Group #16791701 — subgroups

Subgroups — #16791701

Order 3328.

1246 conjugacy classes of subgroups; only the 288 normal subgroups are shown.

normal subgroups only

This group has 1246 conjugacy classes of subgroups — too many to draw. Only its 288 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	#13130023	C₂	1	8	yes	maximal
2	C₄×(C₂×#261)⋊C₄	C₂	1	6	yes	maximal
3	D₁₃×#376	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×#261	C₂²	1	4	yes	—
5	C₂×C₄²×D₁₃	C₂²	1	3	yes	—
6	C₂×(C₂×#261)⋊C₄	C₂²	1	24	yes	—
7	C₁₃×#376	C₄	1	1	yes	characteristic, complemented
8	#11718593	C₄	1	3	yes	complemented
9	D₁₃×#95	C₂²	1	4	yes	—
10	#11718309	C₄	1	4	yes	complemented
11	C₂³×#261	C₂³	1	8	yes	—
12	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
13	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
14	C₂×C₄×#261	—	2	24	no	—
15	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	—
16	C₂×C₄×Dic₁₃	C₂×C₄	1	6	yes	—
17	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	—
18	C₄²×D₁₃	—	2	12	no	—
19	(C₂×#261)⋊C₄	—	2	48	no	—
20	C₁₃×#95	C₂×C₄	1	4	yes	—
21	#88071	C₂×C₄	1	12	yes	—
22	#13855	—	13	1	no	maximal, Sylow
23	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
24	C₂²×#261	—	2	24	no	—
25	C₂²×#261	—	2	24	no	—
26	C₂²×#261	#41	1	16	yes	—
27	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
28	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
29	C₂²×Dic₁₃	C₂²×C₄	1	6	yes	—
30	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×D₁₃	—	2	24	no	—
32	C₂×C₄×D₁₃	—	2	12	no	—
33	C₂×C₄×D₁₃	#41	1	12	yes	—
34	C₄×#261	—	4	16	no	—
35	C₄²×C₁₃	—	2	6	no	—
36	C₄×Dic₁₃	—	2	6	no	—
37	C₄×Dic₁₃	—	2	12	no	—
38	C₂×#376	—	13	1	no	—
39	#1443	—	13	8	no	—
40	C₄×#95	—	13	6	no	—
41	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
42	C₂²×D₁₃	C₂×#41	1	6	yes	—
43	C₂²×D₁₃	C₂×#41	1	8	yes	—
44	C₂×#261	—	2	48	no	—
45	C₂×#261	—	4	8	no	—
46	C₂×#261	—	4	24	no	—
47	C₂×C₄×C₁₃	—	2	6	no	—
48	C₂×C₄×C₁₃	—	2	12	no	—
49	C₂×C₄×C₁₃	#117	1	6	yes	—
50	C₂×Dic₁₃	—	2	6	no	—
51	C₂×Dic₁₃	—	2	12	no	—
52	C₂×Dic₁₃	#117	1	6	yes	—
53	C₄×D₁₃	—	4	24	no	—
54	C₄×D₁₃	#126	1	16	yes	—
55	C₂²×C₄²	—	13	3	no	—
56	C₂²×C₄²	—	13	4	no	—
57	#376	—	13	3	no	—
58	#376	—	13	4	no	—
59	#376	#261	1	1	yes	characteristic, complemented
60	C₂×#95	—	13	4	no	—
61	C₂×#95	—	13	24	no	—
62	C₂²×C₁₃	C₂×#117	1	3	yes	—
63	C₂²×C₁₃	C₄×#41	1	4	yes	—
64	C₂×D₁₃	C₂×#126	1	4	yes	—
65	C₂×D₁₃	#529	1	24	yes	—
66	#261	—	4	16	no	—
67	C₄×C₁₃	—	4	6	no	—
68	C₄×C₁₃	#383	1	4	yes	—
69	Dic₁₃	—	4	6	no	—
70	Dic₁₃	#383	1	4	yes	—
71	C₂³×C₄	—	13	1	no	—
72	C₂³×C₄	—	13	8	no	—
73	C₂³×C₄	—	13	6	no	—
74	C₂×C₄²	—	13	6	no	—
75	C₂×C₄²	—	13	3	no	—
76	C₂×C₄²	—	26	12	no	—
77	C₂×C₄²	—	26	24	no	—
78	C₂×C₄²	C₂×#261	1	3	yes	—
79	#95	—	13	12	no	—
80	#95	—	26	48	no	—
81	#95	C₂×#261	1	4	yes	—
82	C₂×C₁₃	C₂×#383	1	1	yes	characteristic
83	C₂×C₁₃	#2298	1	6	yes	—
84	D₁₃	#2401	1	8	yes	—
85	C₂⁴	—	13	1	no	—
86	C₂²×C₄	—	13	1	no	—
87	C₂²×C₄	—	13	12	no	—
88	C₂²×C₄	—	13	16	no	—
89	C₂²×C₄	—	13	6	no	—
90	C₂²×C₄	—	26	24	no	—
91	C₂²×C₄	—	26	12	no	—
92	C₂²×C₄	—	26	24	no	—
93	C₂²×C₄	—	26	24	no	—
94	C₂²×C₄	C₂²×#261	1	6	yes	—
95	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
96	C₄²	—	2	6	no	—
97	C₄²	—	26	12	no	—
98	C₄²	—	26	6	no	—
99	C₄²	—	52	16	no	—
100	C₁₃	#13855	1	1	yes	characteristic, complemented, Sylow
101	C₂³	—	13	6	no	—
102	C₂³	—	13	8	no	—
103	C₂³	C₂³×#261	1	1	yes	characteristic
104	C₂×C₄	—	2	6	no	—
105	C₂×C₄	—	2	12	no	—
106	C₂×C₄	—	13	6	no	—
107	C₂×C₄	—	13	16	no	—
108	C₂×C₄	—	26	48	no	—
109	C₂×C₄	—	26	6	no	—
110	C₂×C₄	—	26	12	no	—
111	C₂×C₄	—	52	24	no	—
112	C₂×C₄	—	52	8	no	—
113	C₂×C₄	—	52	24	no	—
114	C₂×C₄	#88237	1	6	yes	—
115	C₂²	—	13	4	no	—
116	C₂²	—	13	24	no	—
117	C₂²	C₂×#88237	1	3	yes	—
118	C₂²	#41×#261	1	4	yes	—
119	C₄	—	4	6	no	—
120	C₄	—	13	4	no	—
121	C₄	—	52	16	no	—
122	C₄	—	52	6	no	—
123	C₄	#11719061	1	4	yes	—
124	C₂	—	13	8	no	—
125	C₂	C₂×#11719061	1	1	yes	characteristic
126	C₂	#13131298	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13130023

