Group #16828563 — subgroups

Subgroups — #16828563

Order 3712.

394 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 197 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	#14271235	C₂	1	8	yes	maximal, complemented
2	#14271220	C₂	1	2	yes	maximal, complemented
3	#14271130	C₂	1	4	yes	maximal, complemented
4	C₂₉×#532	C₂	1	1	yes	maximal, characteristic
5	C₂×#41×C₂₉	C₂²	1	2	yes	—
6	C₂₉×C₄⋊Q₈	C₄	1	1	yes	characteristic
7	C₂₉×#127	C₄	1	1	yes	characteristic
8	C₂₉×#124	C₄	1	2	yes	—
9	C₂₉×#121	C₄	1	4	yes	—
10	C₄×D₄×C₂₉	C₂²	1	4	yes	—
11	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
12	C₂×#90777	C₂²	1	4	yes	—
13	C₂²×#6597	C₂²	1	4	yes	—
14	C₂²⋊#6597	C₂²	1	8	yes	—
15	C₂²⋊#6597	C₂²	1	4	yes	—
16	C₄⋊#6597	C₂²	1	4	yes	—
17	#11745151	C₂²	1	4	yes	—
18	#41×C₂₉	—	4	2	no	—
19	#41×C₂₉	—	4	2	no	—
20	C₂×Q₈×C₂₉	C₂×C₄	1	2	yes	—
21	C₂×D₄×C₂₉	C₂×C₄	1	4	yes	—
22	C₂×D₄×C₂₉	C₂×C₄	1	4	yes	—
23	C₂×D₄×C₂₉	C₂×C₄	1	2	yes	—
24	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
25	C₂²×C₄×C₂₉	C₂³	1	4	yes	—
26	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
27	C₄⋊C₄×C₂₉	C₂×C₄	1	4	yes	—
28	C₂²⋊C₄×C₂₉	C₂×C₄	1	8	yes	—
29	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
30	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
31	C₄²×C₂₉	C₂³	1	2	yes	—
32	#90777	—	4	4	no	—
33	C₂×#6597	—	4	4	no	—
34	C₂×#6597	C₂³	1	8	yes	—
35	C₂³×C₂₉	C₂²×C₄	1	4	yes	—
36	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
37	Q₈×C₂₉	—	4	2	no	—
38	D₄×C₂₉	—	4	4	no	—
39	D₄×C₂₉	—	4	2	no	—
40	D₄×C₂₉	—	4	4	no	—
41	C₂×C₄×C₂₉	—	2	4	no	—
42	C₂×C₄×C₂₉	—	2	4	no	—
43	C₂×C₄×C₂₉	—	2	2	no	—
44	C₂×C₄×C₂₉	—	4	2	no	—
45	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
47	C₂×C₄×C₂₉	C₂²×C₄	1	2	yes	—
48	C₂×C₄×C₂₉	C₂²×C₄	1	4	yes	—
49	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
50	#6597	—	2	8	no	—
51	#2980	—	29	1	no	maximal, Sylow
52	C₂²×C₂₉	—	2	1	no	—
53	C₂²×C₂₉	—	2	4	no	—
54	C₂²×C₂₉	—	2	2	no	—
55	C₂²×C₂₉	—	2	8	no	—
56	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
57	C₄×C₂₉	—	2	1	no	—
58	C₄×C₂₉	—	2	4	no	—
59	C₄×C₂₉	—	2	2	no	—
