Group #16836042 — subgroups

Subgroups — C₂×C₄×D₂₉⋊C₈ #16836042

Order 3712.

760 conjugacy classes of subgroups; only the 434 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 434 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	C₂²×D₂₉⋊C₈	C₂	1	2	yes	maximal
2	C₄×D₂₉⋊C₈	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄×#6599	C₂	1	4	yes	maximal, complemented
4	C₂×C₄²×D₂₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×D₂₉	C₄	1	2	yes	—
6	C₂²×C₄×D₂₉	C₂²	1	1	yes	characteristic
7	C₂²×#6599	C₂²	1	4	yes	—
8	C₂×D₂₉⋊C₈	C₄	1	16	yes	direct product factor
9	C₂×D₂₉⋊C₈	C₂²	1	8	yes	—
10	C₂×C₄²×C₂₉	C₄	1	1	yes	characteristic
11	C₂×C₄×Dic₂₉	C₄	1	1	yes	characteristic
12	C₂×C₄×Dic₂₉	C₂²	1	2	yes	—
13	C₄²×D₂₉	C₄	1	4	yes	—
14	C₄²×D₂₉	C₂²	1	4	yes	—
15	C₄×#6599	C₂²	1	16	yes	complemented
16	C₂³×D₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
19	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
20	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
21	C₂×C₄×D₂₉	C₈	1	16	yes	complemented
22	C₂×C₄×D₂₉	C₂×C₄	1	2	yes	—
23	C₂×C₄×D₂₉	C₂×C₄	1	8	yes	—
24	C₂×C₄×D₂₉	C₂×C₄	1	8	yes	—
25	C₂×C₄×D₂₉	C₂³	1	2	yes	—
26	C₂×#6599	C₂×C₄	1	16	yes	complemented
27	C₂×#6599	C₂³	1	8	yes	—
28	D₂₉⋊C₈	C₂×C₄	1	32	yes	direct product factor
29	C₄²×C₂₉	C₂×C₄	1	4	yes	—
30	C₄×Dic₂₉	C₂×C₄	1	4	yes	—
31	C₄×Dic₂₉	C₂×C₄	1	4	yes	—
32	C₄×Dic₂₉	C₂³	1	4	yes	—
33	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
34	C₂²×D₂₉	C₄²	1	4	yes	—
35	C₂²×D₂₉	C₂×C₈	1	8	yes	—
36	C₂²×D₂₉	C₂²×C₄	1	2	yes	—
37	C₂×C₄×C₂₉	C₄²	1	4	yes	—
38	C₂×C₄×C₂₉	C₂×C₈	1	8	yes	complemented
39	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
40	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
41	C₂×Dic₂₉	C₂×C₈	1	8	yes	complemented
42	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
43	C₂×Dic₂₉	C₂²×C₄	1	4	yes	—
44	C₂×Dic₂₉	C₂²×C₄	1	4	yes	—
45	C₂×Dic₂₉	C₂⁴	1	1	yes	characteristic
46	C₄×D₂₉	C₄²	1	8	yes	—
47	C₄×D₂₉	C₂×C₈	1	32	yes	complemented
48	C₄×D₂₉	C₂²×C₄	1	8	yes	—
49	#6599	C₂²×C₄	1	16	yes	complemented
50	C₂²×C₄×C₈	—	29	1	no	maximal, Sylow
51	C₂²×C₂₉	C₂×C₄²	1	2	yes	—
52	C₂²×C₂₉	C₂²×C₈	1	4	yes	—
53	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
