Subgroups — #37511306

Order 22912.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26038868	C₂	1	2	yes	maximal, complemented
2	Dic₂₈₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#26038277	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₁₇₉	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃₂×C₁₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#19153132	—	2	2	no	—
7	Dic₁₄₃₂	C₂²	1	2	yes	—
8	#19153057	—	2	2	no	—
9	C₁₆×D₁₇₉	C₂²	1	1	yes	characteristic
10	C₁₇₉⋊C₃₂	C₂²	1	1	yes	characteristic
11	D₁₆×C₁₇₉	C₂²	1	2	yes	—
12	C₃₂×C₁₇₉	C₂²	1	1	yes	characteristic
13	#15668258	—	4	2	no	—
14	Dic₇₁₆	—	2	2	no	—
15	#15668247	—	4	2	no	—
16	C₈×D₁₇₉	D₄	1	1	yes	characteristic
17	C₁₇₉⋊C₁₆	D₄	1	1	yes	characteristic
18	D₈×C₁₇₉	—	2	2	no	—
19	C₁₆×C₁₇₉	C₂³	1	1	yes	characteristic
20	Dic₃₅₈	—	4	2	no	—
21	C₂²⋊D₁₇₉	—	8	2	no	—
22	C₂×Dic₁₇₉	—	8	2	no	—
23	C₄×D₁₇₉	D₈	1	1	yes	characteristic
24	C₁₇₉⋊C₈	D₈	1	1	yes	characteristic
25	D₄×C₁₇₉	—	4	2	no	—
26	C₈×C₁₇₉	C₂×D₄	1	1	yes	characteristic
27	C₂²×C₁₇₉	—	8	2	no	—
28	C₂×D₁₇₉	D₁₆	1	1	yes	characteristic
29	C₄×C₁₇₉	C₂×D₈	1	1	yes	characteristic
30	Dic₁₇₉	—	8	2	no	—
31	Dic₁₇₉	D₁₆	1	1	yes	characteristic
32	C₂×C₁₇₉	—	16	2	no	—
33	C₂×C₁₇₉	C₂×D₁₆	1	1	yes	characteristic
34	D₁₇₉	—	2	1	no	—
35	C₁₇₉	#2262	1	1	yes	characteristic, complemented, Sylow
36	#2262	—	179	1	no	maximal, Sylow
37	#508	—	179	2	no	—
38	Q₆₄	—	179	1	no	—
39	SD₆₄	—	179	2	no	—
40	D₃₂	D₁₇₉	1	1	yes	characteristic, complemented
41	C₂×C₃₂	—	179	1	no	—
42	#135	—	358	2	no	—
43	Q₃₂	—	179	2	no	—
44	SD₃₂	—	358	2	no	—
45	D₁₆	C₂×D₁₇₉	1	2	yes	—
46	C₂×C₁₆	—	179	1	no	—
47	C₃₂	—	179	1	no	—
48	C₃₂	C₂×D₁₇₉	1	1	yes	characteristic
49	#41	—	716	2	no	—
50	Q₁₆	—	358	2	no	—
51	SD₁₆	—	716	2	no	—
52	D₈	—	2	2	no	—
53	C₂×C₈	—	179	1	no	—
54	C₁₆	—	179	1	no	—
55	C₁₆	C₂²×D₁₇₉	1	1	yes	characteristic
56	Q₈	—	716	2	no	—
57	D₄	—	4	2	no	—
58	D₄	—	1432	2	no	—
59	C₂×C₄	—	1432	2	no	—
60	C₂×C₄	—	179	1	no	—
61	C₈	—	179	1	no	—
62	C₈	D₄×D₁₇₉	1	1	yes	characteristic
63	C₂²	—	8	2	no	—
64	C₂²	—	179	1	no	—
65	C₄	—	1432	2	no	—
66	C₄	—	179	1	no	—
67	C₄	D₈×D₁₇₉	1	1	yes	characteristic
68	C₂	—	16	2	no	—
69	C₂	—	358	1	no	—
70	C₂	D₁₆×D₁₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₁₇₉
commutator, cosocle	C₁₆×C₁₇₉	C₂³
Frattini	C₁₆	C₂²×D₁₇₉
Fitting	D₃₂×C₁₇₉	C₂
socle	C₂×C₁₇₉	C₂×D₁₆
hypercenter	D₃₂	D₁₇₉
hypocenter	C₁₇₉	#2262
LCS	G ▷ C₁₆×C₁₇₉ ▷ C₈×C₁₇₉ ▷ C₄×C₁₇₉ ▷ C₂×C₁₇₉ ▷ C₁₇₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₃₂

Complements

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

N	H ≅ G/N	type
1. #26038868	C₂	semidirect
2. Dic₂₈₆₄	C₂	semidirect
3. #26038277	C₂	semidirect
4. C₃₂×D₁₇₉	C₂	semidirect
5. D₃₂×C₁₇₉	C₂	semidirect
35. C₁₇₉	#2262	semidirect
40. D₃₂	D₁₇₉	semidirect

Maximal subgroups

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

subgroup	index
#26038868	2
Dic₂₈₆₄	2
#26038277	2
C₃₂×D₁₇₉	2
D₃₂×C₁₇₉	2
#2262	179