Group #16829827 — subgroups

Subgroups — C₂×#14271528 #16829827

Order 3712.

488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745236	C₂	1	1	yes	maximal, characteristic
2	C₂×#11745232	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271528	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11745169	C₂	1	4	yes	maximal, complemented
5	C₂×C₂₉×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₁₆	—	2	2	no	—
7	C₂²×D₁₁₆	C₂²	1	2	yes	—
8	C₂²×C₈×C₂₉	C₂²	1	2	yes	—
9	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₂₉	C₂²	1	2	yes	—
11	C₂×#90779	—	2	2	no	—
12	#11745236	—	2	2	no	—
13	#11745236	C₂²	1	4	yes	—
14	#11745232	—	2	2	no	—
15	#11745232	C₂²	1	4	yes	complemented
16	C₂₉×#97	C₂²	1	4	yes	complemented
17	#11745169	C₂²	1	16	yes	complemented
18	C₂³×D₂₉	—	2	2	no	—
19	C₂²×C₄×C₂₉	D₄	1	2	yes	—
20	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
21	C₂²×Dic₂₉	—	2	2	no	—
22	C₂×D₁₁₆	—	2	8	no	—
23	C₂×D₁₁₆	—	2	8	no	—
24	C₂×D₁₁₆	—	2	2	no	—
25	C₂×D₁₁₆	—	4	8	no	—
26	C₂×D₁₁₆	C₂³	1	4	yes	—
27	C₂×C₈×C₂₉	—	2	4	no	—
28	C₂×C₈×C₂₉	C₂³	1	4	yes	—
29	C₄²×C₂₉	D₄	1	2	yes	—
30	C₄²×C₂₉	C₂³	1	2	yes	—
31	C₄⋊Dic₂₉	—	2	2	no	—
32	C₄⋊Dic₂₉	C₂³	1	4	yes	—
33	#90779	—	2	8	no	—
34	C₂³×C₂₉	C₂×D₄	1	1	yes	characteristic
35	C₂²×D₂₉	—	2	4	no	—
36	C₂²×D₂₉	—	4	4	no	—
37	C₂²×D₂₉	—	4	8	no	—
38	C₂×C₄×C₂₉	—	2	4	no	—
39	C₂×C₄×C₂₉	C₂×D₄	1	4	yes	—
40	C₂×C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₂₉	#41	1	4	yes	—
42	C₂×C₄×C₂₉	C₂⁴	1	1	yes	characteristic
43	C₂×Dic₂₉	—	2	4	no	—
44	C₂×Dic₂₉	—	4	4	no	—
45	D₁₁₆	—	2	8	no	—
46	D₁₁₆	—	4	16	no	—
47	D₁₁₆	—	4	4	no	—
48	C₈×C₂₉	—	2	4	no	—
49	C₂×#490	—	29	1	no	maximal, Sylow
50	C₂²×C₂₉	#124	1	2	yes	—
51	C₂²×C₂₉	AGL(1,ℤ/8)	1	4	yes	—
52	C₂²×C₂₉	C₂²×D₄	1	1	yes	characteristic
53	C₂×D₂₉	—	4	4	no	—
54	C₂×D₂₉	—	4	8	no	—
55	C₂×D₂₉	—	8	8	no	—
56	C₄×C₂₉	—	2	4	no	—
57	C₄×C₂₉	#124	1	2	yes	—
58	C₄×C₂₉	C₂×#41	1	2	yes	—
59	Dic₂₉	—	4	4	no	—
60	C₂×#127	—	29	1	no	—
61	C₂×#125	—	29	1	no	—
62	#490	—	29	8	no	—
63	C₂×#102	—	29	4	no	—
64	C₂×#97	D₂₉	1	1	yes	characteristic, complemented
65	C₂×C₂₉	#490	1	4	yes	complemented
66	C₂×C₂₉	C₂×#124	1	1	yes	characteristic
67	C₂×C₂₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
68	D₂₉	—	8	4	no	—
69	C₂²×D₄	—	29	2	no	—
70	C₂²×D₄	—	58	2	no	—
71	C₂²×C₈	C₂×D₂₉	1	2	yes	—
72	#127	—	29	4	no	—
73	#127	—	58	2	no	—
74	#125	—	29	4	no	—
75	#125	—	58	2	no	—
76	C₂×C₄⋊C₄	—	29	2	no	—
77	C₂×C₄⋊C₄	—	58	2	no	—
78	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
79	#102	—	29	16	no	—
80	#97	C₂×D₂₉	1	4	yes	complemented
81	C₂₉	C₂×#490	1	1	yes	characteristic, complemented, Sylow
82	C₂⁴	—	58	2	no	—
83	C₂×D₄	—	29	4	no	—
84	C₂×D₄	—	58	8	no	—
85	C₂×D₄	—	58	2	no	—
86	C₂×D₄	—	58	8	no	—
87	C₂×D₄	—	116	8	no	—
88	C₂²×C₄	—	58	2	no	—
89	C₂²×C₄	D₁₁₆	1	2	yes	—
90	C₂²×C₄	C₂²×D₂₉	1	1	yes	characteristic
91	C₂×C₈	—	2	4	no	—
92	C₂×C₈	C₂²×D₂₉	1	4	yes	—
93	C₄⋊C₄	—	29	4	no	—
94	C₄⋊C₄	—	58	2	no	—
95	C₄⋊C₄	—	58	8	no	—
96	C₄²	D₁₁₆	1	2	yes	—
97	C₄²	C₂²×D₂₉	1	2	yes	—
98	C₂³	—	58	4	no	—
99	C₂³	—	116	4	no	—
100	C₂³	—	116	8	no	—
101	C₂³	C₂×D₁₁₆	1	1	yes	characteristic
102	D₄	—	58	8	no	—
103	D₄	—	116	16	no	—
104	D₄	—	116	4	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	58	4	no	—
107	C₂×C₄	—	116	4	no	—
108	C₂×C₄	C₂×D₁₁₆	1	4	yes	—
109	C₂×C₄	C₂×D₁₁₆	1	1	yes	characteristic
110	C₂×C₄	#90805	1	4	yes	—
111	C₂×C₄	C₂³×D₂₉	1	1	yes	characteristic
112	C₈	—	2	4	no	—
113	C₂²	—	116	4	no	—
114	C₂²	—	116	8	no	—
115	C₂²	—	232	8	no	—
116	C₂²	#11745237	1	2	yes	—
117	C₂²	#11745270	1	4	yes	—
118	C₂²	C₂²×D₁₁₆	1	1	yes	characteristic
119	C₄	—	2	4	no	—
120	C₄	—	116	4	no	—
121	C₄	#11745237	1	2	yes	—
122	C₄	C₂×#90805	1	2	yes	—
123	C₂	—	232	4	no	—
124	C₂	#14271528	1	4	yes	direct product factor
125	C₂	C₂×#11745237	1	1	yes	characteristic
126	C₂	C₂×#11745270	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11745236

