Subgroups — #14557331

Order 2368.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924534	C₂	1	1	yes	maximal, characteristic
2	#11924455	C₂	1	1	yes	maximal, characteristic
3	#101×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₃₇	C₂²	1	1	yes	characteristic
5	C₂×Dic₇₄	C₄	1	1	yes	characteristic
6	M₁₆×C₃₇	—	2	1	no	—
7	#10596936	—	2	1	no	—
8	#10596936	—	2	1	no	—
9	C₄×Dic₃₇	C₄	1	1	yes	characteristic
10	#10596934	—	2	1	no	—
11	Q₈×C₃₇	—	4	1	no	—
12	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
14	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
15	C₂×Dic₃₇	—	2	1	no	—
16	C₂×Dic₃₇	—	2	1	no	—
17	Dic₇₄	—	4	1	no	—
18	C₈×C₃₇	—	4	1	no	—
19	#64436	—	4	1	no	—
20	C₂²×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₃₇	—	2	1	no	—
22	C₄×C₃₇	—	2	1	no	—
23	C₄×C₃₇	—	2	1	no	—
24	Dic₃₇	—	2	2	no	—
25	Dic₃₇	—	4	1	no	—
26	C₂×C₃₇	—	2	1	no	—
27	C₂×C₃₇	#99	1	1	yes	characteristic
28	#356	—	37	1	no	maximal, Sylow
29	C₃₇	#356	1	1	yes	characteristic, complemented, Sylow
30	C₄⋊Q₈	—	37	1	no	—
31	#101	—	37	1	no	—
32	#101	D₃₇	1	1	yes	characteristic
33	C₂×Q₈	—	37	1	no	—
34	C₂×Q₈	C₂×D₃₇	1	1	yes	characteristic
35	M₁₆	—	2	1	no	—
36	M₁₆	—	74	1	no	—
37	C₄⋊C₄	—	74	1	no	—
38	C₄⋊C₄	—	74	1	no	—
39	C₄²	—	37	1	no	—
40	Q₈	—	4	1	no	—
41	Q₈	—	148	1	no	—
42	C₂×C₄	—	74	1	no	—
43	C₂×C₄	—	74	1	no	—
44	C₂×C₄	C₄×D₃₇	1	1	yes	characteristic
45	C₂×C₄	D₁₄₈	1	1	yes	characteristic
46	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
47	C₈	—	4	1	no	—
48	C₈	—	148	1	no	—
49	C₂²	#10596938	1	1	yes	characteristic
50	C₄	—	2	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	2	1	no	—
53	C₄	—	74	2	no	—
54	C₄	—	148	1	no	—
55	C₂	—	2	1	no	—
56	C₂	#11924450	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11924450
commutator	C₂×C₄×C₃₇	C₂×C₄
Frattini	C₂×Q₈	C₂×D₃₇
Fitting	#101×C₃₇	C₂
socle	C₂×C₃₇	#99
prime radical	C₂²×C₃₇	C₂²⋊C₄
cosocle	C₂×Q₈×C₃₇	C₂²
hypercenter	#101	D₃₇
hypocenter	C₃₇	#356
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×Q₈ ◁ #101

Complements

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

N	H ≅ G/N	type
29. C₃₇	#356	semidirect

Maximal subgroups

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

subgroup	index
#11924534	2
#11924455	2
#101×C₃₇	2
#356	37