Finite Group Databasebeta

← #14726552

Subgroups — #14726552

Order 2816.

1250 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1250 conjugacy classes of subgroups — too many to draw. Only its 183 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#13078734C212yesmaximal, complemented
2#13071900C211yesmaximal, characteristic, complemented
3#13067602C214yesmaximal, complemented
4#13067568C214yesmaximal, complemented
5#13067124C212yesmaximal, complemented
6#13066957C211yesmaximal, characteristic, complemented
7C11×#3496C211yesmaximal, characteristic
8C2×C11×H(5,𝔽2)—21no—
9C11×#547—22no—
10C11×#546—24no—
11D42×C11—22no—
12C11×#537—21no—
13C11×#534C2214yes—
14C11×#532C2212yes—
15C2×C11×#121—22no—
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic, complemented
18#10622835—21no—
19C4×C22⋊Dic11—22no—
20#10622704—22no—
21#10622688—22no—
22#10622653C2214yescomplemented
23#10622646C2214yescomplemented
24#10622631—24no—
25#10622595—21no—
26#10622566C2212yescomplemented
27#10622560C2212yescomplemented
28#10622545C2211yescharacteristic, complemented
29#10622539C2212yescomplemented
30#10622175C2218yescomplemented
31#10622163C2214yescomplemented
32C11×H(5,𝔽2)—48no—
33C2×C11×#41—24no—
34C2×C11×#41—22no—
35C22×D4×C11—24no—
36C22×D4×C11—24no—
37C22×D4×C11—22no—
38C22×D4×C11D411yescharacteristic
39C23×C4×C11D412yes—
40C22×Dic22C2311yescharacteristic
41C11×C4⋊Q8D412yes—
42C11×#127D412yes—
43C11×#124—22no—
44C11×#123—28no—
45C11×C22⋊Q8—24no—
46C11×#121—24no—
47C11×#121—24no—
48C11×#121—24no—
49C11×#121—22no—
50C11×#121—24no—
51C11×#121C2314yes—
52C11×#120—28no—
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C4×D4×C11D414yes—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C22⋊C4—24no—
60C2×C11×C22⋊C4C2312yes—
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—22no—
64C2×#4324—24no—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×Dic11⋊C4—21no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11—21no—
69C4×Dic22—22no—
70C4×Dic22—22no—
71#66896—24no—
72C11⋊#95—21no—
73C11⋊#95—22no—
74C11⋊#95—22no—
75C11⋊#95C2312yes—
76C22⋊(C11⋊C8)C2314yes—
77#66874—24no—
78#66871—24no—
79C4⋊(C11⋊C8)—22no—
80#66867—22no—
81#18179—111nomaximal, Sylow
82C24×C11—24no—
83C24×C11C2×D412yes—
84C11×#41—48no—
85C11×#41—416no—
86C2×Q8×C11—22no—
87C2×D4×C11—24no—
88C2×D4×C11—28no—
89C2×D4×C11—24no—
90C2×D4×C11—24no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—416no—
95C2×D4×C11—48no—
96C2×D4×C11—48no—
97C2×D4×C11—84no—
98C2×D4×C11C2×D414yes—
99C22×C4×C11—24no—
100C22×C4×C11—22no—
101C22×C4×C11—24no—
102C22×C4×C11—22no—
103C22×C4×C11—44no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—21no—
109C22×Dic11—22no—
110C22×Dic11—21no—
111C2×Dic22—22no—
112C2×Dic22—42no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4C2×D414yes—
117C11×C22⋊C4—28no—
118C11×C22⋊C4—24no—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—24no—
