Subgroups — #17992698

Order 4736.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557571	C₂	1	2	yes	maximal
2	C₂×M₃₂×C₃₇	C₂	1	1	yes	maximal, characteristic
3	#11924495	—	2	2	no	—
4	#11924470	—	2	2	no	—
5	#11924468	C₄	1	4	yes	complemented
6	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
7	M₃₂×C₃₇	—	2	2	no	—
8	C₂×C₁₆×C₃₇	C₄	1	2	yes	complemented
9	C₂²×C₄×C₃₇	D₄	1	1	yes	characteristic
10	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
11	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₃₇	D₄	1	2	yes	—
13	C₂×C₈×C₃₇	Q₈	1	1	yes	characteristic
14	C₂²⋊Dic₃₇	—	4	2	no	—
15	C₄⋊Dic₃₇	—	2	4	no	—
16	C₄×Dic₃₇	—	4	2	no	—
17	C₁₆×C₃₇	—	2	2	no	—
18	C₂³×C₃₇	D₈	1	1	yes	characteristic
19	C₂×C₄×C₃₇	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₃₇	SD₁₆	1	2	yes	—
22	C₂×C₄×C₃₇	Q₁₆	1	1	yes	characteristic
23	C₂×Dic₃₇	—	4	4	no	—
24	C₈×C₃₇	C₄²	1	1	yes	characteristic
25	C₈×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₃₇	C₄⋊C₄	1	2	yes	—
27	C₂²×C₃₇	—	4	1	no	—
28	C₂²×C₃₇	#102	1	2	yes	—
29	C₂²×C₃₇	#107	1	1	yes	characteristic
30	C₄×C₃₇	#95	1	1	yes	characteristic
31	C₄×C₃₇	#103	1	2	yes	—
32	C₄×C₃₇	#106	1	1	yes	characteristic
33	Dic₃₇	—	8	4	no	—
34	#1384	—	37	1	no	maximal, Sylow
35	C₂×C₃₇	—	2	2	no	—
36	C₂×C₃₇	—	2	1	no	—
37	C₂×C₃₇	#340	1	1	yes	characteristic
38	C₂×M₃₂	D₃₇	1	1	yes	characteristic
39	#427	—	37	2	no	—
40	C₃₇	#1384	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
42	#117	—	74	2	no	—
43	M₃₂	—	2	2	no	—
44	C₂×C₁₆	Dic₃₇	1	2	yes	complemented
45	#107	—	74	2	no	—
46	#106	—	37	4	no	—
47	C₂²×C₄	D₁₄₈	1	1	yes	characteristic
48	C₂×C₈	Dic₇₄	1	1	yes	characteristic
49	C₂×C₈	C₄×D₃₇	1	2	yes	—
50	C₂×C₈	C₂×Dic₃₇	1	1	yes	characteristic
51	C₂×C₈	C₂²⋊D₃₇	1	2	yes	—
52	C₄⋊C₄	—	74	4	no	—
53	C₂²⋊C₄	—	148	2	no	—
54	C₄²	—	148	2	no	—
55	C₁₆	—	2	2	no	—
56	C₂³	D₂₉₆	1	1	yes	characteristic
57	C₂×C₄	—	148	4	no	—
58	C₂×C₄	#10596930	1	2	yes	—
59	C₂×C₄	Dic₁₄₈	1	1	yes	characteristic
60	C₂×C₄	C₄⋊Dic₃₇	1	1	yes	characteristic
61	C₂×C₄	#10596938	1	2	yes	—
62	C₈	C₄×Dic₃₇	1	1	yes	characteristic
63	C₈	#10596936	1	2	yes	—
64	C₈	C₂²⋊Dic₃₇	1	1	yes	characteristic
65	C₂²	—	4	1	no	—
66	C₂²	#11924458	1	2	yes	—
67	C₂²	#11924470	1	1	yes	characteristic
68	C₄	—	296	4	no	—
69	C₄	#11924443	1	1	yes	characteristic
70	C₄	#11924461	1	2	yes	—
71	C₄	#11924468	1	1	yes	characteristic
72	C₂	—	2	2	no	—
73	C₂	—	2	1	no	—
74	C₂	#14557296	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11924468
commutator	C₈×C₃₇	C₄²
Frattini	C₂²×C₈	C₂×D₃₇
Fitting	C₂×M₃₂×C₃₇	C₂
socle	C₂×C₃₇	#340
prime radical	C₂³×C₃₇	D₈
cosocle	C₂²×C₈×C₃₇	C₂²
hypercenter	C₂×M₃₂	D₃₇
hypocenter	C₃₇	#1384
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
5. #11924468	C₄	semidirect
8. C₂×C₁₆×C₃₇	C₄	semidirect
40. C₃₇	#1384	semidirect
44. C₂×C₁₆	Dic₃₇	semidirect

Maximal subgroups

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

subgroup	index
#14557571	2
C₂×M₃₂×C₃₇	2
#1384	37