Subgroups — #18010523

Order 4736.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558399	C₂	1	6	yes	maximal
2	C₄²×Dic₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#64438	C₂²	1	4	yes	—
4	C₂×C₄×Dic₃₇	C₄	1	3	yes	—
5	C₂×C₄×Dic₃₇	C₂²	1	3	yes	—
6	C₂×C₄²×C₃₇	C₄	1	1	yes	characteristic
7	C₂²×C₄×C₃₇	C₂×C₄	1	3	yes	—
8	C₂²×Dic₃₇	C₂×C₄	1	3	yes	—
9	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
10	C₂×#64438	—	2	12	no	—
11	C₄²×C₃₇	C₈	1	4	yes	complemented
12	C₄×Dic₃₇	—	2	6	no	—
13	C₄×Dic₃₇	—	2	6	no	—
14	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
15	C₂×C₄×C₃₇	—	2	3	no	—
16	C₂×C₄×C₃₇	—	2	3	no	—
17	C₂×C₄×C₃₇	C₂×C₈	1	6	yes	—
18	C₂×Dic₃₇	—	2	3	no	—
19	C₂×Dic₃₇	—	2	3	no	—
20	C₂×Dic₃₇	M₁₆	1	6	yes	—
21	C₂×Dic₃₇	#41	1	6	yes	—
22	#64438	—	4	4	no	—
23	C₂²×C₃₇	#117	1	3	yes	—
24	C₂²×C₃₇	C₂²×C₈	1	1	yes	characteristic
25	C₂²×C₃₇	C₂×M₁₆	1	3	yes	—
26	C₄×C₃₇	—	2	6	no	—
27	Dic₃₇	—	2	6	no	—
28	Dic₃₇	#126	1	4	yes	—
29	#1839	—	37	1	no	maximal, Sylow
30	C₂×C₃₇	#383	1	1	yes	characteristic
31	C₂×C₃₇	#431	1	3	yes	—
32	C₂×C₃₇	#432	1	3	yes	—
33	C₄³	—	37	1	no	—
34	#336	—	37	6	no	—
35	C₃₇	#1839	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₈	—	37	4	no	—
37	C₂×C₄²	—	37	3	no	—
38	C₂×C₄²	—	37	3	no	—
39	C₂×C₄²	#3866	1	1	yes	characteristic
40	C₂²×C₄	—	37	1	no	—
41	C₂²×C₄	—	37	3	no	—
42	C₂²×C₄	C₂×#3866	1	3	yes	—
43	C₂×C₈	—	74	12	no	—
44	C₄²	—	74	6	no	—
45	C₄²	—	74	6	no	—
46	C₄²	#64438	1	4	yes	complemented
47	C₂³	C₂²×#3866	1	1	yes	characteristic
48	C₂×C₄	—	2	3	no	—
49	C₂×C₄	—	2	3	no	—
50	C₂×C₄	—	37	6	no	—
51	C₂×C₄	—	37	6	no	—
52	C₂×C₄	—	74	3	no	—
53	C₂×C₄	—	74	3	no	—
54	C₂×C₄	C₂×#64438	1	6	yes	—
55	C₈	—	148	4	no	—
56	C₂²	#11924615	1	3	yes	—
57	C₂²	C₂²×#64438	1	1	yes	characteristic
58	C₂²	D₃₇⋊M₁₆	1	3	yes	—
59	C₄	—	2	6	no	—
60	C₄	—	37	4	no	—
61	C₄	—	74	6	no	—
62	C₂	#14558478	1	1	yes	characteristic
63	C₂	#14558549	1	3	yes	—
64	C₂	#14558556	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#3866
commutator	C₂²×C₃₇	C₂²×C₈
Fitting	C₂×C₄²×C₃₇	C₄
socle, prime radical	C₂³×C₃₇	C₂²×C₄
cosocle	C₂²×Dic₃₇	C₂³
hypercenter	C₂×C₄²	#3866
hypocenter	C₃₇	#1839
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
11. C₄²×C₃₇	C₈	semidirect
35. C₃₇	#1839	semidirect
46. C₄²	#64438	semidirect

Maximal subgroups

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

subgroup	index
#14558399	2
C₄²×Dic₃₇	2
#1839	37