Subgroups — #17996472

Order 4736.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈×Dic₃₇	C₂	1	2	yes	maximal, complemented
2	#14557361	C₂	1	1	yes	maximal, characteristic, complemented
3	#14557334	C₂	1	2	yes	maximal, complemented
4	#14557308	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
6	D₄×Dic₃₇	—	2	2	no	—
7	C₂×#10596925	C₂²	1	1	yes	characteristic
8	#11924470	C₂²	1	2	yes	—
9	#11924457	—	2	2	no	—
10	C₈×Dic₃₇	C₂²	1	1	yes	characteristic
11	C₂×D₈×C₃₇	C₂²	1	2	yes	—
12	D₁₆×C₃₇	C₄	1	4	yes	complemented
13	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
14	C₂×D₄×C₃₇	—	2	2	no	—
15	C₂²×Dic₃₇	—	4	2	no	—
16	D₈×C₃₇	—	2	2	no	—
17	D₈×C₃₇	C₂×C₄	1	4	yes	complemented
18	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
19	C₂²⋊Dic₃₇	—	4	2	no	—
20	C₄⋊Dic₃₇	—	2	2	no	—
21	C₄×Dic₃₇	D₄	1	1	yes	characteristic
22	C₂×#64436	D₄	1	1	yes	characteristic
23	C₁₆×C₃₇	C₂×C₄	1	2	yes	complemented
24	#10596925	—	2	1	no	—
25	C₂³×C₃₇	—	4	2	no	—
26	D₄×C₃₇	—	2	4	no	—
27	D₄×C₃₇	—	4	2	no	—
28	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₃₇	—	4	2	no	—
30	C₂×Dic₃₇	—	8	4	no	—
31	C₂×Dic₃₇	D₈	1	2	yes	—
32	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₃₇	#41	1	1	yes	characteristic
34	#64436	—	2	1	no	—
35	C₂²×C₃₇	—	4	4	no	—
36	C₂²×C₃₇	—	8	2	no	—
37	C₂²×C₃₇	—	8	2	no	—
38	C₂²×C₃₇	C₂×D₈	1	1	yes	characteristic
39	C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
40	C₄×C₃₇	#135	1	1	yes	characteristic
41	Dic₃₇	—	2	2	no	—
42	Dic₃₇	—	8	2	no	—
43	#2177	—	37	1	no	maximal, Sylow
44	C₂×C₃₇	—	8	4	no	—
45	C₂×C₃₇	C₄×D₈	1	1	yes	characteristic
46	C₂×C₃₇	#509	1	2	yes	—
47	C₂×D₁₆	D₃₇	1	1	yes	characteristic
48	C₄×D₈	—	37	2	no	—
49	#367	—	37	1	no	—
50	#357	—	37	2	no	—
51	#346	—	37	1	no	—
52	C₃₇	#2177	1	1	yes	characteristic, complemented, Sylow
53	C₂×D₈	C₂×D₃₇	1	2	yes	—
54	C₄×D₄	—	74	2	no	—
55	D₁₆	Dic₃₇	1	4	yes	complemented
56	C₂×C₁₆	—	37	1	no	—
57	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
58	#107	—	37	2	no	—
59	#102	—	74	2	no	—
60	C₄×C₈	—	37	1	no	—
61	C₂×D₄	—	2	2	no	—
62	C₂²×C₄	—	148	2	no	—
63	D₈	—	2	2	no	—
64	D₈	C₂×Dic₃₇	1	4	yes	complemented
65	C₂×C₈	—	37	1	no	—
66	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
67	C₄⋊C₄	—	74	2	no	—
68	C₂²⋊C₄	—	148	2	no	—
69	C₄²	—	37	1	no	—
70	C₁₆	—	74	1	no	—
71	C₁₆	C₂×Dic₃₇	1	2	yes	complemented
72	C₂³	—	4	2	no	—
73	D₄	—	2	4	no	—
74	D₄	—	4	2	no	—
75	C₂×C₄	—	37	2	no	—
76	C₂×C₄	—	296	4	no	—
77	C₂×C₄	—	148	2	no	—
78	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
79	C₈	—	74	1	no	—
80	C₈	#10596964	1	1	yes	characteristic
81	C₈	C₂²×Dic₃₇	1	1	yes	characteristic
82	C₂²	—	4	4	no	—
83	C₂²	—	8	2	no	—
84	C₂²	—	8	2	no	—
85	C₂²	D₈×D₃₇	1	1	yes	characteristic
86	C₄	—	296	2	no	—
87	C₄	—	74	2	no	—
88	C₄	D₄×Dic₃₇	1	1	yes	characteristic
89	C₄	#11924555	1	1	yes	characteristic
90	C₂	—	8	4	no	—
91	C₂	D₈×Dic₃₇	1	1	yes	characteristic
92	C₂	#14557967	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₃₇
commutator	C₈×C₃₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₃₇
Fitting, prime radical	C₂×D₁₆×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₈
cosocle	C₂×C₈×C₃₇	C₂³
hypercenter	C₂×D₁₆	D₃₇
hypocenter	C₃₇	#2177
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₁₆

Complements

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

N	H ≅ G/N	type
1. D₈×Dic₃₇	C₂	semidirect
2. #14557361	C₂	semidirect
3. #14557334	C₂	semidirect
4. #14557308	C₂	semidirect
12. D₁₆×C₃₇	C₄	semidirect
17. D₈×C₃₇	C₂×C₄	semidirect
23. C₁₆×C₃₇	C₂×C₄	semidirect
52. C₃₇	#2177	semidirect
55. D₁₆	Dic₃₇	semidirect
64. D₈	C₂×Dic₃₇	semidirect
71. C₁₆	C₂×Dic₃₇	semidirect

Maximal subgroups

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

subgroup	index
D₈×Dic₃₇	2
#14557361	2
#14557334	2
#14557308	2
C₂×D₁₆×C₃₇	2
#2177	37