Subgroups — #14558089

Order 2368.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924535	C₂	1	2	yes	maximal, complemented
2	#11924528	C₂	1	1	yes	maximal, characteristic, complemented
3	#11924514	C₂	1	4	yes	maximal
4	#11924501	C₂	1	4	yes	maximal, complemented
5	#11924494	C₂	1	2	yes	maximal
6	C₄²×D₃₇	C₂	1	1	yes	maximal, characteristic
7	#125×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₃₇	C₂²	1	2	yes	—
9	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
10	C₂×Dic₇₄	C₂²	1	4	yes	—
11	C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
12	C₄⋊C₄×C₃₇	C₂²	1	4	yes	—
13	C₄²×C₃₇	C₂²	1	1	yes	characteristic
14	#10596938	C₂²	1	4	yes	—
15	C₄⋊Dic₃₇	C₂²	1	2	yes	—
16	#10596936	C₂²	1	4	yes	—
17	#10596936	C₂²	1	4	yes	—
18	C₄×Dic₃₇	C₂²	1	2	yes	—
19	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
20	C₄×Dic₃₇	C₂²	1	4	yes	—
21	C₂²×D₃₇	C₂³	1	1	yes	characteristic
22	C₂×C₄×C₃₇	C₂³	1	2	yes	—
23	C₂×C₄×C₃₇	C₂³	1	4	yes	—
24	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
25	C₂×Dic₃₇	C₂³	1	4	yes	—
26	C₂×Dic₃₇	C₂³	1	1	yes	characteristic
27	C₂×Dic₃₇	C₂³	1	2	yes	—
28	C₄×D₃₇	—	2	4	no	—
29	C₄×D₃₇	Q₈	1	4	yes	complemented
30	Dic₇₄	—	2	8	no	—
31	C₂²×C₃₇	C₂⁴	1	1	yes	characteristic
32	C₂×D₃₇	—	2	2	no	—
33	C₂×D₃₇	C₂×Q₈	1	2	yes	—
34	C₄×C₃₇	—	2	4	no	—
35	C₄×C₃₇	—	2	2	no	—
36	C₄×C₃₇	C₂×Q₈	1	2	yes	—
37	Dic₃₇	—	2	4	no	—
38	Dic₃₇	C₂×Q₈	1	2	yes	—
39	Dic₃₇	#41	1	4	yes	—
40	C₂×C₃₇	C₂²×Q₈	1	1	yes	characteristic
41	C₂×C₃₇	C₂×#41	1	2	yes	—
42	D₃₇	—	2	2	no	—
43	#533	—	37	1	no	maximal, Sylow
44	C₃₇	#533	1	1	yes	characteristic, complemented, Sylow
45	C₄⋊Q₈	—	37	2	no	—
46	#125	—	37	1	no	—
47	#125	D₃₇	1	1	yes	characteristic, complemented
48	C₂²⋊Q₈	—	37	4	no	—
49	C₄×Q₈	—	37	4	no	—
50	#117	—	37	2	no	—
51	C₂×C₄²	—	37	1	no	—
52	C₂×Q₈	—	37	4	no	—
53	C₂²×C₄	—	37	1	no	—
54	C₂²×C₄	—	37	2	no	—
55	C₄⋊C₄	—	37	4	no	—
56	C₄⋊C₄	—	37	4	no	—
57	C₄⋊C₄	—	37	2	no	—
58	C₄⋊C₄	C₂×D₃₇	1	2	yes	—
59	C₄⋊C₄	C₂×D₃₇	1	4	yes	—
60	C₂²⋊C₄	—	37	4	no	—
61	C₄²	—	37	2	no	—
62	C₄²	—	37	1	no	—
63	C₄²	—	37	4	no	—
64	C₄²	C₂×D₃₇	1	1	yes	characteristic
65	C₂³	—	37	1	no	—
66	Q₈	—	74	8	no	—
67	C₂×C₄	—	37	1	no	—
68	C₂×C₄	—	37	2	no	—
69	C₂×C₄	—	37	4	no	—
70	C₂×C₄	—	37	4	no	—
71	C₂×C₄	—	74	4	no	—
72	C₂×C₄	C₂²×D₃₇	1	2	yes	—
73	C₂×C₄	C₂²×D₃₇	1	4	yes	—
74	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
75	C₂²	—	37	2	no	—
76	C₂²	—	74	2	no	—
77	C₂²	C₂³×D₃₇	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	2	4	no	—
80	C₄	—	37	2	no	—
81	C₄	—	37	4	no	—
82	C₄	—	74	4	no	—
83	C₄	Q₈×D₃₇	1	2	yes	—
84	C₂	—	74	2	no	—
85	C₂	C₂×Q₈×D₃₇	1	1	yes	characteristic
86	C₂	#41×D₃₇	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₃₇
commutator, socle, cosocle	C₂²×C₃₇	C₂⁴
Fitting	#125×C₃₇	C₂
prime radical	C₂²×D₃₇	C₂³
hypercenter	#125	D₃₇
hypocenter	C₃₇	#533
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
1. #11924535	C₂	semidirect
2. #11924528	C₂	semidirect
4. #11924501	C₂	semidirect
7. #125×C₃₇	C₂	semidirect
29. C₄×D₃₇	Q₈	semidirect
44. C₃₇	#533	semidirect
47. #125	D₃₇	semidirect

Maximal subgroups

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

subgroup	index
#11924535	2
#11924528	2
#11924514	2
#11924501	2
#11924494	2
C₄²×D₃₇	2
#125×C₃₇	2
#533	37