Finite Group Databasebeta

← #13120640

Subgroups — #13120640

Order 1664.

668 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 143 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×#88200C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D13C211yesmaximal, characteristic
3C13×#393C211yesmaximal, characteristic, complemented
4#11718892C211yesmaximal, characteristic, complemented
5#11718616C212yesmaximal
6#11718610C211yesmaximal, characteristic, complemented
7#11718609C212yesmaximal, complemented
8#11718338C211yesmaximal, characteristic, complemented
9#11718337C212yesmaximal, complemented
10#11718329C212yesmaximal, complemented
11#11718328C211yesmaximal, characteristic, complemented
12C24×D13C2211yescharacteristic
13C22×Q8×C13C2211yescharacteristic, complemented
14C22×C4×D13C2211yescharacteristic
15C22×C4×D13C2211yescharacteristic
16C2×C13×C22⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2212yes—
18C2×C22⋊Dic13C2211yescharacteristic
19C2×C22⋊Dic13C2212yes—
20#88200—24no—
21C2×#6103C2211yescharacteristic
22C2×#6103C2211yescharacteristic
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×#6103C2212yes—
27C2×C4⋊Dic13C2211yescharacteristic, complemented
28C2×C4⋊Dic13C2212yescomplemented
29C2×#6101C2212yescomplemented
30C2×#6101C2212yescomplemented
31C2×#6101C2212yescomplemented
32C22⋊C4×D13—24no—
33C13×#95C2211yescharacteristic, complemented
34C13×#95C2212yescomplemented
35#88071C2211yescharacteristic, complemented
36#88071C2212yescomplemented
37C24×C13C2311yescharacteristic
38C23×D13—22no—
39C23×D13—22no—
40C23×D13—42no—
41C23×D13—42no—
42C23×D13Q814yescomplemented
43C23×D13C2311yescharacteristic
44C23×D13C2311yescharacteristic
45C2×Q8×C13—22no—
46C2×Q8×C13—42no—
47C22×C4×C13C2312yes—
48C22×C4×C13C2311yescharacteristic
49C22×C4×C13C2312yes—
50C22×C4×C13C2311yescharacteristic
51C22×Dic13C2312yes—
52C22×Dic13C2311yescharacteristic
53C22×Dic13C2312yes—
54C22×Dic13C2311yescharacteristic
55C2×C4×D13—22no—
56C2×C4×D13—42no—
57C2×C4×D13—42no—
58C2×C4×D13D414yes—
59C13×C22⋊C4—22no—
60C13×C22⋊C4—42no—
61C22⋊Dic13—22no—
62C22⋊Dic13—42no—
63#6103—24no—
64#6103—24no—
65#6103—22no—
66#6103—22no—
67#6103—42no—
68#6103—42no—
69C4⋊Dic13—22no—
70C4⋊Dic13—42no—
71#6101—24no—
72#6101—42no—
73#6101—42no—
74#2626—131nomaximal, Sylow
75C23×C13—21no—
76C23×C13—21no—
77C23×C13—22no—
78C23×C13—22no—
79C23×C13C2×Q812yes—
80C23×C13C2411yescharacteristic
81C22×D13—22no—
82C22×D13—22no—
83C22×D13—21no—
84C22×D13—21no—
85C22×D13—22no—
86C22×D13—22no—
87C22×D13—28no—
88C22×D13—48no—
89C22×D13—44no—
90C22×D13—44no—
91C22×D13—48no—
92C22×D13C2×D412yes—
93C22×D13C2×Q812yes—
94C22×D13C2×Q812yes—
95C22×D13#4112yes—
96Q8×C13—44no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—21no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13C2×D412yes—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—21no—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13—22no—
116C2×Dic13C2×D412yes—
117C4×D13—44no—
118C4×D13—44no—
119C2×C22⋊Q8—131no—
120C22×C22⋊C4—131no—
121#399—131no—
122#399—131no—
123#396—132no—
124#396—132no—
125#393—131no—
126#393D1311yescharacteristic, complemented
127#385—132no—
128#380—131no—
129#379—132no—
130C22×C13—22no—
131C22×C13—24no—
132C22×C13—41no—
133C22×C13—41no—
134C22×C13—42no—
135C22×C13C22×D411yescharacteristic
136C22×C13C22×Q811yescharacteristic
137C22×C13C2×#4111yescharacteristic
138C22×C13H(5,𝔽2)12yes—
139C22×C13H(5,𝔽2)12yes—
140C2×D13—22no—
141C2×D13—22no—
142C2×D13—24no—
143C2×D13—24no—
144C2×D13—22no—
145C2×D13—24no—
146C2×D13—416no—
147C2×D13—41no—
148C2×D13—41no—
149C2×D13—42no—
150C2×D13C22⋊Q814yes—
151C4×C13—22no—
152C4×C13—42no—
153C4×C13—41no—
154C4×C13—42no—
155Dic13—22no—
156Dic13—41no—
157Dic13—42no—
158Dic13—42no—
