Finite Group Databasebeta

← #14737448

Subgroups — #14737448

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079942C211yesmaximal, characteristic
2#13079791C211yesmaximal, characteristic, complemented
3#13079334C211yesmaximal, characteristic, complemented
4#13068191C211yesmaximal, characteristic, complemented
5#13068149C211yesmaximal, characteristic, complemented
6#13068144C211yesmaximal, characteristic, complemented
7#13068088C211yesmaximal, characteristic, complemented
8#13068074C211yesmaximal, characteristic, complemented
9#13068032C211yesmaximal, characteristic, complemented
10#13068015C211yesmaximal, characteristic, complemented
11#13067957C211yesmaximal, characteristic, complemented
12#13067368C211yesmaximal, characteristic, complemented
13#13067276C211yesmaximal, characteristic, complemented
14#13067271C211yesmaximal, characteristic, complemented
15C11×#2969C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17#10623008C2211yescharacteristic
18#10623001C2211yescharacteristic
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#10622747—21no—
30#10622747—21no—
31#10622679—21no—
32#10622677—21no—
33#10622670—21no—
34#10622669—21no—
35#10622661—21no—
36#10622658—21no—
37#10622651—21no—
38#10622648—21no—
39#10622640C2211yescharacteristic
40#10622634C2211yescharacteristic
41#10622634C2211yescharacteristic
42#10622633C2211yescharacteristic
43#10622628C2211yescharacteristic
44#10622621C2211yescharacteristic
45#10622621C2211yescharacteristic
46#10622620C2211yescharacteristic
47#10622538C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622323—21no—
50#10622323—21no—
51#10622307C2211yescharacteristic
52#10622306C2211yescharacteristic
53#10622295C2211yescharacteristic
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—
68C2×C11×M16—21no—
69C2×C11×M16D411yescharacteristic
70C2×C11×M16D411yescharacteristic
71C22×C8×C11—21no—
72C11×#126—21no—
73C11×#125D411yescharacteristic
74C11×#124D411yescharacteristic
75C11×#123—21no—
76C11×C22⋊Q8D411yescharacteristic
77C11×#121D411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11C2311yescharacteristic
81C11×#117—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4325—21no—
84C2×#4323—21no—
85#66983—21no—
86#66983—21no—
87#66979—21no—
88#66977—21no—
89#66977—21no—
90C22×C11⋊C8—21no—
91C2×#4314—21no—
92C2×#4314—21no—
93#66928—21no—
94#66927C2311yescharacteristic
95C4×D44—21no—
96C4×D44—21no—
97#66923—21no—
98#66922C2311yescharacteristic
99#66922C2311yescharacteristic
100#66922C2311yescharacteristic
101C4×Dic22—21no—
102C4×Dic22—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8—21no—
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C11×C22⋊C8—21no—
110C11×#97—21no—
111C11×#97D411yescharacteristic
112C11×#97D411yescharacteristic
113C4×C8×C11—21no—
114C4×C8×C11—21no—
115C4×C8×C11C2311yescharacteristic
116C4×C8×C11C2311yescharacteristic
117#66899—21no—
118#66899—21no—
119#66899—21no—
120#66896—21no—
121#66896—21no—
122#66896—21no—
123C22⋊(C11⋊C8)—21no—
124#66885—21no—
125#66885—21no—
126#66882—21no—
127#66882—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
143C4×C11⋊C8—21no—
144#19247—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—
153#4339—82no—
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—
163C11×M16—42no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—42no—
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C2×D411yescharacteristic
176C11×C4⋊C4C2×D411yescharacteristic
