Subgroups — #17992776

Order 4736.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₉₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#11924442	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#366	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₄₈	—	2	1	no	—
5	Dic₂₉₆	—	2	1	no	—
6	Dic₂₉₆	C₄	1	2	yes	complemented
7	#11924442	—	2	1	no	—
8	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
9	#107×C₃₇	—	2	1	no	—
10	C₂×Dic₇₄	—	4	1	no	—
11	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
12	C₄⋊C₄×C₃₇	—	4	1	no	—
13	Dic₁₄₈	—	2	2	no	—
14	Dic₁₄₈	—	4	1	no	—
15	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₃₇	D₄	1	1	yes	characteristic
17	C₂×C₄×C₃₇	—	8	1	no	—
18	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
19	C₂×Dic₃₇	—	8	1	no	—
20	Dic₇₄	—	4	2	no	—
21	Dic₇₄	—	8	1	no	—
22	C₈×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
24	C₂²×C₃₇	D₁₆	1	1	yes	characteristic
25	C₄×C₃₇	—	16	1	no	—
26	C₄×C₃₇	#102	1	1	yes	characteristic
27	C₄×C₃₇	SD₃₂	1	1	yes	characteristic
28	Dic₃₇	—	8	2	no	—
29	#1416	—	37	1	no	maximal, Sylow
30	C₂×C₃₇	#357	1	1	yes	characteristic
31	C₂×C₃₇	SD₆₄	1	1	yes	characteristic
32	C₂×C₃₇	Q₆₄	1	1	yes	characteristic
33	C₂×Q₃₂	—	37	1	no	—
34	C₂×C₃₂	—	37	1	no	—
35	#366	D₃₇	1	1	yes	characteristic
36	C₃₇	#1416	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₁₆	—	74	1	no	—
38	Q₃₂	—	37	2	no	—
39	Q₃₂	—	74	1	no	—
40	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
41	#107	—	2	1	no	—
42	C₃₂	—	74	1	no	—
43	C₂×Q₈	—	148	1	no	—
44	Q₁₆	—	74	2	no	—
45	Q₁₆	—	148	1	no	—
46	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
47	C₄⋊C₄	—	4	1	no	—
48	C₁₆	C₄×D₃₇	1	1	yes	characteristic
49	C₁₆	D₁₄₈	1	1	yes	characteristic
50	Q₈	—	296	1	no	—
51	Q₈	—	148	2	no	—
52	C₂×C₄	—	8	1	no	—
53	C₂×C₄	—	296	1	no	—
54	C₂×C₄	#10596939	1	1	yes	characteristic
55	C₈	#10596938	1	1	yes	characteristic
56	C₈	#10596941	1	1	yes	characteristic
57	C₂²	#11924477	1	1	yes	characteristic
58	C₄	—	16	1	no	—
59	C₄	—	296	2	no	—
60	C₄	#11924456	1	1	yes	characteristic
61	C₄	#11924479	1	1	yes	characteristic
62	C₂	#14557333	1	1	yes	characteristic
63	C₂	#14557371	1	1	yes	characteristic
64	C₂	#14557373	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11924477
commutator	C₁₆×C₃₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₃₇
Fitting	C₃₇×#366	C₂
socle, prime radical	C₂²×C₃₇	D₁₆
cosocle	C₂×C₁₆×C₃₇	C₂²
hypercenter	#366	D₃₇
hypocenter	C₃₇	#1416
LCS	G ▷ C₁₆×C₃₇ ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
6. Dic₂₉₆	C₄	semidirect
36. C₃₇	#1416	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₂₉₆	2
C₂×#11924442	2
C₃₇×#366	2
#1416	37