Finite Group Databasebeta

← #14738770

Subgroups — #14738770

Order 2816.

576 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079999C211yesmaximal, characteristic
2#13079826C211yesmaximal, characteristic, complemented
3#13079334C211yesmaximal, characteristic
4#13068198C211yesmaximal, characteristic, complemented
5#13068156C211yesmaximal, characteristic, complemented
6#13068144C211yesmaximal, characteristic, complemented
7#13068088C211yesmaximal, characteristic, complemented
8#13068074C211yesmaximal, characteristic, complemented
9#13068032C211yesmaximal, characteristic, complemented
10#13068020C211yesmaximal, characteristic, complemented
11#13067964C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067309C211yesmaximal, characteristic
14#13067304C211yesmaximal, characteristic, complemented
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#10622700—21no—
32#10622696—21no—
33#10622695—21no—
34#10622693—21no—
35#10622662—21no—
36#10622662—21no—
37#10622658—21no—
38#10622658—21no—
39#10622640C2211yescharacteristic
40#10622640C2211yescharacteristic
41#10622634C2211yescharacteristic
42#10622634C2211yescharacteristic
43#10622634C2211yescharacteristic
44#10622634C2211yescharacteristic
45#10622633C2211yescharacteristic
46#10622633C2211yescharacteristic
47#10622539C2211yescharacteristic
48#10622537C2211yescharacteristic
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×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×#4325—21no—
83C2×#4325—21no—
84#66983—21no—
85#66983—21no—
86#66979—21no—
87#66977—21no—
88#66977—21no—
89C2×#4318—21no—
90C2×#4314—21no—
91C2×#4314—21no—
92#66928—21no—
93#66927C2311yescharacteristic
94C4×D44—21no—
95C4×D44—21no—
96#66923—21no—
97#66922C2311yescharacteristic
98#66922C2311yescharacteristic
99#66922C2311yescharacteristic
100C4×Dic22—21no—
101C4×Dic22—21no—
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8—21no—
105C11×C4⋊C8—21no—
106C11×C4⋊C8—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×#97—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#66899—21no—
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#66873—21no—
131#66873—21no—
132#66872—21no—
133#66872—21no—
134#66871—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#19373—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—82no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×C4×D11—41no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C11×M16—22no—
161C11×M16—41no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—42no—
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C11×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11#4111yescharacteristic
185C42×C11C2411yescharacteristic
186C22⋊Dic11—41no—
187#4325—81no—
188#4325—81no—
189(C2×D11)⋊C4—41no—
190(C2×D11)⋊C4—41no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197Dic11⋊C4—41no—
198Dic11⋊C4—41no—
199C4×Dic11—41no—
200#4318—81no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205#4314—42no—
206#4314—42no—
207#3254—111no—
208#3237—111no—
209#3182—111no—
210#2962D1111yescharacteristic, complemented
211#1704—111no—
212#1698—111no—
213#1696—111no—
214#1686—111no—
215#1684—111no—
216#1678—111no—
217#1676—111no—
218#1666—111no—
219#1569—111no—
220#1551—111no—
221#1550—111no—
222C23×C11#12111yescharacteristic
223C22×D11—41no—
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—81no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
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—41no—
238C2×C4×C11#12111yescharacteristic
239C2×C4×C11#12111yescharacteristic
240C2×C4×C11#12111yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C22⋊D11—82no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248D44—41no—
249D44—41no—
250D44—41no—
251D44—41no—
252D44—81no—
253C4×D11—82no—
254Dic22—41no—
255Dic22—41no—
256Dic22—81no—
257Dic22—81no—
258C8×C11—21no—
259C8×C11—21no—
260C8×C11—21no—
261C8×C11—41no—
262C8×C11—41no—
263C8×C11#13712yes—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268#533—111no—
269#533C2×D1111yescharacteristic
270#532—111no—
271#501—221no—
272#500—111no—
273#492—111no—
274#491—221no—
275#487—111no—
276#486—111no—
277#485—221no—
278#485—221no—
279#477—111no—
280#477—111no—
281#477—111no—
282#477—111no—
283#475—111no—
284#475—111no—
285#474—221no—
286#468—221no—
287#468—221no—
288#468—221no—
289#468—221no—
290#461—221no—
291#460—111no—
292#460—111no—
293#446—21no—
294#446—21no—
295#446C2×D1111yescharacteristic
296#446C2×D1111yescharacteristic
297C8×Q8C2×D1111yescharacteristic
298C8×Q8C2×D1111yescharacteristic
299#440—221no—
300#440—221no—
301#432—111no—
302#424—21no—
303#423—111no—
304C2×C4⋊C8C2×D1111yescharacteristic
305#405—21no—
306C4×M16C2×D1111yescharacteristic
307#335—111no—
308#335—111no—
309#334—111no—
310#334—111no—
311#333—111no—
312#333—111no—
313#333—111no—
314#333—111no—
315#332—111no—
