Finite Group Databasebeta

← #14726545

Subgroups — #14726545

Order 2816.

1386 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1386 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#13078703C212yesmaximal, complemented
2#13071895C211yesmaximal, characteristic, complemented
3#13067636C214yesmaximal, complemented
4#13067534C214yesmaximal, complemented
5#13067124C212yesmaximal, complemented
6#13066957C211yesmaximal, characteristic, complemented
7C11×#3496C211yesmaximal, characteristic, complemented
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×C22⋊D11—22no—
18C2×C4×D44C2211yescharacteristic, complemented
19#10622836—21no—
20#10622697—22no—
21#10622685—22no—
22#10622649C2214yescomplemented
23#10622647C2214yescomplemented
24#10622627—24no—
25#10622605—21no—
26#10622573C2212yescomplemented
27#10622562C2212yescomplemented
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×C22⋊D11—22no—
41C22×D44C2311yescharacteristic
42C22×C4×D11—21no—
43C11×C4⋊Q8D412yescomplemented
44C11×#127D412yescomplemented
45C11×#124—22no—
46C11×#123—28no—
47C11×C22⋊Q8—24no—
48C11×#121—24no—
49C11×#121—24no—
50C11×#121—24no—
51C11×#121—22no—
52C11×#121—24no—
53C11×#121C2314yes—
54C11×#120—28no—
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C4×D4×C11D414yescomplemented
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C22⋊C4—24no—
62C2×C11×C22⋊C4C2312yes—
63C2×C42×C11C2311yescharacteristic
64C2×C22⋊Dic11—22no—
65C2×#4323—24no—
66C4×C22⋊D11—48no—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—22no—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×Dic11⋊C4—22no—
71C2×C4×Dic11—21no—
72C4×D44—22no—
73C4×D44—22no—
74#66896—24no—
75C11⋊#95—21no—
76C11⋊#95C2312yes—
77C22⋊(C11⋊C8)C2314yes—
78#66873—24no—
79#66872—24no—
80C4⋊(C11⋊C8)—22no—
81#66867—22no—
82#18178—111nomaximal, Sylow
83C24×C11—24no—
84C24×C11C2×D412yes—
85C23×D11—21no—
86C11×#41—48no—
87C11×#41—416no—
88C2×Q8×C11—22no—
89C2×D4×C11—24no—
90C2×D4×C11—28no—
91C2×D4×C11—24no—
92C2×D4×C11—24no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—416no—
97C2×D4×C11—48no—
98C2×D4×C11—48no—
99C2×D4×C11—84no—
100C2×D4×C11C2×D414yes—
101C22×C4×C11—24no—
102C22×C4×C11—22no—
103C22×C4×C11—24no—
104C22×C4×C11—22no—
105C22×C4×C11—44no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2411yescharacteristic
110C2×C22⋊D11—44no—
111C2×C22⋊D11—44no—
112C2×C22⋊D11—44no—
113C22×Dic11—22no—
114C22×Dic11—21no—
115C2×D44—22no—
116C2×D44—42no—
117C2×C4×D11—44no—
118C2×C4×D11—41no—
119C2×C4×D11—41no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4C2×D414yes—
124C11×C22⋊C4—28no—
125C11×C22⋊C4—24no—
126C11×C22⋊C4—24no—
127C11×C22⋊C4—24no—
128C42×C11C2×D412yes—
129C42×C11C2×D412yes—
130C22⋊Dic11—44no—
131#4323—48no—
132(C2×D11)⋊C4—44no—
133(C2×D11)⋊C4—42no—
134C4⋊Dic11—22no—
135Dic11⋊C4—44no—
136C4×Dic11—24no—
137C2×C11⋊C8—24no—
138#3496D1111yescharacteristic, complemented
139#3109—112no—
140#2397—111no—
141#1613—114no—
142#1595—114no—
143#1505—112no—
144#1466—111no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—24no—
148C23×C11—42no—
