Finite Group Databasebeta

← #14738755

Subgroups — #14738755

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080007C211yesmaximal, characteristic, complemented
2#13079623C211yesmaximal, characteristic
3#13079334C211yesmaximal, characteristic
4#13068184C211yesmaximal, characteristic, complemented
5#13068170C211yesmaximal, characteristic, complemented
6#13068134C211yesmaximal, characteristic, complemented
7#13068088C211yesmaximal, characteristic, complemented
8#13068060C211yesmaximal, characteristic, complemented
9#13068046C211yesmaximal, characteristic, complemented
10#13068010C211yesmaximal, characteristic, complemented
11#13067964C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067314C211yesmaximal, characteristic, complemented
14#13067291C211yesmaximal, characteristic
15C11×#2962C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17#10623008C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#446—21no—
20C11×#446—21no—
21C11×#446C2211yescharacteristic
22C11×#446C2211yescharacteristic
23C8×Q8×C11C2211yescharacteristic
24C8×Q8×C11C2211yescharacteristic
25C11×#424—21no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C11×#405—21no—
28C4×C11×M16C2211yescharacteristic
29#10622747—21no—
30#10622747—21no—
31#10622707—21no—
32#10622703—21no—
33#10622702—21no—
34#10622699—21no—
35#10622665—21no—
36#10622665—21no—
37#10622660—21no—
38#10622660—21no—
39#10622644C2211yescharacteristic
40#10622644C2211yescharacteristic
41#10622644C2211yescharacteristic
42#10622644C2211yescharacteristic
43#10622640C2211yescharacteristic
44#10622640C2211yescharacteristic
45#10622633C2211yescharacteristic
46#10622633C2211yescharacteristic
47#10622539C2211yescharacteristic
48#10622537C2211yescharacteristic
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×#4339—21no—
68C2×C11×M16D411yescharacteristic
69C2×C11×M16D411yescharacteristic
70C22×C8×C11—21no—
71C11×C4⋊Q8D411yescharacteristic
72C11×C4⋊Q8D411yescharacteristic
73C11×#125—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8D411yescharacteristic
76C11×C22⋊Q8D411yescharacteristic
77C4×Q8×C11—21no—
78C4×Q8×C11C2311yescharacteristic
79C4×Q8×C11C2311yescharacteristic
80C11×#117—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4326—21no—
83C2×#4326—21no—
84C2×#4326—21no—
85C2×#4326—21no—
86C2×#4325—21no—
87C2×#4325—21no—
88#66983—21no—
89#66983—21no—
90#66979—21no—
91#66977—21no—
92#66977—21no—
93C2×#4318—21no—
94C2×#4314—21no—
95C2×#4314—21no—
96#66928—21no—
97#66927C2311yescharacteristic
98C4×D44—21no—
99C4×D44—21no—
100#66923—21no—
101#66922C2311yescharacteristic
102#66922C2311yescharacteristic
103#66922C2311yescharacteristic
104C4×Dic22—21no—
105C4×Dic22—21no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8—21no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8—21no—
111C11×C4⋊C8C2311yescharacteristic
112C11×C4⋊C8C2311yescharacteristic
113C11×#97—21no—
114C11×#97—21no—
115C11×#97D411yescharacteristic
116C11×#97D411yescharacteristic
117C4×C8×C11—21no—
118C4×C8×C11—21no—
119C4×C8×C11C2311yescharacteristic
120C4×C8×C11C2311yescharacteristic
121#66899—21no—
122#66899—21no—
123C22⋊(C11⋊C8)—21no—
124#66885—21no—
125#66885—21no—
126#66882—21no—
127#66882—21no—
128#66880—21no—
129#66880—21no—
130#66874—21no—
131#66874—21no—
132#66874—21no—
133#66874—21no—
134#66873—21no—
135#66873—21no—
136#66872—21no—
137#66872—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143#66867—21no—
144#19372—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11C2×D411yescharacteristic
147C2×Q8×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4111yescharacteristic
151C2×C22⋊D11—41no—
152#4339—81no—
