Group #16835211 — subgroups

Subgroups — #16835211

Order 3712.

240 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 98 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×#11745218	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	#11745218	C₄	1	4	yes	complemented
10	C₄×#6599	C₄	1	4	yes	complemented
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	4	no	—
20	C₂×#6599	—	2	4	no	—
21	C₂×#6599	C₂×C₄	1	4	yes	—
22	C₂×#6599	C₂×C₄	1	4	yes	—
23	C₄×Dic₂₉	—	2	4	no	—
24	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
25	C₄×Dic₂₉	C₂×C₄	1	2	yes	—
26	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₂₉	—	2	2	no	—
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	C₄²	1	2	yes	—
32	C₂×Dic₂₉	—	2	1	no	—
33	C₂×Dic₂₉	—	2	1	no	—
34	C₂×Dic₂₉	—	2	2	no	—
35	C₂×Dic₂₉	—	2	2	no	—
36	C₂×Dic₂₉	—	2	2	no	—
37	C₂×Dic₂₉	C₄²	1	2	yes	—
38	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
39	C₂×Dic₂₉	C₂²×C₄	1	1	yes	characteristic
40	C₂×Dic₂₉	#41	1	4	yes	—
41	#6599	—	2	4	no	—
42	#6599	—	2	4	no	—
43	#1746	—	29	1	no	maximal, Sylow
44	C₂²×C₂₉	C₂×C₄²	1	1	yes	characteristic
45	C₂²×C₂₉	#117	1	2	yes	—
46	C₂²×C₂₉	#131	1	2	yes	—
47	C₂²×C₂₉	#131	1	1	yes	characteristic
48	C₂²×C₂₉	#131	1	1	yes	characteristic
49	C₄×C₂₉	—	2	2	no	—
50	C₄×C₂₉	—	4	2	no	—
51	Dic₂₉	—	2	2	no	—
52	Dic₂₉	—	4	2	no	—
53	Dic₂₉	#117	1	2	yes	—
54	Dic₂₉	#117	1	2	yes	—
55	C₂×#97	—	29	1	no	—
56	C₂×C₄×C₈	—	29	1	no	—
57	#376	—	29	1	no	—
58	#336	—	29	4	no	—
59	C₂×C₂₉	#376	1	1	yes	characteristic
60	C₂×C₂₉	#405	1	1	yes	characteristic
61	C₂×C₂₉	#405	1	1	yes	characteristic
62	C₂×C₂₉	#433	1	2	yes	—
63	C₂×C₂₉	#433	1	2	yes	—
64	C₂²×C₈	—	29	2	no	—
65	C₂²×C₈	—	29	2	no	—
66	C₂×C₄²	—	29	1	no	—
67	C₂×C₄²	—	29	2	no	—
68	#97	—	29	4	no	—
69	C₄×C₈	—	29	4	no	—
70	#95	—	29	2	no	—
71	#95	—	29	1	no	—
72	#95	#1181	1	1	yes	characteristic
73	C₂₉	#1746	1	1	yes	characteristic, complemented, Sylow
74	C₂²×C₄	—	29	1	no	—
75	C₂²×C₄	—	29	1	no	—
76	C₂²×C₄	—	29	2	no	—
77	C₂²×C₄	C₂×#1181	1	2	yes	—
78	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
79	C₂×C₈	—	29	4	no	—
80	C₂×C₈	—	29	4	no	—
81	C₂×C₈	—	58	4	no	—
82	C₂×C₈	—	58	4	no	—
83	C₄²	—	29	2	no	—
84	C₄²	—	29	2	no	—
85	C₄²	—	58	4	no	—
86	C₂³	C₂²×#1181	1	1	yes	characteristic
87	C₂×C₄	—	2	2	no	—
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	2	2	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	—	29	1	no	—
92	C₂×C₄	—	29	1	no	—
93	C₂×C₄	—	29	4	no	—
94	C₂×C₄	—	29	2	no	—
95	C₂×C₄	—	58	1	no	—
96	C₂×C₄	—	58	1	no	—
97	C₂×C₄	—	58	2	no	—
98	C₂×C₄	—	58	2	no	—
99	C₂×C₄	—	58	2	no	—
100	C₂×C₄	C₄×#1181	1	2	yes	—
101	C₈	—	58	4	no	—
102	C₈	—	58	4	no	—
103	C₂²	C₂×C₄×#1181	1	1	yes	characteristic
104	C₂²	#11745345	1	2	yes	—
105	C₂²	#11745346	1	2	yes	—
106	C₂²	#11745346	1	1	yes	characteristic
107	C₂²	#11745348	1	1	yes	characteristic
108	C₄	—	2	2	no	—
109	C₄	—	4	2	no	—
110	C₄	—	29	2	no	—
111	C₄	—	29	2	no	—
112	C₄	—	58	2	no	—
113	C₄	—	116	2	no	—
114	C₂	#14272099	1	1	yes	characteristic
115	C₂	#14272127	1	1	yes	characteristic
116	C₂	#14272128	1	1	yes	characteristic
117	C₂	#14272187	1	2	yes	—
118	C₂	#14272188	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745218

