Group #16835410 — subgroups

Subgroups — #16835410

Order 3712.

216 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 82 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×#11745220	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#6599	C₂	1	1	yes	maximal, characteristic
3	#14272029	C₂	1	4	yes	maximal
4	#14271008	C₂	1	1	yes	maximal, characteristic
5	C₂²×#6599	C₂²	1	2	yes	—
6	C₂²×#6599	C₂²	1	2	yes	—
7	C₂×C₄×Dic₂₉	C₂²	1	2	yes	—
8	C₂×C₄×Dic₂₉	C₂²	1	1	yes	characteristic
9	#11745220	—	2	2	no	—
10	C₄⋊#6599	—	2	2	no	—
11	C₂₉×#95	C₄	1	1	yes	characteristic
12	#11745179	C₄	1	1	yes	characteristic
13	#11745179	C₄	1	2	yes	—
14	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
15	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂²×Dic₂₉	C₂×C₄	1	2	yes	—
17	C₂²×Dic₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₂₉	C₂³	1	1	yes	characteristic
19	C₂×#6599	—	2	2	no	—
20	C₂×#6599	—	2	2	no	—
21	C₂×#6599	—	2	4	no	—
22	C₂×#6599	—	2	4	no	—
23	C₄×Dic₂₉	—	2	2	no	—
24	C₄×Dic₂₉	—	2	2	no	—
25	C₄×Dic₂₉	D₄	1	2	yes	—
26	C₄×Dic₂₉	Q₈	1	2	yes	—
27	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₉	—	2	2	no	—
29	C₂×C₄×C₂₉	—	2	2	no	—
30	C₂×C₄×C₂₉	—	2	2	no	—
31	C₂×C₄×C₂₉	—	2	2	no	—
32	C₂×C₄×C₂₉	C₄⋊C₄	1	2	yes	—
33	C₂×Dic₂₉	—	2	1	no	—
34	C₂×Dic₂₉	—	2	1	no	—
35	C₂×Dic₂₉	—	2	2	no	—
36	C₂×Dic₂₉	—	2	2	no	—
37	C₂×Dic₂₉	—	2	2	no	—
38	C₂×Dic₂₉	C₄⋊C₄	1	2	yes	—
39	C₂×Dic₂₉	C₂×D₄	1	1	yes	characteristic
40	C₂×Dic₂₉	C₂×Q₈	1	1	yes	characteristic
41	C₂×Dic₂₉	#41	1	2	yes	—
42	C₂×Dic₂₉	#41	1	2	yes	—
43	#6599	—	4	2	no	—
44	#6599	—	4	2	no	—
45	#1832	—	29	1	no	maximal, Sylow
46	C₂²×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂²×C₂₉	#117	1	2	yes	—
48	C₂²×C₂₉	#131	1	2	yes	—
49	C₂²×C₂₉	#131	1	1	yes	characteristic
50	C₂²×C₂₉	#131	1	1	yes	characteristic
51	C₄×C₂₉	—	2	2	no	—
52	C₄×C₂₉	—	4	2	no	—
53	Dic₂₉	—	2	2	no	—
54	Dic₂₉	—	4	2	no	—
55	Dic₂₉	#124	1	1	yes	characteristic
56	Dic₂₉	#124	1	1	yes	characteristic
57	Dic₂₉	#125	1	2	yes	—
58	C₂×C₄⋊C₈	—	29	1	no	—
59	C₂×C₄⋊C₈	—	29	1	no	—
60	#376	—	29	1	no	—
61	#336	—	29	4	no	—
62	C₂×C₂₉	#382	1	1	yes	characteristic
63	C₂×C₂₉	#424	1	1	yes	characteristic
64	C₂×C₂₉	#424	1	1	yes	characteristic
65	C₂×C₂₉	#433	1	2	yes	—
66	C₂×C₂₉	#433	1	2	yes	—
67	C₂²×C₈	—	29	2	no	—
68	C₂²×C₈	—	29	2	no	—
69	C₂×C₄²	—	29	1	no	—
70	C₂×C₄²	—	29	2	no	—
71	C₄⋊C₈	—	58	2	no	—
72	C₄⋊C₈	—	58	2	no	—
73	#95	—	29	2	no	—
74	#95	—	29	1	no	—
75	#95	#1181	1	1	yes	characteristic
76	C₂₉	#1832	1	1	yes	characteristic, complemented, Sylow
77	C₂²×C₄	—	29	1	no	—
78	C₂²×C₄	—	29	1	no	—
79	C₂²×C₄	—	29	2	no	—
80	C₂²×C₄	C₂×#1181	1	2	yes	—
81	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
82	C₂×C₈	—	58	2	no	—
83	C₂×C₈	—	58	2	no	—
84	C₂×C₈	—	58	4	no	—
85	C₂×C₈	—	58	4	no	—
86	C₄²	—	29	2	no	—
87	C₄²	—	29	2	no	—
88	C₄²	—	58	2	no	—
89	C₄²	—	58	2	no	—
90	C₂³	C₂²×#1181	1	1	yes	characteristic
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	29	1	no	—
96	C₂×C₄	—	29	1	no	—
97	C₂×C₄	—	29	2	no	—
98	C₂×C₄	—	29	2	no	—
99	C₂×C₄	—	29	2	no	—
100	C₂×C₄	—	58	1	no	—
101	C₂×C₄	—	58	1	no	—
102	C₂×C₄	—	58	2	no	—
103	C₂×C₄	—	58	2	no	—
104	C₂×C₄	—	58	2	no	—
105	C₂×C₄	C₄⋊#1181	1	2	yes	—
106	C₈	—	116	2	no	—
107	C₈	—	116	2	no	—
108	C₂²	C₂×C₄⋊#1181	1	1	yes	characteristic
109	C₂²	#11745345	1	2	yes	—
110	C₂²	#11745346	1	2	yes	—
111	C₂²	#11745346	1	1	yes	characteristic
112	C₂²	#11745348	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	4	2	no	—
115	C₄	—	29	1	no	—
116	C₄	—	29	1	no	—
117	C₄	—	29	2	no	—
118	C₄	—	58	2	no	—
119	C₄	—	116	2	no	—
120	C₂	#14272107	1	1	yes	characteristic
121	C₂	#14272169	1	1	yes	characteristic
122	C₂	#14272170	1	1	yes	characteristic
123	C₂	#14272187	1	2	yes	—
124	C₂	#14272188	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745220