153#4339—81no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×C4×D11—41no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C11×M16—22no—
162C11×M16—41no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—42no—
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11#4111yescharacteristic
186C42×C11C2411yescharacteristic
187C22⋊Dic11—41no—
188#4326—81no—
189#4326—81no—
190#4326—81no—
191#4326—81no—
192#4325—81no—
193#4325—81no—
194(C2×D11)⋊C4—41no—
195(C2×D11)⋊C4—41no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202Dic11⋊C4—41no—
203Dic11⋊C4—41no—
204C4×Dic11—41no—
205#4318—81no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210#4314—42no—
211#4314—42no—
212#3255—111no—
213#3216—111no—
214#3182—111no—
215#2962D1111yescharacteristic, complemented
216#1702—111no—
217#1700—111no—
218#1694—111no—
219#1686—111no—
220#1682—111no—
221#1680—111no—
222#1674—111no—
223#1666—111no—
224#1569—111no—
225#1552—111no—
226#1547—111no—
227C23×C11#12111yescharacteristic
228C22×D11—41no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—81no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C22⋊D11—82no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253D44—41no—
254D44—41no—
255D44—41no—
256D44—41no—
257D44—81no—
258C4×D11—82no—
259Dic22—41no—
260Dic22—41no—
261Dic22—41no—
262Dic22—41no—
263Dic22—41no—
264Dic22—41no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11#13712yes—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275#533—111no—
276#533C2×D1111yescharacteristic
277#532—111no—
278#500—111no—
279#497—221no—
280#492—111no—
281#489—221no—
282#487—111no—
283#486—111no—
284#475—111no—
285#475—111no—
286#475—221no—
287#470—221no—
288#470—221no—
289#468—221no—
290#468—221no—
291#462—111no—
292#462—111no—
293#462—111no—
294#462—111no—
295#462—221no—
296#460—111no—
297#460—111no—
298#452—221no—
299#452—221no—
300#446—21no—
301#446—21no—
302#446C2×D1111yescharacteristic
303#446C2×D1111yescharacteristic
304C8×Q8C2×D1111yescharacteristic
305C8×Q8C2×D1111yescharacteristic
306#440—221no—
307#440—221no—
308#432—111no—
309#424—21no—
310#423—111no—
311C2×C4⋊C8C2×D1111yescharacteristic
312#405—21no—
313C4×M16C2×D1111yescharacteristic
314#335—111no—
315#335—111no—
316#334—111no—
317#334—111no—
318#332—111no—
319#332—111no—
320#332—111no—
321#332—111no—
322#332—111no—
323#332—111no—
324#331—111no—
325#331—111no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11C2×#12111yescharacteristic
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—81no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11C2×#13711yescharacteristic
342C4×C11#57511yescharacteristic
343C4×C11#57611yescharacteristic
344C4×C11#57711yescharacteristic
345Dic11—81no—
346Dic11—81no—
347Dic11—81no—
348C2×#41—221no—
349C2×Q16—221no—
350C2×Q16—221no—
351C2×Q16—221no—
352C2×Q16—221no—
353C2×SD16—221no—
354C2×SD16—221no—
355C2×SD16—221no—
356C2×SD16—221no—
357C2×M16—221no—
358C2×M16C22⋊D1111yescharacteristic
359C2×M16C22⋊D1111yescharacteristic
360C22×C8—21no—
361C4⋊Q8—111no—
362C4⋊Q8—111no—
363C4⋊Q8—111no—
364C4⋊Q8D4411yescharacteristic
365C4⋊Q8D4411yescharacteristic
366#127—111no—
367#125—21no—
368#125—221no—
369#124—221no—
370C22⋊Q8—21no—
371C22⋊Q8—221no—
372C22⋊Q8—221no—
373C22⋊Q8D4411yescharacteristic
374C22⋊Q8D4411yescharacteristic
375#121—221no—
376#121—221no—
377C4×Q8—21no—
378C4×Q8—221no—
379C4×Q8—221no—
380C4×Q8C22×D1111yescharacteristic
381C4×Q8C22×D1111yescharacteristic
382C4×D4—221no—
383C4×D4—221no—
384#117—21no—
385#117—221no—
386C2×C42C22×D1111yescharacteristic
387#107—221no—
388#107—221no—
389#106—221no—
390#106—221no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—111no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—221no—
401C4⋊C8C22×D1111yescharacteristic
