Subgroups — #17992787

Order 4736.

78 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	#14557363	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₉₆	—	2	1	no	—
5	D₅₉₂	—	2	1	no	—
6	D₅₉₂	C₄	1	2	yes	—
7	#11924472	—	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	#10596934	—	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	D₁₄₈	—	4	2	no	—
20	D₁₄₈	—	8	1	no	—
21	C₈×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
23	#64436	—	8	1	no	—
24	C₂²×C₃₇	SD₃₂	1	1	yes	characteristic
25	C₂×D₃₇	—	8	2	no	—
26	C₂×D₃₇	—	16	2	no	—
27	C₄×C₃₇	#102	1	1	yes	characteristic
28	C₄×C₃₇	D₁₆	1	1	yes	characteristic
29	#1419	—	37	1	no	maximal, Sylow
30	C₂×C₃₇	—	2	1	no	—
31	C₂×C₃₇	#357	1	1	yes	characteristic
32	D₃₇	—	16	2	no	—
33	C₂×D₁₆	—	37	1	no	—
34	M₆₄	D₃₇	1	1	yes	characteristic, complemented
35	#368	—	37	1	no	—
36	C₃₇	#1419	1	1	yes	characteristic, complemented, Sylow
37	C₂×D₈	—	74	1	no	—
38	D₁₆	—	37	2	no	—
39	D₁₆	—	74	1	no	—
40	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
41	#108	—	74	1	no	—
42	C₃₂	—	2	1	no	—
43	C₂×D₄	—	148	1	no	—
44	D₈	—	74	2	no	—
45	D₈	—	148	1	no	—
46	M₁₆	—	148	1	no	—
47	C₂×C₈	D₁₄₈	1	1	yes	characteristic
48	C₁₆	C₄×D₃₇	1	1	yes	characteristic
49	C₁₆	C₂²⋊D₃₇	1	1	yes	characteristic
50	C₂³	—	296	1	no	—
51	D₄	—	296	1	no	—
52	D₄	—	148	2	no	—
53	C₂×C₄	D₂₉₆	1	1	yes	characteristic
54	C₈	—	296	1	no	—
55	C₈	#10596930	1	1	yes	characteristic
56	C₈	#10596938	1	1	yes	characteristic
57	C₂²	—	296	2	no	—
58	C₂²	—	592	2	no	—
59	C₂²	#11924481	1	1	yes	characteristic
60	C₄	#11924458	1	1	yes	characteristic
61	C₄	D₅₉₂	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	592	2	no	—
64	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	C₂×D₅₉₂	C₂
cosocle	C₂×C₁₆×C₃₇	C₂²
hypercenter	M₆₄	D₃₇
hypocenter	C₃₇	#1419
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. #14557363	C₂	semidirect
3. C₃₇×M₆₄	C₂	semidirect
34. M₆₄	D₃₇	semidirect
36. C₃₇	#1419	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
#14557363	2
C₃₇×M₆₄	2
#1419	37