Finite Group Databasebeta

← #14726551

Subgroups — #14726551

Order 2816.

1250 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1250 conjugacy classes of subgroups — too many to draw. Only its 167 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#13082380C211yesmaximal, characteristic
2#13078738C212yesmaximal, complemented
3#13067601C214yesmaximal, complemented
4#13067567C214yesmaximal, complemented
5#13067123C212yesmaximal, complemented
6#13066957C211yesmaximal, characteristic, complemented
7C11×#2398C211yesmaximal, characteristic, complemented
8C2×#67037—21no—
9C2×C4×Q8×C11C2211yescharacteristic, complemented
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66983—22no—
12#10623086—22no—
13#10623085—24no—
14D4×D44—22no—
15#10623041—21no—
16#10623024C2214yes—
17#10623008C2212yes—
18C11×#400—21no—
19C11×#397C2212yescomplemented
20C11×#394—21no—
21C11×#393C2212yescomplemented
22C4×C11×C22⋊C4—22no—
23C11×#376C2211yescharacteristic, complemented
24#10622840C2214yescomplemented
25#10622640—22no—
26#10622639—24no—
27#10622634—22no—
28#10622580C2214yescomplemented
29#10622539C2212yescomplemented
30#10622163C2214yescomplemented
31#10622089C2218yescomplemented
32C22×Q8×C11C2311yescharacteristic
33C22×D4×C11D411yescharacteristic
34C23×C4×C11D412yes—
35C22×C22⋊D11—24no—
36#67037—48no—
37C2×#4341—24no—
38C2×D4×D11—24no—
39C2×#4339—22no—
40C22×D44—22no—
41C4×Q8×C11—22no—
42C4×Q8×C11—22no—
43C4×D4×C11—22no—
44C4×D4×C11—22no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4C2311yescharacteristic
48C2×C11×C22⋊C4—22no—
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4C2312yes—
51C2×C42×C11—21no—
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54C2×#4325—24no—
55#66983—24no—
56#66983—24no—
57#66983—22no—
58#66983—24no—
59#66983C2314yes—
60C2×(C2×D11)⋊C4—24no—
61C2×C4⋊Dic11—22no—
62#66950—24no—
63#66948—24no—
64#66939—28no—
65#66935—28no—
66#66928—22no—
67#66927D412yes—
68C4×D44—22no—
69C4×D44D414yes—
70#66922D412yes—
71C11×#95—21no—
72C11×#95—22no—
73C11×#95—22no—
74C11×#95C2312yes—
75#66899—24no—
76C22⋊(C11⋊C8)C2314yes—
77#66873—24no—
78#66871—24no—
79C4⋊(C11⋊C8)—22no—
80#66867—22no—
81#18179—111nomaximal, Sylow
82C24×C11C2×D412yes—
83C23×D11—24no—
84C2×Q8×C11—22no—
85C2×Q8×C11—42no—
86C2×D4×C11—24no—
87C2×D4×C11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—21no—
93C22×C4×C11—44no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2411yescharacteristic
98C2×C22⋊D11—28no—
99C2×C22⋊D11—24no—
100C2×C22⋊D11—48no—
101C2×C22⋊D11—48no—
102C22×Dic11—24no—
103#4341—416no—
104D4×D11—416no—
105#4339—48no—
106C2×D44—24no—
107C2×D44—22no—
108C2×D44—22no—
109C2×D44—84no—
110C2×D44C2×D414yes—
111C2×C4×D11—24no—
112C2×Dic22—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—42no—
116C11×C22⋊C4—24no—
117C11×C22⋊C4—44no—
118C11×C22⋊C4—44no—
119C42×C11—42no—
120C42×C11—41no—
121C42×C11—41no—
122C42×C11C2×D412yes—
123C42×C11C2×D412yes—
124#4325—48no—
125(C2×D11)⋊C4—28no—
