Finite Group Databasebeta

← #13131435

Subgroups — #13131435

Order 1664.

800 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 198 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×#88251C211yesmaximal, characteristic
2#11719623C212yesmaximal, complemented
3C2×#88119C214yesmaximal, complemented
4#11719142C212yesmaximal, complemented
5D13⋊#99C214yesmaximal, complemented
6#11719116C212yesmaximal, complemented
7C22×D4×C13C411yescharacteristic, complemented
8C22×C22⋊D13C412yescomplemented
9C22×C22⋊D13C2212yes—
10#88251—28no—
11C2×#6129C412yescomplemented
12C2×#6129C411yescharacteristic, complemented
13C2×#6129C2211yescharacteristic
14C2×D4×D13C411yescharacteristic, complemented
15C2×D4×D13C2212yes—
16C2×D4×D13C2211yescharacteristic
17C2×#6127C411yescharacteristic, complemented
18C2×#6127C2211yescharacteristic
19C2×C22⋊#261C2218yescomplemented
20D4×#261—28no—
21#88237C2214yescomplemented
22#88119C2214yescomplemented
23#88119C2218yescomplemented
24#88107C2214yescomplemented
25C24×C13C2×C412yescomplemented
26C23×D13C2×C412yescomplemented
27C23×D13C2312yes—
28C22×#261—28no—
29C2×D4×C13—24no—
30C2×D4×C13C2×C411yescharacteristic
31C2×D4×C13C2×C411yescharacteristic, complemented
32C2×D4×C13C2×C412yescomplemented
33C22×C4×C13C2×C411yescharacteristic, complemented
34C2×C22⋊D13—28no—
35C2×C22⋊D13—28no—
36C2×C22⋊D13C2×C412yes—
37C2×C22⋊D13C2×C412yescomplemented
38C2×C22⋊D13C2×C411yescharacteristic, complemented
39C2×C22⋊D13C2×C412yescomplemented
40C2×C22⋊D13C2×C412yescomplemented
41C2×C22⋊D13C2311yescharacteristic
42C2×C22⋊D13C2312yes—
43C22×Dic13C2×C412yescomplemented
44C22×Dic13C2×C412yescomplemented
45#6129—24no—
46#6129—28no—
47#6129—24no—
48D4×D13—28no—
49D4×D13—24no—
50D4×D13D418yes—
51#6127—24no—
52#6127—24no—
53C2×D52C2×C411yescharacteristic
54C2×D52C2311yescharacteristic
55C2×C4×D13C2×C412yescomplemented
56C2×C4×D13C2×C411yescharacteristic, complemented
57C2×C4×D13C2311yescharacteristic
58C2×Dic26C2×C411yescharacteristic, complemented
59C2×Dic26C2×C411yescharacteristic, complemented
60C22⋊#261—28no—
61C22⋊#261C2318yes—
62C4⋊#261—24no—
63C4×#261—24no—
64#2883—131nomaximal, Sylow
65C23×C13—24no—
66C23×C13—82no—
67C23×C13C22×C412yes—
68C23×C13C22×C411yescharacteristic
69C23×C13C22×C412yes—
70C22×D13—24no—
71C22×D13—82no—
72C22×D13—82no—
73C22×D13C22×C411yescharacteristic
74C22×D13C22×C412yes—
75C22×D13C2×D418yes—
76C22×D13C2411yescharacteristic
77C2×#261—28no—
78C2×#261—88no—
79D4×C13—24no—
80D4×C13—22no—
81D4×C13C22⋊C414yes—
82C2×C4×C13—22no—
83C2×C4×C13C22×C411yescharacteristic
84C2×C4×C13C22×C411yescharacteristic
85C22⋊D13—24no—
86C22⋊D13—24no—
87C22⋊D13—24no—
88C22⋊D13—22no—
89C22⋊D13—24no—
90C22⋊D13—22no—
91C22⋊D13C22⋊C418yes—
92C2×Dic13—24no—
93C2×Dic13—24no—
94C2×Dic13C22×C412yes—
95C2×Dic13C22×C411yescharacteristic
96C2×Dic13C22×C411yescharacteristic
97D52—22no—
98D52C22⋊C414yes—
99C4×D13—24no—
100C4×D13—22no—
101C4×D13C2×D414yes—
102Dic26—22no—
103Dic26—22no—
104C2×H(5,𝔽2)—131no—
105#518—132no—
106#410—132no—
107#410—132no—
108C2×#99—134no—
109C2×#99—134no—
110C22×C13—22no—
111C22×C13—21no—
112C22×C13—42no—
113C22×C13—42no—
114C22×C13—41no—
115C22×C13—84no—
116C22×C13C2×C22⋊C414yes—
117C22×C13C23×C411yescharacteristic
118C2×D13—21no—
119C2×D13—48no—
120C2×D13—42no—
121C2×D13—41no—
122C2×D13—41no—
123C2×D13—84no—
124C2×D13C2×C22⋊C414yes—
125C2×D13C22×D412yes—
126#261—48no—
127C4×C13—21no—
128C4×C13C2×C22⋊C412yes—
129Dic13—22no—
130Dic13—21no—
131Dic13C2×C22⋊C412yes—
132H(5,𝔽2)—268no—
133C2×#41—131no—
134C2×#41—131no—
135C2×#41—132no—
136C2×#41—131no—
137C2×#41—131no—
138C22×D4—131no—
139C22×D4—132no—
140C22×D4—132no—
141C22×D4—132no—
142C22×D4—131no—
