2212yes—
28C2×C11×#121C2214yes—
29C2×C4×D4×C11C2211yescharacteristic
30#10623359C2214yescomplemented
31#10623358C2218yescomplemented
32#10623358C2214yescomplemented
33#41×Dic11C2214yescomplemented
34#41×Dic11C2218yescomplemented
35#10623356C2214yescomplemented
36#10623355C2218yescomplemented
37#10623355C2218yescomplemented
38#10623337C2218yescomplemented
39#10623337C2218yescomplemented
40#10623337C2218yescomplemented
41#10623335C2218yescomplemented
42#10623329C2212yes—
43#10623329C2218yescomplemented
44#10623329C2218yescomplemented
45C2×#66989C2214yescomplemented
46C2×#66988C2218yescomplemented
47C2×D4×Dic11C2211yescharacteristic
48C2×D4×Dic11C2214yescomplemented
49C2×D4×Dic11C2218yescomplemented
50C2×D4×Dic11C2218yescomplemented
51C2×C4×C22⋊D11C2212yescomplemented
52C2×#66977C2214yescomplemented
53C22×C4×Dic11C2212yescomplemented
54#10623259C2212yescomplemented
55#10623259C2212yescomplemented
56#10623252C2214yescomplemented
57#10623247C2212yescomplemented
58#10623247C2212yescomplemented
59#10623244C2214yescomplemented
60#10623211C2214yescomplemented
61#10623211C2214yescomplemented
62#10623202C2218yescomplemented
63#10623196C22116yescomplemented
64#10623181C22116yescomplemented
65#10623181C22116yescomplemented
66#10623180C22116yescomplemented
67#10623173C2218yescomplemented
68#10623172C2218yescomplemented
69#10623156C2218yescomplemented
70#10623153C2218yescomplemented
71#10623149C2218yescomplemented
72#10623149C2218yescomplemented
73#10623148C2218yescomplemented
74#10623147C2218yescomplemented
75#10623137C2214yescomplemented
76#10623137C2214yescomplemented
77#10623134C2218yescomplemented
78#10623133C2218yescomplemented
79#10623133C2218yescomplemented
80#10623132C22116yescomplemented
81#10623131C2214yescomplemented
82#10623131C2218yescomplemented
83#10623131C2218yescomplemented
84#10623131C2218yescomplemented
85#10623131C2218yescomplemented
86#10623131C2218yescomplemented
87#10623131C2218yescomplemented
88#10623131C2218yescomplemented
89#10623131C2214yescomplemented
90#10623131C2218yescomplemented
91#10623129C2218yescomplemented
92#10623124C22116yescomplemented
93#10623118C22116yescomplemented
94#10623118C22116yescomplemented
95#10623117C22116yescomplemented
96#10623088C2214yescomplemented
97#10623088C2214yescomplemented
98#10623074C2214yescomplemented
99#10623074C2214yescomplemented
100#10623073C2214yescomplemented
101#10623072C2218yescomplemented
102#10623070C2218yescomplemented
103D4×Dic22C2214yescomplemented
104C4×#4341C2214yescomplemented
105C4×#4341C2214yescomplemented
106C4×#4341C2214yescomplemented
107C4×#4341C2214yescomplemented
108C4×#4341C2214yescomplemented
109C4×#4341C2214yescomplemented
110#10623044C2218yescomplemented
111C2×#66945C2211yescharacteristic, complemented
112#10623031C2212yescomplemented
113C2×#66943C2214yescomplemented
114C2×#66940C2214yescomplemented
115C2×#66940C2211yescharacteristic, complemented
116#10623026C22116yescomplemented
117C2×(C22⋊D11)⋊C4C2212yescomplemented
118#10623014C2214yescomplemented
119C2×#66932C2218yescomplemented
120C2×#66930C2218yescomplemented
121C2×#66930C2212yescomplemented
122C2×C42×D11C2211yescharacteristic, complemented
123#10623001C2212yescomplemented
