Finite Group Databasebeta

← #14761627

Subgroups — #14761627

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#13078406C211yesmaximal, characteristic
2#13077556C211yesmaximal, characteristic, complemented
3#13077041C211yesmaximal, characteristic
4#13069559C211yesmaximal, characteristic, complemented
5#13069392C211yesmaximal, characteristic, complemented
6#13069216C211yesmaximal, characteristic, complemented
7#13069216C211yesmaximal, characteristic, complemented
8#13068894C211yesmaximal, characteristic
9#13068894C211yesmaximal, characteristic
10#13068637C211yesmaximal, characteristic
11#13068500C211yesmaximal, characteristic, complemented
12#13068495C211yesmaximal, characteristic, complemented
13#13068460C211yesmaximal, characteristic
14#13068453C211yesmaximal, characteristic
15C11×#1771C211yesmaximal, characteristic, complemented
16C2×#66954C2211yescharacteristic
17C2×#66954C2211yescharacteristic
18C4×#4339C2211yescharacteristic
19#10623001C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#97C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25#10622726C2211yescharacteristic
26#10622726C2211yescharacteristic
27C2×#66883C2211yescharacteristic
28C2×#66883C2211yescharacteristic
29#10622719C2211yescharacteristic
30#10622719C2211yescharacteristic
31#10622715C2211yescharacteristic
32#10622715C2211yescharacteristic
33#10622714C2211yescharacteristic
34#10622714C2211yescharacteristic
35#10622714C2211yescharacteristic
36#10622714C2211yescharacteristic
37C2×#66869C2211yescharacteristic
38C2×#66869C2211yescharacteristic
39#10622537C2211yescharacteristic
40C4×#4318C2211yescharacteristic
41#10622464C411yescharacteristic, complemented
42#10622463C411yescharacteristic, complemented
43#10622460C411yescharacteristic, complemented
44#10622460C411yescharacteristic, complemented
45#10622459C411yescharacteristic, complemented
46#10622455C411yescharacteristic, complemented
47#10622442C411yescharacteristic, complemented
48#10622442C411yescharacteristic, complemented
49#10622321—21no—
50#10622321—21no—
51#10622320—21no—
52D11×#97—21no—
53#10622314—21no—
54#10622314—21no—
55#10622314—21no—
56#10622314—21no—
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622190C2211yescharacteristic
60#10622190C2211yescharacteristic
61#10622161C2211yescharacteristic
62#10622161C2211yescharacteristic
63#10622161C2211yescharacteristic
64#10622161C2211yescharacteristic
65#10622161C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×#4339C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C2×C11×C4⋊C4—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C4×C22⋊D11—21no—
77C4×C22⋊D11—21no—
78#66979C2311yescharacteristic
79#66979C2311yescharacteristic
80#66979C2311yescharacteristic
81#66977—21no—
82#66977—21no—
83C2×#4318C2311yescharacteristic
84C2×#4318C2311yescharacteristic
85C2×#4318C2311yescharacteristic
86C2×#4318C2311yescharacteristic
87#66954—22no—
88#66954—22no—
89#66954—22no—
90#66954Q814yescomplemented
91C2×#4313—21no—
92C2×#4313—21no—
93C2×C8×D11—21no—
94C2×C8×D11—21no—
95C4×D44C2×C411yescharacteristic
96C4×D44C2×C411yescharacteristic
97#66925—21no—
98C42×D11—21no—
99#66923C2×C411yescharacteristic
100#66923C2×C411yescharacteristic
101#66922C2×C411yescharacteristic
102#66922C2×C411yescharacteristic
103C4×Dic22—21no—
104C4×Dic22—21no—
105C4×Dic22C2×C411yescharacteristic
106C4×Dic22C2×C411yescharacteristic
107C11×C4⋊C8C2×C411yescharacteristic
108C11×C4⋊C8C2×C411yescharacteristic