54	C₂×D₂₉	C₄×C₈	1	16	yes	complemented
55	C₂×D₂₉	C₂×C₄²	1	4	yes	—
56	C₂×D₂₉	C₂²×C₈	1	8	yes	—
57	C₄×C₂₉	C₂×C₄²	1	4	yes	—
58	C₄×C₂₉	C₂²×C₈	1	8	yes	complemented
59	Dic₂₉	C₂×C₄²	1	2	yes	—
60	Dic₂₉	C₂²×C₈	1	8	yes	complemented
61	Dic₂₉	C₂³×C₄	1	2	yes	—
62	C₂³×C₈	—	29	2	no	—
63	C₂²×C₄²	—	29	1	no	—
64	C₂×C₄×C₈	—	29	4	no	—
65	C₂×C₄×C₈	—	29	8	no	—
66	C₂×C₂₉	C₂×C₄×C₈	1	4	yes	complemented
67	C₂×C₂₉	C₂²×C₄²	1	1	yes	characteristic
68	C₂×C₂₉	C₂³×C₈	1	2	yes	—
69	D₂₉	C₂×C₄×C₈	1	8	yes	complemented
70	C₂³×C₄	—	29	1	no	—
71	C₂³×C₄	—	29	2	no	—
72	C₂²×C₈	—	29	16	no	—
73	C₂²×C₈	—	29	8	no	—
74	C₂²×C₈	—	29	4	no	—
75	C₂×C₄²	—	29	1	no	—
76	C₂×C₄²	—	29	2	no	—
77	C₂×C₄²	—	29	4	no	—
78	C₂×C₄²	—	29	4	no	—
79	C₂×C₄²	#1181	1	1	yes	characteristic
80	C₄×C₈	—	29	16	no	—
81	C₂₉	C₂²×C₄×C₈	1	1	yes	characteristic, complemented, Sylow
82	C₂⁴	—	29	1	no	—
83	C₂²×C₄	—	29	1	no	—
84	C₂²×C₄	—	29	2	no	—
85	C₂²×C₄	—	29	16	no	—
86	C₂²×C₄	—	29	8	no	—
87	C₂²×C₄	—	29	2	no	—
88	C₂²×C₄	—	29	8	no	—
89	C₂²×C₄	—	29	2	no	—
90	C₂²×C₄	C₂×#1181	1	2	yes	—
91	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
92	C₂×C₈	—	29	8	no	—
93	C₂×C₈	—	29	32	no	—
94	C₂×C₈	—	29	16	no	—
95	C₄²	—	29	4	no	—
96	C₄²	—	29	4	no	—
97	C₄²	—	29	4	no	—
98	C₄²	C₂×#1181	1	4	yes	—
99	C₂³	—	29	8	no	—
100	C₂³	—	29	4	no	—
101	C₂³	—	29	2	no	—
102	C₂³	C₂²×#1181	1	1	yes	characteristic
103	C₂×C₄	—	29	8	no	—
104	C₂×C₄	—	29	4	no	—
105	C₂×C₄	—	29	1	no	—
106	C₂×C₄	—	29	1	no	—
107	C₂×C₄	—	29	4	no	—
108	C₂×C₄	—	29	32	no	—
109	C₂×C₄	—	29	8	no	—
110	C₂×C₄	—	29	8	no	—
111	C₂×C₄	D₂₉⋊C₈	1	8	yes	direct product factor
112	C₂×C₄	C₄×#1181	1	4	yes	—
113	C₂×C₄	C₂²×#1181	1	4	yes	—
114	C₂×C₄	C₂²×#1181	1	2	yes	—
115	C₈	—	29	16	no	—
116	C₂²	—	29	16	no	—
117	C₂²	—	29	4	no	—
118	C₂²	—	29	8	no	—
119	C₂²	C₂×D₂₉⋊C₈	1	4	yes	—
120	C₂²	C₂×C₄×#1181	1	2	yes	—
121	C₂²	C₂³×#1181	1	1	yes	characteristic
122	C₄	—	29	2	no	—
123	C₄	—	29	2	no	—
124	C₄	—	29	8	no	—
125	C₄	C₂×D₂₉⋊C₈	1	8	yes	direct product factor
126	C₄	C₂×C₄×#1181	1	4	yes	—
127	C₂	—	29	8	no	—
128	C₂	C₄×D₂₉⋊C₈	1	4	yes	direct product factor
129	C₂	C₂²×C₄×#1181	1	1	yes	characteristic
130	C₂	C₂²×D₂₉⋊C₈	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₂₉⋊C₈

