Subgroups — #14557541

Order 2368.

150 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×#10596934	C₂	1	1	yes	maximal, characteristic
3	#11924459	C₂	1	4	yes	maximal, complemented
4	#117×C₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₃₇	C₂²	1	1	yes	characteristic
6	C₂²×Dic₃₇	—	2	1	no	—
7	C₂×Dic₇₄	—	2	2	no	—
8	C₂×Dic₇₄	—	2	1	no	—
9	C₂×Dic₇₄	C₄	1	4	yes	complemented
10	C₂×Dic₇₄	C₂²	1	2	yes	—
11	C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
12	C₂²⋊C₄×C₃₇	—	2	1	no	—
13	C₄²×C₃₇	—	2	1	no	—
14	#10596934	—	2	2	no	—
15	C₂×#64436	C₂²	1	2	yes	—
16	C₂³×C₃₇	D₄	1	1	yes	characteristic
17	C₂×C₄×C₃₇	—	2	2	no	—
18	C₂×C₄×C₃₇	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₃₇	D₄	1	2	yes	—
20	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
21	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
22	C₂×Dic₃₇	—	2	4	no	—
23	C₂×Dic₃₇	—	2	2	no	—
24	Dic₇₄	—	2	4	no	—
25	Dic₇₄	—	2	2	no	—
26	Dic₇₄	C₂×C₄	1	4	yes	—
27	#64436	—	2	2	no	—
28	C₂²×C₃₇	—	2	2	no	—
29	C₂²×C₃₇	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
31	C₄×C₃₇	—	4	2	no	—
32	C₄×C₃₇	C₂²⋊C₄	1	2	yes	—
33	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
34	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
35	Dic₃₇	—	2	4	no	—
36	C₂×C₃₇	—	2	2	no	—
37	C₂×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₃₇	#137	1	2	yes	—
39	#419	—	37	1	no	maximal, Sylow
40	C₃₇	#419	1	1	yes	characteristic, complemented, Sylow
41	C₂²×Q₈	—	37	1	no	—
42	C₂×M₁₆	—	37	1	no	—
43	#117	D₃₇	1	1	yes	characteristic
44	#103	—	37	4	no	—
45	C₂×Q₈	—	37	4	no	—
46	C₂×Q₈	—	37	2	no	—
47	C₂×Q₈	—	74	2	no	—
48	C₂×Q₈	—	74	1	no	—
49	C₂²×C₄	—	74	1	no	—
50	C₂²×C₄	C₂×D₃₇	1	1	yes	characteristic
51	M₁₆	—	74	2	no	—
52	C₂×C₈	—	37	2	no	—
53	C₄⋊C₄	C₂×D₃₇	1	2	yes	—
54	C₂²⋊C₄	—	2	1	no	—
55	C₄²	—	2	1	no	—
56	C₂³	C₂²⋊D₃₇	1	1	yes	characteristic
57	Q₈	—	37	4	no	—
58	Q₈	—	74	4	no	—
59	Q₈	—	74	2	no	—
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	74	4	no	—
62	C₂×C₄	—	74	2	no	—
63	C₂×C₄	C₄×D₃₇	1	2	yes	—
64	C₂×C₄	D₁₄₈	1	2	yes	—
65	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
66	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
67	C₈	—	74	2	no	—
68	C₂²	—	2	2	no	—
69	C₂²	#10596938	1	2	yes	—
70	C₂²	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
71	C₄	—	4	2	no	—
72	C₄	—	74	4	no	—
73	C₄	#10596938	1	2	yes	—
74	C₄	C₂×C₄×D₃₇	1	1	yes	characteristic
75	C₄	C₂×D₁₄₈	1	1	yes	characteristic
76	C₂	—	2	2	no	—
77	C₂	C₂×#10596938	1	1	yes	characteristic
78	C₂	#11924566	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₇
commutator	C₄×C₃₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	#117×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₄
prime radical	C₂³×C₃₇	D₄
cosocle	C₂×C₄×C₃₇	C₂³
hypercenter	#117	D₃₇
hypocenter	C₃₇	#419
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
3. #11924459	C₂	semidirect
9. C₂×Dic₇₄	C₄	semidirect
40. C₃₇	#419	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×#10596934	2
#11924459	2
#117×C₃₇	2
#419	37