C₂

yes

maximal, characteristic

C₂×#11745232

C₂

yes

maximal, characteristic, complemented

#14271528

C₂

yes

maximal, direct product factor

C₂×#11745169

C₂

yes

maximal, complemented

C₂×C₂₉×#97

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₁₆

—

C₂²×D₁₁₆

C₂²

yes

—

C₂²×C₈×C₂₉

C₂²

yes

—

C₂×C₄²×C₂₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₉

C₂²

yes

—

C₂×#90779

—

#11745236

—

#11745236

C₂²

yes

—

#11745232

—

#11745232

C₂²

yes

complemented

C₂₉×#97

C₂²

yes

complemented

#11745169

C₂²

yes

complemented

C₂³×D₂₉

—

C₂²×C₄×C₂₉

D₄

yes

—

C₂²×C₄×C₂₉

C₂³

yes

characteristic

C₂²×Dic₂₉

—

C₂×D₁₁₆

—

C₂×D₁₁₆

—

C₂×D₁₁₆

—

C₂×D₁₁₆

—

C₂×D₁₁₆

C₂³

yes

—

C₂×C₈×C₂₉

—

C₂×C₈×C₂₉

C₂³

yes

—

C₄²×C₂₉

D₄

yes

—

C₄²×C₂₉

C₂³

yes

—

C₄⋊Dic₂₉

—

C₄⋊Dic₂₉

C₂³

yes

—

#90779

—

C₂³×C₂₉

C₂×D₄

yes

characteristic

C₂²×D₂₉

—

C₂²×D₂₉

—

C₂²×D₂₉

—

C₂×C₄×C₂₉

—

C₂×C₄×C₂₉

C₂×D₄

yes

—

C₂×C₄×C₂₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉

#41

yes

—

C₂×C₄×C₂₉

C₂⁴

yes

characteristic

C₂×Dic₂₉

—

C₂×Dic₂₉

—

D₁₁₆

—

D₁₁₆

—

D₁₁₆

—

C₈×C₂₉

—

C₂×#490

—

maximal, Sylow

C₂²×C₂₉

#124

yes

—

C₂²×C₂₉

AGL(1,ℤ/8)

