Finite Group Databasebeta

← #15773476

Subgroups — #15773476

Order 3328.

482 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 87 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#13119144C211yesmaximal, characteristic
2C4×#88074C211yesmaximal, characteristic
3#13112837C214yesmaximal, complemented
4C13×#1466C211yesmaximal, characteristic
5C2×C4×D4×C13C2211yescharacteristic
6C2×#88189—21no—
7C22×C4⋊Dic13C411yescharacteristic, complemented
8C13×#432—21no—
9C2×#88074—21no—
10#11718873—21no—
11#11718873C411yescharacteristic, complemented
12C4×C22⋊Dic13—21no—
13#11718644C412yescomplemented
14#11718614C2212yes—
15#11718604—21no—
16#11718589—21no—
17C13×#323—21no—
18C13×#323C2212yes—
19#11718118C2212yes—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×Dic13—21no—
24C4×D4×C13—41no—
25C4×D4×C13—41no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C22⋊C4D411yescharacteristic
28C2×C13×C22⋊C4C2311yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C22⋊Dic13—22no—
31C2×C22⋊Dic13—21no—
32C2×C22⋊Dic13—22no—
33#88189—44no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—41no—
37C2×C4⋊Dic13—41no—
38C2×C4⋊Dic13C2×C412yes—
39C2×#6101—22no—
40C2×C4×Dic13—41no—
41C13×C4⋊C8—41no—
42C13×C22⋊C8—22no—
43C13×#97—41no—
44#88074—24no—
45#88071—22no—
46#88071—22no—
47#88071—41no—
48#88071C2×C412yes—
49#11773—131nomaximal, Sylow
50C24×C13C22⋊C411yescharacteristic
51C24×C13C2×D411yescharacteristic
52C2×D4×C13—22no—
53C2×D4×C13—22no—
54C2×D4×C13—41no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—42no—
60C22×C4×C13—42no—
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—22no—
67C22×Dic13—22no—
68C22×Dic13—42no—
69C22×Dic13—42no—
70C22×Dic13—42no—
71C22×Dic13—42no—
72C2×C8×C13—42no—
73C13×C4⋊C4—41no—
74C13×C22⋊C4—41no—
75C13×C22⋊C4—41no—
76C42×C13—21no—
77C42×C13—21no—
78C22⋊Dic13—24no—
79C22⋊Dic13—42no—
80C22⋊Dic13—44no—
81C22⋊Dic13—42no—
82C4⋊Dic13—42no—
83C4⋊Dic13—41no—
84C4⋊Dic13—41no—
85C4⋊Dic13—42no—
86#6101—44no—
87C4×Dic13—82no—
88#2486—131no—
89C4×#99—131no—
90#1466D1311yescharacteristic
91#1344—134no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13—41no—
100C23×C13#10412yes—
101C23×C13C2×C22⋊C411yescharacteristic
102C23×C13AGL(1,ℤ/8)12yes—
103D4×C13—44no—
104C2×C4×C13—22no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—81no—
118C2×C4×C13#9911yescharacteristic
119C2×C4×C13#9911yescharacteristic
120C2×Dic13—42no—
121C2×Dic13—44no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124C2×Dic13—42no—
125C2×Dic13—42no—
126C2×Dic13—42no—
127C2×Dic13—84no—
128C2×Dic13—82no—
129C2×Dic13—82no—
130C8×C13—82no—
131C2×#123—261no—
132C2×C4×D4C2×D1311yescharacteristic
133C22×C4⋊C4—131no—
134#432—21no—
135C2×#99—261no—
136#398—132no—
137#397—132no—
138#389—261no—
139#381—261no—
140#380—131no—
141#380—261no—
142C4×C22⋊C4—261no—
143#342—132no—
144#323—21no—
145#323C2×D1312yes—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—22no—
149C22×C13—22no—
150C22×C13—42no—
151C22×C13—42no—
152C22×C13—42no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—41no—
156C22×C13—41no—
157C22×C13—81no—
158C22×C13C2×#9911yescharacteristic
