Subgroups — #17996379

Order 4736.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₃₇	C₂	1	1	yes	maximal, characteristic
2	#14557570	C₂	1	2	yes	maximal
3	#14557361	C₂	1	1	yes	maximal, characteristic, complemented
4	#14557358	C₂	1	2	yes	maximal, complemented
5	C₃₇×#367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₃₇	C₂²	1	1	yes	characteristic
7	#11924494	—	2	2	no	—
8	C₂×#10596925	C₂²	1	1	yes	characteristic
9	C₁₆×D₃₇	C₄	1	4	yes	complemented
10	#11924470	C₂²	1	2	yes	—
11	#11924467	—	2	2	no	—
12	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	#107×C₃₇	C₂²	1	2	yes	—
14	C₂×C₄×D₃₇	D₄	1	1	yes	characteristic
15	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
16	C₄⋊C₄×C₃₇	—	2	2	no	—
17	#10596938	—	4	2	no	—
18	C₄⋊Dic₃₇	—	2	2	no	—
19	C₄×Dic₃₇	—	4	2	no	—
20	C₂×#64436	D₄	1	1	yes	characteristic
21	C₈×D₃₇	C₂×C₄	1	2	yes	—
22	C₈×D₃₇	Q₈	1	2	yes	—
23	C₁₆×C₃₇	C₂×C₄	1	2	yes	—
24	#10596925	C₂×C₄	1	2	yes	—
25	C₂²×D₃₇	D₈	1	1	yes	characteristic
26	C₂×C₄×C₃₇	—	4	2	no	—
27	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
28	C₂×Dic₃₇	—	4	2	no	—
29	C₂×Dic₃₇	D₈	1	1	yes	characteristic
30	C₄×D₃₇	C₄⋊C₄	1	2	yes	—
31	C₄×D₃₇	Q₁₆	1	2	yes	—
32	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₃₇	C₂×Q₈	1	1	yes	characteristic
34	#64436	C₄⋊C₄	1	2	yes	—
35	C₂²×C₃₇	C₂×D₈	1	1	yes	characteristic
36	C₂×D₃₇	—	2	2	no	—
37	C₂×D₃₇	#107	1	2	yes	—
38	C₄×C₃₇	—	8	2	no	—
39	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₄×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
41	Dic₃₇	—	8	2	no	—
42	Dic₃₇	#107	1	2	yes	—
43	#2158	—	37	1	no	maximal, Sylow
44	C₂×C₃₇	C₂×#107	1	1	yes	characteristic
45	C₂×C₃₇	#508	1	2	yes	—
46	D₃₇	—	2	2	no	—
47	C₂²×C₁₆	—	37	1	no	—
48	#427	—	37	2	no	—
49	#367	—	37	1	no	—
50	#367	D₃₇	1	1	yes	characteristic, complemented
51	#366	—	37	2	no	—
52	C₃₇	#2158	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₈	—	37	1	no	—
54	#117	—	74	2	no	—
55	C₂×C₁₆	—	37	1	no	—
56	C₂×C₁₆	—	37	4	no	—
57	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
58	#107	—	37	2	no	—
59	#107	C₂×D₃₇	1	2	yes	—
60	#106	—	74	2	no	—
61	C₂²×C₄	—	37	1	no	—
62	C₂×C₈	—	37	1	no	—
63	C₂×C₈	—	37	2	no	—
64	C₂×C₈	—	37	2	no	—
65	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
66	C₄⋊C₄	—	2	2	no	—
67	C₄⋊C₄	—	74	2	no	—
68	C₂²⋊C₄	—	148	2	no	—
69	C₄²	—	148	2	no	—
70	C₁₆	—	37	2	no	—
71	C₁₆	C₄×D₃₇	1	2	yes	—
72	C₂³	—	37	1	no	—
73	C₂×C₄	—	4	2	no	—
74	C₂×C₄	—	37	1	no	—
75	C₂×C₄	—	37	2	no	—
76	C₂×C₄	—	37	2	no	—
77	C₂×C₄	—	148	2	no	—
78	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
79	C₈	—	37	2	no	—
80	C₈	C₂×C₄×D₃₇	1	1	yes	characteristic
81	C₈	Q₈×D₃₇	1	1	yes	characteristic
82	C₂²	—	37	2	no	—
83	C₂²	—	74	2	no	—
84	C₂²	D₈×D₃₇	1	1	yes	characteristic
85	C₄	—	8	2	no	—
86	C₄	—	37	2	no	—
87	C₄	—	296	2	no	—
88	C₄	C₄⋊C₄×D₃₇	1	1	yes	characteristic
89	C₄	Q₁₆×D₃₇	1	1	yes	characteristic
90	C₂	—	74	2	no	—
91	C₂	#107×D₃₇	1	1	yes	characteristic
92	C₂	#14557964	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₃₇
commutator	C₈×C₃₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₃₇×#367	C₂
socle	C₂²×C₃₇	C₂×D₈
prime radical	C₂²×D₃₇	D₈
cosocle	C₂×C₈×C₃₇	C₂³
hypercenter	#367	D₃₇
hypocenter	C₃₇	#2158
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #367

Complements

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

N	H ≅ G/N	type
3. #14557361	C₂	semidirect
4. #14557358	C₂	semidirect
5. C₃₇×#367	C₂	semidirect
9. C₁₆×D₃₇	C₄	semidirect
50. #367	D₃₇	semidirect
52. C₃₇	#2158	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₆×D₃₇	2
#14557570	2
#14557361	2
#14557358	2
C₃₇×#367	2
#2158	37