Subgroups — #14558573

Order 2368.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#3866	C₂	1	2	yes	maximal
2	#11924604	C₂	1	1	yes	maximal, characteristic
3	#11924599	C₂	1	2	yes	maximal
4	#11924590	C₂	1	1	yes	maximal, characteristic
5	Q₁₆×D₃₇	C₂	1	1	yes	maximal, characteristic
6	Q₈×D₃₇	C₂²	1	2	yes	—
7	C₄⋊#3866	—	2	2	no	—
8	C₄⋊#3866	C₂²	1	2	yes	—
9	C₄×#3866	—	2	2	no	—
10	C₄×#3866	C₂²	1	1	yes	characteristic
11	D₃₇⋊C₈	C₂²	1	1	yes	characteristic
12	Q₁₆×C₃₇	C₄	1	1	yes	characteristic, complemented
13	#10596942	C₄	1	2	yes	complemented
14	Dic₁₄₈	C₄	1	1	yes	characteristic, complemented
15	C₈×D₃₇	C₂²	1	1	yes	characteristic
16	C₂×#3866	—	2	2	no	—
17	C₂×#3866	D₄	1	2	yes	—
18	Q₈×C₃₇	C₂×C₄	1	2	yes	—
19	C₄×D₃₇	—	2	2	no	—
20	C₄×D₃₇	C₂³	1	1	yes	characteristic
21	Dic₇₄	—	2	2	no	—
22	Dic₇₄	C₂×C₄	1	2	yes	—
23	#64438	—	2	1	no	—
24	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
25	#64436	C₂×C₄	1	1	yes	characteristic
26	C₂×D₃₇	C₂×D₄	1	1	yes	characteristic
27	#3866	—	2	2	no	—
28	#3866	—	4	2	no	—
29	C₄×C₃₇	—	2	2	no	—
30	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
31	Dic₃₇	—	2	2	no	—
32	Dic₃₇	#41	1	1	yes	characteristic
33	C₂×C₃₇	C₄×D₄	1	1	yes	characteristic
34	D₃₇	#137	1	2	yes	—
35	#441	—	37	1	no	maximal, Sylow
36	C₃₇	#441	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₁₆	—	37	1	no	—
38	C₄×Q₈	—	37	2	no	—
39	#106	—	37	1	no	—
40	#103	—	37	2	no	—
41	#97	—	37	1	no	—
42	C₂×Q₈	—	37	2	no	—
43	Q₁₆	—	37	2	no	—
44	Q₁₆	—	37	1	no	—
45	Q₁₆	#3866	1	1	yes	characteristic, complemented
46	C₂×C₈	—	37	1	no	—
47	C₂×C₈	—	37	1	no	—
48	C₄⋊C₄	—	37	2	no	—
49	C₄⋊C₄	—	74	2	no	—
50	C₄²	—	37	1	no	—
51	C₄²	—	74	2	no	—
52	Q₈	—	37	2	no	—
53	Q₈	—	74	2	no	—
54	Q₈	C₂×#3866	1	2	yes	—
55	C₂×C₄	—	37	1	no	—
56	C₂×C₄	—	37	2	no	—
57	C₂×C₄	—	74	2	no	—
58	C₂×C₄	—	74	2	no	—
59	C₈	—	37	1	no	—
60	C₈	—	74	1	no	—
61	C₈	C₂×#3866	1	1	yes	characteristic
62	C₂²	—	37	1	no	—
63	C₄	—	2	2	no	—
64	C₄	—	37	1	no	—
65	C₄	—	74	2	no	—
66	C₄	—	74	2	no	—
67	C₄	—	148	2	no	—
68	C₄	C₂²×#3866	1	1	yes	characteristic
69	C₂	—	37	2	no	—
70	C₂	D₄×#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#3866
commutator	C₄×C₃₇	C₂²×C₄
Frattini	C₄	C₂²×#3866
Fitting	Q₁₆×C₃₇	C₄
socle	C₂×C₃₇	C₄×D₄
prime radical	C₂×D₃₇	C₂×D₄
cosocle	C₄×D₃₇	C₂³
hypercenter	Q₁₆	#3866
hypocenter	C₃₇	#441
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
12. Q₁₆×C₃₇	C₄	semidirect
13. #10596942	C₄	semidirect
14. Dic₁₄₈	C₄	semidirect
36. C₃₇	#441	semidirect
45. Q₁₆	#3866	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#3866	2
#11924604	2
#11924599	2
#11924590	2
Q₁₆×D₃₇	2
#441	37