Finite Group Databasebeta

← #14736777

Subgroups — #14736777

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079334C211yesmaximal, characteristic, complemented
2#13078687C211yesmaximal, characteristic, complemented
3#13078071C211yesmaximal, characteristic
4#13068177C211yesmaximal, characteristic, complemented
5#13068163C211yesmaximal, characteristic, complemented
6#13068129C211yesmaximal, characteristic, complemented
7#13068081C211yesmaximal, characteristic, complemented
8#13068060C211yesmaximal, characteristic, complemented
9#13068046C211yesmaximal, characteristic, complemented
10#13068010C211yesmaximal, characteristic, complemented
11#13067964C211yesmaximal, characteristic, complemented
12#13067368C211yesmaximal, characteristic, complemented
13#13067322C211yesmaximal, characteristic, complemented
14#13067317C211yesmaximal, characteristic, complemented
15C11×#2971C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17C2×#67003—21no—
18#10623008C2211yescharacteristic
19#10623001C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C8×Q8×C11C2211yescharacteristic
22C11×#436—21no—
23C11×#436—21no—
24C11×#436C2211yescharacteristic
25C11×#436C2211yescharacteristic
26C11×#432—21no—
27C11×#432C2211yescharacteristic
28C4×C11×M16—21no—
29C4×C11×M16C2211yescharacteristic
30#10622852—21no—
31#10622747—21no—
32#10622747—21no—
33#10622644C2211yescharacteristic
34#10622644C2211yescharacteristic
35C4×#4326—21no—
36#10622641—21no—
37#10622640C2211yescharacteristic
38#10622633C2211yescharacteristic
39#10622632C2211yescharacteristic
40#10622632C2211yescharacteristic
41C4×#4324—21no—
42#10622629—21no—
43#10622628C2211yescharacteristic
44#10622620C2211yescharacteristic
45#10622615—21no—
46#10622609—21no—
47#10622538C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622323—21no—
50#10622323—21no—
51#10622307C2211yescharacteristic
52#10622306C2211yescharacteristic
53#10622295C2211yescharacteristic
54#10622294C2211yescharacteristic
55#10622124C2211yescharacteristic
56#10622124C2211yescharacteristic
57#10622124C2211yescharacteristic
58#10622124C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C2×#4339—21no—
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C2×C11×M16D411yescharacteristic
72C2×C11×M16D411yescharacteristic
73C4×Q8×C11D411yescharacteristic
74C4×Q8×C11C2311yescharacteristic
75C4×D4×C11—21no—
76C4×D4×C11—21no—
77C4×D4×C11D411yescharacteristic
78C4×D4×C11C2311yescharacteristic
79C11×#117—21no—
80C11×#117D411yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83#67003—44no—
84C2×#4326—21no—
85C2×#4326—21no—
86C2×#4325—21no—
87C2×#4324—21no—
88C2×#4324—21no—
89C2×#4323—21no—
90#66983—21no—
91#66983—21no—
92#66979—21no—
93#66977—21no—
94#66977—21no—
95C22×C11⋊C8—21no—
96C2×#4314—21no—
97C2×#4314—21no—
98#66928—21no—
99#66927C2311yescharacteristic
100C4×D44—21no—
101C4×D44—21no—
102#66923—21no—
103#66922C2311yescharacteristic
104#66922C2311yescharacteristic
105#66922C2311yescharacteristic
106C4×Dic22—21no—
107C4×Dic22—21no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8C2311yescharacteristic
111C11×C4⋊C8C2311yescharacteristic
112C11×C22⋊C8—21no—
113C11×C22⋊C8—21no—
114C11×C22⋊C8—21no—
115C11×#97—21no—
116C11×#97D411yescharacteristic
117C11×#97D411yescharacteristic
118C4×C8×C11—21no—
119C4×C8×C11—21no—
120C4×C8×C11C2311yescharacteristic
121C4×C8×C11C2311yescharacteristic
122#66899—21no—
123#66896—21no—
124C22⋊(C11⋊C8)—21no—
125#66885—21no—
126#66885—21no—
127#66882—21no—
128#66882—21no—
129#66880—21no—
130#66880—21no—
131#66874—21no—
132#66874—21no—
133#66874—21no—
134#66874—21no—
135#66873—21no—
136#66873—21no—
137#66872—21no—
138#66871—21no—
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4×C11⋊C8—21no—
145#19182—111nomaximal, Sylow
146C11×#41—22no—
147C11×#41—41no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11C2×D411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C2×C22⋊D11—41no—
158#4339—42no—
159#4339—42no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×C4×D11—41no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C11×M16—22no—
