Finite Group Databasebeta

← C2×#11718699 #13124402

Subgroups — C2×#11718699 #13124402

Order 1664.

616 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 173 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×#121C211yesmaximal, characteristic, complemented
2C22×#6104C211yesmaximal, characteristic, complemented
3C2×#88184C211yesmaximal, characteristic, complemented
4C23×#1055C211yesmaximal, characteristic, complemented
5C2×#88072C211yesmaximal, characteristic, complemented
6#11718699C218yesmaximal, direct product factor
7C2×#88049C211yesmaximal, characteristic, complemented
8C2×#88047C211yesmaximal, characteristic, complemented
9C22×D4×C13—21no—
10C22×D4×C13C2211yescharacteristic
11C23×C4×C13C2211yescharacteristic
12C22×C22⋊D13—21no—
13C22×D52C2211yescharacteristic
14C13×#121—22no—
15C13×#121C2214yescomplemented
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4—21no—
18C2×#6104—24no—
19C2×#6104C2214yescomplemented
20#88184—22no—
21#88184C2214yescomplemented
22C2×#6103—21no—
23C2×C4⋊Dic13C2211yescharacteristic
24C22×#1055—24no—
25C22×#1055C2211yescharacteristic
26C22×#1055C2211yescharacteristic
27C22×#1055C2214yescomplemented
28#88072C2214yescomplemented
29#88049C2214yescomplemented
30#88047C2214yescomplemented
31C24×C13—21no—
32C24×C13D411yescharacteristic
33C23×D13—21no—
34C2×D4×C13—24no—
35C2×D4×C13—22no—
36C2×D4×C13—21no—
37C2×D4×C13—22no—
38C2×D4×C13—44no—
39C2×D4×C13C2312yes—
40C22×C4×C13—22no—
41C22×C4×C13—22no—
42C22×C4×C13—21no—
43C22×C4×C13D411yescharacteristic
44C22×C4×C13D412yes—
45C22×C4×C13C2312yes—
46C22×C4×C13C2311yescharacteristic
47C2×C22⋊D13—24no—
48C2×C22⋊D13—44no—
49C22×Dic13—21no—
50C2×D52—22no—
51C2×D52—22no—
52C2×D52—21no—
53C2×D52C2312yes—
54C13×C4⋊C4—21no—
55C13×C4⋊C4C2312yes—
56C13×C22⋊C4—24no—
57#6104—28no—
58#6103—24no—
59C4⋊Dic13—21no—
60C4⋊Dic13C2312yes—
61C2×#1055—22no—
62C2×#1055—28no—
63C2×#1055D414yescomplemented
64C2×#1055C2312yes—
65C2×#1055C2312yes—
66C2×#466—131nomaximal, Sylow
67C23×C13—22no—
68C23×C13—22no—
69C23×C13—22no—
70C23×C13—42no—
71C23×C13—42no—
72C23×C13—42no—
73C23×C13D814yescomplemented
74C23×C13C2×D412yes—
75C23×C13C2×D411yescharacteristic
76C22×D13—22no—
77C22×D13—42no—
78C22×D13—42no—
79C22×D13—42no—
80D4×C13—22no—
81D4×C13—22no—
82D4×C13—48no—
83D4×C13—42no—
84C2×C4×C13—22no—
85C2×C4×C13—24no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—42no—
90C2×C4×C13C2×D412yes—
91C2×C4×C13C2×D411yescharacteristic
92C2×C4×C13C2×D412yes—
93C2×C4×C13#4112yes—
94C2×C4×C13C2411yescharacteristic
95C22⋊D13—48no—
96C2×Dic13—22no—
97C2×Dic13—42no—
98D52—22no—
99D52—22no—
100D52—42no—
101#1055—22no—
102#1055C2×D414yescomplemented
103C22×D8—131no—
104C23×C8—131no—
105C2×#121—131no—
106C2×#121D1311yescharacteristic, complemented
107#466—138no—
108C2×#107—131no—
109C2×#102—131no—
110C2×#102—131no—
111C22×C13—22no—
112C22×C13—22no—
113C22×C13—28no—
114C22×C13—42no—
115C22×C13—42no—
116C22×C13—42no—
117C22×C13—84no—
118C22×C13#12112yes—
119C22×C13C2×D812yes—
120C22×C13C2×D814yescomplemented
121C22×C13#13512yes—
122C22×C13C22×D411yescharacteristic
123C2×D13—42no—
124C2×D13—42no—
125C2×D13—42no—
126C2×D13—84no—
127C4×C13—22no—
128C4×C13—42no—
129C4×C13#12112yes—
130C4×C13C22×D411yescharacteristic
131C4×C13C2×#4111yescharacteristic
132Dic13—42no—
133C22×D4—21no—
134C22×D4—131no—
135C22×D4—261no—
136C22×D4C2×D1311yescharacteristic
137C23×C4C2×D1311yescharacteristic