124C2×C4×Dic22C2211yescharacteristic, complemented
125C11×H(5,𝔽2)—216no—
126C2×C11×#41C2318yes—
127C2×C11×#41C2314yes—
128C22×D4×C11C2318yes—
129C22×D4×C11C2318yes—
130C22×D4×C11C2314yes—
131C22×D4×C11C2311yescharacteristic
132C23×C4×C11C2312yes—
133C22×C22⋊D11C2312yes—
134C23×Dic11C2312yes—
135C23×Dic11C2318yes—
136C23×Dic11C2312yes—
137C2×#4341—28no—
138C2×#4341C2314yes—
139C2×#4341C2314yes—
140C2×#4341C2314yes—
141C2×#4341C2314yes—
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×Dic22C2311yescharacteristic
146C22×Dic22C2314yes—
147C11×C4⋊Q8C2312yes—
148C11×#127C2312yes—
149C11×#124C2314yes—
150C11×#123C23116yes—
151C11×C22⋊Q8C2318yes—
152C11×#121C2314yes—
153C11×#121C2318yes—
154C11×#121C2318yes—
155C11×#121C2318yes—
156C11×#121C2314yes—
157C11×#121C2318yes—
158C11×#120C23116yes—
159C4×D4×C11C2314yes—
160C4×D4×C11C2314yes—
161C4×D4×C11C2314yes—
162C4×D4×C11C2314yes—
163C2×C11×C4⋊C4C2314yes—
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4C2318yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C42×C11C2311yescharacteristic
168#67006C23116yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2318yes—
171C2×C22⋊Dic11C2318yes—
172C2×C22⋊Dic11C2318yes—
173C2×C22⋊Dic11C2318yes—
174C2×C22⋊Dic11C23116yes—
175#66999C2314yes—
176#66999C2314yes—
177Q8×Dic11C2318yes—
178Q8×Dic11C2314yes—
179Q8×Dic11C2314yes—
180#66997C2318yes—
181#66992C23116yes—
182#66992C23116yes—
183#66992C23116yes—
184#66991C2314yes—
185#66991C2314yes—
186#66991C2314yes—
187#66991C2314yes—
188#66990C2318yes—
189#66989C2318yes—
190#66989C2318yes—
191#66989C2314yes—
192#66989C2314yes—
193#66989C2318yes—
194#66989C2318yes—
195#66988C23116yes—
196#66988C2318yes—
197#66988C23116yes—
198#66988C23116yes—
199#66988C23116yes—
200#66988C23116yes—
201D4×Dic11C2318yes—
202D4×Dic11C2318yes—
203D4×Dic11C2314yes—
204D4×Dic11C2314yes—
205D4×Dic11C2314yes—
206D4×Dic11C2314yes—
207D4×Dic11C2314yes—
208D4×Dic11C2314yes—
209D4×Dic11C2318yes—
210D4×Dic11C2318yes—
211D4×Dic11C23116yes—
212D4×Dic11C2318yes—
213D4×Dic11C23116yes—
214D4×Dic11C23116yes—
215D4×Dic11C23116yes—
216D4×Dic11C2318yes—
217D4×Dic11C2318yes—
218D4×Dic11C23116yes—
219D4×Dic11C2318yes—
220#66982C23116yes—
221C4×C22⋊D11C2318yes—
222C4×C22⋊D11C2318yes—
223C4×C22⋊D11C2318yes—
224C4×C22⋊D11C2318yes—
225C2×(C2×D11)⋊C4C2312yes—
226#66979C2314yes—
227#66979C23116yes—
228#66979C2318yes—
229#66979C2318yes—
230C2×C4⋊Dic11C2311yescharacteristic
231C2×C4⋊Dic11C2318yes—
232C2×C4⋊Dic11C2314yes—
233C2×C4⋊Dic11C2318yes—
234#66977C2314yes—
235#66977C2314yes—
236#66977C2318yes—
237#66977C2318yes—
238#66977C2318yes—
239#66977C2318yes—
240#66977C2318yes—
241C2×Dic11⋊C4C2312yes—
242C2×Dic11⋊C4C2318yes—
243C2×Dic11⋊C4C2312yes—
244C2×Dic11⋊C4C2318yes—
245C2×Dic11⋊C4C2318yes—
246C2×C4×Dic11C2312yes—
247C2×C4×Dic11C2311yescharacteristic
248C2×C4×Dic11C2311yescharacteristic
249C2×C4×Dic11C2311yescharacteristic
250C2×C4×Dic11C2314yes—
251C2×C4×Dic11C2318yes—
252C2×C4×Dic11C2312yes—
253C2×C4×Dic11C2314yes—
254C2×C4×Dic11C2312yes—
255C2×C4×Dic11C2314yes—
256C2×C4×Dic11C2314yes—
257C2×C4×Dic11C2318yes—
258#66951C23116yes—
259#66950C2314yes—
260#66950C2314yes—
261#66945C2314yes—
262#66945C2314yes—
263#66945C2314yes—
264#66945C2314yes—
