Finite Group Databasebeta

← #13120761

Subgroups — #13120761

Order 1664.

520 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 131 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×#88151C211yesmaximal, characteristic, complemented
2C2×#88147C211yesmaximal, characteristic
3C13×#398C211yesmaximal, characteristic, complemented
4#11718654C211yesmaximal, characteristic, complemented
5#11718652C212yesmaximal
6#11718642C212yesmaximal, complemented
7#11718640C211yesmaximal, characteristic, complemented
8#11718336C212yesmaximal, complemented
9#11718334C211yesmaximal, characteristic, complemented
10#11718329C212yesmaximal, complemented
11#11718325C211yesmaximal, characteristic, complemented
12C22×D52C2211yescharacteristic
13C22×C4×D13C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C22×Dic26C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C4⋊C4C2212yes—
19C2×#6103C2211yescharacteristic
20C2×#6103C2211yescharacteristic
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×C4⋊Dic13C2212yes—
26C2×#6101C2212yes—
27C2×C4×Dic13C2211yescharacteristic
28#88151—24no—
29#88147—24no—
30C13×#95C2211yescharacteristic
31C13×#95C2212yes—
32#88071C2212yes—
33#88071C2211yescharacteristic
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C23×D13C2311yescharacteristic
38C23×D13C2311yescharacteristic
39C22×C4×C13C2312yes—
40C22×C4×C13C2312yes—
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2312yes—
46C22×Dic13C2312yes—
47C22×Dic13C2311yescharacteristic
48C2×D52—22no—
49C2×D52—22no—
50C2×D52—22no—
51C2×C4×D13—22no—
52C2×C4×D13—42no—
53C2×C4×D13—42no—
54C2×C4×D13D414yes—
55C2×Dic26—22no—
56C2×Dic26—42no—
57C13×C4⋊C4—22no—
58C13×C4⋊C4—22no—
59C13×C4⋊C4—24no—
60#6103—22no—
61#6103—24no—
62#6103—24no—
63#6103—22no—
64#6103—42no—
65#6103—42no—
66C4⋊Dic13—24no—
67#6101—42no—
68C4×Dic13—22no—
69#2638—131nomaximal, Sylow
70C23×C13C2411yescharacteristic
71C22×D13—21no—
72C22×D13—21no—
73C22×D13—21no—
74C22×D13—21no—
75C22×D13—22no—
76C22×D13—22no—
77C22×D13—22no—
78C22×D13—22no—
79C22×D13C2×D412yes—
80C22×D13#4112yes—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13C2×D412yes—
93C2×C4×C13#4112yes—
94C2×Dic13—22no—
95C2×Dic13—21no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13C2×D412yes—
104D52—28no—
105C4×D13—44no—
106C4×D13—44no—
107Dic26—44no—
108C2×C22⋊Q8—131no—
109C2×C4×D4—131no—
110#398D1311yescharacteristic, complemented
111#397—131no—
112#397—132no—
113#395—131no—
114#394—132no—
115#393—131no—
116#387—132no—
117#385—132no—
118#381—131no—
119C22×C13C22×D411yescharacteristic
120C22×C13C2×#4111yescharacteristic
121C22×C13C2×#4111yescharacteristic
122C22×C13H(5,𝔽2)12yes—
123C22×C132−1+412yes—
124C2×D13—22no—
125C2×D13—22no—
126C2×D13—22no—
127C2×D13—22no—
128C2×D13—24no—
129C2×D13—41no—
130C2×D13—41no—
131C2×D13—42no—
132C2×D13—42no—
133C2×D13—42no—
134C4×C13—22no—
135C4×C13—22no—
136C4×C13—42no—
137C4×C13—41no—
138C4×C13—42no—
139Dic13—22no—
140Dic13—42no—
141Dic13—41no—
142Dic13—42no—
