Subgroups — #13070474

Order 1408.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₈₈	C₂	1	1	yes	maximal, characteristic
2	#10622486	C₂	1	2	yes	maximal
3	C₁₁×#366	C₂	1	1	yes	maximal, characteristic
4	C₁₆×Dic₁₁	C₂	1	1	yes	maximal, characteristic
5	#10622130	C₂	1	2	yes	maximal
6	C₂×Dic₄₄	C₂²	1	2	yes	—
7	#66940	—	2	2	no	—
8	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
9	C₁₁×#107	C₂²	1	2	yes	—
10	C₈×Dic₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
12	#66874	—	2	2	no	—
13	Dic₈₈	C₄	1	4	yes	complemented
14	C₂×Dic₂₂	—	2	2	no	—
15	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
16	C₁₁×C₄⋊C₄	—	2	2	no	—
17	Dic₁₁⋊C₄	—	4	2	no	—
18	C₄×Dic₁₁	—	4	2	no	—
19	C₄×Dic₁₁	D₄	1	1	yes	characteristic
20	C₂×C₁₁⋊C₈	D₄	1	1	yes	characteristic
21	Dic₄₄	—	2	2	no	—
22	Dic₄₄	C₂×C₄	1	4	yes	—
23	C₁₁×C₁₆	C₂×C₄	1	2	yes	—
24	C₁₁⋊C₁₆	—	2	1	no	—
25	C₄×Q₃₂	—	11	1	no	maximal, Sylow
26	C₂×C₄×C₁₁	—	4	2	no	—
27	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₁₁	—	4	2	no	—
29	C₂×Dic₁₁	D₈	1	1	yes	characteristic
30	C₂×Dic₁₁	D₈	1	1	yes	characteristic
31	Dic₂₂	—	2	4	no	—
32	Dic₂₂	—	4	2	no	—
33	C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₁₁	#41	1	1	yes	characteristic
35	C₁₁⋊C₈	—	2	1	no	—
36	C₂×Q₃₂	—	11	1	no	—
37	C₄×Q₁₆	—	11	2	no	—
38	#366	D₁₁	1	1	yes	characteristic
39	#358	—	11	2	no	—
40	C₄×C₁₆	—	11	1	no	—
41	C₂²×C₁₁	C₂×D₈	1	1	yes	characteristic
42	C₄×C₁₁	—	8	2	no	—
43	C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
44	C₄×C₁₁	#135	1	1	yes	characteristic
45	Dic₁₁	—	2	1	no	—
46	Dic₁₁	—	4	4	no	—
47	Dic₁₁	Q₃₂	1	2	yes	complemented
48	C₂×Q₁₆	—	11	2	no	—
49	C₄×Q₈	—	22	2	no	—
50	Q₃₂	—	11	4	no	—
51	C₂×C₁₆	—	11	1	no	—
52	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
53	#107	C₂×D₁₁	1	2	yes	—
54	#103	—	22	2	no	—
55	C₄×C₈	—	11	1	no	—
56	C₂×C₁₁	C₄×D₈	1	1	yes	characteristic
57	C₂×C₁₁	C₂×Q₃₂	1	1	yes	characteristic
58	C₂×C₁₁	#508	1	1	yes	characteristic
59	C₂×Q₈	—	22	2	no	—
60	Q₁₆	—	11	4	no	—
61	Q₁₆	—	22	2	no	—
62	C₂×C₈	—	11	1	no	—
63	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
64	C₄⋊C₄	—	2	2	no	—
65	C₄⋊C₄	—	44	2	no	—
66	C₄²	—	11	1	no	—
67	C₄²	—	44	2	no	—
68	C₁₆	—	22	1	no	—
69	C₁₆	C₄×D₁₁	1	2	yes	—
70	C₁₁	C₄×Q₃₂	1	1	yes	characteristic, complemented, Sylow
71	Q₈	—	22	4	no	—
72	Q₈	—	44	2	no	—
73	C₂×C₄	—	4	2	no	—
74	C₂×C₄	—	11	1	no	—
75	C₂×C₄	—	11	1	no	—
76	C₂×C₄	—	44	2	no	—
77	C₂×C₄	D₄×D₁₁	1	1	yes	characteristic
78	C₈	—	22	1	no	—
79	C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
80	C₈	#4343	1	1	yes	characteristic
81	C₂²	D₈×D₁₁	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	11	2	no	—
84	C₄	—	22	1	no	—
85	C₄	—	44	4	no	—
86	C₄	#66946	1	1	yes	characteristic
87	C₄	#66972	1	1	yes	characteristic
88	C₂	#10622485	1	1	yes	characteristic
89	C₂	#10622525	1	1	yes	characteristic
90	C₂	D₁₁×Q₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈×D₁₁
commutator	C₈×C₁₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₁
Fitting	C₁₁×#366	C₂
socle, prime radical	C₂²×C₁₁	C₂×D₈
cosocle	C₂×C₈×C₁₁	C₂³
hypercenter	#366	D₁₁
hypocenter	C₁₁	C₄×Q₃₂
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

Complements

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

N	H ≅ G/N	type
13. Dic₈₈	C₄	semidirect
47. Dic₁₁	Q₃₂	semidirect
70. C₁₁	C₄×Q₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₈₈	2
#10622486	2
C₁₁×#366	2
C₁₆×Dic₁₁	2
#10622130	2
C₄×Q₃₂	11