Finite Group Databasebeta

← C2×#11718525 #13124397

Subgroups — C2×#11718525 #13124397

Order 1664.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×#6095C211yesmaximal, characteristic, complemented
2C22×C8×D13C211yesmaximal, characteristic, complemented
3C2×#88151C211yesmaximal, characteristic, complemented
4C2×#88149C211yesmaximal, characteristic
5C2×C13×#106C211yesmaximal, characteristic, complemented
6C2×#88050C211yesmaximal, characteristic, complemented
7C2×#88049C211yesmaximal, characteristic, complemented
8#11718525C218yesmaximal, direct product factor
9C22×D52—21no—
10C22×D52C2211yescharacteristic
11C22×C4×D13C2211yescharacteristic
12C22×Dic26C2211yescharacteristic
13C22×C8×C13C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×#6103—21no—
17C2×#6103—21no—
18C2×C4⋊Dic13—21no—
19C22×#1055C2211yescharacteristic
20C2×#6095—24no—
21C2×#6095C2214yescomplemented
22C2×C8×D13—24no—
23C2×C8×D13C2214yescomplemented
24#88151—22no—
25#88151C2214yescomplemented
26#88149—22no—
27#88149C2214yes—
28C13×#106C2214yescomplemented
29#88050C2214yescomplemented
30#88049C2214yescomplemented
31C23×D13—21no—
32C23×D13D411yescharacteristic
33C22×C4×C13—21no—
34C22×C4×C13—21no—
35C22×C4×C13C2311yescharacteristic
36C22×Dic13—21no—
37C22×Dic13D411yescharacteristic
38C2×D52—22no—
39C2×D52—22no—
40C2×D52—24no—
41C2×D52—21no—
42C2×D52—44no—
43C2×D52C2312yes—
44C2×C4×D13—22no—
45C2×C4×D13—22no—
46C2×C4×D13D412yes—
47C2×C4×D13C2312yes—
48C2×Dic26—22no—
49C2×Dic26—22no—
50C2×Dic26—21no—
51C2×Dic26C2312yes—
52C2×C8×C13D414yescomplemented
53C2×C8×C13C2312yes—
54C13×C4⋊C4—21no—
55C13×C4⋊C4—21no—
56C13×C4⋊C4C2312yes—
57C13×C4⋊C4C2312yes—
58#6103—24no—
59#6103—24no—
60C4⋊Dic13—24no—
61C2×#1055—22no—
62C2×#1055C2312yes—
63#6095—28no—
64C8×D13—28no—
65C2×#465—131nomaximal, Sylow
66C23×C13C2×D411yescharacteristic
67C22×D13—22no—
68C22×D13—22no—
69C22×D13—22no—
70C22×D13—42no—
71C22×D13—42no—
72C22×D13—42no—
73C22×D13SD1614yescomplemented
74C22×D13C2×D412yes—
75C2×C4×C13—22no—
76C2×C4×C13—22no—
77C2×C4×C13—42no—
78C2×C4×C13—42no—
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2×D412yes—
81C2×C4×C13#4112yes—
82C2×C4×C13C2411yescharacteristic
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—42no—
86C2×Dic13C2×D412yes—
87D52—22no—
88D52—22no—
89D52—48no—
90D52—42no—
91C4×D13—24no—
92C4×D13—22no—
93C4×D13—22no—
94Dic26—22no—
95Dic26—22no—
96Dic26—42no—
97C8×C13C2×D414yescomplemented
98#1055—22no—
99C22×SD16—131no—
100C23×C8—131no—
101C2×C22⋊Q8—131no—
102C2×#121—131no—
103#465—138no—
104C2×#106D1311yescharacteristic, complemented
105C2×#103—131no—
106C2×#102—131no—
107C22×C13#12112yes—
108C22×C13C2×SD1612yes—
109C22×C13#13512yes—
110C22×C13C22×D411yescharacteristic
111C2×D13—22no—
112C2×D13—22no—
113C2×D13—28no—
114C2×D13—42no—
115C2×D13—42no—
116C2×D13—42no—
117C2×D13—84no—
118C2×D13C2×SD1614yescomplemented
119C4×C13—42no—
120C4×C13—42no—
121C4×C13#12112yes—
122C4×C13C22×D411yescharacteristic
123C4×C13C2×#4111yescharacteristic
124Dic13—22no—
125Dic13—42no—
126C22×Q8—131no—
127C22×D4—131no—
128C22×D4—261no—
129C23×C4—131no—
130C2×SD16—134no—
131C2×SD16—264no—
132C22×C8—131no—
133C22×C8—134no—
134C22×C8—264no—