126(C2×D11)⋊C4—24no—
127(C2×D11)⋊C4—24no—
128C4⋊Dic11—24no—
129C4⋊Dic11—22no—
130C4⋊Dic11C2×D414yes—
131C2×C11⋊C8—24no—
132#3496—111no—
133#3112—112no—
134#2398D1111yescharacteristic, complemented
135#1607—114no—
136#1601—114no—
137#1505—112no—
138#1466—111no—
139C23×C11—22no—
140C23×C11—22no—
141C23×C11—42no—
142C23×C11—42no—
143C23×C11AGL(1,ℤ/8)14yes—
144C23×C11C22×D411yescharacteristic
145C22×D11—24no—
146C22×D11—48no—
147C22×D11—84no—
148C22×D11—84no—
149Q8×C11—24no—
150Q8×C11—42no—
151D4×C11—28no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—44no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—82no—
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12012yes—
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11C22×D412yes—
171C22⋊D11—416no—
172C22⋊D11—48no—
173C2×Dic11—24no—
174C2×Dic11—48no—
175D44—44no—
176D44—44no—
177D44—44no—
178D44—84no—
179C4×D11—48no—
180Dic22—44no—
181C11⋊C8—44no—
182C2×H(5,𝔽2)—221no—
183#547—222no—
184#546—224no—
185D42—222no—
186#537—221no—
187#534—114no—
188#532—112no—
189C2×#121—222no—
190C2×C4×Q8C2×D1111yescharacteristic, complemented
191C2×C4×D4C2×D1111yescharacteristic
192#480—114no—
193#477—222no—
194#460—222no—
195#448—114no—
196#440—224no—
197#432—112no—
198#400—21no—
199#397C2×D1112yescomplemented
200#394—21no—
201#393C2×D1112yescomplemented
202C4×C22⋊C4—22no—
203#376C2×D1111yescharacteristic, complemented
204#327—118no—
205#323—114no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—24no—
209C22×C11—44no—
210C22×C11—42no—
211C22×C11—42no—
212C22×C11—82no—
213C22×C11C2×#12011yescharacteristic
214C22×C11C2×AGL(1,ℤ/8)12yes—
215C2×D11—44no—
216C2×D11—44no—
217C2×D11—44no—
218C2×D11—168no—
219C4×C11—22no—
220C4×C11—21no—
221C4×C11—22no—
222C4×C11—42no—
223C4×C11—42no—
224C4×C11—82no—
225C4×C11—81no—
226C4×C11#45512yes—
227Dic11—44no—
228H(5,𝔽2)—448no—
229C2×#41—224no—
230C2×#41—222no—
231C22×Q8C22×D1111yescharacteristic
232C22×D4—222no—
233C22×D4—224no—
234C22×D4—224no—
235C22×D4C22⋊D1111yescharacteristic
236C23×C4C22⋊D1112yes—
237C2×SD16—224no—
238C4⋊Q8—112no—
239#127—112no—
240#124—222no—
241#123—228no—
242C22⋊Q8—224no—
243#121—114no—
244#121—224no—
245#121—224no—
246#121—224no—
247#121—222no—
248#121—224no—
249#120—228no—
250C4×Q8—22no—
251C4×Q8—22no—
252C4×D4—22no—
253C4×D4—22no—
254C4×D4—114no—
255C4×D4—222no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—222no—
258C2×C4⋊C4C22⋊D1111yescharacteristic
259C2×C4⋊C4C22×D1111yescharacteristic
260C2×C22⋊C4—22no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—224no—
263C2×C22⋊C4C22×D1112yes—
264C2×C42—21no—
265C2×C42—21no—
266C2×C42C22×D1111yescharacteristic
267#107—224no—
268C4⋊C8—222no—
269#103—224no—
270#102—224no—
271C22⋊C8—114no—
272#97—222no—
273#95—21no—
274#95—22no—
275#95—22no—
276#95C22×D1112yes—
277C2×C11—22no—
278C2×C11—44no—
279C2×C11#300311yescharacteristic
280C2×C11C2×#45511yescharacteristic
281C2×C11#302511yescharacteristic
282D11—84no—
283C24—224no—
