Subgroups — #14557911

Order 2368.

122 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
2	C₂×#10596942	C₂	1	2	yes	maximal
3	#11924534	C₂	1	2	yes	maximal
4	C₈×Dic₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₃₇	C₂²	1	2	yes	—
7	C₂×Dic₇₄	C₂²	1	2	yes	—
8	Q₁₆×C₃₇	—	2	2	no	—
9	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
10	#10596942	—	2	4	no	—
11	#10596936	—	2	4	no	—
12	C₄×Dic₃₇	C₂²	1	1	yes	characteristic
13	C₂×#64436	C₂²	1	1	yes	characteristic
14	Dic₁₄₈	—	2	2	no	—
15	Q₈×C₃₇	—	2	2	no	—
16	Q₈×C₃₇	—	2	2	no	—
17	C₂×C₄×C₃₇	—	2	2	no	—
18	C₂×C₄×C₃₇	C₂³	1	1	yes	characteristic
19	C₂×Dic₃₇	—	2	2	no	—
20	C₂×Dic₃₇	D₄	1	2	yes	—
21	Dic₇₄	—	2	2	no	—
22	Dic₇₄	—	2	2	no	—
23	C₈×C₃₇	D₄	1	2	yes	—
24	#64436	D₄	1	2	yes	—
25	C₂²×C₃₇	C₂×D₄	1	1	yes	characteristic
26	C₄×C₃₇	—	4	2	no	—
27	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
28	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
29	Dic₃₇	—	4	2	no	—
30	Dic₃₇	Q₁₆	1	4	yes	complemented
31	C₂×C₃₇	#127	1	1	yes	characteristic
32	C₂×C₃₇	C₂×Q₁₆	1	2	yes	—
33	#494	—	37	1	no	maximal, Sylow
34	C₃₇	#494	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₁₆	—	37	2	no	—
36	C₂×Q₁₆	—	37	1	no	—
37	C₂×Q₁₆	D₃₇	1	1	yes	characteristic
38	C₄⋊Q₈	—	37	2	no	—
39	C₄×C₈	—	37	1	no	—
40	C₂×Q₈	—	37	2	no	—
41	C₂×Q₈	C₂×D₃₇	1	2	yes	—
42	Q₁₆	—	2	2	no	—
43	Q₁₆	—	74	4	no	—
44	Q₁₆	—	74	2	no	—
45	C₂×C₈	—	37	1	no	—
46	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
47	C₄⋊C₄	—	74	4	no	—
48	C₄²	—	37	1	no	—
49	Q₈	—	2	2	no	—
50	Q₈	—	2	2	no	—
51	Q₈	—	74	2	no	—
52	Q₈	—	74	2	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	37	2	no	—
55	C₂×C₄	—	74	2	no	—
56	C₂×C₄	C₂²×D₃₇	1	1	yes	characteristic
57	C₈	—	37	2	no	—
58	C₈	C₂²⋊D₃₇	1	2	yes	—
59	C₂²	D₄×D₃₇	1	1	yes	characteristic
60	C₄	—	4	2	no	—
61	C₄	—	37	4	no	—
62	C₄	—	148	2	no	—
63	C₄	D₄×D₃₇	1	1	yes	characteristic
64	C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
65	C₂	#11924532	1	1	yes	characteristic
66	C₂	Q₁₆×D₃₇	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₃₇
commutator, cosocle	C₂×C₄×C₃₇	C₂³
Frattini	C₂×C₄	C₂²×D₃₇
Fitting	C₂×Q₁₆×C₃₇	C₂
socle, prime radical	C₂²×C₃₇	C₂×D₄
hypercenter	C₂×Q₁₆	D₃₇
hypocenter	C₃₇	#494
LCS	G ▷ C₂×C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
30. Dic₃₇	Q₁₆	semidirect
34. C₃₇	#494	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
C₂×#10596942	2
#11924534	2
C₈×Dic₃₇	2
C₂×Q₁₆×C₃₇	2
#494	37