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C42×C11—21no—
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11#4111yescharacteristic
186C42×C11C2411yescharacteristic
187C22⋊Dic11—41no—
188#4325—81no—
189#4323—81no—
190(C2×D11)⋊C4—41no—
191(C2×D11)⋊C4—41no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198Dic11⋊C4—41no—
199Dic11⋊C4—41no—
200C4×Dic11—41no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—81no—
206#4314—42no—
207#4314—42no—
208#3247—111no—
209#3233—111no—
210#3182—111no—
211#2969D1111yescharacteristic, complemented
212#1703—111no—
213#1697—111no—
214#1696—111no—
215#1686—111no—
216#1684—111no—
217#1678—111no—
218#1675—111no—
219#1665—111no—
220#1565—111no—
221#1543—111no—
222#1542—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—
251D44—41no—
252D44—41no—
253D44—41no—
254D44—41no—
255D44—81no—
256C4×D11—82no—
257Dic22—41no—
258Dic22—41no—
259Dic22—81no—
260Dic22—81no—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11—41no—
265C8×C11—41no—
266C8×C11#13512yes—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271#533—111no—
272#532—111no—
273#529C2×D1111yescharacteristic
274#500—111no—
275#499—221no—
276#492—111no—
277#488—221no—
278#487—111no—
279#486—111no—
280#485—221no—
281#482—221no—
282#478—221no—
283#477—111no—
284#477—111no—
285#476—111no—
286#476—111no—
287#475—111no—
288#474—111no—
289#468—221no—
290#468—221no—
291#466—221no—
292#465—221no—
293#463—221no—
294#460—111no—
295#459—111no—
296#446C2×D1111yescharacteristic
297C8×Q8C2×D1111yescharacteristic
298#440—221no—
299#440—221no—
300#436—21no—
301#436C2×D1111yescharacteristic
302#435—21no—
303C8×D4C2×D1111yescharacteristic
304#433—21no—
305#431—111no—
306#431C2×D1111yescharacteristic
307C2×C4⋊C8—111no—
308#405—21no—
309C4×M16C2×D1111yescharacteristic
310#335—111no—
311#335—111no—
312#334—111no—
313#334—111no—
314#333—111no—
315#333—111no—
316#333—111no—
317#333—111no—
318#332—111no—
319#332—111no—
320#331—111no—
321#331—111no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11C2×#12111yescharacteristic
329C2×D11—81no—
330C2×D11—81no—
331C2×D11—81no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11C2×#13511yescharacteristic
340C4×C11#57511yescharacteristic
341C4×C11#57711yescharacteristic
342C4×C11#57811yescharacteristic
343Dic11—81no—
344Dic11—81no—
345Dic11—81no—
346C2×#41—221no—
347C2×SD16—221no—
348C2×SD16—221no—
349C2×SD16—221no—
350C2×D8—221no—
351C2×M16—21no—
352C2×M16C22⋊D1111yescharacteristic
353C2×M16C22⋊D1111yescharacteristic
354C22×C8—21no—
355C22×C8—221no—
356C4⋊Q8—111no—
357C4⋊Q8—111no—
358C4⋊Q8—111no—
359#127—111no—
360#126—21no—
361#125—221no—
362#125D4411yescharacteristic
363#124—221no—
364#124D4411yescharacteristic
365#123—21no—
366C22⋊Q8—221no—
367C22⋊Q8—221no—
368C22⋊Q8D4411yescharacteristic
369#121—221no—
370#121—221no—
371#121D4411yescharacteristic
372C4×Q8—221no—
373C4×Q8—221no—
374C4×Q8C22×D1111yescharacteristic
375C4×D4—21no—
376C4×D4—221no—
377C4×D4—221no—
378C4×D4C22×D1111yescharacteristic
379#117—21no—
380#117—221no—
381C2×C42C22×D1111yescharacteristic
382#107—221no—
383#107—221no—
384#107—221no—
385#107—221no—
386#107—221no—
387#106—221no—
388#106—221no—
389#106—221no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—111no—
396C4⋊C8—221no—
397C4⋊C8C22×D1111yescharacteristic
398C4⋊C8C22×D1111yescharacteristic
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—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—221no—
