Group #16798257 — subgroups

Subgroups — D₁₃⋊#1843 #16798257

Order 3328.

1230 conjugacy classes of subgroups; only the 416 normal subgroups are shown.

normal subgroups only

This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 416 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×D₁₃⋊(C₄⋊C₈)	C₂	1	6	yes	maximal
2	#13130770	C₂	1	8	yes	maximal, complemented
3	D₁₃×#376	C₂	1	1	yes	maximal, characteristic
4	C₂²×D₁₃⋊C₈	C₂²	1	4	yes	—
5	C₂×C₄²×D₁₃	C₂²	1	3	yes	—
6	C₂×#88112	C₂²	1	12	yes	—
7	C₂×C₄⋊#1057	C₂²	1	12	yes	—
8	D₁₃⋊(C₄⋊C₈)	—	2	24	no	—
9	C₁₃×#376	C₄	1	1	yes	characteristic
10	#11718593	C₄	1	3	yes	—
11	D₁₃×#95	C₄	1	4	yes	—
12	#11718309	C₂²	1	4	yes	—
13	C₂²×C₄×D₁₃	C₂×C₄	1	6	yes	—
14	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
15	C₂²×#1057	C₂³	1	8	yes	—
16	C₂×D₁₃⋊C₈	—	2	24	no	—
17	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	—
18	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	—
19	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
20	C₄²×D₁₃	D₄	1	12	yes	—
21	C₄²×D₁₃	Q₈	1	12	yes	—
22	#88112	—	2	24	no	—
23	C₄⋊#1057	—	2	24	no	—
24	C₁₃×#95	C₂×C₄	1	4	yes	—
25	#88071	C₂×C₄	1	12	yes	—
26	C₂×#1843	—	13	1	no	maximal, Sylow
27	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
29	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
30	C₂²×Dic₁₃	C₂²×C₄	1	6	yes	—
31	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
32	C₂×C₄×D₁₃	—	2	24	no	—
33	C₂×C₄×D₁₃	C₄⋊C₄	1	24	yes	—
34	C₂×C₄×D₁₃	C₂×D₄	1	6	yes	—
35	C₂×C₄×D₁₃	C₂×Q₈	1	6	yes	—
36	C₂×#1057	—	2	24	no	—
37	D₁₃⋊C₈	—	4	16	no	—
38	C₄²×C₁₃	C₄⋊C₄	1	12	yes	—
39	C₄×Dic₁₃	C₄⋊C₄	1	12	yes	—
40	C₄×Dic₁₃	C₂×D₄	1	12	yes	—
41	C₄×Dic₁₃	C₂×Q₈	1	12	yes	—
42	C₂²×C₄⋊C₈	—	13	6	no	—
43	C₂×#376	—	13	1	no	—
44	#1843	—	13	8	no	—
45	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
46	C₂²×D₁₃	C₂×C₄⋊C₄	1	6	yes	—
47	C₂²×D₁₃	#131	1	8	yes	—
48	C₂×C₄×C₁₃	—	2	12	no	—
49	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	12	yes	—
50	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	6	yes	—
51	C₂×Dic₁₃	—	2	12	no	—
52	C₂×Dic₁₃	C₂×C₄⋊C₄	1	12	yes	—
53	C₂×Dic₁₃	C₂²×D₄	1	3	yes	—
54	C₂×Dic₁₃	C₂²×Q₈	1	3	yes	—
