Finite Group Databasebeta

← #13120210

Subgroups — #13120210

Order 1664.

544 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 159 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
2C2×C4⋊C4×D13C211yesmaximal, characteristic
3C13×#398C211yesmaximal, characteristic, complemented
4#11718650C212yesmaximal
5#11718646C212yesmaximal, complemented
6#11718641C211yesmaximal, characteristic, complemented
7#11718640C211yesmaximal, characteristic, complemented
8#11718329C212yesmaximal
9#11718327C211yesmaximal, characteristic
10#11718317C211yesmaximal, characteristic, complemented
11#11718308C212yesmaximal, complemented
12C22×C4×D13C2211yescharacteristic
13C22×C4×D13C2211yescharacteristic
14C22×C4×D13C2211yescharacteristic
15C22×Dic26C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C4⋊C4C2212yes—
19C2×#6103C2212yes—
20C2×#6103C2212yes—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×C4⋊Dic13C2212yes—
23C2×C4⋊Dic13C2212yes—
24C2×#6101C2211yescharacteristic
25C2×#6101C2211yescharacteristic
26C2×#6101C2212yes—
27C2×#6101C2212yes—
28C2×C4×Dic13C2212yes—
29#88151—24no—
30C4⋊C4×D13—24no—
31C13×#95C2212yes—
32C13×#95C2211yescharacteristic
33#88071C2212yes—
34#88071C2211yescharacteristic
35#88071C2212yes—
36#88071C2212yes—
37C23×D13C2311yescharacteristic
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×Dic13C2311yescharacteristic
44C22×Dic13C2312yes—
45C22×Dic13C2311yescharacteristic
46C22×Dic13C2312yes—
47C22×Dic13C2311yescharacteristic
48C2×C4×D13—22no—
49C2×C4×D13—22no—
50C2×C4×D13—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—24no—
61#6103Q818yescomplemented
62C4⋊Dic13—22no—
63C4⋊Dic13—24no—
64C4⋊Dic13—42no—
65#6101—22no—
66#6101—22no—
67#6101—24no—
68#6101—42no—
69C4×Dic13—42no—
70#2583—131nomaximal, Sylow
71C23×C13C2411yescharacteristic
72C22×D13—21no—
73C22×D13—21no—
74C22×D13—22no—
75C22×D13C2×D412yes—
76C22×D13C2×Q814yes—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—21no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—21no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13C2×D412yes—
88C2×C4×C13C2×Q814yes—
89C2×C4×C13#4112yes—
90C2×Dic13—21no—
91C2×Dic13—22no—
92C2×Dic13—21no—
93C2×Dic13—22no—
94C2×Dic13—22no—
95C2×Dic13—21no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13C2×D412yes—
101C2×Dic13C2×Q814yes—
102C2×Dic13#4112yes—
103C4×D13—28no—
104C4×D13—44no—
105C4×D13—44no—
106Dic26—44no—
107C2×C22⋊Q8—131no—
108C22×C4⋊C4—131no—
109#398—131no—
110#398D1311yescharacteristic, complemented
111#395—131no—
112#395—131no—
113#389—132no—
114#389—132no—
115#385—132no—
116#385—132no—
117C4×C22⋊C4—131no—
118C22×C13C22×D411yescharacteristic
119C22×C13C22×Q812yes—
120C22×C13C2×#4111yescharacteristic
121C22×C13C2×#4111yescharacteristic
122C22×C13H(5,𝔽2)12yes—
123C2×D13—22no—
124C2×D13—22no—
125C2×D13—24no—
126C2×D13—24no—
127C2×D13C4⋊Q814yes—
128C4×C13—22no—
129C4×C13—22no—
130C4×C13—24no—
131C4×C13—42no—
132C4×C13—41no—
133Dic13—22no—
134Dic13—22no—
135Dic13—24no—
