Group #16834992 — subgroups

Subgroups — D₂₉⋊#333 #16834992

Order 3712.

256 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₉⋊(C₄⋊C₈)	C₂	1	2	yes	maximal
2	#14272023	C₂	1	4	yes	maximal, complemented
3	C₄⋊Q₈×D₂₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×D₂₉	C₄	1	2	yes	—
5	C₂×D₂₉⋊C₈	—	2	2	no	—
6	C₂₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
7	#11745306	C₂²	1	2	yes	—
8	C₄⋊C₄×D₂₉	—	2	2	no	—
9	#11745250	—	2	2	no	—
10	C₄²×D₂₉	C₂²	1	1	yes	characteristic
11	#11745231	C₄	1	1	yes	characteristic
12	#11745220	C₂²	1	4	yes	—
13	C₄⋊#6599	—	2	2	no	—
14	C₂×Q₈×C₂₉	C₂×C₄	1	2	yes	—
15	Q₈×D₂₉	—	4	4	no	—
16	C₂×C₄×D₂₉	—	2	2	no	—
17	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×D₂₉	D₄	1	2	yes	—
19	C₂×Dic₅₈	—	2	2	no	—
20	C₂×Dic₅₈	C₂×C₄	1	2	yes	—
21	C₂×#6599	—	2	4	no	—
22	D₂₉⋊C₈	—	4	4	no	—
23	C₄⋊C₄×C₂₉	—	2	2	no	—
24	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
25	C₄⋊Dic₂₉	—	2	2	no	—
26	#90779	—	2	4	no	—
27	C₄×Dic₂₉	D₄	1	2	yes	—
28	C₄×Dic₂₉	C₂³	1	1	yes	characteristic
29	C₂²×D₂₉	C₂²⋊C₄	1	1	yes	characteristic
30	Q₈×C₂₉	—	4	2	no	—
31	C₂×C₄×C₂₉	—	2	2	no	—
32	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
33	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₂₉	—	2	2	no	—
35	C₂×Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×Dic₂₉	C₂×D₄	1	2	yes	—
37	C₄×D₂₉	—	2	2	no	—
38	C₄×D₂₉	—	4	4	no	—
39	C₄×D₂₉	SD₁₆	1	4	yes	—
40	C₄×D₂₉	Q₁₆	1	4	yes	—
41	Dic₅₈	—	4	4	no	—
42	Dic₅₈	—	4	2	no	—
43	#6599	—	4	4	no	—
44	C₂×#333	—	29	1	no	maximal, Sylow
45	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂×D₂₉	#100	1	2	yes	—
47	C₂×D₂₉	#103	1	4	yes	—
48	C₄×C₂₉	—	2	1	no	—
49	C₄×C₂₉	—	4	2	no	—
50	C₄×C₂₉	#103	1	4	yes	—
51	Dic₂₉	—	2	1	no	—
52	Dic₂₉	—	4	2	no	—
53	Dic₂₉	C₂×SD₁₆	1	2	yes	—
54	Dic₂₉	C₂×Q₁₆	1	2	yes	—
55	C₂×C₄⋊Q₈	—	29	1	no	—
56	C₂×C₄⋊C₈	—	29	2	no	—
57	#333	—	29	4	no	—
58	C₂×C₂₉	C₂×#100	1	1	yes	characteristic
59	C₂×C₂₉	C₂×#103	1	2	yes	—
60	D₂₉	#333	1	4	yes	complemented
61	C₂²×Q₈	—	29	2	no	—
62	C₂²×C₈	—	58	2	no	—
63	C₄⋊Q₈	—	29	2	no	—
64	C₄⋊Q₈	—	29	1	no	—
65	C₄⋊Q₈	—	58	2	no	—
66	C₄⋊Q₈	#1181	1	1	yes	characteristic
67	C₂×C₄⋊C₄	—	58	2	no	—
68	C₂×C₄²	—	29	1	no	—
69	C₄⋊C₈	—	29	4	no	—
70	C₄⋊C₈	—	58	2	no	—
71	C₂₉	C₂×#333	1	1	yes	characteristic, complemented, Sylow
72	C₂×Q₈	—	29	2	no	—
73	C₂×Q₈	—	58	2	no	—
74	C₂×Q₈	—	116	4	no	—
75	C₂×Q₈	C₂×#1181	1	2	yes	—
76	C₂²×C₄	—	29	2	no	—
77	C₂²×C₄	—	29	1	no	—
78	C₂²×C₄	—	58	2	no	—
79	C₂×C₈	—	58	4	no	—
80	C₂×C₈	—	116	4	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	58	4	no	—
83	C₄⋊C₄	—	58	2	no	—
84	C₄²	—	29	2	no	—
85	C₄²	—	29	1	no	—
86	C₄²	C₂×#1181	1	1	yes	characteristic
87	C₂³	—	29	1	no	—
88	Q₈	—	4	2	no	—
89	Q₈	—	116	2	no	—
90	Q₈	—	116	4	no	—
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	29	2	no	—
93	C₂×C₄	—	29	4	no	—
94	C₂×C₄	—	29	4	no	—
95	C₂×C₄	—	29	1	no	—
96	C₂×C₄	—	58	2	no	—
97	C₂×C₄	—	58	2	no	—
98	C₂×C₄	—	116	4	no	—
99	C₂×C₄	C₂²⋊#1181	1	2	yes	—
100	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
101	C₈	—	116	4	no	—
102	C₂²	—	29	2	no	—
103	C₂²	—	29	4	no	—
104	C₂²	C₂×C₂²⋊#1181	1	1	yes	characteristic
105	C₄	—	2	1	no	—
106	C₄	—	4	2	no	—
107	C₄	—	29	2	no	—
108	C₄	—	29	2	no	—
109	C₄	—	58	1	no	—
110	C₄	—	116	2	no	—
111	C₄	#11745225	1	4	yes	—
112	C₂	—	29	4	no	—
113	C₂	D₂₉⋊#100	1	1	yes	characteristic
114	C₂	C₂×#11745225	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

