Group #16835722 — subgroups

Subgroups — #16835722

Order 3712.

228 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 90 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×#11745214	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#90770	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊#90770	C₂	1	4	yes	maximal, complemented
4	C₂×#11745310	C₂	1	1	yes	maximal, characteristic
5	C₂×#41×C₂₉	C₄	1	1	yes	characteristic
6	#11745310	—	2	2	no	—
7	#11745310	—	2	2	no	—
8	C₂×#90777	C₄	1	1	yes	characteristic
9	C₂×#90777	C₄	1	2	yes	—
10	C₂²×#6597	C₂²	1	2	yes	—
11	C₂²×#6597	C₂²	1	1	yes	characteristic
12	#11745214	—	2	2	no	—
13	C₂×#90770	—	2	2	no	—
14	C₂×#90770	C₂²	1	2	yes	—
15	C₂×#90770	C₂²	1	2	yes	—
16	#41×C₂₉	—	2	2	no	—
17	#41×C₂₉	—	2	2	no	—
18	C₂×Q₈×C₂₉	C₈	1	1	yes	characteristic
19	C₂×D₄×C₂₉	C₈	1	2	yes	—
20	C₂×D₄×C₂₉	C₈	1	1	yes	characteristic
21	C₂²×C₄×C₂₉	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
23	#90777	—	2	2	no	—
24	#90777	—	2	4	no	—
25	C₂×#6597	—	2	2	no	—
26	C₂×#6597	—	2	2	no	—
27	C₂×#6597	C₂×C₄	1	2	yes	—
28	C₂×#6597	C₂×C₄	1	1	yes	characteristic
29	C₂×#6597	D₄	1	2	yes	—
30	C₂×#6597	D₄	1	2	yes	—
31	C₂×#6597	C₂³	1	1	yes	characteristic
32	#90770	—	2	2	no	—
33	#90770	—	2	2	no	—
34	C₂³×C₂₉	C₂×C₈	1	2	yes	—
35	C₂³×C₂₉	C₂×C₈	1	1	yes	characteristic
36	Q₈×C₂₉	—	2	2	no	—
37	D₄×C₂₉	—	2	4	no	—
38	D₄×C₂₉	—	2	2	no	—
39	C₂×C₄×C₂₉	—	2	2	no	—
40	C₂×C₄×C₂₉	—	2	2	no	—
41	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
42	C₂×C₄×C₂₉	C₂×C₈	1	2	yes	—
43	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
44	C₂×C₄×C₂₉	M₁₆	1	2	yes	—
45	C₂×C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
46	#6597	—	2	2	no	—
47	#6597	C₂²⋊C₄	1	2	yes	—
48	#6597	C₂×D₄	1	1	yes	characteristic
49	#6597	C₂×D₄	1	1	yes	characteristic
50	#2113	—	29	1	no	maximal, Sylow
51	C₂²×C₂₉	—	2	2	no	—
52	C₂²×C₂₉	—	2	2	no	—
53	C₂²×C₂₉	—	2	4	no	—
54	C₂²×C₂₉	C₂²⋊C₈	1	2	yes	—
55	C₂²×C₂₉	C₂²×C₈	1	1	yes	characteristic