265#66943C2318yes—
266#66943C2314yes—
267#66943C2314yes—
268#66943C2318yes—
269#66943C2318yes—
270#66943C2318yes—
271#66942C23116yes—
272#66942C23116yes—
273#66941C2318yes—
274#66940C2318yes—
275#66940C2314yes—
276#66940C2314yes—
277#66940C2314yes—
278#66940C2314yes—
279#66940C2318yes—
280#66940C2318yes—
281#66939C23116yes—
282#66938C23116yes—
283#66936C2318yes—
284#66936C2318yes—
285(C22⋊D11)⋊C4C2318yes—
286(C22⋊D11)⋊C4C2318yes—
287(C22⋊D11)⋊C4C2318yes—
288(C22⋊D11)⋊C4C2318yes—
289#66932C2318yes—
290#66932C23116yes—
291#66932C23116yes—
292#66932C23116yes—
293#66932C23116yes—
294#66932C23116yes—
295#66932C2318yes—
296#66931C23116yes—
297#66931C23116yes—
298#66931C23116yes—
299#66931C23116yes—
300#66930C2318yes—
301#66930C23116yes—
302#66930C2318yes—
303#66930C2318yes—
304#66930C23116yes—
305#66930C23116yes—
306#66930C2318yes—
307C42×D11C2312yes—
308C42×D11C2312yes—
309C42×D11C2312yes—
310C42×D11C2312yes—
311#66923C2314yes—
312#66922C2312yes—
313#66922C2312yes—
314C4×Dic22C2314yes—
315C4×Dic22C2314yes—
316C4×Dic22C2314yes—
317C4×Dic22C2314yes—
318#62781—111nomaximal, Sylow
319C24×C11C2418yes—
320C24×C11C2412yes—
321C23×D11C2411yescharacteristic
322C11×#41—232no—
323C11×#41—216no—
324C2×Q8×C11C2414yes—
325C2×D4×C11—232no—
326C2×D4×C11—232no—
327C2×D4×C11—48no—
328C2×D4×C11#4118yescomplemented
329C2×D4×C11C2418yes—
330C2×D4×C11C24116yes—
331C2×D4×C11C2414yes—
332C2×D4×C11C2414yes—
333C2×D4×C11C2418yes—
334C2×D4×C11C2414yes—
335C2×D4×C11C2414yes—
336C22×C4×C11—44no—
337C22×C4×C11C2411yescharacteristic
338C22×C4×C11C2414yes—
339C22×C4×C11C2418yes—
340C22×C4×C11C2418yes—
341C22×C4×C11C2414yes—
342C22×C4×C11C2412yes—
343C22×C4×C11C2411yescharacteristic
344C22×C4×C11C2411yescharacteristic
345C2×C22⋊D11—28no—
346C2×C22⋊D11C2418yes—
347C2×C22⋊D11C2418yes—
348C2×C22⋊D11C2418yes—
349C22×Dic11—28no—
350C22×Dic11—44no—
351C22×Dic11—416no—
352C22×Dic11C2418yes—
353C22×Dic11C2414yes—
354C22×Dic11C2414yes—
355C22×Dic11C2414yes—
356C22×Dic11C2411yescharacteristic
357C22×Dic11C2411yescharacteristic
358C22×Dic11C2412yes—
359C22×Dic11C24116yes—
360C22×Dic11C2418yes—
361C22×Dic11C2418yes—
362C22×Dic11C2418yes—
363C22×Dic11C2414yes—
364C22×Dic11C2411yescharacteristic
365C22×Dic11C2412yes—
366#4341—216no—
367#4341—216no—
368#4341—48no—
369#4341—48no—
370C2×C4×D11—24no—
371C2×C4×D11—42no—
372C2×C4×D11—42no—
373C2×C4×D11C2412yes—
374C2×C4×D11C2412yes—
375C2×C4×D11C2412yes—
376C2×C4×D11C2412yes—
377C2×C4×D11C2412yes—
378C2×C4×D11C2412yes—
379C2×Dic22—24no—
380C2×Dic22—48no—
381C2×Dic22C2414yes—
382C2×Dic22C2414yes—
383C2×Dic22C2414yes—
384C2×Dic22C2418yes—
385C11×C4⋊C4C2414yes—
386C11×C4⋊C4C2414yes—
387C11×C4⋊C4C2418yes—
388C11×C4⋊C4C2414yes—
389C11×C22⋊C4C2418yes—
390C11×C22⋊C4C2418yes—
391C11×C22⋊C4C24116yes—
392C11×C22⋊C4C2418yes—
393C42×C11C2412yes—
394C42×C11C2412yes—
395C22⋊Dic11C2418yes—
396C22⋊Dic11C24116yes—
397C22⋊Dic11C2418yes—
398C22⋊Dic11C2418yes—
399C22⋊Dic11C24116yes—
400C22⋊Dic11C24116yes—
401C22⋊Dic11C2418yes—
402C22⋊Dic11C2418yes—
403C22⋊Dic11C24116yes—
404C22⋊Dic11C2418yes—
405(C2×D11)⋊C4C2418yes—
406(C2×D11)⋊C4C2418yes—
407(C2×D11)⋊C4C2418yes—
408C4⋊Dic11C2414yes—
409C4⋊Dic11C2414yes—
410C4⋊Dic11C2414yes—
411C4⋊Dic11C2414yes—
