Group #16828130 — subgroups

Subgroups — #16828130

Order 3712.

392 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 213 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	#14271224	C₂	1	8	yes	maximal, complemented
2	#14271187	C₂	1	2	yes	maximal, complemented
3	#14271127	C₂	1	2	yes	maximal
4	C₄×#90777	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₉×#117	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄×C₂₉	C₂²	1	1	yes	characteristic
7	C₂₉×#117	C₄	1	4	yes	—
8	C₂₉×#117	C₂²	1	4	yes	—
9	C₂×C₄⋊C₄×C₂₉	C₄	1	2	yes	—
10	C₂×C₂²⋊C₄×C₂₉	C₄	1	2	yes	—
11	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
13	C₂×#90777	C₂²	1	4	yes	—
14	C₂²⋊#6597	C₂²	1	8	yes	—
15	C₄⋊#6597	C₂²	1	8	yes	complemented
16	#11745151	C₂²	1	4	yes	complemented
17	C₄×#6597	C₂²	1	4	yes	complemented
18	C₂⁴×C₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₂₉	—	2	4	no	—
20	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
24	C₂²×C₄×C₂₉	C₂³	1	2	yes	—
25	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
26	C₄⋊C₄×C₂₉	C₂×C₄	1	8	yes	—
27	C₂²⋊C₄×C₂₉	C₂×C₄	1	8	yes	—
28	C₄²×C₂₉	C₂×C₄	1	2	yes	—
29	C₄²×C₂₉	C₂×C₄	1	2	yes	—
30	C₄²×C₂₉	C₂³	1	2	yes	—
31	C₄²×C₂₉	C₂³	1	2	yes	—
32	#90777	—	2	8	no	—
33	C₂×#6597	C₂³	1	8	yes	—
34	C₂³×C₂₉	—	2	2	no	—
35	C₂³×C₂₉	—	4	2	no	—
36	C₂³×C₂₉	C₂²×C₄	1	2	yes	—
37	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₂₉	—	2	2	no	—
39	C₂×C₄×C₂₉	—	2	4	no	—
40	C₂×C₄×C₂₉	—	2	4	no	—
41	C₂×C₄×C₂₉	—	4	2	no	—
42	C₂×C₄×C₂₉	—	4	2	no	—
43	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
44	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
45	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
46	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₄×C₂₉	#41	1	4	yes	—
48	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
49	#6597	—	2	8	no	—
50	#2921	—	29	1	no	maximal, Sylow
51	C₂²×C₂₉	—	2	2	no	—
52	C₂²×C₂₉	—	2	2	no	—
53	C₂²×C₂₉	—	2	4	no	—
54	C₂²×C₂₉	—	4	4	no	—
55	C₂²×C₂₉	#117	1	2	yes	—
56	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
57	C₄×C₂₉	—	2	2	no	—
58	C₄×C₂₉	—	2	4	no	—
59	C₄×C₂₉	—	2	4	no	—
