Subgroups — #18009554

Order 4736.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558422	C₂	1	1	yes	maximal, characteristic, complemented
2	#14558394	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×Dic₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596927	—	2	1	no	—
5	C₄⋊#64438	—	2	1	no	—
6	D₄×Dic₃₇	—	2	1	no	—
7	#11924470	C₄	1	1	yes	characteristic
8	#11924457	—	2	1	no	—
9	C₈×Dic₃₇	C₂²	1	1	yes	characteristic
10	C₂×D₈×C₃₇	C₄	1	1	yes	characteristic
11	C₂×D₄×C₃₇	—	2	1	no	—
12	C₂²×Dic₃₇	—	4	1	no	—
13	C₂×#64438	—	4	1	no	—
14	D₈×C₃₇	—	2	1	no	—
15	D₈×C₃₇	C₈	1	2	yes	complemented
16	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂²⋊Dic₃₇	—	4	1	no	—
18	C₄⋊Dic₃₇	—	2	1	no	—
19	C₄×Dic₃₇	D₄	1	1	yes	characteristic
20	C₂×#64436	D₄	1	1	yes	characteristic
21	#10596927	—	2	2	no	—
22	C₂³×C₃₇	—	4	1	no	—
23	D₄×C₃₇	—	2	2	no	—
24	D₄×C₃₇	—	4	1	no	—
25	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×Dic₃₇	—	4	1	no	—
27	C₂×Dic₃₇	—	8	2	no	—
28	C₂×Dic₃₇	D₈	1	1	yes	characteristic
29	C₂×Dic₃₇	SD₁₆	1	1	yes	characteristic
30	#64438	—	8	1	no	—
31	C₈×C₃₇	C₂×C₈	1	1	yes	characteristic
32	C₈×C₃₇	M₁₆	1	1	yes	characteristic
33	#64436	—	2	1	no	—
34	C₂²×C₃₇	—	4	2	no	—
35	C₂²×C₃₇	—	8	1	no	—
36	C₂²×C₃₇	—	8	1	no	—
37	C₂²×C₃₇	#102	1	1	yes	characteristic
38	C₄×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₃₇	#104	1	1	yes	characteristic
40	Dic₃₇	—	2	1	no	—
41	Dic₃₇	—	2	1	no	—
42	Dic₃₇	—	8	1	no	—
43	#1333	—	37	1	no	maximal, Sylow
44	C₂×C₃₇	—	8	2	no	—
45	C₂×C₃₇	D₄⋊C₈	1	1	yes	characteristic
46	C₂×C₃₇	#360	1	1	yes	characteristic
47	C₂×C₃₇	#361	1	1	yes	characteristic
48	C₄×D₈	—	37	1	no	—
49	#346	—	37	1	no	—
50	#334	—	37	1	no	—
51	C₃₇	#1333	1	1	yes	characteristic, complemented, Sylow
52	C₂×D₈	#3866	1	1	yes	characteristic
53	C₄×D₄	—	74	1	no	—
54	C₂×C₁₆	—	74	1	no	—
55	#107	—	37	1	no	—
56	C₄⋊C₈	—	74	1	no	—
57	#102	—	74	1	no	—
58	C₄×C₈	—	37	1	no	—
59	C₂×D₄	—	2	1	no	—
60	C₂²×C₄	—	148	1	no	—
61	D₈	—	2	1	no	—
62	D₈	#64438	1	2	yes	complemented
63	C₂×C₈	—	37	1	no	—
64	C₂×C₈	—	148	1	no	—
65	C₂×C₈	C₂×#3866	1	1	yes	characteristic
66	C₄⋊C₄	—	74	1	no	—
67	C₂²⋊C₄	—	148	1	no	—
68	C₄²	—	37	1	no	—
69	C₁₆	—	74	2	no	—
70	C₂³	—	4	1	no	—
71	D₄	—	2	2	no	—
72	D₄	—	4	1	no	—
73	C₂×C₄	—	37	1	no	—
74	C₂×C₄	—	37	1	no	—
75	C₂×C₄	—	296	2	no	—
76	C₂×C₄	—	148	1	no	—
77	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
78	C₈	—	296	1	no	—
79	C₈	—	74	1	no	—
80	C₈	C₂×#64438	1	1	yes	characteristic
81	C₈	#10596957	1	1	yes	characteristic
82	C₂²	—	4	2	no	—
83	C₂²	—	8	1	no	—
84	C₂²	—	8	1	no	—
85	C₂²	#11924598	1	1	yes	characteristic
86	C₄	—	296	1	no	—
87	C₄	—	74	1	no	—
88	C₄	—	74	1	no	—
89	C₄	C₂²⋊#64438	1	1	yes	characteristic
90	C₄	#11924600	1	1	yes	characteristic
91	C₂	—	8	2	no	—
92	C₂	D₄⋊#64438	1	1	yes	characteristic
93	C₂	#14558449	1	1	yes	characteristic
94	C₂	#14558451	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11924598
commutator	C₈×C₃₇	C₂×C₈
Frattini	C₂×C₈	C₂×#3866
Fitting, prime radical	C₂×D₈×C₃₇	C₄
socle	C₂²×C₃₇	#102
cosocle	C₈×Dic₃₇	C₂²
hypercenter	C₂×D₈	#3866
hypocenter	C₃₇	#1333
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. #14558422	C₂	semidirect
2. #14558394	C₂	semidirect
15. D₈×C₃₇	C₈	semidirect
51. C₃₇	#1333	semidirect
62. D₈	#64438	semidirect

Maximal subgroups

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

subgroup	index
#14558422	2
#14558394	2
D₈×Dic₃₇	2
#1333	37