56	C₄×C₂₉	—	2	2	no	—
57	C₄×C₂₉	C₂²⋊C₈	1	2	yes	—
58	C₄×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
59	C₄×C₂₉	C₂×M₁₆	1	1	yes	characteristic
60	C₂×#131	—	29	1	no	—
61	C₂×M₃₂	—	29	1	no	—
62	C₂²×C₁₆	—	29	1	no	—
63	C₂²⋊C₁₆	—	29	4	no	—
64	C₂×C₂₉	—	2	2	no	—
65	C₂×C₂₉	—	4	2	no	—
66	C₂×C₂₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
67	C₂×C₂₉	#504	1	2	yes	—
68	C₂×#41	#1181	1	1	yes	characteristic
69	#131	—	58	2	no	—
70	#131	—	58	2	no	—
71	C₂×M₁₆	—	29	2	no	—
72	C₂×M₁₆	—	29	1	no	—
73	C₂²×C₈	—	29	1	no	—
74	C₂²×C₈	—	29	2	no	—
75	M₃₂	—	58	2	no	—
76	C₂×C₁₆	—	29	2	no	—
77	C₂×C₁₆	—	29	2	no	—
78	C₂×C₁₆	—	58	2	no	—
79	C₂₉	#2113	1	1	yes	characteristic, complemented, Sylow
80	#41	—	2	2	no	—
81	#41	—	2	2	no	—
82	C₂×Q₈	#6599	1	1	yes	characteristic
83	C₂×D₄	#6599	1	2	yes	—
84	C₂×D₄	#6599	1	1	yes	characteristic
85	C₂²×C₄	C₂×#1181	1	2	yes	—
86	C₂²×C₄	C₂×#1181	1	1	yes	characteristic
87	M₁₆	—	58	4	no	—
88	M₁₆	—	58	2	no	—
89	C₂×C₈	—	29	2	no	—
90	C₂×C₈	—	29	2	no	—
91	C₂×C₈	—	29	1	no	—
92	C₂×C₈	—	29	1	no	—
93	C₂×C₈	—	29	2	no	—
94	C₂×C₈	—	58	2	no	—
95	C₂×C₈	—	58	2	no	—
96	C₁₆	—	58	2	no	—
97	C₁₆	—	58	2	no	—
98	C₂³	C₂×#6599	1	2	yes	—
99	C₂³	C₂×#6599	1	1	yes	characteristic
100	Q₈	—	2	2	no	—
101	D₄	—	2	4	no	—
102	D₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	C₂×#6599	1	2	yes	—
106	C₂×C₄	C₂×#6599	1	1	yes	characteristic
107	C₂×C₄	#90800	1	2	yes	—
108	C₂×C₄	C₂²⋊#1181	1	2	yes	—
109	C₂×C₄	C₂²×#1181	1	1	yes	characteristic
110	C₈	—	29	1	no	—
111	C₈	—	29	1	no	—
112	C₈	—	29	2	no	—
113	C₈	—	58	2	no	—
114	C₂²	—	2	2	no	—
115	C₂²	—	2	2	no	—
116	C₂²	—	2	4	no	—
117	C₂²	C₂²⋊#6599	1	2	yes	—
118	C₂²	C₂²×#6599	1	1	yes	characteristic
119	C₄	—	2	2	no	—
120	C₄	C₂²⋊#6599	1	2	yes	—
121	C₄	C₂×#90800	1	1	yes	characteristic
122	C₄	C₂×C₂²⋊#1181	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	4	2	no	—
125	C₂	C₂×C₂²⋊#6599	1	1	yes	characteristic
126	C₂	#14272221	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745214

