Subgroups — #18009556

Order 4736.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558422	C₂	1	1	yes	maximal, characteristic
2	#14558394	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×Dic₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596927	—	2	1	no	—
5	C₄⋊#64438	—	2	1	no	—
6	Q₈×Dic₃₇	—	2	1	no	—
7	#11924470	C₄	1	1	yes	characteristic
8	#11924460	—	2	1	no	—
9	C₈×Dic₃₇	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆×C₃₇	C₄	1	1	yes	characteristic
11	C₂×Q₈×C₃₇	—	2	1	no	—
12	C₂×#64438	—	4	1	no	—
13	Q₁₆×C₃₇	—	2	1	no	—
14	Q₁₆×C₃₇	C₈	1	2	yes	complemented
15	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
16	C₄⋊Dic₃₇	—	2	1	no	—
17	C₄⋊Dic₃₇	—	4	1	no	—
18	C₄×Dic₃₇	—	4	1	no	—
19	C₄×Dic₃₇	D₄	1	1	yes	characteristic
20	C₂×#64436	D₄	1	1	yes	characteristic
21	#10596927	—	2	2	no	—
22	Q₈×C₃₇	—	2	2	no	—
23	Q₈×C₃₇	—	4	1	no	—
24	C₂×C₄×C₃₇	—	4	1	no	—
25	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×Dic₃₇	—	4	1	no	—
27	C₂×Dic₃₇	D₈	1	1	yes	characteristic
28	C₂×Dic₃₇	SD₁₆	1	1	yes	characteristic
29	#64438	—	8	1	no	—
30	C₈×C₃₇	C₂×C₈	1	1	yes	characteristic
31	C₈×C₃₇	M₁₆	1	1	yes	characteristic
32	#64436	—	2	1	no	—
33	C₂²×C₃₇	#102	1	1	yes	characteristic
34	C₄×C₃₇	—	4	2	no	—
35	C₄×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
36	C₄×C₃₇	#104	1	1	yes	characteristic
37	Dic₃₇	—	2	1	no	—
38	Dic₃₇	—	2	1	no	—
39	Dic₃₇	—	8	1	no	—
40	#1334	—	37	1	no	maximal, Sylow
41	C₂×C₃₇	D₄⋊C₈	1	1	yes	characteristic
42	C₂×C₃₇	#360	1	1	yes	characteristic
43	C₂×C₃₇	#362	1	1	yes	characteristic
44	C₄×Q₁₆	—	37	1	no	—
45	#346	—	37	1	no	—
46	#334	—	37	1	no	—
47	C₃₇	#1334	1	1	yes	characteristic, complemented, Sylow
48	C₂×Q₁₆	#3866	1	1	yes	characteristic
49	C₄×Q₈	—	74	1	no	—
50	C₂×C₁₆	—	74	1	no	—
51	#107	—	37	1	no	—
52	C₄⋊C₈	—	74	1	no	—
53	#103	—	74	1	no	—
54	C₄×C₈	—	37	1	no	—
55	C₂×Q₈	—	2	1	no	—
56	Q₁₆	—	2	1	no	—
57	Q₁₆	#64438	1	2	yes	complemented
58	C₂×C₈	—	37	1	no	—
59	C₂×C₈	—	148	1	no	—
60	C₂×C₈	C₂×#3866	1	1	yes	characteristic
61	C₄⋊C₄	—	74	1	no	—
62	C₄⋊C₄	—	148	1	no	—
63	C₄²	—	37	1	no	—
64	C₄²	—	148	1	no	—
65	C₁₆	—	74	2	no	—
66	Q₈	—	2	2	no	—
67	Q₈	—	4	1	no	—
68	C₂×C₄	—	4	1	no	—
69	C₂×C₄	—	37	1	no	—
70	C₂×C₄	—	37	1	no	—
71	C₂×C₄	—	148	1	no	—
72	C₂×C₄	C₂²⋊#3866	1	1	yes	characteristic
73	C₈	—	296	1	no	—
74	C₈	—	74	1	no	—
75	C₈	C₂×#64438	1	1	yes	characteristic
76	C₈	#10596957	1	1	yes	characteristic
77	C₂²	#11924598	1	1	yes	characteristic
78	C₄	—	4	2	no	—
79	C₄	—	296	1	no	—
80	C₄	—	74	1	no	—
81	C₄	—	74	1	no	—
82	C₄	C₂²⋊#64438	1	1	yes	characteristic
83	C₄	#11924600	1	1	yes	characteristic
84	C₂	D₄⋊#64438	1	1	yes	characteristic
85	C₂	#14558450	1	1	yes	characteristic
86	C₂	#14558452	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11924598
commutator	C₈×C₃₇	C₂×C₈
Frattini	C₂×C₈	C₂×#3866
Fitting	C₂×Q₁₆×C₃₇	C₄
socle, prime radical	C₂²×C₃₇	#102
cosocle	C₈×Dic₃₇	C₂²
hypercenter	C₂×Q₁₆	#3866
hypocenter	C₃₇	#1334
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
14. Q₁₆×C₃₇	C₈	semidirect
47. C₃₇	#1334	semidirect
57. Q₁₆	#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
Q₁₆×Dic₃₇	2
#1334	37