Finite Group Databasebeta

← C2×D13×SD32 #13127943

Subgroups — C2×D13×SD32 #13127943

Order 1664.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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×Q16×D13C211yesmaximal, characteristic, complemented
2C2×D8×D13C211yesmaximal, characteristic
3C2×C13×SD32C211yesmaximal, characteristic, complemented
4C2×#88068C211yesmaximal, characteristic, complemented
5C2×#88067C211yesmaximal, characteristic, complemented
6D13×SD32C218yesmaximal, direct product factor
7C2×#88040C211yesmaximal, characteristic, complemented
8C2×C16×D13C211yesmaximal, characteristic, complemented
9C2×Q8×D13—21no—
10C2×D4×D13—21no—
11C2×C13×Q16C2211yescharacteristic, complemented
12C2×C13×D8C2211yescharacteristic
13C2×#6107—21no—
14C2×#6104—21no—
15Q16×D13—22no—
16Q16×D13C2214yescomplemented
17D8×D13—22no—
18D8×D13C2214yes—
19C2×Dic52C2211yescharacteristic, complemented
20C2×D104C2211yescharacteristic
21C2×C8×D13C2211yescharacteristic
22C13×SD32C2214yescomplemented
23C2×C13×C16C2211yescharacteristic, complemented
24#88068C2214yescomplemented
25#88067C2214yescomplemented
26C2×#6090C2211yescharacteristic, complemented
27#88040C2214yescomplemented
28C16×D13C2214yescomplemented
29C23×D13—41no—
30C2×Q8×C13—21no—
31C2×D4×C13—21no—
32C2×C22⋊D13—41no—
33Q8×D13—24no—
34Q8×D13—42no—
35D4×D13—24no—
36D4×D13—42no—
37C2×D52—21no—
38C2×C4×D13—41no—
39C2×C4×D13D411yescharacteristic
40C2×Dic26—21no—
41C2×Dic26—41no—
42C13×Q16—21no—
43C13×Q16C2312yescomplemented
44C13×D8—21no—
45C13×D8C2312yes—
46C2×C8×C13C2311yescharacteristic
47#6107—24no—
48#6104—24no—
49C2×#1055D411yescharacteristic
50Dic52—21no—
51Dic52C2312yescomplemented
52D104—21no—
53D104C2312yes—
54C8×D13D412yes—
55C8×D13C2312yes—
56C13×C16C2312yescomplemented
57#6090C2312yescomplemented
58C22×SD32—131nomaximal, Sylow
59C23×C13—41no—
60C22×D13—41no—
61C22×D13—44no—
62C22×D13—84no—
63C22×D13D811yescharacteristic
64Q8×C13—22no—
65Q8×C13—41no—
66D4×C13—22no—
67D4×C13—41no—
68C2×C4×C13—41no—
69C2×C4×C13C2×D411yescharacteristic
70C22⋊D13—44no—
71C2×Dic13—41no—
72C2×Dic13D811yescharacteristic
73D52—22no—
74D52—41no—
75C4×D13—44no—
76C4×D13D812yes—
77C4×D13C2×D412yes—
78Dic26—22no—
79Dic26—41no—
80Dic26—44no—
81C8×C13C2×D411yescharacteristic
82C8×C13C2411yescharacteristic
83#1055C2×D412yes—
84C22×Q16—131no—
85C22×D8—131no—
86C2×SD32—131no—
87C2×SD32—131no—
88C2×SD32—138no—
89C2×SD32—131no—
90C2×SD32D1311yescharacteristic, direct product factor
91C22×C16—131no—
92C22×C13—42no—
93C22×C13—82no—
94C22×C13C2×D811yescharacteristic
95C2×D13—42no—
96C2×D13—82no—
97C2×D13—88no—
98C2×D13SD3214yesdirect product factor
99C2×D13C2×D812yes—
100C4×C13—42no—
101C4×C13C2×D811yescharacteristic
102C4×C13C22×D411yescharacteristic
103Dic13—42no—
104Dic13C2×D812yes—
105C22×Q8—261no—
106C22×D4—261no—
107C2×Q16—134no—
108C2×Q16—131no—
109C2×Q16—262no—
110C2×Q16—261no—
111C2×Q16C2×D1311yescharacteristic, complemented
112C2×D8—134no—
