Finite Group Databasebeta

← #14726823

Subgroups — #14726823

Order 2816.

1254 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1254 conjugacy classes of subgroups — too many to draw. Only its 187 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#13078647C212yesmaximal, complemented
3#13067635C214yesmaximal, complemented
4#13067567C214yesmaximal, complemented
5#13067175C212yesmaximal, complemented
6#13066937C211yesmaximal, characteristic, complemented
7C11×#2580C211yesmaximal, 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×#399C2212yescomplemented
19C11×#393C2212yescomplemented
20C11×#390—21no—
21C11×#389—21no—
22C11×#385—22no—
23C11×#382C2211yescharacteristic, complemented
24#10622840C2214yescomplemented
25#10622640—22no—
26C4×#4325—24no—
27#10622633—22no—
28#10622581C2214yescomplemented
29#10622538C2212yescomplemented
30#10622163C2214yescomplemented
31#10622089C2218yescomplemented
32C22×Q8×C11C2311yescharacteristic
33C22×D4×C11D411yescharacteristic
34C23×C4×C11D412yes—
35C22×C22⋊D11—24no—
36#67037—44no—
37#67037—44no—
38C2×#4341—24no—
39C2×D4×D11—24no—
40C2×#4339—22no—
41C22×D44—22no—
42C4×Q8×C11—22no—
43C4×Q8×C11—22no—
44C4×D4×C11—22no—
45C4×D4×C11—22no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4C2312yes—
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56C2×#4325—24no—
57#66983—24no—
58#66983—24no—
59#66983—22no—
60#66983—24no—
61#66983C2314yes—
62C2×(C2×D11)⋊C4—24no—
63C2×C4⋊Dic11—22no—
64#66950—24no—
65#66948—24no—
66#66939—28no—
67#66935—28no—
68#66928—22no—
69#66927D412yes—
70C4×D44—22no—
71C4×D44D414yes—
72#66922D412yes—
73C11×#95—21no—
74C11×#95—22no—
75C11×#95C2312yes—
76#66899—24no—
77C22⋊(C11⋊C8)C2314yes—
78#66873—24no—
79#66872—24no—
80C4⋊(C11⋊C8)—22no—
81C4×C11⋊C8—22no—
82#18211—111nomaximal, Sylow
83C24×C11C2×D412yes—
84C23×D11—24no—
85C2×Q8×C11—22no—
86C2×Q8×C11—42no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11SD1614yescomplemented
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11—82no—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C2×C22⋊D11—28no—
101C2×C22⋊D11—24no—
102C2×C22⋊D11—48no—
103C2×C22⋊D11—48no—
104C22×Dic11—24no—
105#4341—416no—
106D4×D11—416no—
107#4339—44no—
108#4339—44no—
109C2×D44—24no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—84no—
113C2×D44C2×D414yes—
114C2×C4×D11—24no—
115C2×Dic22—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4—41no—
120C11×C4⋊C4—42no—
121C11×C4⋊C4—82no—
122C11×C22⋊C4—24no—
123C11×C22⋊C4—44no—
124C11×C22⋊C4—82no—
125C42×C11—42no—
126C42×C11C2×D412yes—
127C42×C11C2×D412yes—
128#4325—48no—
129(C2×D11)⋊C4—28no—
130(C2×D11)⋊C4—24no—
131(C2×D11)⋊C4—24no—
132C4⋊Dic11—24no—
133C4⋊Dic11—22no—
134C4⋊Dic11C2×D414yes—
135C2×C11⋊C8—24no—
136#3496—111no—
137#3103—112no—
138#2580D1111yescharacteristic, complemented
139#1613—114no—
140#1601—114no—
141#1517—112no—
142#1460—111no—
143C23×C11—22no—
144C23×C11—22no—
145C23×C11—42no—
146C23×C11—42no—
147C23×C11C2×SD1614yes—
148C23×C11C22×D411yescharacteristic
149C22×D11—24no—
150C22×D11—48no—
151C22×D11—84no—
152C22×D11—84no—
153Q8×C11—24no—
154Q8×C11—42no—
155D4×C11—28no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—44no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—82no—
171C2×C4×C11#12011yescharacteristic
172C2×C4×C11#12011yescharacteristic
173C2×C4×C11#12012yes—
174C2×C4×C11C2×SD1612yes—
175C2×C4×C11AGL(1,ℤ/8)12yes—
176C2×C4×C11C22×D412yes—
177C22⋊D11—416no—
178C22⋊D11—44no—
179C22⋊D11—44no—
180C2×Dic11—24no—
181C2×Dic11—48no—
182D44—44no—
183D44—44no—
184D44—44no—
185D44—84no—
186C4×D11—48no—
187Dic22—44no—
188C11⋊C8—44no—
189C2×H(5,𝔽2)—221no—
190#547—222no—
191#546—224no—
192D42—222no—
193#537—221no—
194#534—114no—
195#532—112no—
196C2×#121—222no—
197C2×C4×Q8C2×D1111yescharacteristic, complemented
198C2×C4×D4C2×D1111yescharacteristic
199#481—114no—
200#475—222no—
201#460—222no—
202#448—114no—
203C4×SD16—224no—
204#431—112no—
205#399C2×D1112yescomplemented
206#393C2×D1112yescomplemented
207#390—21no—
208#389—21no—
209#385—22no—
210#382C2×D1111yescharacteristic, complemented
211#327—118no—
212#323—114no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—24no—
216C22×C11—44no—
217C22×C11—42no—
218C22×C11—42no—
219C22×C11—82no—
220C22×C11C2×#12011yescharacteristic
221C22×C11C22×SD1611yescharacteristic
222C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
223C2×D11—44no—
224C2×D11—44no—
225C2×D11—44no—
226C2×D11—168no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—22no—
