Subgroups — #13070896

Order 1408.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#500	C₂	1	1	yes	maximal, characteristic
2	#10622295	C₂	1	1	yes	maximal, characteristic
3	#10622128	C₂	1	4	yes	maximal
4	C₄×C₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₁₁×C₄⋊Q₈	—	2	1	no	—
6	#66922	—	2	1	no	—
7	C₁₁×#107	—	2	1	no	—
8	C₁₁×#107	C₂²	1	2	yes	—
9	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	#66882	—	2	1	no	—
11	#66882	C₂²	1	2	yes	—
12	C₂×C₁₁⋊C₁₆	C₂²	1	2	yes	—
13	C₂×Q₈×C₁₁	—	4	1	no	—
14	C₂×Dic₂₂	—	4	1	no	—
15	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
16	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
17	C₁₁×C₄⋊C₄	—	2	2	no	—
18	C₁₁×C₄⋊C₄	—	4	1	no	—
19	C₄²×C₁₁	D₄	1	1	yes	characteristic
20	C₄⋊Dic₁₁	—	2	2	no	—
21	C₄⋊Dic₁₁	—	4	1	no	—
22	C₁₁⋊C₁₆	Q₈	1	4	yes	complemented
23	#2254	—	11	1	no	maximal, Sylow
24	Q₈×C₁₁	—	8	2	no	—
25	C₂×C₄×C₁₁	—	4	2	no	—
26	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
27	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
28	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₁₁	—	4	2	no	—
30	Dic₂₂	—	8	2	no	—
31	C₈×C₁₁	Q₁₆	1	2	yes	—
32	C₈×C₁₁	C₂×Q₈	1	2	yes	—
33	#500	—	11	1	no	—
34	#500	D₁₁	1	1	yes	characteristic
35	#367	—	11	4	no	—
36	C₄×C₁₆	—	11	1	no	—
37	C₂²×C₁₁	C₂×D₈	1	1	yes	characteristic
38	C₄×C₁₁	—	8	2	no	—
39	C₄×C₁₁	SD₃₂	1	2	yes	—
40	C₄×C₁₁	SD₃₂	1	2	yes	—
41	C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
42	C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
43	Dic₁₁	—	8	2	no	—
44	C₄⋊Q₈	—	2	1	no	—
45	C₄⋊Q₈	—	22	1	no	—
46	C₂×C₁₆	—	11	2	no	—
47	#107	—	2	1	no	—
48	#107	—	11	2	no	—
49	#107	—	22	1	no	—
50	#107	C₂×D₁₁	1	2	yes	—
51	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
52	C₂×C₁₁	#500	1	1	yes	characteristic
53	C₂×C₁₁	C₂×SD₃₂	1	1	yes	characteristic
54	C₂×C₁₁	C₂×SD₃₂	1	1	yes	characteristic
55	C₂×Q₈	—	4	1	no	—
56	C₂×Q₈	—	44	1	no	—
57	C₂×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
58	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
59	C₄⋊C₄	—	2	2	no	—
60	C₄⋊C₄	—	4	1	no	—
61	C₄⋊C₄	—	22	2	no	—
62	C₄⋊C₄	—	44	1	no	—
63	C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
64	C₁₆	—	11	4	no	—
65	C₁₁	#2254	1	1	yes	characteristic, complemented, Sylow
66	Q₈	—	8	2	no	—
67	Q₈	—	88	2	no	—
68	C₂×C₄	—	4	2	no	—
69	C₂×C₄	—	44	2	no	—
70	C₂×C₄	#4323	1	1	yes	characteristic
71	C₂×C₄	#4323	1	1	yes	characteristic
72	C₂×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
73	C₈	#4326	1	2	yes	—
74	C₈	Q₈×D₁₁	1	2	yes	—
75	C₂²	C₂×#4323	1	1	yes	characteristic
76	C₄	—	8	2	no	—
77	C₄	—	88	2	no	—
78	C₄	#66891	1	2	yes	—
79	C₄	#66892	1	2	yes	—
80	C₄	C₂×#4326	1	1	yes	characteristic
81	C₄	#66997	1	1	yes	characteristic
82	C₂	#10622691	1	1	yes	characteristic
83	C₂	C₂×#66891	1	1	yes	characteristic
84	C₂	C₂×#66892	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#4323
commutator, cosocle	C₂×C₈×C₁₁	C₂³
Frattini	C₂×C₈	C₂²×D₁₁
Fitting	C₁₁×#500	C₂
socle, prime radical	C₂²×C₁₁	C₂×D₈
hypercenter	#500	D₁₁
hypocenter	C₁₁	#2254
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

Complements

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

N	H ≅ G/N	type
22. C₁₁⋊C₁₆	Q₈	semidirect
65. C₁₁	#2254	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#500	2
#10622295	2
#10622128	2
C₄×C₁₁⋊C₁₆	2
#2254	11