Finite Group Databasebeta

← #14811942

Subgroups — #14811942

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#13073637C211yesmaximal, characteristic, complemented
2#13071587C211yesmaximal, characteristic
3#13070003C211yesmaximal, characteristic
4#13069989C211yesmaximal, characteristic
5#13069763C211yesmaximal, characteristic
6#13069753C211yesmaximal, characteristic
7#13069571C211yesmaximal, characteristic, complemented
8#13069567C211yesmaximal, characteristic, complemented
9#13069386C211yesmaximal, characteristic, complemented
10#13069209C211yesmaximal, characteristic, complemented
11#13069202C211yesmaximal, characteristic, complemented
12#13068747C211yesmaximal, characteristic, complemented
13#13068627C211yesmaximal, characteristic
14C4×#66885C211yesmaximal, characteristic
15C11×#1939C211yesmaximal, characteristic, complemented
16C2×C4×D44C2211yescharacteristic
17C2×#66923C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30#10622603—21no—
31#10622603—21no—
32#10622597—21no—
33#10622592—21no—
34#10622552C2211yescharacteristic
35#10622552C2211yescharacteristic
36#10622549C2211yescharacteristic
37#10622549C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622279—21no—
44#10622277—21no—
45#10622260—21no—
46#10622259—21no—
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×Dic22—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C4×D44—22no—
92C4×D44Q814yescomplemented
93#66923—22no—
94#66923—41no—
95#66922—22no—
96#66922—41no—
97C11×C4⋊C8—22no—
98C11×C4⋊C8—41no—
99C11×C4⋊C8—41no—
100C4×C8×C11—22no—
101C11×#95D411yescharacteristic
102C11×#95D411yescharacteristic
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112#66885—22no—
113#66885—22no—
114#66885—41no—
115#66885—41no—
116#66882—22no—
117#66881—22no—
118#26028—111nomaximal, Sylow
119C23×D11—21no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44C2×Q812yes—
140C2×C4×D11—24no—
141C2×C4×D11—81no—
142C2×C4×D11—81no—
143C2×Dic22—42no—
144C2×Dic22—42no—
145C2×Dic22—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—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—41no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11C2×Q812yes—
165C42×C11#4112yes—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—42no—
168(C2×D11)⋊C4—42no—
169(C2×D11)⋊C4—81no—
170(C2×D11)⋊C4—81no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—42no—
183C4⋊Dic11C2×Q812yes—
184C4⋊Dic11#4112yes—
185C4⋊Dic11#4112yes—
186Dic11⋊C4—42no—
187Dic11⋊C4—42no—
188Dic11⋊C4—42no—
189Dic11⋊C4—81no—
190C4×Dic11—81no—
191C4×Dic11—81no—
192C4×Dic11—81no—
193#2550—111no—
194#2357—111no—
195#2067—111no—
196#2065—111no—
197#2025—111no—
198#2023—111no—
199#1989—111no—
200#1988—111no—
201#1949—111no—
202#1939D1111yescharacteristic, complemented
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—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11C22⋊Q812yes—
232C2×C4×C11C22⋊Q812yes—
233C2×C4×C11#13512yes—
234C2×C4×C11C22×Q811yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
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×Dic11—41no—
261D44—22no—
262D44—22no—
263D44—41no—
264D44—41no—
265C4×D11—84no—
266Dic22—84no—
267C8×C11—41no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11—41no—
271C2×C4⋊Q8—111no—
272C2×#125—111no—
273C2×C4×D4—111no—
274C2×#107—111no—
275C2×#106—111no—
276C2×C4⋊C8C2×D1111yescharacteristic
277C2×C4⋊C8C2×D1111yescharacteristic
278C2×C4⋊C8C2×D1111yescharacteristic
279C2×#102—111no—
280C2×#102—111no—
281C2×#102—111no—
282C2×#102—111no—
283C2×C4×C8C2×D1111yescharacteristic
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#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#336C2×D1111yescharacteristic
313#336C2×D1111yescharacteristic
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—22no—
330C4×C11—22no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11#53311yescharacteristic
335C4×C11#54411yescharacteristic
336C4×C11#55511yescharacteristic
337C4×C11#55611yescharacteristic
338Dic11—42no—
339Dic11—42no—
340Dic11—42no—
341Dic11—81no—
342Dic11—81no—
343Dic11—81no—
344Dic11—81no—
345C22×Q8—221no—
346C22×D4—111no—
