Finite Group Databasebeta

← #14811941

Subgroups — #14811941

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073633C211yesmaximal, characteristic, complemented
2#13071585C211yesmaximal, characteristic
3#13070005C211yesmaximal, characteristic
4#13069989C211yesmaximal, characteristic
5#13069761C211yesmaximal, characteristic
6#13069749C211yesmaximal, characteristic
7#13069572C211yesmaximal, characteristic, complemented
8#13069383C211yesmaximal, characteristic, complemented
9#13069331C211yesmaximal, characteristic, complemented
10#13069208C211yesmaximal, characteristic, complemented
11#13069200C211yesmaximal, characteristic, complemented
12#13068745C211yesmaximal, characteristic, complemented
13#13068625C211yesmaximal, characteristic
14#13068430C211yesmaximal, characteristic
15C11×#1988C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×#66943C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21#10622843—21no—
22#10622842—21no—
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66881C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29#10622601C2211yescharacteristic
30#10622596—21no—
31#10622590C2211yescharacteristic
32#10622590C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622586C2211yescharacteristic
36#10622585—21no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622553—21no—
41#10622552C2211yescharacteristic
42C4×(C2×D11)⋊C4—21no—
43C4×Dic11⋊C4C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622282—21no—
46#10622277—21no—
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11—21no—
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8—41no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4D411yescharacteristic
86C2×Dic11⋊C4D411yescharacteristic
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93#66946—22no—
94#66946Q814yescomplemented
95#66943—22no—
96#66943—41no—
97C11×C4⋊C8—41no—
98C11×#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95D411yescharacteristic
108C11⋊#95D411yescharacteristic
109#66885—22no—
110#66885—41no—
111#66881—22no—
112Dic11⋊C8—22no—
113Dic11⋊C8—41no—
114C8×Dic11—22no—
115#66873—22no—
116#66873—41no—
117#66871—22no—
118#26028—111nomaximal, Sylow
119C23×D11—21no—
120C2×Q8×C11—42no—
121C2×Q8×C11—42no—
122C2×Q8×C11—81no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C22×Dic11C2×D411yescharacteristic
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44C2×Q812yes—
143C2×C4×D11—24no—
144C2×C4×D11—81no—
145C2×C4×D11—81no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4C2×Q812yes—
160C11×C4⋊C4#4112yes—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—81no—
164(C2×D11)⋊C4—24no—
165(C2×D11)⋊C4—42no—
166(C2×D11)⋊C4—42no—
167(C2×D11)⋊C4—81no—
168(C2×D11)⋊C4—81no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—42no—
175C4⋊Dic11#4112yes—
176Dic11⋊C4—22no—
177Dic11⋊C4—41no—
178Dic11⋊C4—42no—
179Dic11⋊C4—42no—
180Dic11⋊C4—81no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—81no—
184C4×Dic11—81no—
185C4×Dic11C2×Q812yes—
186C4×Dic11#4112yes—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193#2550—111no—
194#2357—111no—
195#2067—111no—
196#2065—111no—
197#2025—111no—
198#2023—111no—
199#1989—111no—
200#1988D1111yescharacteristic, complemented
201#1949—111no—
202#1939—111no—
203#1921—111no—
204#1920—111no—
205#1835—111no—
206#1804—111no—
207C4×#102—111no—
208C23×C11C22×D411yescharacteristic
209C22×D11—22no—
210C22×D11—41no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216Q8×C11—84no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11#13512yes—
235C2×C4×C11C22×Q811yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11H(5,𝔽2)11yescharacteristic
240C2×C4×C112−1+411yescharacteristic
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—22no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11C22⋊Q812yes—
261C2×Dic11C22⋊Q812yes—
262D44—22no—
263D44—22no—
264D44—41no—
265D44—41no—
266C4×D11—84no—
267C8×C11—41no—
268C8×C11—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C2×C4⋊Q8C2×D1111yescharacteristic
272C2×#125—111no—
273C2×C4×D4—111no—
274C2×#107—111no—
275C2×#106—111no—
276C2×C4⋊C8—111no—
277C2×C4⋊C8—111no—
278C2×C4⋊C8C2×D1111yescharacteristic
279C2×#102—111no—
280C2×#102—111no—
281C2×#102—111no—
282C2×#102—111no—
283C2×C4×C8—111no—
284#398—221no—
285#395—221no—
286#391—221no—
287#390—111no—
288#390—111no—
289#389—111no—
290#389—111no—
291#389—221no—
292#388—221no—
293#388—221no—
294#382—111no—
295#382—111no—
296#381—221no—
297C4×C4⋊C4—111no—
298C4×C4⋊C4—111no—
299C4×C4⋊C4—111no—
300C4×C4⋊C4C2×D1111yescharacteristic
301C4×C22⋊C4—221no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340C2×D1111yescharacteristic
309#340C2×D1111yescharacteristic
310#340C2×D1111yescharacteristic
311#340C2×D1111yescharacteristic
312#336—111no—
313#336—111no—