121C42×C11C2×D412yes—
122C42×C11C2×D412yes—
123C22⋊Dic11—44no—
124C22⋊Dic11—44no—
125#4324—48no—
126C4⋊Dic11—22no—
127Dic11⋊C4—42no—
128C4×Dic11—42no—
129C4×Dic11—41no—
130C4×Dic11—41no—
131C2×C11⋊C8—24no—
132#3496D1111yescharacteristic
133#3112—112no—
134#2398—111no—
135#1607—114no—
136#1601—114no—
137#1505—112no—
138#1466—111no—
139C23×C11—22no—
140C23×C11—22no—
141C23×C11—24no—
142C23×C11—42no—
143C23×C11—42no—
144C23×C11—48no—
145C23×C11—84no—
146C23×C11—84no—
147C23×C11AGL(1,ℤ/8)14yes—
148C23×C11C22×D411yescharacteristic
149Q8×C11—44no—
150D4×C11—28no—
151D4×C11—44no—
152D4×C11—44no—
153D4×C11—416no—
154D4×C11—48no—
155D4×C11—44no—
156D4×C11—84no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—24no—
161C2×C4×C11—41no—
162C2×C4×C11—48no—
163C2×C4×C11—48no—
164C2×C4×C11—44no—
165C2×C4×C11—42no—
166C2×C4×C11—82no—
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12012yes—
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11C22×D412yes—
171C2×Dic11—22no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11—41no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179Dic22—24no—
180Dic22—42no—
181C11⋊C8—44no—
182C2×H(5,𝔽2)—21no—
183#547—22no—
184#546—24no—
185D42—22no—
186#537—21no—
187#534C2×D1114yes—
188#532C2×D1112yes—
189C2×#121—22no—
190C2×C4×Q8—111no—
191C2×C4×D4C2×D1111yescharacteristic
192#480—114no—
193#477—222no—
194#460—222no—
195#448—114no—
196#440—224no—
197#432—112no—
198#400—221no—
199#397—112no—
200#394—221no—
201#393—112no—
202C4×C22⋊C4—222no—
203#376—111no—
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—44no—
213C22×C11—44no—
214C22×C11—44no—
215C22×C11—82no—
216C22×C11—168no—
217C22×C11C2×#12011yescharacteristic
218C22×C11C2×AGL(1,ℤ/8)12yes—
219C4×C11—22no—
220C4×C11—21no—
221C4×C11—22no—
222C4×C11—44no—
223C4×C11—42no—
224C4×C11#45512yes—
225Dic11—42no—
226Dic11—82no—
227Dic11—81no—
228H(5,𝔽2)—48no—
229C2×#41—24no—
230C2×#41—22no—
231C22×Q8—111no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—22no—
235C22×D4C22⋊D1111yescharacteristic
236C23×C4C22⋊D1112yes—
237C2×SD16—224no—
238C4⋊Q8C22⋊D1112yes—
239#127C22⋊D1112yes—
240#124—22no—
241#123—28no—
242C22⋊Q8—24no—
243#121—24no—
244#121—24no—
245#121—24no—
246#121—22no—
247#121—24no—
248#121C22×D1114yes—
249#120—28no—
250C4×Q8—222no—
251C4×Q8—222no—
252C4×D4—22no—
253C4×D4—22no—
254C4×D4—22no—
255C4×D4C22⋊D1114yes—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4C22⋊D1111yescharacteristic
260C2×C22⋊C4—24no—
261C2×C22⋊C4—222no—
262C2×C22⋊C4—222no—
263C2×C22⋊C4C22×D1112yes—
264C2×C42—221no—
265C2×C42—221no—
266C2×C42C22×D1111yescharacteristic
267#107—224no—
268C4⋊C8—222no—
269#103—224no—
270#102—224no—
271C22⋊C8—114no—
272#97—222no—
273#95—112no—
274#95—221no—
275#95—222no—
276#95—222no—
277C2×C11—22no—
278C2×C11—44no—
279C2×C11—84no—
280C2×C11#300311yescharacteristic
281C2×C11C2×#45511yescharacteristic
282C2×C11#302511yescharacteristic