C₂

yes

maximal

C₄×D₂₉⋊C₈

C₂

yes

maximal, direct product factor

C₂×C₄×#6599

C₂

yes

maximal, complemented

C₂×C₄²×D₂₉

C₂

yes

maximal, characteristic

C₂²×C₄×D₂₉

C₄

yes

—

C₂²×C₄×D₂₉

C₂²

yes

characteristic

C₂²×#6599

C₂²

yes

—

C₂×D₂₉⋊C₈

C₄

yes

direct product factor

C₂×D₂₉⋊C₈

C₂²

yes

—

C₂×C₄²×C₂₉

C₄

yes

characteristic

C₂×C₄×Dic₂₉

C₄

yes

characteristic

C₂×C₄×Dic₂₉

C₂²

yes

—

C₄²×D₂₉

C₄

yes

—

C₄²×D₂₉

C₂²

yes

—

C₄×#6599

C₂²

yes

complemented

C₂³×D₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×Dic₂₉

C₂×C₄

yes

—

C₂²×Dic₂₉

C₂³

yes

characteristic

C₂×C₄×D₂₉

C₈

yes

complemented

C₂×C₄×D₂₉

C₂×C₄

yes

—

C₂×C₄×D₂₉

C₂×C₄

yes

—

C₂×C₄×D₂₉

C₂×C₄

yes

—

C₂×C₄×D₂₉

C₂³

yes

—

C₂×#6599

C₂×C₄

yes

complemented

C₂×#6599

C₂³

yes

—

D₂₉⋊C₈

C₂×C₄

yes

direct product factor

C₄²×C₂₉

C₂×C₄

yes

—

C₄×Dic₂₉

C₂×C₄

yes

—

C₄×Dic₂₉

C₂×C₄

yes

—

C₄×Dic₂₉

C₂³

yes

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂²×D₂₉

C₄²

yes

—

C₂²×D₂₉

C₂×C₈

yes

—

C₂²×D₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₄²

yes

—

C₂×C₄×C₂₉

C₂×C₈

yes

complemented

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×Dic₂₉

C₂×C₈

yes

complemented

C₂×Dic₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₂²×C₄

yes

—

C₂×Dic₂₉

C₂²×C₄

yes

—

C₂×Dic₂₉

C₂⁴

yes

characteristic

C₄×D₂₉

C₄²

yes

—

C₄×D₂₉

C₂×C₈

yes

complemented

C₄×D₂₉

C₂²×C₄

yes

—

#6599

C₂²×C₄

yes

complemented

C₂²×C₄×C₈

—

maximal, Sylow

C₂²×C₂₉

C₂×C₄²

yes

—

C₂²×C₂₉

C₂²×C₈

yes

—

C₂²×C₂₉

C₂³×C₄

yes

characteristic

C₂×D₂₉

C₄×C₈

yes

complemented

C₂×D₂₉

C₂×C₄²

yes

—

C₂×D₂₉

C₂²×C₈

yes

—

C₄×C₂₉

C₂×C₄²

yes

—

C₄×C₂₉

C₂²×C₈

yes

complemented

Dic₂₉

C₂×C₄²

yes

—

Dic₂₉

C₂²×C₈

yes

complemented

Dic₂₉

C₂³×C₄

yes

—

C₂³×C₈

—

C₂²×C₄²

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₂₉

C₂×C₄×C₈

yes

complemented

C₂×C₂₉

C₂²×C₄²

yes

characteristic

C₂×C₂₉

C₂³×C₈

yes

—

D₂₉

C₂×C₄×C₈

yes

complemented

C₂³×C₄

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

#1181

yes

characteristic

C₄×C₈

—

C₂₉

C₂²×C₄×C₈

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#1181

yes

—

C₂²×C₄

C₂×#1181

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#1181

yes

—

C₂³

—

100

C₂³

—

101

C₂³

—

102

C₂³

C₂²×#1181

yes

characteristic

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

D₂₉⋊C₈

yes

direct product factor

112

C₂×C₄

C₄×#1181

yes

—

113

C₂×C₄

C₂²×#1181

yes

—

114

C₂×C₄

C₂²×#1181

yes

—

115

C₈

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

C₂×D₂₉⋊C₈

yes

—

120

C₂²

C₂×C₄×#1181

yes

—

121

C₂²

C₂³×#1181

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

C₂×D₂₉⋊C₈

yes

direct product factor

126

C₄

C₂×C₄×#1181

yes

—

127

C₂

—

128

C₂

C₄×D₂₉⋊C₈

yes

direct product factor

129

C₂

C₂²×C₄×#1181

yes

characteristic

130

C₂

C₂²×D₂₉⋊C₈

yes

—

	subgroup	G/H
center, hypercenter	C₂×C₄²	#1181
commutator, hypocenter	C₂₉	C₂²×C₄×C₈
Frattini	C₂²	C₂³×#1181
Fitting	C₂×C₄²×C₂₉	C₄
socle	C₂³×C₂₉	C₂²×C₄
prime radical	C₂³×D₂₉	C₂×C₄
cosocle	C₂×Dic₂₉	C₂⁴
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂×C₄²

