Subgroups — #17992784

Order 4736.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557965	C₂	1	1	yes	maximal, characteristic
2	#14557361	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924558	—	2	1	no	—
5	Dic₂₉₆	C₄	1	1	yes	characteristic, complemented
6	#11924481	—	2	1	no	—
7	D₅₉₂	C₄	1	1	yes	characteristic, complemented
8	#11924470	—	2	1	no	—
9	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
10	C₃₂×C₃₇	—	2	1	no	—
11	#10596962	—	4	1	no	—
12	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
13	C₄⋊Dic₃₇	—	4	1	no	—
14	Dic₁₄₈	—	2	1	no	—
15	D₂₉₆	—	2	1	no	—
16	#10596930	—	4	1	no	—
17	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₃₇	D₄	1	1	yes	characteristic
19	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
20	C₂²⋊D₃₇	—	8	1	no	—
21	C₂×Dic₃₇	—	8	1	no	—
22	D₁₄₈	—	4	1	no	—
23	C₄×D₃₇	—	8	1	no	—
24	Dic₇₄	—	4	1	no	—
25	C₈×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
27	C₂²×C₃₇	D₁₆	1	1	yes	characteristic
28	C₂×D₃₇	—	8	1	no	—
29	C₄×C₃₇	#102	1	1	yes	characteristic
30	C₄×C₃₇	SD₃₂	1	1	yes	characteristic
31	Dic₃₇	—	8	1	no	—
32	Dic₃₇	—	16	1	no	—
33	#1418	—	37	1	no	maximal, Sylow
34	C₂×C₃₇	—	2	1	no	—
35	C₂×C₃₇	#357	1	1	yes	characteristic
36	D₃₇	—	16	1	no	—
37	#508	—	37	1	no	—
38	M₆₄	D₃₇	1	1	yes	characteristic, complemented
39	#367	—	37	1	no	—
40	C₃₇	#1418	1	1	yes	characteristic, complemented, Sylow
41	#135	—	74	1	no	—
42	Q₃₂	—	37	1	no	—
43	SD₃₂	—	74	1	no	—
44	D₁₆	—	37	1	no	—
45	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
46	#107	—	74	1	no	—
47	C₃₂	—	2	1	no	—
48	#41	—	148	1	no	—
49	Q₁₆	—	74	1	no	—
50	SD₁₆	—	148	1	no	—
51	D₈	—	74	1	no	—
52	C₂×C₈	D₁₄₈	1	1	yes	characteristic
53	C₄⋊C₄	—	148	1	no	—
54	C₁₆	C₄×D₃₇	1	1	yes	characteristic
55	C₁₆	C₂²⋊D₃₇	1	1	yes	characteristic
56	Q₈	—	148	1	no	—
57	D₄	—	296	1	no	—
58	D₄	—	148	1	no	—
59	C₂×C₄	—	296	1	no	—
60	C₂×C₄	—	296	1	no	—
61	C₂×C₄	D₂₉₆	1	1	yes	characteristic
62	C₈	#10596930	1	1	yes	characteristic
63	C₈	#10596938	1	1	yes	characteristic
64	C₂²	—	296	1	no	—
65	C₂²	D₅₉₂	1	1	yes	characteristic
66	C₄	—	296	1	no	—
67	C₄	—	592	1	no	—
68	C₄	#11924458	1	1	yes	characteristic
69	C₄	#11924481	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	592	1	no	—
72	C₂	#14557335	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14557335
commutator	C₁₆×C₃₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₃₇
Fitting	C₃₇×M₆₄	C₂
socle	C₂×C₃₇	#357
prime radical	#14557965	C₂
cosocle	C₂×C₁₆×C₃₇	C₂²
hypercenter	M₆₄	D₃₇
hypocenter	C₃₇	#1418
LCS	G ▷ C₁₆×C₃₇ ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
2. #14557361	C₂	semidirect
3. C₃₇×M₆₄	C₂	semidirect
5. Dic₂₉₆	C₄	semidirect
7. D₅₉₂	C₄	semidirect
38. M₆₄	D₃₇	semidirect
40. C₃₇	#1418	semidirect

Maximal subgroups

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

subgroup	index
#14557965	2
#14557361	2
C₃₇×M₆₄	2
#1418	37