Finite Group Databasebeta

← #15772550

Subgroups — #15772550

Order 3328.

412 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 83 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#13119812C211yesmaximal, characteristic
2#13113160C211yesmaximal, characteristic, complemented
3#13112769C212yesmaximal, complemented
4#13112767C212yesmaximal
5C13×#1467C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88201C411yescharacteristic
8C2×#88198C411yescharacteristic
9C2×#88129C411yescharacteristic
10C13×#432—21no—
11#11718655—21no—
12#11718655—21no—
13#11718649C2211yescharacteristic
14#11718635C2211yescharacteristic
15#11718601—21no—
16#11718601—21no—
17C4×C4⋊Dic13C411yescharacteristic
18#11718586—21no—
19C13×#324—21no—
20C13×#324C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×D52C2×C411yescharacteristic
25C22×Dic26C2×C411yescharacteristic
26C4×Q8×C13—41no—
27C4×Q8×C13—41no—
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C4⋊C4C2311yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34#88201—42no—
35#88198—42no—
36C2×#6103—21no—
37C2×#6103—21no—
38C2×#6103—21no—
39C2×#6103—21no—
40C2×#6103—21no—
41C2×#6103—21no—
42C2×C4⋊Dic13—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×C4×Dic13C2×C411yescharacteristic
46C2×C4×Dic13C2×C411yescharacteristic
47#88129—41no—
48#88129—41no—
49C13×C4⋊C8—41no—
50C13×C22⋊C8—22no—
51C13×#97—41no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55C22⋊#1055—22no—
56C4⋊#1055—41no—
57C4×#1055—41no—
58#11565—131nomaximal, Sylow
59C23×D13—21no—
60C2×Q8×C13—22no—
61C2×Q8×C13—22no—
62C2×Q8×C13—41no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—21no—
73C2×D52—22no—
74C2×D52—41no—
75C2×D52—41no—
76C2×Dic26—22no—
77C2×Dic26—41no—
78C2×Dic26—41no—
79C2×C8×C13—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C42×C13—21no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13—21no—
89#6103—42no—
90#6103—42no—
91#6103—42no—
92#6103—42no—
93#6103—41no—
94#6103—41no—
95#6103—42no—
96C4⋊Dic13—42no—
97#6101—42no—
98#6101—42no—
99C4×Dic13—41no—
100C4×Dic13—41no—
101C2×#1055—42no—
102#2545—131no—
103#1467D1311yescharacteristic, complemented
104#1461—131no—
105#1319—132no—
106#1318—132no—
107C23×C13C2×C22⋊C411yescharacteristic
108C22×D13—41no—
109C22×D13—41no—
110C22×D13—41no—
111C22×D13—41no—
112C22×D13—41no—
113C22×D13—41no—
114C22×D13—41no—
115Q8×C13—44no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13#9911yescharacteristic
131C2×C4×C13#9911yescharacteristic
132C2×C4×C13#10012yes—
133C2×C4×C13#13112yes—
134C2×Dic13—22no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143D52—82no—
144Dic26—82no—
145C8×C13—82no—
146#1055—82no—
147C2×C4⋊Q8—131no—
148C2×#124—131no—
149C2×#124—131no—
150C2×C4×Q8C2×D1311yescharacteristic
151#432—21no—
152#431—261no—
153#396—261no—
154#396—261no—
155#391—131no—
156#390—131no—
157#388—261no—
158#388—261no—
159C4×C4⋊C4—131no—
160#324—21no—
161#324—132no—
162#324—261no—
163#324C2×D1312yes—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13#40811yescharacteristic
167C22×C13C2×#9911yescharacteristic
168C22×C13C2×#10011yescharacteristic
169C2×D13—81no—
170C2×D13—81no—
171C2×D13—81no—
172C2×D13—81no—
173C2×D13—81no—
174C2×D13—81no—
175C2×D13—81no—
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—22no—