412C4⋊Dic11C2414yes—
413C4⋊Dic11C2418yes—
414C4⋊Dic11C2418yes—
415C4⋊Dic11C24116yes—
416C4⋊Dic11C2418yes—
417Dic11⋊C4C2418yes—
418Dic11⋊C4C2418yes—
419Dic11⋊C4C2418yes—
420Dic11⋊C4C2418yes—
421Dic11⋊C4C2418yes—
422Dic11⋊C4C24116yes—
423Dic11⋊C4C24116yes—
424Dic11⋊C4C2418yes—
425Dic11⋊C4C24116yes—
426C4×Dic11C2414yes—
427C4×Dic11C2414yes—
428C4×Dic11C2418yes—
429C4×Dic11C2412yes—
430C4×Dic11C2411yescharacteristic
431C4×Dic11C2412yes—
432C4×Dic11C2411yescharacteristic
433C4×Dic11C2411yescharacteristic
434C4×Dic11C2412yes—
435C4×Dic11C2412yes—
436C4×Dic11C2411yescharacteristic
437C4×Dic11C2414yes—
438C4×Dic11C2414yes—
439C4×Dic11C2418yes—
440C4×Dic11C2414yes—
441C4×Dic11C24116yes—
442C4×Dic11C2418yes—
443C4×Dic11C2414yes—
444#3521—118no—
445#3515—114no—
446#3514—114no—
447#3507—112no—
448#3505—114no—
449#3501—111no—
450#3496D1111yescharacteristic, complemented
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—216no—
464C23×C11—42no—
465C23×C11—42no—
466C23×C11—48no—
467C23×C11—48no—
468C23×C11C2×#4118yes—
469C23×C11C2518yes—
470C23×C11C2511yescharacteristic
471C23×C11C2514yes—
472C22×D11—22no—
473C22×D11—41no—
474C22×D11—41no—
475C22×D11C2512yes—
476Q8×C11—28no—
477D4×C11—232no—
478D4×C11—216no—
479D4×C11—28no—
480D4×C11—28no—
481D4×C11—44no—
482D4×C11—48no—
483D4×C11C2×#41116yes—
484C2×C4×C11—216no—
485C2×C4×C11—216no—
486C2×C4×C11—28no—
487C2×C4×C11—22no—
488C2×C4×C11—41no—
489C2×C4×C11—44no—
490C2×C4×C11—42no—
491C2×C4×C11C2×#4114yes—
492C2×C4×C11C2511yescharacteristic
493C2×C4×C11C2518yes—
494C2×C4×C11C2514yes—
495C2×C4×C11C2512yes—
496C2×C4×C11C2512yes—
497C2×C4×C11C2511yescharacteristic
498C22⋊D11—216no—
499C22⋊D11—48no—
500C22⋊D11—48no—
501C2×Dic11—24no—
502C2×Dic11—22no—
503C2×Dic11—28no—
504C2×Dic11—28no—
505C2×Dic11—22no—
506C2×Dic11—216no—
507C2×Dic11—28no—
508C2×Dic11—48no—
509C2×Dic11—41no—
510C2×Dic11—48no—
511C2×Dic11—48no—
512C2×Dic11—416no—
513C2×Dic11—44no—
514C2×Dic11—42no—
515C2×Dic11C2511yescharacteristic
516C2×Dic11C2511yescharacteristic
517C2×Dic11C2512yes—
518C2×Dic11C2514yes—
519C2×Dic11C2511yescharacteristic
520C2×Dic11C2514yes—
521C2×Dic11C2518yes—
522C2×Dic11C2518yes—
523C2×Dic11C2511yescharacteristic
524C4×D11—24no—
525C4×D11—24no—
526C4×D11—24no—
527C4×D11—24no—
528C4×D11—42no—
529C4×D11—42no—
530Dic22—28no—
531Dic22—28no—
532Dic22—48no—
533Dic22—44no—
534C2×H(5,𝔽2)C2×D1112yes—
535C22×#41—111no—
536#559—114no—
537#557—114no—
538#556—118no—
539#556—118no—
540#556—114no—
541#555—118no—
542#554—118no—
543#554—114no—
544#554—114no—
545#553—1116no—
546#553—118no—
547#553—118no—
548#552—1116no—
549#552—1116no—
550#552—118no—
551#552—118no—
552#552—118no—
553#551—1116no—
554#551—1116no—
555#551—1116no—
556D4×Q8—114no—
557#548—118no—
558#547—118no—
559#547—118no—
560#547C2×D1114yescomplemented
561#546—118no—
562#546—118no—
563#546—118no—
564#546C2×D1118yescomplemented
565D42C2×D1114yescomplemented
566#544—112no—
567#543—114no—
568#542—118no—
569#541—118no—
570#539—1116no—
571#539—118no—
572#539—118no—
573#538—118no—
574#538—1116no—
575#537C2×D1112yes—
576#536—114no—
577#534—118no—
578#534C2×D1114yes—
579#533—112no—
580#533—112no—
581#533—118no—
582#533—112no—
583#532—112no—
584#532—112no—
