Subgroups — #14557791

Order 2368.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₄₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#11924515	C₂	1	2	yes	maximal
3	#11924468	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924461	C₂	1	2	yes	maximal, complemented
5	C₂×M₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×C₃₇	C₂²	1	1	yes	characteristic
7	C₂×Dic₇₄	C₂²	1	2	yes	—
8	M₁₆×C₃₇	—	2	2	no	—
9	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
11	C₂²⋊Dic₃₇	—	2	2	no	—
12	C₄⋊Dic₃₇	C₂²	1	2	yes	—
13	#10596936	—	2	2	no	—
14	Dic₁₄₈	—	2	2	no	—
15	C₂³×C₃₇	D₄	1	1	yes	characteristic
16	C₂×C₄×C₃₇	—	2	1	no	—
17	C₂×C₄×C₃₇	—	2	1	no	—
18	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
19	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
20	C₂×Dic₃₇	—	2	2	no	—
21	C₂×Dic₃₇	—	2	2	no	—
22	Dic₇₄	—	2	2	no	—
23	Dic₇₄	—	2	2	no	—
24	C₈×C₃₇	—	2	1	no	—
25	C₈×C₃₇	D₄	1	2	yes	—
26	C₂²×C₃₇	—	2	1	no	—
27	C₂²×C₃₇	—	2	2	no	—
28	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
29	C₄×C₃₇	—	2	1	no	—
30	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
31	C₄×C₃₇	#41	1	1	yes	characteristic
32	Dic₃₇	—	4	2	no	—
33	Dic₃₇	—	4	2	no	—
34	C₂×C₃₇	—	4	1	no	—
35	C₂×C₃₇	#121	1	1	yes	characteristic
36	C₂×C₃₇	#137	1	2	yes	—
37	#470	—	37	1	no	maximal, Sylow
38	C₃₇	#470	1	1	yes	characteristic, complemented, Sylow
39	C₂×Q₁₆	—	37	1	no	—
40	C₂×M₁₆	D₃₇	1	1	yes	characteristic
41	C₂²⋊Q₈	—	37	2	no	—
42	#106	—	37	1	no	—
43	#103	—	37	2	no	—
44	C₂×Q₈	—	37	2	no	—
45	C₂²×C₄	C₂×D₃₇	1	1	yes	characteristic
46	Q₁₆	—	74	2	no	—
47	M₁₆	—	2	2	no	—
48	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
49	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
50	C₄⋊C₄	—	37	2	no	—
51	C₄⋊C₄	—	74	2	no	—
52	C₂²⋊C₄	—	74	2	no	—
53	C₂³	D₁₄₈	1	1	yes	characteristic
54	Q₈	—	74	2	no	—
55	Q₈	—	74	2	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	74	2	no	—
59	C₂×C₄	—	74	2	no	—
60	C₂×C₄	D₁₄₈	1	1	yes	characteristic
61	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
62	C₈	—	2	1	no	—
63	C₈	C₂²⋊D₃₇	1	2	yes	—
64	C₂²	—	2	1	no	—
65	C₂²	—	2	2	no	—
66	C₂²	C₂×D₁₄₈	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	148	2	no	—
69	C₄	—	148	2	no	—
70	C₄	#10596962	1	1	yes	characteristic
71	C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
72	C₂	—	4	1	no	—
73	C₂	#11924510	1	1	yes	characteristic
74	C₂	#11924569	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₄₈
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	C₂×M₁₆×C₃₇	C₂
socle	C₂²×C₃₇	C₂×D₄
prime radical	C₂³×C₃₇	D₄
hypercenter	C₂×M₁₆	D₃₇
hypocenter	C₃₇	#470
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₁₄₈	C₂	semidirect
3. #11924468	C₂	semidirect
4. #11924461	C₂	semidirect
38. C₃₇	#470	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₄₈	2
#11924515	2
#11924468	2
#11924461	2
C₂×M₁₆×C₃₇	2
#470	37