Subgroups — #17992569

Order 4736.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557354	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈×#64436	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#443	C₂	1	1	yes	maximal, characteristic
4	#11924476	—	2	1	no	—
5	C₄×#64436	—	2	1	no	—
6	#135×C₃₇	C₄	1	1	yes	characteristic
7	#131×C₃₇	—	2	1	no	—
8	#108×C₃₇	C₄	1	1	yes	characteristic
9	#104×C₃₇	—	2	1	no	—
10	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic
11	#41×C₃₇	—	2	1	no	—
12	Q₁₆×C₃₇	C₈	1	1	yes	characteristic, complemented
13	SD₁₆×C₃₇	—	2	1	no	—
14	D₈×C₃₇	C₈	1	1	yes	characteristic, complemented
15	M₁₆×C₃₇	—	2	1	no	—
16	M₁₆×C₃₇	—	4	1	no	—
17	C₂×C₈×C₃₇	—	4	1	no	—
18	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
20	C₄²×C₃₇	D₄	1	1	yes	characteristic
21	C₂×#64436	—	2	2	no	—
22	#10596925	—	4	1	no	—
23	Q₈×C₃₇	—	2	1	no	—
24	D₄×C₃₇	—	2	1	no	—
25	D₄×C₃₇	—	4	1	no	—
26	C₂×C₄×C₃₇	—	2	1	no	—
27	C₂×C₄×C₃₇	—	4	1	no	—
28	C₂×C₄×C₃₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₈×C₃₇	—	4	1	no	—
30	C₈×C₃₇	C₂×C₈	1	1	yes	characteristic
31	C₈×C₃₇	M₁₆	1	1	yes	characteristic
32	C₈×C₃₇	D₈	1	1	yes	characteristic
33	C₈×C₃₇	SD₁₆	1	1	yes	characteristic
34	#64436	—	2	4	no	—
35	C₂²×C₃₇	—	4	1	no	—
36	C₂²×C₃₇	#104	1	1	yes	characteristic
37	C₄×C₃₇	—	2	2	no	—
38	C₄×C₃₇	—	4	1	no	—
39	C₄×C₃₇	C₂²⋊C₈	1	1	yes	characteristic
40	C₄×C₃₇	#102	1	1	yes	characteristic
41	#1335	—	37	1	no	maximal, Sylow
42	C₂×C₃₇	—	2	1	no	—
43	C₂×C₃₇	—	8	1	no	—
44	C₂×C₃₇	D₄⋊C₈	1	1	yes	characteristic
45	#443	D₃₇	1	1	yes	characteristic
46	#364	—	37	1	no	—
47	C₈²	—	37	1	no	—
48	C₃₇	#1335	1	1	yes	characteristic, complemented, Sylow
49	#135	Dic₃₇	1	1	yes	characteristic
50	#131	—	2	1	no	—
51	M₃₂	—	74	1	no	—
52	#108	Dic₃₇	1	1	yes	characteristic
53	#104	—	2	1	no	—
54	C₄×C₈	—	74	1	no	—
55	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic
56	#41	—	2	1	no	—
57	Q₁₆	#64436	1	1	yes	characteristic, complemented
58	SD₁₆	—	2	1	no	—
59	D₈	#64436	1	1	yes	characteristic, complemented
60	M₁₆	—	2	1	no	—
61	M₁₆	—	4	1	no	—
62	C₂×C₈	—	4	1	no	—
63	C₂×C₈	—	74	2	no	—
64	C₂×C₈	C₂×Dic₃₇	1	1	yes	characteristic
65	C₂×C₈	C₂²⋊D₃₇	1	1	yes	characteristic
66	C₄²	C₂²⋊D₃₇	1	1	yes	characteristic
67	C₁₆	—	148	1	no	—
68	Q₈	—	2	1	no	—
69	D₄	—	2	1	no	—
70	D₄	—	4	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	4	1	no	—
73	C₂×C₄	C₂²⋊Dic₃₇	1	1	yes	characteristic
74	C₈	—	4	1	no	—
75	C₈	—	74	4	no	—
76	C₈	C₂×#64436	1	1	yes	characteristic
77	C₈	#10596934	1	1	yes	characteristic
78	C₈	#10596939	1	1	yes	characteristic
79	C₈	#10596940	1	1	yes	characteristic
80	C₂²	—	4	1	no	—
81	C₂²	#11924463	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	4	1	no	—
84	C₄	C₂²⋊#64436	1	1	yes	characteristic
85	C₄	#11924457	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	8	1	no	—
88	C₂	D₄⋊#64436	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#10596939
commutator	C₈×C₃₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₃₇
Fitting	C₃₇×#443	C₂
socle	C₂×C₃₇	D₄⋊C₈
prime radical	#135×C₃₇	C₄
cosocle	C₄×C₈×C₃₇	C₂²
hypercenter	#443	D₃₇
hypocenter	C₃₇	#1335
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #443

Complements

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

N	H ≅ G/N	type
1. #14557354	C₂	semidirect
2. C₈×#64436	C₂	semidirect
12. Q₁₆×C₃₇	C₈	semidirect
14. D₈×C₃₇	C₈	semidirect
48. C₃₇	#1335	semidirect
57. Q₁₆	#64436	semidirect
59. D₈	#64436	semidirect

Maximal subgroups

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

subgroup	index
#14557354	2
C₈×#64436	2
C₃₇×#443	2
#1335	37