Subgroups — #18009707

Order 4736.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558465	C₂	1	2	yes	maximal
2	#14557309	C₂	1	1	yes	maximal, characteristic
3	#11924586	C₄	1	4	yes	complemented
4	C₂×#10596925	C₄	1	1	yes	characteristic
5	C₂×#10596925	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₃₇	C₄	1	1	yes	characteristic
7	C₂×C₈×C₃₇	C₈	1	1	yes	characteristic
8	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₃₇	C₈	1	1	yes	characteristic
10	#10596925	C₈	1	2	yes	—
11	#10596925	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₃₇	—	2	1	no	—
13	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
14	C₈×C₃₇	—	2	1	no	—
15	C₈×C₃₇	C₄²	1	1	yes	characteristic
16	C₈×C₃₇	C₂×C₈	1	1	yes	characteristic
17	C₂²×C₃₇	M₃₂	1	1	yes	characteristic
18	C₄×C₃₇	—	4	1	no	—
19	C₄×C₃₇	C₄×C₈	1	1	yes	characteristic
20	C₄×C₃₇	M₃₂	1	1	yes	characteristic
21	#1398	—	37	1	no	maximal, Sylow
22	C₂×C₃₇	—	2	1	no	—
23	C₂×C₃₇	#346	1	1	yes	characteristic
24	M₆₄	—	37	2	no	—
25	#346	—	37	1	no	—
26	C₃₇	#1398	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₆	—	37	1	no	—
28	C₂×C₁₆	—	37	1	no	—
29	C₄×C₈	#3866	1	1	yes	characteristic
30	C₃₂	—	37	4	no	—
31	C₂×C₈	#64438	1	1	yes	characteristic
32	C₂×C₈	C₂×#3866	1	1	yes	characteristic
33	C₄²	#64438	1	1	yes	characteristic
34	C₁₆	—	37	2	no	—
35	C₁₆	—	37	2	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	C₂×#64438	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	D₃₇⋊C₈	1	1	yes	characteristic
40	C₈	C₄×#3866	1	1	yes	characteristic
41	C₂²	#11924610	1	1	yes	characteristic
42	C₄	—	4	1	no	—
43	C₄	C₄×#64438	1	1	yes	characteristic
44	C₄	#11924610	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#14558421	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×#3866
commutator	C₄×C₃₇	C₄×C₈
Frattini	C₂×C₈	C₂×#3866
Fitting	C₄×C₈×C₃₇	C₄
socle	C₂×C₃₇	#346
prime radical	C₂²×C₃₇	M₃₂
cosocle	C₂×#10596925	C₂²
hypercenter	C₄×C₈	#3866
hypocenter	C₃₇	#1398
LCS	G ▷ C₄×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #11924586	C₄	semidirect
26. C₃₇	#1398	semidirect

Maximal subgroups

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

subgroup	index
#14558465	2
#14557309	2
#1398	37