Finite Group Databasebeta

← C2×#11719393 #13128126

Subgroups — C2×#11719393 #13128126

Order 1664.

1168 conjugacy classes of subgroups; only the 541 normal subgroups are shown.

normal subgroups only

This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 541 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#125C211yesmaximal, characteristic, complemented
2#11719393C2116yesmaximal, direct product factor
3C2×#88150C214yesmaximal
4C2×#88146C212yesmaximal
5C2×#88142C212yesmaximal, complemented
6C2×#88141C214yesmaximal, complemented
7C2×C42×D13C211yesmaximal, characteristic
8C2×#88124C211yesmaximal, characteristic, complemented
9C22×C4×D13C2212yes—
10C22×C4×D13C2211yescharacteristic
11C22×Dic26C2214yes—
12C13×#125C2218yescomplemented
13C2×C13×C4⋊C4C2214yes—
14C2×C13×C4⋊C4C2212yes—
15C2×C42×C13C2211yescharacteristic
16C2×#6103C2214yes—
17C2×C4⋊Dic13C2212yes—
18C2×#6101C2214yes—
19C2×#6101C2214yes—
20C2×C4×Dic13C2212yes—
21C2×C4×Dic13C2211yescharacteristic
22C2×C4×Dic13C2214yes—
23#88150C22132yes—
24#88146C22116yes—
25#88142C22116yescomplemented
26#88141C22132yescomplemented
27C42×D13C2218yes—
28#88124C2218yescomplemented
29C23×D13C2311yescharacteristic
30C22×C4×C13C2312yes—
31C22×C4×C13C2314yes—
32C22×C4×C13C2311yescharacteristic
33C22×Dic13C2314yes—
34C22×Dic13C2311yescharacteristic
35C22×Dic13C2312yes—
36C2×C4×D13—28no—
37C2×C4×D13Q818yescomplemented
38C2×C4×D13C2318yes—
39C2×C4×D13C2314yes—
40C2×Dic26—216no—
41C2×Dic26C23116yes—
42C13×C4⋊C4C23116yes—
43C13×C4⋊C4C2318yes—
44C42×C13C2314yes—
45#6103C23116yes—
46C4⋊Dic13C2318yes—
47#6101C23116yes—
48#6101C23116yes—
49C4×Dic13C2318yes—
50C4×Dic13C2314yes—
51C4×Dic13C23116yes—
52C2×#533—131nomaximal, Sylow
53C23×C13C2411yescharacteristic
54C22×D13—24no—
55C22×D13C2×Q814yes—
56C22×D13C2412yes—
57C2×C4×C13—28no—
58C2×C4×C13—24no—
59C2×C4×C13C2×Q814yes—
60C2×C4×C13C2414yes—
61C2×C4×C13C2418yes—
62C2×C4×C13C2412yes—
63C2×Dic13—28no—
64C2×Dic13C2×Q814yes—
65C2×Dic13#4118yes—
66C2×Dic13C2418yes—
67C2×Dic13C2412yes—
68C2×Dic13C2414yes—
69C4×D13—216no—
70C4×D13C2×Q8116yescomplemented
71Dic26—232no—
72#533—1316no—
73C2×C4⋊Q8—132no—
74C2×#125—131no—
75C2×#125D1311yescharacteristic, complemented
76C2×C22⋊Q8—134no—
77C2×C4×Q8—134no—
78C2×#117—132no—
79C22×C42—131no—
80C22×C13C22×Q812yes—
81C22×C13C2×#4114yes—
82C22×C13C2511yescharacteristic
83C2×D13—28no—
84C2×D13—24no—
85C2×D13C22×Q814yes—
86C4×C13—28no—
87C4×C13—24no—
88C4×C13C22×Q814yes—
89Dic13—28no—
90Dic13C22×Q814yes—
91Dic13C2×#4118yes—
92C22×Q8—134no—
93C23×C4—131no—
94C23×C4—132no—
95C4⋊Q8—1316no—
96#125—138no—
97#125C2×D1318yescomplemented
98C22⋊Q8—1332no—
99C4×Q8—1332no—
100#117—1316no—
101C2×C4⋊C4—132no—
102C2×C4⋊C4—134no—
103C2×C4⋊C4—134no—
104C2×C4⋊C4C2×D1312yes—
105C2×C4⋊C4C2×D1314yes—
106C2×C22⋊C4—134no—
107C2×C42—134no—
108C2×C42—132no—
109C2×C42—131no—
110C2×C42—138no—
111C2×C42C2×D1311yescharacteristic
112C2×C13#53314yescomplemented
113C2×C13C23×Q811yescharacteristic
114C2×C13C22×#4112yes—
115D13—24no—
116C24—131no—
117C2×Q8—1316no—
118C2×Q8—2616no—
119C22×C4—131no—
120C22×C4—132no—
121C22×C4—138no—
122C22×C4—134no—
123C22×C4—134no—
124C22×C4—138no—
125C22×C4—268no—
126C22×C4C22×D1312yes—
127C22×C4C22×D1314yes—
128C22×C4C22×D1311yescharacteristic
129C4⋊C4—138no—
130C4⋊C4—1316no—
131C4⋊C4—1316no—
132C4⋊C4C22×D1318yes—
133C4⋊C4C22×D13116yes—
134C22⋊C4—1316no—
135C42—138no—
136C42—134no—
137C42—1316no—
138C42C22×D1314yes—
139C13C2×#53311yescharacteristic, complemented, Sylow
140C23—134no—
141C23—132no—
142C23—264no—
143C23C23×D1311yescharacteristic
144Q8—2632no—
145C2×C4—24no—
146C2×C4—28no—
147C2×C4—134no—
148C2×C4—138no—
149C2×C4—132no—
150C2×C4—134no—
151C2×C4—1316no—
152C2×C4—138no—
153C2×C4—2616no—
154C2×C4—268no—
155C2×C4Q8×D1314yes—
156C2×C4C23×D1314yes—
157C2×C4C23×D1318yes—
158C2×C4C23×D1312yes—
159C22—134no—
160C22—264no—
161C22—268no—
162C22C2×Q8×D1312yes—
163C22#41×D1314yes—
164C22C24×D1311yescharacteristic
165C4—24no—
166C4—28no—
167C4—134no—
168C4—138no—
169C4—268no—
170C4C2×Q8×D1314yes—
171C2—264no—
172C2#1171939314yesdirect product factor
173C2C22×Q8×D1311yescharacteristic
174C2C2×#41×D1312yes—
subgroupG/H
centerC23C23×D13
commutator, cosocleC22×C13C25
FrattiniC22C24×D13
FittingC2×C13×#125C2
socleC23×C13C24
prime radicalC23×D13C23
hypercenterC2×#125D13
hypocenterC13C2×#533
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#125

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C13×#125C2semidirect
2. #11719393C2direct (N × H)
5. C2×#88142C2semidirect
6. C2×#88141C2semidirect
8. C2×#88124C2semidirect
12. C13×#125C22semidirect
25. #88142C22semidirect
26. #88141C22semidirect
28. #88124C22semidirect
37. C2×C4×D13Q8semidirect
70. C4×D13C2×Q8semidirect
75. C2×#125D13semidirect
97. #125C2×D13semidirect
112. C2×C13#533semidirect
139. C13C2×#533semidirect
172. C2#11719393direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#1252
#117193932
C2×#881502
C2×#881462
C2×#881422
C2×#881412
C2×C42×D132
C2×#881242
C2×#53313