Finite Group Databasebeta

← #14761632

Subgroups — #14761632

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#13078402C211yesmaximal, characteristic
2#13077555C211yesmaximal, characteristic, complemented
3#13077043C211yesmaximal, characteristic
4#13069558C211yesmaximal, characteristic, complemented
5#13069390C211yesmaximal, characteristic, complemented
6#13069215C211yesmaximal, characteristic, complemented
7#13068894C211yesmaximal, characteristic
8#13068890C211yesmaximal, characteristic
9#13068635C211yesmaximal, characteristic
10#13068502C211yesmaximal, characteristic, complemented
11#13068494C211yesmaximal, characteristic, complemented
12#13068487C211yesmaximal, characteristic, complemented
13#13068459C211yesmaximal, characteristic
14#13068450C211yesmaximal, characteristic
15C11×#1922C211yesmaximal, characteristic, complemented
16C2×#66960C2211yescharacteristic
17C2×#66954C2211yescharacteristic
18#10623053C2211yescharacteristic
19#10623048C2211yescharacteristic
20C11×#427C2211yescharacteristic
21C11×#424C2211yescharacteristic
22C11×#405C2211yescharacteristic
23C2×#66889C2211yescharacteristic
24C2×#66886C2211yescharacteristic
25#10622735C2211yescharacteristic
26#10622731C2211yescharacteristic
27M16×Dic11C2211yescharacteristic
28#10622726C2211yescharacteristic
29C2×#66883C2211yescharacteristic
30#10622715C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34#10622615C2211yescharacteristic
35#10622611C2211yescharacteristic
36#10622610C2211yescharacteristic
37#10622610C2211yescharacteristic
38C4×Dic11⋊C4C2211yescharacteristic
39C2×#66869C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622504C411yescharacteristic, complemented
42#10622503C411yescharacteristic, complemented
43#10622490C411yescharacteristic, complemented
44#10622488C411yescharacteristic, complemented
45#10622484C411yescharacteristic, complemented
46#10622483C411yescharacteristic, complemented
47#10622470C411yescharacteristic, complemented
48#10622467C411yescharacteristic, complemented
49#10622444—21no—
50#10622444—21no—
51#10622441—21no—
52#10622441—21no—
53#10622321—21no—
54D11×#97—21no—
55#10622302—21no—
56C4×#4313—21no—
57C11×#341C2211yescharacteristic
58C11×#339C2211yescharacteristic
59C11×#339C2211yescharacteristic
60C11×#336C2211yescharacteristic
61#10622196C2211yescharacteristic
62#10622193C2211yescharacteristic
63#10622188C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622170C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×#4339C2311yescharacteristic
68C2×C11×M16C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×#117C2311yescharacteristic
73C11×#117C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75#66979C2311yescharacteristic
76C2×Dic11⋊C4—21no—
77C2×C4×Dic11C2311yescharacteristic
78C2×C4×Dic11C2311yescharacteristic
79C2×#4318C2311yescharacteristic
80C2×#4318C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83#66960—22no—
84#66960Q814yescomplemented
85#66954—22no—
86#66954—22no—
87C2×#4313—21no—
88C2×#4313—21no—
89C2×C8×D11—21no—
90C2×C8×D11—21no—
91#66946C2×C411yescharacteristic
92#66946C2×C411yescharacteristic
93#66943C2×C411yescharacteristic
94#66943C2×C411yescharacteristic
95#66941C2×C411yescharacteristic
96#66941C2×C411yescharacteristic
97#66940C2×C411yescharacteristic
98#66940C2×C411yescharacteristic
99(C22⋊D11)⋊C4—21no—
100(C22⋊D11)⋊C4—21no—
101#66931—21no—
102#66931—21no—
103#66925—21no—
104C42×D11—21no—
105C4×Dic22—21no—
106C4×Dic22—21no—
107C11×#107C2×C411yescharacteristic
108C11×#107C2×C411yescharacteristic
109C11×#106C2×C411yescharacteristic
110C11×#106C2×C411yescharacteristic
111C11×C4⋊C8—21no—
112C11×C4⋊C8—21no—
113C11×#97—21no—
114C4×C8×C11—21no—
115C11⋊#95—21no—
116#66889—22no—
117#66886—22no—
118#66885C2×C411yescharacteristic
119#66885C2×C411yescharacteristic
120#66883—22no—
121#66880C2×C411yescharacteristic
122#66880C2×C411yescharacteristic
123#66879—21no—
124#66879—21no—
125#66879—22no—
126#66879D411yescharacteristic
127#66879D411yescharacteristic
128#66879D411yescharacteristic
129#66879D411yescharacteristic
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134Dic11⋊C8C2×C411yescharacteristic
135Dic11⋊C8C2×C411yescharacteristic
136Dic11⋊C8C2×C411yescharacteristic
137Dic11⋊C8C2×C411yescharacteristic