D₂₉⋊(C₄⋊C₈)

C₂

yes

maximal

#14272023

C₂

yes

maximal, complemented

C₄⋊Q₈×D₂₉

C₂

yes

maximal, characteristic

C₂×Q₈×D₂₉

C₄

yes

—

C₂×D₂₉⋊C₈

—

C₂₉×C₄⋊Q₈

C₄

yes

characteristic

#11745306

C₂²

yes

—

C₄⋊C₄×D₂₉

—

#11745250

—

C₄²×D₂₉

C₂²

yes

characteristic

#11745231

C₄

yes

characteristic

#11745220

C₂²

yes

—

C₄⋊#6599

—

C₂×Q₈×C₂₉

C₂×C₄

yes

—

Q₈×D₂₉

—

C₂×C₄×D₂₉

—

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×C₄×D₂₉

D₄

yes

—

C₂×Dic₅₈

—

C₂×Dic₅₈

C₂×C₄

yes

—

C₂×#6599

—

D₂₉⋊C₈

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄⋊Dic₂₉

—

#90779

—

C₄×Dic₂₉

D₄

yes

—

C₄×Dic₂₉

C₂³

yes

characteristic

C₂²×D₂₉

C₂²⋊C₄

yes

characteristic

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₂₉

C₂×D₄

yes

—

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

SD₁₆

yes

—

C₄×D₂₉

Q₁₆

yes

—

Dic₅₈

—

Dic₅₈

—

#6599

—

C₂×#333

—

maximal, Sylow

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₂₉

#100

yes

—

C₂×D₂₉

#103

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#103

yes

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

C₂×SD₁₆

yes

—

Dic₂₉

C₂×Q₁₆

yes

—

C₂×C₄⋊Q₈

—

C₂×C₄⋊C₈

—

#333

—

C₂×C₂₉

C₂×#100

yes

characteristic

C₂×C₂₉

C₂×#103

yes

—

D₂₉

#333

yes

complemented

C₂²×Q₈

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

#1181

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂₉

C₂×#333

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

116

—

C₂×Q₈

C₂×#1181

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

116

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂×#1181

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

116

—

Q₈

—

116

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

C₂²⋊#1181

yes

—

100

C₂×C₄

C₂²×#1181

yes

characteristic

101

C₈

—

116

—

102

C₂²

—

103

C₂²

—

104

C₂²

C₂×C₂²⋊#1181

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

116

—

111

C₄

#11745225

yes

—

112

C₂

—

113

C₂

D₂₉⋊#100

yes

characteristic

114

C₂

C₂×#11745225

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#1181
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×#1181
Fitting	C₂₉×C₄⋊Q₈	C₄
socle	C₂²×C₂₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₂₉	C₂²⋊C₄
cosocle	C₄×Dic₂₉	C₂³
hypercenter	C₄⋊Q₈	#1181
hypocenter	C₂₉	C₂×#333
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

subgroup

G/H

center

C₂²

C₂×C₂²⋊#1181

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×#1181

Fitting

C₂₉×C₄⋊Q₈

C₄

socle

C₂²×C₂₉

C₂×C₂²⋊C₄

prime radical

C₂²×D₂₉

C₂²⋊C₄

cosocle

C₄×Dic₂₉

C₂³

C₄⋊Q₈

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

N	H ≅ G/N	type
2. #14272023	C₂	semidirect
60. D₂₉	#333	semidirect
71. C₂₉	C₂×#333	semidirect

H ≅ G/N

type

2. #14272023

C₂

semidirect

60. D₂₉

#333

semidirect

71. C₂₉

C₂×#333

semidirect

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

subgroup	index
D₂₉⋊(C₄⋊C₈)	2
#14272023	2
C₄⋊Q₈×D₂₉	2
C₂×#333	29

subgroup

index

D₂₉⋊(C₄⋊C₈)

#14272023

C₄⋊Q₈×D₂₉

C₂×#333

Subgroups — D₂₉⋊#333 #16834992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D29⋊#333 #16834992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉⋊#333 #16834992