Subgroups — D₂₉⋊(C₄⋊C₈) #14272164

Order 1856.

138 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	#11745220	C₂	1	2	yes	maximal, complemented
4	C₄⋊#6599	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×D₂₉	C₄	1	1	yes	characteristic
6	C₂×C₄×D₂₉	C₄	1	1	yes	characteristic
7	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
8	C₂×#6599	C₂²	1	4	yes	—
9	D₂₉⋊C₈	—	2	4	no	—
10	C₄²×C₂₉	C₄	1	1	yes	characteristic
11	C₄×Dic₂₉	C₄	1	1	yes	characteristic
12	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
13	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
14	C₂²×D₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
21	C₄×D₂₉	—	2	2	no	—
22	C₄×D₂₉	C₈	1	4	yes	complemented
23	C₄×D₂₉	D₄	1	2	yes	—
24	C₄×D₂₉	Q₈	1	2	yes	—
25	#6599	—	2	4	no	—
26	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₂₉	C₄⋊C₄	1	2	yes	—
28	C₂×D₂₉	C₂×C₈	1	2	yes	—
29	C₂×D₂₉	M₁₆	1	2	yes	—
30	C₄×C₂₉	—	2	1	no	—
31	C₄×C₂₉	C₄⋊C₄	1	2	yes	—
32	C₄×C₂₉	C₂×C₈	1	2	yes	complemented
33	Dic₂₉	—	2	1	no	—
34	Dic₂₉	C₂×C₈	1	2	yes	complemented
35	Dic₂₉	C₂×D₄	1	1	yes	characteristic
36	Dic₂₉	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₄⋊C₈	—	29	1	no	maximal, Sylow
38	C₂×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₂₉	C₂²×C₈	1	1	yes	characteristic
40	C₂×C₂₉	C₂×M₁₆	1	1	yes	characteristic
41	D₂₉	C₄⋊C₈	1	4	yes	complemented
42	C₂²×C₈	—	29	2	no	—
43	C₂×C₄²	—	29	1	no	—
44	C₄⋊C₈	—	29	2	no	—
45	C₄⋊C₈	—	29	2	no	—
46	C₂₉	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₄	—	29	1	no	—
48	C₂²×C₄	—	29	1	no	—
49	C₂²×C₄	—	29	1	no	—
50	C₂×C₈	—	29	4	no	—
51	C₂×C₈	—	58	4	no	—
52	C₄²	—	29	1	no	—
53	C₄²	—	29	1	no	—
54	C₄²	—	29	1	no	—
55	C₄²	#1181	1	1	yes	characteristic
56	C₂³	—	29	1	no	—
57	C₂×C₄	—	29	1	no	—
58	C₂×C₄	—	29	1	no	—
59	C₂×C₄	—	29	4	no	—
60	C₂×C₄	—	29	2	no	—
61	C₂×C₄	—	29	2	no	—
62	C₂×C₄	—	29	1	no	—
63	C₂×C₄	—	58	2	no	—
64	C₂×C₄	C₂×#1181	1	1	yes	characteristic
65	C₂×C₄	C₂×#1181	1	1	yes	characteristic
66	C₂×C₄	C₂×#1181	1	1	yes	characteristic
67	C₈	—	58	4	no	—
68	C₂²	—	29	2	no	—
69	C₂²	—	29	2	no	—
70	C₂²	—	29	2	no	—
71	C₂²	C₂²×#1181	1	1	yes	characteristic
72	C₄	—	2	1	no	—
73	C₄	—	29	2	no	—
74	C₄	—	29	1	no	—
75	C₄	—	29	1	no	—
76	C₄	—	58	1	no	—
77	C₄	D₂₉⋊C₈	1	2	yes	complemented
78	C₄	C₄⋊#1181	1	2	yes	—
79	C₂	—	29	4	no	—
80	C₂	C₂×D₂₉⋊C₈	1	1	yes	characteristic
81	C₂	D₂₉⋊M₁₆	1	1	yes	characteristic
82	C₂	C₂×C₄⋊#1181	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. #11745220	C₂	semidirect
4. C₄⋊#6599	C₂	semidirect
22. C₄×D₂₉	C₈	semidirect
32. C₄×C₂₉	C₂×C₈	semidirect
34. Dic₂₉	C₂×C₈	semidirect
41. D₂₉	C₄⋊C₈	semidirect
46. C₂₉	C₂×C₄⋊C₈	semidirect
77. C₄	D₂₉⋊C₈	semidirect

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
#11745220	2
C₄⋊#6599	2
C₂×C₄⋊C₈	29

Subgroups — D29⋊(C4⋊C8) #14272164

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉⋊(C₄⋊C₈) #14272164