Finite Group Databasebeta

← #14761625

Subgroups — #14761625

Order 2816.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078404C211yesmaximal, characteristic
2#13077556C211yesmaximal, characteristic, complemented
3#13069560C211yesmaximal, characteristic, complemented
4#13069391C211yesmaximal, characteristic, complemented
5#13069215C211yesmaximal, characteristic, complemented
6#13069215C211yesmaximal, characteristic, complemented
7#13068891C211yesmaximal, characteristic
8#13068891C211yesmaximal, characteristic
9#13068636C211yesmaximal, characteristic
10#13068501C211yesmaximal, characteristic, complemented
11#13068496C211yesmaximal, characteristic, complemented
12#13068488C211yesmaximal, characteristic, complemented
13#13068458C211yesmaximal, characteristic
14#13068451C211yesmaximal, characteristic
15C11×#2875C211yesmaximal, characteristic
16C2×C11×#131C2211yescharacteristic
17C2×C11×#131C2211yescharacteristic
18C4×C11×#41C2211yescharacteristic
19#10623001C2211yescharacteristic
20C11×#405—21no—
21C11×#405—21no—
22C11×#405C2211yescharacteristic
23C11×#405C2211yescharacteristic
24C4×C11×M16—21no—
25C4×C11×M16C2211yescharacteristic
26C2×C11×#97—21no—
27C2×C11×#97C2211yescharacteristic
28C2×#66901C2211yescharacteristic
29C2×#66901C2211yescharacteristic
30#10622846C2211yescharacteristic
31#10622846C2211yescharacteristic
32C2×#66886C2211yescharacteristic
33C2×#66886C2211yescharacteristic
34#10622715C2211yescharacteristic
35#10622715C2211yescharacteristic
36#10622714C2211yescharacteristic
37#10622714C2211yescharacteristic
38C2×#66879C2211yescharacteristic
39C2×C8×Dic11C2211yescharacteristic
40#10622635C411yescharacteristic, complemented
41#10622635C411yescharacteristic, complemented
42#10622634C411yescharacteristic, complemented
43#10622633C411yescharacteristic, complemented
44#10622622C411yescharacteristic, complemented
45#10622622C411yescharacteristic, complemented
46#10622621C411yescharacteristic, complemented
47#10622620C411yescharacteristic, complemented
48#10622611C2211yescharacteristic
49#10622611C2211yescharacteristic
50C4×C4⋊Dic11C2211yescharacteristic
51#10622537C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622314—21no—
54#10622314—21no—
55#10622314—21no—
56#10622314—21no—
57#10622196C2211yescharacteristic
58#10622196C2211yescharacteristic
59#10622193C2211yescharacteristic
60#10622193C2211yescharacteristic
61#10622193C2211yescharacteristic
62#10622193C2211yescharacteristic
63#10622188C2211yescharacteristic
64#10622188C2211yescharacteristic
65#10622170C2211yescharacteristic
66#10622170C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C11×#131—22no—
69C11×#131—22no—
70C11×#131—22no—
71C11×#131Q814yescomplemented
72C2×C11×M16—21no—
73C2×C11×M16—21no—
74C2×C11×M16C2311yescharacteristic
75C2×C11×M16C2311yescharacteristic
76C22×C8×C11—21no—
77C22×C8×C11—21no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C4×Q8×C11C2×C411yescharacteristic
81C4×Q8×C11C2×C411yescharacteristic
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11C2×C411yescharacteristic
85C4×D4×C11C2×C411yescharacteristic
86C11×#117—21no—
87C11×#117C2311yescharacteristic
88C2×C42×C11—21no—
89C2×C42×C11C2311yescharacteristic
90#66979C2311yescharacteristic
91#66979C2311yescharacteristic
92C2×C4⋊Dic11—21no—
93#66977—21no—
94#66977—21no—
95C2×C4×Dic11C2311yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C2×#4318C2311yescharacteristic
98C2×#4318C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66923C2×C411yescharacteristic
102#66923C2×C411yescharacteristic
103#66922C2×C411yescharacteristic
104#66922C2×C411yescharacteristic
105C4×Dic22—21no—
106C4×Dic22—21no—
107C11×#97—21no—
108C11×#97—21no—
109C11×#97—21no—
110C11×#97D411yescharacteristic
111C11×#97D411yescharacteristic
112C11×#97D411yescharacteristic
