Subgroups — #14557454

Order 2368.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₇₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₃₇	C₂	1	2	yes	maximal
3	C₂×#10596936	C₂	1	1	yes	maximal, characteristic
4	#11924443	C₂	1	2	yes	maximal
5	#95×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×C₃₇	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₃₇	C₂²	1	2	yes	—
8	C₂²×Dic₃₇	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₇	C₂²	1	2	yes	—
10	C₂²×Dic₃₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₇₄	—	2	2	no	—
12	C₂×Dic₇₄	—	2	4	no	—
13	C₄⋊Dic₃₇	—	2	4	no	—
14	#10596936	—	2	2	no	—
15	C₂³×C₃₇	C₂³	1	1	yes	characteristic
16	C₂×C₄×C₃₇	—	2	2	no	—
17	C₂×C₄×C₃₇	—	2	2	no	—
18	C₂×C₄×C₃₇	—	2	2	no	—
19	C₂×C₄×C₃₇	D₄	1	2	yes	—
20	C₂×C₄×C₃₇	Q₈	1	4	yes	complemented
21	C₂×Dic₃₇	—	2	1	no	—
22	C₂×Dic₃₇	—	2	2	no	—
23	C₂×Dic₃₇	—	2	2	no	—
24	C₂×Dic₃₇	—	2	1	no	—
25	C₂×Dic₃₇	—	2	1	no	—
26	C₂×Dic₃₇	—	2	2	no	—
27	C₂×Dic₃₇	D₄	1	4	yes	—
28	C₂×Dic₃₇	Q₈	1	2	yes	complemented
29	Dic₇₄	—	2	8	no	—
30	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₃₇	C₂×D₄	1	2	yes	—
32	C₂²×C₃₇	C₂×Q₈	1	2	yes	—
33	C₂²×C₃₇	C₂×Q₈	1	1	yes	characteristic
34	C₂²×C₃₇	#41	1	1	yes	characteristic
35	C₄×C₃₇	—	2	2	no	—
36	C₄×C₃₇	—	2	4	no	—
37	Dic₃₇	—	2	4	no	—
38	Dic₃₇	—	2	2	no	—
39	Dic₃₇	—	4	1	no	—
40	C₂×C₃₇	#120	1	1	yes	characteristic
41	C₂×C₃₇	C₂²⋊Q₈	1	2	yes	—
42	C₂×C₃₇	C₂²⋊Q₈	1	1	yes	characteristic
43	C₂×C₃₇	C₄⋊Q₈	1	2	yes	—
44	C₂×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
45	#395	—	37	1	no	maximal, Sylow
46	C₃₇	#395	1	1	yes	characteristic, complemented, Sylow
47	C₂²×Q₈	—	37	1	no	—
48	C₂×C₄⋊C₄	—	37	1	no	—
49	C₂×C₄⋊C₄	—	37	2	no	—
50	#95	—	37	2	no	—
51	#95	D₃₇	1	1	yes	characteristic
52	C₂×Q₈	—	74	4	no	—
53	C₂×Q₈	—	74	2	no	—
54	C₂²×C₄	—	37	1	no	—
55	C₂²×C₄	—	37	2	no	—
56	C₂²×C₄	—	37	1	no	—
57	C₂²×C₄	C₂×D₃₇	1	2	yes	—
58	C₂²×C₄	C₂×D₃₇	1	1	yes	characteristic
59	C₄⋊C₄	—	74	4	no	—
60	C₄⋊C₄	—	74	2	no	—
61	C₂³	C₂²×D₃₇	1	1	yes	characteristic
62	Q₈	—	74	8	no	—
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	2	2	no	—
66	C₂×C₄	—	37	4	no	—
67	C₂×C₄	—	37	2	no	—
68	C₂×C₄	—	74	1	no	—
69	C₂×C₄	—	74	2	no	—
70	C₂×C₄	—	74	2	no	—
71	C₂×C₄	—	74	1	no	—
72	C₂×C₄	—	74	1	no	—
73	C₂×C₄	—	74	2	no	—
74	C₂×C₄	Dic₇₄	1	4	yes	complemented
75	C₂×C₄	D₁₄₈	1	2	yes	—
76	C₂²	C₂×Dic₇₄	1	2	yes	—
77	C₂²	C₂×D₁₄₈	1	1	yes	characteristic
78	C₂²	D₄×D₃₇	1	2	yes	—
79	C₂²	#10596964	1	1	yes	characteristic
80	C₂²	Q₈×D₃₇	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	2	4	no	—
83	C₄	—	74	4	no	—
84	C₄	—	74	2	no	—
85	C₄	—	148	1	no	—
86	C₂	#11924506	1	1	yes	characteristic
87	C₂	#11924513	1	2	yes	—
88	C₂	#11924516	1	1	yes	characteristic
89	C₂	#11924535	1	2	yes	—
90	C₂	#11924536	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃₇
commutator, socle, prime radical, cosocle	C₂³×C₃₇	C₂³
Fitting	#95×C₃₇	C₂
hypercenter	#95	D₃₇
hypocenter	C₃₇	#395
LCS	G ▷ C₂³×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
20. C₂×C₄×C₃₇	Q₈	semidirect
28. C₂×Dic₃₇	Q₈	semidirect
46. C₃₇	#395	semidirect
74. C₂×C₄	Dic₇₄	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₇₄	2
C₂×C₄⋊Dic₃₇	2
C₂×#10596936	2
#11924443	2
#95×C₃₇	2
#395	37