284C24C2×C22⋊D1112yes—
285#41—448no—
286#41—4416no—
287C2×Q8—22no—
288C2×Q8—42no—
289C2×Q8—222no—
290C2×D4—24no—
291C2×D4—22no—
292C2×D4—114no—
293C2×D4—224no—
294C2×D4—228no—
295C2×D4—224no—
296C2×D4—222no—
297C2×D4—222no—
298C2×D4—4416no—
299C2×D4—448no—
300C2×D4—448no—
301C2×D4—884no—
302C22×C4—21no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—21no—
307C22×C4—44no—
308C22×C4—224no—
309C22×C4—224no—
310C22×C4C2×C22⋊D1111yescharacteristic
311C22×C4C2×C22⋊D1111yescharacteristic
312C22×C4C2×C22⋊D1112yes—
313C22×C4C23×D1111yescharacteristic
314SD16—448no—
315C2×C8—224no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—42no—
319C4⋊C4—114no—
320C4⋊C4—224no—
321C4⋊C4—222no—
322C22⋊C4—24no—
323C22⋊C4—44no—
324C22⋊C4—44no—
325C22⋊C4—228no—
326C22⋊C4—224no—
327C22⋊C4—224no—
328C42—42no—
329C42—41no—
330C42—41no—
331C42D4×D1112yes—
332C42D4×D1112yes—
333C11#1817911yescharacteristic, complemented, Sylow
334C23—22no—
335C23—22no—
336C23—42no—
337C23—42no—
338C23—224no—
339C23—448no—
340C23—884no—
341C23—884no—
342C23#6700214yes—
343C23C22×C22⋊D1111yescharacteristic
344Q8—24no—
345Q8—42no—
346Q8—444no—
347D4—28no—
348D4—444no—
349D4—444no—
350D4—4416no—
351D4—448no—
352D4—444no—
353D4—884no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—44no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4—224no—
370C2×C4—448no—
371C2×C4—448no—
372C2×C4#6699011yescharacteristic
373C2×C4#6699012yes—
374C2×C4#6699011yescharacteristic
375C2×C4C2×D4×D1112yes—
376C8—444no—
377C22—21no—
378C22—21no—
379C22—24no—
380C22—44no—
381C22—42no—
382C22—42no—
383C22—82no—
384C22—444no—
385C22—444no—
386C22—444no—
387C22—1768no—
388C22C2×#6699011yescharacteristic
389C22C2×#6700212yes—
390C4—22no—
391C4—21no—
392C4—22no—
393C4—42no—
394C4—42no—
395C4—82no—
396C4—81no—
397C4—444no—
398C4#1062267412yes—
399C2—22no—
400C2—44no—
401C2—884no—
402C2#1307784211yescharacteristic
403C2C2×#1062267411yescharacteristic
404C2#1307800711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2398C2
socleC22×C11C2×#120
prime radical#13082380C2
hypercenter#2398D11
hypocenterC11#18179
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2398

Complements

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

NH ≅ G/Ntype
2. #13078738C2semidirect
3. #13067601C2semidirect
4. #13067567C2semidirect
5. #13067123C2semidirect
6. #13066957C2semidirect
7. C11×#2398C2semidirect
9. C2×C4×Q8×C11C22semidirect
19. C11×#397C22semidirect
21. C11×#393C22semidirect
23. C11×#376C22semidirect
24. #10622840C22semidirect
28. #10622580C22semidirect
29. #10622539C22semidirect
30. #10622163C22semidirect
31. #10622089C22semidirect
134. #2398D11semidirect
190. C2×C4×Q8C2×D11semidirect
199. #397C2×D11semidirect
201. #393C2×D11semidirect
203. #376C2×D11semidirect
333. C11#18179semidirect

Maximal subgroups

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

subgroupindex
#130823802
#130787382
#130676012
#130675672
#130671232
#130669572
C11×#23982
#1817911