585#532C2×D1112yes—
586#529—114no—
587#529—114no—
588#529—1116no—
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—118no—
599#529—114no—
600#529—114no—
601C2×#126—118no—
602C2×#125—114no—
603C2×#124—114no—
604#525—114no—
605#525—114no—
606#525—114no—
607#525—1116no—
608C2×#123—118no—
609C2×C22⋊Q8—114no—
610C2×#121C2×D1114yes—
611#520—114no—
612#520—118no—
613#518—112no—
614#518—118no—
615#518—118no—
616C4×#41—114no—
617C4×#41—118no—
618C4×#41—114no—
619C4×#41—114no—
620C4×#41—114no—
621C4×#41—114no—
622C4×#41—114no—
623C4×#41—114no—
624C2×C4×Q8—111no—
625C2×C4×Q8—114no—
626C2×C4×Q8—111no—
627C2×C4×D4—111no—
628C2×C4×D4—118no—
629C2×C4×D4—118no—
630C2×C4×D4—114no—
631C2×C4×D4—112no—
632C2×C4×D4—112no—
633C2×C4×D4C2×D1111yescharacteristic
634C2×#117—111no—
635C2×#117—112no—
636C2×#117—118no—
637C22×C42—112no—
638C22×C42—111no—
639C22×C11—21no—
640C22×C11—24no—
641C22×C11—21no—
642C22×C11—24no—
643C22×C11—28no—
644C22×C11—28no—
645C22×C11—28no—
646C22×C11—48no—
647C22×C11—816no—
648C22×C11C22×#4118yes—
649C22×C11C22×#4112yes—
650C22×C11C2611yescharacteristic
651C2×D11—22no—
652C2×D11—22no—
653C2×D11—22no—
654C2×D11—44no—
655C4×C11—28no—
656C4×C11—21no—
657C4×C11—24no—
658C4×C11—22no—
659C4×C11C22×#4114yes—
660C4×C11#58512yes—
661Dic11—24no—
662Dic11—21no—
663Dic11—21no—
664Dic11—28no—
665Dic11—28no—
666Dic11—22no—
667Dic11—21no—
668Dic11—24no—
669Dic11#58512yes—
670H(5,𝔽2)—216no—
671C2×#41—114no—
672C2×#41—114no—
673C2×#41—114no—
674C2×#41—114no—
675C2×#41—228no—
676C2×#41C22×D1114yes—
677C2×#41C22×D1118yes—
678C22×Q8—111no—
679C22×Q8—114no—
680C22×D4—112no—
681C22×D4C22×D1118yes—
682C22×D4C22×D1118yes—
683C22×D4C22×D1114yes—
684C22×D4C22×D1111yescharacteristic
685C23×C4—112no—
686C23×C4—118no—
687C23×C4—112no—
688C23×C4—111no—
689C23×C4—111no—
690C23×C4—111no—
691C23×C4C22×D1112yes—
692C4⋊Q8—118no—
693C4⋊Q8—118no—
694C4⋊Q8—112no—
695C4⋊Q8—112no—
696C4⋊Q8C22×D1112yes—
697#127C22×D1112yes—
698#126—1116no—
699#126—118no—
700#126—1116no—
701#126—1116no—
702#126—1116no—
703#126—118no—
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—118no—
713#125—1116no—
714#125—114no—
715#124—114no—
716#124—118no—
717#124—118no—
718#124—118no—
719#124—114no—
720#124—118no—
721#124—1116no—
722#124C22×D1114yes—
723#123—118no—
724#123—1116no—
725#123—1116no—
726#123—1116no—
727#123—1116no—
728#123—1116no—
729#123—1116no—
730#123—118no—
731#123—118no—
732#123—1116no—
733#123C22×D11116yes—
734C22⋊Q8—114no—
735C22⋊Q8—114no—
736C22⋊Q8—114no—
737C22⋊Q8—118no—
738C22⋊Q8—118no—
739C22⋊Q8—118no—
740C22⋊Q8—114no—
741C22⋊Q8—118no—
742C22⋊Q8—118no—
743C22⋊Q8—114no—
744C22⋊Q8—114no—
745C22⋊Q8—1116no—
746C22⋊Q8—1116no—
747C22⋊Q8—1116no—
748C22⋊Q8—1116no—
749C22⋊Q8C22×D1118yes—
750#121—114no—
751#121—114no—
752#121—114no—
753#121—114no—
754#121—1116no—
755#121—1116no—
756#121—1116no—
757#121C22×D1114yes—
758#121C22×D1118yes—
759#121C22×D1118yes—
760#121C22×D1118yes—
761#121C22×D1114yes—
762#121C22×D1118yes—
763#120—1116no—
764#120—118no—
765#120C22×D11116yes—
766C4×Q8—114no—
767C4×Q8—114no—
768C4×Q8—118no—
769C4×Q8—114no—
770C4×Q8—114no—
771C4×Q8—114no—
772C4×Q8—118no—
773C4×Q8—118no—
774C4×Q8—118no—
775C4×Q8—114no—
776C4×Q8—114no—
777C4×Q8—114no—
