Subgroups — #18009751

Order 4736.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558466	C₂	1	1	yes	maximal, characteristic, complemented
2	#14558462	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₆×D₃₇	C₂	1	1	yes	maximal, characteristic
4	#11924607	—	2	1	no	—
5	#11924586	—	2	1	no	—
6	D₈×D₃₇	—	2	1	no	—
7	D₅₉₂	C₄	1	1	yes	characteristic
8	#11924477	—	2	1	no	—
9	C₁₆×D₃₇	C₂²	1	1	yes	characteristic
10	D₁₆×C₃₇	C₄	1	1	yes	characteristic
11	D₄×D₃₇	—	4	1	no	—
12	#10596953	—	4	1	no	—
13	D₈×C₃₇	—	2	1	no	—
14	#10596939	—	4	1	no	—
15	D₂₉₆	—	2	1	no	—
16	C₈×D₃₇	D₄	1	1	yes	characteristic
17	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
18	#10596925	D₄	1	1	yes	characteristic
19	C₂²×D₃₇	—	8	1	no	—
20	D₄×C₃₇	—	4	1	no	—
21	C₂²⋊D₃₇	—	8	1	no	—
22	D₁₄₈	—	4	1	no	—
23	C₄×D₃₇	D₈	1	1	yes	characteristic
24	#64438	—	8	1	no	—
25	C₈×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
26	#64436	SD₁₆	1	1	yes	characteristic
27	C₂²×C₃₇	—	8	1	no	—
28	C₂×D₃₇	—	8	1	no	—
29	C₂×D₃₇	—	16	2	no	—
30	C₂×D₃₇	SD₃₂	1	1	yes	characteristic
31	C₄×C₃₇	#102	1	1	yes	characteristic
32	Dic₃₇	D₁₆	1	1	yes	characteristic
33	#1419	—	37	1	no	maximal, Sylow
34	C₂×C₃₇	—	16	1	no	—
35	C₂×C₃₇	#357	1	1	yes	characteristic
36	D₃₇	—	2	1	no	—
37	D₃₇	—	16	1	no	—
38	C₂×D₁₆	—	37	1	no	—
39	M₆₄	—	37	1	no	—
40	#368	—	37	1	no	—
41	C₃₇	#1419	1	1	yes	characteristic, complemented, Sylow
42	C₂×D₈	—	74	1	no	—
43	D₁₆	—	37	1	no	—
44	D₁₆	—	74	1	no	—
45	D₁₆	#3866	1	1	yes	characteristic
46	C₂×C₁₆	—	37	1	no	—
47	#108	—	74	1	no	—
48	C₃₂	—	74	1	no	—
49	C₂×D₄	—	148	1	no	—
50	D₈	—	2	1	no	—
51	D₈	—	74	1	no	—
52	D₈	—	148	1	no	—
53	M₁₆	—	148	1	no	—
54	C₂×C₈	—	37	1	no	—
55	C₁₆	—	37	1	no	—
56	C₁₆	C₂×#3866	1	1	yes	characteristic
57	C₂³	—	296	1	no	—
58	D₄	—	4	1	no	—
59	D₄	—	296	1	no	—
60	D₄	—	148	1	no	—
61	C₂×C₄	—	37	1	no	—
62	C₈	—	37	1	no	—
63	C₈	—	296	1	no	—
64	C₈	C₂²⋊#3866	1	1	yes	characteristic
65	C₂²	—	8	1	no	—
66	C₂²	—	37	1	no	—
67	C₂²	—	296	1	no	—
68	C₂²	—	592	2	no	—
69	C₄	—	37	1	no	—
70	C₄	#11924598	1	1	yes	characteristic
71	C₂	—	16	1	no	—
72	C₂	—	74	1	no	—
73	C₂	—	592	1	no	—
74	C₂	#14558445	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14558445
commutator	C₁₆×C₃₇	C₂×C₄
Frattini	C₁₆	C₂×#3866
Fitting	D₁₆×C₃₇	C₄
socle	C₂×C₃₇	#357
prime radical	D₁₆×D₃₇	C₂
cosocle	C₁₆×D₃₇	C₂²
hypercenter	D₁₆	#3866
hypocenter	C₃₇	#1419
LCS	G ▷ C₁₆×C₃₇ ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. #14558466	C₂	semidirect
2. #14558462	C₂	semidirect
41. C₃₇	#1419	semidirect

Maximal subgroups

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

subgroup	index
#14558466	2
#14558462	2
D₁₆×D₃₇	2
#1419	37