Subgroups — C₄×D₂₉⋊C₈ #14272119

Order 1856.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₄²	#1181
commutator, hypocenter	C₂₉	C₂×C₄×C₈
Frattini	C₂²	C₂²×#1181
Fitting	C₄²×C₂₉	C₄
socle	C₂²×C₂₉	C₂²×C₄
prime radical	C₂²×D₂₉	C₂×C₄
cosocle	C₂×Dic₂₉	C₂³
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₄²

Complements

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

N	H ≅ G/N	type
3. C₄×#6599	C₂	semidirect
7. D₂₉⋊C₈	C₄	direct (N × H)
16. C₄×D₂₉	C₈	semidirect
18. #6599	C₂×C₄	semidirect
23. C₄×C₂₉	C₂×C₈	semidirect
24. Dic₂₉	C₂×C₈	semidirect
29. D₂₉	C₄×C₈	semidirect
33. C₂₉	C₂×C₄×C₈	semidirect
54. C₄	D₂₉⋊C₈	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×D₂₉⋊C₈	2
C₄²×D₂₉	2
C₄×#6599	2
C₂×C₄×C₈	29

Subgroups — C4×D29⋊C8 #14272119

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₂₉⋊C₈ #14272119