Group #16830014 — subgroups

Subgroups — #16830014

Order 3712.

348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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	#14271720	C₂	1	1	yes	maximal, characteristic
2	#14271573	C₂	1	4	yes	maximal, complemented
3	#14271569	C₂	1	4	yes	maximal, complemented
4	#14271199	C₂	1	4	yes	maximal
5	C₂×#11745151	C₂	1	1	yes	maximal, characteristic
6	C₂₉×#533	C₂	1	1	yes	maximal, characteristic
7	C₂₉×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₂₉×#125	C₂²	1	2	yes	—
9	C₂₉×C₂²⋊Q₈	—	2	2	no	—
10	C₄×Q₈×C₂₉	—	2	2	no	—
11	C₂₉×#117	C₂²	1	2	yes	—
12	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
13	#11745288	C₂²	1	2	yes	—
14	#11745286	—	2	2	no	—
15	C₂²×#6597	C₂²	1	2	yes	—
16	#11745232	C₂²	1	2	yes	—
17	#11745231	C₂²	1	2	yes	—
18	C₄×Dic₅₈	—	2	2	no	—
19	#11745156	C₂²	1	8	yes	—
20	#11745155	C₂²	1	8	yes	—
21	#11745151	C₂²	1	2	yes	—
22	#11745151	C₂²	1	2	yes	—
23	C₂×Q₈×C₂₉	—	2	2	no	—
24	C₂²×C₄×C₂₉	D₄	1	2	yes	—
25	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
26	C₂×Dic₅₈	—	2	2	no	—
27	C₄⋊C₄×C₂₉	—	2	4	no	—
28	C₄⋊C₄×C₂₉	—	2	2	no	—
29	C₄⋊C₄×C₂₉	C₂³	1	4	yes	—
30	C₂²⋊C₄×C₂₉	—	2	2	no	—
31	C₄²×C₂₉	—	2	2	no	—
32	C₄²×C₂₉	D₄	1	2	yes	—
33	C₄²×C₂₉	C₂³	1	1	yes	characteristic
34	C₄²×C₂₉	C₂³	1	1	yes	characteristic
35	C₂²⋊Dic₂₉	—	2	2	no	—
36	C₄⋊Dic₂₉	—	2	2	no	—
37	C₄⋊Dic₂₉	C₂³	1	4	yes	—
38	#90779	—	2	4	no	—
39	C₄×Dic₂₉	—	2	2	no	—
40	C₂×#6597	Q₈	1	8	yes	complemented
41	C₂×#6597	C₂³	1	4	yes	—
42	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
43	Q₈×C₂₉	—	4	4	no	—
44	C₂×C₄×C₂₉	—	2	4	no	—
45	C₂×C₄×C₂₉	—	4	2	no	—
46	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
48	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
49	C₂×C₄×C₂₉	C₂×Q₈	1	4	yes	—
50	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
51	C₂×Dic₂₉	—	2	4	no	—
52	Dic₅₈	—	4	4	no	—
53	#6597	C₂×Q₈	1	8	yes	—
54	#3162	—	29	1	no	maximal, Sylow
55	C₂²×C₂₉	—	2	2	no	—
56	C₂²×C₂₉	C₄⋊Q₈	1	2	yes	—
57	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
58	C₄×C₂₉	—	2	2	no	—
59	C₄×C₂₉	—	2	2	no	—
60	C₄×C₂₉	—	4	4	no	—
61	C₄×C₂₉	C₄⋊Q₈	1	2	yes	—
62	C₄×C₂₉	C₂²×Q₈	1	2	yes	—
63	Dic₂₉	—	4	4	no	—
64	#533	—	29	1	no	—
65	#533	D₂₉	1	1	yes	characteristic
66	#501	—	29	4	no	—
67	#501	—	29	4	no	—
68	#427	—	29	4	no	—
69	C₂×#97	—	29	1	no	—
70	C₂×C₂₉	—	2	2	no	—
71	C₂×C₂₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
72	C₂×C₂₉	#575	1	2	yes	—
73	C₂²×C₈	—	29	2	no	—
74	C₄⋊Q₈	—	29	2	no	—
75	C₄⋊Q₈	C₂×D₂₉	1	2	yes	—
76	#125	—	29	2	no	—
77	#125	C₂×D₂₉	1	2	yes	—
78	C₂²⋊Q₈	—	2	2	no	—
79	C₂²⋊Q₈	—	58	2	no	—
80	C₄×Q₈	—	2	2	no	—
81	C₄×Q₈	—	58	2	no	—
82	#117	—	29	2	no	—
83	#117	C₂×D₂₉	1	2	yes	—
84	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
85	#107	—	29	8	no	—
86	#106	—	29	8	no	—
87	#97	—	29	2	no	—
88	#97	—	29	2	no	—
89	C₂₉	#3162	1	1	yes	characteristic, complemented, Sylow
90	C₂×Q₈	—	2	2	no	—
91	C₂×Q₈	—	58	2	no	—
92	C₂²×C₄	C₂²⋊D₂₉	1	2	yes	—
93	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
94	C₂×C₈	—	29	8	no	—
95	C₂×C₈	—	29	4	no	—
96	C₄⋊C₄	—	2	4	no	—
97	C₄⋊C₄	—	2	2	no	—
98	C₄⋊C₄	—	29	4	no	—
99	C₄⋊C₄	—	58	4	no	—
100	C₄⋊C₄	—	58	2	no	—
101	C₄⋊C₄	C₂²×D₂₉	1	4	yes	—
102	C₂²⋊C₄	—	2	2	no	—
103	C₂²⋊C₄	—	58	2	no	—
104	C₄²	—	2	2	no	—
105	C₄²	—	58	2	no	—
106	C₄²	C₂²⋊D₂₉	1	2	yes	—
107	C₄²	C₂²×D₂₉	1	1	yes	characteristic
108	C₄²	C₂²×D₂₉	1	1	yes	characteristic
109	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
110	Q₈	—	4	4	no	—
111	Q₈	—	116	4	no	—
112	C₂×C₄	—	2	4	no	—
113	C₂×C₄	—	4	2	no	—
114	C₂×C₄	—	58	4	no	—
115	C₂×C₄	Q₈×D₂₉	1	4	yes	—
116	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
117	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
118	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
119	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
120	C₈	—	29	8	no	—
121	C₂²	—	2	2	no	—
122	C₂²	#11745306	1	2	yes	—
123	C₂²	C₂²×C₂²⋊D₂₉	1	1	yes	characteristic
124	C₄	—	2	2	no	—
125	C₄	—	2	2	no	—
126	C₄	—	4	4	no	—
127	C₄	—	116	4	no	—
128	C₄	#11745306	1	2	yes	—
129	C₄	C₂×Q₈×D₂₉	1	2	yes	—
130	C₂	—	2	2	no	—
131	C₂	C₂×#11745306	1	1	yes	characteristic
132	C₂	#14271961	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14271720

