Subgroups — #18009756

Order 4736.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558465	C₂	1	2	yes	maximal
2	C₁₆×Dic₃₇	C₂	1	1	yes	maximal, characteristic
3	#11924586	—	2	2	no	—
4	C₂×#10596925	C₂²	1	1	yes	characteristic
5	C₈×Dic₃₇	C₄	1	1	yes	characteristic
6	C₂×C₁₆×C₃₇	C₄	1	1	yes	characteristic
7	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
8	C₄×Dic₃₇	C₈	1	1	yes	characteristic
9	C₂×#64436	C₈	1	1	yes	characteristic
10	C₁₆×C₃₇	—	2	1	no	—
11	#10596925	D₄	1	1	yes	characteristic
12	#10596925	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
14	C₂×Dic₃₇	—	2	1	no	—
15	C₈×C₃₇	C₄⋊C₄	1	1	yes	characteristic
16	C₈×C₃₇	M₁₆	1	1	yes	characteristic
17	#64436	C₁₆	1	2	yes	—
18	C₂²×C₃₇	M₃₂	1	1	yes	characteristic
19	C₄×C₃₇	C₄⋊C₈	1	1	yes	characteristic
20	C₄×C₃₇	C₂×C₁₆	1	1	yes	characteristic
21	Dic₃₇	—	2	2	no	—
22	#1422	—	37	1	no	maximal, Sylow
23	C₂×C₃₇	—	2	1	no	—
24	C₂×C₃₇	C₄⋊C₁₆	1	1	yes	characteristic
25	M₆₄	—	37	2	no	—
26	C₄×C₁₆	—	37	1	no	—
27	C₃₇	#1422	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₁₆	—	37	1	no	—
29	C₂×C₁₆	#3866	1	1	yes	characteristic
30	C₄×C₈	—	37	1	no	—
31	C₃₂	—	74	2	no	—
32	C₂×C₈	—	37	1	no	—
33	C₂×C₈	C₂×#3866	1	1	yes	characteristic
34	C₄²	—	37	1	no	—
35	C₁₆	—	2	1	no	—
36	C₁₆	—	37	1	no	—
37	C₁₆	—	37	1	no	—
38	C₂×C₄	—	74	1	no	—
39	C₂×C₄	D₃₇⋊C₈	1	1	yes	characteristic
40	C₈	—	37	2	no	—
41	C₈	C₄⋊#3866	1	1	yes	characteristic
42	C₈	#10596957	1	1	yes	characteristic
43	C₂²	#11924611	1	1	yes	characteristic
44	C₄	—	74	2	no	—
45	C₄	#11924603	1	1	yes	characteristic
46	C₄	D₃₇⋊C₁₆	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#14558454	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄⋊#3866
commutator	C₄×C₃₇	C₂×C₁₆
Frattini	C₂×C₈	C₂×#3866
Fitting	C₂×C₁₆×C₃₇	C₄
socle	C₂×C₃₇	C₄⋊C₁₆
prime radical	C₂²×C₃₇	M₃₂
cosocle	C₂×#10596925	C₂²
hypercenter	C₂×C₁₆	#3866
hypocenter	C₃₇	#1422
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
27. C₃₇	#1422	semidirect

Maximal subgroups

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

subgroup	index
#14558465	2
C₁₆×Dic₃₇	2
#1422	37