Subgroups — C₄²×#64438 #18010248

Order 4736.

408 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#64438	C₂	1	6	yes	maximal
2	C₄²×Dic₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#64438	C₂²	1	4	yes	—
4	C₄×#64438	C₄	1	24	yes	direct product factor
5	C₂×C₄×Dic₃₇	C₄	1	3	yes	—
6	C₂×C₄×Dic₃₇	C₂²	1	3	yes	—
7	C₂×C₄²×C₃₇	C₄	1	1	yes	characteristic
8	C₂²×C₄×C₃₇	C₂×C₄	1	3	yes	—
9	C₂²×Dic₃₇	C₂×C₄	1	3	yes	—
10	C₂²×Dic₃₇	C₂³	1	1	yes	characteristic
11	C₂×#64438	C₂×C₄	1	24	yes	—
12	C₄²×C₃₇	C₈	1	4	yes	complemented
13	C₄×Dic₃₇	C₈	1	12	yes	complemented
14	C₄×Dic₃₇	C₂×C₄	1	12	yes	—
15	C₂³×C₃₇	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₄×C₃₇	C₄²	1	6	yes	—
17	C₂×C₄×C₃₇	C₂×C₈	1	6	yes	—
18	C₂×C₄×C₃₇	C₂×C₈	1	6	yes	—
19	C₂×Dic₃₇	C₄²	1	6	yes	—
20	C₂×Dic₃₇	C₂×C₈	1	12	yes	—
21	C₂×Dic₃₇	C₂²×C₄	1	6	yes	—
22	#64438	C₄²	1	16	yes	direct product factor
23	C₂²×C₃₇	C₂×C₄²	1	3	yes	—
24	C₂²×C₃₇	C₂²×C₈	1	1	yes	characteristic
25	C₂²×C₃₇	C₂²×C₈	1	3	yes	—
26	C₄×C₃₇	C₄×C₈	1	12	yes	complemented
27	Dic₃₇	C₄×C₈	1	12	yes	complemented
28	Dic₃₇	C₂×C₄²	1	4	yes	—
29	C₄²×C₈	—	37	1	no	maximal, Sylow
30	C₂×C₃₇	C₄³	1	1	yes	characteristic
31	C₂×C₃₇	C₂×C₄×C₈	1	3	yes	—
32	C₂×C₃₇	C₂×C₄×C₈	1	3	yes	—
33	C₂×C₄×C₈	—	37	6	no	—
34	C₄³	—	37	1	no	—
35	C₃₇	C₄²×C₈	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₈	—	37	4	no	—
37	C₂×C₄²	—	37	3	no	—
38	C₂×C₄²	—	37	3	no	—
39	C₂×C₄²	#3866	1	1	yes	characteristic
40	C₄×C₈	—	37	24	no	—
41	C₂²×C₄	—	37	3	no	—
42	C₂²×C₄	—	37	1	no	—
43	C₂²×C₄	C₂×#3866	1	3	yes	—
44	C₂×C₈	—	37	24	no	—
45	C₄²	—	37	12	no	—
46	C₄²	—	37	12	no	—
47	C₄²	#64438	1	4	yes	direct product factor
48	C₂³	C₂²×#3866	1	1	yes	characteristic
49	C₂×C₄	—	37	6	no	—
50	C₂×C₄	—	37	6	no	—
51	C₂×C₄	—	37	12	no	—
52	C₂×C₄	D₃₇⋊C₈	1	6	yes	—
53	C₂×C₄	C₄×#3866	1	6	yes	—
54	C₂×C₄	C₂×#64438	1	6	yes	—
55	C₈	—	37	16	no	—
56	C₂²	C₂×C₄×#3866	1	3	yes	—
57	C₂²	C₂²×#64438	1	1	yes	characteristic
58	C₂²	C₂×D₃₇⋊C₈	1	3	yes	—
59	C₄	—	37	4	no	—
60	C₄	—	37	12	no	—
61	C₄	C₄×#64438	1	12	yes	direct product factor
62	C₂	C₄²×#3866	1	1	yes	characteristic
63	C₂	C₂×C₄×#64438	1	3	yes	—
64	C₂	C₄×D₃₇⋊C₈	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₄²	#3866
commutator, hypocenter	C₃₇	C₄²×C₈
Frattini	C₂³	C₂²×#3866
Fitting	C₂×C₄²×C₃₇	C₄
socle, prime radical	C₂³×C₃₇	C₂²×C₄
cosocle	C₂²×Dic₃₇	C₂³
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
4. C₄×#64438	C₄	direct (N × H)
12. C₄²×C₃₇	C₈	semidirect
13. C₄×Dic₃₇	C₈	semidirect
22. #64438	C₄²	direct (N × H)
26. C₄×C₃₇	C₄×C₈	semidirect
27. Dic₃₇	C₄×C₈	semidirect
35. C₃₇	C₄²×C₈	semidirect
47. C₄²	#64438	direct (N × H)
61. C₄	C₄×#64438	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#64438	2
C₄²×Dic₃₇	2
C₄²×C₈	37

Subgroups — C42×#64438 #18010248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×#64438 #18010248