Group #16827834 — subgroups

Subgroups — #16827834

Order 3712.

924 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 924 conjugacy classes of subgroups — too many to draw. Only its 209 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	C₂×#11745300	C₂	1	6	yes	maximal, complemented
2	C₂×C₄²×D₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271066	C₂	1	6	yes	maximal, complemented
4	#14271033	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₉×#127	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₄×C₂₉	C₂²	1	6	yes	—
7	C₂²×C₂²⋊D₂₉	C₂²	1	4	yes	—
8	C₂²×C₄×D₂₉	C₂²	1	3	yes	—
9	C₂₉×#127	—	2	4	no	—
10	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊Dic₂₉	C₂²	1	12	yes	—
12	#11745300	—	2	24	no	—
13	C₂×C₄⋊Dic₂₉	C₂²	1	6	yes	—
14	C₂×C₄×Dic₂₉	C₂²	1	3	yes	—
15	C₄²×D₂₉	—	2	4	no	—
16	C₂⁴×C₂₉	C₂³	1	4	yes	—
17	C₂³×D₂₉	C₂³	1	1	yes	characteristic
18	C₂×D₄×C₂₉	—	2	12	no	—
19	C₂×D₄×C₂₉	—	2	12	no	—
20	C₂×D₄×C₂₉	—	2	12	no	—
21	C₂²×C₄×C₂₉	C₂³	1	3	yes	—
22	C₂×C₂²⋊D₂₉	—	2	24	no	—
23	C₂²×Dic₂₉	C₂³	1	4	yes	—
24	C₂²×Dic₂₉	C₂³	1	3	yes	—
25	C₂×C₄×D₂₉	—	2	6	no	—
26	C₂×C₄×D₂₉	—	2	6	no	—
27	C₂×C₄×D₂₉	D₄	1	12	yes	complemented
28	C₄²×C₂₉	D₄	1	4	yes	complemented
29	C₂²⋊Dic₂₉	—	2	24	no	—
30	C₄⋊Dic₂₉	—	2	12	no	—
31	C₄×Dic₂₉	—	2	6	no	—
32	C₂³×C₂₉	—	2	12	no	—
33	C₂³×C₂₉	—	2	4	no	—
34	C₂³×C₂₉	—	2	12	no	—
35	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
36	C₂²×D₂₉	—	2	1	no	—
37	C₂²×D₂₉	—	2	3	no	—
38	C₂²×D₂₉	C₂×D₄	1	6	yes	—
39	D₄×C₂₉	—	4	24	no	—
40	C₂×C₄×C₂₉	C₂×D₄	1	6	yes	—
41	C₂×C₄×C₂₉	C₂×D₄	1	6	yes	—
42	C₂×C₄×C₂₉	#41	1	6	yes	—
43	C₂²⋊D₂₉	—	4	16	no	—
44	C₂×Dic₂₉	—	2	3	no	—
45	C₂×Dic₂₉	—	2	3	no	—
46	C₂×Dic₂₉	—	2	12	no	—
47	C₂×Dic₂₉	C₂×D₄	1	6	yes	—
48	C₄×D₂₉	—	2	24	no	—
49	#2856	—	29	1	no	maximal, Sylow
50	C₂²×C₂₉	—	4	12	no	—
51	C₂²×C₂₉	—	4	4	no	—
52	C₂²×C₂₉	—	4	12	no	—
53	C₂²×C₂₉	C₂²×D₄	1	3	yes	—
54	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
55	C₂²×C₂₉	C₂×#41	1	3	yes	—
56	C₂×D₂₉	—	2	6	no	—
57	C₂×D₂₉	—	2	6	no	—
