Finite Group Databasebeta

← #14726544

Subgroups — #14726544

Order 2816.

1386 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1386 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, complemented
2#13078707C212yesmaximal, complemented
3#13067635C214yesmaximal, complemented
4#13067533C214yesmaximal, complemented
5#13067123C212yesmaximal, complemented
6#13066957C211yesmaximal, characteristic, complemented
7C11×#2397C211yesmaximal, characteristic, complemented
8C2×#67037—21no—
9C2×C4×D4×C11—22no—
10C2×C4×D4×C11C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic, complemented
12C2×#66983—22no—
13#10623086—22no—
14#10623085—24no—
15D4×D44—22no—
16#10623041—21no—
17#10623024C2214yes—
18#10623008C2212yes—
19C11×#399—21no—
20C11×#399C2212yescomplemented
21C11×#392—21no—
22C11×#392C2212yescomplemented
23C11×#376C2211yescharacteristic, complemented
24#10622830C2214yescomplemented
25#10622628—22no—
26#10622627—24no—
27#10622621—22no—
28#10622581C2214yescomplemented
29#10622539C2212yescomplemented
30#10622163C2214yescomplemented
31#10622089C2218yescomplemented
32C22×D4×C11—22no—
33C22×D4×C11D411yescharacteristic
34C22×D4×C11C2311yescharacteristic
35C23×C4×C11—21no—
36C23×C4×C11D412yes—
37C22×C22⋊D11—24no—
38#67037—48no—
39C2×#4341—24no—
40C2×D4×D11—24no—
41C2×#4339—22no—
42C22×D44—22no—
43C4×D4×C11—22no—
44C4×D4×C11—22no—
45C4×D4×C11—22no—
46C4×D4×C11—22no—
47C4×D4×C11—48no—
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⋊C4—21no—
54C2×C11×C22⋊C4C2312yes—
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57C2×#4323—24no—
58#66983—24no—
59#66983—24no—
60#66983—22no—
61#66983—24no—
62#66983C2314yes—
63C2×(C2×D11)⋊C4—24no—
64C2×C4⋊Dic11—22no—
65#66950—24no—
66#66948—24no—
67#66939—28no—
68#66935—28no—
69#66928—22no—
70#66927D412yescomplemented
71C4×D44—22no—
72C4×D44D414yescomplemented
73#66922D412yescomplemented
74C11×#95—21no—
75C11×#95C2312yes—
76#66896—24no—
77C22⋊(C11⋊C8)C2314yes—
78#66873—24no—
79#66872—24no—
80C4⋊(C11⋊C8)—22no—
81#66867—22no—
82#18178—111nomaximal, Sylow
83C24×C11—21no—
84C24×C11C2×D412yes—
85C23×D11—24no—
86C2×D4×C11—24no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—44no—
90C2×D4×C11—42no—
91C2×D4×C11—44no—
92C2×D4×C11—44no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—44no—
98C22×C4×C11—44no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2411yescharacteristic
105C2×C22⋊D11—28no—
106C2×C22⋊D11—24no—
107C2×C22⋊D11—48no—
108C2×C22⋊D11—48no—
109C22×Dic11—24no—
110#4341—416no—
111D4×D11—416no—
112#4339—48no—
113C2×D44—24no—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44—84no—
117C2×D44C2×D414yes—
118C2×C4×D11—24no—
119C2×Dic22—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—44no—
123C11×C22⋊C4—24no—
124C11×C22⋊C4—44no—
125C11×C22⋊C4—44no—
126C11×C22⋊C4—42no—
127C42×C11—24no—
128C42×C11C2×D412yes—
129C42×C11C2×D412yes—
130#4323—48no—
131(C2×D11)⋊C4—28no—
132(C2×D11)⋊C4—24no—
133(C2×D11)⋊C4—24no—
134C4⋊Dic11—24no—
135C4⋊Dic11—22no—
136C4⋊Dic11C2×D414yes—