230C4×C11—42no—
231C4×C11—42no—
232C4×C11—82no—
233C4×C11—81no—
234C4×C11#45014yes—
235Dic11—44no—
236H(5,𝔽2)—444no—
237H(5,𝔽2)—444no—
238C2×#41—224no—
239C2×#41—222no—
240C22×Q8C22×D1111yescharacteristic
241C22×D4—222no—
242C22×D4—224no—
243C22×D4—224no—
244C22×D4C22⋊D1111yescharacteristic
245C23×C4C22⋊D1112yes—
246C2×SD16—224no—
247C4⋊Q8—112no—
248#127—112no—
249#124—222no—
250#123—228no—
251C22⋊Q8—224no—
252#121—114no—
253#121—224no—
254#121—224no—
255#121—224no—
256#121—222no—
257#121—224no—
258#120—228no—
259C4×Q8—22no—
260C4×Q8—22no—
261C4×D4—22no—
262C4×D4—22no—
263C4×D4—114no—
264C4×D4—222no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—222no—
269C2×C4⋊C4C22⋊D1111yescharacteristic
270C2×C4⋊C4C22×D1111yescharacteristic
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—224no—
274C2×C22⋊C4C22×D1112yes—
275C2×C42—21no—
276C2×C42C22×D1111yescharacteristic
277#106—224no—
278C4⋊C8—222no—
279#103—224no—
280#102—224no—
281C22⋊C8—114no—
282C4×C8—222no—
283#95—21no—
284#95—22no—
285#95C22×D1112yes—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—44no—
289C2×C11C2×#45011yescharacteristic
290C2×C11#301911yescharacteristic
291C2×C11#302511yescharacteristic
292D11—84no—
293C24—224no—
294C24C2×C22⋊D1112yes—
295#41—4416no—
296#41—444no—
297#41—444no—
298C2×Q8—22no—
299C2×Q8—42no—
300C2×Q8—222no—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—114no—
304C2×D4—224no—
305C2×D4—228no—
306C2×D4—224no—
307C2×D4—222no—
308C2×D4—222no—
309C2×D4—4416no—
310C2×D4—448no—
311C2×D4—448no—
312C2×D4—884no—
313C2×D4#432514yescomplemented
314C22×C4—21no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—82no—
320C22×C4—224no—
321C22×C4—224no—
322C22×C4C2×C22⋊D1112yes—
323C22×C4C2×C22⋊D1111yescharacteristic
324C22×C4C2×C22⋊D1111yescharacteristic
325C22×C4C23×D1111yescharacteristic
326SD16—448no—
327C2×C8—224no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—42no—
333C4⋊C4—82no—
334C4⋊C4—114no—
335C4⋊C4—224no—
336C4⋊C4—222no—
337C22⋊C4—24no—
338C22⋊C4—44no—
339C22⋊C4—82no—
340C22⋊C4—228no—
341C22⋊C4—224no—
342C22⋊C4—224no—
343C42—42no—
344C42D4×D1112yes—
345C42D4×D1112yes—
346C11#1821111yescharacteristic, complemented, Sylow
347C23—22no—
348C23—22no—
349C23—42no—
350C23—42no—
351C23—224no—
352C23—448no—
353C23—884no—
354C23—884no—
355C23C2×#432514yes—
356C23C22×C22⋊D1111yescharacteristic
357Q8—24no—
358Q8—42no—
359Q8—444no—
360D4—28no—
361D4—444no—
362D4—444no—
363D4—4416no—
364D4—444no—
365D4—444no—
366D4—444no—
367D4—884no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—44no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—224no—
384C2×C4—448no—
385C2×C4—448no—
386C2×C4#6699011yescharacteristic
387C2×C4#6699011yescharacteristic
388C2×C4#6699012yes—
389C2×C4C2×#432512yes—
390C2×C4#6700212yes—
391C2×C4C2×D4×D1112yes—
392C8—444no—
393C22—21no—
394C22—21no—
395C22—24no—
396C22—44no—
397C22—42no—
398C22—42no—
399C22—82no—
400C22—444no—
401C22—444no—
402C22—444no—
403C22—1768no—
404C22C2×#6699011yescharacteristic
405C22C22×#432511yescharacteristic
406C22C2×#6700211yescharacteristic
407C4—21no—
408C4—21no—
409C4—22no—
410C4—42no—
411C4—42no—
412C4—82no—
413C4—81no—
414C4—444no—
415C4#1062265914yes—
416C2—21no—
417C2—21no—
418C2—44no—
419C2—884no—
420C2C2×#1062265911yescharacteristic
421C2#1307797211yescharacteristic
422C2#1307800711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2580C2
socleC22×C11C2×#120
prime radical#13082380C2
hypercenter#2580D11
hypocenterC11#18211
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2580

Complements

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

NH ≅ G/Ntype
2. #13078647C2semidirect
3. #13067635C2semidirect
4. #13067567C2semidirect
5. #13067175C2semidirect
6. #13066937C2semidirect
7. C11×#2580C2semidirect
9. C2×C4×Q8×C11C22semidirect
18. C11×#399C22semidirect
19. C11×#393C22semidirect
23. C11×#382C22semidirect
24. #10622840C22semidirect
28. #10622581C22semidirect
29. #10622538C22semidirect
30. #10622163C22semidirect
31. #10622089C22semidirect
89. C2×D4×C11SD16semidirect
138. #2580D11semidirect
197. C2×C4×Q8C2×D11semidirect
205. #399C2×D11semidirect
206. #393C2×D11semidirect
210. #382C2×D11semidirect
313. C2×D4#4325semidirect
346. C11#18211semidirect

Maximal subgroups

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

subgroupindex
#130823802
#130786472
#130676352
#130675672
#130671752
#130669372
C11×#25802
#1821111