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

#11745218

C₄

yes

complemented

C₄×#6599

C₄

yes

complemented

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

—

—

C₂×C₄

yes

—

C₂×#6599

C₂×C₄

yes

—

C₄×Dic₂₉

—

C₄×Dic₂₉

C₂×C₄

yes

—

C₄×Dic₂₉

C₂×C₄

yes

—

C₂³×C₂₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₄²

yes

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

—

C₂×Dic₂₉

C₄²

yes

—

C₂×Dic₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

C₂²×C₄

yes

characteristic

C₂×Dic₂₉

#41

yes

—

—

—

—

C₂²×C₂₉

C₂×C₄²

yes

characteristic

C₂²×C₂₉

#117

yes

—

C₂²×C₂₉

#131

yes

—

C₂²×C₂₉

yes

C₂²×C₂₉

yes

C₄×C₂₉

—

C₄×C₂₉

—

Dic₂₉

—

Dic₂₉

—

Dic₂₉

#117

yes

—

Dic₂₉

#117

yes

—

C₂×#97

—

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

—

#97

—

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

—

C₂³

C₂²×#1181

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₄×#1181

yes

—

101

C₈

—

102

C₈

—

103

C₂²

C₂×C₄×#1181

yes

characteristic

104

C₂²

#11745345

yes

—

105

C₂²

#11745346

yes

—

106

C₂²

#11745346

yes

characteristic

107

C₂²

#11745348

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

116

—

114

C₂

#14272099

yes

characteristic

115

C₂

#14272127

yes

characteristic

116

C₂

#14272128

yes

characteristic

117

C₂

#14272187

yes

—

118

C₂

#14272188

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#1181
commutator	C₂²×C₂₉	C₂×C₄²
Fitting	C₂₉×#95	C₄
socle, prime radical	C₂³×C₂₉	C₂²×C₄
cosocle	C₂²×Dic₂₉	C₂³
hypercenter	#95	#1181
hypocenter	C₂₉	#1746
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×#1181

commutator

C₂²×C₂₉

C₂×C₄²

Fitting

C₂₉×#95

C₄

socle, prime radical

C₂³×C₂₉

C₂²×C₄

cosocle

C₂²×Dic₂₉

C₂³

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
9. #11745218	C₄	semidirect
10. C₄×#6599	C₄	semidirect
73. C₂₉	#1746	semidirect

H ≅ G/N

type

9. #11745218

C₄

semidirect

10. C₄×#6599

C₄

semidirect

73. C₂₉

#1746

semidirect

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

subgroup	index
C₂×#11745218	2
C₂×C₄×#6599	2
#14272029	2
#14271008	2
#1746	29

subgroup

index

C₂×C₄×#6599

Subgroups — #16835211

Conjugacy classes of subgroups

Complements

Maximal subgroups