168C11×M16—41no—
169C11×M16—42no—
170C11×M16—42no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C4⋊C4C2×D411yescharacteristic
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11#4111yescharacteristic
190C42×C11C2411yescharacteristic
191C22⋊Dic11—41no—
192#4326—42no—
193#4326—42no—
194#4325—42no—
195#4324—42no—
196#4324—42no—
197#4323—42no—
198(C2×D11)⋊C4—41no—
199(C2×D11)⋊C4—41no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206Dic11⋊C4—41no—
207Dic11⋊C4—41no—
208C4×Dic11—41no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—42no—
214#4314—42no—
215#4314—42no—
216#3182—111no—
217#3107—111no—
218#3035—111no—
219#2971D1111yescharacteristic, complemented
220#1701—111no—
221#1699—111no—
222#1693—111no—
223#1685—111no—
224#1682—111no—
225#1680—111no—
226#1674—111no—
227#1666—111no—
228#1565—111no—
229#1553—111no—
230#1552—111no—
231C23×C11—21no—
232C23×C11#12111yescharacteristic
233C22×D11—41no—
234Q8×C11—21no—
235Q8×C11AGL(1,ℤ/8)12yes—
236D4×C11—21no—
237D4×C11—21no—
238D4×C11—42no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—81no—
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C22⋊D11—82no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261D44—41no—
262D44—41no—
263D44—41no—
264D44—41no—
265D44—81no—
266C4×D11—82no—
267Dic22—41no—
268Dic22—41no—
269Dic22—41no—
270Dic22—41no—
271Dic22—41no—
272Dic22—41no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—41no—
277C8×C11—41no—
278C8×C11#13512yescomplemented
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C2×#135—221no—
284#533—111no—
285#532—111no—
286C4×#41C2×D1111yescharacteristic
287#500—111no—
288#492—111no—
289#487—111no—
290#486—111no—
291#485—221no—
292#475—111no—
293#474—111no—
294#468—221no—
295#468—221no—
296#464—221no—
297#463—221no—
298#462—111no—
299#462—111no—
300#461—111no—
301#461—111no—
302#460—111no—
303#459—111no—
304#452—221no—
305C8×Q8C2×D1111yescharacteristic
306C8×Q8C2×D1111yescharacteristic
307#440—221no—
308#440—221no—
309C4×Q16—221no—
310C4×SD16—221no—
311#436—21no—
312#436—21no—
313#436C2×D1111yescharacteristic
314#436C2×D1111yescharacteristic
315#432—21no—
316#432C2×D1111yescharacteristic
317#431—111no—
318C2×C4⋊C8—111no—
319#416—221no—
320C4×M16—21no—
321C4×M16C2×D1111yescharacteristic
322#335—111no—
323#335—111no—
324#334—111no—
325#334—111no—
326#332—111no—
327#332—111no—
328#332—111no—
329#332—111no—
330#332—111no—
331#332—111no—
332#331—111no—
333#331—111no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11C2×#12111yescharacteristic
341C2×D11—81no—
342C2×D11—81no—
343C2×D11—81no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—22no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11C2×#13511yescharacteristic
352C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
353C4×C11#57511yescharacteristic
354C4×C11#57511yescharacteristic
355Dic11—81no—
356Dic11—81no—
357Dic11—81no—
358C2×#41—221no—
359C2×#41D4411yescharacteristic
360#135—444no—
361C2×Q16—221no—
362C2×Q16—221no—
363C2×SD16—221no—
364C2×SD16—221no—
365C2×SD16—221no—
366C2×SD16—221no—
367C2×SD16—221no—
368C2×D8—221no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16C22⋊D1111yescharacteristic
372C2×M16C22⋊D1111yescharacteristic
373C22×C8—221no—
374C4⋊Q8—111no—
375C4⋊Q8—111no—
376C4⋊Q8—111no—
377#127—111no—
378#125—221no—
379#124—221no—
380C22⋊Q8—221no—
381C22⋊Q8—221no—
382#121—221no—
383#121—221no—
384C4×Q8—221no—
385C4×Q8—221no—
386C4×Q8D4411yescharacteristic
387C4×Q8C22×D1111yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—221no—
391C4×D4—221no—
392C4×D4D4411yescharacteristic
393C4×D4C22×D1111yescharacteristic
394#117—21no—
395#117—221no—
396#117D4411yescharacteristic
397C2×C42—21no—
398C2×C42C22×D1111yescharacteristic
399#107—221no—
400#107—221no—
401#107—221no—
402#106—221no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—221no—
410C4⋊C8C22×D1111yescharacteristic
411C4⋊C8C22×D1111yescharacteristic
412#103—221no—
413#103—221no—
414#103—221no—
415#103—221no—
416#103—221no—
417#103—221no—
418#103—221no—