137C2×C11⋊C8—24no—
138#3496—111no—
139#3109—112no—
140#2397D1111yescharacteristic, complemented
141#1613—114no—
142#1595—114no—
143#1505—112no—
144#1466—111no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11—22no—
148C23×C11—42no—
149C23×C11—42no—
150C23×C11—42no—
151C23×C11—41no—
152C23×C11—41no—
153C23×C11—42no—
154C23×C11AGL(1,ℤ/8)14yes—
155C23×C11C22×D411yescharacteristic
156C22×D11—24no—
157C22×D11—48no—
158C22×D11—84no—
159C22×D11—84no—
160D4×C11—28no—
161D4×C11—24no—
162D4×C11—42no—
163D4×C11—416no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—24no—
167C2×C4×C11—22no—
168C2×C4×C11—41no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—44no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—82no—
176C2×C4×C11—82no—
177C2×C4×C11—82no—
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12012yes—
180C2×C4×C11#12011yescharacteristic
181C2×C4×C11C22×D412yes—
182C22⋊D11—416no—
183C22⋊D11—48no—
184C2×Dic11—24no—
185C2×Dic11—48no—
186D44—44no—
187D44—44no—
188D44—44no—
189D44—84no—
190C4×D11—48no—
191Dic22—44no—
192C11⋊C8—44no—
193C2×H(5,𝔽2)—221no—
194#547—222no—
195#546—224no—
196D42—222no—
197#537—221no—
198#534—114no—
199#532—112no—
200C2×#121—222no—
201C2×C4×D4—22no—
202C2×C4×D4C2×D1111yescharacteristic
203C2×C4×D4C2×D1111yescharacteristic, complemented
204#481—114no—
205#476—222no—
206#459—222no—
207#447—114no—
208#442—224no—
209#432—112no—
210#399—21no—
211#399C2×D1112yescomplemented
212#392—21no—
213#392C2×D1112yescomplemented
214#376C2×D1111yescharacteristic, complemented
215#327—118no—
216#323—114no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—24no—
220C22×C11—44no—
221C22×C11—44no—
222C22×C11—42no—
223C22×C11—42no—
224C22×C11—42no—
225C22×C11—82no—
226C22×C11—82no—
227C22×C11—81no—
228C22×C11—81no—
229C22×C11C2×#12011yescharacteristic
230C22×C11C2×AGL(1,ℤ/8)12yes—
231C2×D11—44no—
232C2×D11—44no—
233C2×D11—44no—
234C2×D11—168no—
235C4×C11—22no—
236C4×C11—21no—
237C4×C11—22no—
238C4×C11—44no—
239C4×C11—42no—
240C4×C11—81no—
241C4×C11#45312yes—
242Dic11—44no—
243H(5,𝔽2)—448no—
244C2×#41—224no—
245C2×#41—222no—
246C22×D4—22no—
247C22×D4—222no—
248C22×D4—224no—
249C22×D4—224no—
250C22×D4C22⋊D1111yescharacteristic
251C22×D4C22×D1111yescharacteristic
252C23×C4—21no—
253C23×C4C22⋊D1112yes—
254C2×D8—224no—
255C4⋊Q8—112no—
256#127—112no—
257#124—222no—
258#123—228no—
259C22⋊Q8—224no—
260#121—114no—
261#121—224no—
262#121—224no—
263#121—224no—
264#121—222no—
265#121—224no—
266#120—228no—
267C4×D4—22no—
268C4×D4—22no—
269C4×D4—22no—
270C4×D4—22no—
271C4×D4—48no—
272C4×D4—114no—
273C4×D4—222no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—222no—
276C2×C4⋊C4C22⋊D1111yescharacteristic
277C2×C4⋊C4C22×D1111yescharacteristic
278C2×C22⋊C4—22no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—224no—
282C2×C22⋊C4C22×D1112yes—
283C2×C42—21no—
284C2×C42C22×D1111yescharacteristic
285#106—224no—
286C4⋊C8—222no—
287#102—224no—
288#102—224no—
289C22⋊C8—114no—
290#97—222no—
291#95—21no—
