Group #16827869 — subgroups

Subgroups — #16827869

Order 3712.

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

normal subgroups only

This group has 504 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	C₂×#11745231	C₂	1	1	yes	maximal, characteristic
2	#14271070	C₂	1	4	yes	maximal
3	#14271068	C₂	1	4	yes	maximal
4	#14271028	C₂	1	4	yes	maximal
5	C₄²×Dic₂₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₂₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₈×C₂₉	C₂²	1	2	yes	—
8	C₂²×Dic₅₈	C₂²	1	2	yes	—
9	C₂₉×C₄⋊Q₈	—	2	4	no	—
10	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
11	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
12	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
14	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
15	C₂×C₄×Dic₂₉	C₂²	1	2	yes	—
16	C₂×C₄×Dic₂₉	C₂²	1	2	yes	—
17	C₂×C₄×Dic₂₉	C₂²	1	2	yes	—
18	#11745231	—	2	4	no	—
19	#11745179	C₂²	1	16	yes	—
20	C₂×Q₈×C₂₉	—	2	4	no	—
21	C₂×Q₈×C₂₉	—	2	8	no	—
22	C₂²×C₄×C₂₉	C₂³	1	4	yes	—
23	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
25	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
26	C₂²×Dic₂₉	C₂³	1	4	yes	—
27	C₂²×Dic₂₉	C₂³	1	4	yes	—
28	C₂×Dic₅₈	—	2	4	no	—
29	C₂×Dic₅₈	—	2	8	no	—
30	C₄⋊C₄×C₂₉	—	2	4	no	—
31	C₄⋊C₄×C₂₉	—	2	4	no	—
32	C₄²×C₂₉	D₄	1	4	yes	—
33	C₄⋊Dic₂₉	—	2	4	no	—
34	C₄⋊Dic₂₉	—	2	4	no	—
35	C₄×Dic₂₉	—	2	4	no	—
36	C₄×Dic₂₉	—	2	4	no	—
37	C₄×Dic₂₉	Q₈	1	8	yes	complemented
38	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
39	Q₈×C₂₉	—	4	8	no	—
40	C₂×C₄×C₂₉	—	2	4	no	—
41	C₂×C₄×C₂₉	—	2	8	no	—
42	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₂₉	C₂×Q₈	1	4	yes	—
46	C₂×C₄×C₂₉	#41	1	4	yes	—
47	C₂×C₄×C₂₉	#41	1	4	yes	—
48	C₂×Dic₂₉	—	2	4	no	—
49	C₂×Dic₂₉	—	2	4	no	—
50	C₂×Dic₂₉	—	2	4	no	—
51	C₂×Dic₂₉	—	2	8	no	—
52	C₂×Dic₂₉	C₂×Q₈	1	8	yes	—
53	Dic₅₈	—	4	8	no	—
54	#2862	—	29	1	no	maximal, Sylow
55	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
56	C₂²×C₂₉	C₂²×Q₈	1	2	yes	—
57	C₂²×C₂₉	C₂×#41	1	2	yes	—
58	C₂²×C₂₉	C₂×#41	1	2	yes	—
59	C₄×C₂₉	—	4	4	no	—
60	C₄×C₂₉	#124	1	4	yes	—
61	C₄×C₂₉	#124	1	4	yes	—
62	C₄×C₂₉	C₄⋊Q₈	1	4	yes	—
63	Dic₂₉	—	2	8	no	—
64	Dic₂₉	—	4	4	no	—
65	C₂×C₄⋊Q₈	—	29	1	no	—
66	C₂×C₄⋊Q₈	D₂₉	1	1	yes	characteristic
67	#391	—	29	4	no	—
68	#391	—	29	4	no	—
69	#382	—	29	4	no	—
70	C₄³	—	29	1	no	—
71	C₂×C₂₉	C₂×#124	1	1	yes	characteristic
72	C₂×C₂₉	C₂×#124	1	1	yes	characteristic
73	C₂×C₂₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
74	C₂×C₂₉	#533	1	4	yes	—
75	C₂²×Q₈	—	29	2	no	—
76	C₂²×Q₈	C₂×D₂₉	1	2	yes	—
77	C₄⋊Q₈	—	2	4	no	—
78	C₄⋊Q₈	—	58	4	no	—
79	C₂×C₄⋊C₄	—	29	2	no	—
80	C₂×C₄⋊C₄	—	29	2	no	—
81	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
82	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
83	C₂×C₄²	—	29	2	no	—
84	C₂×C₄²	—	29	2	no	—
85	C₂×C₄²	—	29	2	no	—
86	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
87	#95	—	29	16	no	—
88	C₂₉	#2862	1	1	yes	characteristic, complemented, Sylow
89	C₂×Q₈	—	2	8	no	—
90	C₂×Q₈	—	2	4	no	—
91	C₂×Q₈	—	58	8	no	—
92	C₂×Q₈	—	58	4	no	—
93	C₂²×C₄	—	29	4	no	—
94	C₂²×C₄	—	29	4	no	—
95	C₂²×C₄	C₂²×D₂₉	1	4	yes	—
96	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
97	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
98	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
99	C₄⋊C₄	—	2	4	no	—
100	C₄⋊C₄	—	2	4	no	—
101	C₄⋊C₄	—	58	4	no	—
102	C₄⋊C₄	—	58	4	no	—
103	C₄²	—	29	8	no	—
104	C₄²	—	58	4	no	—
105	C₄²	—	58	4	no	—
106	C₄²	C₂²⋊D₂₉	1	4	yes	—
107	C₂³	C₂³×D₂₉	1	1	yes	characteristic
108	Q₈	—	4	8	no	—
109	Q₈	—	116	8	no	—
110	C₂×C₄	—	2	8	no	—
111	C₂×C₄	—	2	4	no	—
112	C₂×C₄	—	29	8	no	—
113	C₂×C₄	—	58	4	no	—
114	C₂×C₄	—	58	4	no	—
115	C₂×C₄	—	58	8	no	—
116	C₂×C₄	—	58	4	no	—
117	C₂×C₄	#90807	1	4	yes	—
118	C₂×C₄	Q₈×D₂₉	1	4	yes	—
119	C₂×C₄	#90809	1	4	yes	—
120	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
121	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
122	C₂×C₄	C₂×C₂²⋊D₂₉	1	2	yes	—
123	C₂²	C₂×#90807	1	2	yes	—
124	C₂²	C₂×Q₈×D₂₉	1	2	yes	—
125	C₂²	C₂×#90809	1	2	yes	—
126	C₂²	C₂²×C₂²⋊D₂₉	1	1	yes	characteristic
127	C₄	—	4	4	no	—
128	C₄	—	58	8	no	—
129	C₄	—	116	4	no	—
130	C₄	#11745298	1	4	yes	—
131	C₄	#11745306	1	4	yes	—
132	C₄	#11745309	1	4	yes	—
133	C₂	C₂×#11745298	1	1	yes	characteristic
134	C₂	C₂×#11745309	1	1	yes	characteristic
135	C₂	C₂×#11745306	1	1	yes	characteristic
136	C₂	#14271718	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745231

