Group #16834342 — subgroups

Subgroups — #16834342

Order 3712.

164 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 44 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	#14272186	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊#1181	C₂	1	1	yes	maximal, characteristic
3	#14271218	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊#1181	—	2	1	no	—
5	C₂×C₄×#1181	C₄	1	2	yes	—
6	C₄²×D₂₉	C₂²	1	1	yes	characteristic
7	(C₂×#1181)⋊C₄	—	2	1	no	—
8	#11745220	C₄	1	2	yes	complemented
9	#11745219	—	2	1	no	—
10	#11745218	—	2	1	no	—
11	C₂₉×#97	C₄	1	1	yes	characteristic, complemented
12	#11745168	—	2	1	no	—
13	#11745162	—	2	1	no	—
14	#11745151	C₄	1	1	yes	characteristic, complemented
15	C₂²×#1181	—	2	2	no	—
16	C₂×C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
18	C₂×C₄×D₂₉	D₄	1	1	yes	characteristic
19	C₂×#6599	—	2	2	no	—
20	C₄⋊#1181	—	2	4	no	—
21	C₄×#1181	—	4	2	no	—
22	C₂×C₈×C₂₉	—	2	1	no	—
23	C₄²×C₂₉	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₂₉	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₂₉	D₄	1	1	yes	characteristic
26	C₄×Dic₂₉	Q₈	1	1	yes	characteristic
27	C₂×#6597	—	2	1	no	—
28	C₂²×D₂₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×#1181	—	2	4	no	—
30	C₂×#1181	—	4	2	no	—
31	C₂×#1181	—	4	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	C₄⋊C₄	1	1	yes	characteristic
35	C₂×Dic₂₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×Dic₂₉	C₄⋊C₄	1	1	yes	characteristic
37	C₂×Dic₂₉	C₄⋊C₄	1	1	yes	characteristic
38	C₄×D₂₉	—	2	1	no	—
39	C₄×D₂₉	—	2	1	no	—
40	C₄×D₂₉	—	2	2	no	—
41	C₄×D₂₉	—	4	1	no	—
42	#6599	—	4	2	no	—
43	C₈×C₂₉	—	4	1	no	—
44	#6597	—	4	1	no	—
45	#1285	—	29	1	no	maximal, Sylow
46	C₂²×C₂₉	#95	1	1	yes	characteristic
47	C₂×D₂₉	—	2	1	no	—
48	C₂×D₂₉	—	2	1	no	—
49	C₂×D₂₉	#100	1	1	yes	characteristic
50	C₂×D₂₉	#101	1	1	yes	characteristic
51	#1181	—	4	4	no	—
52	C₄×C₂₉	—	2	1	no	—
53	C₄×C₂₉	—	2	1	no	—
54	C₄×C₂₉	—	2	1	no	—
55	Dic₂₉	—	2	1	no	—
56	Dic₂₉	—	2	1	no	—
57	Dic₂₉	#104	1	2	yes	—
58	#432	—	29	1	no	—
59	#432	—	29	1	no	—
60	C₄×C₄⋊C₄	—	29	1	no	—
61	C₂×C₂₉	H(3,ℤ/4)	1	1	yes	characteristic
62	C₂×C₂₉	#339	1	1	yes	characteristic
63	C₂×C₂₉	#343	1	1	yes	characteristic
64	D₂₉	—	2	1	no	—
65	D₂₉	—	2	1	no	—
66	C₂×C₄⋊C₄	—	58	1	no	—
67	C₂×C₄²	—	29	1	no	—
68	C₂×C₄²	—	29	2	no	—
69	C₄⋊C₈	—	29	2	no	—
70	C₄⋊C₈	—	58	1	no	—
71	C₂²⋊C₈	—	58	1	no	—
72	C₂²⋊C₈	—	58	1	no	—
73	#97	—	29	1	no	—
74	#97	—	58	1	no	—
75	#97	#1181	1	1	yes	characteristic, complemented
76	#95	—	58	1	no	—
77	C₂₉	#1285	1	1	yes	characteristic, complemented, Sylow
78	C₂²×C₄	—	29	1	no	—
79	C₂²×C₄	—	29	1	no	—
80	C₂²×C₄	—	29	1	no	—
81	C₂²×C₄	—	58	2	no	—
82	C₂×C₈	—	2	1	no	—
83	C₂×C₈	—	58	2	no	—
84	C₂×C₈	—	58	1	no	—
85	C₄⋊C₄	—	58	4	no	—
86	C₄²	—	29	1	no	—
87	C₄²	—	29	1	no	—
88	C₄²	—	29	1	no	—
89	C₄²	—	116	2	no	—
90	C₄²	C₂×#1181	1	1	yes	characteristic
91	C₂³	—	29	1	no	—
92	C₂×C₄	—	29	1	no	—
93	C₂×C₄	—	29	1	no	—
94	C₂×C₄	—	29	1	no	—
95	C₂×C₄	—	58	2	no	—
96	C₂×C₄	—	58	1	no	—
97	C₂×C₄	—	58	1	no	—
98	C₂×C₄	—	58	4	no	—
99	C₂×C₄	—	116	1	no	—
100	C₂×C₄	—	116	2	no	—
101	C₂×C₄	—	116	2	no	—
102	C₂×C₄	C₄×#1181	1	1	yes	characteristic
103	C₂×C₄	C₄⋊#1181	1	1	yes	characteristic
104	C₂×C₄	C₂²⋊#1181	1	1	yes	characteristic
105	C₈	—	4	1	no	—
106	C₈	—	116	1	no	—
107	C₈	—	116	2	no	—
108	C₂²	—	29	1	no	—
109	C₂²	—	29	1	no	—
110	C₂²	—	58	1	no	—
111	C₂²	—	58	1	no	—
112	C₂²	(C₂×#1181)⋊C₄	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	2	1	no	—
115	C₄	—	2	1	no	—
116	C₄	—	29	2	no	—
117	C₄	—	58	1	no	—
118	C₄	—	58	1	no	—
119	C₄	—	116	4	no	—
120	C₂	—	58	1	no	—
121	C₂	—	58	1	no	—
122	C₂	#14272030	1	1	yes	characteristic
123	C₂	#14272035	1	1	yes	characteristic
124	C₂	#14272042	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14272186