subgroup

G/H

center, hypercenter

C₂×C₄²

#1181

commutator, hypocenter

C₂₉

C₂²×C₄×C₈

Frattini

C₂²

C₂³×#1181

Fitting

C₂×C₄²×C₂₉

C₄

socle

C₂³×C₂₉

C₂²×C₄

prime radical

C₂³×D₂₉

C₂×C₄

cosocle

C₂×Dic₂₉

C₂⁴

LCS

G ▷ C₂₉

UCS

C₁ ◁ C₂×C₄²

N	H ≅ G/N	type
2. C₄×D₂₉⋊C₈	C₂	direct (N × H)
3. C₂×C₄×#6599	C₂	semidirect
8. C₂×D₂₉⋊C₈	C₄	direct (N × H)
15. C₄×#6599	C₂²	semidirect
21. C₂×C₄×D₂₉	C₈	semidirect
26. C₂×#6599	C₂×C₄	semidirect
28. D₂₉⋊C₈	C₂×C₄	direct (N × H)
38. C₂×C₄×C₂₉	C₂×C₈	semidirect
41. C₂×Dic₂₉	C₂×C₈	semidirect
47. C₄×D₂₉	C₂×C₈	semidirect
49. #6599	C₂²×C₄	semidirect
54. C₂×D₂₉	C₄×C₈	semidirect
58. C₄×C₂₉	C₂²×C₈	semidirect
60. Dic₂₉	C₂²×C₈	semidirect
66. C₂×C₂₉	C₂×C₄×C₈	semidirect
69. D₂₉	C₂×C₄×C₈	semidirect
81. C₂₉	C₂²×C₄×C₈	semidirect
111. C₂×C₄	D₂₉⋊C₈	direct (N × H)
125. C₄	C₂×D₂₉⋊C₈	direct (N × H)
128. C₂	C₄×D₂₉⋊C₈	direct (N × H)

H ≅ G/N

type

2. C₄×D₂₉⋊C₈

C₂

direct (N × H)

3. C₂×C₄×#6599

C₂

semidirect

8. C₂×D₂₉⋊C₈

C₄

direct (N × H)

15. C₄×#6599

C₂²

semidirect

21. C₂×C₄×D₂₉

C₈

semidirect

26. C₂×#6599

C₂×C₄

semidirect

28. D₂₉⋊C₈

C₂×C₄

direct (N × H)

38. C₂×C₄×C₂₉

C₂×C₈

semidirect

41. C₂×Dic₂₉

C₂×C₈

semidirect

47. C₄×D₂₉

C₂×C₈

semidirect

49. #6599

C₂²×C₄

semidirect

54. C₂×D₂₉

C₄×C₈

semidirect

58. C₄×C₂₉

C₂²×C₈

semidirect

60. Dic₂₉

C₂²×C₈

semidirect

66. C₂×C₂₉

C₂×C₄×C₈

semidirect

69. D₂₉

C₂×C₄×C₈

semidirect

81. C₂₉

C₂²×C₄×C₈

semidirect

111. C₂×C₄

D₂₉⋊C₈

direct (N × H)

125. C₄

C₂×D₂₉⋊C₈

direct (N × H)

128. C₂

C₄×D₂₉⋊C₈

direct (N × H)

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

subgroup	index
C₂²×D₂₉⋊C₈	2
C₄×D₂₉⋊C₈	2
C₂×C₄×#6599	2
C₂×C₄²×D₂₉	2
C₂²×C₄×C₈	29

subgroup

index

C₂²×D₂₉⋊C₈

C₄×D₂₉⋊C₈

C₂×C₄×#6599

C₂×C₄²×D₂₉

C₂²×C₄×C₈

Subgroups — C₂×C₄×D₂₉⋊C₈ #16836042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C4×D29⋊C8 #16836042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×D₂₉⋊C₈ #16836042