Subgroups — #14557708

Order 2368.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924584	C₂	1	1	yes	maximal, characteristic, complemented
2	#11924564	C₂	1	2	yes	maximal, complemented
3	#11924525	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924462	C₂	1	2	yes	maximal, complemented
5	#101×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₃₇	C₂²	1	1	yes	characteristic
7	#10596966	—	2	2	no	—
8	Q₈×D₃₇	—	2	2	no	—
9	#10596962	—	2	2	no	—
10	#10596962	C₂²	1	2	yes	—
11	C₂×D₁₄₈	C₂²	1	1	yes	characteristic
12	M₁₆×C₃₇	C₂²	1	2	yes	—
13	#10596938	—	2	2	no	—
14	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
15	D₂₉₆	—	2	2	no	—
16	#10596930	—	2	2	no	—
17	C₂²×D₃₇	—	2	1	no	—
18	Q₈×C₃₇	—	2	2	no	—
19	C₂×C₄×C₃₇	D₄	1	2	yes	—
20	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
21	C₂²⋊D₃₇	—	2	2	no	—
22	C₂×Dic₃₇	—	2	1	no	—
23	D₁₄₈	—	2	2	no	—
24	D₁₄₈	—	2	2	no	—
25	D₁₄₈	D₄	1	2	yes	—
26	C₄×D₃₇	—	2	4	no	—
27	C₄×D₃₇	—	2	2	no	—
28	Dic₇₄	—	2	2	no	—
29	Dic₇₄	D₄	1	2	yes	—
30	C₈×C₃₇	—	2	2	no	—
31	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
32	C₂×D₃₇	—	2	2	no	—
33	C₂×D₃₇	—	4	2	no	—
34	C₂×D₃₇	—	4	1	no	—
35	C₄×C₃₇	—	2	2	no	—
36	C₄×C₃₇	C₂×D₄	1	2	yes	—
37	Dic₃₇	—	2	2	no	—
38	Dic₃₇	—	4	1	no	—
39	C₂×C₃₇	—	2	1	no	—
40	C₂×C₃₇	#120	1	1	yes	characteristic
41	D₃₇	—	4	2	no	—
42	D₃₇	—	8	1	no	—
43	#454	—	37	1	no	maximal, Sylow
44	C₃₇	#454	1	1	yes	characteristic, complemented, Sylow
45	2₋¹⁺⁴	—	37	1	no	—
46	AGL(1,ℤ/8)	—	37	2	no	—
47	#124	—	37	1	no	—
48	#104	—	37	2	no	—
49	#101	D₃₇	1	1	yes	characteristic, complemented
50	#41	—	37	2	no	—
51	#41	—	74	2	no	—
52	#41	—	74	2	no	—
53	C₂×Q₈	—	74	2	no	—
54	C₂×Q₈	C₂×D₃₇	1	1	yes	characteristic
55	C₂×D₄	—	37	1	no	—
56	SD₁₆	—	74	2	no	—
57	D₈	—	74	2	no	—
58	M₁₆	C₂×D₃₇	1	2	yes	—
59	C₂²⋊C₄	—	74	2	no	—
60	C₄²	—	37	1	no	—
61	C₂³	—	74	1	no	—
62	Q₈	—	2	2	no	—
63	Q₈	—	37	2	no	—
64	Q₈	—	74	2	no	—
65	D₄	—	37	2	no	—
66	D₄	—	74	2	no	—
67	D₄	—	74	2	no	—
68	D₄	—	74	2	no	—
69	C₂×C₄	—	74	4	no	—
70	C₂×C₄	—	74	2	no	—
71	C₂×C₄	—	74	1	no	—
72	C₂×C₄	D₁₄₈	1	2	yes	—
73	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
74	C₈	—	2	2	no	—
75	C₂²	—	74	2	no	—
76	C₂²	—	148	2	no	—
77	C₂²	—	148	1	no	—
78	C₂²	C₂×D₁₄₈	1	1	yes	characteristic
79	C₄	—	2	2	no	—
80	C₄	—	74	2	no	—
81	C₄	—	148	1	no	—
82	C₄	D₄×D₃₇	1	2	yes	—
83	C₂	—	2	1	no	—
84	C₂	—	296	1	no	—
85	C₂	—	148	2	no	—
86	C₂	#11924506	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11924506
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	#101×C₃₇	C₂
socle	C₂×C₃₇	#120
hypercenter	#101	D₃₇
hypocenter	C₃₇	#454
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #101

Complements

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

N	H ≅ G/N	type
1. #11924584	C₂	semidirect
2. #11924564	C₂	semidirect
3. #11924525	C₂	semidirect
4. #11924462	C₂	semidirect
5. #101×C₃₇	C₂	semidirect
44. C₃₇	#454	semidirect
49. #101	D₃₇	semidirect

Maximal subgroups

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

subgroup	index
#11924584	2
#11924564	2
#11924525	2
#11924462	2
#101×C₃₇	2
#454	37