C₂

yes

maximal, characteristic

C₄×C₄⋊#1181

C₂

yes

maximal, characteristic

#14271218

C₂

yes

maximal, characteristic

C₂×C₄⋊#1181

—

C₂×C₄×#1181

C₄

yes

—

C₄²×D₂₉

C₂²

yes

characteristic

(C₂×#1181)⋊C₄

—

#11745220

C₄

yes

complemented

#11745219

—

#11745218

—

C₂₉×#97

C₄

yes

characteristic, complemented

#11745168

—

#11745162

—

#11745151

C₄

yes

characteristic, complemented

C₂²×#1181

—

C₂×C₄×D₂₉

C₂×C₄

yes

characteristic

C₂×C₄×D₂₉

D₄

yes

characteristic

C₂×C₄×D₂₉

D₄

yes

—

—

—

C₂×C₈×C₂₉

—

C₄²×C₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

C₂×C₄

yes

characteristic

C₄×Dic₂₉

D₄

yes

characteristic

C₄×Dic₂₉

Q₈

yes

characteristic

C₂×#6597

—

C₂²×D₂₉

C₂²⋊C₄

yes

—

—

—

C₂×C₄×C₂₉

C₄²

yes

characteristic

C₂×C₄×C₂₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₉

C₄⋊C₄

yes

characteristic

C₂×Dic₂₉

C₂²⋊C₄

yes

characteristic

C₂×Dic₂₉

C₄⋊C₄

yes

characteristic

C₂×Dic₂₉

C₄⋊C₄

yes

characteristic

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

C₄×D₂₉

—

#6599

—

C₈×C₂₉

—

—

—

C₂²×C₂₉

yes

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

yes

C₂×D₂₉

yes

—

C₄×C₂₉

—

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

#104

yes

—

#432

—

#432

—

C₄×C₄⋊C₄

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

D₂₉

—

D₂₉

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

—

—

yes

characteristic, complemented

#95

—

C₂₉

#1285

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

116

—

C₄²

C₂×#1181

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

116

—

100

C₂×C₄

—

116

—

101

C₂×C₄

—

116

—

102

C₂×C₄

C₄×#1181

yes

characteristic

103

C₂×C₄

C₄⋊#1181

yes

characteristic

104

C₂×C₄

C₂²⋊#1181

yes

characteristic

105

C₈

—

106

C₈

—

116

—

107

C₈

—

116

—

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

—

112

C₂²

(C₂×#1181)⋊C₄

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

116

—

120

C₂

—

121

C₂

—

122

C₂

#14272030

yes

characteristic

123

C₂

#14272035

yes

characteristic

124

C₂

#14272042

yes

characteristic

	subgroup	G/H
center	C₂²	(C₂×#1181)⋊C₄
commutator	C₂×C₄×C₂₉	C₄²
Frattini	C₄²	C₂×#1181
Fitting	C₂₉×#97	C₄
socle	C₂²×C₂₉	#95
prime radical	C₂²×D₂₉	C₂²⋊C₄
cosocle	C₄²×D₂₉	C₂²
hypercenter	#97	#1181
hypocenter	C₂₉	#1285
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

(C₂×#1181)⋊C₄

commutator

C₂×C₄×C₂₉

C₄²

Frattini

C₄²

C₂×#1181

Fitting

C₂₉×#97

C₄

socle

C₂²×C₂₉

#95

prime radical

C₂²×D₂₉

C₂²⋊C₄

cosocle

C₄²×D₂₉

C₂²

C₂₉

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
8. #11745220	C₄	semidirect
11. C₂₉×#97	C₄	semidirect
14. #11745151	C₄	semidirect
75. #97	#1181	semidirect
77. C₂₉	#1285	semidirect

H ≅ G/N

type

8. #11745220

C₄

semidirect

11. C₂₉×#97

C₄

semidirect

14. #11745151

C₄

semidirect

75. #97

#1181

semidirect

77. C₂₉

#1285

semidirect

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

subgroup	index
#14272186	2
C₄×C₄⋊#1181	2
#14271218	2
#1285	29

subgroup

index

#14272186

C₄×C₄⋊#1181

#14271218

#1285

Subgroups — #16834342

Conjugacy classes of subgroups

Complements

Maximal subgroups