Finite Group Databasebeta

← #13118118

Subgroups — #13118118

Order 1664.

568 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 147 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×Q8×Dic13C211yesmaximal, characteristic, complemented
2C2×#88135C211yesmaximal, characteristic
3C13×#393C211yesmaximal, characteristic, complemented
4#11718892C211yesmaximal, characteristic, complemented
5#11718622C212yesmaximal
6#11718614C211yesmaximal, characteristic, complemented
7C22⋊C4×Dic13C212yesmaximal, complemented
8#11718335C211yesmaximal, characteristic, complemented
9#11718327C212yesmaximal, complemented
10#11718321C212yesmaximal, complemented
11#11718309C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C22×C22⋊D13C2211yescharacteristic
14C23×Dic13C2211yescharacteristic
15C22×C4×D13C2211yescharacteristic
16C2×C13×C22⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2212yes—
18C2×C22⋊Dic13C2212yes—
19Q8×Dic13—24no—
20C2×#6103C2211yescharacteristic
21C2×#6103C2212yes—
22C2×#6103C2212yes—
23C2×C4⋊Dic13C2212yes—
24C2×C4⋊Dic13C2211yescharacteristic
25C2×#6101C2211yescharacteristic
26C2×C4×Dic13C2212yes—
27C2×C4×Dic13C2212yes—
28C2×C4×Dic13C2211yescharacteristic
29#88135—24no—
30C13×#95C2211yescharacteristic
31C13×#95C2212yes—
32#88071C2212yes—
33#88071C2211yescharacteristic
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C23×D13C2311yescharacteristic
39C2×Q8×C13—22no—
40C2×Q8×C13—24no—
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2312yes—
45C2×C22⋊D13—22no—
46C2×C22⋊D13—22no—
47C2×C22⋊D13—22no—
48C22×Dic13—22no—
49C22×Dic13—24no—
50C22×Dic13C2312yes—
51C22×Dic13C2311yescharacteristic
52C22×Dic13C2312yes—
53C22×Dic13C2311yescharacteristic
54C22×Dic13C2311yescharacteristic
55C2×C4×D13—22no—
56C2×C4×D13—24no—
57C13×C22⋊C4—22no—
58C13×C22⋊C4—24no—
59C22⋊Dic13—24no—
60#6103—24no—
61#6103—22no—
62#6103—24no—
63C4⋊Dic13—22no—
64C4⋊Dic13—24no—
65#6101—22no—
66C4×Dic13—24no—
67C4×Dic13—24no—
68C4×Dic13D414yes—
69#2398—131nomaximal, Sylow
70C23×C13—21no—
71C23×C13—22no—
72C23×C13—22no—
73C23×C13—21no—
74C23×C13#4112yes—
75C23×C13C2411yescharacteristic
76C22×D13—21no—
77C22×D13—22no—
78C22×D13—22no—
79C22×D13—21no—
80C22×D13#4112yes—
81Q8×C13—28no—
82C2×C4×C13—22no—
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×C13C2×D412yes—
91C2×C4×C13#4114yes—
92C22⋊D13—28no—
93C2×Dic13—21no—
94C2×Dic13—21no—
95C2×Dic13—22no—
96C2×Dic13—21no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—44no—
104C2×Dic13C2×D412yes—
105C2×Dic13C2×D412yes—
106C2×Dic13#4114yes—
107C4×D13—44no—
108C2×C4×Q8—131no—
109C2×C4×D4—131no—
110#400—132no—
111#397—131no—
112#397—131no—
113#394—132no—
114#393—131no—
115#393D1311yescharacteristic, complemented
116C4×C22⋊C4—132no—
117C4×C22⋊C4—132no—
118#376—131no—
119C22×C13—22no—
120C22×C13—24no—
121C22×C13—41no—
122C22×C13—41no—
123C22×C13—42no—
124C22×C13C22×D411yescharacteristic
125C22×C13C2×#4112yes—
126C22×C13C2×#4111yescharacteristic
127C22×C13C2×#4111yescharacteristic
128C22×C13C2×#4112yes—
129C2×D13—22no—
130C2×D13—24no—
131C2×D13—41no—
132C2×D13—41no—
133C2×D13—42no—