yes

—

C₂²×C₂₉

C₂²×D₄

yes

characteristic

C₂×D₂₉

—

C₂×D₂₉

—

C₂×D₂₉

—

C₄×C₂₉

—

C₄×C₂₉

#124

yes

—

C₄×C₂₉

C₂×#41

yes

—

Dic₂₉

—

—

—

—

—

C₂×#97

D₂₉

yes

characteristic, complemented

C₂×C₂₉

yes

C₂×C₂₉

yes

C₂×C₂₉

yes

—

D₂₉

—

C₂²×D₄

—

C₂²×D₄

—

C₂²×C₈

C₂×D₂₉

yes

—

—

—

—

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₂₉

yes

characteristic

#102

—

#97

C₂×D₂₉

yes

complemented

C₂₉

C₂×#490

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

116

—

C₂²×C₄

—

C₂²×C₄

D₁₁₆

yes

—

C₂²×C₄

C₂²×D₂₉

yes

characteristic

C₂×C₈

—

C₂×C₈

C₂²×D₂₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₁₁₆

yes

—

C₄²

C₂²×D₂₉

yes

—

C₂³

—

C₂³

—

116

—

100

C₂³

—

116

—

101

C₂³

C₂×D₁₁₆

yes

characteristic

102

D₄

—

103

D₄

—

116

—

104

D₄

—

116

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

116

—

108

C₂×C₄

C₂×D₁₁₆

yes

—

109

C₂×C₄

C₂×D₁₁₆

yes

characteristic

110

C₂×C₄

#90805

yes

—

111

C₂×C₄

C₂³×D₂₉

yes

characteristic

112

C₈

—

113

C₂²

—

116

—

114

C₂²

—

116

—

115

C₂²

—

232

—

116

C₂²

#11745237

yes

—

117

C₂²

#11745270

yes

—

118

C₂²

C₂²×D₁₁₆

yes

characteristic

119

C₄

—

120

C₄

—

116

—

121

C₄

#11745237

yes

—

122

C₄

C₂×#90805

yes

—

123

C₂

—

232

—

124

C₂

#14271528

yes

direct product factor

125

C₂

C₂×#11745237

yes

characteristic

126

C₂

C₂×#11745270

yes

—

	subgroup	G/H
center	C₂³	C₂×D₁₁₆
commutator, cosocle	C₂×C₄×C₂₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₉
Fitting	C₂×C₂₉×#97	C₂
socle	C₂³×C₂₉	C₂×D₄
prime radical	C₂×#11745236	C₂
hypercenter	C₂×#97	D₂₉
hypocenter	C₂₉	C₂×#490
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₁₁₆

commutator, cosocle

C₂×C₄×C₂₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₂₉

Fitting

C₂×C₂₉×#97

C₂

socle

C₂³×C₂₉

C₂×D₄

prime radical

C₂×#11745236

C₂

hypercenter

C₂×#97

D₂₉

hypocenter

C₂₉

C₂×#490

LCS

G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
2. C₂×#11745232	C₂	semidirect
3. #14271528	C₂	direct (N × H)
4. C₂×#11745169	C₂	semidirect
5. C₂×C₂₉×#97	C₂	semidirect
15. #11745232	C₂²	semidirect
16. C₂₉×#97	C₂²	semidirect
17. #11745169	C₂²	semidirect
64. C₂×#97	D₂₉	semidirect
65. C₂×C₂₉	#490	semidirect
80. #97	C₂×D₂₉	semidirect
81. C₂₉	C₂×#490	semidirect
124. C₂	#14271528	direct (N × H)

H ≅ G/N

type

2. C₂×#11745232

C₂

semidirect

3. #14271528

C₂

direct (N × H)

4. C₂×#11745169

C₂

semidirect

5. C₂×C₂₉×#97

C₂

semidirect

15. #11745232

C₂²

semidirect

16. C₂₉×#97

C₂²

semidirect

17. #11745169

C₂²

semidirect

64. C₂×#97

D₂₉

semidirect

65. C₂×C₂₉

#490

semidirect

80. #97

C₂×D₂₉

semidirect

81. C₂₉

C₂×#490

semidirect

124. C₂

#14271528

direct (N × H)

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

subgroup	index
C₂×#11745236	2
C₂×#11745232	2
#14271528	2
C₂×#11745169	2
C₂×C₂₉×#97	2
C₂×#490	29

subgroup

index

C₂×C₂₉×#97

Subgroups — C₂×#14271528 #16829827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#14271528 #16829827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14271528 #16829827