Finite Group Databasebeta

← #13119105

Subgroups — #13119105

Order 1664.

672 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 139 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×#88146C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D13C211yesmaximal, characteristic
3C13×#397C211yesmaximal, characteristic, complemented
4#11718654C211yesmaximal, characteristic, complemented
5#11718616C212yesmaximal
6#11718612C212yesmaximal, complemented
7#11718610C211yesmaximal, characteristic, complemented
8#11718338C211yesmaximal, characteristic, complemented
9#11718330C212yesmaximal, complemented
10#11718329C212yesmaximal, complemented
11#11718325C211yesmaximal, characteristic, complemented
12C24×D13C2211yescharacteristic
13C22×C4×D13C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic, complemented
16C2×C13×C22⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2212yes—
18C2×C22⋊Dic13C2211yescharacteristic
19C2×C22⋊Dic13C2212yes—
20C2×#6103C2211yescharacteristic
21C2×#6103C2211yescharacteristic
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×C4⋊Dic13C2211yescharacteristic, complemented
27C2×C4⋊Dic13C2212yescomplemented
28C2×#6101C2212yescomplemented
29C2×C4×Dic13C2212yescomplemented
30#88146—24no—
31C22⋊C4×D13—24no—
32C13×#95C2211yescharacteristic, complemented
33C13×#95C2212yescomplemented
34#88071C2212yescomplemented
35#88071C2211yescharacteristic, complemented
36#88071C2212yescomplemented
37C24×C13C2311yescharacteristic
38C23×D13—22no—
39C23×D13—22no—
40C23×D13—22no—
41C23×D13—24no—
42C23×D13—42no—
43C23×D13C2311yescharacteristic
44C23×D13C2311yescharacteristic
45C22×C4×C13C2312yes—
46C22×C4×C13C2312yes—
47C22×C4×C13C2311yescharacteristic
48C22×C4×C13C2311yescharacteristic
49C22×Dic13C2312yes—
50C22×Dic13C2311yescharacteristic
51C22×Dic13C2312yes—
52C22×Dic13C2311yescharacteristic
53C2×C4×D13—24no—
54C2×C4×D13—22no—
55C2×C4×D13—42no—
56C2×C4×D13D414yes—
57C13×C4⋊C4—22no—
58C13×C22⋊C4—24no—
59C13×C22⋊C4—22no—
60C22⋊Dic13—22no—
61C22⋊Dic13—42no—
62#6103—24no—
63#6103—24no—
64#6103—24no—
65#6103—22no—
66#6103—22no—
67#6103—42no—
68C4⋊Dic13—22no—
69C4⋊Dic13—42no—
70#6101—42no—
71C4×Dic13—24no—
72#2482—131nomaximal, Sylow
73C23×C13—21no—
74C23×C13—21no—
75C23×C13—22no—
76C23×C13—22no—
77C23×C13#4112yes—
78C23×C13C2411yescharacteristic
79C22×D13—21no—
80C22×D13—21no—
81C22×D13—22no—
82C22×D13—28no—
83C22×D13—21no—
84C22×D13—21no—
85C22×D13—22no—
86C22×D13—22no—
87C22×D13—48no—
88C22×D13—48no—
89C22×D13—44no—
90C22×D13—44no—
91C22×D13C2×D412yes—
92C22×D13#4112yes—
93C22×D13#4114yes—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—21no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13C2×D412yes—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—21no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13C2×D412yes—
114C4×D13—28no—
115C4×D13—44no—
116C2×#117—131no—
117C22×C22⋊C4—131no—
118#399—131no—
119#399—131no—
120#397—131no—
121#397D1311yescharacteristic, complemented
122#388—132no—
123#388—132no—
124#385—132no—
125#381—131no—
126#379—132no—
127C22×C13—22no—
128C22×C13—24no—
129C22×C13—41no—
130C22×C13—41no—
131C22×C13—42no—
132C22×C13C22×D411yescharacteristic
133C22×C13C2×#4111yescharacteristic
134C22×C13C2×#4112yes—
135C22×C13C2×#4111yescharacteristic
136C22×C13H(5,𝔽2)12yes—
137C2×D13—22no—
138C2×D13—22no—
139C2×D13—24no—
140C2×D13—24no—
141C2×D13—22no—
142C2×D13—24no—
143C2×D13—416no—
144C2×D13—41no—
145C2×D13—41no—
146C2×D13—42no—
147C2×D13#12314yes—
148C4×C13—22no—
149C4×C13—42no—
150C4×C13—41no—
151C4×C13—42no—
152Dic13—22no—
153Dic13—41no—
154Dic13—42no—
155Dic13—42no—
156C25—131no—
157C23×C4—131no—
