Subgroups — C₄²×#6597 #16819174

Order 3712.

408 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6597	C₂	1	6	yes	maximal
2	C₄³×C₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₂₉	C₄	1	4	yes	—
4	C₂×C₄²×C₂₉	C₂²	1	3	yes	—
5	C₂²×#6597	C₂²	1	4	yes	—
6	C₄×#6597	C₄	1	24	yes	direct product factor
7	C₂²×C₄×C₂₉	C₂×C₄	1	6	yes	—
8	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
9	C₄²×C₂₉	C₈	1	16	yes	complemented
10	C₄²×C₂₉	C₂×C₄	1	12	yes	—
11	C₂×#6597	C₂×C₄	1	24	yes	—
12	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₄×C₂₉	C₄²	1	12	yes	—
14	C₂×C₄×C₂₉	C₂×C₈	1	24	yes	—
15	C₂×C₄×C₂₉	C₂²×C₄	1	6	yes	—
16	#6597	C₄²	1	16	yes	direct product factor
17	C₄²×C₈	—	29	1	no	maximal, Sylow
18	C₂²×C₂₉	C₂×C₄²	1	3	yes	—
19	C₂²×C₂₉	C₂²×C₈	1	4	yes	—
20	C₄×C₂₉	C₄×C₈	1	24	yes	complemented
21	C₄×C₂₉	C₂×C₄²	1	4	yes	—
22	C₂×C₄×C₈	—	29	6	no	—
23	C₄³	D₂₉	1	1	yes	characteristic
24	C₂×C₂₉	C₄³	1	1	yes	characteristic
25	C₂×C₂₉	C₂×C₄×C₈	1	6	yes	—
26	C₂²×C₈	—	29	4	no	—
27	C₂×C₄²	Dic₂₉	1	4	yes	—
28	C₂×C₄²	C₂×D₂₉	1	3	yes	—
29	C₄×C₈	—	29	24	no	—
30	C₂₉	C₄²×C₈	1	1	yes	characteristic, complemented, Sylow
31	C₂²×C₄	C₂×Dic₂₉	1	6	yes	—
32	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
33	C₂×C₈	—	29	24	no	—
34	C₄²	#6597	1	16	yes	direct product factor
35	C₄²	C₄×D₂₉	1	12	yes	—
36	C₂³	C₂²×Dic₂₉	1	1	yes	characteristic
37	C₂×C₄	C₂×#6597	1	24	yes	—
38	C₂×C₄	C₄×Dic₂₉	1	12	yes	—
39	C₂×C₄	C₂×C₄×D₂₉	1	6	yes	—
40	C₈	—	29	16	no	—
41	C₂²	C₂²×#6597	1	4	yes	—
42	C₂²	C₂×C₄×Dic₂₉	1	3	yes	—
43	C₄	C₄×#6597	1	24	yes	direct product factor
44	C₄	C₄²×D₂₉	1	4	yes	—
45	C₂	C₄²×Dic₂₉	1	1	yes	characteristic
46	C₂	C₂×C₄×#6597	1	6	yes	—

	subgroup	G/H
center, hypercenter	C₄³	D₂₉
commutator, hypocenter	C₂₉	C₄²×C₈
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₄³×C₂₉	C₂
socle, prime radical	C₂³×C₂₉	C₂²×C₄
cosocle	C₂²×C₄×C₂₉	C₂³
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₄³

Complements

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

N	H ≅ G/N	type
6. C₄×#6597	C₄	direct (N × H)
9. C₄²×C₂₉	C₈	semidirect
16. #6597	C₄²	direct (N × H)
20. C₄×C₂₉	C₄×C₈	semidirect
30. C₂₉	C₄²×C₈	semidirect
34. C₄²	#6597	direct (N × H)
43. C₄	C₄×#6597	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×#6597	2
C₄³×C₂₉	2
C₄²×C₈	29

Subgroups — C42×#6597 #16819174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×#6597 #16819174