Subgroups — #14641650

Order 2816.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₅₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#1423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₇₆	—	2	1	no	—
5	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
6	C₁₁×#366	—	2	1	no	—
7	D₃₅₂	—	2	1	no	—
8	D₃₅₂	C₄	1	2	yes	complemented
9	C₁₁⋊C₆₄	—	2	1	no	—
10	C₂×D₈₈	—	4	1	no	—
11	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
12	C₁₁×#107	—	4	1	no	—
13	D₁₇₆	—	2	2	no	—
14	D₁₇₆	—	4	1	no	—
15	C₁₁×C₃₂	C₂×C₄	1	1	yes	characteristic
16	C₁₁×C₃₂	D₄	1	1	yes	characteristic
17	#7537	—	11	1	no	maximal, Sylow
18	C₂×D₄₄	—	8	1	no	—
19	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
20	C₁₁×C₄⋊C₄	—	8	1	no	—
21	D₈₈	—	4	2	no	—
22	D₈₈	—	8	1	no	—
23	C₁₁×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
24	C₁₁×C₁₆	SD₁₆	1	1	yes	characteristic
25	C₂×D₃₂	—	11	1	no	—
26	C₂×C₆₄	—	11	1	no	—
27	#1423	D₁₁	1	1	yes	characteristic, complemented
28	C₂²×D₁₁	—	16	1	no	—
29	C₂×C₄×C₁₁	—	16	1	no	—
30	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
31	D₄₄	—	8	2	no	—
32	D₄₄	—	16	1	no	—
33	C₈×C₁₁	#102	1	1	yes	characteristic
34	C₈×C₁₁	SD₃₂	1	1	yes	characteristic
35	C₂×D₁₆	—	22	1	no	—
36	D₃₂	—	11	2	no	—
37	D₃₂	—	22	1	no	—
38	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
39	#366	—	2	1	no	—
40	C₆₄	—	22	1	no	—
41	C₂²×C₁₁	D₃₂	1	1	yes	characteristic
42	C₂×D₁₁	—	16	2	no	—
43	C₂×D₁₁	—	32	1	no	—
44	C₂×D₁₁	—	32	1	no	—
45	C₄×C₁₁	—	32	1	no	—
46	C₄×C₁₁	#357	1	1	yes	characteristic
47	C₄×C₁₁	SD₆₄	1	1	yes	characteristic
48	C₂×D₈	—	44	1	no	—
49	D₁₆	—	22	2	no	—
50	D₁₆	—	44	1	no	—
51	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
52	#107	—	4	1	no	—
53	C₃₂	C₄×D₁₁	1	1	yes	characteristic
54	C₃₂	D₄₄	1	1	yes	characteristic
55	C₂×C₁₁	#1415	1	1	yes	characteristic
56	C₂×C₁₁	D₆₄	1	1	yes	characteristic
57	C₂×C₁₁	SD₁₂₈	1	1	yes	characteristic
58	D₁₁	—	32	2	no	—
59	C₂×D₄	—	88	1	no	—
60	D₈	—	44	2	no	—
61	D₈	—	88	1	no	—
62	C₂×C₈	#4323	1	1	yes	characteristic
63	C₄⋊C₄	—	8	1	no	—
64	C₁₆	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
65	C₁₆	#4325	1	1	yes	characteristic
66	C₁₁	#7537	1	1	yes	characteristic, complemented, Sylow
67	C₂³	—	176	1	no	—
68	D₄	—	88	2	no	—
69	D₄	—	176	1	no	—
70	C₂×C₄	—	16	1	no	—
71	C₂×C₄	#66890	1	1	yes	characteristic
72	C₈	#66873	1	1	yes	characteristic
73	C₈	#66892	1	1	yes	characteristic
74	C₂²	—	352	1	no	—
75	C₂²	—	352	1	no	—
76	C₂²	—	176	2	no	—
77	C₂²	#10622157	1	1	yes	characteristic
78	C₄	—	32	1	no	—
79	C₄	#10622129	1	1	yes	characteristic
80	C₄	#10622159	1	1	yes	characteristic
81	C₂	—	352	2	no	—
82	C₂	#13066793	1	1	yes	characteristic
83	C₂	#13066828	1	1	yes	characteristic
84	C₂	#13066830	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10622157
commutator	C₁₁×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₁
Fitting	C₁₁×#1423	C₂
socle	C₂²×C₁₁	D₃₂
prime radical	C₂×D₃₅₂	C₂
cosocle	C₂×C₁₁×C₃₂	C₂²
hypercenter	#1423	D₁₁
hypocenter	C₁₁	#7537
LCS	G ▷ C₁₁×C₃₂ ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1423

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁⋊C₆₄	C₂	semidirect
3. C₁₁×#1423	C₂	semidirect
8. D₃₅₂	C₄	semidirect
27. #1423	D₁₁	semidirect
66. C₁₁	#7537	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₅₂	2
C₂×C₁₁⋊C₆₄	2
C₁₁×#1423	2
#7537	11