Subgroups — #14558283

Order 2368.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924534	C₂	1	2	yes	maximal, complemented
2	#11924529	C₂	1	4	yes	maximal, complemented
3	#11924528	C₂	1	2	yes	maximal, complemented
4	#11924517	C₂	1	2	yes	maximal
5	#11924513	C₂	1	4	yes	maximal, complemented
6	#124×C₃₇	C₂	1	1	yes	maximal, characteristic
7	C₂×Q₈×C₃₇	C₂²	1	1	yes	characteristic
8	C₂×D₄×C₃₇	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₇	C₂²	1	2	yes	—
10	C₂×Dic₇₄	C₂²	1	2	yes	—
11	C₂²⋊C₄×C₃₇	C₂²	1	4	yes	—
12	C₄²×C₃₇	C₂²	1	1	yes	characteristic
13	C₂²⋊Dic₃₇	C₂²	1	4	yes	—
14	C₂²⋊Dic₃₇	C₂²	1	2	yes	—
15	C₄⋊Dic₃₇	C₂²	1	2	yes	—
16	C₄⋊Dic₃₇	C₂²	1	2	yes	—
17	#10596936	C₂²	1	4	yes	—
18	#10596936	C₂²	1	4	yes	—
19	#10596936	C₂²	1	4	yes	—
20	C₄×Dic₃₇	C₂²	1	2	yes	—
21	C₂³×C₃₇	C₂³	1	2	yes	—
22	Q₈×C₃₇	—	4	1	no	—
23	D₄×C₃₇	—	4	1	no	—
24	C₂×C₄×C₃₇	C₂³	1	2	yes	—
25	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
26	C₂×C₄×C₃₇	C₂³	1	2	yes	—
27	C₂×Dic₃₇	—	4	2	no	—
28	C₂×Dic₃₇	C₂³	1	4	yes	—
29	C₂×Dic₃₇	C₂³	1	4	yes	—
30	Dic₇₄	—	4	2	no	—
31	C₂²×C₃₇	—	2	2	no	—
32	C₂²×C₃₇	—	2	4	no	—
33	C₂²×C₃₇	C₂⁴	1	1	yes	characteristic
34	C₄×C₃₇	—	2	2	no	—
35	C₄×C₃₇	—	2	1	no	—
36	C₄×C₃₇	—	2	2	no	—
37	Dic₃₇	—	2	4	no	—
38	Dic₃₇	—	2	4	no	—
39	C₂×C₃₇	—	4	2	no	—
40	C₂×C₃₇	H(5,𝔽₂)	1	1	yes	characteristic
41	C₂×C₃₇	2₋¹⁺⁴	1	2	yes	—
42	#563	—	37	1	no	maximal, Sylow
43	C₃₇	#563	1	1	yes	characteristic, complemented, Sylow
44	C₄⋊Q₈	—	37	2	no	—
45	#126	—	37	4	no	—
46	#125	—	37	2	no	—
47	#124	D₃₇	1	1	yes	characteristic
48	#123	—	37	2	no	—
49	C₂²⋊Q₈	—	37	4	no	—
50	C₂×Q₈	—	37	2	no	—
51	C₂×Q₈	C₂×D₃₇	1	1	yes	characteristic
52	C₂×D₄	C₂×D₃₇	1	1	yes	characteristic
53	C₂²×C₄	—	37	2	no	—
54	C₄⋊C₄	—	37	4	no	—
55	C₄⋊C₄	—	37	4	no	—
56	C₄⋊C₄	—	37	4	no	—
57	C₄⋊C₄	—	37	2	no	—
58	C₄⋊C₄	—	37	2	no	—
59	C₂²⋊C₄	—	37	4	no	—
60	C₂²⋊C₄	—	37	2	no	—
61	C₂²⋊C₄	C₂×D₃₇	1	4	yes	—
62	C₄²	—	37	2	no	—
63	C₄²	C₂×D₃₇	1	1	yes	characteristic
64	C₂³	C₂²×D₃₇	1	2	yes	—
65	Q₈	—	4	1	no	—
66	Q₈	—	148	2	no	—
67	D₄	—	4	1	no	—
68	C₂×C₄	—	37	4	no	—
69	C₂×C₄	—	37	4	no	—
70	C₂×C₄	—	148	2	no	—
71	C₂×C₄	C₂²×D₃₇	1	2	yes	—
72	C₂×C₄	C₂²×D₃₇	1	2	yes	—
73	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
74	C₂²	—	2	2	no	—
75	C₂²	—	2	4	no	—
76	C₂²	C₂³×D₃₇	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	2	2	no	—
79	C₄	—	2	2	no	—
80	C₄	—	74	4	no	—
81	C₄	—	74	4	no	—
82	C₂	—	4	2	no	—
83	C₂	#11924581	1	1	yes	characteristic
84	C₂	#11924583	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₃₇
commutator, socle, cosocle	C₂²×C₃₇	C₂⁴
Fitting	#124×C₃₇	C₂
prime radical	C₂×D₄×C₃₇	C₂²
hypercenter	#124	D₃₇
hypocenter	C₃₇	#563
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ #124

Complements

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

N	H ≅ G/N	type
1. #11924534	C₂	semidirect
2. #11924529	C₂	semidirect
3. #11924528	C₂	semidirect
5. #11924513	C₂	semidirect
43. C₃₇	#563	semidirect

Maximal subgroups

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

subgroup	index
#11924534	2
#11924529	2
#11924528	2
#11924517	2
#11924513	2
#124×C₃₇	2
#563	37