402C4⋊C8C22×D1111yescharacteristic
403#103—221no—
404#103—221no—
405#103—221no—
406#103—221no—
407#103—221no—
408#103—221no—
409#103—221no—
410#103—221no—
411#102—221no—
412#102—221no—
413#102—221no—
414#102—221no—
415C22⋊C8—221no—
416#97—21no—
417#97—21no—
418#97—221no—
419#97C22⋊D1111yescharacteristic
420#97C22⋊D1111yescharacteristic
421C4×C8—21no—
422C4×C8—21no—
423C4×C8C22×D1111yescharacteristic
424C4×C8C22×D1111yescharacteristic
425C2×C11—41no—
426C2×C11#303711yescharacteristic
427C2×C11#306211yescharacteristic
428C2×C11#306911yescharacteristic
429D11—161no—
430#41—881no—
431#41—881no—
432C2×Q8—21no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8C2×D4411yescharacteristic
437C2×Q8C2×D4411yescharacteristic
438C2×D4—221no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—441no—
442C22×C4—441no—
443C22×C4C2×D4411yescharacteristic
444C22×C4#433911yescharacteristic
445C22×C4C2×C22⋊D1111yescharacteristic
446Q16—881no—
447Q16—881no—
448Q16—881no—
449Q16—881no—
450SD16—442no—
451SD16—442no—
452SD16—881no—
453SD16—881no—
454M16—22no—
455M16—41no—
456M16—881no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—42no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8C2×C22⋊D1111yescharacteristic
465C2×C8C2×C22⋊D1111yescharacteristic
466C2×C8C2×C22⋊D1111yescharacteristic
467C2×C8C2×C22⋊D1111yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—441no—
482C4⋊C4—441no—
483C4⋊C4C2×D4411yescharacteristic
484C4⋊C4C2×D4411yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—441no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C42—21no—
491C42—21no—
492C42—441no—
493C42C2×D4411yescharacteristic
494C42#433911yescharacteristic
495C42C2×C22⋊D1111yescharacteristic
496C42C23×D1111yescharacteristic
497C11#1937211yescharacteristic, complemented, Sylow
498C23—441no—
499C23#6698311yescharacteristic
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—21no—
504Q8—81no—
505Q8—441no—
506Q8—441no—
507Q8—441no—
508Q8—441no—
509Q8—441no—
510Q8—441no—
511D4—441no—
512D4—441no—
513D4—441no—
514D4—441no—
515D4—881no—
516D4—882no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—882no—
530C2×C4#6698311yescharacteristic
531C2×C4#6698311yescharacteristic
532C2×C4#6698311yescharacteristic
533C2×C4C22×D4411yescharacteristic
534C2×C4C2×#433911yescharacteristic
535C2×C4C22×C22⋊D1111yescharacteristic
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—441no—
542C8—441no—
543C8—441no—
544C8—441no—
545C8#6699512yes—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—881no—
550C22—881no—
551C22—881no—
552C22C2×#6698311yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—881no—
562C4—881no—
563C4—881no—
564C4#1062328211yescharacteristic
565C4#1062328311yescharacteristic
566C4C2×#6699511yescharacteristic
567C4#1062335311yescharacteristic
568C2—41no—
569C2—1761no—
570C2#1307808811yescharacteristic
571C2#1307829611yescharacteristic
572C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2962C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#2962D11
hypocenterC11#19372
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
1. #13080007C2semidirect
4. #13068184C2semidirect
5. #13068170C2semidirect
6. #13068134C2semidirect
7. #13068088C2semidirect
8. #13068060C2semidirect
9. #13068046C2semidirect
10. #13068010C2semidirect
11. #13067964C2semidirect
12. #13067383C2semidirect
13. #13067314C2semidirect
15. C11×#2962C2semidirect
215. #2962D11semidirect
497. C11#19372semidirect

Maximal subgroups

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

subgroupindex
#130800072
#130796232
#130793342
#130681842
#130681702
#130681342
#130680882
#130680602
#130680462
#130680102
#130679642
#130673832
#130673142
#130672912
C11×#29622
#1937211