Finite Group Databasebeta

← #15772581

Subgroups — #15772581

Order 3328.

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

normal subgroups only

This group has 416 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#13120032C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3#13112781C212yesmaximal, complemented
4#13112779C212yesmaximal, complemented
5C13×#1465C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88124C411yescharacteristic
8C13×#407—21no—
9#11718882C411yescharacteristic
10#11718882C411yescharacteristic
11#11718871—21no—
12#11718871—21no—
13C2×C22⋊#1055—21no—
14#11718638C2211yescharacteristic
15#11718637C2211yescharacteristic
16#11718609—21no—
17#11718609—21no—
18C4×C4⋊Dic13C411yescharacteristic
19C13×#324C2212yes—
20C13×#323—21no—
21#11718120C2212yes—
22#11718117—21no—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C2×C13×M16—41no—
27C4×D4×C13—41no—
28C4×D4×C13—41no—
29C2×C13×C4⋊C4C2311yescharacteristic
30C2×C13×C22⋊C4D411yescharacteristic
31C2×C13×C22⋊C4D411yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33C2×C22⋊Dic13—21no—
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13C2×C411yescharacteristic
46C22×#1055—41no—
47#88124—41no—
48#88124—41no—
49C13×C22⋊C8—22no—
50C13×C22⋊C8—41no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54C22⋊#1055—22no—
55C22⋊#1055—41no—
56#11572—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C24×C13C22⋊C411yescharacteristic
59C2×D4×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13—41no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—81no—
67C22×C4×C13—81no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C13×M16—82no—
78C2×C8×C13—42no—
79C13×C4⋊C4—41no—
80C13×C22⋊C4—41no—
81C13×C22⋊C4—41no—
82C42×C13—21no—
83C42×C13—21no—
84C22⋊Dic13—42no—
85C22⋊Dic13—42no—
86C22⋊Dic13—81no—
87C22⋊Dic13—81no—
88C4⋊Dic13—42no—
89C4⋊Dic13—41no—
90C4⋊Dic13—41no—
91#6101—42no—
92#6101—41no—
93#6101—41no—
94#6101—81no—
95#6101—81no—
96C4×Dic13—22no—
97C4×Dic13—22no—
98C2×#1055—42no—
99C2×#1055—82no—
100#2566—131no—
101#1465D1311yescharacteristic
102#1459—131no—
103#1325—132no—
104#1324—132no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13#10112yes—
115C23×C13C2×C22⋊C411yescharacteristic
116D4×C13—44no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—41no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—81no—
129C2×C4×C13—81no—
130C2×C4×C13#9911yescharacteristic
131C2×C4×C13#9911yescharacteristic
132C2×C4×C13#13112yes—
133C2×Dic13—22no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C8×C13—82no—
146#1055—82no—
147C2×#125—131no—
148C2×C4×D4C2×D1311yescharacteristic
149#407—21no—
150C2×C22⋊C8—261no—
151#396—261no—
152#396—261no—
153#390—131no—
154#390—131no—
155#385—261no—
156#385—261no—
157#384—131no—
158#382—131no—
159C4×C4⋊C4—131no—
160#324—132no—
161#324C2×D1312yes—
162#323—21no—
163#323—261no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—22no—
167C22×C13—42no—
168C22×C13—42no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—81no—
175C22×C13—81no—
176C22×C13#40811yescharacteristic
177C22×C13C2×#9911yescharacteristic
178C22×C13C2×#10111yescharacteristic
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—22no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—41no—
185Dic13—42no—
186Dic13—81no—
187Dic13—81no—
188Dic13—81no—
189C22×D4C4×D1311yescharacteristic
190C23×C4D5211yescharacteristic
191C23×C4C22⋊D1311yescharacteristic
192C2×M16—41no—
193C22×C8—521no—
194#125—521no—
195#125—521no—
196C4×D4—41no—
197C4×D4—41no—
198C2×C4⋊C4—131no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4C22×D1311yescharacteristic
206C2×C22⋊C4—261no—
207C2×C22⋊C4—261no—
208C2×C22⋊C4—261no—
209C2×C22⋊C4—261no—
210C2×C22⋊C4D5211yescharacteristic
211C2×C22⋊C4C22⋊D1311yescharacteristic
212C2×C42—131no—
213C2×C42—131no—
214C2×C42C4×D1311yescharacteristic
215C22⋊C8—22no—
216C22⋊C8—41no—
217C22⋊C8—262no—
218C22⋊C8—521no—
219#95—261no—
220#95—261no—
221#95—261no—
222C2×C13—21no—
223C2×C13—21no—
224C2×C13—42no—
225C2×C13—81no—
226C2×C13#147211yescharacteristic
227C2×C13#212711yescharacteristic
228C2×C13#213211yescharacteristic
229C24#610311yescharacteristic
230C24#610311yescharacteristic
231C2×D4—22no—
232C2×D4—22no—
233C2×D4—41no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—81no—
239C22×C4—81no—
240C22×C4—261no—
241C22×C4—261no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4#610311yescharacteristic
245C22×C4#610311yescharacteristic
246C22×C4C2×C4×D1311yescharacteristic
247C22×C4C2×D5211yescharacteristic
248C22×C4C2×C22⋊D1311yescharacteristic
249M16—82no—
250C2×C8—42no—
251C2×C8—522no—
252C2×C8—1042no—
253C4⋊C4—41no—
254C4⋊C4—521no—
255C4⋊C4—521no—
256C4⋊C4—522no—
257C4⋊C4—522no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C4⋊C4—1041no—
261C4⋊C4—1041no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—522no—
265C22⋊C4—522no—
266C22⋊C4—1041no—
267C22⋊C4—1041no—
268C42—21no—
269C42—21no—
270C42—262no—
271C42—262no—
272C13#1157211yescharacteristic, complemented, Sylow
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23#8806412yes—
283C23C2×#610311yescharacteristic
284D4—44no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—262no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4#8804611yescharacteristic
311C2×C4#8804611yescharacteristic
312C2×C4#8816112yes—
313C8—82no—
314C8—1042no—
315C22—21no—
316C22—21no—
317C22—22no—
318C22—42no—
319C22—42no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—81no—
326C22—81no—
327C22C2×#8804611yescharacteristic
328C22#1171879011yescharacteristic
329C22C2×#8806411yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—522no—
337C4—1041no—
338C4—1041no—
339C4—1041no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—81no—
344C2#1311320111yescharacteristic
345C2#1311650311yescharacteristic
346C2#1311651911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1465C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1465D13
hypocenterC13#11572
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #13112781C2semidirect
4. #13112779C2semidirect
272. C13#11572semidirect

Maximal subgroups

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

subgroupindex
#131200322
#131131542
#131127812
#131127792
C13×#14652
#1157213