Subgroups — #14558392

Order 2368.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924603	C₂	1	1	yes	maximal, characteristic
2	#11924603	C₂	1	1	yes	maximal, characteristic
3	#11924535	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₄	—	2	1	no	—
5	C₂×#64438	—	2	1	no	—
6	C₂×#64438	—	2	1	no	—
7	C₄⋊C₄×C₃₇	C₄	1	1	yes	characteristic
8	C₄⋊Dic₃₇	C₄	1	1	yes	characteristic
9	#10596936	—	2	1	no	—
10	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₃₇	—	2	1	no	—
12	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₃₇	—	2	1	no	—
14	C₂×Dic₃₇	D₄	1	1	yes	characteristic
15	C₂×Dic₃₇	D₄	1	1	yes	characteristic
16	Dic₇₄	—	4	1	no	—
17	Dic₇₄	—	4	1	no	—
18	#64438	—	4	1	no	—
19	#64438	—	4	1	no	—
20	C₂²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₃₇	—	2	1	no	—
22	C₄×C₃₇	—	4	1	no	—
23	Dic₃₇	—	4	1	no	—
24	Dic₃₇	D₈	1	1	yes	characteristic
25	Dic₃₇	SD₁₆	1	1	yes	characteristic
26	Dic₃₇	SD₁₆	1	1	yes	characteristic
27	Dic₃₇	Q₁₆	1	1	yes	characteristic
28	C₂×C₃₇	#101	1	1	yes	characteristic
29	C₂×C₃₇	#102	1	1	yes	characteristic
30	C₂×C₃₇	#103	1	1	yes	characteristic
31	#332	—	37	1	no	maximal, Sylow
32	C₃₇	#332	1	1	yes	characteristic, complemented, Sylow
33	C₄⋊Q₈	—	37	1	no	—
34	C₄⋊C₈	—	37	1	no	—
35	C₄⋊C₈	—	37	1	no	—
36	C₂×Q₈	—	74	1	no	—
37	C₂×C₈	—	74	1	no	—
38	C₂×C₈	—	74	1	no	—
39	C₄⋊C₄	—	37	1	no	—
40	C₄⋊C₄	—	74	1	no	—
41	C₄⋊C₄	#3866	1	1	yes	characteristic
42	C₄²	—	37	1	no	—
43	Q₈	—	148	1	no	—
44	Q₈	—	148	1	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	37	1	no	—
47	C₂×C₄	—	37	1	no	—
48	C₂×C₄	—	74	1	no	—
49	C₂×C₄	C₂×#3866	1	1	yes	characteristic
50	C₈	—	148	1	no	—
51	C₈	—	148	1	no	—
52	C₂²	C₂²⋊#3866	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	4	1	no	—
55	C₄	—	37	1	no	—
56	C₄	—	37	1	no	—
57	C₄	—	37	1	no	—
58	C₄	—	37	1	no	—
59	C₄	—	148	1	no	—
60	C₂	#11924597	1	1	yes	characteristic
61	C₂	#11924598	1	1	yes	characteristic
62	C₂	#11924599	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#3866
commutator	C₂×C₄×C₃₇	C₂×C₄
Frattini	C₂×C₄	C₂×#3866
Fitting	C₄⋊C₄×C₃₇	C₄
socle, prime radical	C₂²×C₃₇	C₂²⋊C₄
cosocle	C₄×Dic₃₇	C₂²
hypercenter	C₄⋊C₄	#3866
hypocenter	C₃₇	#332
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
32. C₃₇	#332	semidirect

Maximal subgroups

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

subgroup	index
#11924603	2
#11924535	2
#332	37