415#97—21no—
416#97C22⋊D1111yescharacteristic
417#97C22⋊D1111yescharacteristic
418C4×C8—21no—
419C4×C8—21no—
420C4×C8—221no—
421C4×C8C22×D1111yescharacteristic
422C4×C8C22×D1111yescharacteristic
423C2×C11—41no—
424C2×C11—81no—
425C2×C11#303511yescharacteristic
426C2×C11#306311yescharacteristic
427C2×C11#306811yescharacteristic
428D11—161no—
429#41—882no—
430C2×Q8—221no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8C2×D4411yescharacteristic
434C2×D4—21no—
435C2×D4—221no—
436C2×D4—221no—
437C2×D4—221no—
438C2×D4—441no—
439C2×D4C2×D4411yescharacteristic
440C22×C4—21no—
441C22×C4—441no—
442C22×C4C2×D4411yescharacteristic
443C22×C4#433911yescharacteristic
444C22×C4C2×C22⋊D1111yescharacteristic
445SD16—442no—
446SD16—442no—
447SD16—881no—
448D8—881no—
449M16—22no—
450M16—41no—
451M16—42no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—42no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—881no—
460C2×C8C2×C22⋊D1111yescharacteristic
461C2×C8C2×C22⋊D1111yescharacteristic
462C2×C8C2×C22⋊D1111yescharacteristic
463C2×C8C2×C22⋊D1111yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—441no—
475C4⋊C4—441no—
476C4⋊C4C2×D4411yescharacteristic
477C4⋊C4C2×D4411yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—441no—
484C22⋊C4—441no—
485C22⋊C4—441no—
486C42—21no—
487C42—441no—
488C42C2×D4411yescharacteristic
489C42#433911yescharacteristic
490C42C2×C22⋊D1111yescharacteristic
491C42C23×D1111yescharacteristic
492C11#1924711yescharacteristic, complemented, Sylow
493C23—21no—
494C23—441no—
495C23#6698311yescharacteristic
496Q8—21no—
497Q8—21no—
498Q8—441no—
499Q8—441no—
500Q8—881no—
501Q8—881no—
502D4—21no—
503D4—21no—
504D4—81no—
505D4—441no—
506D4—441no—
507D4—441no—
508D4—441no—
509D4—881no—
510D4—882no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—882no—
525C2×C4#6698311yescharacteristic
526C2×C4#6698311yescharacteristic
527C2×C4#6698311yescharacteristic
528C2×C4C22×D4411yescharacteristic
529C2×C4C2×#433911yescharacteristic
530C2×C4C22×C22⋊D1111yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—441no—
537C8—441no—
538C8—441no—
539C8—441no—
540C8#6700312yes—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—881no—
548C22—881no—
549C22—881no—
550C22C2×#6698311yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—881no—
559C4—881no—
560C4—881no—
561C4#1062328211yescharacteristic
562C4#1062328411yescharacteristic
563C4C2×#6700311yescharacteristic
564C4#1062335311yescharacteristic
565C2—41no—
566C2—81no—
567C2—1761no—
568C2#1307807111yescharacteristic
569C2#1307830711yescharacteristic
570C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2969C2
socleC22×C11C2×#121
prime radical#13079942C2
hypercenter#2969D11
hypocenterC11#19247
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. #13079791C2semidirect
3. #13079334C2semidirect
4. #13068191C2semidirect
5. #13068149C2semidirect
6. #13068144C2semidirect
7. #13068088C2semidirect
8. #13068074C2semidirect
9. #13068032C2semidirect
10. #13068015C2semidirect
11. #13067957C2semidirect
12. #13067368C2semidirect
13. #13067276C2semidirect
14. #13067271C2semidirect
15. C11×#2969C2semidirect
211. #2969D11semidirect
492. C11#19247semidirect

Maximal subgroups

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

subgroupindex
#130799422
#130797912
#130793342
#130681912
#130681492
#130681442
#130680882
#130680742
#130680322
#130680152
#130679572
#130673682
#130672762
#130672712
C11×#29692
#1924711