135C22×C8C2×D1311yescharacteristic
136C22⋊Q8—134no—
137C22⋊Q8—262no—
138#121—134no—
139#121—262no—
140C2×C4⋊C4—261no—
141C2×C4⋊C4C2×D1311yescharacteristic
142C2×C4⋊C4C2×D1311yescharacteristic
143C2×C22⋊C4—261no—
144C2×C22⋊C4—261no—
145#106C2×D1314yescomplemented
146#103—134no—
147#102—134no—
148C2×C13#46514yescomplemented
149C2×C13C2×#12111yescharacteristic
150C2×C13C22×SD1611yescharacteristic
151C2×C13C2×#13511yescharacteristic
152D13—24no—
153D13—82no—
154C24—131no—
155C24—261no—
156C2×Q8—132no—
157C2×Q8—261no—
158C2×Q8—262no—
159C2×Q8—262no—
160C2×D4—132no—
161C2×D4—264no—
162C2×D4—262no—
163C2×D4—261no—
164C2×D4—262no—
165C2×D4—524no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—131no—
169C22×C4—132no—
170C22×C4—132no—
171C22×C4—262no—
172C22×C4—262no—
173C22×C4—261no—
174C22×C4C22×D1311yescharacteristic
175SD16—268no—
176C2×C8—132no—
177C2×C8—262no—
178C2×C8—268no—
179C2×C8D5214yescomplemented
180C2×C8C22×D1312yes—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—264no—
184C4⋊C4C22×D1312yes—
185C4⋊C4C22×D1312yes—
186C22⋊C4—264no—
187C22⋊C4—264no—
188C13C2×#46511yescharacteristic, complemented, Sylow
189C23—134no—
190C23—132no—
191C23—262no—
192C23—262no—
193C23—262no—
194C23—522no—
195C23—522no—
196C23—522no—
197C23D4×D1311yescharacteristic
198Q8—262no—
199Q8—262no—
200Q8—522no—
201D4—262no—
202D4—262no—
203D4—528no—
204D4—522no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—132no—
210C2×C4—262no—
211C2×C4—264no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—522no—
216C2×C4C2×D5212yes—
217C2×C4D4×D1311yescharacteristic
218C2×C4#613112yes—
219C2×C4C23×D1311yescharacteristic
220C8—262no—
221C8C2×D5214yescomplemented
222C22—134no—
223C22—262no—
224C22—262no—
225C22—268no—
226C22—522no—
227C22—522no—
228C22—522no—
229C22—1044no—
230C22#8814912yes—
231C22SD16×D1312yes—
232C22#8817012yes—
233C22C2×D4×D1311yescharacteristic
234C4—42no—
235C4—42no—
236C4—262no—
237C4—522no—
238C4#8814912yes—
239C4C22×D5211yescharacteristic
240C4C2×#613111yescharacteristic
241C2—264no—
242C2—1042no—
243C2#1171852514yesdirect product factor
244C2C2×#8814911yescharacteristic
245C2C2×SD16×D1311yescharacteristic
246C2C2×#8817011yescharacteristic
subgroupG/H
centerC23D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#106C2
socleC23×C13C2×D4
prime radicalC2×#88149C2
hypercenterC2×#106D13
hypocenterC13C2×#465
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
1. C22×#6095C2semidirect
2. C22×C8×D13C2semidirect
3. C2×#88151C2semidirect
5. C2×C13×#106C2semidirect
6. C2×#88050C2semidirect
7. C2×#88049C2semidirect
8. #11718525C2direct (N × H)
21. C2×#6095C22semidirect
23. C2×C8×D13C22semidirect
25. #88151C22semidirect
28. C13×#106C22semidirect
29. #88050C22semidirect
30. #88049C22semidirect
52. C2×C8×C13D4semidirect
73. C22×D13SD16semidirect
97. C8×C13C2×D4semidirect
104. C2×#106D13semidirect
118. C2×D13C2×SD16semidirect
145. #106C2×D13semidirect
148. C2×C13#465semidirect
179. C2×C8D52semidirect
188. C13C2×#465semidirect
221. C8C2×D52semidirect
243. C2#11718525direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#60952
C22×C8×D132
C2×#881512
C2×#881492
C2×C13×#1062
C2×#880502
C2×#880492
#117185252
C2×#46513