283C24—24no—
284C24C2×C22⋊D1112yes—
285#41—48no—
286#41—416no—
287C2×Q8—22no—
288C2×Q8—222no—
289C2×Q8—442no—
290C2×D4—24no—
291C2×D4—28no—
292C2×D4—24no—
293C2×D4—24no—
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—416no—
298C2×D4—48no—
299C2×D4—48no—
300C2×D4—84no—
301C2×D4C2×C22⋊D1114yes—
302C22×C4—24no—
303C22×C4—22no—
304C22×C4—24no—
305C22×C4—22no—
306C22×C4—44no—
307C22×C4—221no—
308C22×C4—222no—
309C22×C4—221no—
310C22×C4C2×C22⋊D1111yescharacteristic
311C22×C4C2×C22⋊D1111yescharacteristic
312C22×C4C2×C22⋊D1112yes—
313C22×C4C23×D1111yescharacteristic
314SD16—448no—
315C2×C8—224no—
316C4⋊C4—24no—
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—222no—
320C4⋊C4—442no—
321C4⋊C4C2×C22⋊D1114yes—
322C22⋊C4—28no—
323C22⋊C4—24no—
324C22⋊C4—24no—
325C22⋊C4—24no—
326C22⋊C4—444no—
327C22⋊C4—444no—
328C42—442no—
329C42—441no—
330C42—441no—
331C42C2×C22⋊D1112yes—
332C42C2×C22⋊D1112yes—
333C11#1817911yescharacteristic, complemented, Sylow
334C23—22no—
335C23—22no—
336C23—24no—
337C23—42no—
338C23—42no—
339C23—48no—
340C23—84no—
341C23—84no—
342C23#6698514yes—
343C23C22×C22⋊D1111yescharacteristic
344Q8—44no—
345Q8—224no—
346Q8—442no—
347D4—28no—
348D4—44no—
349D4—44no—
350D4—416no—
351D4—48no—
352D4—44no—
353D4—84no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—24no—
358C2×C4—41no—
359C2×C4—48no—
360C2×C4—48no—
361C2×C4—44no—
362C2×C4—42no—
363C2×C4—82no—
364C2×C4—222no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—442no—
368C2×C4—442no—
369C2×C4—442no—
370C2×C4—442no—
371C2×C4—441no—
372C2×C4#6700611yescharacteristic
373C2×C4#6700612yes—
374C2×C4#6700611yescharacteristic
375C2×C4C22×C22⋊D1112yes—
376C8—444no—
377C22—21no—
378C22—21no—
379C22—24no—
380C22—44no—
381C22—42no—
382C22—42no—
383C22—44no—
384C22—44no—
385C22—44no—
386C22—82no—
387C22—168no—
388C22C2×#6698512yes—
389C22C2×#6700611yescharacteristic
390C4—22no—
391C4—21no—
392C4—22no—
393C4—44no—
394C4—42no—
395C4—442no—
396C4—882no—
397C4—881no—
398C4#1062285512yes—
399C2—22no—
400C2—44no—
401C2—84no—
402C2#1307784311yescharacteristic
403C2C2×#1062285511yescharacteristic
404C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3496C2
socleC22×C11C2×#120
hypercenter#3496D11
hypocenterC11#18179
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #13078734C2semidirect
2. #13071900C2semidirect
3. #13067602C2semidirect
4. #13067568C2semidirect
5. #13067124C2semidirect
6. #13066957C2semidirect
17. C2×C4×Dic22C22semidirect
22. #10622653C22semidirect
23. #10622646C22semidirect
26. #10622566C22semidirect
27. #10622560C22semidirect
28. #10622545C22semidirect
29. #10622539C22semidirect
30. #10622175C22semidirect
31. #10622163C22semidirect
333. C11#18179semidirect

Maximal subgroups

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

subgroupindex
#130787342
#130719002
#130676022
#130675682
#130671242
#130669572
C11×#34962
#1817911