58	C₂×D₂₉	#127	1	4	yes	complemented
59	C₄×C₂₉	#121	1	12	yes	complemented
60	Dic₂₉	—	2	6	no	—
61	Dic₂₉	—	4	4	no	—
62	C₂×#127	D₂₉	1	1	yes	characteristic, complemented
63	C₂×#121	—	29	6	no	—
64	C₂²×C₄²	—	29	1	no	—
65	#390	—	29	6	no	—
66	#384	—	29	1	no	—
67	C₂×C₂₉	—	8	4	no	—
68	C₂×C₂₉	C₂×#121	1	3	yes	—
69	C₂×C₂₉	C₂×#127	1	1	yes	characteristic
70	C₂×C₂₉	#532	1	3	yes	—
71	D₂₉	—	2	4	no	—
72	C₂²×D₄	—	29	4	no	—
73	C₂²×D₄	C₂×D₂₉	1	6	yes	—
74	C₂³×C₄	—	29	3	no	—
75	#127	—	2	4	no	—
76	#121	—	58	24	no	—
77	C₂×C₄⋊C₄	—	29	6	no	—
78	C₂×C₂²⋊C₄	—	29	12	no	—
79	C₂×C₄²	—	29	3	no	—
80	C₂×C₄²	—	58	4	no	—
81	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
82	C₂₉	#2856	1	1	yes	characteristic, complemented, Sylow
83	C₂⁴	—	29	1	no	—
84	C₂⁴	C₂²×D₂₉	1	4	yes	—
85	C₂×D₄	—	2	12	no	—
86	C₂×D₄	—	2	12	no	—
87	C₂×D₄	—	2	12	no	—
88	C₂×D₄	—	58	24	no	—
89	C₂²×C₄	—	29	3	no	—
90	C₂²×C₄	—	29	12	no	—
91	C₂²×C₄	—	29	4	no	—
92	C₂²×C₄	—	58	6	no	—
93	C₂²×C₄	—	58	6	no	—
94	C₂²×C₄	C₂²×D₂₉	1	3	yes	—
95	C₄⋊C₄	—	58	12	no	—
96	C₂²⋊C₄	—	58	24	no	—
97	C₄²	—	58	6	no	—
98	C₄²	C₂²⋊D₂₉	1	4	yes	complemented
99	C₂³	—	2	12	no	—
100	C₂³	—	2	12	no	—
101	C₂³	—	2	4	no	—
102	C₂³	—	29	6	no	—
103	C₂³	—	58	3	no	—
104	C₂³	—	58	1	no	—
105	C₂³	C₂³×D₂₉	1	1	yes	characteristic
106	D₄	—	4	24	no	—
107	D₄	—	116	16	no	—
108	C₂×C₄	—	29	6	no	—
109	C₂×C₄	—	58	3	no	—
110	C₂×C₄	—	58	3	no	—
111	C₂×C₄	—	58	24	no	—
112	C₂×C₄	—	58	12	no	—
113	C₂×C₄	D₄×D₂₉	1	6	yes	—
114	C₂×C₄	#90807	1	6	yes	—
115	C₂×C₄	C₂×C₂²⋊D₂₉	1	6	yes	—
116	C₂²	—	4	12	no	—
117	C₂²	—	4	4	no	—
118	C₂²	—	4	12	no	—
119	C₂²	—	29	4	no	—
120	C₂²	—	58	6	no	—
121	C₂²	—	58	6	no	—
122	C₂²	C₂×D₄×D₂₉	1	3	yes	—
123	C₂²	C₂×#90807	1	3	yes	—
124	C₂²	C₂²×C₂²⋊D₂₉	1	1	yes	characteristic
125	C₄	—	58	6	no	—
126	C₄	—	116	4	no	—
127	C₄	#11745300	1	12	yes	complemented
128	C₂	—	8	4	no	—
129	C₂	—	58	4	no	—
130	C₂	C₂×#11745300	1	3	yes	—
131	C₂	#127×D₂₉	1	1	yes	characteristic
132	C₂	#14271711	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745300

