Subgroups — #17996869

Order 4736.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557938	C₂	1	1	yes	maximal, characteristic
2	#14557358	C₂	1	4	yes	maximal
3	C₄×#10596925	C₂	1	1	yes	maximal, characteristic
4	C₃₇×#500	C₂	1	1	yes	maximal, characteristic
5	#11924536	—	2	1	no	—
6	C₂×#10596925	C₂²	1	2	yes	—
7	#11924470	—	2	1	no	—
8	#11924470	C₂²	1	2	yes	—
9	C₄⋊Q₈×C₃₇	—	2	1	no	—
10	#107×C₃₇	—	2	1	no	—
11	#107×C₃₇	C₂²	1	2	yes	—
12	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₃₇	—	4	1	no	—
14	C₂×Dic₇₄	—	4	1	no	—
15	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
16	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
17	C₄⋊C₄×C₃₇	—	2	2	no	—
18	C₄⋊C₄×C₃₇	—	4	1	no	—
19	C₄²×C₃₇	D₄	1	1	yes	characteristic
20	C₄⋊Dic₃₇	—	2	2	no	—
21	C₄⋊Dic₃₇	—	4	1	no	—
22	#10596925	Q₈	1	4	yes	complemented
23	Q₈×C₃₇	—	8	2	no	—
24	C₂×C₄×C₃₇	—	4	2	no	—
25	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
26	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
27	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₃₇	—	4	2	no	—
29	Dic₇₄	—	8	2	no	—
30	C₈×C₃₇	Q₁₆	1	2	yes	—
31	C₈×C₃₇	C₂×Q₈	1	2	yes	—
32	C₂²×C₃₇	C₂×D₈	1	1	yes	characteristic
33	C₄×C₃₇	—	8	2	no	—
34	C₄×C₃₇	D₁₆	1	2	yes	—
35	C₄×C₃₇	Q₃₂	1	2	yes	—
36	C₄×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
37	C₄×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
38	Dic₃₇	—	8	2	no	—
39	#2252	—	37	1	no	maximal, Sylow
40	C₂×C₃₇	#500	1	1	yes	characteristic
41	C₂×C₃₇	C₂×D₁₆	1	1	yes	characteristic
42	C₂×C₃₇	C₂×Q₃₂	1	1	yes	characteristic
43	#500	—	37	1	no	—
44	#500	D₃₇	1	1	yes	characteristic
45	#366	—	37	4	no	—
46	C₄×C₁₆	—	37	1	no	—
47	C₃₇	#2252	1	1	yes	characteristic, complemented, Sylow
48	C₄⋊Q₈	—	2	1	no	—
49	C₄⋊Q₈	—	74	1	no	—
50	C₂×C₁₆	—	37	2	no	—
51	#107	—	2	1	no	—
52	#107	—	37	2	no	—
53	#107	—	74	1	no	—
54	#107	C₂×D₃₇	1	2	yes	—
55	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
56	C₂×Q₈	—	4	1	no	—
57	C₂×Q₈	—	148	1	no	—
58	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
59	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
60	C₄⋊C₄	—	2	2	no	—
61	C₄⋊C₄	—	4	1	no	—
62	C₄⋊C₄	—	74	2	no	—
63	C₄⋊C₄	—	148	1	no	—
64	C₄²	C₂²⋊D₃₇	1	1	yes	characteristic
65	C₁₆	—	37	4	no	—
66	Q₈	—	8	2	no	—
67	Q₈	—	296	2	no	—
68	C₂×C₄	—	4	2	no	—
69	C₂×C₄	—	148	2	no	—
70	C₂×C₄	#10596939	1	1	yes	characteristic
71	C₂×C₄	#10596939	1	1	yes	characteristic
72	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
73	C₈	#10596942	1	2	yes	—
74	C₈	Q₈×D₃₇	1	2	yes	—
75	C₂²	C₂×#10596939	1	1	yes	characteristic
76	C₄	—	8	2	no	—
77	C₄	—	296	2	no	—
78	C₄	#11924477	1	2	yes	—
79	C₄	#11924482	1	2	yes	—
80	C₄	#11924534	1	1	yes	characteristic
81	C₄	C₂×#10596942	1	1	yes	characteristic
82	C₂	#14557936	1	1	yes	characteristic
83	C₂	C₂×#11924477	1	1	yes	characteristic
84	C₂	C₂×#11924482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#10596939
commutator, cosocle	C₂×C₈×C₃₇	C₂³
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₃₇×#500	C₂
socle, prime radical	C₂²×C₃₇	C₂×D₈
hypercenter	#500	D₃₇
hypocenter	C₃₇	#2252
LCS	G ▷ C₂×C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

Complements

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

N	H ≅ G/N	type
22. #10596925	Q₈	semidirect
47. C₃₇	#2252	semidirect

Maximal subgroups

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

subgroup	index
#14557938	2
#14557358	2
C₄×#10596925	2
C₃₇×#500	2
#2252	37