55	C₄×D₁₃	—	2	48	no	—
56	C₄×D₁₃	#127	1	4	yes	—
57	C₄×D₁₃	C₄⋊Q₈	1	12	yes	—
58	#1057	—	4	8	no	—
59	C₂³×C₈	—	13	4	no	—
60	C₂²×C₄²	—	13	3	no	—
61	C₂×C₄⋊C₈	—	13	12	no	—
62	C₂×C₄⋊C₈	—	13	12	no	—
63	C₂×C₄⋊C₈	—	26	24	no	—
64	#376	—	13	3	no	—
65	#376	—	13	4	no	—
66	#376	#261	1	1	yes	characteristic
67	C₂×#95	—	13	4	no	—
68	C₂²×C₁₃	C₂²×C₄⋊C₄	1	3	yes	—
69	C₂²×C₁₃	C₂×#131	1	4	yes	—
70	C₂×D₁₃	#384	1	4	yes	—
71	C₂×D₁₃	#424	1	24	yes	—
72	C₄×C₁₃	—	2	12	no	—
73	C₄×C₁₃	#384	1	4	yes	—
74	Dic₁₃	—	2	12	no	—
75	Dic₁₃	C₂×#127	1	1	yes	characteristic
76	Dic₁₃	C₂×C₄⋊Q₈	1	3	yes	—
77	C₂³×C₄	—	13	1	no	—
78	C₂³×C₄	—	13	6	no	—
79	C₂²×C₈	—	13	8	no	—
80	C₂²×C₈	—	26	24	no	—
81	C₂×C₄²	—	13	6	no	—
82	C₂×C₄²	—	13	3	no	—
83	C₂×C₄²	—	13	12	no	—
84	C₂×C₄²	—	13	12	no	—
85	C₂×C₄²	C₂×#261	1	3	yes	—
86	C₄⋊C₈	—	26	24	no	—
87	C₄⋊C₈	—	26	24	no	—
88	#95	—	13	12	no	—
89	#95	C₂×#261	1	4	yes	—
90	C₂×C₁₃	C₂×#384	1	1	yes	characteristic
91	C₂×C₁₃	C₂×#424	1	6	yes	—
92	D₁₃	#1843	1	8	yes	complemented
93	C₂⁴	—	13	1	no	—
94	C₂²×C₄	—	13	1	no	—
95	C₂²×C₄	—	13	6	no	—
96	C₂²×C₄	—	13	6	no	—
97	C₂²×C₄	—	13	6	no	—
98	C₂²×C₄	—	13	24	no	—
99	C₂²×C₄	—	26	24	no	—
100	C₂²×C₄	C₂²×#261	1	6	yes	—
101	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
102	C₂×C₈	—	26	24	no	—
103	C₂×C₈	—	52	16	no	—
104	C₄²	—	13	12	no	—
105	C₄²	—	13	12	no	—
106	C₄²	—	13	12	no	—
107	C₄²	C₄⋊#261	1	12	yes	—
108	C₁₃	C₂×#1843	1	1	yes	characteristic, complemented, Sylow
109	C₂³	—	13	6	no	—
110	C₂³	—	13	8	no	—
111	C₂³	C₂³×#261	1	1	yes	characteristic
112	C₂×C₄	—	2	12	no	—
113	C₂×C₄	—	13	3	no	—
114	C₂×C₄	—	13	3	no	—
115	C₂×C₄	—	13	4	no	—
116	C₂×C₄	—	13	12	no	—
117	C₂×C₄	—	13	12	no	—
118	C₂×C₄	—	26	48	no	—
119	C₂×C₄	—	26	12	no	—
120	C₂×C₄	C₂×C₄⋊#261	1	12	yes	—
121	C₂×C₄	C₂×C₄⋊#261	1	6	yes	—
122	C₈	—	52	8	no	—
123	C₂²	—	13	4	no	—
124	C₂²	—	13	24	no	—
125	C₂²	C₂²×C₄⋊#261	1	3	yes	—
126	C₂²	D₁₃⋊#131	1	4	yes	—
127	C₄	—	2	12	no	—
128	C₄	—	13	1	no	—
129	C₄	—	13	3	no	—
130	C₄	—	26	12	no	—
131	C₄	#11719059	1	4	yes	—
132	C₂	—	13	8	no	—
133	C₂	C₂×#11719059	1	1	yes	characteristic
134	C₂	D₁₃⋊#424	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₁₃⋊(C₄⋊C₈)