347C23×C4—221no—
348C22×C8C22×D1111yescharacteristic
349C22×C8C22×D1111yescharacteristic
350C22×C8C22×D1111yescharacteristic
351C22×C8C22×D1111yescharacteristic
352C4⋊Q8—222no—
353C4⋊Q8—441no—
354#125—222no—
355#125—441no—
356C4×D4—114no—
357C4×D4—222no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4D4411yescharacteristic
371C2×C4⋊C4D4411yescharacteristic
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C42—221no—
378C2×C42—221no—
379C2×C42—221no—
380C2×C42C22×D1111yescharacteristic
381C2×C42C22×D1111yescharacteristic
382C2×C42C22×D1111yescharacteristic
383#107—222no—
384#106—222no—
385C4⋊C8—22no—
386C4⋊C8—41no—
387C4⋊C8—41no—
388#102—222no—
389#102—222no—
390#102—441no—
391#102—441no—
392C4×C8—22no—
393#95—221no—
394#95—221no—
395#95—221no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95D4411yescharacteristic
403#95D4411yescharacteristic
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—442no—
414C2×Q8—442no—
415C2×Q8—881no—
416C2×D4—112no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—221no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—224no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—881no—
431C22×C4—881no—
432C22×C4C2×D4411yescharacteristic
433C22×C4C2×D4411yescharacteristic
434C22×C4C2×D4411yescharacteristic
435C22×C4C2×D4411yescharacteristic
436C22×C4C2×D4411yescharacteristic
437C22×C4C2×D4411yescharacteristic
438C22×C4C23×D1111yescharacteristic
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C4⋊C4—22no—
452C4⋊C4—41no—
453C4⋊C4—112no—
454C4⋊C4—112no—
455C4⋊C4—112no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—442no—
468C4⋊C4—442no—
469C4⋊C4—442no—
470C4⋊C4—442no—
471C4⋊C4—881no—
472C22⋊C4—224no—
473C22⋊C4—442no—
474C22⋊C4—442no—
475C22⋊C4—881no—
476C22⋊C4—881no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—881no—
482C42—881no—
483C42—881no—
484C42#434112yes—
485C42Q8×D1112yes—
486C11#2602811yescharacteristic, complemented, Sylow
487C23—222no—
488C23—441no—
489C23—441no—
490C23—441no—
491C23—441no—
492C23—441no—
493C23—441no—
494C23C22×D4411yescharacteristic
495Q8—884no—
496D4—222no—
497D4—222no—
498D4—441no—
499D4—441no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—884no—
537C2×C4#6695012yes—
538C2×C4#6695012yes—
539C2×C4#6695712yes—
540C2×C4C2×#434111yescharacteristic
541C2×C4#6703711yescharacteristic
542C2×C4C2×Q8×D1111yescharacteristic
543C2×C4#6704011yescharacteristic
544C2×C4#41×D1111yescharacteristic
545C2×C4#41×D1111yescharacteristic
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C22—442no—
551C22—442no—
552C22—442no—
553C22—881no—
554C22—881no—
555C22—881no—
556C22—881no—
557C22C2×#6695011yescharacteristic
558C22#1062308511yescharacteristic
559C22#1062310711yescharacteristic
560C22C2×#6695711yescharacteristic
561C22#1062327911yescharacteristic
562C22#1062328211yescharacteristic
563C22#1062328311yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—442no—
571C4—442no—
572C4—442no—
573C4—881no—
574C4—881no—
575C4—881no—
576C4—881no—
577C4#1062314711yescharacteristic
578C4#1062317211yescharacteristic
579C4#1062321911yescharacteristic
580C4#1062326011yescharacteristic
581C2—882no—
582C2#1307230511yescharacteristic
583C2#1307840611yescharacteristic
584C2#1307844811yescharacteristic
585C2#1308046811yescharacteristic
586C2#1308087111yescharacteristic
587C2#1308131411yescharacteristic
588C2#1308137111yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1939C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1939D11
hypocenterC11#26028
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. #13073637C2semidirect
7. #13069571C2semidirect
8. #13069567C2semidirect
9. #13069386C2semidirect
10. #13069209C2semidirect
11. #13069202C2semidirect
12. #13068747C2semidirect
15. C11×#1939C2semidirect
92. C4×D44Q8semidirect
202. #1939D11semidirect
486. C11#26028semidirect

Maximal subgroups

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

subgroupindex
#130736372
#130715872
#130700032
#130699892
#130697632
#130697532
#130695712
#130695672
#130693862
#130692092
#130692022
#130687472
#130686272
C4×#668852
C11×#19392
#2602811