Group #16817374 — subgroups

Subgroups — #16817374

Order 3712.

180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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	C₂×C₂₉×#97	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₉	—	2	1	no	—
5	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
6	C₂×C₄⋊Dic₂₉	C₄	1	2	yes	—
7	C₂²×#6597	—	2	1	no	—
8	C₂₉×#97	—	2	1	no	—
9	C₂₉×#97	C₄	1	2	yes	complemented
10	#11745179	—	2	1	no	—
11	#11745179	—	2	1	no	—
12	#11745151	—	2	1	no	—
13	#11745151	C₄	1	2	yes	complemented
14	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
17	C₂²×Dic₂₉	—	2	2	no	—
18	C₂×C₈×C₂₉	—	2	4	no	—
19	C₂×C₈×C₂₉	—	2	2	no	—
20	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
21	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₂₉	D₄	1	1	yes	characteristic
23	C₄²×C₂₉	Q₈	1	1	yes	characteristic
24	C₄⋊Dic₂₉	—	4	2	no	—
25	C₂×#6597	—	2	4	no	—
26	C₂×#6597	—	2	2	no	—
27	C₂³×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₉	—	2	1	no	—
29	C₂×C₄×C₂₉	—	2	1	no	—
30	C₂×C₄×C₂₉	—	2	2	no	—
31	C₂×C₄×C₂₉	—	2	2	no	—
32	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
38	C₂×Dic₂₉	—	4	2	no	—
39	C₂×Dic₂₉	—	4	2	no	—
40	C₂×Dic₂₉	—	4	2	no	—
41	C₈×C₂₉	—	2	4	no	—
42	#6597	—	2	4	no	—
43	#1295	—	29	1	no	maximal, Sylow
44	C₂²×C₂₉	#95	1	1	yes	characteristic
45	C₂²×C₂₉	#100	1	1	yes	characteristic
46	C₂²×C₂₉	#101	1	1	yes	characteristic
47	C₂²×C₂₉	#104	1	2	yes	—
48	C₂²×C₂₉	#104	1	2	yes	—
49	C₄×C₂₉	—	2	1	no	—
50	C₄×C₂₉	—	2	1	no	—
51	C₄×C₂₉	—	2	1	no	—
52	C₄×C₂₉	—	2	1	no	—
53	C₄×C₂₉	—	2	1	no	—
54	C₄×C₂₉	—	2	1	no	—
55	Dic₂₉	—	8	2	no	—
56	C₂×#97	—	29	1	no	—
57	C₂×#97	D₂₉	1	1	yes	characteristic
58	#382	—	29	1	no	—
59	C₂×C₂₉	#329	1	2	yes	—
60	C₂×C₂₉	#330	1	2	yes	—
61	C₂×C₂₉	#339	1	1	yes	characteristic
62	C₂×C₂₉	#339	1	1	yes	characteristic
63	C₂×C₂₉	#343	1	1	yes	characteristic
64	C₂²×C₈	—	2	1	no	—
65	C₂²×C₈	—	58	1	no	—
66	C₂×C₄⋊C₄	—	29	2	no	—
67	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
68	#97	—	2	1	no	—
69	#97	—	29	2	no	—
70	#97	—	58	1	no	—
71	#97	Dic₂₉	1	2	yes	complemented
72	#95	—	58	1	no	—
73	#95	—	58	1	no	—
74	C₂₉	#1295	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₄	—	58	2	no	—
76	C₂²×C₄	C₄×D₂₉	1	1	yes	characteristic
77	C₂²×C₄	D₁₁₆	1	1	yes	characteristic
78	C₂²×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
79	C₂×C₈	—	2	4	no	—
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	58	4	no	—
82	C₂×C₈	—	58	2	no	—
83	C₄⋊C₄	—	116	2	no	—
84	C₄²	Dic₅₈	1	1	yes	characteristic
85	C₄²	C₄×D₂₉	1	1	yes	characteristic
86	C₄²	C₂×Dic₂₉	1	1	yes	characteristic
87	C₄²	C₂²⋊D₂₉	1	1	yes	characteristic
88	C₂³	#90781	1	1	yes	characteristic
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	116	2	no	—
94	C₂×C₄	—	116	2	no	—
95	C₂×C₄	—	116	2	no	—
96	C₂×C₄	C₄×Dic₂₉	1	1	yes	characteristic
97	C₂×C₄	#90779	1	1	yes	characteristic
98	C₂×C₄	#90779	1	1	yes	characteristic
99	C₂×C₄	C₄⋊Dic₂₉	1	1	yes	characteristic
100	C₂×C₄	#90781	1	1	yes	characteristic
101	C₂×C₄	C₂²⋊Dic₂₉	1	1	yes	characteristic
102	C₈	—	2	4	no	—
103	C₈	—	58	4	no	—
104	C₂²	#11745153	1	2	yes	—
105	C₂²	#11745171	1	1	yes	characteristic
106	C₂²	#11745172	1	1	yes	characteristic
107	C₂²	#11745173	1	2	yes	—
108	C₂²	#11745179	1	1	yes	characteristic
109	C₄	—	2	1	no	—
110	C₄	—	2	1	no	—
111	C₄	—	2	1	no	—
112	C₄	—	2	1	no	—
113	C₄	—	2	1	no	—
114	C₄	—	2	1	no	—
115	C₄	—	232	2	no	—
116	C₂	#14270902	1	2	yes	—
117	C₂	#14270904	1	2	yes	—
118	C₂	#14270923	1	1	yes	characteristic
119	C₂	#14270924	1	1	yes	characteristic
120	C₂	#14270931	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745151