113C2×D8—131no—
114C2×D8—262no—
115C2×D8—261no—
116C2×D8C2×D1311yescharacteristic
117C22×C8—131no—
118SD32—134no—
119SD32—134no—
120SD32—134no—
121SD32C2×D1314yesdirect product factor
122C2×C16—131no—
123C2×C16—134no—
124C2×C16C2×D1311yescharacteristic, complemented
125C2×C13—82no—
126C2×C13C2×SD3212yescomplemented
127C2×C13C22×D811yescharacteristic
128D13—82no—
129D13C2×SD3214yesdirect product factor
130C24—521no—
131C2×Q8—21no—
132C2×Q8—264no—
133C2×Q8—261no—
134C2×Q8—521no—
135C2×Q8—522no—
136C2×D4—21no—
137C2×D4—264no—
138C2×D4—261no—
139C2×D4—522no—
140C2×D4—521no—
141C22×C4—131no—
142C22×C4—521no—
143Q16—21no—
144Q16—132no—
145Q16—264no—
146Q16—261no—
147Q16C22×D1312yescomplemented
148D8—21no—
149D8—132no—
150D8—264no—
151D8—261no—
152D8C22×D1312yes—
153C2×C8—131no—
154C2×C8—132no—
155C2×C8—132no—
156C2×C8C22×D1311yescharacteristic
157C16—132no—
158C16C22×D1312yescomplemented
159C13C22×SD3211yescharacteristic, complemented, Sylow
160C23—41no—
161C23—131no—
162C23—524no—
163C23—521no—
164C23—1044no—
165Q8—22no—
166Q8—41no—
167Q8—262no—
168Q8—524no—
169Q8—521no—
170D4—22no—
171D4—41no—
172D4—262no—
173D4—524no—
174D4—521no—
175C2×C4—41no—
176C2×C4—131no—
177C2×C4—132no—
178C2×C4—132no—
179C2×C4—524no—
180C2×C4—521no—
181C2×C4D4×D1311yescharacteristic
182C8—132no—
183C8D4×D1311yescharacteristic
184C8C23×D1311yescharacteristic
185C22—42no—
186C22—82no—
187C22—132no—
188C22—134no—
189C22—522no—
190C22—1048no—
191C22—1042no—
192C22D8×D1311yescharacteristic
193C4—42no—
194C4—132no—
195C4—522no—
196C4D8×D1311yescharacteristic
197C4C2×D4×D1311yescharacteristic
198C2—82no—
199C2—134no—
200C2—1042no—
201C2D13×SD3212yesdirect product factor
202C2C2×D8×D1311yescharacteristic
subgroupG/H
centerC22D8×D13
commutator, cosocleC8×C13C24
FrattiniC8C23×D13
FittingC2×C13×SD32C2
socleC22×C13C2×D8
prime radicalC2×D8×D13C2
hypercenterC2×SD32D13
hypocenterC13C22×SD32
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D13C2semidirect
3. C2×C13×SD32C2semidirect
4. C2×#88068C2semidirect
5. C2×#88067C2semidirect
6. D13×SD32C2direct (N × H)
7. C2×#88040C2semidirect
8. C2×C16×D13C2semidirect
11. C2×C13×Q16C22semidirect
16. Q16×D13C22semidirect
19. C2×Dic52C22semidirect
22. C13×SD32C22semidirect
23. C2×C13×C16C22semidirect
24. #88068C22semidirect
25. #88067C22semidirect
26. C2×#6090C22semidirect
27. #88040C22semidirect
28. C16×D13C22semidirect
43. C13×Q16C23semidirect
51. Dic52C23semidirect
56. C13×C16C23semidirect
57. #6090C23semidirect
90. C2×SD32D13direct (N × H)
98. C2×D13SD32direct (N × H)
111. C2×Q16C2×D13semidirect
121. SD32C2×D13direct (N × H)
124. C2×C16C2×D13semidirect
126. C2×C13C2×SD32semidirect
129. D13C2×SD32direct (N × H)
147. Q16C22×D13semidirect
158. C16C22×D13semidirect
159. C13C22×SD32semidirect
201. C2D13×SD32direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q16×D132
C2×D8×D132
C2×C13×SD322
C2×#880682
C2×#880672
D13×SD322
C2×#880402
C2×C16×D132
C22×SD3213