149C23×C11—42no—
150C23×C11—48no—
151C23×C11—84no—
152C23×C11—84no—
153C23×C11AGL(1,ℤ/8)14yes—
154C23×C11C22×D411yescharacteristic
155C22×D11—22no—
156C22×D11—42no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—42no—
160Q8×C11—44no—
161D4×C11—28no—
162D4×C11—44no—
163D4×C11—44no—
164D4×C11—416no—
165D4×C11—48no—
166D4×C11—44no—
167D4×C11—84no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—24no—
172C2×C4×C11—41no—
173C2×C4×C11—48no—
174C2×C4×C11—48no—
175C2×C4×C11—44no—
176C2×C4×C11—42no—
177C2×C4×C11—82no—
178C2×C4×C11#12012yes—
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12011yescharacteristic
181C2×C4×C11C22×D412yes—
182C22⋊D11—416no—
183C2×Dic11—24no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—41no—
188D44—24no—
189D44—42no—
190C4×D11—82no—
191C4×D11—82no—
192C11⋊C8—44no—
193C2×H(5,𝔽2)—21no—
194#547—22no—
195#546—24no—
196D42—22no—
197#537—21no—
198#534C2×D1114yes—
199#532C2×D1112yes—
200C2×#121—22no—
201C2×C4×D4—111no—
202C2×C4×D4—222no—
203C2×C4×D4C2×D1111yescharacteristic
204#481—114no—
205#476—222no—
206#459—222no—
207#447—114no—
208#442—224no—
209#432—112no—
210#399—112no—
211#399—221no—
212#392—112no—
213#392—221no—
214#376—111no—
215#327—118no—
216#323—114no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—24no—
220C22×C11—44no—
221C22×C11—42no—
222C22×C11—42no—
223C22×C11—44no—
224C22×C11—44no—
225C22×C11—44no—
226C22×C11—82no—
227C22×C11—168no—
228C22×C11C2×#12011yescharacteristic
229C22×C11C2×AGL(1,ℤ/8)12yes—
230C2×D11—44no—
231C2×D11—42no—
232C2×D11—82no—
233C2×D11—81no—
234C2×D11—81no—
235C4×C11—22no—
236C4×C11—21no—
237C4×C11—22no—
238C4×C11—44no—
239C4×C11—42no—
240C4×C11#45312yes—
241Dic11—44no—
242Dic11—81no—
243H(5,𝔽2)—48no—
244C2×#41—24no—
245C2×#41—22no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—22no—
249C22×D4—111no—
250C22×D4—222no—
251C22×D4C22⋊D1111yescharacteristic
252C23×C4—221no—
253C23×C4C22⋊D1112yes—
254C2×D8—224no—
255C4⋊Q8C22⋊D1112yescomplemented
256#127C22⋊D1112yescomplemented
257#124—22no—
258#123—28no—
259C22⋊Q8—24no—
260#121—24no—
261#121—24no—
262#121—24no—
263#121—22no—
264#121—24no—
265#121C22×D1114yes—
266#120—28no—
267C4×D4—22no—
268C4×D4—22no—
269C4×D4—22no—
270C4×D4—222no—
271C4×D4—222no—
272C4×D4—448no—
273C4×D4C22⋊D1114yescomplemented
274C2×C4⋊C4—22no—
275C2×C4⋊C4—111no—
276C2×C4⋊C4—222no—
277C2×C4⋊C4C22⋊D1111yescharacteristic
278C2×C22⋊C4—24no—
279C2×C22⋊C4—222no—
280C2×C22⋊C4—221no—
281C2×C22⋊C4—222no—
282C2×C22⋊C4C22×D1112yes—
283C2×C42—221no—
284C2×C42C22×D1111yescharacteristic
285#106—224no—
286C4⋊C8—222no—
287#102—224no—
288#102—224no—
289C22⋊C8—114no—
290#97—222no—
291#95—112no—
292#95—221no—
293C2×C11—22no—
294C2×C11—44no—
295C2×C11—84no—
296C2×C11#300311yescharacteristic
297C2×C11C2×#45311yescharacteristic
298C2×C11#302511yescharacteristic
299D11—82no—
300C24—24no—
301C24—221no—
302C24C2×C22⋊D1112yes—
303#41—48no—
304#41—416no—
305C2×Q8—22no—
306C2×D4—24no—
307C2×D4—28no—
308C2×D4—24no—
309C2×D4—24no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—416no—
314C2×D4—48no—