159C25—131no—
160C22×Q8C2×D1311yescharacteristic, complemented
161C23×C4—131no—
162C23×C4—131no—
163C22⋊Q8—264no—
164C2×C4⋊C4—132no—
165C2×C4⋊C4—131no—
166C2×C4⋊C4—132no—
167C2×C4⋊C4—132no—
168C2×C4⋊C4—132no—
169C2×C22⋊C4—131no—
170C2×C22⋊C4—131no—
171C2×C22⋊C4—131no—
172C2×C22⋊C4—132no—
173C2×C22⋊C4—132no—
174C2×C22⋊C4—132no—
175C2×C22⋊C4—132no—
176C2×C22⋊C4—132no—
177C2×C22⋊C4—264no—
178C2×C22⋊C4C2×D1311yescharacteristic
179C2×C22⋊C4C2×D1312yes—
180#95—131no—
181#95—132no—
182#95C2×D1311yescharacteristic, complemented
183#95C2×D1312yescomplemented
184C2×C13—42no—
185C2×C13C2×C22⋊Q811yescharacteristic
186C2×C13#53411yescharacteristic
187C2×C13#53511yescharacteristic
188C2×C13#53812yes—
189C2×C13#54312yes—
190D13—24no—
191D13—42no—
192C24—131no—
193C24—131no—
194C24—134no—
195C24—262no—
196C24—262no—
197C24—522no—
198C24—522no—
199C24C22×D1311yescharacteristic
200C2×Q8—22no—
201C2×Q8—42no—
202C22×C4—131no—
203C22×C4—134no—
204C22×C4—132no—
205C22×C4—131no—
206C22×C4—132no—
207C22×C4—262no—
208C22×C4—522no—
209C22×C4—522no—
210C22×C4C22×D1312yes—
211C22×C4C22×D1312yes—
212C22×C4C22×D1311yescharacteristic
213C22×C4C22×D1311yescharacteristic
214C4⋊C4—264no—
215C4⋊C4—262no—
216C4⋊C4—522no—
217C4⋊C4—522no—
218C4⋊C4—522no—
219C22⋊C4—22no—
220C22⋊C4—42no—
221C22⋊C4—262no—
222C22⋊C4—264no—
223C22⋊C4—264no—
224C22⋊C4—262no—
225C22⋊C4—262no—
226C22⋊C4—522no—
227C22⋊C4—522no—
228C22⋊C4—522no—
229C13#262611yescharacteristic, complemented, Sylow
230C23—21no—
231C23—22no—
232C23—21no—
233C23—22no—
234C23—132no—
235C23—132no—
236C23—132no—
237C23—132no—
238C23—268no—
239C23—262no—
240C23—262no—
241C23—261no—
242C23—262no—
243C23—261no—
244C23—262no—
245C23—528no—
246C23—524no—
247C23—524no—
248C23—528no—
249C23Q8×D1312yes—
250C23C23×D1311yescharacteristic
251Q8—44no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—132no—
262C2×C4—262no—
263C2×C4—261no—
264C2×C4—262no—
265C2×C4—262no—
266C2×C4—262no—
267C2×C4—262no—
268C2×C4—262no—
269C2×C4—262no—
270C2×C4—262no—
271C2×C4—524no—
272C2×C4—524no—
273C2×C4D4×D1312yes—
274C22—22no—
275C22—24no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—134no—
280C22—262no—
281C22—264no—
282C22—262no—
283C22—264no—
284C22—262no—
285C22—264no—
286C22—5216no—
287C22—521no—
288C22—521no—
289C22—522no—
290C22C2×D4×D1311yescharacteristic
291C22#8825112yes—
292C22C2×Q8×D1311yescharacteristic
293C22#41×D1311yescharacteristic
294C22#8825612yes—
295C4—22no—
296C4—42no—
297C4—41no—
298C4—42no—
299C4—262no—
300C4—522no—
301C4—521no—
302C4—522no—
303C2—42no—
304C2—264no—
305C2—522no—
306C2#1171929411yescharacteristic
307C2D13×C22⋊Q811yescharacteristic
308C2#1171933912yes—
309C2#1171937911yescharacteristic
310C2#1171938312yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#393C2
prime radicalC24×D13C22
hypercenter#393D13
hypocenterC13#2626
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#88200C2semidirect
3. C13×#393C2semidirect
4. #11718892C2semidirect
6. #11718610C2semidirect
7. #11718609C2semidirect
8. #11718338C2semidirect
9. #11718337C2semidirect
10. #11718329C2semidirect
11. #11718328C2semidirect
13. C22×Q8×C13C22semidirect
27. C2×C4⋊Dic13C22semidirect
28. C2×C4⋊Dic13C22semidirect
29. C2×#6101C22semidirect
30. C2×#6101C22semidirect
31. C2×#6101C22semidirect
33. C13×#95C22semidirect
34. C13×#95C22semidirect
35. #88071C22semidirect
36. #88071C22semidirect
42. C23×D13Q8semidirect
126. #393D13semidirect
160. C22×Q8C2×D13semidirect
182. #95C2×D13semidirect
183. #95C2×D13semidirect
229. C13#2626semidirect

Maximal subgroups

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

subgroupindex
C2×#882002
C2×C22⋊C4×D132
C13×#3932
#117188922
#117186162
#117186102
#117186092
#117183382
#117183372
#117183292
#117183282
#262613