419#102—221no—
420#102—221no—
421#102—221no—
422#102—221no—
423#102—221no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—221no—
428#97—21no—
429#97C22⋊D1111yescharacteristic
430#97C22⋊D1111yescharacteristic
431C4×C8—21no—
432C4×C8—21no—
433C4×C8—221no—
434C4×C8C22×D1111yescharacteristic
435C4×C8C22×D1111yescharacteristic
436C2×C11—41no—
437C2×C11—81no—
438C2×C11#303511yescharacteristic
439C2×C11#305511yescharacteristic
440C2×C11#306911yescharacteristic
441D11—161no—
442#41—22no—
443#41—41no—
444#41—442no—
445#41—442no—
446C2×Q8—221no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8C2×D4411yescharacteristic
450C2×D4—21no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4—441no—
455C2×D4C2×D4411yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—441no—
460C22×C4C2×D4411yescharacteristic
461C22×C4#433911yescharacteristic
462C22×C4C2×C22⋊D1111yescharacteristic
463Q16—442no—
464Q16—442no—
465SD16—442no—
466SD16—442no—
467SD16—442no—
468SD16—442no—
469SD16—442no—
470D8—442no—
471M16—22no—
472M16—41no—
473M16—42no—
474M16—42no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—442no—
482C2×C8C2×C22⋊D1111yescharacteristic
483C2×C8C2×C22⋊D1111yescharacteristic
484C2×C8C2×C22⋊D1111yescharacteristic
485C2×C8C2×C22⋊D1111yescharacteristic
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—441no—
495C4⋊C4—441no—
496C4⋊C4C2×D4411yescharacteristic
497C4⋊C4C2×D4411yescharacteristic
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—441no—
502C22⋊C4—441no—
503C22⋊C4—441no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—441no—
508C42C2×D4411yescharacteristic
509C42#433911yescharacteristic
510C42C2×C22⋊D1111yescharacteristic
511C42C23×D1111yescharacteristic
512C11#1918211yescharacteristic, complemented, Sylow
513C23—21no—
514C23—441no—
515C23#6698311yescharacteristic
516Q8—21no—
517Q8—441no—
518Q8—441no—
519Q8—441no—
520Q8—441no—
521Q8—441no—
522Q8—441no—
523Q8#6696112yes—
524D4—21no—
525D4—21no—
526D4—42no—
527D4—441no—
528D4—441no—
529D4—441no—
530D4—441no—
531D4—881no—
532D4—882no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—81no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—882no—
549C2×C4#6698311yescharacteristic
550C2×C4#6698311yescharacteristic
551C2×C4#6698311yescharacteristic
552C2×C4C22×D4411yescharacteristic
553C2×C4C2×#433911yescharacteristic
554C2×C4C22×C22⋊D1111yescharacteristic
555C8—21no—
556C8—21no—
557C8—21no—
558C8—41no—
559C8—41no—
560C8—441no—
561C8—441no—
562C8—441no—
563C8—441no—
564C8#6700312yescomplemented
565C22—21no—
566C22—21no—
567C22—21no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—881no—
572C22—881no—
573C22—881no—
574C22C2×#6698311yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—22no—
580C4—41no—
581C4—41no—
582C4—881no—
583C4—881no—
584C4—881no—
585C4C2×#6696111yescharacteristic
586C4#1062327911yescharacteristic
587C4C2×#6700311yescharacteristic
588C4#1062335311yescharacteristic
589C2—41no—
590C2—81no—
591C2—1761no—
592C2#1307807111yescharacteristic
593C2#1307823511yescharacteristic
594C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2971C2
socleC22×C11C2×#121
prime radical#13078071C2
hypercenter#2971D11
hypocenterC11#19182
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2971

Complements

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

NH ≅ G/Ntype
1. #13079334C2semidirect
2. #13078687C2semidirect
4. #13068177C2semidirect
5. #13068163C2semidirect
6. #13068129C2semidirect
7. #13068081C2semidirect
8. #13068060C2semidirect
9. #13068046C2semidirect
10. #13068010C2semidirect
11. #13067964C2semidirect
12. #13067368C2semidirect
13. #13067322C2semidirect
14. #13067317C2semidirect
15. C11×#2971C2semidirect
219. #2971D11semidirect
278. C8×C11#135semidirect
512. C11#19182semidirect
564. C8#67003semidirect

Maximal subgroups

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

subgroupindex
#130793342
#130786872
#130780712
#130681772
#130681632
#130681292
#130680812
#130680602
#130680462
#130680102
#130679642
#130673682
#130673222
#130673172
C11×#29712
#1918211