143C22×D4#26111yescharacteristic, complemented
144C4×D4—268no—
145#117—134no—
146C2×C22⋊C4—138no—
147#99—134no—
148#99—134no—
149#99—138no—
150C2×C13—21no—
151C2×C13—24no—
152C2×C13—42no—
153C2×C13—41no—
154C2×C13C22×C22⋊C411yescharacteristic
155D13—22no—
156D13—24no—
157D13—41no—
158C24—132no—
159C24—132no—
160C24C2×#26112yescomplemented
161#41—264no—
162#41—264no—
163#41—264no—
164#41—268no—
165#41—264no—
166C2×Q8—131no—
167C2×Q8—131no—
168C2×D4—24no—
169C2×D4—132no—
170C2×D4—138no—
171C2×D4—132no—
172C2×D4—131no—
173C2×D4—131no—
174C2×D4—132no—
175C2×D4—132no—
176C2×D4—132no—
177C2×D4—131no—
178C2×D4—131no—
179C2×D4—264no—
180C2×D4—268no—
181C2×D4—268no—
182C2×D4—268no—
183C2×D4C2×#26111yescharacteristic
184C2×D4C2×#26112yescomplemented
185C2×D4C2×#26111yescharacteristic, complemented
186C22×C4—131no—
187C22×C4—132no—
188C22×C4—132no—
189C22×C4—132no—
190C22×C4—131no—
191C22×C4—268no—
192C22×C4C2×#26111yescharacteristic, complemented
193C4⋊C4—264no—
194C22⋊C4—138no—
195C22⋊C4—268no—
196C42—264no—
197C13#288311yescharacteristic, complemented, Sylow
198C23—24no—
199C23—82no—
200C23—138no—
201C23—131no—
202C23—132no—
203C23—131no—
204C23—264no—
205C23—1042no—
206C23—1042no—
207C23C22×#26112yes—
208C23C22×#26111yescharacteristic
209C23C22×#26112yes—
210Q8—262no—
211Q8—262no—
212D4—24no—
213D4—22no—
214D4—138no—
215D4—134no—
216D4—262no—
217D4—262no—
218D4—264no—
219D4—262no—
220D4—264no—
221D4—264no—
222D4—264no—
223D4C22⋊#26114yes—
224C2×C4—22no—
225C2×C4—131no—
226C2×C4—134no—
227C2×C4—132no—
228C2×C4—131no—
229C2×C4—264no—
230C2×C4—264no—
231C2×C4—264no—
232C2×C4—262no—
233C2×C4—268no—
234C2×C4—1048no—
235C2×C4C22×#26111yescharacteristic
236C2×C4C22×#26111yescharacteristic
237C22—21no—
238C22—22no—
239C22—42no—
240C22—41no—
241C22—42no—
242C22—84no—
243C22—134no—
244C22—132no—
245C22—261no—
246C22—528no—
247C22—521no—
248C22—522no—
249C22—521no—
250C22—1044no—
251C22C2×C22⋊#26114yes—
252C22C23×#26111yescharacteristic
253C4—21no—
254C4—132no—
255C4—262no—
256C4—261no—
257C4—528no—
258C4C2×C22⋊#26112yes—
259C2—21no—
260C2—24no—
261C2—41no—
262C2—42no—
263C2—262no—
264C2—264no—
265C2—521no—
266C2C22×C22⋊#26111yescharacteristic
subgroupG/H
centerC2C22×C22⋊#261
commutatorC22×C13C23×C4
FrattiniC22C23×#261
FittingC22×D4×C13C4
socleC2×C13C22×C22⋊C4
prime radicalC2×#88251C2
cosocleC22×D13C24
hypercenterC22×D4#261
hypocenterC13#2883
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×D4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11719623C2semidirect
3. C2×#88119C2semidirect
4. #11719142C2semidirect
5. D13⋊#99C2semidirect
6. #11719116C2semidirect
7. C22×D4×C13C4semidirect
8. C22×C22⋊D13C4semidirect
11. C2×#6129C4semidirect
12. C2×#6129C4semidirect
14. C2×D4×D13C4semidirect
17. C2×#6127C4semidirect
19. C2×C22⋊#261C22semidirect
21. #88237C22semidirect
22. #88119C22semidirect
23. #88119C22semidirect
24. #88107C22semidirect
25. C24×C13C2×C4semidirect
26. C23×D13C2×C4semidirect
31. C2×D4×C13C2×C4semidirect
32. C2×D4×C13C2×C4semidirect
33. C22×C4×C13C2×C4semidirect
37. C2×C22⋊D13C2×C4semidirect
38. C2×C22⋊D13C2×C4semidirect
39. C2×C22⋊D13C2×C4semidirect
40. C2×C22⋊D13C2×C4semidirect
43. C22×Dic13C2×C4semidirect
44. C22×Dic13C2×C4semidirect
55. C2×C4×D13C2×C4semidirect
56. C2×C4×D13C2×C4semidirect
58. C2×Dic26C2×C4semidirect
59. C2×Dic26C2×C4semidirect
143. C22×D4#261semidirect
160. C24C2×#261semidirect
184. C2×D4C2×#261semidirect
185. C2×D4C2×#261semidirect
192. C22×C4C2×#261semidirect
197. C13#2883semidirect

Maximal subgroups

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

subgroupindex
C2×#882512
#117196232
C2×#881192
#117191422
D13⋊#992
#117191162
#288313