Subgroups — #17994345

Order 4736.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924447	C₂	1	2	yes	maximal
2	#14557288	C₂	1	4	yes	maximal
3	C₄³×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#64436	C₂²	1	4	yes	—
5	#11924447	C₄	1	8	yes	complemented
6	C₂×C₄²×C₃₇	C₄	1	4	yes	—
7	C₂×C₄²×C₃₇	C₂²	1	2	yes	—
8	C₂×C₄²×C₃₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄×C₃₇	C₂×C₄	1	2	yes	—
10	C₂²×C₄×C₃₇	C₂×C₄	1	4	yes	—
11	C₂²×C₄×C₃₇	C₂³	1	1	yes	characteristic
12	C₄²×C₃₇	—	2	8	no	—
13	C₄²×C₃₇	—	2	4	no	—
14	C₄²×C₃₇	C₂×C₄	1	4	yes	—
15	C₂×#64436	—	2	8	no	—
16	C₂×#64436	C₂×C₄	1	8	yes	—
17	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₄×C₃₇	—	2	4	no	—
19	C₂×C₄×C₃₇	—	2	4	no	—
20	C₂×C₄×C₃₇	—	2	4	no	—
21	C₂×C₄×C₃₇	C₄²	1	4	yes	—
22	C₂×C₄×C₃₇	M₁₆	1	8	yes	—
23	C₂×C₄×C₃₇	C₂²×C₄	1	2	yes	—
24	C₂×C₄×C₃₇	#41	1	4	yes	—
25	#64436	—	2	8	no	—
26	C₂²×C₃₇	C₂×C₄²	1	1	yes	characteristic
27	C₂²×C₃₇	#117	1	2	yes	—
28	C₂²×C₃₇	C₂×M₁₆	1	4	yes	—
29	C₄×C₃₇	—	2	4	no	—
30	C₄×C₃₇	—	2	8	no	—
31	C₄×C₃₇	#117	1	4	yes	—
32	#1745	—	37	1	no	maximal, Sylow
33	C₂×C₃₇	#376	1	1	yes	characteristic
34	C₂×C₃₇	C₄×M₁₆	1	2	yes	—
35	C₂×C₃₇	#432	1	4	yes	—
36	C₂×#97	—	37	2	no	—
37	C₄³	D₃₇	1	1	yes	characteristic
38	#336	—	37	4	no	—
39	C₃₇	#1745	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₈	—	37	4	no	—
41	C₂×C₄²	Dic₃₇	1	4	yes	—
42	C₂×C₄²	C₂×D₃₇	1	2	yes	—
43	C₂×C₄²	C₂×D₃₇	1	1	yes	characteristic
44	#97	—	37	8	no	—
45	C₂²×C₄	C₂×Dic₃₇	1	4	yes	—
46	C₂²×C₄	C₂×Dic₃₇	1	2	yes	—
47	C₂²×C₄	C₂²×D₃₇	1	1	yes	characteristic
48	C₂×C₈	—	37	8	no	—
49	C₂×C₈	—	74	8	no	—
50	C₄²	—	2	8	no	—
51	C₄²	—	2	4	no	—
52	C₄²	C₄×D₃₇	1	4	yes	—
53	C₂³	C₂²×Dic₃₇	1	1	yes	characteristic
54	C₂×C₄	—	2	4	no	—
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	2	4	no	—
57	C₂×C₄	#10596934	1	8	yes	—
58	C₂×C₄	C₄×Dic₃₇	1	4	yes	—
59	C₂×C₄	C₂×C₄×D₃₇	1	2	yes	—
60	C₂×C₄	#10596962	1	4	yes	—
61	C₈	—	74	8	no	—
62	C₂²	C₂×C₄×Dic₃₇	1	1	yes	characteristic
63	C₂²	#11924495	1	2	yes	—
64	C₂²	C₂×#10596934	1	4	yes	—
65	C₄	—	2	4	no	—
66	C₄	—	2	8	no	—
67	C₄	#11924493	1	4	yes	—
68	C₂	#14557379	1	1	yes	characteristic
69	C₂	C₄×#10596934	1	2	yes	—
70	C₂	#14557590	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₃₇
commutator	C₂²×C₃₇	C₂×C₄²
Fitting	C₄³×C₃₇	C₂
socle, prime radical	C₂³×C₃₇	C₂²×C₄
cosocle	C₂²×C₄×C₃₇	C₂³
hypercenter	C₄³	D₃₇
hypocenter	C₃₇	#1745
LCS	G ▷ C₂²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

Complements

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

N	H ≅ G/N	type
5. #11924447	C₄	semidirect
39. C₃₇	#1745	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11924447	2
#14557288	2
C₄³×C₃₇	2
#1745	37