314C22×C11C2×C22⋊Q811yescharacteristic
315C22×C11#54611yescharacteristic
316C22×C11#54811yescharacteristic
317C22×C11C2×#13511yescharacteristic
318C22×C11#57511yescharacteristic
319C22×C11#57611yescharacteristic
320C22×C11#57711yescharacteristic
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—42no—
324C2×D11—81no—
325C2×D11—81no—
326C2×D11—81no—
327C2×D11—81no—
328C4×C11—22no—
329C4×C11—42no—
330C4×C11—42no—
331C4×C11—41no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11#53311yescharacteristic
335C4×C11#54411yescharacteristic
336C4×C11#55511yescharacteristic
337C4×C11#55611yescharacteristic
338Dic11—22no—
339Dic11—22no—
340Dic11—42no—
341Dic11—41no—
342Dic11—41no—
343Dic11—81no—
344Dic11—81no—
345C22×Q8—21no—
346C22×D4—111no—
347C23×C4—221no—
348C22×C8—111no—
349C22×C8—111no—
350C22×C8C22×D1111yescharacteristic
351C22×C8C22×D1111yescharacteristic
352C4⋊Q8—22no—
353C4⋊Q8—41no—
354#125—222no—
355#125—441no—
356C4×D4—114no—
357C4×D4—222no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C42—21no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—221no—
381C2×C42—221no—
382C2×C42C22×D1111yescharacteristic
383#107—222no—
384#106—222no—
385C4⋊C8—41no—
386C4⋊C8—222no—
387C4⋊C8—441no—
388#102—222no—
389#102—222no—
390#102—441no—
391#102—441no—
392C4×C8—222no—
393#95—21no—
394#95—111no—
395#95—111no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404C2×C11#243911yescharacteristic
405C2×C11#307611yescharacteristic
406C2×C11#308111yescharacteristic
407C2×C11#329711yescharacteristic
408C2×C11#332611yescharacteristic
409C2×C11#336511yescharacteristic
410C2×C11#337011yescharacteristic
411D11—82no—
412C24—221no—
413C2×Q8—42no—
414C2×Q8—42no—
415C2×Q8—81no—
416C2×D4—112no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—221no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—224no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—881no—
435C22×C4—881no—
436C22×C4D4×D1111yescharacteristic
437C22×C4D4×D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—42no—
458C4⋊C4—112no—
459C4⋊C4—222no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—441no—
466C4⋊C4—442no—
467C4⋊C4—442no—
468C4⋊C4—442no—
469C4⋊C4—881no—
470C4⋊C4#433912yes—
471C4⋊C4Q8×D1112yes—
472C22⋊C4—224no—
473C22⋊C4—442no—
474C22⋊C4—442no—
475C22⋊C4—881no—
476C22⋊C4—881no—
477C42—21no—
478C42—21no—
479C42—81no—
480C42—112no—
481C42—112no—
482C42—221no—
483C42—221no—
484C42—881no—
485C42—881no—
486C11#2602811yescharacteristic, complemented, Sylow
487C23—222no—
488C23—441no—
489C23—441no—
490C23—441no—
491C23—441no—
492C23—441no—
493C23—441no—
494C23C2×D4×D1111yescharacteristic
495Q8—84no—
496D4—222no—
497D4—222no—
498D4—441no—
499D4—441no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—112no—
518C2×C4—112no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—222no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—884no—
539C2×C4#6696912yes—
540C2×C4C2×#433911yescharacteristic
541C2×C4#6703711yescharacteristic
542C2×C4C2×Q8×D1111yescharacteristic
543C2×C4#6704011yescharacteristic
544C2×C4#41×D1111yescharacteristic
545C2×C4#41×D1111yescharacteristic
546C8—41no—
547C8—41no—
548C8—441no—
549C8—441no—
550C22—442no—
551C22—442no—
552C22—442no—
553C22—881no—
554C22—881no—
555C22—881no—
556C22—881no—
557C22#1062302111yescharacteristic
558C22D11×C22⋊Q811yescharacteristic
559C22#1062316411yescharacteristic
560C22#1062328811yescharacteristic
561C22C2×#6696911yescharacteristic
562C22#1062330811yescharacteristic
563C22#1062330911yescharacteristic
564C4—22no—
565C4—41no—
566C4—42no—
567C4—42no—
568C4—81no—
569C4—81no—
570C4—222no—
571C4—222no—
572C4—442no—
573C4—441no—
574C4—441no—
575C4—881no—
576C4—881no—
577C4#1062309911yescharacteristic
578C4#1062310911yescharacteristic
579C4#1062320111yescharacteristic
580C4#1062326011yescharacteristic
581C2—882no—
582C2#1307230411yescharacteristic
583C2#1307839911yescharacteristic
584C2#1307844011yescharacteristic
585C2#1308046211yescharacteristic
586C2#1308086511yescharacteristic
587C2#1308131111yescharacteristic
588C2#1308137611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1988C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1988D11
hypocenterC11#26028
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
1. #13073633C2semidirect
7. #13069572C2semidirect
8. #13069383C2semidirect
9. #13069331C2semidirect
10. #13069208C2semidirect
11. #13069200C2semidirect
12. #13068745C2semidirect
15. C11×#1988C2semidirect
94. #66946Q8semidirect
200. #1988D11semidirect
486. C11#26028semidirect

Maximal subgroups

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

subgroupindex
#130736332
#130715852
#130700052
#130699892
#130697612
#130697492
#130695722
#130693832
#130693312
#130692082
#130692002
#130687452
#130686252
#130684302
C11×#19882
#2602811