C₂

yes

maximal

C₄×(C₂×#261)⋊C₄

C₂

yes

maximal

D₁₃×#376

C₂

yes

maximal, characteristic

C₂²×C₄×#261

C₂²

yes

—

C₂×C₄²×D₁₃

C₂²

yes

—

C₂×(C₂×#261)⋊C₄

C₂²

yes

—

C₁₃×#376

C₄

yes

characteristic, complemented

#11718593

C₄

yes

complemented

D₁₃×#95

C₂²

yes

—

#11718309

C₄

yes

complemented

C₂³×#261

C₂³

yes

—

C₂²×C₄×D₁₃

C₂³

yes

—

C₂²×C₄×D₁₃

C₂³

yes

characteristic

C₂×C₄×#261

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄×Dic₁₃

C₂×C₄

yes

—

C₂×C₄×Dic₁₃

C₂×C₄

yes

—

C₄²×D₁₃

—

(C₂×#261)⋊C₄

—

C₁₃×#95

C₂×C₄

yes

—

#88071

C₂×C₄

yes

—

#13855

—

maximal, Sylow

C₂³×D₁₃

C₂⁴

yes

characteristic

C₂²×#261

—

C₂²×#261

—

C₂²×#261

#41

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×Dic₁₃

C₂²×C₄

yes

—

C₂²×Dic₁₃

C₂²×C₄

yes

characteristic

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

—

C₂×C₄×D₁₃

#41

yes

—

C₄×#261

—

C₄²×C₁₃

—

C₄×Dic₁₃

—

C₄×Dic₁₃

—

C₂×#376

—

#1443

—

C₄×#95

—

C₂³×C₁₃

C₂³×C₄

yes

characteristic

C₂²×D₁₃

C₂×#41

yes

—

C₂²×D₁₃

C₂×#41

yes

—

C₂×#261

—

C₂×#261

—

C₂×#261

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

#117

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

C₂×Dic₁₃

#117

yes

—

C₄×D₁₃

—

C₄×D₁₃

#126

yes

—

C₂²×C₄²

—

C₂²×C₄²

—

—

—

yes

characteristic, complemented

C₂×#95

—

C₂×#95

—

C₂²×C₁₃

C₂×#117

yes

—

C₂²×C₁₃

C₄×#41

yes

—

C₂×D₁₃

C₂×#126

yes

—

C₂×D₁₃

#529

yes

—

#261

—

C₄×C₁₃

—

C₄×C₁₃

#383

yes

—

Dic₁₃

—

Dic₁₃

#383

yes

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×#261

yes

—

—

—

yes

—

C₂×C₁₃

C₂×#383

yes

characteristic

C₂×C₁₃

#2298

yes

—

D₁₃

#2401

yes

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×#261

yes

—

C₂²×C₄

C₂²×#261

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₄²

—

100

C₁₃

#13855

yes

characteristic, complemented, Sylow

101

C₂³

—

102

C₂³

—

103

C₂³

C₂³×#261

yes

characteristic

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

#88237

yes

—

115

C₂²

—

116

C₂²

—

117

C₂²

C₂×#88237

yes

—

118

C₂²

#41×#261

yes

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

#11719061

yes

—

124

C₂

—

125

C₂

C₂×#11719061

yes

characteristic

126

C₂

#13131298

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, cosocle	C₂³×D₁₃	C₂⁴
hypercenter	#376	#261
hypocenter	C₁₃	#13855
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, cosocle

C₂³×D₁₃

C₂⁴

C₁₃

G ▷ C₂³×C₁₃ ▷ C₁₃

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
7. C₁₃×#376	C₄	semidirect
8. #11718593	C₄	semidirect
10. #11718309	C₄	semidirect
59. #376	#261	semidirect
100. C₁₃	#13855	semidirect

H ≅ G/N

type

7. C₁₃×#376

C₄

semidirect

8. #11718593

C₄

semidirect

10. #11718309

C₄

semidirect

59. #376

#261

semidirect

100. C₁₃

#13855

semidirect

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

subgroup	index
#13130023	2
C₄×(C₂×#261)⋊C₄	2
D₁₃×#376	2
#13855	13

subgroup

index

#13130023

C₄×(C₂×#261)⋊C₄

D₁₃×#376

#13855

Subgroups — #16791701

Conjugacy classes of subgroups

Complements

Maximal subgroups