Subgroups — D₃₇⋊#101 #14558518

Order 2368.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₇⋊M₁₆	C₂	1	2	yes	maximal
2	#11924597	C₂	1	4	yes	maximal, complemented
3	C₂×Q₈×D₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₃₇	C₄	1	1	yes	characteristic
5	Q₈×D₃₇	—	2	2	no	—
6	Q₈×D₃₇	—	2	2	no	—
7	C₂×C₄×D₃₇	C₄	1	2	yes	—
8	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
9	C₂×Dic₇₄	C₄	1	1	yes	characteristic
10	C₂×Dic₇₄	C₂²	1	2	yes	—
11	#10596957	C₂²	1	4	yes	—
12	#10596953	—	2	2	no	—
13	D₃₇⋊C₈	—	2	2	no	—
14	C₂²×D₃₇	C₂×C₄	1	1	yes	characteristic
15	Q₈×C₃₇	—	2	2	no	—
16	C₂×C₄×C₃₇	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₃₇	C₂×C₄	1	2	yes	—
19	C₂×Dic₃₇	C₂³	1	1	yes	characteristic
20	C₄×D₃₇	—	2	2	no	—
21	C₄×D₃₇	—	2	2	no	—
22	C₄×D₃₇	D₄	1	2	yes	—
23	C₄×D₃₇	D₄	1	2	yes	—
24	Dic₇₄	—	2	2	no	—
25	Dic₇₄	—	2	4	no	—
26	#64438	—	2	4	no	—
27	C₂²×C₃₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×D₃₇	—	2	2	no	—
29	C₂×D₃₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×D₃₇	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×C₃₇	—	2	2	no	—
32	C₄×C₃₇	C₂²⋊C₄	1	2	yes	—
33	Dic₃₇	—	2	2	no	—
34	Dic₃₇	C₂×D₄	1	2	yes	—
35	C₂×C₃₇	—	2	1	no	—
36	C₂×C₃₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
37	D₃₇	—	2	1	no	—
38	D₃₇	#101	1	2	yes	complemented
39	C₂×#101	—	37	1	no	maximal, Sylow
40	C₃₇	C₂×#101	1	1	yes	characteristic, complemented, Sylow
41	C₂²×Q₈	—	37	1	no	—
42	C₂×M₁₆	—	37	2	no	—
43	#101	—	37	4	no	—
44	C₂×Q₈	—	37	2	no	—
45	C₂×Q₈	—	37	1	no	—
46	C₂×Q₈	—	74	2	no	—
47	C₂×Q₈	—	74	2	no	—
48	C₂×Q₈	#3866	1	1	yes	characteristic
49	C₂²×C₄	—	37	1	no	—
50	C₂²×C₄	—	37	2	no	—
51	M₁₆	—	37	4	no	—
52	M₁₆	—	74	2	no	—
53	C₂×C₈	—	74	2	no	—
54	C₂³	—	37	1	no	—
55	Q₈	—	2	2	no	—
56	Q₈	—	74	4	no	—
57	Q₈	—	74	2	no	—
58	C₂×C₄	—	37	1	no	—
59	C₂×C₄	—	37	2	no	—
60	C₂×C₄	—	37	2	no	—
61	C₂×C₄	—	37	2	no	—
62	C₂×C₄	—	74	2	no	—
63	C₂×C₄	—	74	2	no	—
64	C₂×C₄	C₂×#3866	1	2	yes	—
65	C₂×C₄	C₂×#3866	1	1	yes	characteristic
66	C₈	—	74	4	no	—
67	C₂²	—	37	1	no	—
68	C₂²	—	37	1	no	—
69	C₂²	—	74	2	no	—
70	C₂²	C₂²×#3866	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	—	37	2	no	—
73	C₄	—	74	2	no	—
74	C₄	C₂²⋊#3866	1	2	yes	—
75	C₂	—	2	1	no	—
76	C₂	—	37	2	no	—
77	C₂	—	74	1	no	—
78	C₂	C₂×C₂²⋊#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊#3866
commutator	C₂²×C₃₇	C₂²×C₄
Frattini	C₂²	C₂²×#3866
Fitting	C₂×Q₈×C₃₇	C₄
socle	C₂×C₃₇	C₂×C₂²⋊C₄
prime radical	C₂²×D₃₇	C₂×C₄
cosocle	C₂×Dic₃₇	C₂³
hypercenter	C₂×Q₈	#3866
hypocenter	C₃₇	C₂×#101
LCS	G ▷ C₂²×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #11924597	C₂	semidirect
38. D₃₇	#101	semidirect
40. C₃₇	C₂×#101	semidirect

Maximal subgroups

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

subgroup	index
D₃₇⋊M₁₆	2
#11924597	2
C₂×Q₈×D₃₇	2
C₂×#101	37

Subgroups — D37⋊#101 #14558518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₇⋊#101 #14558518