C₂

yes

maximal, characteristic

C₂×C₄⋊#6599

C₂

yes

maximal, characteristic

#14272029

C₂

yes

maximal

#14271008

C₂

yes

maximal, characteristic

C₂²×#6599

C₂²

yes

—

C₂²×#6599

C₂²

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

—

C₂×C₄×Dic₂₉

C₂²

yes

characteristic

#11745220

—

C₄⋊#6599

—

C₂₉×#95

C₄

yes

characteristic

#11745179

C₄

yes

characteristic

#11745179

C₄

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂×C₄

yes

—

C₂²×Dic₂₉

C₂×C₄

yes

characteristic

C₂²×Dic₂₉

C₂³

yes

—

—

—

—

C₄×Dic₂₉

—

C₄×Dic₂₉

—

C₄×Dic₂₉

D₄

yes

—

C₄×Dic₂₉

Q₈

yes

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄⋊C₄

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₄⋊C₄

yes

—

C₂×Dic₂₉

C₂×D₄

yes

characteristic

C₂×Dic₂₉

C₂×Q₈

yes

characteristic

C₂×Dic₂₉

#41

yes

—

C₂×Dic₂₉

#41

yes

—

—

—

—

C₂²×C₂₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉

#117

yes

—

C₂²×C₂₉

#131

yes

—

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

yes

Dic₂₉

yes

Dic₂₉

yes

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

#376

—

#336

—

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

C₂×C₂₉

#433

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

—

—

yes

C₂₉

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#1181

yes

—

C₂²×C₄

C₂×#1181

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂²×#1181

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₄⋊#1181

yes

—

106

C₈

—

116

—

107

C₈

—

116

—

108

C₂²

C₂×C₄⋊#1181

yes

characteristic

109

C₂²

#11745345

yes

—

110

C₂²

#11745346

yes

—

111

C₂²

#11745346

yes

characteristic

112

C₂²

#11745348

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

116

—

120

C₂

#14272107

yes

characteristic

121

C₂

#14272169

yes

characteristic

122

C₂

#14272170

yes

characteristic

123

C₂

#14272187

yes

—

124

C₂

#14272188

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#1181
commutator, socle, prime radical	C₂³×C₂₉	C₂²×C₄
Fitting	C₂₉×#95	C₄
cosocle	C₂²×Dic₂₉	C₂³
hypercenter	#95	#1181
hypocenter	C₂₉	#1832
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×#1181

commutator, socle, prime radical

C₂³×C₂₉

C₂²×C₄

Fitting

C₂₉×#95

C₄

cosocle

C₂²×Dic₂₉

C₂³

C₂₉

G ▷ C₂³×C₂₉ ▷ C₂₉

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
76. C₂₉	#1832	semidirect

H ≅ G/N

type

76. C₂₉

#1832

semidirect

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

subgroup	index
C₂×#11745220	2
C₂×C₄⋊#6599	2
#14272029	2
#14271008	2
#1832	29

subgroup

index

C₂×C₄⋊#6599

Subgroups — #16835410

Conjugacy classes of subgroups

Complements

Maximal subgroups