Subgroups — #17996454

Order 4736.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₉₆	C₂	1	1	yes	maximal, characteristic
2	#14557627	C₂	1	2	yes	maximal
3	#14557336	C₂	1	2	yes	maximal
4	C₁₆×Dic₃₇	C₂	1	1	yes	maximal, characteristic
5	C₃₇×#366	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₄₈	C₂²	1	2	yes	—
7	#11924501	—	2	2	no	—
8	Dic₂₉₆	C₄	1	4	yes	complemented
9	C₂×#10596925	C₂²	1	1	yes	characteristic
10	#11924459	—	2	2	no	—
11	C₈×Dic₃₇	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
13	#107×C₃₇	C₂²	1	2	yes	—
14	C₂×Dic₇₄	—	2	2	no	—
15	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
16	C₄⋊C₄×C₃₇	—	2	2	no	—
17	#10596936	—	4	2	no	—
18	C₄×Dic₃₇	—	4	2	no	—
19	C₄×Dic₃₇	D₄	1	1	yes	characteristic
20	C₂×#64436	D₄	1	1	yes	characteristic
21	Dic₁₄₈	—	2	2	no	—
22	Dic₁₄₈	C₂×C₄	1	4	yes	—
23	C₁₆×C₃₇	C₂×C₄	1	2	yes	—
24	#10596925	—	2	1	no	—
25	C₂×C₄×C₃₇	—	4	2	no	—
26	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₃₇	—	4	2	no	—
28	C₂×Dic₃₇	D₈	1	1	yes	characteristic
29	C₂×Dic₃₇	D₈	1	1	yes	characteristic
30	Dic₇₄	—	2	4	no	—
31	Dic₇₄	—	4	2	no	—
32	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₃₇	#41	1	1	yes	characteristic
34	#64436	—	2	1	no	—
35	C₂²×C₃₇	C₂×D₈	1	1	yes	characteristic
36	C₄×C₃₇	—	8	2	no	—
37	C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
38	C₄×C₃₇	#135	1	1	yes	characteristic
39	Dic₃₇	—	2	1	no	—
40	Dic₃₇	—	4	4	no	—
41	Dic₃₇	Q₃₂	1	2	yes	complemented
42	C₄×Q₃₂	—	37	1	no	maximal, Sylow
43	C₂×C₃₇	C₄×D₈	1	1	yes	characteristic
44	C₂×C₃₇	C₂×Q₃₂	1	1	yes	characteristic
45	C₂×C₃₇	#508	1	1	yes	characteristic
46	C₂×Q₃₂	—	37	1	no	—
47	C₄×Q₁₆	—	37	2	no	—
48	#366	D₃₇	1	1	yes	characteristic
49	#358	—	37	2	no	—
50	C₄×C₁₆	—	37	1	no	—
51	C₃₇	C₄×Q₃₂	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₁₆	—	37	2	no	—
53	C₄×Q₈	—	74	2	no	—
54	Q₃₂	—	37	4	no	—
55	C₂×C₁₆	—	37	1	no	—
56	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
57	#107	C₂×D₃₇	1	2	yes	—
58	#103	—	74	2	no	—
59	C₄×C₈	—	37	1	no	—
60	C₂×Q₈	—	74	2	no	—
61	Q₁₆	—	37	4	no	—
62	Q₁₆	—	74	2	no	—
63	C₂×C₈	—	37	1	no	—
64	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	—	148	2	no	—
67	C₄²	—	37	1	no	—
68	C₄²	—	148	2	no	—
69	C₁₆	—	74	1	no	—
70	C₁₆	C₄×D₃₇	1	2	yes	—
71	Q₈	—	74	4	no	—
72	Q₈	—	148	2	no	—
73	C₂×C₄	—	4	2	no	—
74	C₂×C₄	—	37	1	no	—
75	C₂×C₄	—	37	1	no	—
76	C₂×C₄	—	148	2	no	—
77	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
78	C₈	—	74	1	no	—
79	C₈	C₂×C₄×D₃₇	1	1	yes	characteristic
80	C₈	#10596966	1	1	yes	characteristic
81	C₂²	D₈×D₃₇	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	37	2	no	—
84	C₄	—	74	1	no	—
85	C₄	—	148	4	no	—
86	C₄	#11924498	1	1	yes	characteristic
87	C₄	#11924559	1	1	yes	characteristic
88	C₂	#14557615	1	1	yes	characteristic
89	C₂	Q₃₂×D₃₇	1	1	yes	characteristic
90	C₂	#14557962	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈×D₃₇
commutator	C₈×C₃₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₃₇×#366	C₂
socle, prime radical	C₂²×C₃₇	C₂×D₈
cosocle	C₂×C₈×C₃₇	C₂³
hypercenter	#366	D₃₇
hypocenter	C₃₇	C₄×Q₃₂
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

Complements

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

N	H ≅ G/N	type
8. Dic₂₉₆	C₄	semidirect
41. Dic₃₇	Q₃₂	semidirect
51. C₃₇	C₄×Q₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₂₉₆	2
#14557627	2
#14557336	2
C₁₆×Dic₃₇	2
C₃₇×#366	2
C₄×Q₃₂	37