Finite Group Databasebeta

← #15760794

Subgroups — #15760794

Order 3328.

522 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 119 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#13123921C211yesmaximal, 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—
15#11718685—24no—
16#11718587—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—44no—
25C4×Q8×C13—22no—
26C4×Q8×C13—22no—
27C4×D4×C13—22no—
28C4×D4×C13—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4C2×C412yes—
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—21no—
37C2×C42×C13D412yes—
38C2×C42×C13C2311yescharacteristic
39C2×#6099—22no—
40C13×#95—22no—
41C13×#95—21no—
42C13×#95C2×C412yes—
43#88076—42no—
44C22⋊#1055—22no—
45C4⋊#1055—24no—
46C4⋊#1055—22no—
47C4⋊#1055—22no—
48C4⋊#1055—22no—
49#88043—24no—
50C4×#1055D414yes—
51#9490—131nomaximal, Sylow
52C24×C13—21no—
53C2×Q8×C13—22no—
54C2×Q8×C13—21no—
55C2×Q8×C13—22no—
56C2×Q8×C13—21no—
57C2×D4×C13—22no—
58C2×D4×C13—42no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13C22⋊C412yes—
66C22×C4×C13C22⋊C412yes—
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C13×C4⋊C4—24no—
71C13×C4⋊C4—22no—
72C13×C4⋊C4—22no—
73C13×C4⋊C4—44no—
74C13×C4⋊C4—42no—
75C13×C22⋊C4—44no—
76C13×C22⋊C4—44no—
77C13×C22⋊C4—41no—
78C13×C22⋊C4—41no—
79C42×C13—22no—
80C42×C13—22no—
81C42×C13C2×D412yes—
82C42×C13#4112yes—
83#6099—42no—
84#6099—42no—
85C2×#1055—24no—
86C2×#1055—42no—
87#2983—131no—
88#2536D1311yescharacteristic
89#1801—131no—
90#1486—132no—
91#1286—132no—
92C23×C13—22no—
93C23×C13—41no—
94C23×C13—41no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13C2×C22⋊C411yescharacteristic
100Q8×C13—42no—
101Q8×C13—42no—
102D4×C13—24no—
103D4×C13—42no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—22no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—42no—
116C2×C4×C13—41no—
117C2×C4×C13—82no—
118C2×C4×C13—82no—
119C2×C4×C13C4×D412yes—
120C2×C4×C13#12011yescharacteristic
121C2×C4×C13#12112yes—
122C2×C4×C13#12311yescharacteristic
123C2×C4×C13AGL(1,ℤ/8)12yes—
124C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C13#13711yescharacteristic
126#1055—44no—
127#1055—82no—
128C2×C22⋊Q8—21no—
129C2×C4×Q8C2×D1311yescharacteristic
130C2×C4×D4C2×D1311yescharacteristic
131#446—264no—
132#432—262no—
133#431—132no—
134#423—132no—
135C2×#101—261no—
136#398Dic1312yes—
137#394Dic1312yes—
138#388—22no—
139#382C2×D1311yescharacteristic
140#380—21no—
141#343—261no—
142D4⋊C8—264no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—42no—
146C22×C13—42no—
147C22×C13—42no—
148C22×C13—81no—
149C22×C13—81no—
150C22×C13—81no—
151C22×C13—81no—
152C22×C13#38611yescharacteristic
153C22×C13#41711yescharacteristic
154C22×C13#41811yescharacteristic
155C4×C13—22no—
156C4×C13—21no—
157C4×C13—21no—
158C4×C13—42no—
159C4×C13—42no—
160C4×C13—82no—
161C4×C13—81no—
162C4×C13#46812yes—
163C4×C13#46912yes—
164C22×Q8C22⋊D1311yescharacteristic
165C22×D4C2×Dic1311yescharacteristic
166C23×C4—21no—
167C2×M16—262no—
168C22⋊Q8—44no—
169C4×Q8—22no—
170C4×Q8—22no—
171C4×D4—22no—
172C4×D4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4C2×Dic1311yescharacteristic
176C2×C4⋊C4C2×Dic1312yes—
177C2×C4⋊C4C22⋊D1311yescharacteristic
178C2×C22⋊C4—22no—
179C2×C22⋊C4—22no—
180C2×C22⋊C4—21no—
181C2×C42C22⋊D1312yes—
182C2×C42C22×D1311yescharacteristic
183C4⋊C8—264no—
184C4⋊C8—262no—
185C4⋊C8—262no—
186C4⋊C8—262no—
187#101—522no—
188C22⋊C8—262no—
189#97—264no—
190C4×C8—134no—
191#95—22no—
192#95—21no—
193#95C2×Dic1312yes—
194C2×C13—21no—
195C2×C13—21no—
196C2×C13—82no—
197C2×C13#189111yescharacteristic
198C2×C13#189511yescharacteristic
199C2×C13#191211yescharacteristic
200C24—21no—
201C2×Q8—22no—
202C2×Q8—22no—
203C2×Q8—21no—
204C2×Q8—21no—
205C2×D4—22no—
206C2×D4—42no—
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4C22⋊Dic1312yes—
214C22×C4C22⋊Dic1312yes—
215C22×C4C22×Dic1311yescharacteristic
216C22×C4C2×C22⋊D1311yescharacteristic
217C22×C4C2×C22⋊D1311yescharacteristic
218M16—522no—
219M16—522no—
220C2×C8—264no—
221C2×C8—522no—
222C4⋊C4—24no—
223C4⋊C4—22no—
224C4⋊C4—22no—
225C4⋊C4—44no—
226C4⋊C4—42no—
227C22⋊C4—44no—
228C22⋊C4—44no—
229C22⋊C4—41no—
230C22⋊C4—41no—
231C42—22no—
232C42—22no—
233C42D4×D1312yes—
234C42#612912yes—
235C13#949011yescharacteristic, complemented, Sylow
236C23—22no—
237C23—41no—
238C23—41no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23—41no—
243C23C2×C22⋊Dic1311yescharacteristic
244Q8—42no—
245Q8—42no—
246D4—24no—
247D4—42no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4#8818612yes—
264C2×C4D4×Dic1312yes—
265C2×C4#8818911yescharacteristic
266C2×C4#8819111yescharacteristic
267C2×C4#8819312yes—
268C2×C4#8820311yescharacteristic
269C2×C4#8820511yescharacteristic
270C8—524no—
271C8—1042no—
272C22—21no—
273C22—21no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—81no—
278C22—81no—
279C22—81no—
280C22—81no—
281C22#1171887611yescharacteristic
282C22#1171888111yescharacteristic
283C22#1171889311yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—42no—
288C4—42no—
289C4—82no—
290C4—81no—
291C4#1171870012yes—
292C4#1171870312yes—
293C2—21no—
294C2—21no—
295C2—82no—
296C2#1311525511yescharacteristic
297C2#1311527511yescharacteristic
298C2#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#9490
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. #13123921C2semidirect
2. #13114832C2semidirect
4. #13112694C2semidirect
235. C13#9490semidirect

Maximal subgroups

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

subgroupindex
#131239212
#131148322
#131132612
#131126942
C13×#25362
#949013