C₂

yes

maximal, complemented

C₂×C₄²×D₂₉

C₂

yes

maximal, characteristic, complemented

#14271066

C₂

yes

maximal, complemented

#14271033

C₂

yes

maximal, characteristic, complemented

C₂×C₂₉×#127

C₂

yes

maximal, characteristic, complemented

C₂²×D₄×C₂₉

C₂²

yes

—

C₂²×C₂²⋊D₂₉

C₂²

yes

—

C₂²×C₄×D₂₉

C₂²

yes

—

C₂₉×#127

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₂²⋊Dic₂₉

C₂²

yes

—

#11745300

—

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

—

C₄²×D₂₉

—

C₂⁴×C₂₉

C₂³

yes

—

C₂³×D₂₉

C₂³

yes

characteristic

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂×D₄×C₂₉

—

C₂²×C₄×C₂₉

C₂³

yes

—

C₂×C₂²⋊D₂₉

—

C₂²×Dic₂₉

C₂³

yes

—

C₂²×Dic₂₉

C₂³

yes

—

C₂×C₄×D₂₉

—

C₂×C₄×D₂₉

—

C₂×C₄×D₂₉

D₄

yes

complemented

C₄²×C₂₉

D₄

yes

complemented

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄×Dic₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

C₂⁴

yes

characteristic

C₂²×D₂₉

—

C₂²×D₂₉

—

C₂²×D₂₉

C₂×D₄

yes

—

D₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂²⋊D₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂×D₄

yes

—

C₄×D₂₉

—

#2856

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂²×D₄

yes

—

C₂²×C₂₉

C₂²×D₄

yes

characteristic

C₂²×C₂₉

C₂×#41

yes

—

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

yes

C₄×C₂₉

yes

Dic₂₉

—

Dic₂₉

—

C₂×#127

D₂₉

yes

characteristic, complemented

C₂×#121

—

C₂²×C₄²

—

#390

—

#384

—

C₂×C₂₉

—

C₂×C₂₉

C₂×#121

yes

—

C₂×C₂₉

C₂×#127

yes

characteristic

C₂×C₂₉

#532

yes

—

D₂₉

—

C₂²×D₄

—

C₂²×D₄

C₂×D₂₉

yes

—

C₂³×C₄

—

#127

—

#121

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₂₉

#2856

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂⁴

C₂²×D₂₉

yes

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₉

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂²⋊D₂₉

yes

complemented

C₂³

—

100

C₂³

—

101

C₂³

—

102

C₂³

—

103

C₂³

—

104

C₂³

—

105

C₂³

C₂³×D₂₉

yes

characteristic

106

D₄

—

107

D₄

—

116

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

D₄×D₂₉

yes

—

114

C₂×C₄

#90807

yes

—

115

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

—

122

C₂²

C₂×D₄×D₂₉

yes

—

123

C₂²

C₂×#90807

yes

—

124

C₂²

C₂²×C₂²⋊D₂₉

yes

characteristic

125

C₄

—

126

C₄

—

116

—

127

C₄

#11745300

yes

complemented

128

C₂

—

129

C₂

—

130

C₂

C₂×#11745300

yes

—

131

C₂

#127×D₂₉

yes

characteristic

132

C₂

#14271711

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₉
commutator, socle, cosocle	C₂³×C₂₉	C₂⁴
Fitting	C₂×C₂₉×#127	C₂
hypercenter	C₂×#127	D₂₉
hypocenter	C₂₉	#2856
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×#127

subgroup

G/H

center, Frattini

C₂³

C₂³×D₂₉

commutator, socle, cosocle

C₂³×C₂₉

C₂⁴

Fitting

C₂×C₂₉×#127

C₂

D₂₉

C₂₉

G ▷ C₂³×C₂₉ ▷ C₂₉

C₁ ◁ C₂³ ◁ C₂×#127

N	H ≅ G/N	type
1. C₂×#11745300	C₂	semidirect
2. C₂×C₄²×D₂₉	C₂	semidirect
3. #14271066	C₂	semidirect
4. #14271033	C₂	semidirect
5. C₂×C₂₉×#127	C₂	semidirect
27. C₂×C₄×D₂₉	D₄	semidirect
28. C₄²×C₂₉	D₄	semidirect
58. C₂×D₂₉	#127	semidirect
59. C₄×C₂₉	#121	semidirect
62. C₂×#127	D₂₉	semidirect
82. C₂₉	#2856	semidirect
98. C₄²	C₂²⋊D₂₉	semidirect
127. C₄	#11745300	semidirect

H ≅ G/N

type

1. C₂×#11745300

C₂

semidirect

2. C₂×C₄²×D₂₉

C₂

semidirect

3. #14271066

C₂

semidirect

4. #14271033

C₂

semidirect

5. C₂×C₂₉×#127

C₂

semidirect

27. C₂×C₄×D₂₉

D₄

semidirect

28. C₄²×C₂₉

D₄

semidirect

58. C₂×D₂₉

#127

semidirect

59. C₄×C₂₉

#121

semidirect

62. C₂×#127

D₂₉

semidirect

82. C₂₉

#2856

semidirect

98. C₄²

C₂²⋊D₂₉

semidirect

127. C₄

#11745300

semidirect

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

subgroup	index
C₂×#11745300	2
C₂×C₄²×D₂₉	2
#14271066	2
#14271033	2
C₂×C₂₉×#127	2
#2856	29

subgroup

index

C₂×C₄²×D₂₉

C₂×C₂₉×#127

Subgroups — #16827834

Conjugacy classes of subgroups

Complements

Maximal subgroups