Subgroups — #17992775

Order 4736.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₉₂	C₂	1	1	yes	maximal, characteristic
2	#14557359	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₂×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₉₆	—	2	1	no	—
5	D₅₉₂	—	2	1	no	—
6	D₅₉₂	C₄	1	2	yes	complemented
7	#11924470	—	2	1	no	—
8	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
9	C₃₂×C₃₇	—	2	1	no	—
10	C₂×D₁₄₈	—	4	1	no	—
11	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
12	C₄⋊Dic₃₇	—	4	1	no	—
13	D₂₉₆	—	2	2	no	—
14	D₂₉₆	—	4	1	no	—
15	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₃₇	D₄	1	1	yes	characteristic
17	C₂²×D₃₇	—	8	1	no	—
18	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
19	C₂×Dic₃₇	—	8	1	no	—
20	D₁₄₈	—	4	2	no	—
21	D₁₄₈	—	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	C₂×D₃₇	—	8	2	no	—
26	C₂×D₃₇	—	16	1	no	—
27	C₂×D₃₇	—	16	1	no	—
28	C₄×C₃₇	#102	1	1	yes	characteristic
29	C₄×C₃₇	SD₃₂	1	1	yes	characteristic
30	Dic₃₇	—	16	1	no	—
31	#1415	—	37	1	no	maximal, Sylow
32	C₂×C₃₇	#357	1	1	yes	characteristic
33	C₂×C₃₇	D₃₂	1	1	yes	characteristic
34	C₂×C₃₇	SD₆₄	1	1	yes	characteristic
35	D₃₇	—	16	2	no	—
36	C₂×D₁₆	—	37	1	no	—
37	C₂×C₃₂	D₃₇	1	1	yes	characteristic, complemented
38	#366	—	37	1	no	—
39	C₃₇	#1415	1	1	yes	characteristic, complemented, Sylow
40	C₂×D₈	—	74	1	no	—
41	D₁₆	—	37	2	no	—
42	D₁₆	—	74	1	no	—
43	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
44	#107	—	74	1	no	—
45	C₃₂	—	2	1	no	—
46	C₂×D₄	—	148	1	no	—
47	D₈	—	74	2	no	—
48	D₈	—	148	1	no	—
49	C₂×C₈	D₁₄₈	1	1	yes	characteristic
50	C₄⋊C₄	—	148	1	no	—
51	C₁₆	C₄×D₃₇	1	1	yes	characteristic
52	C₁₆	C₂²⋊D₃₇	1	1	yes	characteristic
53	C₂³	—	296	1	no	—
54	D₄	—	296	1	no	—
55	D₄	—	148	2	no	—
56	C₂×C₄	—	296	1	no	—
57	C₂×C₄	D₂₉₆	1	1	yes	characteristic
58	C₈	#10596930	1	1	yes	characteristic
59	C₈	#10596938	1	1	yes	characteristic
60	C₂²	—	296	2	no	—
61	C₂²	—	592	1	no	—
62	C₂²	—	592	1	no	—
63	C₂²	D₅₉₂	1	1	yes	characteristic
64	C₄	—	592	1	no	—
65	C₄	#11924458	1	1	yes	characteristic
66	C₄	#11924481	1	1	yes	characteristic
67	C₂	—	592	2	no	—
68	C₂	#14557335	1	1	yes	characteristic
69	C₂	D₁₁₈₄	1	1	yes	characteristic
70	C₂	#14557372	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₅₉₂
commutator	C₁₆×C₃₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₃₇
Fitting	C₂×C₃₂×C₃₇	C₂
socle	C₂²×C₃₇	D₁₆
prime radical	C₂×D₅₉₂	C₂
cosocle	C₂×C₁₆×C₃₇	C₂²
hypercenter	C₂×C₃₂	D₃₇
hypocenter	C₃₇	#1415
LCS	G ▷ C₁₆×C₃₇ ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #14557359	C₂	semidirect
3. C₂×C₃₂×C₃₇	C₂	semidirect
6. D₅₉₂	C₄	semidirect
37. C₂×C₃₂	D₃₇	semidirect
39. C₃₇	#1415	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅₉₂	2
#14557359	2
C₂×C₃₂×C₃₇	2
#1415	37