138C8×Dic11—21no—
139C8×Dic11—21no—
140#66874C2×C411yescharacteristic
141#66874C2×C411yescharacteristic
142#66873C2×C411yescharacteristic
143#66873C2×C411yescharacteristic
144#66872C2×C411yescharacteristic
145#66872C2×C411yescharacteristic
146#66871C2×C411yescharacteristic
147#66871C2×C411yescharacteristic
148#66869—22no—
149#66867—21no—
150#66867—21no—
151C4×C11⋊C8—21no—
152C4×C11⋊C8—21no—
153C4×C11⋊C8—22no—
154#21629—111nomaximal, Sylow
155C22×C4×C11—21no—
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—21no—
158C22×Dic11—21no—
159C22×Dic11#4111yescharacteristic
160C22×Dic11#4111yescharacteristic
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
172C11×M16—21no—
173C11×M16—21no—
174C11×M16—21no—
175C11×M16C2×Q812yes—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11C22×C411yescharacteristic
183C2×C8×C11C22×C411yescharacteristic
184C2×C8×C11C2×D411yescharacteristic
185C2×C8×C11C2×D411yescharacteristic
186C11×C4⋊C4C22×C411yescharacteristic
187C11×C4⋊C4C22×C411yescharacteristic
188C11×C4⋊C4C22×C411yescharacteristic
189C11×C4⋊C4C22×C411yescharacteristic
190C11×C22⋊C4—21no—
191C11×C22⋊C4—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C22⋊Dic11—21no—
197(C2×D11)⋊C4—21no—
198(C2×D11)⋊C4—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11C22×C411yescharacteristic
202C4⋊Dic11C22×C411yescharacteristic
203Dic11⋊C4—21no—
204Dic11⋊C4—21no—
205Dic11⋊C4—21no—
206Dic11⋊C4—21no—
207Dic11⋊C4—21no—
208Dic11⋊C4—21no—
209Dic11⋊C4—42no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11C22×C411yescharacteristic
216C4×Dic11C22×C411yescharacteristic
217C4×Dic11C2×D411yescharacteristic
218C4×Dic11C2×D411yescharacteristic
219#4318—21no—
220#4318—21no—
221#4318—21no—
222#4318#4112yes—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8C22×C411yescharacteristic
228C2×C11⋊C8C22×C411yescharacteristic
229C2×C11⋊C8C2×D411yescharacteristic
230C2×C11⋊C8C2×D411yescharacteristic
231C2×C11⋊C8C2×Q812yes—
232C2×C11⋊C8#4112yes—
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#1922D1111yescharacteristic, complemented
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×C11C2×#4111yescharacteristic
253C22×D11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×Q811yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C22⋊D11—22no—
268C22⋊D11—22no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11C4×D411yescharacteristic
278C2×Dic11C4×D411yescharacteristic
279C2×Dic11C4×D411yescharacteristic
280C2×Dic11C4×D411yescharacteristic
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—22no—
294C8×C11—21no—
295C8×C11—21no—
296C8×C11—41no—
297C11⋊C8—21no—
298C11⋊C8—21no—
299C11⋊C8—22no—
300C11⋊C8—41no—
301C11⋊C8C22⋊Q812yes—
302C11⋊C8C22⋊Q812yes—
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#427C2×D1111yescharacteristic
323#424—111no—
324#424C2×D1111yescharacteristic
325#423—111no—
326C2×C4⋊C8—111no—
327C2×#104—111no—
328C2×#104—111no—
329#416—111no—
330#416—111no—
331#405—111no—
332#405—111no—
333#405—111no—
334#405—221no—
335#405—221no—
336#405C2×D1111yescharacteristic
337C4×M16—111no—
338C4×M16—221no—
339C2×#97—111no—
340C2×#97—111no—
341C2×#97—221no—
342C2×C4×C8—111no—
343C4×C4⋊C4—111no—
344#341—111no—
345#341C2×D1111yescharacteristic
346#339—111no—
347#339—111no—
348#339—111no—
349#339—111no—
350#339C2×D1111yescharacteristic
351#339C2×D1111yescharacteristic
352#336—111no—
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—42no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11C2×C4×Q811yescharacteristic
368C4×C11C4×#4111yescharacteristic
369C4×C11C2×C22⋊Q811yescharacteristic
370C4×C11#52511yescharacteristic
371Dic11—21no—
372Dic11—21no—
373Dic11—21no—
374Dic11—21no—
375Dic11—22no—
376Dic11—41no—
377Dic11—41no—
378Dic11—81no—
379C2×#41—111no—
380#131—114no—
381#131—222no—
382#131—222no—
383#131—222no—
384C2×M16—111no—
385C2×M16—111no—
386C2×M16—221no—
387C2×M16—221no—
388C2×M16C22×D1111yescharacteristic
389C2×M16C22×D1111yescharacteristic
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—221no—
393C22×C8—221no—
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—221no—
412#117C22×D1111yescharacteristic
413#117C22×D1111yescharacteristic
414C2×C4⋊C4—221no—
415C2×C42—111no—
416C2×C42—111no—
417C2×C42—221no—
