Subgroups — #17992781

Order 4736.

72 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	#14557363	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₂×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924558	—	2	1	no	—
5	Dic₂₉₆	C₄	1	1	yes	characteristic
6	#11924481	—	2	1	no	—
7	D₅₉₂	C₄	1	1	yes	characteristic
8	#11924472	—	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	#10596934	—	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	D₁₄₈	—	4	1	no	—
22	C₄×D₃₇	—	8	1	no	—
23	Dic₇₄	—	4	1	no	—
24	C₈×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
26	#64436	—	8	1	no	—
27	C₂²×C₃₇	SD₃₂	1	1	yes	characteristic
28	C₂×D₃₇	—	8	1	no	—
29	C₄×C₃₇	#102	1	1	yes	characteristic
30	C₄×C₃₇	D₁₆	1	1	yes	characteristic
31	Dic₃₇	—	8	1	no	—
32	#1417	—	37	1	no	maximal, Sylow
33	C₂×C₃₇	—	2	1	no	—
34	C₂×C₃₇	#357	1	1	yes	characteristic
35	D₃₇	—	16	1	no	—
36	#508	—	37	1	no	—
37	C₂×C₃₂	D₃₇	1	1	yes	characteristic, complemented
38	#368	—	37	1	no	—
39	C₃₇	#1417	1	1	yes	characteristic, complemented, Sylow
40	#135	—	74	1	no	—
41	Q₃₂	—	37	1	no	—
42	SD₃₂	—	74	1	no	—
43	D₁₆	—	37	1	no	—
44	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
45	#108	—	74	1	no	—
46	C₃₂	—	2	1	no	—
47	#41	—	148	1	no	—
48	Q₁₆	—	74	1	no	—
49	SD₁₆	—	148	1	no	—
50	D₈	—	74	1	no	—
51	M₁₆	—	148	1	no	—
52	C₂×C₈	D₁₄₈	1	1	yes	characteristic
53	C₁₆	C₄×D₃₇	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₃₇	1	1	yes	characteristic
55	Q₈	—	148	1	no	—
56	D₄	—	296	1	no	—
57	D₄	—	148	1	no	—
58	C₂×C₄	—	296	1	no	—
59	C₂×C₄	D₂₉₆	1	1	yes	characteristic
60	C₈	—	296	1	no	—
61	C₈	#10596930	1	1	yes	characteristic
62	C₈	#10596938	1	1	yes	characteristic
63	C₂²	—	296	1	no	—
64	C₂²	#11924481	1	1	yes	characteristic
65	C₄	—	296	1	no	—
66	C₄	#11924458	1	1	yes	characteristic
67	C₄	D₅₉₂	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	592	1	no	—
70	C₂	#14557335	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₅₉₂
commutator	C₁₆×C₃₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₃₇
Fitting	C₂×C₃₂×C₃₇	C₂
socle	C₂×C₃₇	#357
prime radical	#14557965	C₂
cosocle	C₂×C₁₆×C₃₇	C₂²
hypercenter	C₂×C₃₂	D₃₇
hypocenter	C₃₇	#1417
LCS	G ▷ C₁₆×C₃₇ ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ 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. #14557363	C₂	semidirect
3. C₂×C₃₂×C₃₇	C₂	semidirect
37. C₂×C₃₂	D₃₇	semidirect
39. C₃₇	#1417	semidirect

Maximal subgroups

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

subgroup	index
#14557965	2
#14557363	2
C₂×C₃₂×C₃₇	2
#1417	37