Group #16820466 — subgroups

Subgroups — #16820466

Order 3712.

276 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 113 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×#11745151	C₂	1	1	yes	maximal, characteristic
2	#14271029	C₂	1	1	yes	maximal, characteristic
3	#14270925	C₂	1	4	yes	maximal
4	C₂×C₂₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₈×C₂₉	—	2	1	no	—
6	C₂₉×C₄⋊Q₈	—	2	2	no	—
7	C₂₉×C₄⋊Q₈	C₄	1	4	yes	complemented
8	C₂×C₄⋊C₄×C₂₉	—	2	1	no	—
9	C₂×C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
10	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
12	C₂²×#6597	C₂²	1	2	yes	—
13	#11745179	—	2	1	no	—
14	#11745179	—	2	1	no	—
15	#11745151	—	2	2	no	—
16	C₂×Q₈×C₂₉	—	2	4	no	—
17	C₂×Q₈×C₂₉	—	4	4	no	—
18	C₂²×C₄×C₂₉	—	2	2	no	—
19	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
21	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
22	C₂²×Dic₂₉	—	2	2	no	—
23	C₄⋊C₄×C₂₉	—	2	4	no	—
24	C₄⋊C₄×C₂₉	—	2	2	no	—
25	C₄⋊C₄×C₂₉	C₂×C₄	1	4	yes	—
26	C₄²×C₂₉	C₂×C₄	1	2	yes	—
27	C₄²×C₂₉	D₄	1	2	yes	—
28	C₄⋊Dic₂₉	—	2	4	no	—
29	C₂×#6597	—	2	2	no	—
30	C₂×#6597	—	2	2	no	—
31	C₂×#6597	Q₈	1	4	yes	complemented
32	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
33	Q₈×C₂₉	—	4	8	no	—
34	C₂×C₄×C₂₉	—	2	2	no	—
35	C₂×C₄×C₂₉	—	2	2	no	—
36	C₂×C₄×C₂₉	—	2	4	no	—
37	C₂×C₄×C₂₉	—	4	4	no	—
38	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
39	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
40	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₂₉	C₂×Q₈	1	2	yes	—
43	C₂×C₄×C₂₉	#41	1	2	yes	—
44	C₂×Dic₂₉	—	4	2	no	—
45	C₂×Dic₂₉	—	4	2	no	—
46	C₂×Dic₂₉	—	4	2	no	—
47	#6597	—	2	4	no	—
48	#1993	—	29	1	no	maximal, Sylow
49	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₂₉	#124	1	1	yes	characteristic
51	C₂²×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
52	C₂²×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
53	C₂²×C₂₉	#137	1	2	yes	—
54	C₄×C₂₉	—	2	2	no	—
55	C₄×C₂₉	—	2	2	no	—
56	C₄×C₂₉	—	4	4	no	—
57	C₄×C₂₉	C₄×Q₈	1	2	yes	—
58	C₄×C₂₉	C₂²⋊Q₈	1	2	yes	—
59	Dic₂₉	—	8	2	no	—
60	C₂×C₄⋊Q₈	D₂₉	1	1	yes	characteristic
61	C₂×#97	—	29	1	no	—
62	#382	—	29	1	no	—
63	#340	—	29	4	no	—
64	C₂×C₂₉	#391	1	1	yes	characteristic
65	C₂×C₂₉	#418	1	1	yes	characteristic
66	C₂×C₂₉	#419	1	1	yes	characteristic
67	C₂×C₂₉	#489	1	2	yes	—
68	C₂×C₂₉	#501	1	2	yes	—
69	C₂²×Q₈	—	2	1	no	—
70	C₂²×C₈	—	29	2	no	—
71	C₄⋊Q₈	—	2	2	no	—
72	C₄⋊Q₈	Dic₂₉	1	4	yes	complemented
73	C₂×C₄⋊C₄	—	2	1	no	—
74	C₂×C₄⋊C₄	—	29	2	no	—
75	C₂×C₄⋊C₄	C₂×D₂₉	1	2	yes	—
76	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
77	#97	—	58	2	no	—
78	#95	—	58	1	no	—
79	#95	—	58	1	no	—
80	C₂₉	#1993	1	1	yes	characteristic, complemented, Sylow
81	C₂×Q₈	—	2	4	no	—
82	C₂×Q₈	—	4	4	no	—
83	C₂²×C₄	—	2	2	no	—
84	C₂²×C₄	—	58	2	no	—
85	C₂²×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
86	C₂²×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
87	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
88	C₂×C₈	—	29	4	no	—
89	C₂×C₈	—	58	2	no	—
90	C₂×C₈	—	58	2	no	—
91	C₄⋊C₄	—	2	4	no	—
92	C₄⋊C₄	—	2	2	no	—
93	C₄⋊C₄	—	58	4	no	—
94	C₄⋊C₄	C₂×Dic₂₉	1	4	yes	—
95	C₄²	C₂×Dic₂₉	1	2	yes	—
96	C₄²	C₂²⋊D₂₉	1	2	yes	—
97	C₂³	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
98	Q₈	—	4	8	no	—
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	2	2	no	—
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	—	4	4	no	—
103	C₂×C₄	—	116	2	no	—
104	C₂×C₄	—	116	2	no	—
105	C₂×C₄	—	116	2	no	—
106	C₂×C₄	C₂²⋊Dic₂₉	1	2	yes	—
107	C₂×C₄	C₂²⋊Dic₂₉	1	2	yes	—
108	C₂×C₄	Q₈×D₂₉	1	2	yes	—
109	C₂×C₄	#90809	1	2	yes	—
110	C₂×C₄	C₂²×Dic₂₉	1	1	yes	characteristic
111	C₂×C₄	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
112	C₈	—	58	4	no	—
113	C₂²	#11745294	1	2	yes	—
114	C₂²	#11745304	1	2	yes	—
115	C₂²	#11745306	1	1	yes	characteristic
116	C₂²	#11745309	1	1	yes	characteristic
117	C₂²	C₂×C₂²⋊Dic₂₉	1	1	yes	characteristic
118	C₄	—	2	2	no	—
119	C₄	—	2	2	no	—
120	C₄	—	4	4	no	—
121	C₄	—	232	2	no	—
122	C₄	Q₈×Dic₂₉	1	2	yes	—
123	C₄	#11745308	1	2	yes	—
124	C₂	#14271070	1	1	yes	characteristic
125	C₂	#14271168	1	1	yes	characteristic
126	C₂	#14271172	1	1	yes	characteristic
127	C₂	#14271525	1	2	yes	—
128	C₂	#14271569	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745151

