Finite Group Databasebeta

← #14738744

Subgroups — #14738744

Order 2816.

622 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079810C211yesmaximal, characteristic
2#13079357C211yesmaximal, characteristic, complemented
3#13077360C211yesmaximal, characteristic
4#13068189C211yesmaximal, characteristic, complemented
5#13068165C211yesmaximal, characteristic, complemented
6#13068113C211yesmaximal, characteristic, complemented
7#13068103C211yesmaximal, characteristic, complemented
8#13068065C211yesmaximal, characteristic, complemented
9#13068041C211yesmaximal, characteristic, complemented
10#13067989C211yesmaximal, characteristic, complemented
11#13067979C211yesmaximal, characteristic, complemented
12#13067381C211yesmaximal, characteristic, complemented
13#13067316C211yesmaximal, characteristic, complemented
14#13067307C211yesmaximal, characteristic, complemented
15C11×#3254C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C2×#67001—21no—
19#10623001C2211yescharacteristic
20C11×#477—21no—
21C11×#474C2211yescharacteristic
22C11×#474C2211yescharacteristic
23C11×#468—21no—
24C11×#468—21no—
25C11×#461C2211yescharacteristic
26C11×#461C2211yescharacteristic
27C11×#460—21no—
28C11×#423C2211yescharacteristic
29#10622847—21no—
30#10622706C2211yescharacteristic
31#10622705C2211yescharacteristic
32#10622694C2211yescharacteristic
33#10622693—21no—
34#10622692C2211yescharacteristic
35#10622684—21no—
36#10622665—21no—
37#10622665—21no—
38#10622648—21no—
39#10622648—21no—
40#10622643—21no—
41#10622643—21no—
42#10622625C2211yescharacteristic
43#10622625C2211yescharacteristic
44#10622624—21no—
45#10622624—21no—
46D4×C11⋊C8C2211yescharacteristic
47D4×C11⋊C8C2211yescharacteristic
48#10622621C2211yescharacteristic
49#10622621C2211yescharacteristic
50#10622620C2211yescharacteristic
51#10622620C2211yescharacteristic
52#10622539C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×SD16—21no—
69C2×C11×SD16—21no—
70C2×C11×M16—21no—
71C11×C4⋊Q8D411yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×#127D411yescharacteristic
75C11×#125—21no—
76C11×#124—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×#121—21no—
80C11×#121D411yescharacteristic
81C11×#121D411yescharacteristic
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11C2311yescharacteristic
86C4×D4×C11C2311yescharacteristic
87C11×#117—21no—
88C2×C42×C11C2311yescharacteristic
89#67001—44no—
90C2×#4326—21no—
91C2×#4326—21no—
92#66979—21no—
93#66977—21no—
94#66977—21no—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×#4318D411yescharacteristic
98C2×#4318D411yescharacteristic
99C22×C11⋊C8—21no—
100C22×C11⋊C8—21no—
101C22×C11⋊C8—21no—
102#66923—21no—
103#66922C2311yescharacteristic
104#66922C2311yescharacteristic
105C4×Dic22—21no—
106C4×Dic22—21no—
107C11×#107—21no—
108C11×#107—21no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8C2311yescharacteristic
111C11×C4⋊C8C2311yescharacteristic
112C11×#103—21no—
113C11×#103—21no—
114C11×#102—21no—
115C11×#102—21no—
116#66899—21no—
117#66899—21no—
118#66896—21no—
119#66896—21no—
120#66896—21no—
121#66896—21no—
122C22⋊(C11⋊C8)—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126C22⋊(C11⋊C8)—21no—
127#66874—21no—
128#66874—21no—
129#66872—21no—
130#66872—21no—
131#66872—21no—
132#66872—21no—
133#66871—21no—
134#66871—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140#66867—21no—
141#66867D411yescharacteristic
142#66867D411yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19371—111nomaximal, Sylow
146C11×#41—42no—
147C11×#41—42no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11C2×D411yescharacteristic
156C2×D4×C11C2×D411yescharacteristic
