Subgroups — #17996879

Order 4736.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557935	C₂	1	1	yes	maximal, characteristic
2	#14557360	C₂	1	2	yes	maximal
3	#14557358	C₂	1	2	yes	maximal
4	#14557309	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#500	C₂	1	1	yes	maximal, characteristic
6	#11924528	—	2	1	no	—
7	C₂×#10596925	C₂²	1	2	yes	—
8	#11924470	C₂²	1	1	yes	characteristic
9	#11924470	C₂²	1	1	yes	characteristic
10	#11924468	—	2	1	no	—
11	C₄⋊Q₈×C₃₇	—	2	1	no	—
12	#107×C₃₇	—	2	1	no	—
13	#107×C₃₇	C₂²	1	2	yes	—
14	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₃₇	—	4	1	no	—
16	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
17	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
18	C₄⋊C₄×C₃₇	—	2	2	no	—
19	C₄⋊C₄×C₃₇	—	4	1	no	—
20	C₄²×C₃₇	D₄	1	1	yes	characteristic
21	C₄⋊Dic₃₇	—	2	1	no	—
22	C₄⋊Dic₃₇	—	2	1	no	—
23	#10596936	—	4	1	no	—
24	#10596936	—	4	1	no	—
25	#10596925	Q₈	1	4	yes	complemented
26	Q₈×C₃₇	—	8	2	no	—
27	C₂×C₄×C₃₇	—	4	2	no	—
28	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
29	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
30	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₃₇	—	4	1	no	—
32	C₂×Dic₃₇	—	4	1	no	—
33	C₈×C₃₇	Q₁₆	1	2	yes	—
34	C₈×C₃₇	C₂×Q₈	1	2	yes	—
35	C₂²×C₃₇	C₂×D₈	1	1	yes	characteristic
36	C₄×C₃₇	—	2	1	no	—
37	C₄×C₃₇	—	2	1	no	—
38	C₄×C₃₇	—	8	2	no	—
39	C₄×C₃₇	C₄⋊Q₈	1	1	yes	characteristic
40	C₄×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
41	Dic₃₇	—	8	1	no	—
42	Dic₃₇	—	8	1	no	—
43	#2255	—	37	1	no	maximal, Sylow
44	C₂×C₃₇	#500	1	1	yes	characteristic
45	C₂×C₃₇	#509	1	1	yes	characteristic
46	C₂×C₃₇	#510	1	1	yes	characteristic
47	#500	D₃₇	1	1	yes	characteristic
48	#499	—	37	1	no	—
49	#367	—	37	2	no	—
50	#366	—	37	2	no	—
51	#346	—	37	1	no	—
52	C₃₇	#2255	1	1	yes	characteristic, complemented, Sylow
53	C₄⋊Q₈	—	2	1	no	—
54	#125	—	74	1	no	—
55	C₂×C₁₆	—	37	2	no	—
56	#107	—	2	1	no	—
57	#107	—	37	1	no	—
58	#107	—	37	1	no	—
59	#107	C₂×D₃₇	1	2	yes	—
60	#106	—	74	1	no	—
61	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
62	C₂×Q₈	—	4	1	no	—
63	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	—	4	1	no	—
67	C₄⋊C₄	—	74	1	no	—
68	C₄⋊C₄	—	74	1	no	—
69	C₄⋊C₄	—	148	1	no	—
70	C₄⋊C₄	—	148	1	no	—
71	C₄²	C₂²⋊D₃₇	1	1	yes	characteristic
72	C₁₆	—	37	4	no	—
73	Q₈	—	8	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	148	1	no	—
76	C₂×C₄	—	148	1	no	—
77	C₂×C₄	#10596939	1	1	yes	characteristic
78	C₂×C₄	#10596939	1	1	yes	characteristic
79	C₂×C₄	C₂×C₂²⋊D₃₇	1	1	yes	characteristic
80	C₈	#10596942	1	2	yes	—
81	C₈	Q₈×D₃₇	1	2	yes	—
82	C₂²	C₂×#10596939	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	2	1	no	—
85	C₄	—	8	2	no	—
86	C₄	—	296	1	no	—
87	C₄	—	296	1	no	—
88	C₄	#11924534	1	1	yes	characteristic
89	C₄	C₂×#10596942	1	1	yes	characteristic
90	C₂	#14557936	1	1	yes	characteristic
91	C₂	#14557969	1	1	yes	characteristic
92	C₂	#14557974	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	#2255
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
25. #10596925	Q₈	semidirect
52. C₃₇	#2255	semidirect

Maximal subgroups

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

subgroup	index
#14557935	2
#14557360	2
#14557358	2
#14557309	2
C₃₇×#500	2
#2255	37