Subgroups — #17992669

Order 4736.

70 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	#14557286	C₂	1	1	yes	maximal, characteristic
3	C₃₇×#335	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596925	C₄	1	1	yes	characteristic
5	C₂×#10596925	C₄	1	1	yes	characteristic
6	C₄⋊#64436	—	2	1	no	—
7	C₄⋊C₈×C₃₇	—	2	1	no	—
8	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₃₇	—	4	1	no	—
10	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₃₇	Q₈	1	1	yes	characteristic
12	C₄²×C₃₇	D₄	1	1	yes	characteristic
13	C₂×#64436	—	4	1	no	—
14	#10596925	—	2	1	no	—
15	#10596925	C₈	1	2	yes	complemented
16	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
18	C₂×C₄×C₃₇	Q₁₆	1	1	yes	characteristic
19	C₈×C₃₇	—	2	1	no	—
20	C₈×C₃₇	—	8	1	no	—
21	C₈×C₃₇	C₂×C₈	1	1	yes	characteristic
22	C₈×C₃₇	M₁₆	1	1	yes	characteristic
23	#64436	—	8	1	no	—
24	C₂²×C₃₇	#107	1	1	yes	characteristic
25	C₄×C₃₇	—	2	1	no	—
26	C₄×C₃₇	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₃₇	#108	1	1	yes	characteristic
28	C₄×C₃₇	SD₃₂	1	1	yes	characteristic
29	C₄×C₃₇	SD₃₂	1	1	yes	characteristic
30	#1372	—	37	1	no	maximal, Sylow
31	C₂×C₃₇	#335	1	1	yes	characteristic
32	C₂×C₃₇	#367	1	1	yes	characteristic
33	C₂×C₃₇	#368	1	1	yes	characteristic
34	C₄×C₁₆	—	37	1	no	—
35	#335	—	37	1	no	—
36	#335	D₃₇	1	1	yes	characteristic
37	C₃₇	#1372	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₁₆	—	37	1	no	—
39	C₂×C₁₆	—	37	1	no	—
40	C₄⋊C₈	—	2	1	no	—
41	C₄⋊C₈	—	74	1	no	—
42	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
43	C₂×C₈	—	4	1	no	—
44	C₂×C₈	—	148	1	no	—
45	C₂×C₈	Dic₇₄	1	1	yes	characteristic
46	C₂×C₈	C₄×D₃₇	1	1	yes	characteristic
47	C₄²	C₂²⋊D₃₇	1	1	yes	characteristic
48	C₁₆	—	37	2	no	—
49	C₁₆	—	74	1	no	—
50	C₂×C₄	#10596936	1	1	yes	characteristic
51	C₂×C₄	#10596939	1	1	yes	characteristic
52	C₂×C₄	#10596942	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	—	8	1	no	—
55	C₈	—	296	1	no	—
56	C₈	C₈×D₃₇	1	1	yes	characteristic
57	C₈	#10596929	1	1	yes	characteristic
58	C₂²	#11924469	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	#11924465	1	1	yes	characteristic
61	C₄	#11924471	1	1	yes	characteristic
62	C₄	#11924479	1	1	yes	characteristic
63	C₄	#11924480	1	1	yes	characteristic
64	C₂	#14557285	1	1	yes	characteristic
65	C₂	#14557360	1	1	yes	characteristic
66	C₂	#14557362	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10596939
commutator	C₈×C₃₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₃₇
Fitting	C₃₇×#335	C₂
socle, prime radical	C₂²×C₃₇	#107
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	#335	D₃₇
hypocenter	C₃₇	#1372
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
15. #10596925	C₈	semidirect
37. C₃₇	#1372	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
#14557286	2
C₃₇×#335	2
#1372	37