109C11×C4⋊C8C2×C411yescharacteristic
110C11×C4⋊C8C2×C411yescharacteristic
111C11×#97—22no—
112C11×#97D411yescharacteristic
113C11×#97D411yescharacteristic
114C11×#97D411yescharacteristic
115C11×#97D411yescharacteristic
116C4×C8×C11—22no—
117C11×#95—21no—
118#66885C2×C411yescharacteristic
119#66885C2×C411yescharacteristic
120#66885C2×C411yescharacteristic
121#66885C2×C411yescharacteristic
122#66883—22no—
123#66883—22no—
124#66882C2×C411yescharacteristic
125#66882C2×C411yescharacteristic
126#66882C2×C411yescharacteristic
127#66882C2×C411yescharacteristic
128#66881C2×C411yescharacteristic
129#66881C2×C411yescharacteristic
130#66881C2×C411yescharacteristic
131#66881C2×C411yescharacteristic
132#66880C2×C411yescharacteristic
133#66880C2×C411yescharacteristic
134#66880C2×C411yescharacteristic
135#66880C2×C411yescharacteristic
136#66879—21no—
137#66879—21no—
138#66879—21no—
139#66879—21no—
140Dic11⋊C8—21no—
141Dic11⋊C8—21no—
142Dic11⋊C8—21no—
143Dic11⋊C8—21no—
144C8×Dic11—21no—
145C8×Dic11—21no—
146C8×Dic11—21no—
147C8×Dic11—21no—
148#66869—22no—
149#66869—22no—
150C4⋊(C11⋊C8)—21no—
151C4⋊(C11⋊C8)—21no—
152#66867—21no—
153C4×C11⋊C8—21no—
154#21629—111nomaximal, Sylow
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11#4111yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—21no—
161#4339—21no—
162#4339—21no—
163#4339C2×Q812yes—
164#4339#4112yes—
165C2×D44C22×C411yescharacteristic
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22C22×C411yescharacteristic
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11C22×C411yescharacteristic
179C2×C8×C11C22×C411yescharacteristic
180C2×C8×C11C22×C411yescharacteristic
181C2×C8×C11C22×C411yescharacteristic
182C2×C8×C11C2×D411yescharacteristic
183C2×C8×C11C2×D411yescharacteristic
184C2×C8×C11C2×D411yescharacteristic
185C2×C8×C11C2×D411yescharacteristic
186C2×C8×C11C2×Q812yes—
187C2×C8×C11#4112yes—
188C11×C4⋊C4—42no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11C22×C411yescharacteristic
194C42×C11C22×C411yescharacteristic
195C42×C11C2×D411yescharacteristic
196C42×C11C2×D411yescharacteristic
197C22⋊Dic11—21no—
198C22⋊Dic11—21no—
199C22⋊Dic11—21no—
200(C2×D11)⋊C4—21no—
201(C2×D11)⋊C4—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11C22×C411yescharacteristic
205C4⋊Dic11C22×C411yescharacteristic
206C4⋊Dic11C22×C411yescharacteristic
207C4⋊Dic11C22×C411yescharacteristic
208C4⋊Dic11C22×C411yescharacteristic
209C4⋊Dic11C22×C411yescharacteristic
210Dic11⋊C4—21no—
211Dic11⋊C4—21no—
212Dic11⋊C4—21no—
213Dic11⋊C4—21no—
214Dic11⋊C4—21no—
215Dic11⋊C4—21no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221#4318—21no—
222#4318—21no—
223#4318—21no—
224#4318—21no—
225#4318—21no—
226#4318—21no—
227#4318C2×Q812yes—
228#4318#4112yes—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233#4313—24no—
234#4313—24no—
235C8×D11—24no—
236C8×D11—24no—
237#3076—111no—
238#2961—111no—
239#2875—111no—
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#1771D1111yescharacteristic, complemented
250#1765—111no—
251#1764—111no—
252C23×C11C2×#4111yescharacteristic
253C22×D11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11C4×D411yescharacteristic
263C2×C4×C11C4×D411yescharacteristic
264C2×C4×C11C4×D411yescharacteristic
265C2×C4×C11C4×D411yescharacteristic
266C2×C4×C11C23×C411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×Q811yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C22⋊D11—22no—
