Finite Group Databasebeta

← #13120018

Subgroups — #13120018

Order 1664.

584 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 161 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
5C2×#88071C211yesmaximal, characteristic, complemented
6#11718653C211yesmaximal, characteristic, complemented
7#11718650C212yesmaximal, complemented
8#11718643C211yesmaximal, characteristic, complemented
9#11718639C212yesmaximal, complemented
10#11718619C212yesmaximal
11#11718603C212yesmaximal, complemented
12C22×Q8×C13C2211yescharacteristic
13C23×C4×C13C2211yescharacteristic
14C22×C22⋊D13C2211yescharacteristic
15C23×Dic13C2212yes—
16C22×C4×D13C2211yescharacteristic
17C13×C22⋊Q8—24no—
18C2×C13×C4⋊C4C2212yes—
19C2×C13×C4⋊C4C2211yescharacteristic
20C2×C13×C22⋊C4C2212yes—
21C2×C22⋊Dic13C2211yescharacteristic
22C4×C22⋊D13—24no—
23C2×#6103C2211yescharacteristic
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×#6101C2211yescharacteristic
27C2×#6101C2212yes—
28C2×#6101C2212yes—
29C2×C4×Dic13C2211yescharacteristic
30#88071C2212yes—
31#88071C2212yes—
32#88071C2211yescharacteristic
33#88071C2211yescharacteristic
34#88071C2212yes—
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⋊D13Q814yescomplemented
50C22×Dic13—24no—
51C22×Dic13—24no—
52C22×Dic13—42no—
53C22×Dic13C2312yes—
54C22×Dic13C2311yescharacteristic
55C22×Dic13C2311yescharacteristic
56C22×Dic13C2311yescharacteristic
57C22×Dic13C2312yes—
58C2×C4×D13—22no—
59C2×C4×D13—42no—
60C13×C4⋊C4—22no—
61C13×C4⋊C4—24no—
62C13×C22⋊C4—24no—
63C22⋊Dic13—22no—
64#6103—22no—
65#6103—24no—
66#6103—42no—
67#6101—22no—
68#6101—24no—
69#6101—42no—
70C4×Dic13—22no—
71#2564—131nomaximal, Sylow
72C23×C13—22no—
73C23×C13—22no—
74C23×C13C2×D412yes—
75C23×C13C2×Q812yes—
76C23×C13#4112yes—
77C23×C13C2411yescharacteristic
78C22×D13—21no—
79C22×D13—22no—
80C22×D13—21no—
81C22×D13—22no—
82C22×D13C2×Q812yes—
83Q8×C13—44no—
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—22no—
91C2×C4×C13—22no—
92C2×C4×C13—44no—
93C2×C4×C13C2×D412yes—
94C2×C4×C13C2×D412yes—
95C22⋊D13—28no—
96C2×Dic13—21no—
97C2×Dic13—22no—
98C2×Dic13—21no—
99C2×Dic13—22no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—48no—
108C2×Dic13C2×Q812yes—
109C2×Dic13#4114yes—
110C4×D13—44no—
111C2×C22⋊Q8D1311yescharacteristic, complemented
112C2×C4×D4—131no—
113#400—131no—
114#399—131no—
115#395—131no—
116#393—131no—
117#387—132no—
118#386—132no—
119#385—132no—
120#380—132no—
121C2×#95—131no—
122C22×C13—22no—
123C22×C13—22no—
124C22×C13—24no—
125C22×C13—24no—
126C22×C13C22⋊Q814yes—
127C22×C13C22×D411yescharacteristic
128C22×C13C22×Q811yescharacteristic
129C22×C13C2×#4111yescharacteristic
130C22×C13C2×#4112yes—
131C22×C13H(5,𝔽2)12yes—
132C2×D13—22no—
133C2×D13—24no—
134C2×D13—41no—
135C2×D13—41no—
136C2×D13—42no—
137C4×C13—22no—
138C4×C13—22no—
139C4×C13—42no—
140C4×C13—42no—
141Dic13—22no—
142Dic13—24no—
143Dic13—41no—
144Dic13—41no—
145Dic13—42no—
146C22×Q8C2×D1311yescharacteristic
147C22×D4—131no—
148C23×C4—132no—