C₂

yes

maximal, characteristic

#14271029

C₂

yes

maximal, characteristic

#14270925

C₂

yes

maximal

C₂×C₂₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂²×Q₈×C₂₉

—

C₂₉×C₄⋊Q₈

—

C₂₉×C₄⋊Q₈

C₄

yes

complemented

C₂×C₄⋊C₄×C₂₉

—

C₂×C₄⋊C₄×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂²×#6597

C₂²

yes

—

#11745179

—

#11745179

—

#11745151

—

C₂×Q₈×C₂₉

—

C₂×Q₈×C₂₉

—

C₂²×C₄×C₂₉

—

C₂²×C₄×C₂₉

D₄

yes

characteristic

C₂²×C₄×C₂₉

D₄

yes

characteristic

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

—

C₄⋊C₄×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

C₂×C₄

yes

—

C₄²×C₂₉

D₄

yes

—

C₄⋊Dic₂₉

—

C₂×#6597

—

C₂×#6597

—

C₂×#6597

Q₈

yes

complemented

C₂³×C₂₉

C₂×D₄

yes

characteristic

Q₈×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

characteristic

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

C₂×Q₈

yes

—

C₂×C₄×C₂₉

#41

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

#6597

—

#1993

—

maximal, Sylow

C₂²×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₂₉

#124

yes

characteristic

C₂²×C₂₉

C₄⋊Q₈

yes

characteristic

C₂²×C₂₉

AGL(1,ℤ/8)

