Subgroups — #14558451

Order 2368.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924611	C₂	1	1	yes	maximal, characteristic, complemented
2	#11924606	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×D₃₇	C₂	1	1	yes	maximal, characteristic
4	D₄×D₃₇	—	2	1	no	—
5	#10596953	—	2	1	no	—
6	D₈×C₃₇	C₄	1	1	yes	characteristic
7	#10596939	—	2	1	no	—
8	D₂₉₆	C₄	1	1	yes	characteristic
9	C₈×D₃₇	C₂²	1	1	yes	characteristic
10	#10596927	—	2	1	no	—
11	C₂²×D₃₇	—	4	1	no	—
12	D₄×C₃₇	—	2	1	no	—
13	C₂²⋊D₃₇	—	4	1	no	—
14	D₁₄₈	—	2	1	no	—
15	C₄×D₃₇	D₄	1	1	yes	characteristic
16	#64438	—	4	1	no	—
17	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
18	#64436	D₄	1	1	yes	characteristic
19	C₂²×C₃₇	—	4	1	no	—
20	C₂×D₃₇	—	4	1	no	—
21	C₂×D₃₇	—	8	2	no	—
22	C₂×D₃₇	SD₁₆	1	1	yes	characteristic
23	C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₃₇	D₈	1	1	yes	characteristic
25	C₂×C₃₇	—	8	1	no	—
26	C₂×C₃₇	#102	1	1	yes	characteristic
27	D₃₇	—	2	1	no	—
28	D₃₇	—	8	1	no	—
29	#361	—	37	1	no	maximal, Sylow
30	C₃₇	#361	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₈	—	37	1	no	—
32	M₃₂	—	37	1	no	—
33	#108	—	37	1	no	—
34	C₂×D₄	—	74	1	no	—
35	D₈	—	37	1	no	—
36	D₈	—	74	1	no	—
37	D₈	#3866	1	1	yes	characteristic
38	M₁₆	—	74	1	no	—
39	C₂×C₈	—	37	1	no	—
40	C₁₆	—	74	1	no	—
41	C₂³	—	148	1	no	—
42	D₄	—	2	1	no	—
43	D₄	—	74	1	no	—
44	D₄	—	148	1	no	—
45	C₂×C₄	—	37	1	no	—
46	C₈	—	37	1	no	—
47	C₈	—	148	1	no	—
48	C₈	C₂×#3866	1	1	yes	characteristic
49	C₂²	—	4	1	no	—
50	C₂²	—	37	1	no	—
51	C₂²	—	296	2	no	—
52	C₂²	—	148	1	no	—
53	C₄	—	37	1	no	—
54	C₄	C₂²⋊#3866	1	1	yes	characteristic
55	C₂	—	8	1	no	—
56	C₂	—	296	1	no	—
57	C₂	—	74	1	no	—
58	C₂	#11924598	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11924598
commutator	C₈×C₃₇	C₂×C₄
Frattini	C₈	C₂×#3866
Fitting	D₈×C₃₇	C₄
socle	C₂×C₃₇	#102
prime radical	D₈×D₃₇	C₂
cosocle	C₈×D₃₇	C₂²
hypercenter	D₈	#3866
hypocenter	C₃₇	#361
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #11924611	C₂	semidirect
2. #11924606	C₂	semidirect
30. C₃₇	#361	semidirect

Maximal subgroups

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

subgroup	index
#11924611	2
#11924606	2
D₈×D₃₇	2
#361	37