Subgroups — #13066596

Order 1408.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Dic₂₂	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₁₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₂₂	C₄	1	1	yes	characteristic
5	C₂×C₁₁×C₁₆	—	2	1	no	—
6	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	Dic₁₁⋊C₈	—	2	1	no	—
8	C₈×Dic₁₁	—	2	1	no	—
9	C₂×C₁₁⋊C₁₆	—	2	1	no	—
10	C₄⋊(C₁₁⋊C₈)	C₄	1	1	yes	characteristic
11	C₂×Dic₂₂	C₈	1	1	yes	characteristic
12	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
13	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
14	C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₄⋊Dic₁₁	C₈	1	1	yes	characteristic
16	Dic₁₁⋊C₄	—	2	1	no	—
17	C₄×Dic₁₁	—	2	1	no	—
18	C₂×C₁₁⋊C₈	—	2	1	no	—
19	C₁₁×C₁₆	—	2	2	no	—
20	C₁₁⋊C₁₆	—	4	1	no	—
21	Q₈⋊C₁₆	—	11	1	no	maximal, Sylow
22	C₂×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
24	C₂×C₄×C₁₁	M₁₆	1	1	yes	characteristic
25	C₂×Dic₁₁	—	2	1	no	—
26	C₂×Dic₁₁	—	2	1	no	—
27	Dic₂₂	—	2	1	no	—
28	Dic₂₂	C₁₆	1	2	yes	complemented
29	C₈×C₁₁	—	2	1	no	—
30	C₈×C₁₁	SD₁₆	1	1	yes	characteristic
31	C₈×C₁₁	Q₁₆	1	1	yes	characteristic
32	C₁₁⋊C₈	—	4	1	no	—
33	C₈×Q₈	—	11	1	no	—
34	C₄⋊C₁₆	—	11	1	no	—
35	C₄×C₁₆	D₁₁	1	1	yes	characteristic
36	C₂²×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
37	C₄×C₁₁	—	2	1	no	—
38	C₄×C₁₁	#103	1	1	yes	characteristic
39	C₄×C₁₁	#104	1	1	yes	characteristic
40	C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
41	C₄×C₁₁	M₃₂	1	1	yes	characteristic
42	Dic₁₁	—	2	2	no	—
43	Dic₁₁	—	4	1	no	—
44	C₄×Q₈	—	11	1	no	—
45	C₂×C₁₆	—	2	1	no	—
46	C₂×C₁₆	—	22	1	no	—
47	C₄⋊C₈	—	11	1	no	—
48	C₄⋊C₈	—	22	1	no	—
49	C₄×C₈	—	22	1	no	—
50	C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
51	C₂×C₁₁	Q₈⋊C₈	1	1	yes	characteristic
52	C₂×C₁₁	C₂²⋊C₁₆	1	1	yes	characteristic
53	C₂×C₁₁	#350	1	1	yes	characteristic
54	C₂×Q₈	—	11	1	no	—
55	C₂×C₈	—	22	1	no	—
56	C₂×C₈	D₄₄	1	1	yes	characteristic
57	C₂×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
58	C₄⋊C₄	—	11	1	no	—
59	C₄⋊C₄	—	22	1	no	—
60	C₄²	—	22	1	no	—
61	C₄²	C₄×D₁₁	1	1	yes	characteristic
62	C₁₆	—	2	2	no	—
63	C₁₆	—	44	1	no	—
64	C₁₁	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
65	Q₈	—	11	2	no	—
66	Q₈	—	22	1	no	—
67	C₂×C₄	—	22	1	no	—
68	C₂×C₄	—	22	1	no	—
69	C₂×C₄	C₈×D₁₁	1	1	yes	characteristic
70	C₂×C₄	#4313	1	1	yes	characteristic
71	C₂×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
72	C₈	—	2	1	no	—
73	C₈	—	44	1	no	—
74	C₈	#4314	1	1	yes	characteristic
75	C₈	Dic₄₄	1	1	yes	characteristic
76	C₂²	(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	22	2	no	—
79	C₄	—	44	1	no	—
80	C₄	C₁₆×D₁₁	1	1	yes	characteristic
81	C₄	#66862	1	1	yes	characteristic
82	C₄	#66869	1	1	yes	characteristic
83	C₄	#66880	1	1	yes	characteristic
84	C₂	#10622094	1	1	yes	characteristic
85	C₂	(C₂×D₁₁)⋊C₁₆	1	1	yes	characteristic
86	C₂	#10622146	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄₄
commutator	C₄×C₁₁	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₁₁
Fitting	C₄×C₁₁×C₁₆	C₂
socle, prime radical	C₂²×C₁₁	C₂²⋊C₈
cosocle	C₄×C₈×C₁₁	C₂²
hypercenter	C₄×C₁₆	D₁₁
hypocenter	C₁₁	Q₈⋊C₁₆
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
28. Dic₂₂	C₁₆	semidirect
64. C₁₁	Q₈⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₈×Dic₂₂	2
C₄×C₁₁×C₁₆	2
C₄⋊(C₁₁⋊C₁₆)	2
Q₈⋊C₁₆	11