136Dic13—42no—
137Dic13—41no—
138C22×Q8—131no—
139C23×C4—131no—
140C23×C4—131no—
141C23×C4—131no—
142C22⋊Q8—264no—
143C2×C4⋊C4—131no—
144C2×C4⋊C4—131no—
145C2×C4⋊C4—131no—
146C2×C4⋊C4—132no—
147C2×C4⋊C4—132no—
148C2×C4⋊C4—132no—
149C2×C4⋊C4—132no—
150C2×C4⋊C4—264no—
151C2×C4⋊C4C2×D1311yescharacteristic
152C2×C4⋊C4C2×D1311yescharacteristic
153C2×C4⋊C4C2×D1312yes—
154C2×C22⋊C4—132no—
155C2×C22⋊C4—132no—
156C2×C42—132no—
157#95—131no—
158#95—132no—
159#95—132no—
160#95—132no—
161#95C2×D1311yescharacteristic
162#95C2×D1312yes—
163C2×C13#52511yescharacteristic
164C2×C13C2×C4⋊Q811yescharacteristic
165C2×C13#53411yescharacteristic
166C2×C13#55412yes—
167C2×C13#55412yes—
168D13—24no—
169C24—131no—
170C2×Q8—262no—
171C2×Q8—522no—
172C22×C4—132no—
173C22×C4—131no—
174C22×C4—131no—
175C22×C4—134no—
176C22×C4—132no—
177C22×C4—131no—
178C22×C4—262no—
179C22×C4—262no—
180C22×C4—262no—
181C22×C4—262no—
182C22×C4—522no—
183C22×C4—522no—
184C22×C4C22×D1312yes—
185C22×C4C22×D1311yescharacteristic
186C22×C4C22×D1311yescharacteristic
187C22×C4C22×D1311yescharacteristic
188C22×C4C22×D1312yes—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—24no—
192C4⋊C4—262no—
193C4⋊C4—262no—
194C4⋊C4—264no—
195C4⋊C4—264no—
196C4⋊C4—262no—
197C4⋊C4—522no—
198C4⋊C4—522no—
199C22⋊C4—138no—
200C22⋊C4—264no—
201C42—522no—
202C13#258311yescharacteristic, complemented, Sylow
203C23—132no—
204C23—134no—
205C23—261no—
206C23—261no—
207C23—262no—
208C23C23×D1311yescharacteristic
209Q8—524no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—132no—
221C2×C4—134no—
222C2×C4—132no—
223C2×C4—268no—
224C2×C4—261no—
225C2×C4—261no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4—262no—
229C2×C4—262no—
230C2×C4—261no—
231C2×C4—262no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—524no—
235C2×C4—524no—
236C2×C4D4×D1312yes—
237C2×C4#612912yes—
238C2×C4Q8×D1314yes—
239C22—134no—
240C22—262no—
241C22—264no—
242C22—262no—
243C22—264no—
244C22C2×D4×D1311yescharacteristic
245C22C2×#612911yescharacteristic
246C22C2×Q8×D1312yes—
247C22#41×D1311yescharacteristic
248C22#8825612yes—
249C4—22no—
250C4—24no—
251C4—22no—
252C4—42no—
253C4—41no—
254C4—262no—
255C4—262no—
256C4—264no—
257C4—521no—
258C4—522no—
259C2—264no—
260C2#1171931111yescharacteristic
261C2#1171934012yes—
262C2#1171935811yescharacteristic
263C2#1171939512yes—
264C2D13×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#398C2
prime radicalC23×D13C23
hypercenter#398D13
hypocenterC13#2583
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
3. C13×#398C2semidirect
5. #11718646C2semidirect
6. #11718641C2semidirect
7. #11718640C2semidirect
10. #11718317C2semidirect
11. #11718308C2semidirect
61. #6103Q8semidirect
110. #398D13semidirect
202. C13#2583semidirect

Maximal subgroups

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

subgroupindex
C2×#881512
C2×C4⋊C4×D132
C13×#3982
#117186502
#117186462
#117186412
#117186402
#117183292
#117183272
#117183172
#117183082
#258313