Finite Group Databasebeta

← #13118194

Subgroups — #13118194

Order 1664.

840 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 171 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
1C22×Q8×D13C211yesmaximal, characteristic, complemented
2C2×#88135C211yesmaximal, characteristic
3C2×#88132C212yesmaximal, complemented
4C13×#393C211yesmaximal, characteristic, complemented
5#11718890C211yesmaximal, characteristic, complemented
6#11718617C212yesmaximal
7#11718608C211yesmaximal, characteristic, complemented
8#11718329C212yesmaximal, complemented
9#11718328C211yesmaximal, characteristic, complemented
10#11718317C211yesmaximal, characteristic, complemented
11#11718307C212yesmaximal, complemented
12C22×Q8×C13C2211yescharacteristic
13C22×C22⋊D13C2211yescharacteristic
14C23×Dic13C2211yescharacteristic
15C2×Q8×D13—24no—
16C2×Q8×D13—28no—
17C22×C4×D13C2212yes—
18C22×C4×D13C2211yescharacteristic
19C22×Dic26C2211yescharacteristic
20C22×Dic26C2212yes—
21C2×C13×C22⋊C4C2212yes—
22C2×C13×C22⋊C4C2211yescharacteristic
23C2×C22⋊Dic13C2212yes—
24C2×#6103C2211yescharacteristic
25C2×#6103C2212yes—
26C2×C4⋊Dic13C2212yes—
27C2×#6101C2212yes—
28C2×#6101C2212yes—
29C2×#6101C2211yescharacteristic
30C2×C4×Dic13C2211yescharacteristic
31#88135—24no—
32#88132—28no—
33C13×#95C2212yes—
34C13×#95C2211yescharacteristic
35#88071C2212yes—
36#88071C2212yes—
37#88071C2212yes—
38#88071C2211yescharacteristic
39C24×C13C2311yescharacteristic
40C23×D13C2311yescharacteristic
41C2×Q8×C13—22no—
42C2×Q8×C13—24no—
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2312yes—
45C22×C4×C13C2311yescharacteristic
46C22×C4×C13C2312yes—
47C2×C22⋊D13—22no—
48C2×C22⋊D13—22no—
49C2×C22⋊D13Q814yescomplemented
50C22×Dic13—24no—
51C22×Dic13—22no—
52C22×Dic13C2312yes—
53C22×Dic13C2311yescharacteristic
54C22×Dic13C2312yes—
55C22×Dic13C2311yescharacteristic
56C22×Dic13C2311yescharacteristic
57Q8×D13—232no—
58C2×C4×D13—24no—
59C2×C4×D13—24no—
60C2×C4×D13—24no—
61C2×C4×D13—24no—
62C2×C4×D13D414yes—
63C2×Dic26—22no—
64C2×Dic26—24no—
65C2×Dic26—24no—
66C2×Dic26—24no—
67C2×Dic26D418yescomplemented
68C13×C22⋊C4—24no—
69C13×C22⋊C4—22no—
70C22⋊Dic13—24no—
71#6103—22no—
72#6103—24no—
73C4⋊Dic13—24no—
74#6101—24no—
75#6101—22no—
76#6101—24no—
77C4×Dic13—22no—
78#2409—131nomaximal, Sylow
79C23×C13—22no—
80C23×C13—21no—
81C23×C13—21no—
82C23×C13—22no—
83C23×C13C2×Q812yescomplemented
84C23×C13C2411yescharacteristic
85C22×D13—22no—
86C22×D13—22no—
87C22×D13C2×D412yes—
88C22×D13C2×Q812yes—
89C22×D13#4112yes—
90Q8×C13—28no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—21no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13C2×D412yes—
100C2×C4×C13C2×D414yes—
101C22⋊D13—28no—
102C2×Dic13—21no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—21no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—21no—
109C2×Dic13—22no—
110C2×Dic13—22no—
111C2×Dic13—44no—
112C2×Dic13C2×D414yes—
113C2×Dic13C2×D412yes—
114C2×Dic13C2×D414yes—
115C2×Dic13C2×Q812yescomplemented
116C4×D13—216no—
117C4×D13—28no—
118Dic26—28no—
119Dic26—216no—
120C23×Q8—131no—
121C2×C22⋊Q8—132no—
122C2×C4×D4—131no—
123#395—131no—
124#395—131no—
125#393—131no—
126#393D1311yescharacteristic, complemented
127#391—132no—
128#386—132no—
129#385—132no—
130#380—131no—
131C22×C13—22no—
132C22×C13—24no—
133C22×C13—41no—
134C22×C13—41no—
135C22×C13—42no—
136C22×C13C22×D411yescharacteristic
137C22×C13C22×D412yes—
138C22×C13C22×Q811yescharacteristic
139C22×C13C2×#4111yescharacteristic
140C22×C132−1+412yes—
141C2×D13—22no—
142C2×D13—22no—
143C2×D13—24no—
144C2×D13—24no—