60	C₄×C₂₉	—	2	2	no	—
61	C₄×C₂₉	H(5,𝔽₂)	1	2	yes	—
62	#532	D₂₉	1	1	yes	characteristic
63	#435	—	29	8	no	—
64	#432	—	29	2	no	—
65	#408	—	29	4	no	—
66	C₂×C₂₉	—	4	1	no	—
67	C₂×C₂₉	—	4	4	no	—
68	C₂×C₂₉	#518	1	1	yes	characteristic
69	C₂×C₂₉	#568	1	2	yes	—
70	C₂×#41	C₂×D₂₉	1	2	yes	—
71	C₂×M₁₆	—	29	4	no	—
72	C₂²×C₈	—	29	4	no	—
73	C₄⋊Q₈	Dic₂₉	1	1	yes	characteristic
74	#127	Dic₂₉	1	1	yes	characteristic
75	#124	Dic₂₉	1	2	yes	—
76	#121	Dic₂₉	1	4	yes	—
77	C₄×D₄	C₂×D₂₉	1	4	yes	—
78	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
79	C₄⋊C₈	—	29	4	no	—
80	C₂²⋊C₈	—	29	4	no	—
81	C₂²⋊C₈	—	29	8	no	—
82	#97	—	29	4	no	—
83	C₂₉	#2980	1	1	yes	characteristic, complemented, Sylow
84	#41	—	4	2	no	—
85	#41	—	4	2	no	—
86	C₂×Q₈	C₂×Dic₂₉	1	2	yes	—
87	C₂×D₄	C₂×Dic₂₉	1	4	yes	—
88	C₂×D₄	C₂×Dic₂₉	1	4	yes	—
89	C₂×D₄	C₂×Dic₂₉	1	2	yes	—
90	C₂²×C₄	C₂×Dic₂₉	1	2	yes	—
91	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
92	C₂²×C₄	C₂²×D₂₉	1	4	yes	—
93	M₁₆	—	116	4	no	—
94	C₂×C₈	—	29	8	no	—
95	C₂×C₈	—	116	4	no	—
96	C₄⋊C₄	C₂×Dic₂₉	1	4	yes	—
97	C₂²⋊C₄	C₂×Dic₂₉	1	8	yes	—
98	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
99	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
100	C₄²	C₂²×D₂₉	1	2	yes	—
101	C₂³	C₂²×Dic₂₉	1	4	yes	—
102	C₂³	C₂²×Dic₂₉	1	1	yes	characteristic
103	Q₈	—	4	2	no	—
104	D₄	—	4	2	no	—
105	D₄	—	4	4	no	—
106	D₄	—	4	4	no	—
107	C₂×C₄	—	2	4	no	—
108	C₂×C₄	—	2	4	no	—
109	C₂×C₄	—	2	2	no	—
110	C₂×C₄	—	4	2	no	—
111	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
112	C₂×C₄	C₂²×Dic₂₉	1	2	yes	—
113	C₂×C₄	C₂²×Dic₂₉	1	2	yes	—
114	C₂×C₄	C₂²×Dic₂₉	1	4	yes	—
115	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
116	C₈	—	58	8	no	—
117	C₂²	—	2	1	no	—
118	C₂²	—	2	4	no	—
119	C₂²	—	2	2	no	—
120	C₂²	—	2	8	no	—
121	C₂²	C₂³×Dic₂₉	1	1	yes	characteristic
122	C₄	—	2	1	no	—
123	C₄	—	2	4	no	—
124	C₄	—	2	2	no	—
125	C₄	—	2	2	no	—
126	C₄	#11745359	1	2	yes	—
127	C₂	—	4	1	no	—
128	C₂	—	4	4	no	—
129	C₂	#14271638	1	1	yes	characteristic
130	C₂	#14271930	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271235

