Subgroups — #17992665

Order 4736.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#10596925	C₂	1	1	yes	maximal, characteristic
2	C₈×#64436	C₂	1	1	yes	maximal, characteristic
3	C₃₇×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596925	—	2	1	no	—
5	C₄×#64436	C₄	1	1	yes	characteristic
6	C₄×#64436	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₃₇	—	2	1	no	—
8	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
10	C₂×C₈×C₃₇	Q₈	1	1	yes	characteristic
11	C₄²×C₃₇	C₂×C₄	1	1	yes	characteristic
12	C₂×#64436	—	2	1	no	—
13	C₂×#64436	C₈	1	1	yes	characteristic
14	C₂×#64436	C₈	1	1	yes	characteristic
15	C₁₆×C₃₇	—	4	1	no	—
16	#10596925	—	4	1	no	—
17	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
19	C₂×C₄×C₃₇	M₁₆	1	1	yes	characteristic
20	C₈×C₃₇	—	2	1	no	—
21	C₈×C₃₇	D₈	1	1	yes	characteristic
22	C₈×C₃₇	Q₁₆	1	1	yes	characteristic
23	#64436	—	2	2	no	—
24	#64436	—	2	1	no	—
25	#64436	C₁₆	1	2	yes	complemented
26	C₂²×C₃₇	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₃₇	—	2	1	no	—
28	C₄×C₃₇	#107	1	1	yes	characteristic
29	C₄×C₃₇	#108	1	1	yes	characteristic
30	C₄×C₃₇	C₂×C₁₆	1	1	yes	characteristic
31	C₄×C₃₇	M₃₂	1	1	yes	characteristic
32	#1370	—	37	1	no	maximal, Sylow
33	C₂×C₃₇	#335	1	1	yes	characteristic
34	C₂×C₃₇	C₄⋊C₁₆	1	1	yes	characteristic
35	C₂×C₃₇	#364	1	1	yes	characteristic
36	C₄⋊C₁₆	—	37	1	no	—
37	C₄⋊C₁₆	D₃₇	1	1	yes	characteristic
38	C₈²	—	37	1	no	—
39	C₃₇	#1370	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₁₆	—	2	1	no	—
41	C₂×C₁₆	—	74	1	no	—
42	C₄×C₈	—	37	1	no	—
43	C₄×C₈	—	37	1	no	—
44	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
45	C₂×C₈	—	37	1	no	—
46	C₂×C₈	—	37	1	no	—
47	C₂×C₈	—	74	1	no	—
48	C₂×C₈	Dic₇₄	1	1	yes	characteristic
49	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
50	C₄²	C₄×D₃₇	1	1	yes	characteristic
51	C₁₆	—	4	1	no	—
52	C₁₆	—	148	1	no	—
53	C₂×C₄	C₈×D₃₇	1	1	yes	characteristic
54	C₂×C₄	#10596929	1	1	yes	characteristic
55	C₂×C₄	#10596936	1	1	yes	characteristic
56	C₈	—	2	1	no	—
57	C₈	—	37	2	no	—
58	C₈	—	74	2	no	—
59	C₈	—	74	1	no	—
60	C₈	#10596939	1	1	yes	characteristic
61	C₈	#10596942	1	1	yes	characteristic
62	C₂²	#11924465	1	1	yes	characteristic
63	C₄	—	2	1	no	—
64	C₄	#11924469	1	1	yes	characteristic
65	C₄	#11924471	1	1	yes	characteristic
66	C₄	C₁₆×D₃₇	1	1	yes	characteristic
67	C₄	#11924475	1	1	yes	characteristic
68	C₂	#14557285	1	1	yes	characteristic
69	C₂	#14557351	1	1	yes	characteristic
70	C₂	#14557353	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊D₃₇
commutator	C₄×C₃₇	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₃₇
Fitting	C₃₇×C₄⋊C₁₆	C₂
socle, prime radical	C₂²×C₃₇	C₄⋊C₈
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	C₄⋊C₁₆	D₃₇
hypocenter	C₃₇	#1370
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
25. #64436	C₁₆	semidirect
39. C₃₇	#1370	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#10596925	2
C₈×#64436	2
C₃₇×C₄⋊C₁₆	2
#1370	37