C₂

yes

maximal, characteristic

#14271573

C₂

yes

maximal, complemented

#14271569

C₂

yes

maximal, complemented

#14271199

C₂

yes

maximal

C₂×#11745151

C₂

yes

maximal, characteristic

C₂₉×#533

C₂

yes

maximal, characteristic

C₂₉×C₄⋊Q₈

C₂²

yes

—

C₂₉×#125

C₂²

yes

—

C₂₉×C₂²⋊Q₈

—

C₄×Q₈×C₂₉

—

C₂₉×#117

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

#11745288

C₂²

yes

—

#11745286

—

C₂²×#6597

C₂²

yes

—

#11745232

C₂²

yes

—

#11745231

C₂²

yes

—

C₄×Dic₅₈

—

#11745156

C₂²

yes

—

#11745155

C₂²

yes

—

#11745151

C₂²

yes

—

#11745151

C₂²

yes

—

C₂×Q₈×C₂₉

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂×Dic₅₈

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

C₂³

yes

—

C₂²⋊C₄×C₂₉

—

C₄²×C₂₉

—

C₄²×C₂₉

D₄

yes

—

C₄²×C₂₉

C₂³

yes

characteristic

C₄²×C₂₉

C₂³

yes

characteristic

C₂²⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

C₂³

yes

—

#90779

—

C₄×Dic₂₉

—

C₂×#6597

Q₈

yes

complemented

C₂×#6597

C₂³

yes

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

Q₈×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×C₄×C₂₉

C₂⁴

yes

characteristic

C₂×Dic₂₉

—

Dic₅₈

—

#6597

C₂×Q₈

yes

—

#3162

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

C₄⋊Q₈

yes

—

C₂²×C₂₉

C₂²×D₄

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₄⋊Q₈

yes

—

C₄×C₂₉

C₂²×Q₈

yes

—

Dic₂₉

—

#533

—

#533

D₂₉

yes

—

—

—

C₂×#97

—

C₂×C₂₉

—

C₂×C₂₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₂₉

#575

yes

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₂₉

yes

—

#125

—

#125

C₂×D₂₉

yes

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

#117

C₂×D₂₉

yes

—

C₂×C₄²

C₂×D₂₉

yes

—

—

—

—

C₂₉

#3162

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

C₂²⋊D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

C₂²×D₂₉

yes

—

102

C₂²⋊C₄

—

103

C₂²⋊C₄

—

104

C₄²

—

105

C₄²

—

106

C₄²

C₂²⋊D₂₉

yes

—

107

C₄²

C₂²×D₂₉

yes

characteristic

108

C₄²

C₂²×D₂₉

yes

characteristic

109

C₂³

C₂×C₂²⋊D₂₉

yes

characteristic

110

Q₈

—

111

Q₈

—

116

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

Q₈×D₂₉

yes

—

116

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

117

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

118

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

119

C₂×C₄

C₂³×D₂₉

yes

characteristic

120

C₈

—

121

C₂²

—

122

C₂²

#11745306

yes

—

123

C₂²

C₂²×C₂²⋊D₂₉

yes

characteristic

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

—

116

—

128

C₄

#11745306

yes

—

129

C₄

C₂×Q₈×D₂₉

yes

—

130

C₂

—

131

C₂

C₂×#11745306

yes

characteristic

132

C₂

#14271961

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₉
Fitting	C₂₉×#533	C₂
socle	C₂²×C₂₉	C₂²×D₄
prime radical	C₂³×C₂₉	C₂×D₄
hypercenter	#533	D₂₉
hypocenter	C₂₉	#3162
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #533

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₂₉

commutator, cosocle

C₂×C₄×C₂₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₂₉

Fitting

C₂₉×#533

C₂

socle

C₂²×C₂₉

C₂²×D₄

prime radical

C₂³×C₂₉

C₂×D₄

D₂₉

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #533

N	H ≅ G/N	type
2. #14271573	C₂	semidirect
3. #14271569	C₂	semidirect
40. C₂×#6597	Q₈	semidirect
89. C₂₉	#3162	semidirect

H ≅ G/N

type

2. #14271573

C₂

semidirect

3. #14271569

C₂

semidirect

40. C₂×#6597

Q₈

semidirect

89. C₂₉

#3162

semidirect

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

subgroup	index
#14271720	2
#14271573	2
#14271569	2
#14271199	2
C₂×#11745151	2
C₂₉×#533	2
#3162	29

subgroup

index

C₂₉×#533

Subgroups — #16830014

Conjugacy classes of subgroups

Complements

Maximal subgroups