778C4×Q8—114no—
779C4×Q8—114no—
780C4×D4—114no—
781C4×D4—118no—
782C4×D4—1116no—
783C4×D4—114no—
784C4×D4—114no—
785C4×D4—114no—
786C4×D4—1116no—
787C4×D4—1116no—
788C4×D4—118no—
789C4×D4—1116no—
790C4×D4—118no—
791C4×D4—118no—
792C4×D4—118no—
793C4×D4—118no—
794C4×D4—118no—
795C4×D4—114no—
796C4×D4—118no—
797C4×D4—1116no—
798C4×D4—114no—
799C4×D4—118no—
800C4×D4—118no—
801C4×D4—118no—
802C4×D4—118no—
803C4×D4—118no—
804C4×D4—118no—
805C4×D4—118no—
806C4×D4—118no—
807C4×D4C22×D1114yes—
808C4×D4C22×D1114yes—
809C4×D4C22×D1114yes—
810C4×D4C22×D1114yes—
811#117—114no—
812#117—118no—
813#117—1116no—
814#117—118no—
815#117—114no—
816#117—114no—
817#117—114no—
818#117—114no—
819#117—118no—
820#117—118no—
821#117—118no—
822#117—1116no—
823#117—1116no—
824#117—1116no—
825#117—118no—
826C2×C4⋊C4—111no—
827C2×C4⋊C4—112no—
828C2×C4⋊C4—112no—
829C2×C4⋊C4—118no—
830C2×C4⋊C4—118no—
831C2×C4⋊C4—118no—
832C2×C4⋊C4—118no—
833C2×C4⋊C4—114no—
834C2×C4⋊C4—118no—
835C2×C4⋊C4C22×D1111yescharacteristic
836C2×C4⋊C4C22×D1114yes—
837C2×C22⋊C4—112no—
838C2×C22⋊C4—118no—
839C2×C22⋊C4—118no—
840C2×C22⋊C4—118no—
841C2×C22⋊C4—1116no—
842C2×C22⋊C4—118no—
843C2×C22⋊C4—112no—
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—118no—
855C2×C42—114no—
856C2×C42—114no—
857C2×C42—111no—
858C2×C42—112no—
859C2×C42—112no—
860C2×C42—112no—
861C2×C42—112no—
862C2×C42C22×D1111yescharacteristic
863C2×C11—22no—
864C2×C11—28no—
865C2×C11—48no—
866C2×C11C23×#4111yescharacteristic
867C2×C11C2×#58511yescharacteristic
868C2×C11C2×#58511yescharacteristic
869D11—42no—
870C24—111no—
871C24C23×D1118yes—
872C24C23×D1112yes—
873#41—232no—
874#41—216no—
875#41—2216no—
876#41—2216no—
877#41—448no—
878#41—448no—
879C2×Q8—114no—
880C2×Q8—114no—
881C2×Q8—114no—
882C2×Q8—118no—
883C2×Q8—224no—
884C2×Q8—448no—
885C2×Q8C23×D1114yes—
886C2×D4—232no—
887C2×D4—232no—
888C2×D4—48no—
889C2×D4—118no—
890C2×D4—118no—
891C2×D4—118no—
892C2×D4—228no—
893C2×D4#434118yescomplemented
894C2×D4C23×D1118yes—
895C2×D4C23×D11116yes—
896C2×D4C23×D1114yes—
897C2×D4C23×D1114yes—
898C2×D4C23×D1118yes—
899C2×D4C23×D1114yes—
900C2×D4C23×D1114yes—
901C22×C4—44no—
902C22×C4—111no—
903C22×C4—114no—
904C22×C4—111no—
905C22×C4—114no—
906C22×C4—114no—
907C22×C4—112no—
908C22×C4—118no—
909C22×C4—111no—
910C22×C4—112no—
911C22×C4—114no—
912C22×C4—118no—
913C22×C4—118no—
914C22×C4—118no—
915C22×C4—1116no—
916C22×C4—112no—
917C22×C4—112no—
918C22×C4—112no—
919C22×C4—112no—
920C22×C4—112no—
921C22×C4—112no—
922C22×C4—228no—
923C22×C4—224no—
924C22×C4—442no—
925C22×C4—442no—
926C22×C4—444no—
927C22×C4—4416no—
928C22×C4C23×D1111yescharacteristic
929C22×C4C23×D1114yes—
930C22×C4C23×D1118yes—
931C22×C4C23×D1118yes—
932C22×C4C23×D1112yes—
933C22×C4C23×D1114yes—
934C22×C4C23×D1111yescharacteristic
935C22×C4C23×D1111yescharacteristic
936C4⋊C4—114no—
937C4⋊C4—118no—
938C4⋊C4—118no—
939C4⋊C4—114no—
940C4⋊C4—114no—
941C4⋊C4—118no—
942C4⋊C4—1116no—
943C4⋊C4—118no—
944C4⋊C4—118no—
945C4⋊C4—118no—
946C4⋊C4—1116no—
947C4⋊C4—1116no—
948C4⋊C4—118no—
949C4⋊C4—1116no—
950C4⋊C4—114no—
951C4⋊C4—118no—
952C4⋊C4—114no—
953C4⋊C4—118no—
954C4⋊C4C23×D1114yes—
955C4⋊C4C23×D1114yes—
956C4⋊C4C23×D1118yes—
957C4⋊C4C23×D1114yes—