273C22⋊D11—22no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281D44—21no—
282D44C4×Q812yes—
283C4×D11—22no—
284C4×D11—22no—
285C4×D11—81no—
286C4×D11—81no—
287Dic22—21no—
288Dic22—81no—
289Dic22—81no—
290Dic22C4×Q812yes—
291C8×C11—21no—
292C8×C11—21no—
293C8×C11—21no—
294C8×C11—21no—
295C8×C11—21no—
296C8×C11—21no—
297C8×C11C22⋊Q812yes—
298C8×C11C22⋊Q812yes—
299C11⋊C8—22no—
300C11⋊C8—22no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C2×#131—111no—
304C2×#131—111no—
305#533—111no—
306C4×#41—111no—
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⋊C8C2×D1111yescharacteristic
327C2×#104—111no—
328C2×#104—111no—
329#416—111no—
330#416—111no—
331#405—111no—
332#405—111no—
333#405—111no—
334#405—111no—
335#405—221no—
336#405—221no—
337C4×M16—111no—
338C4×M16—221no—
339C2×#97—221no—
340C2×#97C2×D1111yescharacteristic
341C2×#97C2×D1111yescharacteristic
342C2×C4×C8C2×D1111yescharacteristic
343C4×C4⋊C4C2×D1111yescharacteristic
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#336C2×D1111yescharacteristic
353#336C2×D1111yescharacteristic
354C22×C11—21no—
355C22×C11—21no—
356C22×C11C2×C4×D411yescharacteristic
357C22×C11#52911yescharacteristic
358C22×C11#53311yescharacteristic
359C2×D11—22no—
360C2×D11—41no—
361C2×D11—41no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—21no—
365C4×C11—21no—
366C4×C11—42no—
367C4×C11—81no—
368C4×C11C2×C4×Q811yescharacteristic
369C4×C11C4×#4111yescharacteristic
370C4×C11C2×C22⋊Q811yescharacteristic
371C4×C11#52511yescharacteristic
372Dic11—22no—
373Dic11—41no—
374Dic11—41no—
375Dic11—41no—
376Dic11—41no—
377Dic11—41no—
378Dic11—41no—
379C2×#41—111no—
380#131—114no—
381#131—222no—
382#131—222no—
383#131—222no—
384C2×M16—111no—
385C2×M16—111no—
386C2×M16—111no—
387C2×M16—111no—
388C2×M16—221no—
389C2×M16—221no—
390C22×C8—221no—
391C22×C8—221no—
392C22×C8C22×D1111yescharacteristic
393C22×C8C22×D1111yescharacteristic
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—111no—
403C4×Q8—111no—
404C4×Q8—221no—
405C4×Q8—221no—
406C4×D4—111no—
407C4×D4—111no—
408C4×D4—221no—
409C4×D4—221no—
410#117—111no—
411#117—111no—
412#117—111no—
413#117—221no—
414C2×C4⋊C4—21no—
415C2×C42—221no—
416C2×C42C22×D1111yescharacteristic
417C2×C42C22×D1111yescharacteristic
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—221no—
430C4⋊C8—221no—
431C4⋊C8—221no—
432C4⋊C8—221no—
433C4⋊C8—221no—
434C4⋊C8—221no—
435C4⋊C8C4×D1111yescharacteristic
436C4⋊C8C4×D1111yescharacteristic
437C4⋊C8C4×D1111yescharacteristic
438C4⋊C8C4×D1111yescharacteristic
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—22no—
450#97—221no—
451#97—221no—
452#97—221no—
453#97—221no—
454#97—221no—
455#97D4411yescharacteristic
456#97D4411yescharacteristic
457#97D4411yescharacteristic
458#97D4411yescharacteristic
459C4×C8—22no—
460C4×C8—221no—
461C4×C8—221no—
462C4×C8—221no—
463C4×C8—221no—
464C4×C8—221no—
465#95—21no—
466C2×C11—21no—
467C2×C11—21no—
468C2×C11C4×C22⋊Q811yescharacteristic
469C2×C11#295611yescharacteristic
470C2×C11#295711yescharacteristic
471D11—42no—
472#41—112no—
473#41—112no—
474#41—221no—
475#41—221no—
476C2×Q8—111no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×D4—111no—
480C2×D4—221no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4#433911yescharacteristic
487C22×C4#433911yescharacteristic
488C22×C4C23×D1111yescharacteristic
489M16—112no—
490M16—112no—
491M16—224no—
492M16—221no—
493M16—221no—
494M16—224no—
495M16—221no—
496M16—221no—
497M16—221no—
