Subgroups — #13070018

Order 1408.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#66888	C₂	1	3	yes	maximal
2	#10622737	C₂	1	3	yes	maximal
3	C₁₁×#338	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₂₂	C₂²	1	1	yes	characteristic
5	C₂×C₁₁×M₁₆	C₂²	1	3	yes	—
6	C₂×#4318	C₂²	1	3	yes	—
7	#66888	—	2	6	no	—
8	#66886	—	2	6	no	—
9	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
10	C₂²×Dic₁₁	Q₈	1	2	yes	—
11	C₂×Dic₂₂	—	2	3	no	—
12	C₂×Dic₂₂	—	2	3	no	—
13	C₁₁×M₁₆	—	2	3	no	—
14	C₁₁×M₁₆	—	2	3	no	—
15	C₂×C₈×C₁₁	—	2	3	no	—
16	#4318	—	2	3	no	—
17	#4318	D₄	1	6	yes	—
18	C₂×C₁₁⋊C₈	—	2	3	no	—
19	#2070	—	11	1	no	maximal, Sylow
20	C₂³×C₁₁	C₂×Q₈	1	1	yes	characteristic
21	C₂×C₄×C₁₁	C₂×D₄	1	3	yes	—
22	C₂×C₄×C₁₁	#41	1	3	yes	—
23	C₂×Dic₁₁	—	2	6	no	—
24	Dic₂₂	—	4	3	no	—
25	Dic₂₂	—	4	1	no	—
26	C₈×C₁₁	—	4	3	no	—
27	C₁₁⋊C₈	—	2	6	no	—
28	#430	—	11	3	no	—
29	C₂×#101	—	11	3	no	—
30	#338	D₁₁	1	1	yes	characteristic
31	C₂²×C₁₁	—	4	1	no	—
32	C₂²×C₁₁	C₂²⋊Q₈	1	3	yes	—
33	C₄×C₁₁	#121	1	3	yes	—
34	C₄×C₁₁	#126	1	1	yes	characteristic
35	Dic₁₁	—	4	2	no	—
36	C₂²×Q₈	—	11	1	no	—
37	C₂×M₁₆	—	11	3	no	—
38	C₂×M₁₆	C₂×D₁₁	1	3	yes	—
39	#108	—	22	6	no	—
40	#101	—	22	6	no	—
41	C₂×C₁₁	—	2	3	no	—
42	C₂×C₁₁	#396	1	1	yes	characteristic
43	C₂×Q₈	—	22	3	no	—
44	C₂×Q₈	—	22	3	no	—
45	C₂²×C₄	—	11	2	no	—
46	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
47	M₁₆	—	2	3	no	—
48	M₁₆	—	2	3	no	—
49	M₁₆	—	11	6	no	—
50	M₁₆	—	22	3	no	—
51	C₂×C₈	—	2	3	no	—
52	C₂×C₈	—	22	3	no	—
53	C₁₁	#2070	1	1	yes	characteristic, complemented, Sylow
54	C₂³	Q₈×D₁₁	1	1	yes	characteristic
55	Q₈	—	44	1	no	—
56	Q₈	—	44	3	no	—
57	C₂×C₄	—	22	6	no	—
58	C₂×C₄	#4339	1	3	yes	—
59	C₂×C₄	D₄×D₁₁	1	3	yes	—
60	C₈	—	4	3	no	—
61	C₈	—	22	6	no	—
62	C₂²	—	4	1	no	—
63	C₂²	#66949	1	3	yes	—
64	C₄	—	44	2	no	—
65	C₄	#66929	1	1	yes	characteristic
66	C₄	#66937	1	3	yes	—
67	C₂	—	2	3	no	—
68	C₂	#10622289	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10622289
commutator, cosocle	C₂²×C₄×C₁₁	C₂³
Frattini	C₂²×C₄	C₂²×D₁₁
Fitting	C₁₁×#338	C₂
socle	C₂×C₁₁	#396
prime radical	C₂³×C₁₁	C₂×Q₈
hypercenter	#338	D₁₁
hypocenter	C₁₁	#2070
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
53. C₁₁	#2070	semidirect

Maximal subgroups

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

subgroup	index
C₂×#66888	2
#10622737	2
C₁₁×#338	2
#2070	11