143C22×Q8—131no—
144C22×D4—131no—
145C23×C4—131no—
146C23×C4—131no—
147C22⋊Q8—264no—
148C4×D4—264no—
149C2×C4⋊C4—132no—
150C2×C4⋊C4—132no—
151C2×C4⋊C4C2×D1311yescharacteristic
152C2×C4⋊C4C2×D1311yescharacteristic
153C2×C4⋊C4C2×D1312yes—
154C2×C22⋊C4—131no—
155C2×C22⋊C4—131no—
156C2×C22⋊C4—132no—
157C2×C22⋊C4—132no—
158C2×C22⋊C4—132no—
159C2×C22⋊C4—132no—
160C2×C42—131no—
161#95—132no—
162#95—131no—
163#95—132no—
164#95—132no—
165#95—132no—
166#95C2×D1311yescharacteristic
167#95C2×D1312yes—
168C2×C13#52511yescharacteristic
169C2×C13#53411yescharacteristic
170C2×C13#53611yescharacteristic
171C2×C13#53912yes—
172C2×C13#54212yes—
173D13—42no—
174D13—42no—
175C24—131no—
176C24—131no—
177C2×Q8—262no—
178C2×Q8—522no—
179C2×D4—262no—
180C2×D4—262no—
181C2×D4—262no—
182C22×C4—131no—
183C22×C4—134no—
184C22×C4—131no—
185C22×C4—132no—
186C22×C4—132no—
187C22×C4—262no—
188C22×C4—522no—
189C22×C4—522no—
190C22×C4C22×D1312yes—
191C22×C4C22×D1312yes—
192C22×C4C22×D1311yescharacteristic
193C22×C4C22×D1311yescharacteristic
194C22×C4C22×D1311yescharacteristic
195C4⋊C4—22no—
196C4⋊C4—22no—
197C4⋊C4—24no—
198C4⋊C4—264no—
199C4⋊C4—522no—
200C22⋊C4—262no—
201C22⋊C4—264no—
202C22⋊C4—264no—
203C22⋊C4—262no—
204C22⋊C4—522no—
205C22⋊C4—522no—
206C42—262no—
207C13#263811yescharacteristic, complemented, Sylow
208C23—132no—
209C23—132no—
210C23—261no—
211C23—261no—
212C23—261no—
213C23—262no—
214C23—262no—
215C23—261no—
216C23—262no—
217C23—262no—
218C23C23×D1311yescharacteristic
219Q8—524no—
220D4—268no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—132no—
233C2×C4—262no—
234C2×C4—261no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4—262no—
240C2×C4—262no—
241C2×C4—262no—
242C2×C4—524no—
243C2×C4—524no—
244C2×C4D4×D1312yes—
245C2×C4#612912yes—
246C22—262no—
247C22—262no—
248C22—262no—
249C22—262no—
250C22—264no—
251C22—521no—
252C22—522no—
253C22—522no—
254C22—521no—
255C22—522no—
256C22C2×D4×D1311yescharacteristic
257C22C2×#612911yescharacteristic
258C22#8825412yes—
259C22#41×D1311yescharacteristic
260C22#8825612yes—
261C4—22no—
262C4—22no—
263C4—42no—
264C4—42no—
265C4—41no—
266C4—262no—
267C4—521no—
268C4—522no—
269C4—522no—
270C2—522no—
271C2—522no—
272C2#1171931111yescharacteristic
273C2#1171934812yes—
274C2#1171935811yescharacteristic
275C2#1171939712yes—
276C2#1171942911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#398C2
prime radicalC22×D52C22
hypercenter#398D13
hypocenterC13#2638
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#88151C2semidirect
3. C13×#398C2semidirect
4. #11718654C2semidirect
6. #11718642C2semidirect
7. #11718640C2semidirect
8. #11718336C2semidirect
9. #11718334C2semidirect
10. #11718329C2semidirect
11. #11718325C2semidirect
110. #398D13semidirect
207. C13#2638semidirect

Maximal subgroups

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

subgroupindex
C2×#881512
C2×#881472
C13×#3982
#117186542
#117186522
#117186422
#117186402
#117183362
#117183342
#117183292
#117183252
#263813