Subgroups — #14557830

Order 2368.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₁₄₈	C₂	1	1	yes	maximal, characteristic
2	#11924469	C₂	1	1	yes	maximal, characteristic, complemented
3	#11924467	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊#64436	C₂	1	1	yes	maximal, characteristic, complemented
5	#11924456	C₂	1	1	yes	maximal, characteristic
6	#11924456	C₂	1	1	yes	maximal, characteristic
7	#125×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₁₄₈	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₃₇	—	2	1	no	—
10	C₄⋊C₄×C₃₇	—	2	1	no	—
11	C₄⋊C₄×C₃₇	—	2	1	no	—
12	C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₃₇	C₂²	1	1	yes	characteristic
14	C₄²×C₃₇	C₂²	1	1	yes	characteristic
15	#10596938	—	2	1	no	—
16	C₄⋊Dic₃₇	C₂²	1	1	yes	characteristic
17	C₂×#64436	C₂²	1	1	yes	characteristic
18	C₂×#64436	C₂²	1	1	yes	characteristic
19	C₂²×D₃₇	—	2	1	no	—
20	C₂×C₄×C₃₇	—	2	1	no	—
21	C₂×C₄×C₃₇	—	2	1	no	—
22	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
23	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
24	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
25	C₂×Dic₃₇	—	2	1	no	—
26	D₁₄₈	—	2	1	no	—
27	D₁₄₈	Q₈	1	2	yes	—
28	C₄×D₃₇	—	4	2	no	—
29	#64436	—	2	1	no	—
30	#64436	—	2	1	no	—
31	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
32	C₂×D₃₇	—	2	2	no	—
33	C₂×D₃₇	—	4	1	no	—
34	C₂×D₃₇	—	4	1	no	—
35	C₄×C₃₇	—	2	1	no	—
36	C₄×C₃₇	—	2	1	no	—
37	C₄×C₃₇	—	4	1	no	—
38	C₄×C₃₇	—	4	1	no	—
39	C₄×C₃₇	C₂×Q₈	1	1	yes	characteristic
40	C₄×C₃₇	#41	1	1	yes	characteristic
41	Dic₃₇	—	4	1	no	—
42	C₂×C₃₇	C₂²⋊Q₈	1	1	yes	characteristic
43	C₂×C₃₇	#135	1	1	yes	characteristic
44	C₂×C₃₇	AGL(1,ℤ/8)	1	1	yes	characteristic
45	D₃₇	—	4	2	no	—
46	#478	—	37	1	no	maximal, Sylow
47	C₃₇	#478	1	1	yes	characteristic, complemented, Sylow
48	#125	D₃₇	1	1	yes	characteristic, complemented
49	C₄×D₄	—	37	1	no	—
50	#107	—	37	1	no	—
51	#106	—	37	1	no	—
52	C₄⋊C₈	—	37	1	no	—
53	#102	—	37	1	no	—
54	#102	—	37	1	no	—
55	C₂×D₄	—	37	1	no	—
56	C₂²×C₄	—	74	1	no	—
57	C₂×C₈	—	37	1	no	—
58	C₂×C₈	—	37	1	no	—
59	C₄⋊C₄	—	2	1	no	—
60	C₄⋊C₄	—	2	1	no	—
61	C₄⋊C₄	—	37	1	no	—
62	C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
63	C₄⋊C₄	C₂×D₃₇	1	1	yes	characteristic
64	C₂²⋊C₄	—	74	1	no	—
65	C₄²	C₂×D₃₇	1	1	yes	characteristic
66	C₂³	—	74	1	no	—
67	D₄	—	37	2	no	—
68	D₄	—	74	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	74	1	no	—
72	C₂×C₄	—	148	2	no	—
73	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
74	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
75	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
76	C₈	—	74	1	no	—
77	C₈	—	74	1	no	—
78	C₂²	—	74	2	no	—
79	C₂²	—	148	1	no	—
80	C₂²	—	148	1	no	—
81	C₂²	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	148	1	no	—
87	C₄	Q₈×D₃₇	1	1	yes	characteristic
88	C₄	#10596966	1	1	yes	characteristic
89	C₂	—	148	2	no	—
90	C₂	#11924512	1	1	yes	characteristic
91	C₂	#11924556	1	1	yes	characteristic
92	C₂	#11924561	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₇
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	#125×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₄
prime radical	C₂×D₁₄₈	C₂²
hypercenter	#125	D₃₇
hypocenter	C₃₇	#478
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
2. #11924469	C₂	semidirect
3. #11924467	C₂	semidirect
4. C₄⋊#64436	C₂	semidirect
7. #125×C₃₇	C₂	semidirect
47. C₃₇	#478	semidirect
48. #125	D₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₁₄₈	2
#11924469	2
#11924467	2
C₄⋊#64436	2
#11924456	2
#125×C₃₇	2
#478	37