Subgroups — #17992895

Order 4736.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557584	C₂	1	3	yes	maximal
2	#14557255	C₂	1	3	yes	maximal, complemented
3	C₈²×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄²×D₃₇	C₂²	1	1	yes	characteristic
5	#11924465	C₄	1	6	yes	—
6	#11924448	C₄	1	6	yes	—
7	C₄×#64436	C₂²	1	3	yes	—
8	C₄×C₈×C₃₇	C₂²	1	3	yes	—
9	C₂×C₄×D₃₇	C₂×C₄	1	3	yes	—
10	C₂×C₈×C₃₇	C₂×C₄	1	6	yes	—
11	C₄²×C₃₇	C₂³	1	1	yes	characteristic
12	C₄×Dic₃₇	C₂×C₄	1	3	yes	—
13	C₂×#64436	C₂×C₄	1	6	yes	—
14	C₂²×D₃₇	C₄²	1	1	yes	characteristic
15	C₂×C₄×C₃₇	C₂²×C₄	1	3	yes	—
16	C₂×Dic₃₇	C₄²	1	3	yes	—
17	C₄×D₃₇	—	2	6	no	—
18	C₈×C₃₇	—	2	6	no	—
19	#64436	—	2	6	no	—
20	C₂²×C₃₇	C₂×C₄²	1	1	yes	characteristic
21	C₂×D₃₇	—	2	3	no	—
22	C₄×C₃₇	#131	1	6	yes	—
23	Dic₃₇	—	2	3	no	—
24	#1454	—	37	1	no	maximal, Sylow
25	C₂×C₃₇	#405	1	3	yes	—
26	D₃₇	—	4	1	no	—
27	#431	—	37	3	no	—
28	#322	—	37	3	no	—
29	C₈²	D₃₇	1	1	yes	characteristic, complemented
30	C₃₇	#1454	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₄²	—	37	1	no	—
32	C₄⋊C₈	—	37	6	no	—
33	C₂²⋊C₈	—	37	6	no	—
34	C₄×C₈	—	37	3	no	—
35	C₄×C₈	C₂×D₃₇	1	3	yes	—
36	C₂²×C₄	—	37	3	no	—
37	C₂×C₈	—	37	6	no	—
38	C₂×C₈	C₄×D₃₇	1	6	yes	—
39	C₄²	—	37	3	no	—
40	C₄²	C₂²×D₃₇	1	1	yes	characteristic
41	C₂³	—	37	1	no	—
42	C₂×C₄	—	37	3	no	—
43	C₂×C₄	—	74	6	no	—
44	C₂×C₄	C₂×C₄×D₃₇	1	3	yes	—
45	C₈	—	2	6	no	—
46	C₈	—	74	6	no	—
47	C₂²	—	74	3	no	—
48	C₂²	C₄²×D₃₇	1	1	yes	characteristic
49	C₄	—	74	3	no	—
50	C₄	#11924542	1	6	yes	—
51	C₂	—	148	1	no	—
52	C₂	#14557487	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₃₇
commutator, socle	C₂²×C₃₇	C₂×C₄²
Fitting	C₈²×C₃₇	C₂
prime radical	C₂²×D₃₇	C₄²
cosocle	C₄²×C₃₇	C₂³
hypercenter	C₈²	D₃₇
hypocenter	C₃₇	#1454
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. #14557255	C₂	semidirect
3. C₈²×C₃₇	C₂	semidirect
29. C₈²	D₃₇	semidirect
30. C₃₇	#1454	semidirect

Maximal subgroups

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

subgroup	index
#14557584	2
#14557255	2
C₈²×C₃₇	2
#1454	37