Subgroups — #13066798

Order 1408.

74 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	C₂×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic
3	#10622142	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₄₄	—	2	1	no	—
5	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
6	#66882	—	2	1	no	—
7	Dic₈₈	—	2	1	no	—
8	Dic₈₈	C₄	1	2	yes	complemented
9	C₁₁×C₃₂	—	2	1	no	—
10	C₂×Dic₂₂	—	4	1	no	—
11	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
12	C₄⋊Dic₁₁	—	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	#1416	—	11	1	no	maximal, Sylow
18	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
19	C₂×Dic₁₁	—	8	1	no	—
20	C₂×Dic₁₁	—	8	1	no	—
21	Dic₂₂	—	4	2	no	—
22	Dic₂₂	—	8	1	no	—
23	C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
24	C₈×C₁₁	SD₁₆	1	1	yes	characteristic
25	C₂×Q₃₂	—	11	1	no	—
26	C₂×C₃₂	D₁₁	1	1	yes	characteristic
27	#366	—	11	1	no	—
28	C₂²×C₁₁	D₁₆	1	1	yes	characteristic
29	C₄×C₁₁	#102	1	1	yes	characteristic
30	C₄×C₁₁	SD₃₂	1	1	yes	characteristic
31	Dic₁₁	—	8	2	no	—
32	Dic₁₁	—	16	1	no	—
33	C₂×Q₁₆	—	22	1	no	—
34	Q₃₂	—	11	2	no	—
35	Q₃₂	—	22	1	no	—
36	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
37	#107	—	22	1	no	—
38	C₃₂	—	2	1	no	—
39	C₂×C₁₁	#357	1	1	yes	characteristic
40	C₂×C₁₁	SD₆₄	1	1	yes	characteristic
41	C₂×C₁₁	Q₆₄	1	1	yes	characteristic
42	C₂×Q₈	—	44	1	no	—
43	Q₁₆	—	22	2	no	—
44	Q₁₆	—	44	1	no	—
45	C₂×C₈	D₄₄	1	1	yes	characteristic
46	C₄⋊C₄	—	44	1	no	—
47	C₁₆	C₄×D₁₁	1	1	yes	characteristic
48	C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
49	C₁₁	#1416	1	1	yes	characteristic, complemented, Sylow
50	Q₈	—	44	2	no	—
51	Q₈	—	88	1	no	—
52	C₂×C₄	—	88	1	no	—
53	C₂×C₄	—	88	1	no	—
54	C₂×C₄	D₈₈	1	1	yes	characteristic
55	C₈	#4314	1	1	yes	characteristic
56	C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
57	C₂²	D₁₇₆	1	1	yes	characteristic
58	C₄	—	88	2	no	—
59	C₄	—	176	1	no	—
60	C₄	#66864	1	1	yes	characteristic
61	C₄	#66885	1	1	yes	characteristic
62	C₂	#10622087	1	1	yes	characteristic
63	C₂	Dic₁₇₆	1	1	yes	characteristic
64	C₂	#10622147	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₇₆
commutator	C₁₁×C₁₆	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₁
Fitting	C₂×C₁₁×C₃₂	C₂
socle, prime radical	C₂²×C₁₁	D₁₆
cosocle	C₂×C₁₁×C₁₆	C₂²
hypercenter	C₂×C₃₂	D₁₁
hypocenter	C₁₁	#1416
LCS	G ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
8. Dic₈₈	C₄	semidirect
49. C₁₁	#1416	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
C₂×C₁₁×C₃₂	2
#10622142	2
#1416	11