113C11×#97D411yescharacteristic
114C4×C8×C11—21no—
115C4×C8×C11—21no—
116C4×C8×C11—21no—
117#66901—22no—
118#66901—22no—
119#66899C2×C411yescharacteristic
120#66899C2×C411yescharacteristic
121#66899C2×C411yescharacteristic
122#66899C2×C411yescharacteristic
123#66896C2×C411yescharacteristic
124#66896C2×C411yescharacteristic
125#66896C2×C411yescharacteristic
126#66896C2×C411yescharacteristic
127C11⋊#95—21no—
128#66886—22no—
129#66886—22no—
130#66879—21no—
131#66879—21no—
132#66879—22no—
133Dic11⋊C8—21no—
134Dic11⋊C8—21no—
135Dic11⋊C8—21no—
136Dic11⋊C8—21no—
137C8×Dic11—21no—
138C8×Dic11—21no—
139C8×Dic11—22no—
140#66872C2×C411yescharacteristic
141#66872C2×C411yescharacteristic
142#66872C2×C411yescharacteristic
143#66872C2×C411yescharacteristic
144#66871C2×C411yescharacteristic
145#66871C2×C411yescharacteristic
146#66871C2×C411yescharacteristic
147#66871C2×C411yescharacteristic
148C4⋊(C11⋊C8)—21no—
149C4⋊(C11⋊C8)—21no—
150C4⋊(C11⋊C8)C2×C411yescharacteristic
151C4⋊(C11⋊C8)C2×C411yescharacteristic
152C4⋊(C11⋊C8)C2×C411yescharacteristic
153C4⋊(C11⋊C8)C2×C411yescharacteristic
154#21629—111nomaximal, Sylow
155C11×#41—21no—
156C11×#41—21no—
157C11×#41C2×Q812yes—
158C11×#41#4112yes—
159C2×Q8×C11C22×C411yescharacteristic
160C2×D4×C11—21no—
161C2×D4×C11C22×C411yescharacteristic
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11#4111yescharacteristic
166C22×C4×C11#4111yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C22×Dic11—21no—
169C22×Dic11—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C11×M16—24no—
173C11×M16—24no—
174C11×M16—21no—
175C11×M16—21no—
176C11×M16C2×Q812yes—
177C11×M16#4112yes—
178C2×C8×C11—24no—
179C2×C8×C11—24no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11C2×D411yescharacteristic
185C2×C8×C11C2×D411yescharacteristic
186C2×C8×C11C2×D411yescharacteristic
187C2×C8×C11C2×D411yescharacteristic
188C2×C8×C11C2×Q812yes—
189C2×C8×C11#4112yes—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4C22×C411yescharacteristic
193C11×C4⋊C4C22×C411yescharacteristic
194C11×C22⋊C4—21no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—21no—
197C42×C11—21no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11C22×C411yescharacteristic
201C42×C11C22×C411yescharacteristic
202C42×C11C2×D411yescharacteristic
203C42×C11C2×D411yescharacteristic
204C22⋊Dic11—21no—
205C22⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—42no—
209C4⋊Dic11C22×C411yescharacteristic
210C4⋊Dic11C22×C411yescharacteristic
211C4⋊Dic11C22×C411yescharacteristic
212C4⋊Dic11C22×C411yescharacteristic
213Dic11⋊C4—21no—
214Dic11⋊C4—21no—
215Dic11⋊C4—21no—
216Dic11⋊C4—21no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221C4×Dic11—21no—
222C4×Dic11—21no—
223#4318—21no—
224#4318—21no—
225#4318—21no—
226#4318—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8C22×C411yescharacteristic
234C2×C11⋊C8C22×C411yescharacteristic
235C2×C11⋊C8C22×C411yescharacteristic
236C2×C11⋊C8C22×C411yescharacteristic
237#3076—111no—
238#2961—111no—
239#2875D1111yescharacteristic
240#1986—111no—
241#1950—111no—
242#1922—111no—
243#1922—111no—
244#1866—111no—
245#1866—111no—
246#1806—111no—
247#1773—111no—
248#1772—111no—
249#1771—111no—
250#1765—111no—
251#1764—111no—
252C23×C11—21no—
253C23×C11C2×#4111yescharacteristic
254Q8×C11—21no—
255Q8×C11C4×Q812yes—
256D4×C11—22no—
257D4×C11—22no—
258D4×C11—21no—
259D4×C11C4×Q812yes—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—81no—
268C2×C4×C11—81no—
269C2×C4×C11C4×D411yescharacteristic
270C2×C4×C11C4×D411yescharacteristic
271C2×C4×C11C4×D411yescharacteristic
272C2×C4×C11C4×D411yescharacteristic
273C2×C4×C11C23×C411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×Q811yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×Dic11—22no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289Dic22—81no—