C₂

yes

maximal, characteristic, complemented

C₂²×#90770

C₂

yes

maximal, characteristic, complemented

C₂²⋊#90770

C₂

yes

maximal, complemented

C₂×#11745310

C₂

yes

maximal, characteristic

C₂×#41×C₂₉

C₄

yes

—

—

C₄

yes

characteristic

C₂×#90777

C₄

yes

—

C₂²×#6597

C₂²

yes

—

C₂²×#6597

C₂²

yes

—

—

C₂²

yes

—

C₂×#90770

C₂²

yes

—

#41×C₂₉

—

#41×C₂₉

—

C₂×Q₈×C₂₉

C₈

yes

characteristic

C₂×D₄×C₂₉

C₈

yes

—

C₂×D₄×C₂₉

C₈

yes

characteristic

C₂²×C₄×C₂₉

C₂×C₄

yes

—

C₂²×C₄×C₂₉

C₂×C₄

yes

—

—

—

—

C₂×C₄

yes

—

C₂×#6597

C₂×C₄

yes

characteristic

C₂×#6597

D₄

yes

—

C₂×#6597

D₄

yes

—

C₂×#6597

C₂³

yes

characteristic

#90770

—

#90770

—

C₂³×C₂₉

C₂×C₈

yes

—

C₂³×C₂₉

C₂×C₈

yes

characteristic

Q₈×C₂₉

—

D₄×C₂₉

—

D₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂²⋊C₄

yes

—

C₂×C₄×C₂₉

C₂×C₈

yes

—

C₂×C₄×C₂₉

C₂×C₈

yes

characteristic

C₂×C₄×C₂₉

M₁₆

yes

—

C₂×C₄×C₂₉

C₂²×C₄

yes

characteristic

#6597

—

#6597

C₂²⋊C₄

yes

—

#6597

C₂×D₄

yes

characteristic

#6597

C₂×D₄

yes

characteristic

#2113

—

maximal, Sylow

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

—

C₂²×C₂₉

C₂²⋊C₈

yes

—

C₂²×C₂₉

C₂²×C₈

yes

characteristic

C₄×C₂₉

—

C₄×C₂₉

C₂²⋊C₈

yes

—

C₄×C₂₉

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₂₉

C₂×M₁₆

yes

characteristic

C₂×#131

—

C₂×M₃₂

—

C₂²×C₁₆

—

C₂²⋊C₁₆

—

C₂×C₂₉

—

C₂×C₂₉

—

C₂×C₂₉

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₂₉

#504

yes

—

C₂×#41

yes

—

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂₉

#2113

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

#6599

yes

characteristic

C₂×D₄

#6599

yes

—

C₂×D₄

#6599

yes

characteristic

C₂²×C₄

C₂×#1181

yes

—

C₂²×C₄

C₂×#1181

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₁₆

—

C₁₆

—

C₂³

C₂×#6599

yes

—

C₂³

C₂×#6599

yes

characteristic

100

Q₈

—

101

D₄

—

102

D₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂×#6599

yes

—

106

C₂×C₄

C₂×#6599

yes

characteristic

107

C₂×C₄

#90800

yes

—

108

C₂×C₄

C₂²⋊#1181

yes

—

109

C₂×C₄

C₂²×#1181

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

C₂²⋊#6599

yes

—

118

C₂²

C₂²×#6599

yes

characteristic

119

C₄

—

120

C₄

C₂²⋊#6599

yes

—

121

C₄

C₂×#90800

yes

characteristic

122

C₄

C₂×C₂²⋊#1181

yes

characteristic

123

C₂

—

124

C₂

—

125

C₂

C₂×C₂²⋊#6599

yes

characteristic

126

C₂

#14272221

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#1181
commutator, socle	C₂²×C₂₉	C₂²×C₈
Fitting, prime radical	C₂×#41×C₂₉	C₄
cosocle	C₂×#6597	C₂³
hypercenter	C₂×#41	#1181
hypocenter	C₂₉	#2113
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#1181

commutator, socle

C₂²×C₂₉

C₂²×C₈

Fitting, prime radical

C₂×#41×C₂₉

C₄

C₂³

C₂×#41

C₂₉

G ▷ C₂²×C₂₉ ▷ C₂₉

C₁ ◁ C₂×C₄ ◁ C₂×#41

N	H ≅ G/N	type
1. C₂×#11745214	C₂	semidirect
2. C₂²×#90770	C₂	semidirect
3. C₂²⋊#90770	C₂	semidirect
79. C₂₉	#2113	semidirect

H ≅ G/N

type

1. C₂×#11745214

C₂

semidirect

2. C₂²×#90770

C₂

semidirect

3. C₂²⋊#90770

C₂

semidirect

79. C₂₉

#2113

semidirect

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

subgroup	index
C₂×#11745214	2
C₂²×#90770	2
C₂²⋊#90770	2
C₂×#11745310	2
#2113	29

subgroup

index

C₂²×#90770

Subgroups — #16835722

Conjugacy classes of subgroups

Complements

Maximal subgroups