Subgroups — #17996878

Order 4736.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557938	C₂	1	2	yes	maximal
2	#14557361	C₂	1	4	yes	maximal
3	C₄×C₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
4	#11924536	—	2	2	no	—
5	#11924470	—	2	2	no	—
6	#11924470	C₂²	1	4	yes	—
7	C₂×C₁₆×C₃₇	C₂²	1	2	yes	—
8	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
9	C₂×Dic₇₄	—	4	2	no	—
10	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
11	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
12	C₄²×C₃₇	D₄	1	1	yes	characteristic
13	C₄⋊Dic₃₇	—	2	4	no	—
14	C₄⋊Dic₃₇	—	4	2	no	—
15	C₁₆×C₃₇	Q₈	1	4	yes	complemented
16	C₂×C₄×C₃₇	D₈	1	2	yes	—
17	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
18	C₂×Dic₃₇	—	4	4	no	—
19	Dic₇₄	—	8	4	no	—
20	C₈×C₃₇	Q₁₆	1	2	yes	—
21	C₈×C₃₇	C₂×Q₈	1	2	yes	—
22	C₂²×C₃₇	C₂×D₈	1	1	yes	characteristic
23	C₄×C₃₇	SD₃₂	1	4	yes	—
24	C₄×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
25	C₄×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
26	Dic₃₇	—	8	4	no	—
27	#2254	—	37	1	no	maximal, Sylow
28	C₂×C₃₇	#500	1	1	yes	characteristic
29	C₂×C₃₇	C₂×SD₃₂	1	2	yes	—
30	#500	—	37	2	no	—
31	#367	—	37	4	no	—
32	C₄×C₁₆	D₃₇	1	1	yes	characteristic
33	C₃₇	#2254	1	1	yes	characteristic, complemented, Sylow
34	C₄⋊Q₈	—	74	2	no	—
35	C₂×C₁₆	C₂×D₃₇	1	2	yes	—
36	#107	—	37	4	no	—
37	#107	—	74	2	no	—
38	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
39	C₂×Q₈	—	148	2	no	—
40	C₂×C₈	D₁₄₈	1	1	yes	characteristic
41	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
42	C₄⋊C₄	—	74	4	no	—
43	C₄⋊C₄	—	148	2	no	—
44	C₄²	D₁₄₈	1	1	yes	characteristic
45	C₁₆	Dic₇₄	1	4	yes	complemented
46	Q₈	—	296	4	no	—
47	C₂×C₄	—	148	4	no	—
48	C₂×C₄	D₂₉₆	1	2	yes	—
49	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
50	C₈	Dic₁₄₈	1	2	yes	—
51	C₈	C₂×Dic₇₄	1	2	yes	—
52	C₂²	C₂×D₂₉₆	1	1	yes	characteristic
53	C₄	—	296	4	no	—
54	C₄	#11924481	1	4	yes	—
55	C₄	#11924536	1	1	yes	characteristic
56	C₄	C₂×Dic₁₄₈	1	1	yes	characteristic
57	C₂	#14557938	1	1	yes	characteristic
58	C₂	C₂×#11924481	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₂₉₆
commutator, cosocle	C₂×C₈×C₃₇	C₂³
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₄×C₁₆×C₃₇	C₂
socle, prime radical	C₂²×C₃₇	C₂×D₈
hypercenter	C₄×C₁₆	D₃₇
hypocenter	C₃₇	#2254
LCS	G ▷ C₂×C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
15. C₁₆×C₃₇	Q₈	semidirect
33. C₃₇	#2254	semidirect
45. C₁₆	Dic₇₄	semidirect

Maximal subgroups

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

subgroup	index
#14557938	2
#14557361	2
C₄×C₁₆×C₃₇	2
#2254	37