60	C₄×C₂₉	#117	1	2	yes	—
61	C₄×C₂₉	C₂×#41	1	2	yes	—
62	C₂×#117	D₂₉	1	1	yes	characteristic
63	#433	—	29	8	no	—
64	#423	—	29	2	no	—
65	#407	—	29	2	no	—
66	C₄×M₁₆	—	29	2	no	—
67	C₂×C₂₉	—	2	2	no	—
68	C₂×C₂₉	—	4	2	no	—
69	C₂×C₂₉	C₂×#117	1	1	yes	characteristic
70	C₂×C₂₉	#568	1	2	yes	—
71	C₂³×C₄	C₂×D₂₉	1	1	yes	characteristic
72	C₂×M₁₆	—	29	4	no	—
73	#117	Dic₂₉	1	4	yes	—
74	#117	C₂×D₂₉	1	4	yes	—
75	C₂×C₄⋊C₄	Dic₂₉	1	2	yes	—
76	C₂×C₂²⋊C₄	Dic₂₉	1	2	yes	—
77	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
78	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
79	C₄⋊C₈	—	29	8	no	—
80	C₂²⋊C₈	—	29	8	no	—
81	#97	—	29	4	no	—
82	C₄×C₈	—	29	4	no	—
83	C₂₉	#2921	1	1	yes	characteristic, complemented, Sylow
84	C₂⁴	C₂×Dic₂₉	1	1	yes	characteristic
85	C₂²×C₄	—	2	4	no	—
86	C₂²×C₄	C₂×Dic₂₉	1	1	yes	characteristic
87	C₂²×C₄	C₂×Dic₂₉	1	2	yes	—
88	C₂²×C₄	C₂×Dic₂₉	1	2	yes	—
89	C₂²×C₄	C₂×Dic₂₉	1	2	yes	—
90	C₂²×C₄	C₂²×D₂₉	1	2	yes	—
91	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
92	M₁₆	—	58	8	no	—
93	C₂×C₈	—	29	8	no	—
94	C₄⋊C₄	C₂×Dic₂₉	1	8	yes	—
95	C₂²⋊C₄	C₂×Dic₂₉	1	8	yes	—
96	C₄²	C₂×Dic₂₉	1	2	yes	—
97	C₄²	C₂×Dic₂₉	1	2	yes	—
98	C₄²	C₂²×D₂₉	1	2	yes	—
99	C₄²	C₂²×D₂₉	1	2	yes	—
100	C₂³	—	2	2	no	—
101	C₂³	—	4	2	no	—
102	C₂³	C₂²×Dic₂₉	1	2	yes	—
103	C₂³	C₂²×Dic₂₉	1	1	yes	characteristic
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	4	2	no	—
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	#90805	1	4	yes	—
110	C₂×C₄	C₂²×Dic₂₉	1	4	yes	—
111	C₂×C₄	C₂²×Dic₂₉	1	4	yes	—
112	C₂×C₄	C₂²×Dic₂₉	1	2	yes	—
113	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
114	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
115	C₈	—	58	8	no	—
116	C₂²	—	2	2	no	—
117	C₂²	—	2	2	no	—
118	C₂²	—	2	4	no	—
119	C₂²	—	4	4	no	—
120	C₂²	#11745288	1	2	yes	—
121	C₂²	C₂³×Dic₂₉	1	1	yes	characteristic
122	C₄	—	2	2	no	—
123	C₄	—	2	4	no	—
124	C₄	—	2	4	no	—
125	C₄	#11745288	1	2	yes	—
126	C₄	C₂×#90805	1	2	yes	—
127	C₂	—	2	2	no	—
128	C₂	—	4	2	no	—
129	C₂	C₂×#11745288	1	1	yes	characteristic
130	C₂	#14271930	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271224

