Finite Group Databasebeta

← #13120754

Subgroups — #13120754

Order 1664.

520 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 137 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×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D13C211yesmaximal, characteristic
3#11718892C211yesmaximal, characteristic, complemented
4#11718890C211yesmaximal, characteristic, complemented
5#11718872C211yesmaximal, characteristic, complemented
6#11718654C211yesmaximal, characteristic, complemented
7#11718650C212yesmaximal, complemented
8#11718641C211yesmaximal, characteristic, complemented
9#11718639C212yesmaximal, complemented
10#11718620C212yesmaximal
11#11718613C212yesmaximal, complemented
12C22×Q8×C13C2211yescharacteristic
13C23×C4×C13C2211yescharacteristic
14C22×C22⋊D13C2211yescharacteristic
15C22×C4×D13C2211yescharacteristic
16C13×C22⋊Q8—24no—
17C2×C13×C4⋊C4C2212yes—
18C2×C13×C4⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2212yes—
20C2×C22⋊Dic13C2211yescharacteristic
21C2×C22⋊Dic13C2212yes—
22C4×C22⋊D13—24no—
23C2×#6103C2211yescharacteristic
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×#6101C2211yescharacteristic
27C2×#6101C2212yes—
28C2×#6101C2212yes—
29C2×C4×Dic13C2211yescharacteristic
30#88071C2212yes—
31#88071C2212yes—
32#88071C2212yes—
33#88071C2211yescharacteristic
34#88071C2211yescharacteristic
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C23×D13C2311yescharacteristic
39C2×Q8×C13—22no—
40C2×Q8×C13—42no—
41C22×C4×C13—42no—
42C22×C4×C13D414yes—
43C22×C4×C13C2312yes—
44C22×C4×C13C2312yes—
45C22×C4×C13C2311yescharacteristic
46C22×C4×C13C2311yescharacteristic
47C2×C22⋊D13—22no—
48C2×C22⋊D13—22no—
49C2×C22⋊D13—22no—
50C22×Dic13C2311yescharacteristic
51C22×Dic13C2312yes—
52C22×Dic13C2312yes—
53C22×Dic13C2311yescharacteristic
54C22×Dic13C2311yescharacteristic
55C2×C4×D13—22no—
56C2×C4×D13—42no—
57C13×C4⋊C4—22no—
58C13×C4⋊C4—24no—
59C13×C22⋊C4—24no—
60C22⋊Dic13—22no—
61C22⋊Dic13—42no—
62#6103—24no—
63#6103—22no—
64#6103—42no—
65#6101—22no—
66#6101—24no—
67#6101—42no—
68C4×Dic13—22no—
69#2638—131nomaximal, Sylow
70C23×C13—21no—
71C23×C13—21no—
72C23×C13—22no—
73C23×C13—22no—
74C23×C13C2×D412yes—
75C23×C13C2411yescharacteristic
76C22×D13—21no—
77C22×D13—21no—
78C22×D13—22no—
79C22×D13—22no—
80C22×D13#4112yes—
81Q8×C13—44no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—44no—
91C2×C4×C13C2×D412yes—
92C2×C4×C13C2×D412yes—
93C22⋊D13—28no—
94C2×Dic13—21no—
95C2×Dic13—21no—
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13#4112yes—
107C4×D13—44no—
108C2×C22⋊Q8D1311yescharacteristic, complemented
109C2×C4×D4—131no—
110#398—131no—
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×C13—22no—
120C22×C13—22no—
121C22×C13—22no—
122C22×C13—42no—
123C22×C13—42no—
124C22×C13C22×D411yescharacteristic
125C22×C13C2×#4111yescharacteristic
126C22×C13C2×#4111yescharacteristic
127C22×C13H(5,𝔽2)12yes—
128C22×C132−1+412yes—
129C2×D13—22no—
130C2×D13—24no—
131C2×D13—41no—
132C2×D13—41no—
133C2×D13—42no—
134C4×C13—22no—
135C4×C13—22no—
136C4×C13—42no—
137C4×C13—42no—
138Dic13—22no—
139Dic13—41no—
140Dic13—41no—