179C4×C13—22no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13—41no—
184Dic13—42no—
185Dic13—81no—
186Dic13—81no—
187C22×Q8—131no—
188C22×Q8C4×D1311yescharacteristic
189C22×D4—131no—
190C4⋊Q8—522no—
191#124—521no—
192#124—521no—
193#124—522no—
194C4×Q8—41no—
195C4×Q8—41no—
196C2×C4⋊C4—261no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4D5211yescharacteristic
200C2×C4⋊C4C22⋊D1311yescharacteristic
201C2×C4⋊C4C22×D1311yescharacteristic
202C2×C22⋊C4—261no—
203C2×C22⋊C4—261no—
204C2×C22⋊C4—261no—
205C2×C22⋊C4—261no—
206C2×C22⋊C4—261no—
207C2×C22⋊C4—261no—
208C2×C42—131no—
209C2×C42—131no—
210C2×C42C4×D1311yescharacteristic
211C2×C42D5211yescharacteristic
212C2×C42C22⋊D1311yescharacteristic
213C4⋊C8—41no—
214C4⋊C8—521no—
215C22⋊C8—22no—
216C22⋊C8—262no—
217#97—41no—
218C4×C8—521no—
219#95—261no—
220#95—261no—
221#95—261no—
222C2×C13—21no—
223C2×C13—21no—
224C2×C13#147111yescharacteristic
225C2×C13#212611yescharacteristic
226C2×C13#213311yescharacteristic
227D13—161no—
228C24—261no—
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8—41no—
232C2×Q8—262no—
233C2×Q8—521no—
234C2×Q8—521no—
235C2×D4—262no—
236C2×D4—521no—
237C2×D4—521no—
238C22×C4—261no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4#610311yescharacteristic
242C22×C4#610311yescharacteristic
243C22×C4#610311yescharacteristic
244C22×C4#610311yescharacteristic
245C22×C4C2×C4×D1311yescharacteristic
246C22×C4C2×D5211yescharacteristic
247C22×C4C2×C22⋊D1311yescharacteristic
248C2×C8—42no—
249C2×C8—522no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—522no—
254C4⋊C4—522no—
255C4⋊C4—522no—
256C22⋊C4—522no—
257C22⋊C4—522no—
258C22⋊C4—522no—
259C22⋊C4—522no—
260C22⋊C4—521no—
261C22⋊C4—521no—
262C22⋊C4—522no—
263C42—21no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—521no—
270C42—521no—
271C13#1156511yescharacteristic, complemented, Sylow
272C23—521no—
273C23—521no—
274C23—521no—
275C23—521no—
276C23—521no—
277C23—521no—
278C23—521no—
279C23C2×#610311yescharacteristic
280Q8—44no—
281Q8—1042no—
282D4—1042no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—262no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4#8804611yescharacteristic
307C2×C4#8804611yescharacteristic
308C2×C4#8806312yes—
309C2×C4#8816112yes—
310C8—82no—
311C8—1042no—
312C22—21no—
313C22—21no—
314C22—1041no—
315C22—1041no—
316C22—1041no—
317C22—1041no—
318C22—1041no—
319C22—1041no—
320C22—1041no—
321C22C2×#8804611yescharacteristic
322C22#1171879011yescharacteristic
323C22C2×#8806311yescharacteristic
324C4—21no—
325C4—21no—
326C4—22no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—522no—
333C4—1041no—
334C4—1041no—
335C2—21no—
336C2—21no—
337C2—2081no—
338C2#1311319711yescharacteristic
339C2#1311649911yescharacteristic
340C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1467C2
socleC22×C13C2×#99
prime radicalC22×D52C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1467D13
hypocenterC13#11565
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
2. #13113160C2semidirect
3. #13112769C2semidirect
5. C13×#1467C2semidirect
103. #1467D13semidirect
271. C13#11565semidirect

Maximal subgroups

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

subgroupindex
#131198122
#131131602
#131127692
#131127672
C13×#14672
#1156513