C₂

yes

maximal, characteristic

#14271029

C₂

yes

maximal, characteristic

C₂×C₂₉×#97

C₂

yes

maximal, characteristic

C₂²×C₈×C₂₉

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₄

yes

—

C₂²×#6597

—

C₂₉×#97

—

C₂₉×#97

C₄

yes

—

—

—

C₄

yes

complemented

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₉

D₄

yes

characteristic

C₂²×C₄×C₂₉

D₄

yes

characteristic

C₂²×Dic₂₉

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄²×C₂₉

D₄

yes

characteristic

C₄²×C₂₉

Q₈

yes

characteristic

C₄⋊Dic₂₉

—

C₂×#6597

—

C₂×#6597

—

C₂³×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄²

yes

characteristic

C₂×C₄×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₄⋊C₄

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₈×C₂₉

—

—

—

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₂²×C₂₉

yes

—

C₂²×C₂₉

#104

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

C₂×#97

—

C₂×#97

D₂₉

yes

characteristic

#382

—

C₂×C₂₉

#329

yes

—

C₂×C₂₉

#330

yes

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₂₉

yes

—

—

—

Dic₂₉

yes

complemented

#95

—

#95

—

C₂₉

#1295

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₄×D₂₉

yes

characteristic

C₂²×C₄

D₁₁₆

yes

characteristic

C₂²×C₄

C₂²⋊D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

116

—

C₄²

Dic₅₈

yes

characteristic

C₄²

C₄×D₂₉

yes

characteristic

C₄²

C₂×Dic₂₉

yes

characteristic

C₄²

C₂²⋊D₂₉

yes

characteristic

C₂³

#90781

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

C₂×C₄

—

116

—

C₂×C₄

—

116

—

C₂×C₄

C₄×Dic₂₉

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₄⋊Dic₂₉

yes

characteristic

100

C₂×C₄

#90781

yes

characteristic

101

C₂×C₄

C₂²⋊Dic₂₉

yes

characteristic

102

C₈

—

103

C₈

—

104

C₂²

#11745153

yes

—

105

C₂²

#11745171

yes

characteristic

106

C₂²

#11745172

yes

characteristic

107

C₂²

#11745173

yes

—

108

C₂²

#11745179

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

232

—

116

C₂

#14270902

yes

—

117

C₂

#14270904

yes

—

118

C₂

#14270923

yes

characteristic

119

C₂

#14270924

yes

characteristic

120

C₂

#14270931

yes

characteristic

	subgroup	G/H
center	C₂³	#90781
commutator	C₂×C₄×C₂₉	C₄²
Frattini	C₂×C₄²	C₂×D₂₉
Fitting	C₂×C₂₉×#97	C₂
socle, prime radical	C₂³×C₂₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₂₉	C₂²
hypercenter	C₂×#97	D₂₉
hypocenter	C₂₉	#1295
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

#90781

commutator

C₂×C₄×C₂₉

C₄²

Frattini

C₂×C₄²

C₂×D₂₉

Fitting

C₂×C₂₉×#97

C₂

socle, prime radical

C₂³×C₂₉

C₂²⋊C₄

cosocle

C₂×C₄²×C₂₉

C₂²

hypercenter

C₂×#97

D₂₉

hypocenter

C₂₉

#1295

LCS

G ▷ C₂×C₄×C₂₉ ▷ C₂²×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
9. C₂₉×#97	C₄	semidirect
13. #11745151	C₄	semidirect
71. #97	Dic₂₉	semidirect
74. C₂₉	#1295	semidirect

H ≅ G/N

type

9. C₂₉×#97

C₄

semidirect

13. #11745151

C₄

semidirect

71. #97

Dic₂₉

semidirect

74. C₂₉

#1295

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
C₂×C₂₉×#97	2
#1295	29

subgroup

index

C₂×#11745151

#14271029

C₂×C₂₉×#97

#1295

Subgroups — #16817374

Conjugacy classes of subgroups

Complements

Maximal subgroups