958C22⋊C4—118no—
959C22⋊C4—118no—
960C22⋊C4—118no—
961C22⋊C4—1116no—
962C22⋊C4—118no—
963C22⋊C4—118no—
964C22⋊C4—118no—
965C22⋊C4—1116no—
966C22⋊C4—1116no—
967C22⋊C4—1116no—
968C22⋊C4—118no—
969C22⋊C4—118no—
970C22⋊C4—118no—
971C22⋊C4C23×D1118yes—
972C22⋊C4C23×D1118yes—
973C22⋊C4C23×D11116yes—
974C22⋊C4C23×D1118yes—
975C42—111no—
976C42—112no—
977C42—111no—
978C42—111no—
979C42—111no—
980C42—114no—
981C42—112no—
982C42—118no—
983C42—114no—
984C42—112no—
985C42—114no—
986C42—112no—
987C42—114no—
988C42—114no—
989C42—114no—
990C42—118no—
991C42—1116no—
992C42—118no—
993C42C23×D1112yes—
994C42C23×D1112yes—
995C11#6278111yescharacteristic, complemented, Sylow
996C23—216no—
997C23—42no—
998C23—42no—
999C23—48no—
1000C23—48no—
1001C23—112no—
1002C23—222no—
1003C23—441no—
1004C23—441no—
1005C23C2×#434118yes—
1006C23C24×D1118yes—
1007C23C24×D1111yescharacteristic
1008C23C24×D1114yes—
1009Q8—28no—
1010Q8—228no—
1011Q8—228no—
1012Q8—448no—
1013Q8—444no—
1014D4—232no—
1015D4—216no—
1016D4—28no—
1017D4—28no—
1018D4—48no—
1019D4—44no—
1020D4—2216no—
1021D4—448no—
1022D4—448no—
1023D4C2×#4341116yes—
1024C2×C4—216no—
1025C2×C4—216no—
1026C2×C4—22no—
1027C2×C4—28no—
1028C2×C4—44no—
1029C2×C4—42no—
1030C2×C4—41no—
1031C2×C4—111no—
1032C2×C4—111no—
1033C2×C4—111no—
1034C2×C4—111no—
1035C2×C4—114no—
1036C2×C4—112no—
1037C2×C4—118no—
1038C2×C4—114no—
1039C2×C4—118no—
1040C2×C4—224no—
1041C2×C4—222no—
1042C2×C4—228no—
1043C2×C4—2216no—
1044C2×C4—222no—
1045C2×C4—224no—
1046C2×C4—228no—
1047C2×C4—228no—
1048C2×C4—224no—
1049C2×C4—224no—
1050C2×C4—224no—
1051C2×C4—442no—
1052C2×C4—442no—
1053C2×C4—442no—
1054C2×C4—444no—
1055C2×C4—4416no—
1056C2×C4—448no—
1057C2×C4—441no—
1058C2×C4—448no—
1059C2×C4—448no—
1060C2×C4C2×#434114yes—
1061C2×C4C24×D1111yescharacteristic
1062C2×C4C24×D1114yes—
1063C2×C4C24×D1118yes—
1064C2×C4C24×D1112yes—
1065C2×C4C24×D1112yes—
1066C2×C4C24×D1111yescharacteristic
1067C22—21no—
1068C22—24no—
1069C22—21no—
1070C22—24no—
1071C22—28no—
1072C22—28no—
1073C22—28no—
1074C22—48no—
1075C22—816no—
1076C22—222no—
1077C22—222no—
1078C22—222no—
1079C22—444no—
1080C22C22×#434118yes—
1081C22C22×#434112yes—
1082C22C25×D1111yescharacteristic
1083C4—28no—
1084C4—22no—
1085C4—21no—
1086C4—24no—
1087C4—112no—
1088C4—221no—
1089C4—221no—
1090C4—224no—
1091C4—221no—
1092C4—224no—
1093C4—228no—
1094C4—222no—
1095C4—228no—
1096C4C22×#434114yes—
1097C4#1062345512yes—
1098C2—22no—
1099C2—28no—
1100C2—48no—
1101C2—442no—
1102C2C23×#434111yescharacteristic
1103C2D11×#58511yescharacteristic
1104C2C2×#1062345511yescharacteristic
subgroupG/H
center, FrattiniC22C25×D11
commutator, socle, cosocleC22×C11C26
FittingC11×#3496C2
hypercenter#3496D11
hypocenterC11#62781
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #13082673C2semidirect
2. #13082585C2semidirect
3. #13082568C2semidirect
4. #13082478C2semidirect
5. #13082450C2semidirect
6. #13082419C2semidirect
7. #13082335C2semidirect
8. #13082313C2semidirect
9. #13082256C2semidirect
10. #13082228C2semidirect
11. #13082217C2semidirect
12. #13082167C2semidirect
13. #13082044C2semidirect
14. #13082022C2semidirect
15. #13081911C2semidirect
16. C2×#10623131C2semidirect
17. H(5,𝔽2)×Dic11C2semidirect
