Subgroups — #14557929

Order 2368.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924536	C₂	1	1	yes	maximal, characteristic
2	#11924467	C₂	1	4	yes	maximal
3	C₄×#64436	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Q₈×C₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₃₇	—	2	1	no	—
6	C₂×Dic₇₄	—	2	1	no	—
7	C₄⋊C₄×C₃₇	—	2	1	no	—
8	C₄⋊C₄×C₃₇	C₂²	1	2	yes	—
9	C₄²×C₃₇	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₃₇	—	2	1	no	—
11	C₄⋊Dic₃₇	C₂²	1	2	yes	—
12	C₂×#64436	C₂²	1	2	yes	—
13	Q₈×C₃₇	—	4	2	no	—
14	C₂×C₄×C₃₇	—	2	2	no	—
15	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
16	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
17	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
18	C₂×Dic₃₇	—	2	2	no	—
19	Dic₇₄	—	4	2	no	—
20	#64436	Q₈	1	4	yes	complemented
21	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
22	C₄×C₃₇	—	4	2	no	—
23	C₄×C₃₇	SD₁₆	1	2	yes	—
24	C₄×C₃₇	SD₁₆	1	2	yes	—
25	C₄×C₃₇	C₂×Q₈	1	2	yes	—
26	Dic₃₇	—	4	2	no	—
27	C₂×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
28	C₂×C₃₇	C₂×SD₁₆	1	1	yes	characteristic
29	C₂×C₃₇	C₂×SD₁₆	1	1	yes	characteristic
30	#498	—	37	1	no	maximal, Sylow
31	C₃₇	#498	1	1	yes	characteristic, complemented, Sylow
32	C₄⋊Q₈	—	37	1	no	—
33	C₄⋊Q₈	D₃₇	1	1	yes	characteristic
34	#106	—	37	4	no	—
35	C₄×C₈	—	37	1	no	—
36	C₂×Q₈	—	2	1	no	—
37	C₂×Q₈	—	74	1	no	—
38	C₂×C₈	—	37	2	no	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	—	37	2	no	—
41	C₄⋊C₄	—	74	1	no	—
42	C₄⋊C₄	C₂×D₃₇	1	2	yes	—
43	C₄²	C₂×D₃₇	1	1	yes	characteristic
44	Q₈	—	4	2	no	—
45	Q₈	—	148	2	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	74	2	no	—
48	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
49	C₂×C₄	C₂²⋊D₃₇	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
51	C₈	—	37	4	no	—
52	C₂²	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	148	2	no	—
55	C₄	#10596940	1	2	yes	—
56	C₄	#10596941	1	2	yes	—
57	C₄	Q₈×D₃₇	1	2	yes	—
58	C₂	#11924534	1	1	yes	characteristic
59	C₂	C₂×#10596941	1	1	yes	characteristic
60	C₂	C₂×#10596940	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₇
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	C₄⋊Q₈×C₃₇	C₂
socle, prime radical	C₂²×C₃₇	C₂×D₄
hypercenter	C₄⋊Q₈	D₃₇
hypocenter	C₃₇	#498
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
20. #64436	Q₈	semidirect
31. C₃₇	#498	semidirect

Maximal subgroups

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

subgroup	index
#11924536	2
#11924467	2
C₄×#64436	2
C₄⋊Q₈×C₃₇	2
#498	37