Subgroups — #13070897

Order 1408.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10622487	C₂	1	2	yes	maximal
2	C₁₁×#367	C₂	1	1	yes	maximal, characteristic
3	#10622143	C₂	1	1	yes	maximal, characteristic
4	C₁₆×Dic₁₁	C₂	1	1	yes	maximal, characteristic
5	#10622128	C₂	1	2	yes	maximal
6	#66941	—	2	2	no	—
7	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
8	C₁₁×#107	C₂²	1	2	yes	—
9	#66882	C₂²	1	2	yes	—
10	C₈×Dic₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
12	#66871	—	2	2	no	—
13	C₂×Dic₂₂	—	4	2	no	—
14	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
15	C₁₁×C₄⋊C₄	—	2	2	no	—
16	C₄⋊Dic₁₁	—	2	2	no	—
17	Dic₁₁⋊C₄	—	4	2	no	—
18	C₄×Dic₁₁	D₄	1	1	yes	characteristic
19	C₂×C₁₁⋊C₈	D₄	1	1	yes	characteristic
20	C₁₁×C₁₆	Q₈	1	2	yes	complemented
21	C₁₁⋊C₁₆	Q₈	1	2	yes	complemented
22	#2254	—	11	1	no	maximal, Sylow
23	C₂×C₄×C₁₁	—	4	2	no	—
24	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
25	C₂×Dic₁₁	—	4	2	no	—
26	C₂×Dic₁₁	D₈	1	2	yes	—
27	Dic₂₂	—	8	4	no	—
28	C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
29	C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
30	C₁₁⋊C₈	Q₁₆	1	2	yes	—
31	#500	—	11	2	no	—
32	#367	—	11	1	no	—
33	#367	—	11	2	no	—
34	#367	D₁₁	1	1	yes	characteristic
35	C₄×C₁₆	—	11	1	no	—
36	C₂²×C₁₁	C₂×D₈	1	1	yes	characteristic
37	C₄×C₁₁	—	8	2	no	—
38	C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
39	C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
40	Dic₁₁	—	8	2	no	—
41	Dic₁₁	SD₃₂	1	4	yes	—
42	C₄⋊Q₈	—	22	2	no	—
43	C₂×C₁₆	—	11	1	no	—
44	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
45	#107	—	11	2	no	—
46	#107	—	22	2	no	—
47	#107	C₂×D₁₁	1	2	yes	—
48	C₄×C₈	—	11	1	no	—
49	C₂×C₁₁	#500	1	1	yes	characteristic
50	C₂×C₁₁	C₂×SD₃₂	1	2	yes	—
51	C₂×Q₈	—	44	2	no	—
52	C₂×C₈	—	11	1	no	—
53	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
54	C₄⋊C₄	—	2	2	no	—
55	C₄⋊C₄	—	22	2	no	—
56	C₄⋊C₄	—	44	2	no	—
57	C₄²	—	11	1	no	—
58	C₁₆	—	11	2	no	—
59	C₁₆	Dic₂₂	1	2	yes	complemented
60	C₁₁	#2254	1	1	yes	characteristic, complemented, Sylow
61	Q₈	—	88	4	no	—
62	C₂×C₄	—	4	2	no	—
63	C₂×C₄	—	11	2	no	—
64	C₂×C₄	—	44	2	no	—
65	C₂×C₄	D₄×D₁₁	1	1	yes	characteristic
66	C₈	—	11	2	no	—
67	C₈	C₂×Dic₂₂	1	1	yes	characteristic
68	C₈	Q₈×D₁₁	1	1	yes	characteristic
69	C₂²	D₈×D₁₁	1	1	yes	characteristic
70	C₄	—	8	2	no	—
71	C₄	—	11	4	no	—
72	C₄	—	88	2	no	—
73	C₄	#66941	1	1	yes	characteristic
74	C₄	Q₁₆×D₁₁	1	1	yes	characteristic
75	C₂	#10622487	1	1	yes	characteristic
76	C₂	D₁₁×SD₃₂	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₁₁
commutator, cosocle	C₂×C₈×C₁₁	C₂³
Frattini	C₂×C₈	C₂²×D₁₁
Fitting	C₁₁×#367	C₂
socle, prime radical	C₂²×C₁₁	C₂×D₈
hypercenter	#367	D₁₁
hypocenter	C₁₁	#2254
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #367

Complements

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

N	H ≅ G/N	type
20. C₁₁×C₁₆	Q₈	semidirect
21. C₁₁⋊C₁₆	Q₈	semidirect
59. C₁₆	Dic₂₂	semidirect
60. C₁₁	#2254	semidirect

Maximal subgroups

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

subgroup	index
#10622487	2
C₁₁×#367	2
#10622143	2
C₁₆×Dic₁₁	2
#10622128	2
#2254	11