149C23×C4—131no—
150C23×C4C2×D1311yescharacteristic
151C22⋊Q8—24no—
152C4×D4—264no—
153C2×C4⋊C4—131no—
154C2×C4⋊C4—132no—
155C2×C4⋊C4—132no—
156C2×C4⋊C4C2×D1312yes—
157C2×C4⋊C4C2×D1311yescharacteristic
158C2×C22⋊C4—131no—
159C2×C22⋊C4—131no—
160C2×C22⋊C4—132no—
161C2×C22⋊C4—132no—
162C2×C22⋊C4C2×D1312yes—
163C2×C42—131no—
164#95—132no—
165#95—131no—
166#95—131no—
167#95—132no—
168#95—132no—
169#95—132no—
170#95—132no—
171C2×C13—24no—
172C2×C13C2×C22⋊Q811yescharacteristic
173C2×C13#53211yescharacteristic
174C2×C13#53411yescharacteristic
175C2×C13#55112yes—
176C2×C13#55412yes—
177D13—42no—
178C24—131no—
179C24C22×D1311yescharacteristic
180C2×Q8—22no—
181C2×Q8—42no—
182C2×D4—134no—
183C2×D4—262no—
184C2×D4—262no—
185C22×C4—42no—
186C22×C4—131no—
187C22×C4—132no—
188C22×C4—132no—
189C22×C4—131no—
190C22×C4—131no—
191C22×C4—264no—
192C22×C4—264no—
193C22×C4—262no—
194C22×C4—522no—
195C22×C4—522no—
196C22×C4C22⋊D1314yes—
197C22×C4C22×D1312yes—
198C22×C4C22×D1312yes—
199C22×C4C22×D1311yescharacteristic
200C22×C4C22×D1311yescharacteristic
201C4⋊C4—22no—
202C4⋊C4—24no—
203C4⋊C4—264no—
204C4⋊C4—262no—
205C4⋊C4—522no—
206C22⋊C4—24no—
207C22⋊C4—264no—
208C22⋊C4—262no—
209C22⋊C4—262no—
210C22⋊C4—522no—
211C42—262no—
212C13#256411yescharacteristic, complemented, Sylow
213C23—22no—
214C23—22no—
215C23—132no—
216C23—262no—
217C23—261no—
218C23—262no—
219C23—261no—
220C23Q8×D1312yes—
221C23#613112yes—
222C23C2×C22⋊D1312yes—
223C23C23×D1311yescharacteristic
224Q8—44no—
225D4—268no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—44no—
235C2×C4—132no—
236C2×C4—134no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4—261no—
240C2×C4—261no—
241C2×C4—262no—
242C2×C4—262no—
243C2×C4—262no—
244C2×C4—262no—
245C2×C4—262no—
246C2×C4—261no—
247C2×C4—261no—
248C2×C4—524no—
249C2×C4—528no—
250C2×C4C2×C22⋊D1312yes—
251C2×C4C2×C22⋊D1312yes—
252C22—22no—
253C22—22no—
254C22—24no—
255C22—24no—
256C22—262no—
257C22—264no—
258C22—521no—
259C22—521no—
260C22—522no—
261C22#8820014yes—
262C22#8825112yes—
263C22C2×Q8×D1311yescharacteristic
264C22C2×#613111yescharacteristic
265C22#41×D1312yes—
266C22C22×C22⋊D1311yescharacteristic
267C4—22no—
268C4—22no—
269C4—42no—
270C4—42no—
271C4—262no—
272C4—264no—
273C4—521no—
274C4—521no—
275C4—522no—
276C2—24no—
277C2—522no—
278C2#1171934112yes—
279C2#1171934212yes—
280C2#1171950911yescharacteristic
281C2C2×#8820011yescharacteristic
282C2#1171953711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×C22⋊Q8C2
prime radicalC22×C22⋊D13C22
hypercenterC2×C22⋊Q8D13
hypocenterC13#2564
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. C2×#88071C2semidirect
6. #11718653C2semidirect
7. #11718650C2semidirect
8. #11718643C2semidirect
9. #11718639C2semidirect
11. #11718603C2semidirect
49. C2×C22⋊D13Q8semidirect
111. C2×C22⋊Q8D13semidirect
212. C13#2564semidirect

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
C2×#880712
#117186532
#117186502
#117186432
#117186392
#117186192
#117186032
#256413