Subgroups — #14674827

Order 2816.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13070925	C₂	1	2	yes	maximal, complemented
2	Dic₃₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#13066832	C₂	1	2	yes	maximal, complemented
4	D₇₀₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	#10622517	—	2	2	no	—
7	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
8	Dic₁₇₆	C₂²	1	2	yes	—
9	#10622087	—	2	2	no	—
10	D₃₅₂	C₂²	1	2	yes	—
11	C₁₁×C₆₄	C₂²	1	1	yes	characteristic
12	C₁₁×C₆₄	C₂²	1	1	yes	characteristic
13	#66957	—	4	2	no	—
14	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
15	Dic₈₈	—	2	2	no	—
16	#66864	—	4	2	no	—
17	D₁₇₆	—	2	2	no	—
18	C₁₁×C₃₂	D₄	1	1	yes	characteristic
19	C₁₁×C₃₂	C₂³	1	1	yes	characteristic
20	#13741	—	11	1	no	maximal, Sylow
21	#4339	—	8	2	no	—
22	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
23	Dic₄₄	—	4	2	no	—
24	D₈₈	—	4	2	no	—
25	#4314	—	8	2	no	—
26	C₁₁×C₁₆	D₈	1	1	yes	characteristic
27	C₁₁×C₁₆	C₂×D₄	1	1	yes	characteristic
28	#2262	—	11	2	no	—
29	Q₁₂₈	—	11	1	no	—
30	SD₁₂₈	—	11	2	no	—
31	D₆₄	—	11	1	no	—
32	C₂×C₆₄	D₁₁	1	1	yes	characteristic, complemented
33	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
34	C₂²⋊D₁₁	—	16	2	no	—
35	D₄₄	—	8	2	no	—
36	C₄×D₁₁	—	16	2	no	—
37	Dic₂₂	—	8	2	no	—
38	C₈×C₁₁	D₁₆	1	1	yes	characteristic
39	C₈×C₁₁	C₂×D₈	1	1	yes	characteristic
40	#508	—	22	2	no	—
41	Q₆₄	—	11	2	no	—
42	SD₆₄	—	22	2	no	—
43	D₃₂	—	11	2	no	—
44	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
45	C₆₄	C₂×D₁₁	1	1	yes	characteristic
46	C₆₄	C₂×D₁₁	1	1	yes	characteristic
47	C₂²×C₁₁	D₃₂	1	1	yes	characteristic
48	C₂×D₁₁	—	16	2	no	—
49	C₄×C₁₁	D₃₂	1	1	yes	characteristic
50	C₄×C₁₁	C₂×D₁₆	1	1	yes	characteristic
51	Dic₁₁	—	16	2	no	—
52	#135	—	44	2	no	—
53	Q₃₂	—	22	2	no	—
54	SD₃₂	—	44	2	no	—
55	D₁₆	—	22	2	no	—
56	C₂×C₁₆	D₄₄	1	1	yes	characteristic
57	C₃₂	D₄₄	1	1	yes	characteristic
58	C₃₂	C₂²×D₁₁	1	1	yes	characteristic
59	C₂×C₁₁	—	2	1	no	—
60	C₂×C₁₁	C₂×D₃₂	1	1	yes	characteristic
61	D₁₁	—	32	2	no	—
62	#41	—	88	2	no	—
63	Q₁₆	—	44	2	no	—
64	SD₁₆	—	88	2	no	—
65	D₈	—	44	2	no	—
66	C₂×C₈	D₈₈	1	1	yes	characteristic
67	C₁₆	D₈₈	1	1	yes	characteristic
68	C₁₆	C₂×D₄₄	1	1	yes	characteristic
69	C₁₁	#13741	1	1	yes	characteristic, complemented, Sylow
70	Q₈	—	88	2	no	—
71	D₄	—	88	2	no	—
72	D₄	—	176	2	no	—
73	C₂×C₄	—	176	2	no	—
74	C₂×C₄	D₁₇₆	1	1	yes	characteristic
75	C₈	D₁₇₆	1	1	yes	characteristic
76	C₈	C₂×D₈₈	1	1	yes	characteristic
77	C₂²	—	176	2	no	—
78	C₂²	D₃₅₂	1	1	yes	characteristic
79	C₄	—	176	2	no	—
80	C₄	D₃₅₂	1	1	yes	characteristic
81	C₄	C₂×D₁₇₆	1	1	yes	characteristic
82	C₂	—	2	1	no	—
83	C₂	—	352	2	no	—
84	C₂	C₂×D₃₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₃₅₂
commutator, cosocle	C₁₁×C₃₂	C₂³
Frattini	C₃₂	C₂²×D₁₁
Fitting	C₂×C₁₁×C₆₄	C₂
socle	C₂×C₁₁	C₂×D₃₂
hypercenter	C₂×C₆₄	D₁₁
hypocenter	C₁₁	#13741
LCS	G ▷ C₁₁×C₃₂ ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
1. #13070925	C₂	semidirect
2. Dic₃₅₂	C₂	semidirect
3. #13066832	C₂	semidirect
4. D₇₀₄	C₂	semidirect
5. C₂×C₁₁×C₆₄	C₂	semidirect
32. C₂×C₆₄	D₁₁	semidirect
69. C₁₁	#13741	semidirect

Maximal subgroups

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

subgroup	index
#13070925	2
Dic₃₅₂	2
#13066832	2
D₇₀₄	2
C₂×C₁₁×C₆₄	2
#13741	11