Finite Group Databasebeta

← #13131436

Subgroups — #13131436

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×#88256C211yesmaximal, characteristic
2#11719623C212yesmaximal, complemented
3#11719156C212yesmaximal, complemented
4D13⋊#99C214yesmaximal, complemented
5#11719116C212yesmaximal, complemented
6C2×#88107C214yesmaximal, complemented
7C2×C13×#41C411yescharacteristic, complemented
8#88256—28no—
9C2×#6131C411yescharacteristic, complemented
10C2×#6131C2211yescharacteristic
11C2×D4×D13C412yescomplemented
12C2×D4×D13C411yescharacteristic, complemented
13C2×D4×D13C2212yes—
14C2×D4×D13C2211yescharacteristic
15C2×#6127C412yescomplemented
16C2×#6127C2211yescharacteristic
17C22×D52C411yescharacteristic, complemented
18C22×D52C2212yes—
19C2×C22⋊#261C2218yescomplemented
20D4×#261—28no—
21#88237C2214yescomplemented
22#88119C2214yescomplemented
23#88107C2214yescomplemented
24#88107C2218yescomplemented
25C23×D13C2×C412yescomplemented
26C23×D13C2×C412yescomplemented
27C23×D13C2312yes—
28C22×#261—28no—
29C13×#41—24no—
30C2×Q8×C13C2×C411yescharacteristic, complemented
31C2×D4×C13C2×C411yescharacteristic
32C2×D4×C13C2×C412yescomplemented
33C22×C4×C13C2×C411yescharacteristic, complemented
34C22×C4×C13C2×C412yescomplemented
35C2×C22⋊D13C2×C412yes—
36C2×C22⋊D13C2×C412yescomplemented
37C2×C22⋊D13C2×C411yescharacteristic, complemented
38C2×C22⋊D13C2311yescharacteristic
39#6131—24no—
40#6131—24no—
41D4×D13—28no—
42D4×D13—24no—
43D4×D13—28no—
44D4×D13D418yes—
45#6127—28no—
46#6127—24no—
47C2×D52—28no—
48C2×D52—24no—
49C2×D52C2×C411yescharacteristic
50C2×D52C2×C412yescomplemented
51C2×D52C2×C411yescharacteristic, complemented
52C2×D52C2×C412yescomplemented
53C2×D52C2311yescharacteristic
54C2×D52C2312yes—
55C2×C4×D13C2×C412yescomplemented
56C2×C4×D13C2×C412yescomplemented
57C2×C4×D13C2×C411yescharacteristic, complemented
58C2×C4×D13C2311yescharacteristic
59C2×Dic26C2×C411yescharacteristic, complemented
60C22⋊#261—28no—
61C22⋊#261C2318yes—
62C4⋊#261—24no—
63C4×#261—24no—
64#2883—131nomaximal, Sylow
65C23×C13C22×C411yescharacteristic
66C23×C13C22×C412yes—
67C22×D13—24no—
68C22×D13—24no—
69C22×D13—82no—
70C22×D13—82no—
71C22×D13—82no—
72C22×D13C22×C412yes—
73C22×D13C22×C411yescharacteristic
74C22×D13C22×C412yes—
75C22×D13C2×D418yes—
76C22×D13C2411yescharacteristic
77C2×#261—28no—
78C2×#261—88no—
79Q8×C13—22no—
80D4×C13—24no—
81D4×C13C22⋊C414yes—
82C2×C4×C13—24no—
83C2×C4×C13—22no—
84C2×C4×C13C22×C411yescharacteristic
85C2×C4×C13C22×C412yes—
86C2×C4×C13C22×C411yescharacteristic
87C22⋊D13—24no—
88C22⋊D13—22no—
89C22⋊D13—22no—
90C22⋊D13C22⋊C418yes—
91C2×Dic13C22×C411yescharacteristic
92C2×Dic13C22×C411yescharacteristic
93D52—24no—
94D52—24no—
95D52—22no—
96D52—24no—
97D52—22no—
98D52C22⋊C414yes—
99C4×D13—24no—
100C4×D13—22no—
101C4×D13—24no—
102C4×D13C2×D414yes—
103Dic26—22no—
104C2×H(5,𝔽2)—131no—
105#518—132no—
106#410—132no—
107#410—132no—
108C2×#99—134no—
109C2×#99—134no—
110C22×C13—21no—
111C22×C13—42no—
112C22×C13—41no—
113C22×C13C2×C22⋊C414yes—
114C22×C13C23×C411yescharacteristic
115C2×D13—21no—
116C2×D13—22no—
117C2×D13—48no—
118C2×D13—42no—
119C2×D13—41no—
120C2×D13—42no—
121C2×D13—41no—
122C2×D13—84no—
123C2×D13—84no—
124C2×D13C2×C22⋊C414yes—
125C2×D13C22×D412yes—
126#261—48no—
127C4×C13—21no—
128C4×C13—22no—
129C4×C13C2×C22⋊C412yes—
130Dic13—21no—
131Dic13C2×C22⋊C412yes—
132H(5,𝔽2)—268no—
133C2×#41—131no—
134C2×#41—131no—
135C2×#41—131no—
136C2×#41—132no—
137C2×#41#26111yescharacteristic, complemented
138C22×D4—131no—
139C22×D4—131no—
140C22×D4—132no—
141C22×D4—132no—