290Dic22—81no—
291C8×C11—22no—
292C8×C11—21no—
293C8×C11—22no—
294C8×C11—21no—
295C8×C11C22⋊Q812yes—
296C8×C11C22⋊Q812yes—
297C11⋊C8—21no—
298C11⋊C8—21no—
299C11⋊C8—21no—
300C11⋊C8—21no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C2×#131C2×D1111yescharacteristic
304C2×#131C2×D1111yescharacteristic
305#533—111no—
306C4×#41C2×D1111yescharacteristic
307#479—111no—
308#479—111no—
309#478—111no—
310#478—111no—
311#477—111no—
312#476—111no—
313#475—111no—
314#474—111no—
315#446—221no—
316#446—221no—
317#446—221no—
318#446—221no—
319C2×#108—111no—
320C2×#108—111no—
321#427—111no—
322#427—111no—
323#424—111no—
324#424—111no—
325#423—111no—
326C2×C4⋊C8—111no—
327C2×#104—111no—
328C2×#104—111no—
329#416—111no—
330#416—111no—
331#405—21no—
332#405—21no—
333#405—111no—
334#405—111no—
335#405C2×D1111yescharacteristic
336#405C2×D1111yescharacteristic
337C4×M16—21no—
338C4×M16C2×D1111yescharacteristic
339C2×#97—21no—
340C2×#97—111no—
341C2×#97C2×D1111yescharacteristic
342C2×C4×C8—111no—
343C4×C4⋊C4—111no—
344#341—111no—
345#341—111no—
346#339—111no—
347#339—111no—
348#339—111no—
349#339—111no—
350#339—111no—
351#339—111no—
352#336—111no—
353#336—111no—
354C22×C11—21no—
355C22×C11—21no—
356C22×C11—22no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11C2×C4×D411yescharacteristic
360C22×C11#52911yescharacteristic
361C22×C11#53311yescharacteristic
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—22no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11C2×C4×Q811yescharacteristic
370C4×C11C4×#4111yescharacteristic
371C4×C11C2×C22⋊Q811yescharacteristic
372C4×C11#52511yescharacteristic
373Dic11—42no—
374Dic11—41no—
375Dic11—41no—
376Dic11—41no—
377Dic11—41no—
378Dic11—81no—
379C2×#41C22×D1111yescharacteristic
380#131—22no—
381#131—22no—
382#131—22no—
383#131Dic2214yescomplemented
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—111no—
387C2×M16—111no—
388C2×M16C22×D1111yescharacteristic
389C2×M16C22×D1111yescharacteristic
390C22×C8—21no—
391C22×C8—21no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8C22×D1111yescharacteristic
395C22×C8C22×D1111yescharacteristic
396C4⋊Q8—111no—
397C4⋊Q8—111no—
398#125—111no—
399#125—111no—
400C22⋊Q8—221no—
401C22⋊Q8—221no—
402C4×Q8—221no—
403C4×Q8—221no—
404C4×Q8C4×D1111yescharacteristic
405C4×Q8C4×D1111yescharacteristic
406C4×D4—21no—
407C4×D4—21no—
408C4×D4C4×D1111yescharacteristic
409C4×D4C4×D1111yescharacteristic
410#117—21no—
411#117—111no—
412#117—111no—
413#117C22×D1111yescharacteristic
414C2×C4⋊C4—221no—
415C2×C42—21no—
416C2×C42—111no—
417C2×C42—111no—
418C2×C42C22×D1111yescharacteristic
419#108—222no—
420#108—222no—
421#107—111no—
422#107—111no—
423#107—111no—
424#107—111no—
425#106—111no—
426#106—111no—
427#106—111no—
428#106—111no—
429C4⋊C8—111no—
430C4⋊C8—111no—
431C4⋊C8—111no—
432C4⋊C8—111no—
433C4⋊C8—221no—
434C4⋊C8—221no—
435C4⋊C8—221no—
436C4⋊C8—221no—
437C4⋊C8—221no—
438C4⋊C8—221no—
439#104—222no—
440#104—222no—
441#103—111no—
442#103—111no—
443#103—111no—
444#103—111no—
445#102—111no—
446#102—111no—
447#102—111no—
448#102—111no—
449#97—21no—
450#97—21no—
451#97—21no—
452#97—222no—
453#97—221no—
454#97—221no—
455#97C22⋊D1111yescharacteristic
456#97C22⋊D1111yescharacteristic
457#97C22⋊D1111yescharacteristic
458#97C22⋊D1111yescharacteristic
459C4×C8—21no—
460C4×C8—21no—
461C4×C8—21no—
462C4×C8—222no—
463C4×C8—221no—
464C4×C8—221no—
465#95—221no—
466C2×C11—21no—
467C2×C11—21no—
468C2×C11—42no—
469C2×C11C4×C22⋊Q811yescharacteristic
470C2×C11#295611yescharacteristic
471C2×C11#295711yescharacteristic
472#41—21no—
473#41—21no—
474#41C2×Dic2212yes—
475#41#433912yes—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×Q8C2×C4×D1111yescharacteristic
479C2×D4—21no—