315C2×D4—48no—
316C2×D4—84no—
317C2×D4—222no—
318C2×D4—442no—
319C2×D4—444no—
320C2×D4—444no—
321C2×D4—444no—
322C2×D4C2×C22⋊D1114yes—
323C22×C4—24no—
324C22×C4—22no—
325C22×C4—24no—
326C22×C4—22no—
327C22×C4—44no—
328C22×C4—222no—
329C22×C4—221no—
330C22×C4—444no—
331C22×C4—441no—
332C22×C4—441no—
333C22×C4C2×C22⋊D1111yescharacteristic
334C22×C4C2×C22⋊D1111yescharacteristic
335C22×C4C2×C22⋊D1112yes—
336C22×C4C23×D1111yescharacteristic
337D8—448no—
338C2×C8—224no—
339C4⋊C4—24no—
340C4⋊C4—22no—
341C4⋊C4—22no—
342C4⋊C4—222no—
343C4⋊C4—444no—
344C4⋊C4C2×C22⋊D1114yes—
345C22⋊C4—28no—
346C22⋊C4—24no—
347C22⋊C4—24no—
348C22⋊C4—24no—
349C22⋊C4—444no—
350C22⋊C4—444no—
351C22⋊C4—442no—
352C42—224no—
353C42C2×C22⋊D1112yes—
354C42C2×C22⋊D1112yes—
355C11#1817811yescharacteristic, complemented, Sylow
356C23—22no—
357C23—22no—
358C23—24no—
359C23—42no—
360C23—42no—
361C23—48no—
362C23—84no—
363C23—84no—
364C23—222no—
365C23—442no—
366C23—441no—
367C23—442no—
368C23—441no—
369C23#6698514yes—
370C23C22×C22⋊D1111yescharacteristic
371Q8—44no—
372D4—28no—
373D4—44no—
374D4—44no—
375D4—416no—
376D4—48no—
377D4—44no—
378D4—84no—
379D4—224no—
380D4—442no—
381D4—4416no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—24no—
386C2×C4—41no—
387C2×C4—48no—
388C2×C4—48no—
389C2×C4—44no—
390C2×C4—42no—
391C2×C4—82no—
392C2×C4—224no—
393C2×C4—442no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—441no—
397C2×C4—882no—
398C2×C4—882no—
399C2×C4#6700611yescharacteristic
400C2×C4#6700612yes—
401C2×C4#6700611yescharacteristic
402C2×C4C22×C22⋊D1112yes—
403C8—444no—
404C22—21no—
405C22—21no—
406C22—24no—
407C22—44no—
408C22—42no—
409C22—42no—
410C22—44no—
411C22—44no—
412C22—44no—
413C22—82no—
414C22—168no—
415C22—444no—
416C22—442no—
417C22—882no—
418C22—881no—
419C22—881no—
420C22C2×#6698512yes—
421C22C2×#6700611yescharacteristic
422C4—22no—
423C4—21no—
424C4—22no—
425C4—44no—
426C4—42no—
427C4—444no—
428C4—881no—
429C4#1062285412yes—
430C2—22no—
431C2—44no—
432C2—84no—
433C2—882no—
434C2#1307784311yescharacteristic
435C2C2×#1062285411yescharacteristic
436C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3496C2
socleC22×C11C2×#120
hypercenter#3496D11
hypocenterC11#18178
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. #13078703C2semidirect
2. #13071895C2semidirect
3. #13067636C2semidirect
4. #13067534C2semidirect
5. #13067124C2semidirect
6. #13066957C2semidirect
7. C11×#3496C2semidirect
18. C2×C4×D44C22semidirect
22. #10622649C22semidirect
23. #10622647C22semidirect
26. #10622573C22semidirect
27. #10622562C22semidirect
28. #10622545C22semidirect
29. #10622539C22semidirect
30. #10622175C22semidirect
31. #10622163C22semidirect
43. C11×C4⋊Q8D4semidirect
44. C11×#127D4semidirect
58. C4×D4×C11D4semidirect
138. #3496D11semidirect
255. C4⋊Q8C22⋊D11semidirect
256. #127C22⋊D11semidirect
273. C4×D4C22⋊D11semidirect
355. C11#18178semidirect

Maximal subgroups

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

subgroupindex
#130787032
#130718952
#130676362
#130675342
#130671242
#130669572
C11×#34962
#1817811