134C4×C13—22no—
135C4×C13—24no—
136C4×C13—41no—
137C4×C13—42no—
138Dic13—22no—
139Dic13—42no—
140Dic13—41no—
141Dic13—42no—
142Dic13#12414yes—
143C22×Q8C2×D1311yescharacteristic
144C22×D4—131no—
145C23×C4—131no—
146C23×C4—131no—
147C4×Q8—264no—
148C4×D4—264no—
149C2×C4⋊C4—131no—
150C2×C4⋊C4—132no—
151C2×C4⋊C4—131no—
152C2×C22⋊C4—132no—
153C2×C22⋊C4—131no—
154C2×C22⋊C4—132no—
155C2×C22⋊C4—132no—
156C2×C22⋊C4C2×D1311yescharacteristic
157C2×C22⋊C4C2×D1312yes—
158C2×C42—131no—
159C2×C42—132no—
160C2×C42—132no—
161#95—131no—
162#95—132no—
163#95—132no—
164#95—132no—
165#95—132no—
166#95C2×D1311yescharacteristic
167#95C2×D1312yes—
168C2×C13—42no—
169C2×C13#52511yescharacteristic
170C2×C13#52511yescharacteristic
171C2×C13C2×#12411yescharacteristic
172C2×C13#52912yes—
173C2×C13#52912yes—
174D13—42no—
175C24—131no—
176C24C22×D1311yescharacteristic
177C2×Q8—22no—
178C2×Q8—24no—
179C2×D4—262no—
180C2×D4—262no—
181C2×D4—262no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—132no—
185C22×C4—131no—
186C22×C4—132no—
187C22×C4—262no—
188C22×C4—264no—
189C22×C4—262no—
190C22×C4—264no—
191C22×C4C22×D1312yes—
192C22×C4C22×D1311yescharacteristic
193C22×C4C22×D1311yescharacteristic
194C22×C4C22×D1312yes—
195C4⋊C4—262no—
196C4⋊C4—264no—
197C4⋊C4—262no—
198C22⋊C4—22no—
199C22⋊C4—24no—
200C22⋊C4—264no—
201C22⋊C4—264no—
202C22⋊C4—262no—
203C22⋊C4—264no—
204C42—134no—
205C42—264no—
206C42—264no—
207C13#239811yescharacteristic, complemented, Sylow
208C23—21no—
209C23—22no—
210C23—22no—
211C23—21no—
212C23—132no—
213C23—261no—
214C23—262no—
215C23—261no—
216C23—262no—
217C23#613112yes—
218C23C23×D1311yescharacteristic
219Q8—28no—
220D4—268no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—132no—
230C2×C4—134no—
231C2×C4—132no—
232C2×C4—261no—
233C2×C4—261no—
234C2×C4—262no—
235C2×C4—261no—
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#612914yes—
246C22—24no—
247C22—22no—
248C22—41no—
249C22—41no—
250C22—42no—
251C22—262no—
252C22—264no—
253C22—521no—
254C22—522no—
255C22—521no—
256C22C2×D4×D1311yescharacteristic
257C22C2×#612912yes—
258C22C2×#613111yescharacteristic
259C22#41×D1312yes—
260C22#41×D1311yescharacteristic
261C4—22no—
262C4—24no—
263C4—41no—
264C4—42no—
265C4—134no—
266C4—262no—
267C4—522no—
268C4—522no—
269C4—521no—
270C2—42no—
271C2—522no—
272C2#1171929111yescharacteristic
273C2#1171932912yes—
274C2#1171933211yescharacteristic
275C2D13×#12411yescharacteristic
276C2#1171938512yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#393C2
prime radicalC22×C22⋊D13C22
hypercenter#393D13
hypocenterC13#2398
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic13C2semidirect
3. C13×#393C2semidirect
4. #11718892C2semidirect
6. #11718614C2semidirect
7. C22⋊C4×Dic13C2semidirect
8. #11718335C2semidirect
9. #11718327C2semidirect
10. #11718321C2semidirect
11. #11718309C2semidirect
115. #393D13semidirect
207. C13#2398semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic132
C2×#881352
C13×#3932
#117188922
#117186222
#117186142
C22⋊C4×Dic132
#117183352
#117183272
#117183212
#117183092
#239813