Subgroups — D₃₇⋊#108 #14558546

Order 2368.

106 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	#11924607	C₂	1	2	yes	maximal, complemented
3	#11924606	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×D₃₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×D₃₇	C₂²	1	1	yes	characteristic
6	#10596957	—	2	2	no	—
7	#10596953	C₂²	1	4	yes	—
8	D₃₇⋊C₈	—	2	2	no	—
9	C₂×C₈×C₃₇	C₄	1	1	yes	characteristic
10	C₂×#64436	C₄	1	1	yes	characteristic
11	C₈×D₃₇	C₄	1	1	yes	characteristic
12	C₈×D₃₇	C₄	1	1	yes	characteristic
13	C₈×D₃₇	C₂²	1	1	yes	characteristic
14	C₈×D₃₇	C₂²	1	1	yes	characteristic
15	C₂²×D₃₇	Q₈	1	1	yes	characteristic
16	C₂×C₄×C₃₇	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₃₇	D₄	1	1	yes	characteristic
18	C₄×D₃₇	C₂×C₄	1	1	yes	characteristic
19	C₄×D₃₇	D₄	1	1	yes	characteristic
20	C₄×D₃₇	Q₈	1	1	yes	characteristic
21	C₄×D₃₇	C₂³	1	1	yes	characteristic
22	#64438	—	2	4	no	—
23	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
24	C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
25	#64436	C₂×C₄	1	1	yes	characteristic
26	#64436	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₃₇	C₄⋊C₄	1	1	yes	characteristic
28	C₂×D₃₇	—	2	2	no	—
29	C₂×D₃₇	C₄⋊C₄	1	1	yes	characteristic
30	C₂×D₃₇	C₂×Q₈	1	1	yes	characteristic
31	C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
32	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
33	Dic₃₇	C₄⋊C₄	1	1	yes	characteristic
34	Dic₃₇	C₂×D₄	1	1	yes	characteristic
35	C₂×C₃₇	—	2	1	no	—
36	C₂×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
37	D₃₇	—	2	1	no	—
38	D₃₇	#108	1	2	yes	complemented
39	C₂×#108	—	37	1	no	maximal, Sylow
40	C₃₇	C₂×#108	1	1	yes	characteristic, complemented, Sylow
41	C₂×M₁₆	—	37	2	no	—
42	C₂²×C₈	—	37	1	no	—
43	#108	—	37	2	no	—
44	#108	—	37	2	no	—
45	C₂²×C₄	—	37	1	no	—
46	M₁₆	—	37	4	no	—
47	M₁₆	—	74	2	no	—
48	C₂×C₈	—	37	1	no	—
49	C₂×C₈	—	37	1	no	—
50	C₂×C₈	—	37	1	no	—
51	C₂×C₈	—	37	1	no	—
52	C₂×C₈	—	37	1	no	—
53	C₂×C₈	—	74	2	no	—
54	C₂×C₈	#3866	1	1	yes	characteristic
55	C₂³	—	37	1	no	—
56	C₂×C₄	—	37	1	no	—
57	C₂×C₄	—	37	1	no	—
58	C₂×C₄	—	37	1	no	—
59	C₂×C₄	—	37	1	no	—
60	C₂×C₄	—	37	1	no	—
61	C₂×C₄	C₂×#3866	1	1	yes	characteristic
62	C₈	—	37	1	no	—
63	C₈	—	37	1	no	—
64	C₈	—	74	4	no	—
65	C₈	C₂×#3866	1	1	yes	characteristic
66	C₈	C₂×#3866	1	1	yes	characteristic
67	C₂²	—	37	1	no	—
68	C₂²	—	37	1	no	—
69	C₂²	—	74	2	no	—
70	C₂²	C₄⋊#3866	1	1	yes	characteristic
71	C₄	—	37	1	no	—
72	C₄	—	37	1	no	—
73	C₄	C₄⋊#3866	1	1	yes	characteristic
74	C₄	C₂²×#3866	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	37	2	no	—
77	C₂	—	74	1	no	—
78	C₂	C₂×C₄⋊#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄⋊#3866
commutator	C₄×C₃₇	C₂²×C₄
Frattini	C₄	C₂²×#3866
Fitting	C₂×C₈×C₃₇	C₄
socle	C₂×C₃₇	C₂×C₄⋊C₄
prime radical	C₂²×D₃₇	Q₈
cosocle	C₄×D₃₇	C₂³
hypercenter	C₂×C₈	#3866
hypocenter	C₃₇	C₂×#108
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #11924607	C₂	semidirect
3. #11924606	C₂	semidirect
38. D₃₇	#108	semidirect
40. C₃₇	C₂×#108	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
#11924607	2
#11924606	2
C₂×C₈×D₃₇	2
C₂×#108	37

Subgroups — D37⋊#108 #14558546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₇⋊#108 #14558546