yes

—

C₂²×C₂₉

#137

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

C₄×Q₈

yes

—

C₄×C₂₉

C₂²⋊Q₈

yes

—

Dic₂₉

—

C₂×C₄⋊Q₈

D₂₉

yes

characteristic

C₂×#97

—

#382

—

#340

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂×C₂₉

#501

yes

—

C₂²×Q₈

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

Dic₂₉

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₂₉

yes

—

C₂×C₄²

C₂×D₂₉

yes

—

—

—

C₂₉

#1993

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₂₉

yes

characteristic

C₂²×C₄

C₂²⋊D₂₉

yes

characteristic

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×Dic₂₉

yes

—

C₄²

C₂×Dic₂₉

yes

—

C₄²

C₂²⋊D₂₉

yes

—

C₂³

C₂×C₂²⋊D₂₉

yes

characteristic

Q₈

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

116

—

104

C₂×C₄

—

116

—

105

C₂×C₄

—

116

—

106

C₂×C₄

C₂²⋊Dic₂₉

yes

—

107

C₂×C₄

C₂²⋊Dic₂₉

yes

—

108

C₂×C₄

Q₈×D₂₉

yes

—

109

C₂×C₄

#90809

yes

—

110

C₂×C₄

C₂²×Dic₂₉

yes

characteristic

111

C₂×C₄

C₂×C₂²⋊D₂₉

yes

characteristic

112

C₈

—

113

C₂²

#11745294

yes

—

114

C₂²

#11745304

yes

—

115

C₂²

#11745306

yes

characteristic

116

C₂²

#11745309

yes

characteristic

117

C₂²

C₂×C₂²⋊Dic₂₉

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

232

—

122

C₄

Q₈×Dic₂₉

yes

—

123

C₄

#11745308

yes

—

124

C₂

#14271070

yes

characteristic

125

C₂

#14271168

yes

characteristic

126

C₂

#14271172

yes

characteristic

127

C₂

#14271525

yes

—

128

C₂

#14271569

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₂₉
commutator	C₂×C₄×C₂₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₉
Fitting	C₂×C₂₉×C₄⋊Q₈	C₂
socle, prime radical	C₂³×C₂₉	C₂×D₄
cosocle	C₂²×C₄×C₂₉	C₂³
hypercenter	C₂×C₄⋊Q₈	D₂₉
hypocenter	C₂₉	#1993
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₂₉

commutator

C₂×C₄×C₂₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₉

Fitting

C₂×C₂₉×C₄⋊Q₈

C₂

socle, prime radical

C₂³×C₂₉

C₂×D₄

cosocle

C₂²×C₄×C₂₉

C₂³

hypercenter

C₂×C₄⋊Q₈

D₂₉

hypocenter

C₂₉

#1993

LCS

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
7. C₂₉×C₄⋊Q₈	C₄	semidirect
31. C₂×#6597	Q₈	semidirect
72. C₄⋊Q₈	Dic₂₉	semidirect
80. C₂₉	#1993	semidirect

H ≅ G/N

type

7. C₂₉×C₄⋊Q₈

C₄

semidirect

31. C₂×#6597

Q₈

semidirect

72. C₄⋊Q₈

Dic₂₉

semidirect

80. C₂₉

#1993

semidirect

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

subgroup	index
C₂×#11745151	2
#14271029	2
#14270925	2
C₂×C₂₉×C₄⋊Q₈	2
#1993	29

subgroup

index

C₂×C₂₉×C₄⋊Q₈

Subgroups — #16820466

Conjugacy classes of subgroups

Complements

Maximal subgroups