Subgroups — C₄²×#6599 #16835144

Order 3712.

408 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6599	C₂	1	6	yes	maximal
2	C₄²×Dic₂₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×#6599	C₂²	1	4	yes	—
4	C₂×C₄²×C₂₉	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₂₉	C₄	1	3	yes	—
6	C₂×C₄×Dic₂₉	C₂²	1	3	yes	—
7	C₄×#6599	C₄	1	24	yes	direct product factor
8	C₂²×C₄×C₂₉	C₂×C₄	1	3	yes	—
9	C₂²×Dic₂₉	C₂×C₄	1	3	yes	—
10	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
11	C₂×#6599	C₂×C₄	1	24	yes	—
12	C₄²×C₂₉	C₈	1	4	yes	complemented
13	C₄×Dic₂₉	C₈	1	12	yes	complemented
14	C₄×Dic₂₉	C₂×C₄	1	12	yes	—
15	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₄×C₂₉	C₄²	1	6	yes	—
17	C₂×C₄×C₂₉	C₂×C₈	1	6	yes	—
18	C₂×C₄×C₂₉	C₂×C₈	1	6	yes	—
19	C₂×Dic₂₉	C₄²	1	6	yes	—
20	C₂×Dic₂₉	C₂×C₈	1	12	yes	—
21	C₂×Dic₂₉	C₂²×C₄	1	6	yes	—
22	#6599	C₄²	1	16	yes	direct product factor
23	C₄²×C₈	—	29	1	no	maximal, Sylow
24	C₂²×C₂₉	C₂×C₄²	1	3	yes	—
25	C₂²×C₂₉	C₂²×C₈	1	3	yes	—
26	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
27	C₄×C₂₉	C₄×C₈	1	12	yes	complemented
28	Dic₂₉	C₄×C₈	1	12	yes	complemented
29	Dic₂₉	C₂×C₄²	1	4	yes	—
30	C₂×C₄×C₈	—	29	6	no	—
31	C₄³	—	29	1	no	—
32	C₂×C₂₉	C₄³	1	1	yes	characteristic
33	C₂×C₂₉	C₂×C₄×C₈	1	3	yes	—
34	C₂×C₂₉	C₂×C₄×C₈	1	3	yes	—
35	C₂²×C₈	—	29	4	no	—
36	C₂×C₄²	—	29	3	no	—
37	C₂×C₄²	—	29	3	no	—
38	C₂×C₄²	#1181	1	1	yes	characteristic
39	C₄×C₈	—	29	24	no	—
40	C₂₉	C₄²×C₈	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₄	—	29	1	no	—
42	C₂²×C₄	—	29	3	no	—
43	C₂²×C₄	C₂×#1181	1	3	yes	—
44	C₂×C₈	—	29	24	no	—
45	C₄²	—	29	12	no	—
46	C₄²	—	29	12	no	—
47	C₄²	#6599	1	4	yes	direct product factor
48	C₂³	C₂²×#1181	1	1	yes	characteristic
49	C₂×C₄	—	29	12	no	—
50	C₂×C₄	—	29	6	no	—
51	C₂×C₄	—	29	6	no	—
52	C₂×C₄	D₂₉⋊C₈	1	6	yes	—
53	C₂×C₄	C₄×#1181	1	6	yes	—
54	C₂×C₄	C₂×#6599	1	6	yes	—
55	C₈	—	29	16	no	—
56	C₂²	C₂×D₂₉⋊C₈	1	3	yes	—
57	C₂²	C₂×C₄×#1181	1	3	yes	—
58	C₂²	C₂²×#6599	1	1	yes	characteristic
59	C₄	—	29	4	no	—
60	C₄	—	29	12	no	—
61	C₄	C₄×#6599	1	12	yes	direct product factor
62	C₂	C₄²×#1181	1	1	yes	characteristic
63	C₂	C₂×C₄×#6599	1	3	yes	—
64	C₂	C₄×D₂₉⋊C₈	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₄²	#1181
commutator, hypocenter	C₂₉	C₄²×C₈
Frattini	C₂³	C₂²×#1181
Fitting	C₂×C₄²×C₂₉	C₄
socle, prime radical	C₂³×C₂₉	C₂²×C₄
cosocle	C₂²×Dic₂₉	C₂³
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
7. C₄×#6599	C₄	direct (N × H)
12. C₄²×C₂₉	C₈	semidirect
13. C₄×Dic₂₉	C₈	semidirect
22. #6599	C₄²	direct (N × H)
27. C₄×C₂₉	C₄×C₈	semidirect
28. Dic₂₉	C₄×C₈	semidirect
40. C₂₉	C₄²×C₈	semidirect
47. C₄²	#6599	direct (N × H)
61. C₄	C₄×#6599	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×#6599	2
C₄²×Dic₂₉	2
C₄²×C₈	29

Subgroups — C42×#6599 #16835144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×#6599 #16835144