C₂

yes

maximal, characteristic

#14271070

C₂

yes

maximal

#14271068

C₂

yes

maximal

#14271028

C₂

yes

maximal

C₄²×Dic₂₉

C₂

yes

maximal, characteristic

C₂×C₂₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂²×Q₈×C₂₉

C₂²

yes

—

C₂²×Dic₅₈

C₂²

yes

—

C₂₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₂₉

C₂²

yes

—

C₂×C₄⋊C₄×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

—

#11745231

—

#11745179

C₂²

yes

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂²×C₄×C₂₉

C₂³

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

C₂³

yes

—

C₂²×Dic₂₉

C₂³

yes

—

C₂×Dic₅₈

—

C₂×Dic₅₈

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄²×C₂₉

D₄

yes

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

Q₈

yes

complemented

C₂³×C₂₉

C₂⁴

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

—

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₂×Q₈

yes

—

Dic₅₈

—

#2862

—

maximal, Sylow

C₂²×C₂₉

C₂²×D₄

yes

characteristic

C₂²×C₂₉

C₂²×Q₈

yes

—

C₂²×C₂₉

C₂×#41

yes

—

C₂²×C₂₉

C₂×#41

yes

—

C₄×C₂₉

—

C₄×C₂₉

#124

yes

—

C₄×C₂₉

#124

yes

—

C₄×C₂₉

C₄⋊Q₈

yes

—

Dic₂₉

—

Dic₂₉

—

C₂×C₄⋊Q₈

—

C₂×C₄⋊Q₈

D₂₉

yes

—

—

—

C₄³

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₂₉

#533

yes

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₂₉

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

#95

—

C₂₉

#2862

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₉

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄²

—

104

C₄²

—

105

C₄²

—

106

C₄²

C₂²⋊D₂₉

yes

—

107

C₂³

C₂³×D₂₉

yes

characteristic

108

Q₈

—

109

Q₈

—

116

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

#90807

yes

—

118

C₂×C₄

Q₈×D₂₉

yes

—

119

C₂×C₄

#90809

yes

—

120

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

121

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

122

C₂×C₄

C₂×C₂²⋊D₂₉

yes

—

123

C₂²

C₂×#90807

yes

—

124

C₂²

C₂×Q₈×D₂₉

yes

—

125

C₂²

C₂×#90809

yes

—

126

C₂²

C₂²×C₂²⋊D₂₉

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

116

—

130

C₄

#11745298

yes

—

131

C₄

#11745306

yes

—

132

C₄

#11745309

yes

—

133

C₂

C₂×#11745298

yes

characteristic

134

C₂

C₂×#11745309

yes

characteristic

135

C₂

C₂×#11745306

yes

characteristic

136

C₂

#14271718

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₉
commutator, socle, prime radical, cosocle	C₂³×C₂₉	C₂⁴
Fitting	C₂×C₂₉×C₄⋊Q₈	C₂
hypercenter	C₂×C₄⋊Q₈	D₂₉
hypocenter	C₂₉	#2862
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₂₉

commutator, socle, prime radical, cosocle

C₂³×C₂₉

C₂⁴

Fitting

C₂×C₂₉×C₄⋊Q₈

C₂

hypercenter

C₂×C₄⋊Q₈

D₂₉

C₂₉

G ▷ C₂³×C₂₉ ▷ C₂₉

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
37. C₄×Dic₂₉	Q₈	semidirect
88. C₂₉	#2862	semidirect

H ≅ G/N

type

37. C₄×Dic₂₉

Q₈

semidirect

88. C₂₉

#2862

semidirect

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

subgroup	index
C₂×#11745231	2
#14271070	2
#14271068	2
#14271028	2
C₄²×Dic₂₉	2
C₂×C₂₉×C₄⋊Q₈	2
#2862	29

subgroup

index

C₄²×Dic₂₉

C₂×C₂₉×C₄⋊Q₈

#2862

Subgroups — #16827869

Conjugacy classes of subgroups

Complements

Maximal subgroups