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11#4111yescharacteristic
162C2×Dic22—21no—
163C2×Dic22—21no—
164C11×SD16—81no—
165C11×SD16—81no—
166C11×M16—81no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4C2×D411yescharacteristic
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—41no—
183C42×C11—41no—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11#4111yescharacteristic
187C42×C11C2411yescharacteristic
188C22⋊Dic11—41no—
189#4326—42no—
190#4326—42no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195Dic11⋊C4—41no—
196Dic11⋊C4—41no—
197C4×Dic11—41no—
198#4318—22no—
199#4318—41no—
200#4318—42no—
201#4318—42no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—42no—
207C2×C11⋊C8—42no—
208C2×C11⋊C8—42no—
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213#3254D1111yescharacteristic
214#3235—111no—
215#3185—111no—
216#2935—111no—
217#1703—111no—
218#1699—111no—
219#1691—111no—
220#1689—111no—
221#1683—111no—
222#1679—111no—
223#1671—111no—
224#1669—111no—
225#1569—111no—
226#1552—111no—
227#1550—111no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11#12111yescharacteristic
231Q8×C11—42no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236D4×C11—21no—
237D4×C11—21no—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—42no—
241D4×C11—42no—
242D4×C11—42no—
243D4×C11—81no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×Dic11—41no—
264C2×Dic11—41no—
265Dic22—41no—
266Dic22—41no—
267Dic22—81no—
268C8×C11—41no—
269C8×C11—41no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8AGL(1,ℤ/8)12yes—
278C2×#131—221no—
279#533—111no—
280#533C2×D1111yescharacteristic
281#532C2×D1111yescharacteristic
282#501—221no—
283#498—111no—
284#494—111no—
285#490—221no—
286#487—111no—
287#487—111no—
288#482—221no—
289#482—221no—
290#477—21no—
291#476—111no—
292#476—111no—
293#474—111no—
294#474—111no—
295#474C2×D1111yescharacteristic
296#474C2×D1111yescharacteristic
297#470—221no—
298#470—221no—
299#468—21no—
300#468—21no—
301#461C2×D1111yescharacteristic
302#461C2×D1111yescharacteristic
303#460—21no—
304#441—221no—
305#441—221no—
306#436—111no—
307#436—111no—
308#435—221no—
309#435—221no—
310C8×D4—111no—
311C8×D4—111no—
312#432—111no—
313#423C2×D1111yescharacteristic
314C2×C4⋊C8—111no—
315#408—221no—
316C4×M16—111no—
317#335—111no—
318#335—111no—
319#334—111no—
320#334—111no—
321#333—111no—
322#333—111no—
323#332—111no—
324#332—111no—
325#332—111no—
326#332—111no—
327#332—111no—
328#332—111no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11C2×#12111yescharacteristic
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—81no—
346C4×C11—81no—
347C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
348C4×C11#57511yescharacteristic
349C4×C11#57711yescharacteristic
350C4×C11#57811yescharacteristic
351Dic11—81no—
352Dic11—81no—
353C2×#41—21no—
354C2×Q16—221no—
355C2×Q16—221no—
356C2×SD16—21no—
357C2×SD16—21no—
358#131—444no—
359C2×M16—21no—
360C2×M16—111no—
361C2×M16—111no—
362C2×M16—221no—
363C2×M16—221no—
364C22×C8—221no—
365C22×C8—221no—
366C22×C8—221no—
367C4⋊Q8—111no—
368C4⋊Q8—111no—
369C4⋊Q8C22⋊D1111yescharacteristic
370C4⋊Q8C22×D1111yescharacteristic
371C4⋊Q8C22×D1111yescharacteristic
372#127C22⋊D1111yescharacteristic
373#125—21no—
374#125—221no—
375#124—21no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378C22⋊Q8—221no—
379C22⋊Q8—221no—
380#121—21no—
381#121C22⋊D1111yescharacteristic
382#121C22⋊D1111yescharacteristic
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8—221no—
386C4×Q8—221no—
387C4×D4—21no—
388C4×D4C22×D1111yescharacteristic
389C4×D4C22×D1111yescharacteristic
390#117—21no—
391#117—221no—
392C2×C42C22×D1111yescharacteristic
393#107—21no—
394#107—21no—