141Dic13—42no—
142Dic13—42no—
143C22×Q8C2×D1311yescharacteristic
144C22×D4—131no—
145C23×C4—131no—
146C23×C4C2×D1311yescharacteristic
147C22⋊Q8—24no—
148C4×D4—264no—
149C2×C4⋊C4—131no—
150C2×C4⋊C4—132no—
151C2×C4⋊C4—132no—
152C2×C4⋊C4C2×D1312yes—
153C2×C4⋊C4C2×D1311yescharacteristic
154C2×C22⋊C4—131no—
155C2×C22⋊C4—131no—
156C2×C22⋊C4—132no—
157C2×C22⋊C4—132no—
158C2×C22⋊C4—132no—
159C2×C22⋊C4C2×D1312yes—
160C2×C42—131no—
161#95—132no—
162#95—131no—
163#95—131no—
164#95—132no—
165#95—132no—
166#95—132no—
167#95—132no—
168C2×C13—42no—
169C2×C13#52511yescharacteristic
170C2×C13#53411yescharacteristic
171C2×C13#53611yescharacteristic
172C2×C13#53912yes—
173C2×C13#54212yes—
174D13—42no—
175C24—131no—
176C24C22×D1311yescharacteristic
177C2×Q8—22no—
178C2×Q8—42no—
179C2×D4—262no—
180C2×D4—262no—
181C2×D4—262no—
182C22×C4—42no—
183C22×C4—131no—
184C22×C4—131no—
185C22×C4—132no—
186C22×C4—132no—
187C22×C4—131no—
188C22×C4—262no—
189C22×C4—522no—
190C22×C4C22⋊D1314yes—
191C22×C4C22×D1312yes—
192C22×C4C22×D1312yes—
193C22×C4C22×D1311yescharacteristic
194C22×C4C22×D1311yescharacteristic
195C4⋊C4—22no—
196C4⋊C4—24no—
197C4⋊C4—264no—
198C4⋊C4—262no—
199C4⋊C4—522no—
200C22⋊C4—24no—
201C22⋊C4—264no—
202C22⋊C4—262no—
203C22⋊C4—262no—
204C22⋊C4—522no—
205C22⋊C4—522no—
206C42—262no—
207C13#263811yescharacteristic, complemented, Sylow
208C23—22no—
209C23—22no—
210C23—21no—
211C23—21no—
212C23—132no—
213C23—262no—
214C23—262no—
215C23—261no—
216C23—261no—
217C23C2×C22⋊D1312yes—
218C23C23×D1311yescharacteristic
219Q8—44no—
220D4—268no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—44no—
230C2×C4—132no—
231C2×C4—261no—
232C2×C4—261no—
233C2×C4—262no—
234C2×C4—262no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4—262no—
240C2×C4—262no—
241C2×C4—261no—
242C2×C4—261no—
243C2×C4—524no—
244C2×C4C2×C22⋊D1312yes—
245C2×C4C2×C22⋊D1312yes—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—42no—
250C22—42no—
251C22—262no—
252C22—264no—
253C22—521no—
254C22—521no—
255C22—522no—
256C22#8825112yes—
257C22#8825412yes—
258C22#41×D1311yescharacteristic
259C22#41×D1311yescharacteristic
260C22C22×C22⋊D1311yescharacteristic
261C4—22no—
262C4—22no—
263C4—42no—
264C4—42no—
265C4—262no—
266C4—521no—
267C4—521no—
268C4—522no—
269C4—522no—
270C2—42no—
271C2—522no—
272C2#1171934312yes—
273C2#1171934512yes—
274C2#1171950911yescharacteristic
275C2#1171952111yescharacteristic
276C2#1171953311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×C22⋊Q8C2
prime radicalC22×C22⋊D13C22
hypercenterC2×C22⋊Q8D13
hypocenterC13#2638
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C13×C22⋊Q8C2semidirect
3. #11718892C2semidirect
4. #11718890C2semidirect
5. #11718872C2semidirect
6. #11718654C2semidirect
7. #11718650C2semidirect
8. #11718641C2semidirect
9. #11718639C2semidirect
11. #11718613C2semidirect
108. C2×C22⋊Q8D13semidirect
207. C13#2638semidirect

Maximal subgroups

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

subgroupindex
C2×C13×C22⋊Q82
C2×C4×C22⋊D132
#117188922
#117188902
#117188722
#117186542
#117186502
#117186412
#117186392
#117186202
#117186132
#263813