138C2×D8—134no—
139C2×D8—264no—
140C22×C8—131no—
141C22×C8—131no—
142C22×C8—134no—
143C22×C8—264no—
144#121—22no—
145#121—134no—
146#121—262no—
147#121C2×D1314yescomplemented
148C2×C4⋊C4—131no—
149C2×C4⋊C4C2×D1311yescharacteristic
150C2×C22⋊C4—21no—
151C2×C22⋊C4—261no—
152#107—134no—
153#102—134no—
154#102—134no—
155C2×C13—24no—
156C2×C13—82no—
157C2×C13#46614yescomplemented
158C2×C13C2×#12111yescharacteristic
159C2×C13C22×D811yescharacteristic
160C2×C13C2×#13511yescharacteristic
161D13—82no—
162C24—21no—
163C24—261no—
164C24C22⋊D1311yescharacteristic
165C2×D4—24no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—21no—
169C2×D4—44no—
170C2×D4—132no—
171C2×D4—264no—
172C2×D4—262no—
173C2×D4—262no—
174C2×D4—261no—
175C2×D4—524no—
176C2×D4C22×D1312yes—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4—21no—
180C22×C4—261no—
181C22×C4C22⋊D1312yes—
182C22×C4C22⋊D1311yescharacteristic
183C22×C4C22×D1312yes—
184C22×C4C22×D1311yescharacteristic
185D8—268no—
186C2×C8—134no—
187C2×C8—132no—
188C2×C8—132no—
189C2×C8—268no—
190C2×C8—262no—
191C4⋊C4—21no—
192C4⋊C4—132no—
193C4⋊C4—261no—
194C4⋊C4C22×D1312yes—
195C22⋊C4—24no—
196C22⋊C4—264no—
197C13C2×#46611yescharacteristic, complemented, Sylow
198C23—22no—
199C23—22no—
200C23—22no—
201C23—42no—
202C23—42no—
203C23—42no—
204C23—262no—
205C23—522no—
206C23—522no—
207C23—522no—
208C23#610414yescomplemented
209C23C2×C22⋊D1312yes—
210C23C2×C22⋊D1311yescharacteristic
211D4—22no—
212D4—22no—
213D4—48no—
214D4—42no—
215D4—262no—
216D4—262no—
217D4—528no—
218D4—522no—
219C2×C4—22no—
220C2×C4—24no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—262no—
226C2×C4—522no—
227C2×C4D4×D1312yes—
228C2×C4#612912yes—
229C2×C4C2×C22⋊D1312yes—
230C2×C4C2×C22⋊D1311yescharacteristic
231C2×C4C23×D1311yescharacteristic
232C8—134no—
233C8—262no—
234C22—28no—
235C22—22no—
236C22—22no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—84no—
241C22—522no—
242C22—522no—
243C22—522no—
244C22—1044no—
245C22C2×#610412yes—
246C22C2×#610414yescomplemented
247C22#8819312yes—
248C22#8820412yes—
249C22C22×C22⋊D1311yescharacteristic
250C4—22no—
251C4—42no—
252C4—522no—
253C4#8819312yes—
254C4C2×D4×D1311yescharacteristic
255C4C2×#612911yescharacteristic
256C2—24no—
257C2—82no—
258C2—1042no—
259C2#1171869914yesdirect product factor
260C2C22×#610411yescharacteristic
261C2C2×#8819311yescharacteristic
262C2C2×#8820411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#121C2
socleC23×C13C2×D4
hypercenterC2×#121D13
hypocenterC13C2×#466
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C13×#121C2semidirect
2. C22×#6104C2semidirect
3. C2×#88184C2semidirect
4. C23×#1055C2semidirect
5. C2×#88072C2semidirect
6. #11718699C2direct (N × H)
7. C2×#88049C2semidirect
8. C2×#88047C2semidirect
15. C13×#121C22semidirect
19. C2×#6104C22semidirect
21. #88184C22semidirect
27. C22×#1055C22semidirect
28. #88072C22semidirect
29. #88049C22semidirect
30. #88047C22semidirect
63. C2×#1055D4semidirect
73. C23×C13D8semidirect
102. #1055C2×D4semidirect
106. C2×#121D13semidirect
120. C22×C13C2×D8semidirect
147. #121C2×D13semidirect
157. C2×C13#466semidirect
197. C13C2×#466semidirect
208. C23#6104semidirect
246. C22C2×#6104semidirect
259. C2#11718699direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#1212
C22×#61042
C2×#881842
C23×#10552
C2×#880722
#117186992
C2×#880492
C2×#880472
C2×#46613