395#107—221no—
396#107—221no—
397#106—221no—
398#106—221no—
399#106—221no—
400#106—221no—
401C4⋊C8—21no—
402C4⋊C8—111no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—221no—
407C4⋊C8C22×D1111yescharacteristic
408C4⋊C8C22×D1111yescharacteristic
409#103—21no—
410#103—21no—
411#103—221no—
412#103—221no—
413#103—221no—
414#103—221no—
415#102—21no—
416#102—21no—
417#102—221no—
418#102—221no—
419#102—221no—
420#102—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426#97—111no—
427#97—111no—
428#97—221no—
429C4×C8—111no—
430C4×C8—111no—
431C2×C11—41no—
432C2×C11—81no—
433C2×C11—81no—
434C2×C11#303611yescharacteristic
435C2×C11#306311yescharacteristic
436C2×C11#306911yescharacteristic
437#41—42no—
438#41—42no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—221no—
443C2×Q8—221no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4C2×C22⋊D1111yescharacteristic
449C2×D4C2×C22⋊D1111yescharacteristic
450C22×C4—21no—
451C22×C4—21no—
452C22×C4D4×D1111yescharacteristic
453C22×C4#434111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455Q16—442no—
456Q16—442no—
457SD16—81no—
458SD16—81no—
459M16—81no—
460M16—222no—
461M16—442no—
462M16—441no—
463M16—442no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—111no—
467C2×C8—111no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—442no—
475C2×C8—442no—
476C2×C8—442no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—441no—
489C4⋊C4—441no—
490C4⋊C4C2×C22⋊D1111yescharacteristic
491C4⋊C4C2×C22⋊D1111yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—441no—
498C42—41no—
499C42—441no—
500C42D4×D1111yescharacteristic
501C42#434111yescharacteristic
502C42C2×C22⋊D1111yescharacteristic
503C42C23×D1111yescharacteristic
504C11#1937111yescharacteristic, complemented, Sylow
505C23—21no—
506C23—21no—
507C23#6699211yescharacteristic
508Q8—42no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—441no—
514Q8—441no—
515Q8—881no—
516D4—21no—
517D4—21no—
518D4—21no—
519D4—21no—
520D4—42no—
521D4—42no—
522D4—42no—
523D4—81no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4#6699211yescharacteristic
540C2×C4#6699211yescharacteristic
541C2×C4#6699211yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4C2×#434111yescharacteristic
544C2×C4C22×C22⋊D1111yescharacteristic
545C8—41no—
546C8—41no—
547C8—112no—
548C8—221no—
549C8—221no—
550C8—221no—
551C8—441no—
552C8—441no—
553C8—441no—
554C8—441no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22C2×#6699211yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—881no—
574C4—881no—
575C4D11×AGL(1,ℤ/8)11yescharacteristic
576C4#1062330411yescharacteristic
577C4#1062336711yescharacteristic
578C4#1062336911yescharacteristic
579C2—41no—
580C2—81no—
581C2—81no—
582C2#1307807711yescharacteristic
583C2#1307830911yescharacteristic
584C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3254C2
socleC22×C11C2×#121
prime radicalC11×#532C22
hypercenter#3254D11
hypocenterC11#19371
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3254

Complements

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

NH ≅ G/Ntype
2. #13079357C2semidirect
4. #13068189C2semidirect
5. #13068165C2semidirect
6. #13068113C2semidirect
7. #13068103C2semidirect
8. #13068065C2semidirect
9. #13068041C2semidirect
10. #13067989C2semidirect
11. #13067979C2semidirect
12. #13067381C2semidirect
13. #13067316C2semidirect
14. #13067307C2semidirect
504. C11#19371semidirect

Maximal subgroups

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

subgroupindex
#130798102
#130793572
#130773602
#130681892
#130681652
#130681132
#130681032
#130680652
#130680412
#130679892
#130679792
#130673812
#130673162
#130673072
C11×#32542
#1937111