145C2×D13C22⋊Q814yescomplemented
146C4×C13—22no—
147C4×C13—24no—
148C4×C13—41no—
149C4×C13—42no—
150Dic13—24no—
151Dic13—22no—
152Dic13—41no—
153Dic13—42no—
154Dic13#12014yes—
155C22×Q8—132no—
156C22×Q8—131no—
157C22×Q8—264no—
158C22×Q8—268no—
159C22×Q8C2×D1311yescharacteristic
160C22×D4—131no—
161C23×C4—131no—
162C23×C4—131no—
163C23×C4—132no—
164C22⋊Q8—268no—
165C4×D4—264no—
166C2×C4⋊C4—131no—
167C2×C4⋊C4—132no—
168C2×C4⋊C4—132no—
169C2×C4⋊C4—132no—
170C2×C22⋊C4—132no—
171C2×C22⋊C4—131no—
172C2×C22⋊C4—132no—
173C2×C22⋊C4C2×D1311yescharacteristic
174C2×C22⋊C4C2×D1312yes—
175C2×C42—131no—
176#95—131no—
177#95—132no—
178#95—132no—
179#95—132no—
180#95C2×D1311yescharacteristic
181#95C2×D1312yes—
182C2×C13—42no—
183C2×C13C2×#12011yescharacteristic
184C2×C13C2×C22⋊Q811yescharacteristic
185C2×C13#53611yescharacteristic
186C2×C13#54812yes—
187C2×C13D4×Q812yes—
188D13—24no—
189C24—131no—
190C24C22×D1311yescharacteristic
191C2×Q8—22no—
192C2×Q8—24no—
193C2×Q8—138no—
194C2×Q8—264no—
195C2×Q8—264no—
196C2×Q8—264no—
197C2×Q8—2632no—
198C2×Q8—262no—
199C2×D4—134no—
200C2×D4—262no—
201C2×D4—262no—
202C22×C4—131no—
203C22×C4—131no—
204C22×C4—132no—
205C22×C4—134no—
206C22×C4—132no—
207C22×C4—131no—
208C22×C4—264no—
209C22×C4—264no—
210C22×C4—264no—
211C22×C4—262no—
212C22×C4—264no—
213C22×C4—264no—
214C22×C4C22×D1311yescharacteristic
215C22×C4C22×D1312yes—
216C22×C4C22×D1311yescharacteristic
217C22×C4C22×D1312yes—
218C4⋊C4—264no—
219C4⋊C4—264no—
220C4⋊C4—262no—
221C4⋊C4—264no—
222C22⋊C4—22no—
223C22⋊C4—24no—
224C22⋊C4—262no—
225C22⋊C4—264no—
226C22⋊C4—264no—
227C42—262no—
228C13#240911yescharacteristic, complemented, Sylow
229C23—22no—
230C23—21no—
231C23—21no—
232C23—22no—
233C23—132no—
234C23—132no—
235C23—132no—
236C23—262no—
237C23—262no—
238C23Q8×D1312yescomplemented
239C23C23×D1311yescharacteristic
240Q8—28no—
241Q8—2616no—
242Q8—268no—
243D4—268no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—132no—
253C2×C4—134no—
254C2×C4—134no—
255C2×C4—132no—
256C2×C4—268no—
257C2×C4—2616no—
258C2×C4—261no—
259C2×C4—262no—
260C2×C4—262no—
261C2×C4—261no—
262C2×C4—262no—
263C2×C4—261no—
264C2×C4—262no—
265C2×C4—262no—
266C2×C4—262no—
267C2×C4—524no—
268C2×C4D4×D1312yes—
269C2×C4D4×D1314yes—
270C22—22no—
271C22—24no—
272C22—41no—
273C22—41no—
274C22—42no—
275C22—134no—
276C22—262no—
277C22—264no—
278C22—262no—
279C22—264no—
280C22C2×D4×D1311yescharacteristic
281C22C2×D4×D1312yes—
282C22C2×Q8×D1311yescharacteristic
283C22#41×D1311yescharacteristic
284C22#8825712yes—
285C4—22no—
286C4—24no—
287C4—41no—
288C4—42no—
289C4—134no—
290C4—264no—
291C4—262no—
292C4—521no—
293C4—522no—
294C2—42no—
295C2—264no—
296C2D13×#12011yescharacteristic
297C2D13×C22⋊Q811yescharacteristic
298C2#1171933712yes—
299C2#1171938011yescharacteristic
300C2#1171938212yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#393C2
prime radicalC22×C22⋊D13C22
hypercenter#393D13
hypocenterC13#2409
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D13C2semidirect
3. C2×#88132C2semidirect
4. C13×#393C2semidirect
5. #11718890C2semidirect
7. #11718608C2semidirect
8. #11718329C2semidirect
9. #11718328C2semidirect
10. #11718317C2semidirect
11. #11718307C2semidirect
49. C2×C22⋊D13Q8semidirect
67. C2×Dic26D4semidirect
83. C23×C13C2×Q8semidirect
115. C2×Dic13C2×Q8semidirect
126. #393D13semidirect
145. C2×D13C22⋊Q8semidirect
228. C13#2409semidirect
238. C23Q8×D13semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D132
C2×#881352
C2×#881322
C13×#3932
#117188902
#117186172
#117186082
#117183292
#117183282
#117183172
#117183072
#240913