Subgroups — C₃₇×#7460 #22628713

Order 9472.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃₂×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#1371	C₂	1	2	yes	maximal
3	C₂×C₃₂×C₃₇	C₄	1	1	yes	characteristic
4	C₂×C₃₂×C₃₇	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
6	C₃₇×#335	—	2	2	no	—
7	C₂×C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
8	C₂×C₁₆×C₃₇	Q₈	1	1	yes	characteristic
9	C₄⋊C₈×C₃₇	—	4	2	no	—
10	C₄×C₈×C₃₇	D₄	1	1	yes	characteristic
11	C₃₂×C₃₇	—	2	1	no	—
12	C₃₂×C₃₇	C₈	1	2	yes	complemented
13	C₂×C₈×C₃₇	—	8	2	no	—
14	C₂×C₈×C₃₇	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₈×C₃₇	Q₁₆	1	1	yes	characteristic
16	C₄²×C₃₇	D₈	1	1	yes	characteristic
17	C₁₆×C₃₇	—	2	1	no	—
18	C₁₆×C₃₇	C₂×C₈	1	1	yes	characteristic
19	C₁₆×C₃₇	M₁₆	1	1	yes	characteristic
20	C₂×C₄×C₃₇	#107	1	1	yes	characteristic
21	C₂×C₄×C₃₇	D₁₆	1	1	yes	characteristic
22	C₂×C₄×C₃₇	Q₃₂	1	1	yes	characteristic
23	C₈×C₃₇	—	2	1	no	—
24	C₈×C₃₇	—	16	2	no	—
25	C₈×C₃₇	C₄⋊C₈	1	1	yes	characteristic
26	C₈×C₃₇	#108	1	1	yes	characteristic
27	#7460	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×C₃₇	#366	1	1	yes	characteristic
29	C₄×C₃₇	—	2	1	no	—
30	C₄×C₃₇	#335	1	1	yes	characteristic
31	C₄×C₃₇	#368	1	1	yes	characteristic
32	C₄×C₃₇	D₃₂	1	1	yes	characteristic
33	C₄×C₃₇	Q₆₄	1	1	yes	characteristic
34	C₄×C₃₂	C₂×C₃₇	1	1	yes	characteristic
35	#1371	C₂×C₃₇	1	2	yes	—
36	C₂×C₃₇	#1371	1	1	yes	characteristic
37	C₂×C₃₇	#1423	1	1	yes	characteristic
38	C₂×C₃₇	#1425	1	1	yes	characteristic
39	C₂×C₃₂	C₄×C₃₇	1	1	yes	characteristic
40	C₂×C₃₂	C₄×C₃₇	1	1	yes	characteristic
41	C₄×C₁₆	C₂²×C₃₇	1	1	yes	characteristic
42	#335	—	2	2	no	—
43	C₃₇	#7460	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×C₁₆	C₂×C₄×C₃₇	1	1	yes	characteristic
45	C₂×C₁₆	Q₈×C₃₇	1	1	yes	characteristic
46	C₄⋊C₈	—	4	2	no	—
47	C₄×C₈	D₄×C₃₇	1	1	yes	characteristic
48	C₃₂	—	2	1	no	—
49	C₃₂	C₈×C₃₇	1	2	yes	complemented
50	C₂×C₈	—	8	2	no	—
51	C₂×C₈	C₄⋊C₄×C₃₇	1	1	yes	characteristic
52	C₂×C₈	Q₁₆×C₃₇	1	1	yes	characteristic
53	C₄²	D₈×C₃₇	1	1	yes	characteristic
54	C₁₆	—	2	1	no	—
55	C₁₆	C₂×C₈×C₃₇	1	1	yes	characteristic
56	C₁₆	M₁₆×C₃₇	1	1	yes	characteristic
57	C₂×C₄	#107×C₃₇	1	1	yes	characteristic
58	C₂×C₄	D₁₆×C₃₇	1	1	yes	characteristic
59	C₂×C₄	Q₃₂×C₃₇	1	1	yes	characteristic
60	C₈	—	2	1	no	—
61	C₈	—	16	2	no	—
62	C₈	C₄⋊C₈×C₃₇	1	1	yes	characteristic
63	C₈	#108×C₃₇	1	1	yes	characteristic
64	C₂²	C₃₇×#366	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	C₃₇×#335	1	1	yes	characteristic
67	C₄	C₃₇×#368	1	1	yes	characteristic
68	C₄	C₃₇×D₃₂	1	1	yes	characteristic
69	C₄	C₃₇×Q₆₄	1	1	yes	characteristic
70	C₂	C₃₇×#1371	1	1	yes	characteristic
71	C₂	C₃₇×#1423	1	1	yes	characteristic
72	C₂	C₃₇×#1425	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₇	D₁₆
commutator	C₁₆	C₂×C₈×C₃₇
Frattini, cosocle	C₄×C₁₆	C₂²×C₃₇
socle, prime radical	C₂²×C₃₇	#366
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₇ ◁ C₄²×C₃₇ ◁ C₄×C₈×C₃₇ ◁ C₄×C₁₆×C₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₃₂×C₃₇	C₈	semidirect
27. #7460	C₃₇	direct (N × H)
43. C₃₇	#7460	direct (N × H)
49. C₃₂	C₈×C₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₃₂×C₃₇	2
C₃₇×#1371	2
#7460	37

Subgroups — C37×#7460 #22628713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₇×#7460 #22628713