C₂

yes

maximal, complemented

#14271187

C₂

yes

maximal, complemented

#14271127

C₂

yes

maximal

C₄×#90777

C₂

yes

maximal, complemented

C₂×C₂₉×#117

C₂

yes

maximal, characteristic

C₂³×C₄×C₂₉

C₂²

yes

characteristic

C₂₉×#117

C₄

yes

—

C₂₉×#117

C₂²

yes

—

C₂×C₄⋊C₄×C₂₉

C₄

yes

—

C₂×C₂²⋊C₄×C₂₉

C₄

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

C₂²⋊#6597

C₂²

yes

—

C₄⋊#6597

C₂²

yes

complemented

#11745151

C₂²

yes

complemented

C₄×#6597

C₂²

yes

complemented

C₂⁴×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₂²⋊C₄×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂³

yes

—

C₄²×C₂₉

C₂³

yes

—

#90777

—

C₂×#6597

C₂³

yes

—

C₂³×C₂₉

—

C₂³×C₂₉

—

C₂³×C₂₉

C₂²×C₄

yes

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×C₄×C₂₉

C₂⁴

yes

—

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

#117

yes

—

C₂²×C₂₉

C₂³×C₄

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#117

yes

—

C₄×C₂₉

C₂×#41

yes

—

C₂×#117

D₂₉

yes

—

—

—

C₄×M₁₆

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

C₂×#117

yes

characteristic

C₂×C₂₉

#568

yes

—

C₂³×C₄

C₂×D₂₉

yes

characteristic

C₂×M₁₆

—

#117

Dic₂₉

yes

—

#117

C₂×D₂₉

yes

—

C₂×C₄⋊C₄

Dic₂₉

yes

—

C₂×C₂²⋊C₄

Dic₂₉

yes

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₂₉

#2921

yes

characteristic, complemented, Sylow

C₂⁴

C₂×Dic₂₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂×Dic₂₉

yes

characteristic

C₂²×C₄

C₂×Dic₂₉

yes

—

C₂²×C₄

C₂×Dic₂₉

yes

—

C₂²×C₄

C₂×Dic₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₄⋊C₄

C₂×Dic₂₉

yes

—

C₂²⋊C₄

C₂×Dic₂₉

yes

—

C₄²

C₂×Dic₂₉

yes

—

C₄²

C₂×Dic₂₉

yes

—

C₄²

C₂²×D₂₉

yes

—

C₄²

C₂²×D₂₉

yes

—

100

C₂³

—

101

C₂³

—

102

C₂³

C₂²×Dic₂₉

yes

—

103

C₂³

C₂²×Dic₂₉

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

#90805

yes

—

110

C₂×C₄

C₂²×Dic₂₉

yes

—

111

C₂×C₄

C₂²×Dic₂₉

yes

—

112

C₂×C₄

C₂²×Dic₂₉

yes

—

113

C₂×C₄

C₂²×Dic₂₉

yes

characteristic

114

C₂×C₄

C₂³×D₂₉

yes

characteristic

115

C₈

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

#11745288

yes

—

121

C₂²

C₂³×Dic₂₉

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

#11745288

yes

—

126

C₄

C₂×#90805

yes

—

127

C₂

—

128

C₂

—

129

C₂

C₂×#11745288

yes

characteristic

130

C₂

#14271930

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₂₉
commutator, socle	C₂²×C₂₉	C₂³×C₄
Fitting	C₂×C₂₉×#117	C₂
prime radical	C₂⁴×C₂₉	C₂×C₄
cosocle	C₂×C₄×C₂₉	C₂⁴
hypercenter	C₂×#117	D₂₉
hypocenter	C₂₉	#2921
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₂₉

commutator, socle

C₂²×C₂₉

C₂³×C₄

Fitting

C₂×C₂₉×#117

C₂

prime radical

C₂⁴×C₂₉

C₂×C₄

cosocle

C₂×C₄×C₂₉

C₂⁴

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂×C₄ ◁ C₂×#117

N	H ≅ G/N	type
1. #14271224	C₂	semidirect
2. #14271187	C₂	semidirect
4. C₄×#90777	C₂	semidirect
15. C₄⋊#6597	C₂²	semidirect
16. #11745151	C₂²	semidirect
17. C₄×#6597	C₂²	semidirect
83. C₂₉	#2921	semidirect

H ≅ G/N

type

1. #14271224

C₂

semidirect

2. #14271187

C₂

semidirect

4. C₄×#90777

C₂

semidirect

15. C₄⋊#6597

C₂²

semidirect

16. #11745151

C₂²

semidirect

17. C₄×#6597

C₂²

semidirect

83. C₂₉

#2921

semidirect

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

subgroup	index
#14271224	2
#14271187	2
#14271127	2
C₄×#90777	2
C₂×C₂₉×#117	2
#2921	29

subgroup

index

C₂×C₂₉×#117

Subgroups — #16828130

Conjugacy classes of subgroups

Complements

Maximal subgroups