C₂

yes

maximal, complemented

#14271220

C₂

yes

maximal, complemented

#14271130

C₂

yes

maximal, complemented

C₂₉×#532

C₂

yes

maximal, characteristic

C₂×#41×C₂₉

C₂²

yes

—

C₂₉×C₄⋊Q₈

C₄

yes

characteristic

C₂₉×#127

C₄

yes

characteristic

C₂₉×#124

C₄

yes

—

C₂₉×#121

C₄

yes

—

C₄×D₄×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×#90777

C₂²

yes

—

C₂²×#6597

C₂²

yes

—

C₂²⋊#6597

C₂²

yes

—

C₂²⋊#6597

C₂²

yes

—

C₄⋊#6597

C₂²

yes

—

#11745151

C₂²

yes

—

#41×C₂₉

—

#41×C₂₉

—

C₂×Q₈×C₂₉

C₂×C₄

yes

—

C₂×D₄×C₂₉

C₂×C₄

yes

—

C₂×D₄×C₂₉

C₂×C₄

yes

—

C₂×D₄×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

characteristic

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄²×C₂₉

C₂³

yes

—

#90777

—

C₂×#6597

—

C₂×#6597

C₂³

yes

—

C₂³×C₂₉

C₂²×C₄

yes

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

Q₈×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

—

C₂×C₄×C₂₉

C₂⁴

yes

—

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂³×C₄

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

H(5,𝔽₂)

yes

—

#532

D₂₉

yes

—

—

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

#518

yes

characteristic

C₂×C₂₉

#568

yes

—

C₂×#41

C₂×D₂₉

yes

—

C₂×M₁₆

—

C₂²×C₈

—

C₄⋊Q₈

Dic₂₉

yes

characteristic

#127

Dic₂₉

yes

characteristic

#124

Dic₂₉

yes

—

#121

Dic₂₉

yes

—

C₄×D₄

C₂×D₂₉

yes

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

C₂₉

#2980

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

C₂×Dic₂₉

yes

—

C₂×D₄

C₂×Dic₂₉

yes

—

C₂×D₄

C₂×Dic₂₉

yes

—

C₂×D₄

C₂×Dic₂₉

yes

—

C₂²×C₄

C₂×Dic₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂²×C₄

C₂²×D₂₉

yes

—

M₁₆

—

116

—

C₂×C₈

—

C₂×C₈

—

116

—

C₄⋊C₄

C₂×Dic₂₉

yes

—

C₂²⋊C₄

C₂×Dic₂₉

yes

—

C₄²

C₂×Dic₂₉

yes

characteristic

C₄²

C₂×Dic₂₉

yes

characteristic

100

C₄²

C₂²×D₂₉

yes

—

101

C₂³

C₂²×Dic₂₉

yes

—

102

C₂³

C₂²×Dic₂₉

yes

characteristic

103

Q₈

—

104

D₄

—

105

D₄

—

106

D₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

C₂²×Dic₂₉

yes

characteristic

112

C₂×C₄

C₂²×Dic₂₉

yes

—

113

C₂×C₄

C₂²×Dic₂₉

yes

—

114

C₂×C₄

C₂²×Dic₂₉

yes

—

115

C₂×C₄

C₂³×D₂₉

yes

characteristic

116

C₈

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

—

121

C₂²

C₂³×Dic₂₉

yes

characteristic

122

C₄

—

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

#11745359

yes

—

127

C₂

—

128

C₂

—

129

C₂

#14271638

yes

characteristic

130

C₂

#14271930

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₂₉
commutator, socle	C₂²×C₂₉	C₂³×C₄
Fitting, prime radical	C₂₉×#532	C₂
cosocle	C₂×C₄×C₂₉	C₂⁴
hypercenter	#532	D₂₉
hypocenter	C₂₉	#2980
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ #532

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₂₉

commutator, socle

C₂²×C₂₉

C₂³×C₄

Fitting, prime radical

C₂₉×#532

C₂

cosocle

C₂×C₄×C₂₉

C₂⁴

D₂₉

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂×C₄ ◁ #532

N	H ≅ G/N	type
1. #14271235	C₂	semidirect
2. #14271220	C₂	semidirect
3. #14271130	C₂	semidirect
83. C₂₉	#2980	semidirect

H ≅ G/N

type

1. #14271235

C₂

semidirect

2. #14271220

C₂

semidirect

3. #14271130

C₂

semidirect

83. C₂₉

#2980

semidirect

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

subgroup	index
#14271235	2
#14271220	2
#14271130	2
C₂₉×#532	2
#2980	29

subgroup

index

C₂₉×#532

Subgroups — #16828563

Conjugacy classes of subgroups

Complements

Maximal subgroups