Subgroups — D₂₉⋊M₃₂ #14272219

Order 1856.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
2	#11745214	C₂	1	2	yes	maximal, complemented
3	#11745206	C₂	1	2	yes	maximal, complemented
4	D₂₉⋊C₁₆	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×D₂₉	C₄	1	1	yes	characteristic
6	C₂×C₈×C₂₉	C₄	1	1	yes	characteristic
7	C₂×#6597	C₂²	1	1	yes	characteristic
8	C₈×D₂₉	C₄	1	1	yes	characteristic
9	C₈×D₂₉	C₄	1	1	yes	characteristic
10	C₈×D₂₉	C₂²	1	1	yes	characteristic
11	C₈×D₂₉	C₂²	1	1	yes	characteristic
12	#90770	C₂²	1	4	yes	complemented
13	C₂²×D₂₉	C₈	1	1	yes	characteristic
14	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₂₉	C₈	1	1	yes	characteristic
16	C₄×D₂₉	C₈	1	1	yes	characteristic
17	C₄×D₂₉	C₈	1	1	yes	characteristic
18	C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
19	C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
20	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
21	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
22	#6597	C₂×C₄	1	1	yes	characteristic
23	#6597	C₂³	1	1	yes	characteristic
24	C₂²×C₂₉	C₂×C₈	1	1	yes	characteristic
25	C₂×D₂₉	—	2	2	no	—
26	C₂×D₂₉	C₂×C₈	1	1	yes	characteristic
27	C₂×D₂₉	C₂×C₈	1	1	yes	characteristic
28	C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
29	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
30	Dic₂₉	C₂×C₈	1	1	yes	characteristic
31	Dic₂₉	C₂×C₈	1	1	yes	characteristic
32	C₂×M₃₂	—	29	1	no	maximal, Sylow
33	C₂×C₂₉	—	2	1	no	—
34	C₂×C₂₉	C₂²×C₈	1	1	yes	characteristic
35	D₂₉	—	2	1	no	—
36	D₂₉	M₃₂	1	2	yes	complemented
37	C₂²×C₈	—	29	1	no	—
38	M₃₂	—	29	2	no	—
39	M₃₂	—	29	2	no	—
40	C₂×C₁₆	—	29	2	no	—
41	C₂₉	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
42	C₂²×C₄	—	29	1	no	—
43	C₂×C₈	—	29	1	no	—
44	C₂×C₈	—	29	1	no	—
45	C₂×C₈	—	29	1	no	—
46	C₂×C₈	—	29	1	no	—
47	C₂×C₈	—	29	1	no	—
48	C₂×C₈	#1181	1	1	yes	characteristic
49	C₁₆	—	29	4	no	—
50	C₂³	—	29	1	no	—
51	C₂×C₄	—	29	1	no	—
52	C₂×C₄	—	29	1	no	—
53	C₂×C₄	—	29	1	no	—
54	C₂×C₄	—	29	1	no	—
55	C₂×C₄	—	29	1	no	—
56	C₂×C₄	C₂×#1181	1	1	yes	characteristic
57	C₈	—	29	1	no	—
58	C₈	—	29	1	no	—
59	C₈	C₂×#1181	1	1	yes	characteristic
60	C₈	C₂×#1181	1	1	yes	characteristic
61	C₂²	—	29	1	no	—
62	C₂²	—	29	1	no	—
63	C₂²	—	58	2	no	—
64	C₂²	D₂₉⋊C₈	1	1	yes	characteristic
65	C₄	—	29	1	no	—
66	C₄	—	29	1	no	—
67	C₄	D₂₉⋊C₈	1	1	yes	characteristic
68	C₄	C₂²×#1181	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	—	29	2	no	—
71	C₂	—	58	1	no	—
72	C₂	C₂×D₂₉⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×#1181
commutator, socle	C₂×C₂₉	C₂²×C₈
Frattini	C₄	C₂²×#1181
Fitting	C₂×C₈×C₂₉	C₄
prime radical	C₂²×D₂₉	C₈
cosocle	#6597	C₂³
hypercenter	C₂×C₈	#1181
hypocenter	C₂₉	C₂×M₃₂
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #11745214	C₂	semidirect
3. #11745206	C₂	semidirect
4. D₂₉⋊C₁₆	C₂	semidirect
12. #90770	C₂²	semidirect
36. D₂₉	M₃₂	semidirect
41. C₂₉	C₂×M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₂₉	2
#11745214	2
#11745206	2
D₂₉⋊C₁₆	2
C₂×M₃₂	29

Subgroups — D29⋊M32 #14272219

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉⋊M₃₂ #14272219