Finite Group Databasebeta

← #15760774

Subgroups — #15760774

Order 3328.

542 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 135 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
1#13123917C211yesmaximal, characteristic, complemented
2#13114832C211yesmaximal, characteristic, complemented
3#13113261C212yesmaximal
4#13112694C212yesmaximal, complemented
5C13×#2536C211yesmaximal, characteristic
6C2×C13×C22⋊Q8—21no—
7C2×C4×Q8×C13C2211yescharacteristic
8C2×C4×D4×C13C2211yescharacteristic
9C13×#398C412yes—
10C13×#394C412yes—
11C13×#388—22no—
12C13×#382C2211yescharacteristic
13C13×#380—21no—
14C2×#88076—21no—
15Q8×#1055—24no—
16#11718586—22no—
17#11718586C2212yes—
18#11718585C2212yes—
19D4⋊#1055—24no—
20#11718122—21no—
21C22×Q8×C13D411yescharacteristic
22C22×D4×C13C2×C411yescharacteristic
23C23×C4×C13—21no—
24C13×C22⋊Q8—42no—
25C13×C22⋊Q8—42no—
26C4×Q8×C13—22no—
27C4×Q8×C13—22no—
28C4×D4×C13—22no—
29C4×D4×C13—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C412yes—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—21no—
38C2×C42×C13D412yes—
39C2×C42×C13C2311yescharacteristic
40C2×#6099—22no—
41C13×#95—22no—
42C13×#95—21no—
43C13×#95C2×C412yes—
44#88076—42no—
45C22⋊#1055—22no—
46C4⋊#1055—24no—
47C4⋊#1055—22no—
48C4⋊#1055—22no—
49C4⋊#1055—22no—
50C4×#1055—24no—
51C4×#1055D414yes—
52#9486—131nomaximal, Sylow
53C24×C13—21no—
54C2×Q8×C13—22no—
55C2×Q8×C13—22no—
56C2×Q8×C13D812yes—
57C2×Q8×C13SD1612yes—
58C2×D4×C13—22no—
59C2×D4×C13—42no—
60C22×C4×C13—22no—
61C22×C4×C13—21no—
62C22×C4×C13—42no—
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13—42no—
66C22×C4×C13C22⋊C412yes—
67C22×C4×C13C22⋊C412yes—
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C13×C4⋊C4—24no—
72C13×C4⋊C4—22no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—44no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C22⋊C4—44no—
78C13×C22⋊C4—44no—
79C13×C22⋊C4—41no—
80C13×C22⋊C4—41no—
81C42×C13—22no—
82C42×C13—22no—
83C42×C13C2×D412yes—
84C42×C13#4112yes—
85#6099—42no—
86#6099—42no—
87C2×#1055—24no—
88C2×#1055—42no—
89#2982—131no—
90#2536D1311yescharacteristic
91#1801—131no—
92#1486—132no—
93#1286—132no—
94C23×C13—22no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13C2×C22⋊C411yescharacteristic
102Q8×C13—24no—
103Q8×C13—24no—
104D4×C13—24no—
105D4×C13—42no—
106C2×C4×C13—22no—
107C2×C4×C13—22no—
108C2×C4×C13—22no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—41no—
115C2×C4×C13—42no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—82no—
119C2×C4×C13—82no—
120C2×C4×C13#10214yes—
121C2×C4×C13C4×D412yes—
122C2×C4×C13#12011yescharacteristic
123C2×C4×C13#12112yes—
124C2×C4×C13#12311yescharacteristic
125C2×C4×C13C2×D811yescharacteristic
126C2×C4×C13C2×SD1611yescharacteristic
127C2×C4×C13#13512yes—
128#1055—44no—
129#1055—82no—
130C2×C22⋊Q8—21no—
131C2×C4×Q8C2×D1311yescharacteristic
132C2×C4×D4C2×D1311yescharacteristic
133C8×Q8—264no—
134#431—132no—
135#431—262no—
136#423—132no—
137C2×#101—261no—
138#398Dic1312yes—
139#394Dic1312yes—
140#388—22no—
141#382C2×D1311yescharacteristic
142#380—21no—
143#343—261no—
144D4⋊C8—264no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—42no—
148C22×C13—42no—
149C22×C13—42no—
150C22×C13—81no—
151C22×C13—81no—
152C22×C13—81no—
153C22×C13—81no—