18. C2×C4×#4341C2semidirect
19. C11×#3496C2semidirect
22. C11×#547C22semidirect
23. C11×#546C22semidirect
24. D42×C11C22semidirect
30. #10623359C22semidirect
31. #10623358C22semidirect
32. #10623358C22semidirect
33. #41×Dic11C22semidirect
34. #41×Dic11C22semidirect
35. #10623356C22semidirect
36. #10623355C22semidirect
37. #10623355C22semidirect
38. #10623337C22semidirect
39. #10623337C22semidirect
40. #10623337C22semidirect
41. #10623335C22semidirect
43. #10623329C22semidirect
44. #10623329C22semidirect
45. C2×#66989C22semidirect
46. C2×#66988C22semidirect
48. C2×D4×Dic11C22semidirect
49. C2×D4×Dic11C22semidirect
50. C2×D4×Dic11C22semidirect
51. C2×C4×C22⋊D11C22semidirect
52. C2×#66977C22semidirect
53. C22×C4×Dic11C22semidirect
54. #10623259C22semidirect
55. #10623259C22semidirect
56. #10623252C22semidirect
57. #10623247C22semidirect
58. #10623247C22semidirect
59. #10623244C22semidirect
60. #10623211C22semidirect
61. #10623211C22semidirect
62. #10623202C22semidirect
63. #10623196C22semidirect
64. #10623181C22semidirect
65. #10623181C22semidirect
66. #10623180C22semidirect
67. #10623173C22semidirect
68. #10623172C22semidirect
69. #10623156C22semidirect
70. #10623153C22semidirect
71. #10623149C22semidirect
72. #10623149C22semidirect
73. #10623148C22semidirect
74. #10623147C22semidirect
75. #10623137C22semidirect
76. #10623137C22semidirect
77. #10623134C22semidirect
78. #10623133C22semidirect
79. #10623133C22semidirect
80. #10623132C22semidirect
81. #10623131C22semidirect
82. #10623131C22semidirect
83. #10623131C22semidirect
84. #10623131C22semidirect
85. #10623131C22semidirect
86. #10623131C22semidirect
87. #10623131C22semidirect
88. #10623131C22semidirect
89. #10623131C22semidirect
90. #10623131C22semidirect
91. #10623129C22semidirect
92. #10623124C22semidirect
93. #10623118C22semidirect
94. #10623118C22semidirect
95. #10623117C22semidirect
96. #10623088C22semidirect
97. #10623088C22semidirect
98. #10623074C22semidirect
99. #10623074C22semidirect
100. #10623073C22semidirect
101. #10623072C22semidirect
102. #10623070C22semidirect
103. D4×Dic22C22semidirect
104. C4×#4341C22semidirect
105. C4×#4341C22semidirect
106. C4×#4341C22semidirect
107. C4×#4341C22semidirect
108. C4×#4341C22semidirect
109. C4×#4341C22semidirect
110. #10623044C22semidirect
111. C2×#66945C22semidirect
112. #10623031C22semidirect
113. C2×#66943C22semidirect
114. C2×#66940C22semidirect
115. C2×#66940C22semidirect
116. #10623026C22semidirect
117. C2×(C22⋊D11)⋊C4C22semidirect
118. #10623014C22semidirect
119. C2×#66932C22semidirect
120. C2×#66930C22semidirect
121. C2×#66930C22semidirect
122. C2×C42×D11C22semidirect
123. #10623001C22semidirect
124. C2×C4×Dic22C22semidirect
328. C2×D4×C11#41semidirect
450. #3496D11semidirect
560. #547C2×D11semidirect
564. #546C2×D11semidirect
565. D42C2×D11semidirect
893. C2×D4#4341semidirect
995. C11#62781semidirect

Maximal subgroups

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

subgroupindex
#130826732
#130825852
#130825682
#130824782
#130824502
#130824192
#130823352
#130823132
#130822562
#130822282
#130822172
#130821672
#130820442
#130820222
#130819112
C2×#106231312
H(5,𝔽2)×Dic112
C2×C4×#43412
C11×#34962
#6278111