Finite Group Databasebeta

← #14738905

Subgroups — #14738905

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079978C211yesmaximal, characteristic
2#13079834C211yesmaximal, characteristic, complemented
3#13079010C211yesmaximal, characteristic, complemented
4#13068198C211yesmaximal, characteristic, complemented
5#13068191C211yesmaximal, characteristic, complemented
6#13068156C211yesmaximal, characteristic, complemented
7#13068149C211yesmaximal, characteristic, complemented
8#13068074C211yesmaximal, characteristic, complemented
9#13068067C211yesmaximal, characteristic, complemented
10#13068032C211yesmaximal, characteristic, complemented
11#13068025C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067319C211yesmaximal, characteristic, complemented
14#13067296C211yesmaximal, characteristic, complemented
15C11×#2969C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17#10623008C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C11×#446C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C11×#436—21no—
22C11×#436C2211yescharacteristic
23C11×#435—21no—
24C8×D4×C11C2211yescharacteristic
25C11×#433—21no—
26C11×#431C2211yescharacteristic
27C11×#405—21no—
28C4×C11×M16C2211yescharacteristic
29#10622746—21no—
30#10622746—21no—
31#10622679—21no—
32#10622678—21no—
33#10622670—21no—
34#10622668—21no—
35#10622662—21no—
36#10622656—21no—
37#10622652—21no—
38#10622646—21no—
39#10622640C2211yescharacteristic
40#10622634C2211yescharacteristic
41#10622634C2211yescharacteristic
42#10622633C2211yescharacteristic
43#10622628C2211yescharacteristic
44#10622621C2211yescharacteristic
45#10622621C2211yescharacteristic
46#10622620C2211yescharacteristic
47#10622539C2211yescharacteristic
48#10622537C2211yescharacteristic
49#10622327—21no—
50#10622327—21no—
51#10622307C2211yescharacteristic
52#10622307C2211yescharacteristic
53#10622294C2211yescharacteristic
54#10622294C2211yescharacteristic
55#10622123C2211yescharacteristic
56#10622123C2211yescharacteristic
57#10622120C2211yescharacteristic
58#10622120C2211yescharacteristic
59#10622119C2211yescharacteristic
60#10622119C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×#4339—21no—
68C22×Dic22—21no—
69C2×C11×M16—21no—
70C2×C11×M16D411yescharacteristic
71C2×C11×M16D411yescharacteristic
72C22×C8×C11—21no—
73C11×#126—21no—
74C11×#125D411yescharacteristic
75C11×#124D411yescharacteristic
76C11×#123—21no—
77C11×C22⋊Q8D411yescharacteristic
78C11×#121D411yescharacteristic
79C4×Q8×C11C2311yescharacteristic
80C4×D4×C11—21no—
81C4×D4×C11C2311yescharacteristic
82C11×#117—21no—
83C2×C42×C11C2311yescharacteristic
84C2×#4325—21no—
85C2×#4323—21no—
86#66983—21no—
87#66983—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×#4318—21no—
91#66928—21no—
92#66927C2311yescharacteristic
93C4×D44—21no—
94C4×D44—21no—
95#66922—21no—
96#66922—21no—
97#66922—21no—
98#66922C2311yescharacteristic
99#66922C2311yescharacteristic
100#66922C2311yescharacteristic
101C11×C4⋊C8—21no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C22⋊C8—21no—
106C11×C22⋊C8—21no—
107C11×C22⋊C8—21no—
108C11×#97—21no—
109C11×#97D411yescharacteristic
110C11×#97D411yescharacteristic
111C4×C8×C11—21no—
112C4×C8×C11—21no—
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115#66899—21no—
116#66899—21no—
117#66899—21no—
118#66896—21no—
119#66896—21no—
120#66896—21no—
121C22⋊(C11⋊C8)—21no—
122#66885—21no—
123#66885—21no—
124#66885—21no—
125#66885—21no—
126#66880—21no—
127#66880—21no—
128#66880—21no—
129#66880—21no—
130#66873—21no—
131#66873—21no—
132#66872—21no—
133#66872—21no—
134#66872—21no—
135#66871—21no—
136#66871—21no—
137#66871—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#19382—111nomaximal, Sylow