158C23×C4—131no—
159#117—264no—
160C2×C4⋊C4—131no—
161C2×C4⋊C4—132no—
162C2×C4⋊C4—132no—
163C2×C4⋊C4C2×D1311yescharacteristic, complemented
164C2×C22⋊C4—131no—
165C2×C22⋊C4—131no—
166C2×C22⋊C4—131no—
167C2×C22⋊C4—132no—
168C2×C22⋊C4—132no—
169C2×C22⋊C4—132no—
170C2×C22⋊C4—132no—
171C2×C22⋊C4—132no—
172C2×C22⋊C4—264no—
173C2×C22⋊C4C2×D1311yescharacteristic
174C2×C22⋊C4C2×D1312yes—
175C2×C42—132no—
176#95—132no—
177#95—131no—
178#95—132no—
179#95C2×D1311yescharacteristic, complemented
180#95C2×D1312yescomplemented
181C2×C13—42no—
182C2×C13C2×#12311yescharacteristic
183C2×C13#52511yescharacteristic
184C2×C13#53511yescharacteristic
185C2×C13#55112yes—
186C2×C13#55112yes—
187D13—24no—
188D13—42no—
189C24—131no—
190C24—131no—
191C24—262no—
192C24—262no—
193C24—264no—
194C24—262no—
195C24—522no—
196C24C22×D1311yescharacteristic
197C22×C4—131no—
198C22×C4—134no—
199C22×C4—132no—
200C22×C4—131no—
201C22×C4—132no—
202C22×C4—264no—
203C22×C4—262no—
204C22×C4—522no—
205C22×C4C22×D1312yes—
206C22×C4C22×D1312yes—
207C22×C4C22×D1311yescharacteristic
208C22×C4C22×D1311yescharacteristic
209C4⋊C4—22no—
210C4⋊C4—262no—
211C4⋊C4—522no—
212C4⋊C4—522no—
213C22⋊C4—24no—
214C22⋊C4—22no—
215C22⋊C4—262no—
216C22⋊C4—264no—
217C22⋊C4—264no—
218C22⋊C4—264no—
219C22⋊C4—262no—
220C22⋊C4—262no—
221C22⋊C4—522no—
222C22⋊C4—522no—
223C42—264no—
224C13#248211yescharacteristic, complemented, Sylow
225C23—21no—
226C23—21no—
227C23—22no—
228C23—22no—
229C23—132no—
230C23—134no—
231C23—132no—
232C23—268no—
233C23—261no—
234C23—261no—
235C23—262no—
236C23—261no—
237C23—261no—
238C23—262no—
239C23—262no—
240C23—528no—
241C23—524no—
242C23—528no—
243C23—524no—
244C23#612912yes—
245C23C23×D1311yescharacteristic
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—132no—
256C2×C4—268no—
257C2×C4—262no—
258C2×C4—262no—
259C2×C4—261no—
260C2×C4—262no—
261C2×C4—262no—
262C2×C4—262no—
263C2×C4—262no—
264C2×C4—262no—
265C2×C4—262no—
266C2×C4—524no—
267C2×C4D4×D1312yes—
268C22—22no—
269C22—24no—
270C22—41no—
271C22—41no—
272C22—42no—
273C22—134no—
274C22—262no—
275C22—264no—
276C22—262no—
277C22—264no—
278C22—262no—
279C22—264no—
280C22—5216no—
281C22—521no—
282C22—522no—
283C22—521no—
284C22C2×D4×D1311yescharacteristic
285C22C2×#612911yescharacteristic
286C22#41×D1311yescharacteristic
287C22#41×D1312yes—
288C22#8825612yes—
289C4—22no—
290C4—42no—
291C4—42no—
292C4—41no—
293C4—262no—
294C4—522no—
295C4—521no—
296C4—522no—
297C2—42no—
298C2—264no—
299C2—522no—
300C2#1171931111yescharacteristic
301C2D13×#12311yescharacteristic
302C2#1171936312yes—
303C2#1171937911yescharacteristic
304C2#1171941012yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#397C2
prime radicalC24×D13C22
hypercenter#397D13
hypocenterC13#2482
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#88146C2semidirect
3. C13×#397C2semidirect
4. #11718654C2semidirect
6. #11718612C2semidirect
7. #11718610C2semidirect
8. #11718338C2semidirect
9. #11718330C2semidirect
10. #11718329C2semidirect
11. #11718325C2semidirect
15. C2×C13×C4⋊C4C22semidirect
26. C2×C4⋊Dic13C22semidirect
27. C2×C4⋊Dic13C22semidirect
28. C2×#6101C22semidirect
29. C2×C4×Dic13C22semidirect
32. C13×#95C22semidirect
33. C13×#95C22semidirect
34. #88071C22semidirect
35. #88071C22semidirect
36. #88071C22semidirect
121. #397D13semidirect
163. C2×C4⋊C4C2×D13semidirect
179. #95C2×D13semidirect
180. #95C2×D13semidirect
224. C13#2482semidirect

Maximal subgroups

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

subgroupindex
C2×#881462
C2×C22⋊C4×D132
C13×#3972
#117186542
#117186162
#117186122
#117186102
#117183382
#117183302
#117183292
#117183252
#248213