Subgroups — #18002988

Order 4736.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557424	C₂	1	7	yes	maximal
2	#14557417	C₂	1	7	yes	maximal, complemented
3	C₄³×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10596936	C₂²	1	7	yes	—
5	C₂×#10596938	C₂²	1	7	yes	—
6	#11924443	C₂²	1	14	yes	—
7	C₂×C₄²×C₃₇	C₂²	1	7	yes	—
8	C₂³×D₃₇	C₂³	1	1	yes	characteristic
9	C₂²×C₄×C₃₇	C₂³	1	7	yes	—
10	C₂²×Dic₃₇	C₂³	1	7	yes	—
11	C₄²×C₃₇	—	2	14	no	—
12	#10596938	—	2	14	no	—
13	#10596936	—	2	14	no	—
14	C₂³×C₃₇	C₂⁴	1	1	yes	characteristic
15	C₂²×D₃₇	—	2	7	no	—
16	C₂×C₄×C₃₇	—	2	14	no	—
17	C₂×C₄×C₃₇	#41	1	14	yes	—
18	C₂×Dic₃₇	—	2	14	no	—
19	C₂×Dic₃₇	—	2	7	no	—
20	C₂²×C₃₇	C₂×#41	1	7	yes	—
21	C₂×D₃₇	—	4	7	no	—
22	C₄×C₃₇	—	2	14	no	—
23	Dic₃₇	—	4	7	no	—
24	#2866	—	37	1	no	maximal, Sylow
25	C₂×C₃₇	#529	1	7	yes	—
26	D₃₇	—	8	1	no	—
27	#388	—	37	7	no	—
28	#387	—	37	7	no	—
29	C₄³	D₃₇	1	1	yes	characteristic, complemented
30	C₃₇	#2866	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₄⋊C₄	—	37	7	no	—
32	C₂×C₂²⋊C₄	—	37	7	no	—
33	C₂×C₄²	C₂×D₃₇	1	7	yes	—
34	#95	—	37	14	no	—
35	C₂⁴	—	37	1	no	—
36	C₂²×C₄	—	37	7	no	—
37	C₂²×C₄	C₂²×D₃₇	1	7	yes	—
38	C₄⋊C₄	—	74	14	no	—
39	C₂²⋊C₄	—	74	14	no	—
40	C₄²	—	2	14	no	—
41	C₂³	—	74	7	no	—
42	C₂³	C₂³×D₃₇	1	1	yes	characteristic
43	C₂×C₄	—	2	14	no	—
44	C₂×C₄	—	74	7	no	—
45	C₂×C₄	—	74	14	no	—
46	C₂×C₄	#10596962	1	14	yes	—
47	C₂²	—	148	7	no	—
48	C₂²	C₂×#10596962	1	7	yes	—
49	C₄	—	2	14	no	—
50	C₄	—	148	7	no	—
51	C₂	—	296	1	no	—
52	C₂	#14558067	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₃₇
commutator, socle, cosocle	C₂³×C₃₇	C₂⁴
Fitting	C₄³×C₃₇	C₂
prime radical	C₂³×D₃₇	C₂³
hypercenter	C₄³	D₃₇
hypocenter	C₃₇	#2866
LCS	G ▷ C₂³×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
2. #14557417	C₂	semidirect
3. C₄³×C₃₇	C₂	semidirect
29. C₄³	D₃₇	semidirect
30. C₃₇	#2866	semidirect

Maximal subgroups

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

subgroup	index
#14557424	2
#14557417	2
C₄³×C₃₇	2
#2866	37