145C2×Q8×C11C2×D411yescharacteristic
146C2×D4×C11—21no—
147C2×D4×C11C2×D411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11#4111yescharacteristic
152C2×C22⋊D11—41no—
153C22×Dic11—41no—
154#4339—42no—
155#4339—42no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×C4×D11—41no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—41no—
164C2×Dic22—82no—
165C11×M16—41no—
166C11×M16—41no—
167C11×M16—42no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—42no—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
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—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C42×C11—21no—
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11#4111yescharacteristic
190C42×C11C2411yescharacteristic
191#4325—81no—
192#4323—81no—
193(C2×D11)⋊C4—41no—
194(C2×D11)⋊C4—41no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—41no—
202C4⋊Dic11—41no—
203#4318—81no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208#3251—111no—
209#3238—111no—
210#3141—111no—
211#2969D1111yescharacteristic, complemented
212#1704—111no—
213#1703—111no—
214#1698—111no—
215#1697—111no—
216#1684—111no—
217#1683—111no—
218#1678—111no—
219#1677—111no—
220#1569—111no—
221#1553—111no—
222#1548—111no—
223C23×C11—21no—
224C23×C11#12111yescharacteristic
225C22×D11—41no—
226Q8×C11—21no—
227Q8×C11—21no—
228D4×C11—21no—
229D4×C11—21no—
230D4×C11—81no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C22⋊D11—82no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—82no—
252D44—41no—
253D44—41no—
254D44—41no—
255D44—41no—
256D44—81no—
257C4×D11—82no—
258Dic22—41no—
259Dic22—41no—
260Dic22—82no—
261Dic22—81no—
262Dic22—81no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—41no—
268C8×C11—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273#532—111no—
274C2×C4⋊Q8—111no—
275#529C2×D1111yescharacteristic
276#501—221no—
277#489—221no—
278#489—221no—
279#489—221no—
280#487—111no—
281#487—111no—
282#486—111no—
283#486—111no—
284#483—221no—
285#480—221no—
286#478—221no—
287#477—111no—
288#477—111no—
289#476—111no—
290#476—111no—
291#475—111no—
292#474—111no—
293#469—221no—
294#468—221no—
295#463—221no—
296#460—111no—
297#459—111no—
298#446C2×D1111yescharacteristic
299C8×Q8C2×D1111yescharacteristic
300#436—21no—
301#436C2×D1111yescharacteristic
302#435—21no—
303C8×D4C2×D1111yescharacteristic
304#433—21no—
305#432—111no—
306#431C2×D1111yescharacteristic
307#423—111no—
308#417—221no—
309#417—221no—
310#405—21no—
311C4×M16C2×D1111yescharacteristic
312#335—111no—
313#335—111no—
314#334—111no—
315#334—111no—
316#333—111no—
317#333—111no—
318#333—111no—
319#333—111no—
320#332—111no—
321#332—111no—
322#331—111no—
323#331—111no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11C2×#12111yescharacteristic
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11#57511yescharacteristic
342C4×C11#57511yescharacteristic
343C4×C11#57711yescharacteristic
344C4×C11#57811yescharacteristic
345Dic11—81no—
346Dic11—81no—
347Dic11—81no—
348C2×#41—221no—
349C22×Q8—221no—
350C2×SD16—221no—
351C2×D8—221no—
352C2×M16—21no—
353C2×M16—221no—
354C2×M16C22⋊D1111yescharacteristic
355C2×M16C22⋊D1111yescharacteristic
356C22×C8—21no—
357C4⋊Q8—111no—
358C4⋊Q8—111no—
359C4⋊Q8—111no—
360C4⋊Q8—221no—
361C4⋊Q8—221no—
362C4⋊Q8—221no—
363#127—111no—
364#126—21no—
365#125D4411yescharacteristic
366#124—221no—
367#124D4411yescharacteristic
368#123—21no—
369C22⋊Q8D4411yescharacteristic
370#121—221no—
371#121—221no—
372#121D4411yescharacteristic
373C4×Q8C22×D1111yescharacteristic
374C4×D4—21no—
375C4×D4—221no—
376C4×D4—221no—
377C4×D4C22×D1111yescharacteristic