316#332—111no—
317#331—111no—
318#331—111no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11C2×#12111yescharacteristic
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—81no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11C2×#13711yescharacteristic
335C4×C11#57511yescharacteristic
336C4×C11#57711yescharacteristic
337C4×C11#57811yescharacteristic
338Dic11—81no—
339Dic11—81no—
340Dic11—81no—
341C2×#41—221no—
342C2×SD16—221no—
343C2×SD16—221no—
344C2×SD16—221no—
345C2×SD16—221no—
346C2×M16—221no—
347C2×M16C22⋊D1111yescharacteristic
348C2×M16C22⋊D1111yescharacteristic
349C22×C8—21no—
350C4⋊Q8—111no—
351C4⋊Q8—111no—
352C4⋊Q8—111no—
353C4⋊Q8D4411yescharacteristic
354C4⋊Q8D4411yescharacteristic
355#127—111no—
356#125—21no—
357#125—221no—
358#124—221no—
359C22⋊Q8—21no—
360C22⋊Q8—221no—
361C22⋊Q8—221no—
362C22⋊Q8D4411yescharacteristic
363C22⋊Q8D4411yescharacteristic
364#121—221no—
365#121—221no—
366C4×Q8—21no—
367C4×Q8—221no—
368C4×Q8—221no—
369C4×Q8C22×D1111yescharacteristic
370C4×Q8C22×D1111yescharacteristic
371C4×D4—221no—
372C4×D4—221no—
373#117—21no—
374#117—221no—
375C2×C42C22×D1111yescharacteristic
376#107—221no—
377#107—221no—
378#107—221no—
379#107—221no—
380#107—221no—
381#107—221no—
382#106—221no—
383#106—221no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—221no—
394C4⋊C8C22×D1111yescharacteristic
395C4⋊C8C22×D1111yescharacteristic
396#103—221no—
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—
408C22⋊C8—221no—
409#97—21no—
410#97—21no—
411#97—221no—
412#97C22⋊D1111yescharacteristic
413#97C22⋊D1111yescharacteristic
414C4×C8—21no—
415C4×C8—21no—
416C4×C8C22×D1111yescharacteristic
417C4×C8C22×D1111yescharacteristic
418C2×C11—41no—
419C2×C11#303711yescharacteristic
420C2×C11#306311yescharacteristic
421C2×C11#306811yescharacteristic
422D11—161no—
423#41—882no—
424C2×Q8—21no—
425C2×Q8—221no—
426C2×Q8—221no—
427C2×Q8—221no—
428C2×Q8C2×D4411yescharacteristic
429C2×Q8C2×D4411yescharacteristic
430C2×D4—221no—
431C2×D4—221no—
432C2×D4—221no—
433C2×D4—441no—
434C22×C4—441no—
435C22×C4C2×D4411yescharacteristic
436C22×C4#433911yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438SD16—442no—
439SD16—442no—
440SD16—881no—
441SD16—881no—
442M16—22no—
443M16—41no—
444M16—881no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—42no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8C2×C22⋊D1111yescharacteristic
453C2×C8C2×C22⋊D1111yescharacteristic
454C2×C8C2×C22⋊D1111yescharacteristic
455C2×C8C2×C22⋊D1111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—441no—
470C4⋊C4—441no—
471C4⋊C4C2×D4411yescharacteristic
472C4⋊C4C2×D4411yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—441no—
476C22⋊C4—441no—
477C22⋊C4—441no—
478C42—21no—
479C42—21no—
480C42—441no—
481C42C2×D4411yescharacteristic
482C42#433911yescharacteristic
483C42C2×C22⋊D1111yescharacteristic
484C42C23×D1111yescharacteristic
485C11#1937311yescharacteristic, complemented, Sylow
486C23—441no—
487C23#6698311yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—81no—
493Q8—441no—
494Q8—441no—
495Q8—881no—
496Q8—881no—
497D4—441no—
498D4—441no—
499D4—441no—
500D4—441no—
501D4—881no—
502D4—882no—
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—41no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—882no—
516C2×C4#6698311yescharacteristic
517C2×C4#6698311yescharacteristic
518C2×C4#6698311yescharacteristic
519C2×C4C22×D4411yescharacteristic
520C2×C4C2×#433911yescharacteristic
521C2×C4C22×C22⋊D1111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—441no—
528C8—441no—
529C8—441no—
530C8—441no—
531C8#6699512yes—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—881no—
536C22—881no—
537C22—881no—
538C22C2×#6698311yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—881no—
548C4—881no—
549C4—881no—
550C4#1062328211yescharacteristic
551C4#1062328411yescharacteristic
552C4C2×#6699511yescharacteristic
553C4#1062335311yescharacteristic
554C2—41no—
555C2—1761no—
556C2#1307808811yescharacteristic
557C2#1307830711yescharacteristic
558C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2962C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#2962D11
hypocenterC11#19373
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
2. #13079826C2semidirect
4. #13068198C2semidirect
5. #13068156C2semidirect
6. #13068144C2semidirect
7. #13068088C2semidirect
8. #13068074C2semidirect
9. #13068032C2semidirect
10. #13068020C2semidirect
11. #13067964C2semidirect
12. #13067383C2semidirect
14. #13067304C2semidirect
15. C11×#2962C2semidirect
210. #2962D11semidirect
485. C11#19373semidirect

Maximal subgroups

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

subgroupindex
#130799992
#130798262
#130793342
#130681982
#130681562
#130681442
#130680882
#130680742
#130680322
#130680202
#130679642
#130673832
#130673092
#130673042
C11×#29622
#1937311