Subgroups — #17994750

Order 4736.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#64436	C₂	1	6	yes	maximal
2	C₃₇×#376	C₂	1	1	yes	maximal, characteristic
3	C₂²×#64436	C₂²	1	4	yes	—
4	C₄⋊#64436	—	2	12	no	—
5	C₂×C₄²×C₃₇	C₂²	1	3	yes	—
6	#95×C₃₇	C₄	1	4	yes	—
7	C₂²×C₄×C₃₇	C₂×C₄	1	6	yes	—
8	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
9	C₄²×C₃₇	D₄	1	6	yes	—
10	C₄²×C₃₇	Q₈	1	6	yes	—
11	C₂×#64436	—	2	12	no	—
12	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₄×C₃₇	—	2	12	no	—
14	C₂×C₄×C₃₇	C₄⋊C₄	1	12	yes	—
15	C₂×C₄×C₃₇	C₂×D₄	1	3	yes	—
16	C₂×C₄×C₃₇	C₂×Q₈	1	3	yes	—
17	#64436	—	4	4	no	—
18	C₂²×C₃₇	C₂×C₄⋊C₄	1	3	yes	—
19	C₂²×C₃₇	#131	1	4	yes	—
20	C₄×C₃₇	—	2	12	no	—
21	C₄×C₃₇	#127	1	1	yes	characteristic
22	C₄×C₃₇	C₄⋊Q₈	1	3	yes	—
23	#1843	—	37	1	no	maximal, Sylow
24	C₂×C₃₇	#384	1	1	yes	characteristic
25	C₂×C₃₇	#424	1	6	yes	—
26	C₂×C₄⋊C₈	—	37	6	no	—
27	#376	D₃₇	1	1	yes	characteristic
28	C₃₇	#1843	1	1	yes	characteristic, complemented, Sylow
29	C₂²×C₈	—	37	4	no	—
30	C₂×C₄²	C₂×D₃₇	1	3	yes	—
31	C₄⋊C₈	—	74	12	no	—
32	#95	Dic₃₇	1	4	yes	—
33	C₂²×C₄	C₂×Dic₃₇	1	6	yes	—
34	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
35	C₂×C₈	—	74	12	no	—
36	C₄²	Dic₇₄	1	6	yes	—
37	C₄²	D₁₄₈	1	6	yes	—
38	C₂³	C₂²×Dic₃₇	1	1	yes	characteristic
39	C₂×C₄	—	2	12	no	—
40	C₂×C₄	C₄⋊Dic₃₇	1	12	yes	—
41	C₂×C₄	C₂×Dic₇₄	1	3	yes	—
42	C₂×C₄	C₂×D₁₄₈	1	3	yes	—
43	C₈	—	148	4	no	—
44	C₂²	C₂×C₄⋊Dic₃₇	1	3	yes	—
45	C₂²	#11924543	1	4	yes	—
46	C₄	—	2	12	no	—
47	C₄	#11924533	1	1	yes	characteristic
48	C₄	#11924536	1	3	yes	—
49	C₂	#14557403	1	1	yes	characteristic
50	C₂	#14557560	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₃₇
commutator, socle, prime radical	C₂³×C₃₇	C₂²×C₄
Fitting	C₃₇×#376	C₂
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	#376	D₃₇
hypocenter	C₃₇	#1843
LCS	G ▷ C₂³×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
28. C₃₇	#1843	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊#64436	2
C₃₇×#376	2
#1843	37