418C2×C42C22×D1111yescharacteristic
419#108—222no—
420#108—222no—
421#107—111no—
422#107—111no—
423#107C4×D1111yescharacteristic
424#107C4×D1111yescharacteristic
425#106—111no—
426#106—111no—
427#106C4×D1111yescharacteristic
428#106C4×D1111yescharacteristic
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8—111no—
432C4⋊C8—111no—
433C4⋊C8—111no—
434C4⋊C8—111no—
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—111no—
451#97—111no—
452#97—111no—
453#97—111no—
454#97—221no—
455#97—221no—
456#97—221no—
457#97—222no—
458#97—221no—
459C4×C8—21no—
460C4×C8—222no—
461C4×C8—221no—
462C4×C8—221no—
463C4×C8—221no—
464C4×C8—221no—
465#95—221no—
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—111no—
483C22×C4—111no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4C23×D1111yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—112no—
493M16—224no—
494M16—224no—
495M16—221no—
496M16—221no—
497M16—221no—
498M16Q8×D1112yes—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—111no—
506C2×C8—111no—
507C2×C8—112no—
508C2×C8—112no—
509C2×C8—111no—
510C2×C8—111no—
511C2×C8—224no—
512C2×C8—224no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8C2×C4×D1111yescharacteristic
518C2×C8C2×C4×D1111yescharacteristic
519C2×C8D4×D1111yescharacteristic
520C2×C8D4×D1111yescharacteristic
521C4⋊C4—111no—
522C4⋊C4—111no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—442no—
532C4⋊C4C2×C4×D1111yescharacteristic
533C4⋊C4C2×C4×D1111yescharacteristic
534C4⋊C4C2×C4×D1111yescharacteristic
535C4⋊C4C2×C4×D1111yescharacteristic
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—221no—
539C22⋊C4—221no—
540C22⋊C4—221no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—111no—
546C42—111no—
547C42—111no—
548C42—111no—
549C42—221no—
550C42—221no—
551C42—221no—
552C42—221no—
553C42—221no—
554C11#2162911yescharacteristic, complemented, Sylow
555C23—221no—
556C23#41×D1111yescharacteristic
557Q8—112no—
558Q8—221no—
559Q8—881no—
560Q8—881no—
561D4—112no—
562D4—222no—
563D4—222no—
564D4—221no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—111no—
573C2×C4—111no—
574C2×C4—111no—
575C2×C4—111no—
576C2×C4—221no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—881no—
587C2×C4—881no—
588C2×C4C22×C4×D1111yescharacteristic
589C2×C4C2×D4×D1111yescharacteristic
590C2×C4C2×Q8×D1111yescharacteristic
591C2×C4#41×D1111yescharacteristic
592C2×C4#41×D1111yescharacteristic
593C2×C4#41×D1111yescharacteristic
594C8—21no—
595C8—21no—
596C8—22no—
597C8—21no—
598C8—21no—
599C8—41no—
600C8—112no—
601C8—112no—
602C8—221no—
603C8—221no—
604C8—222no—
605C8—441no—
606C22—21no—
607C22—21no—
608C22—222no—
609C22—441no—
610C22—441no—
611C22C4×D4×D1111yescharacteristic
612C22#1062321911yescharacteristic
613C22#1062323711yescharacteristic
614C4—42no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—221no—
620C4—221no—
621C4—221no—
622C4—221no—
623C4—222no—
624C4—441no—
625C4—441no—
626C4—881no—
627C4#1062305311yescharacteristic
628C4C4×Q8×D1111yescharacteristic
629C4D11×C22⋊Q811yescharacteristic
630C4#1062318711yescharacteristic
631C2—21no—
632C2—21no—
633C2—442no—
634C2#1307115011yescharacteristic
635C2#1307752111yescharacteristic
636C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1922C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C23
cosocleC22×C4×C11C24
hypercenter#1922D11
hypocenterC11#21629
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1922

Complements

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

NH ≅ G/Ntype
2. #13077555C2semidirect
4. #13069558C2semidirect
5. #13069390C2semidirect
6. #13069215C2semidirect
10. #13068502C2semidirect
11. #13068494C2semidirect
12. #13068487C2semidirect
15. C11×#1922C2semidirect
41. #10622504C4semidirect
42. #10622503C4semidirect
43. #10622490C4semidirect
44. #10622488C4semidirect
45. #10622484C4semidirect
46. #10622483C4semidirect
47. #10622470C4semidirect
48. #10622467C4semidirect
84. #66960Q8semidirect
243. #1922D11semidirect
554. C11#21629semidirect

Maximal subgroups

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

subgroupindex
#130784022
#130775552
#130770432
#130695582
#130693902
#130692152
#130688942
#130688902
#130686352
#130685022
#130684942
#130684872
#130684592
#130684502
C11×#19222
#2162911