480C2×D4C2×C4×D1111yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4#433911yescharacteristic
487C22×C4#433911yescharacteristic
488C22×C4C23×D1111yescharacteristic
489M16—24no—
490M16—21no—
491M16—21no—
492M16—24no—
493M16—221no—
494M16—221no—
495M16—221no—
496M16—221no—
497M16C2×Dic2212yes—
498M16#433912yes—
499C2×C8—24no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—24no—
505C2×C8—111no—
506C2×C8—111no—
507C2×C8—111no—
508C2×C8—111no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8C2×Dic2212yes—
516C2×C8#433912yes—
517C2×C8C2×C22⋊D1111yescharacteristic
518C2×C8C2×C22⋊D1111yescharacteristic
519C2×C8C2×C22⋊D1111yescharacteristic
520C2×C8C2×C22⋊D1111yescharacteristic
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—111no—
524C4⋊C4—111no—
525C4⋊C4—111no—
526C4⋊C4—111no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—442no—
534C4⋊C4C2×C4×D1111yescharacteristic
535C4⋊C4C2×C4×D1111yescharacteristic
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—221no—
540C22⋊C4—221no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—221no—
545C42—221no—
546C42—221no—
547C42—221no—
548C42—221no—
549C42—221no—
550C42C2×C4×D1111yescharacteristic
551C42C2×C4×D1111yescharacteristic
552C42C2×C22⋊D1111yescharacteristic
553C42C2×C22⋊D1111yescharacteristic
554C11#2162911yescharacteristic, complemented, Sylow
555C23—21no—
556C23C2×#433911yescharacteristic
557Q8—21no—
558Q8—881no—
559Q8—881no—
560Q8C4×Dic2212yes—
561D4—22no—
562D4—22no—
563D4—21no—
564D4C4×Dic2212yes—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—81no—
573C2×C4—81no—
574C2×C4—222no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4C4×C22⋊D1111yescharacteristic
585C2×C4C4×C22⋊D1111yescharacteristic
586C2×C4C4×C22⋊D1111yescharacteristic
587C2×C4C4×C22⋊D1111yescharacteristic
588C2×C4C22×Dic2211yescharacteristic
589C2×C4C22×C4×D1111yescharacteristic
590C2×C4C2×#433911yescharacteristic
591C2×C4C2×#433911yescharacteristic
592C2×C4C2×#433911yescharacteristic
593C2×C4C22×C22⋊D1111yescharacteristic
594C8—22no—
595C8—21no—
596C8—22no—
597C8—21no—
598C8—221no—
599C8—221no—
600C8—221no—
601C8—221no—
602C8—441no—
603C8—441no—
604C8#6697712yes—
605C8#6697712yes—
606C22—21no—
607C22—21no—
608C22—22no—
609C22—41no—
610C22—41no—
611C22#1062300111yescharacteristic
612C22#1062301011yescharacteristic
613C22C2×C4×C22⋊D1111yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—22no—
619C4—41no—
620C4—41no—
621C4—442no—
622C4—441no—
623C4—441no—
624C4—441no—
625C4—441no—
626C4—881no—
627C4C2×C4×Dic2211yescharacteristic
628C4C4×#433911yescharacteristic
629C4C2×#6697711yescharacteristic
630C4#1062332211yescharacteristic
631C2—21no—
632C2—21no—
633C2—42no—
634C2C4×#6697711yescharacteristic
635C2#1307752311yescharacteristic
636C2#1307753111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2875C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#41C23
cosocleC22×C4×C11C24
hypercenter#2875D11
hypocenterC11#21629
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #2875

Complements

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

NH ≅ G/Ntype
2. #13077556C2semidirect
3. #13069560C2semidirect
4. #13069391C2semidirect
5. #13069215C2semidirect
6. #13069215C2semidirect
10. #13068501C2semidirect
11. #13068496C2semidirect
12. #13068488C2semidirect
40. #10622635C4semidirect
41. #10622635C4semidirect
42. #10622634C4semidirect
43. #10622633C4semidirect
44. #10622622C4semidirect
45. #10622622C4semidirect
46. #10622621C4semidirect
47. #10622620C4semidirect
71. C11×#131Q8semidirect
383. #131Dic22semidirect
554. C11#21629semidirect

Maximal subgroups

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

subgroupindex
#130784042
#130775562
#130695602
#130693912
#130692152
#130688912
#130686362
#130685012
#130684962
#130684882
#130684582
#130684512
C11×#28752
#2162911