378#117—21no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C42C22×D1111yescharacteristic
382#107—221no—
383#107—221no—
384#107—221no—
385#106—221no—
386#106—221no—
387#106—221no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—221no—
395C4⋊C8C22×D1111yescharacteristic
396C4⋊C8C22×D1111yescharacteristic
397#103—221no—
398#103—221no—
399#103—221no—
400#103—221no—
401#103—221no—
402#103—221no—
403#103—221no—
404#102—221no—
405#102—221no—
406#102—221no—
407#102—221no—
408#102—221no—
409#102—221no—
410#102—221no—
411#102—221no—
412#102—221no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—221no—
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—81no—
427C2×C11#304011yescharacteristic
428C2×C11#306311yescharacteristic
429C2×C11#306811yescharacteristic
430D11—161no—
431#41—442no—
432#41—442no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8—441no—
437C2×Q8—882no—
438C2×Q8C2×D4411yescharacteristic
439C2×D4—21no—
440C2×D4—221no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—441no—
444C2×D4C2×D4411yescharacteristic
445C22×C4—21no—
446C22×C4—441no—
447C22×C4—441no—
448C22×C4C2×D4411yescharacteristic
449C22×C4#433911yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451SD16—881no—
452D8—881no—
453M16—41no—
454M16—41no—
455M16—42no—
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—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—441no—
479C4⋊C4—441no—
480C4⋊C4C2×D4411yescharacteristic
481C4⋊C4C2×D4411yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—441no—
488C22⋊C4—441no—
489C42—21no—
490C42C2×D4411yescharacteristic
491C42#433911yescharacteristic
492C42C2×C22⋊D1111yescharacteristic
493C42C23×D1111yescharacteristic
494C11#1938211yescharacteristic, complemented, Sylow
495C23—21no—
496C23—441no—
497C23#6698311yescharacteristic
498Q8—21no—
499Q8—21no—
500Q8—441no—
501Q8—441no—
502Q8—881no—
503Q8—881no—
504Q8—882no—
505D4—21no—
506D4—21no—
507D4—81no—
508D4—441no—
509D4—441no—
510D4—441no—
511D4—441no—
512D4—881no—
513D4—882no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—882no—
528C2×C4—882no—
529C2×C4#6698311yescharacteristic
530C2×C4#6698311yescharacteristic
531C2×C4#6698311yescharacteristic
532C2×C4C22×D4411yescharacteristic
533C2×C4C2×#433911yescharacteristic
534C2×C4C22×C22⋊D1111yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—441no—
542C8—441no—
543C8—441no—
544C8—441no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—881no—
552C22—881no—
553C22—881no—
554C22C2×#6698311yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—881no—
563C4—881no—
564C4—881no—
565C4#1062328211yescharacteristic
566C4#1062328411yescharacteristic
567C4#1062335311yescharacteristic
568C4#1062335311yescharacteristic
569C2—41no—
570C2—81no—
571C2—1761no—
572C2#1307811011yescharacteristic
573C2#1307830711yescharacteristic
574C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2969C2
socleC22×C11C2×#121
prime radical#13079978C2
hypercenter#2969D11
hypocenterC11#19382
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. #13079834C2semidirect
3. #13079010C2semidirect
4. #13068198C2semidirect
5. #13068191C2semidirect
6. #13068156C2semidirect
7. #13068149C2semidirect
8. #13068074C2semidirect
9. #13068067C2semidirect
10. #13068032C2semidirect
11. #13068025C2semidirect
12. #13067383C2semidirect
13. #13067319C2semidirect
14. #13067296C2semidirect
15. C11×#2969C2semidirect
211. #2969D11semidirect
494. C11#19382semidirect

Maximal subgroups

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

subgroupindex
#130799782
#130798342
#130790102
#130681982
#130681912
#130681562
#130681492
#130680742
#130680672
#130680322
#130680252
#130673832
#130673192
#130672962
C11×#29692
#1938211