159C22×C13#41811yescharacteristic
160C22×C13C2×#10411yescharacteristic
161C4×C13—21no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13#35212yes—
167Dic13—82no—
168Dic13—84no—
169Dic13—82no—
170C22×D4D5211yescharacteristic
171C23×C4—261no—
172C23×C4C4×D1311yescharacteristic
173C23×C4D5211yescharacteristic
174#123—524no—
175C4×D4—41no—
176C4×D4—41no—
177C2×C4⋊C4—132no—
178C2×C4⋊C4—262no—
179C2×C4⋊C4—261no—
180C2×C4⋊C4—261no—
181C2×C4⋊C4—521no—
182C2×C4⋊C4—521no—
183C2×C4⋊C4C4×D1311yescharacteristic
184C2×C22⋊C4—262no—
185C2×C22⋊C4—261no—
186C2×C22⋊C4—262no—
187C2×C22⋊C4C22⋊D1311yescharacteristic
188C2×C22⋊C4C22×D1311yescharacteristic
189C2×C42—521no—
190C2×C42C22⋊D1311yescharacteristic
191C4⋊C8—41no—
192#99—264no—
193C22⋊C8—22no—
194#97—41no—
195#95—132no—
196#95—262no—
197#95—262no—
198#95—521no—
199C2×C13—21no—
200C2×C13—21no—
201C2×C13—42no—
202C2×C13—42no—
203C2×C13#150711yescharacteristic
204C2×C13C2×#35211yescharacteristic
205C2×C13#212911yescharacteristic
206C24#610311yescharacteristic
207C24C2×D5211yescharacteristic
208C2×D4—22no—
209C2×D4—22no—
210C2×D4—41no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—262no—
218C22×C4—262no—
219C22×C4—522no—
220C22×C4—522no—
221C22×C4—522no—
222C22×C4—522no—
223C22×C4#610311yescharacteristic
224C22×C4#610311yescharacteristic
225C22×C4#610311yescharacteristic
226C22×C4C2×C4×D1311yescharacteristic
227C22×C4C2×C22⋊D1311yescharacteristic
228C2×C8—42no—
229C4⋊C4—41no—
230C4⋊C4—522no—
231C4⋊C4—524no—
232C4⋊C4—522no—
233C4⋊C4—521no—
234C4⋊C4—521no—
235C22⋊C4—41no—
236C22⋊C4—41no—
237C22⋊C4—264no—
238C22⋊C4—522no—
239C22⋊C4—524no—
240C22⋊C4—522no—
241C42—21no—
242C42—21no—
243C42—1042no—
244C13#1177311yescharacteristic, complemented, Sylow
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—41no—
250C23—41no—
251C23—41no—
252C23—41no—
253C23#8806512yes—
254C23#8816212yes—
255C23C2×#610311yescharacteristic
256D4—44no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—81no—
271C2×C4—524no—
272C2×C4—522no—
273C2×C4—522no—
274C2×C4—522no—
275C2×C4—522no—
276C2×C4—522no—
277C2×C4—522no—
278C2×C4—1044no—
279C2×C4—1042no—
280C2×C4—1042no—
281C2×C4#8804611yescharacteristic
282C2×C4#8804611yescharacteristic
283C8—82no—
284C22—21no—
285C22—21no—
286C22—22no—
287C22—22no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22C2×#8804611yescharacteristic
297C22#1171879211yescharacteristic
298C22C2×#8806511yescharacteristic
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—1042no—
305C4—1044no—
306C4—1042no—
307C4#1171806812yes—
308C2—21no—
309C2—21no—
310C2—42no—
311C2—42no—
312C2#1311335311yescharacteristic
313C2C2×#1171806811yescharacteristic
314C2#1311651011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1466C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#1466D13
hypocenterC13#11773
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #13112837C2semidirect
7. C22×C4⋊Dic13C4semidirect
11. #11718873C4semidirect
13. #11718644C4semidirect
244. C13#11773semidirect

Maximal subgroups

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

subgroupindex
#131191442
C4×#880742
#131128372
C13×#14662
#1177313