154C22×C13#38611yescharacteristic
155C22×C13C2×#10211yescharacteristic
156C22×C13#41611yescharacteristic
157C4×C13—22no—
158C4×C13—24no—
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—42no—
162C4×C13—82no—
163C4×C13—81no—
164C4×C13#46512yes—
165C4×C13#46612yes—
166C22×Q8C22⋊D1311yescharacteristic
167C22×D4C2×Dic1311yescharacteristic
168C23×C4—21no—
169C2×M16—262no—
170C22⋊Q8—42no—
171C22⋊Q8—42no—
172C4×Q8—22no—
173C4×Q8—22no—
174C4×D4—22no—
175C4×D4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4C2×Dic1311yescharacteristic
179C2×C4⋊C4C2×Dic1312yes—
180C2×C4⋊C4C22⋊D1311yescharacteristic
181C2×C22⋊C4—22no—
182C2×C22⋊C4—22no—
183C2×C22⋊C4—21no—
184C2×C42C22⋊D1312yes—
185C2×C42C22×D1311yescharacteristic
186C4⋊C8—264no—
187C4⋊C8—262no—
188C4⋊C8—262no—
189C4⋊C8—262no—
190#101—522no—
191C22⋊C8—262no—
192C4×C8—134no—
193C4×C8—264no—
194#95—22no—
195#95—21no—
196#95C2×Dic1312yes—
197C2×C13—21no—
198C2×C13—21no—
199C2×C13—82no—
200C2×C13#189111yescharacteristic
201C2×C13#189311yescharacteristic
202C2×C13#191211yescharacteristic
203C24—21no—
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8#610412yes—
207C2×Q8#610512yes—
208C2×D4—22no—
209C2×D4—42no—
210C22×C4—22no—
211C22×C4—21no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4C22⋊Dic1312yes—
217C22×C4C22⋊Dic1312yes—
218C22×C4C22×Dic1311yescharacteristic
219C22×C4C2×C22⋊D1311yescharacteristic
220C22×C4C2×C22⋊D1311yescharacteristic
221M16—522no—
222M16—522no—
223C2×C8—264no—
224C2×C8—522no—
225C4⋊C4—24no—
226C4⋊C4—22no—
227C4⋊C4—22no—
228C4⋊C4—44no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C22⋊C4—44no—
232C22⋊C4—44no—
233C22⋊C4—41no—
234C22⋊C4—41no—
235C42—22no—
236C42—22no—
237C42D4×D1312yes—
238C42#612912yes—
239C13#948611yescharacteristic, complemented, Sylow
240C23—22no—
241C23—41no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23—41no—
246C23—41no—
247C23C2×C22⋊Dic1311yescharacteristic
248Q8—24no—
249Q8—24no—
250D4—24no—
251D4—42no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4#8807214yes—
267C2×C4C2×#610411yescharacteristic
268C2×C4C2×#610511yescharacteristic
269C2×C4D4×Dic1312yes—
270C2×C4#8818911yescharacteristic
271C2×C4#8819111yescharacteristic
272C2×C4#8819312yes—
273C2×C4#8820412yes—
274C8—524no—
275C8—1042no—
276C22—21no—
277C22—21no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—81no—
282C22—81no—
283C22—81no—
284C22—81no—
285C22C2×#8807211yescharacteristic
286C22#1171888111yescharacteristic
287C22#1171889411yescharacteristic
288C4—22no—
289C4—24no—
290C4—21no—
291C4—21no—
292C4—42no—
293C4—82no—
294C4—81no—
295C4#1171869912yes—
296C4#1171870212yes—
297C2—21no—
298C2—21no—
299C2—82no—
300C2#1311525511yescharacteristic
301C2#1311526511yescharacteristic
302C2#1311537411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2536C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenter#2536D13
hypocenterC13#9486
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2536

Complements

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

NH ≅ G/Ntype
1. #13123917C2semidirect
2. #13114832C2semidirect
4. #13112694C2semidirect
239. C13#9486semidirect

Maximal subgroups

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

subgroupindex
#131239172
#131148322
#131132612
#131126942
C13×#25362
#948613