498M16—221no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—224no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—224no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8C2×C4×D1111yescharacteristic
512C2×C8C2×C4×D1111yescharacteristic
513C2×C8C2×C4×D1111yescharacteristic
514C2×C8C2×C4×D1111yescharacteristic
515C2×C8C2×D4411yescharacteristic
516C2×C8C2×D4411yescharacteristic
517C2×C8C2×D4411yescharacteristic
518C2×C8C2×D4411yescharacteristic
519C2×C8#434112yes—
520C2×C8Q8×D1112yes—
521C4⋊C4—42no—
522C4⋊C4—111no—
523C4⋊C4—111no—
524C4⋊C4—111no—
525C4⋊C4—111no—
526C4⋊C4—111no—
527C4⋊C4—111no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C22⋊C4—221no—
537C22⋊C4—221no—
538C22⋊C4—221no—
539C22⋊C4—221no—
540C22⋊C4—221no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—221no—
546C42—221no—
547C42—221no—
548C42—221no—
549C42—221no—
550C42C2×C4×D1111yescharacteristic
551C42C2×C4×D1111yescharacteristic
552C42C2×D4411yescharacteristic
553C42C2×D4411yescharacteristic
554C11#2162911yescharacteristic, complemented, Sylow
555C23—221no—
556C23C2×#433911yescharacteristic
557Q8—112no—
558Q8—221no—
559Q8—881no—
560Q8—881no—
561D4—112no—
562D4—222no—
563D4—222no—
564D4—221no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—221no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—881no—
583C2×C4—881no—
584C2×C4C4×D4411yescharacteristic
585C2×C4C4×D4411yescharacteristic
586C2×C4C4×D4411yescharacteristic
587C2×C4C4×D4411yescharacteristic
588C2×C4C22×C4×D1111yescharacteristic
589C2×C4C22×D4411yescharacteristic
590C2×C4C2×#434111yescharacteristic
591C2×C4C2×Q8×D1111yescharacteristic
592C2×C4#41×D1111yescharacteristic
593C2×C4#41×D1111yescharacteristic
594C8—21no—
595C8—21no—
596C8—21no—
597C8—21no—
598C8—21no—
599C8—21no—
600C8—222no—
601C8—222no—
602C8—441no—
603C8—441no—
604C8#6695012yes—
605C8#6695012yes—
606C22—21no—
607C22—21no—
608C22—222no—
609C22—441no—
610C22—441no—
611C22C2×C4×D4411yescharacteristic
612C22#1062308811yescharacteristic
613C22#1062310911yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—42no—
619C4—81no—
620C4—222no—
621C4—441no—
622C4—441no—
623C4—441no—
624C4—441no—
625C4—441no—
626C4—441no—
627C4C2×#6695011yescharacteristic
628C4#1062305511yescharacteristic
629C4C4×#434111yescharacteristic
630C4C4×Q8×D1111yescharacteristic
631C2—21no—
632C2—21no—
633C2—442no—
634C2C4×#6695011yescharacteristic
635C2#1307752711yescharacteristic
636C2#1307753411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1771C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C23
cosocleC22×C4×C11C24
hypercenter#1771D11
hypocenterC11#21629
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #1771

Complements

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

NH ≅ G/Ntype
2. #13077556C2semidirect
4. #13069559C2semidirect
5. #13069392C2semidirect
6. #13069216C2semidirect
7. #13069216C2semidirect
11. #13068500C2semidirect
12. #13068495C2semidirect
15. C11×#1771C2semidirect
41. #10622464C4semidirect
42. #10622463C4semidirect
43. #10622460C4semidirect
44. #10622460C4semidirect
45. #10622459C4semidirect
46. #10622455C4semidirect
47. #10622442C4semidirect
48. #10622442C4semidirect
90. #66954Q8semidirect
249. #1771D11semidirect
554. C11#21629semidirect

Maximal subgroups

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

subgroupindex
#130784062
#130775562
#130770412
#130695592
#130693922
#130692162
#130688942
#130686372
#130685002
#130684952
#130684602
#130684532
C11×#17712
#2162911