C₂

yes

maximal

#13130770

C₂

yes

maximal, complemented

D₁₃×#376

C₂

yes

maximal, characteristic

C₂²×D₁₃⋊C₈

C₂²

yes

—

C₂×C₄²×D₁₃

C₂²

yes

—

C₂×#88112

C₂²

yes

—

C₂×C₄⋊#1057

C₂²

yes

—

D₁₃⋊(C₄⋊C₈)

—

C₁₃×#376

C₄

yes

characteristic

#11718593

C₄

yes

—

D₁₃×#95

C₄

yes

—

#11718309

C₂²

yes

—

C₂²×C₄×D₁₃

C₂×C₄

yes

—

C₂²×C₄×D₁₃

C₂³

yes

characteristic

C₂²×#1057

C₂³

yes

—

C₂×D₁₃⋊C₈

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄×Dic₁₃

C₂×C₄

yes

—

C₂×C₄×Dic₁₃

C₂³

yes

—

C₄²×D₁₃

D₄

yes

—

C₄²×D₁₃

Q₈

yes

—

#88112

—

C₄⋊#1057

—

C₁₃×#95

C₂×C₄

yes

—

#88071

C₂×C₄

yes

—

C₂×#1843

—

maximal, Sylow

C₂³×D₁₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂²×C₄

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×Dic₁₃

C₂²×C₄

yes

—

C₂²×Dic₁₃

C₂⁴

yes

characteristic

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

C₄⋊C₄

yes

—

C₂×C₄×D₁₃

C₂×D₄

yes

—

C₂×C₄×D₁₃

C₂×Q₈

yes

—

C₂×#1057

—

D₁₃⋊C₈

—

C₄²×C₁₃

C₄⋊C₄

yes

—

C₄×Dic₁₃

C₄⋊C₄

yes

—

C₄×Dic₁₃

C₂×D₄

yes

—

C₄×Dic₁₃

C₂×Q₈

yes

—

C₂²×C₄⋊C₈

—

C₂×#376

—

#1843

—

C₂³×C₁₃

C₂³×C₄

yes

characteristic

C₂²×D₁₃

C₂×C₄⋊C₄

yes

—

C₂²×D₁₃

#131

yes

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

C₂×C₄⋊C₄

yes

—

C₂×Dic₁₃

C₂²×D₄

yes

—

C₂×Dic₁₃

C₂²×Q₈

yes

—

C₄×D₁₃

—

C₄×D₁₃

#127

yes

—

C₄×D₁₃

C₄⋊Q₈

yes

—

#1057

—

C₂³×C₈

—

C₂²×C₄²

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

—

—

yes

C₂×#95

—

C₂²×C₁₃

C₂²×C₄⋊C₄

yes

—

C₂²×C₁₃

C₂×#131

yes

—

C₂×D₁₃

#384

yes

—

C₂×D₁₃

#424

yes

—

C₄×C₁₃

—

C₄×C₁₃

#384

yes

—

Dic₁₃

—

Dic₁₃

C₂×#127

yes

characteristic

Dic₁₃

C₂×C₄⋊Q₈

yes

—

C₂³×C₄

—

C₂³×C₄

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×#261

yes

—

C₄⋊C₈

—

C₄⋊C₈

—

#95

—

#95

C₂×#261

yes

—

C₂×C₁₃

C₂×#384

yes

characteristic

C₂×C₁₃

C₂×#424

yes

—

D₁₃

#1843

yes

complemented

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂²×C₄

C₂²×#261

yes

—

101

C₂²×C₄

C₂²×#261

yes

characteristic

102

C₂×C₈

—

103

C₂×C₈

—

104

C₄²

—

105

C₄²

—

106

C₄²

—

107

C₄²

C₄⋊#261

yes

—

108

C₁₃

C₂×#1843

yes

characteristic, complemented, Sylow

109

C₂³

—

110

C₂³

—

111

C₂³

C₂³×#261

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

C₂×C₄⋊#261

yes

—

121

C₂×C₄

C₂×C₄⋊#261

yes

—

122

C₈

—

123

C₂²

—

124

C₂²

—

125

C₂²

C₂²×C₄⋊#261

yes

—

126

C₂²

D₁₃⋊#131

yes

—

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

#11719059

yes

—

132

C₂

—

133

C₂

C₂×#11719059

yes

characteristic

134

C₂

D₁₃⋊#424

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×#261
commutator, socle	C₂³×C₁₃	C₂³×C₄
Frattini	C₂³	C₂³×#261
Fitting	C₁₃×#376	C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂²×Dic₁₃	C₂⁴
hypercenter	#376	#261
hypocenter	C₁₃	C₂×#1843
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center

C₂²×C₄

C₂²×#261

commutator, socle

C₂³×C₁₃

C₂³×C₄

Frattini

C₂³

C₂³×#261

Fitting

C₁₃×#376

C₄

prime radical

C₂³×D₁₃

C₂²×C₄

cosocle

C₂²×Dic₁₃

C₂⁴

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
2. #13130770	C₂	semidirect
92. D₁₃	#1843	semidirect
108. C₁₃	C₂×#1843	semidirect

H ≅ G/N

type

2. #13130770

C₂

semidirect

92. D₁₃

#1843

semidirect

108. C₁₃

C₂×#1843

semidirect

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

subgroup	index
C₂×D₁₃⋊(C₄⋊C₈)	2
#13130770	2
D₁₃×#376	2
C₂×#1843	13

subgroup

index

C₂×D₁₃⋊(C₄⋊C₈)

#13130770

D₁₃×#376

C₂×#1843

Subgroups — D₁₃⋊#1843 #16798257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D13⋊#1843 #16798257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊#1843 #16798257