Subgroups — #17996871

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	#14557359	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	1	yes	characteristic
17	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
18	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
19	C₂×Dic₃₇	—	4	4	no	—
20	Dic₇₄	—	8	4	no	—
21	C₈×C₃₇	Q₁₆	1	2	yes	—
22	C₈×C₃₇	C₂×Q₈	1	2	yes	—
23	C₂²×C₃₇	C₂×D₈	1	1	yes	characteristic
24	C₄×C₃₇	D₁₆	1	2	yes	—
25	C₄×C₃₇	Q₃₂	1	2	yes	—
26	C₄×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
27	C₄×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
28	Dic₃₇	—	8	4	no	—
29	#2252	—	37	1	no	maximal, Sylow
30	C₂×C₃₇	#500	1	1	yes	characteristic
31	C₂×C₃₇	C₂×D₁₆	1	1	yes	characteristic
32	C₂×C₃₇	C₂×Q₃₂	1	1	yes	characteristic
33	#500	—	37	2	no	—
34	#366	—	37	4	no	—
35	C₄×C₁₆	D₃₇	1	1	yes	characteristic
36	C₃₇	#2252	1	1	yes	characteristic, complemented, Sylow
37	C₄⋊Q₈	—	74	2	no	—
38	C₂×C₁₆	C₂×D₃₇	1	2	yes	—
39	#107	—	37	4	no	—
40	#107	—	74	2	no	—
41	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
42	C₂×Q₈	—	148	2	no	—
43	C₂×C₈	D₁₄₈	1	1	yes	characteristic
44	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
45	C₄⋊C₄	—	74	4	no	—
46	C₄⋊C₄	—	148	2	no	—
47	C₄²	D₁₄₈	1	1	yes	characteristic
48	C₁₆	Dic₇₄	1	4	yes	complemented
49	Q₈	—	296	4	no	—
50	C₂×C₄	—	148	4	no	—
51	C₂×C₄	D₂₉₆	1	1	yes	characteristic
52	C₂×C₄	D₂₉₆	1	1	yes	characteristic
53	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
54	C₈	Dic₁₄₈	1	2	yes	—
55	C₈	C₂×Dic₇₄	1	2	yes	—
56	C₂²	C₂×D₂₉₆	1	1	yes	characteristic
57	C₄	—	296	4	no	—
58	C₄	D₅₉₂	1	2	yes	—
59	C₄	Dic₂₉₆	1	2	yes	—
60	C₄	#11924536	1	1	yes	characteristic
61	C₄	C₂×Dic₁₄₈	1	1	yes	characteristic
62	C₂	#14557938	1	1	yes	characteristic
63	C₂	C₂×D₅₉₂	1	1	yes	characteristic
64	C₂	C₂×Dic₂₉₆	1	1	yes	characteristic

	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	#2252
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
36. C₃₇	#2252	semidirect
48. 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
#14557359	2
C₄×C₁₆×C₃₇	2
#2252	37