Subgroups — D₃₇⋊M₆₄ #18011017

Order 4736.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558466	C₂	1	2	yes	maximal, complemented
2	#14558465	C₂	1	2	yes	maximal, complemented
3	D₃₇⋊C₃₂	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₆×D₃₇	C₂	1	1	yes	maximal, characteristic
5	#11924586	C₂²	1	4	yes	complemented
6	C₂×C₈×D₃₇	C₄	1	1	yes	characteristic
7	C₂×#10596925	C₂²	1	1	yes	characteristic
8	C₁₆×D₃₇	C₄	1	1	yes	characteristic
9	C₁₆×D₃₇	C₄	1	1	yes	characteristic
10	C₁₆×D₃₇	C₂²	1	1	yes	characteristic
11	C₁₆×D₃₇	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₃₇	C₄	1	1	yes	characteristic
13	C₂×C₄×D₃₇	C₈	1	1	yes	characteristic
14	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂×#64436	C₈	1	1	yes	characteristic
16	C₈×D₃₇	C₈	1	1	yes	characteristic
17	C₈×D₃₇	C₈	1	1	yes	characteristic
18	C₈×D₃₇	C₂×C₄	1	1	yes	characteristic
19	C₈×D₃₇	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
21	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
22	#10596925	C₂×C₄	1	1	yes	characteristic
23	#10596925	C₂³	1	1	yes	characteristic
24	C₂²×D₃₇	C₁₆	1	1	yes	characteristic
25	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
26	C₂×Dic₃₇	C₁₆	1	1	yes	characteristic
27	C₄×D₃₇	C₁₆	1	1	yes	characteristic
28	C₄×D₃₇	C₁₆	1	1	yes	characteristic
29	C₄×D₃₇	C₂×C₈	1	1	yes	characteristic
30	C₄×D₃₇	C₂×C₈	1	1	yes	characteristic
31	C₈×C₃₇	C₂×C₈	1	1	yes	characteristic
32	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
33	#64436	C₂×C₈	1	1	yes	characteristic
34	#64436	C₂×C₈	1	1	yes	characteristic
35	C₂²×C₃₇	C₂×C₁₆	1	1	yes	characteristic
36	C₂×D₃₇	—	2	2	no	—
37	C₂×D₃₇	C₂×C₁₆	1	1	yes	characteristic
38	C₂×D₃₇	C₂×C₁₆	1	1	yes	characteristic
39	C₄×C₃₇	C₂×C₁₆	1	1	yes	characteristic
40	C₄×C₃₇	C₂²×C₈	1	1	yes	characteristic
41	Dic₃₇	C₂×C₁₆	1	1	yes	characteristic
42	Dic₃₇	C₂×C₁₆	1	1	yes	characteristic
43	C₂×M₆₄	—	37	1	no	maximal, Sylow
44	C₂×C₃₇	—	2	1	no	—
45	C₂×C₃₇	C₂²×C₁₆	1	1	yes	characteristic
46	D₃₇	—	2	1	no	—
47	D₃₇	M₆₄	1	2	yes	complemented
48	C₂²×C₁₆	—	37	1	no	—
49	M₆₄	—	37	2	no	—
50	M₆₄	—	37	2	no	—
51	C₂×C₃₂	—	37	2	no	—
52	C₃₇	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₈	—	37	1	no	—
54	C₂×C₁₆	—	37	1	no	—
55	C₂×C₁₆	—	37	1	no	—
56	C₂×C₁₆	—	37	1	no	—
57	C₂×C₁₆	—	37	1	no	—
58	C₂×C₁₆	—	37	1	no	—
59	C₂×C₁₆	#3866	1	1	yes	characteristic
60	C₃₂	—	37	4	no	—
61	C₂²×C₄	—	37	1	no	—
62	C₂×C₈	—	37	1	no	—
63	C₂×C₈	—	37	1	no	—
64	C₂×C₈	—	37	1	no	—
65	C₂×C₈	—	37	1	no	—
66	C₂×C₈	—	37	1	no	—
67	C₂×C₈	C₂×#3866	1	1	yes	characteristic
68	C₁₆	—	37	1	no	—
69	C₁₆	—	37	1	no	—
70	C₁₆	C₂×#3866	1	1	yes	characteristic
71	C₁₆	C₂×#3866	1	1	yes	characteristic
72	C₂³	—	37	1	no	—
73	C₂×C₄	—	37	1	no	—
74	C₂×C₄	—	37	1	no	—
75	C₂×C₄	—	37	1	no	—
76	C₂×C₄	—	37	1	no	—
77	C₂×C₄	—	37	1	no	—
78	C₂×C₄	D₃₇⋊C₈	1	1	yes	characteristic
79	C₈	—	37	1	no	—
80	C₈	—	37	1	no	—
81	C₈	D₃₇⋊C₈	1	1	yes	characteristic
82	C₈	C₂²×#3866	1	1	yes	characteristic
83	C₂²	—	37	1	no	—
84	C₂²	—	37	1	no	—
85	C₂²	—	74	2	no	—
86	C₂²	D₃₇⋊C₁₆	1	1	yes	characteristic
87	C₄	—	37	1	no	—
88	C₄	—	37	1	no	—
89	C₄	D₃₇⋊C₁₆	1	1	yes	characteristic
90	C₄	C₂×D₃₇⋊C₈	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	37	2	no	—
93	C₂	—	74	1	no	—
94	C₂	C₂×D₃₇⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂×#3866
commutator, socle	C₂×C₃₇	C₂²×C₁₆
Frattini	C₈	C₂²×#3866
Fitting	C₂×C₁₆×C₃₇	C₄
prime radical	C₂²×D₃₇	C₁₆
cosocle	#10596925	C₂³
hypercenter	C₂×C₁₆	#3866
hypocenter	C₃₇	C₂×M₆₄
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. #14558466	C₂	semidirect
2. #14558465	C₂	semidirect
3. D₃₇⋊C₃₂	C₂	semidirect
5. #11924586	C₂²	semidirect
47. D₃₇	M₆₄	semidirect
52. C₃₇	C₂×M₆₄	semidirect

Maximal subgroups

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

subgroup	index
#14558466	2
#14558465	2
D₃₇⋊C₃₂	2
C₂×C₁₆×D₃₇	2
C₂×M₆₄	37

Subgroups — D37⋊M64 #18011017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₇⋊M₆₄ #18011017