Subgroups — #13066810

Order 1408.

70 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	C₁₁×M₆₄	C₂	1	1	yes	maximal, characteristic
3	#10622144	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₄₄	—	2	1	no	—
5	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
6	#66883	—	2	1	no	—
7	Dic₈₈	—	2	1	no	—
8	Dic₈₈	C₄	1	2	yes	—
9	C₁₁×C₃₂	—	2	1	no	—
10	C₂×Dic₂₂	—	4	1	no	—
11	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
12	#4318	—	4	1	no	—
13	Dic₄₄	—	2	2	no	—
14	Dic₄₄	—	4	1	no	—
15	C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₁₁×C₁₆	D₄	1	1	yes	characteristic
17	#1420	—	11	1	no	maximal, Sylow
18	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
19	C₂×Dic₁₁	—	8	1	no	—
20	Dic₂₂	—	4	2	no	—
21	Dic₂₂	—	8	1	no	—
22	C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₁₁	SD₁₆	1	1	yes	characteristic
24	C₁₁⋊C₈	—	8	1	no	—
25	C₂×Q₃₂	—	11	1	no	—
26	M₆₄	D₁₁	1	1	yes	characteristic
27	#368	—	11	1	no	—
28	C₂²×C₁₁	SD₃₂	1	1	yes	characteristic
29	C₄×C₁₁	#102	1	1	yes	characteristic
30	C₄×C₁₁	D₁₆	1	1	yes	characteristic
31	Dic₁₁	—	8	2	no	—
32	C₂×Q₁₆	—	22	1	no	—
33	Q₃₂	—	11	2	no	—
34	Q₃₂	—	22	1	no	—
35	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
36	#108	—	22	1	no	—
37	C₃₂	—	2	1	no	—
38	C₂×C₁₁	—	2	1	no	—
39	C₂×C₁₁	#357	1	1	yes	characteristic
40	C₂×Q₈	—	44	1	no	—
41	Q₁₆	—	22	2	no	—
42	Q₁₆	—	44	1	no	—
43	M₁₆	—	44	1	no	—
44	C₂×C₈	D₄₄	1	1	yes	characteristic
45	C₁₆	C₄×D₁₁	1	1	yes	characteristic
46	C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
47	C₁₁	#1420	1	1	yes	characteristic, complemented, Sylow
48	Q₈	—	44	2	no	—
49	Q₈	—	88	1	no	—
50	C₂×C₄	—	88	1	no	—
51	C₂×C₄	D₈₈	1	1	yes	characteristic
52	C₈	—	88	1	no	—
53	C₈	#4314	1	1	yes	characteristic
54	C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
55	C₂²	#66864	1	1	yes	characteristic
56	C₄	—	88	2	no	—
57	C₄	D₁₇₆	1	1	yes	characteristic
58	C₄	#66885	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#10622147	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10622147
commutator	C₁₁×C₁₆	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₁
Fitting	C₁₁×M₆₄	C₂
socle	C₂×C₁₁	#357
prime radical	C₂²×C₁₁	SD₃₂
cosocle	C₂×C₁₁×C₁₆	C₂²
hypercenter	M₆₄	D₁₁
hypocenter	C₁₁	#1420
LCS	G ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
47. C₁₁	#1420	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
C₁₁×M₆₄	2
#10622144	2
#1420	11