142C22×D4—132no—
143C22×D4—131no—
144C4×D4—268no—
145#117—134no—
146C2×C22⋊C4—138no—
147#99—134no—
148#99—138no—
149#99—134no—
150C2×C13—21no—
151C2×C13—24no—
152C2×C13—41no—
153C2×C13C22×C22⋊C411yescharacteristic
154D13—22no—
155D13—24no—
156D13—42no—
157D13—41no—
158C24—132no—
159C24—132no—
160C24—132no—
161#41—24no—
162#41—264no—
163#41—268no—
164#41—264no—
165#41—264no—
166C2×Q8—131no—
167C2×Q8C2×#26111yescharacteristic, complemented
168C2×D4—132no—
169C2×D4—138no—
170C2×D4—131no—
171C2×D4—131no—
172C2×D4—132no—
173C2×D4—131no—
174C2×D4—132no—
175C2×D4—131no—
176C2×D4—132no—
177C2×D4—132no—
178C2×D4—131no—
179C2×D4—264no—
180C2×D4—268no—
181C2×D4—268no—
182C2×D4—268no—
183C2×D4—264no—
184C2×D4C2×#26111yescharacteristic
185C2×D4C2×#26112yescomplemented
186C22×C4—131no—
187C22×C4—132no—
188C22×C4—132no—
189C22×C4—131no—
190C22×C4—268no—
191C22×C4C2×#26112yescomplemented
192C22×C4C2×#26111yescharacteristic, complemented
193C4⋊C4—264no—
194C22⋊C4—138no—
195C22⋊C4—268no—
196C42—264no—
197C13#288311yescharacteristic, complemented, Sylow
198C23—138no—
199C23—131no—
200C23—132no—
201C23—132no—
202C23—131no—
203C23—264no—
204C23—264no—
205C23—1042no—
206C23—1042no—
207C23—1042no—
208C23C22×#26111yescharacteristic
209C23C22×#26112yes—
210Q8—22no—
211Q8—262no—
212D4—24no—
213D4—138no—
214D4—134no—
215D4—264no—
216D4—262no—
217D4—264no—
218D4—264no—
219D4—262no—
220D4—262no—
221D4—264no—
222D4—262no—
223D4C22⋊#26114yes—
224C2×C4—24no—
225C2×C4—22no—
226C2×C4—131no—
227C2×C4—134no—
228C2×C4—131no—
229C2×C4—264no—
230C2×C4—264no—
231C2×C4—262no—
232C2×C4—268no—
233C2×C4—1048no—
234C2×C4C22×#26112yes—
235C2×C4C22×#26111yescharacteristic
236C2×C4C22×#26111yescharacteristic
237C22—21no—
238C22—42no—
239C22—41no—
240C22—134no—
241C22—132no—
242C22—262no—
243C22—261no—
244C22—528no—
245C22—521no—
246C22—522no—
247C22—521no—
248C22—522no—
249C22—1044no—
250C22—1044no—
251C22C2×C22⋊#26114yes—
252C22C23×#26111yescharacteristic
253C4—21no—
254C4—22no—
255C4—132no—
256C4—261no—
257C4—528no—
258C4C2×C22⋊#26112yes—
259C2—21no—
260C2—24no—
261C2—41no—
262C2—262no—
263C2—264no—
264C2—521no—
265C2—522no—
266C2C22×C22⋊#26111yescharacteristic
subgroupG/H
centerC2C22×C22⋊#261
commutatorC22×C13C23×C4
FrattiniC22C23×#261
FittingC2×C13×#41C4
socleC2×C13C22×C22⋊C4
prime radicalC2×#88256C2
cosocleC22×D13C24
hypercenterC2×#41#261
hypocenterC13#2883
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×D4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11719623C2semidirect
3. #11719156C2semidirect
4. D13⋊#99C2semidirect
5. #11719116C2semidirect
6. C2×#88107C2semidirect
7. C2×C13×#41C4semidirect
9. C2×#6131C4semidirect
11. C2×D4×D13C4semidirect
12. C2×D4×D13C4semidirect
15. C2×#6127C4semidirect
17. C22×D52C4semidirect
19. C2×C22⋊#261C22semidirect
21. #88237C22semidirect
22. #88119C22semidirect
23. #88107C22semidirect
24. #88107C22semidirect
25. C23×D13C2×C4semidirect
26. C23×D13C2×C4semidirect
30. C2×Q8×C13C2×C4semidirect
32. C2×D4×C13C2×C4semidirect
33. C22×C4×C13C2×C4semidirect
34. C22×C4×C13C2×C4semidirect
36. C2×C22⋊D13C2×C4semidirect
37. C2×C22⋊D13C2×C4semidirect
50. C2×D52C2×C4semidirect
51. C2×D52C2×C4semidirect
52. C2×D52C2×C4semidirect
55. C2×C4×D13C2×C4semidirect
56. C2×C4×D13C2×C4semidirect
57. C2×C4×D13C2×C4semidirect
59. C2×Dic26C2×C4semidirect
137. C2×#41#261semidirect
167. C2×Q8C2×#261semidirect
185. C2×D4C2×#261semidirect
191. C22×C4C2×#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×#882562
#117196232
#117191562
D13⋊#992
#117191162
C2×#881072
#288313