292#95C22×D1112yes—
293C2×C11—22no—
294C2×C11—44no—
295C2×C11—82no—
296C2×C11#300311yescharacteristic
297C2×C11C2×#45311yescharacteristic
298C2×C11#302511yescharacteristic
299D11—84no—
300C24—21no—
301C24—224no—
302C24C2×C22⋊D1112yes—
303#41—448no—
304#41—4416no—
305C2×Q8—222no—
306C2×D4—24no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—44no—
310C2×D4—42no—
311C2×D4—44no—
312C2×D4—44no—
313C2×D4—114no—
314C2×D4—224no—
315C2×D4—228no—
316C2×D4—224no—
317C2×D4—222no—
318C2×D4—222no—
319C2×D4—4416no—
320C2×D4—448no—
321C2×D4—448no—
322C2×D4—884no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—21no—
327C22×C4—44no—
328C22×C4—44no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—224no—
332C22×C4—224no—
333C22×C4C2×C22⋊D1111yescharacteristic
334C22×C4C2×C22⋊D1111yescharacteristic
335C22×C4C2×C22⋊D1112yes—
336C22×C4C23×D1111yescharacteristic
337D8—448no—
338C2×C8—224no—
339C4⋊C4—22no—
340C4⋊C4—22no—
341C4⋊C4—44no—
342C4⋊C4—114no—
343C4⋊C4—224no—
344C4⋊C4—222no—
345C22⋊C4—24no—
346C22⋊C4—44no—
347C22⋊C4—44no—
348C22⋊C4—42no—
349C22⋊C4—228no—
350C22⋊C4—224no—
351C22⋊C4—224no—
352C42—24no—
353C42D4×D1112yes—
354C42D4×D1112yes—
355C11#1817811yescharacteristic, complemented, Sylow
356C23—22no—
357C23—22no—
358C23—22no—
359C23—42no—
360C23—42no—
361C23—42no—
362C23—41no—
363C23—41no—
364C23—42no—
365C23—224no—
366C23—448no—
367C23—884no—
368C23—884no—
369C23#6700214yes—
370C23C22×C22⋊D1111yescharacteristic
371Q8—444no—
372D4—28no—
373D4—24no—
374D4—42no—
375D4—416no—
376D4—444no—
377D4—444no—
378D4—4416no—
379D4—448no—
380D4—444no—
381D4—884no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—24no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—44no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—82no—
396C2×C4—224no—
397C2×C4—448no—
398C2×C4—448no—
399C2×C4#6699012yes—
400C2×C4#6699011yescharacteristic
401C2×C4#6699011yescharacteristic
402C2×C4C2×D4×D1112yes—
403C8—444no—
404C22—21no—
405C22—21no—
406C22—24no—
407C22—44no—
408C22—44no—
409C22—42no—
410C22—42no—
411C22—42no—
412C22—82no—
413C22—82no—
414C22—81no—
415C22—81no—
416C22—444no—
417C22—444no—
418C22—444no—
419C22—1768no—
420C22C2×#6699011yescharacteristic
421C22C2×#6700212yes—
422C4—22no—
423C4—21no—
424C4—22no—
425C4—44no—
426C4—42no—
427C4—81no—
428C4—444no—
429C4#1062269012yes—
430C2—22no—
431C2—44no—
432C2—82no—
433C2—884no—
434C2#1307784211yescharacteristic
435C2C2×#1062269011yescharacteristic
436C2#1307800711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2397C2
socleC22×C11C2×#120
hypercenter#2397D11
hypocenterC11#18178
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2397

Complements

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

NH ≅ G/Ntype
1. #13082380C2semidirect
2. #13078707C2semidirect
3. #13067635C2semidirect
4. #13067533C2semidirect
5. #13067123C2semidirect
6. #13066957C2semidirect
7. C11×#2397C2semidirect
11. C2×C4×D4×C11C22semidirect
20. C11×#399C22semidirect
22. C11×#392C22semidirect
23. C11×#376C22semidirect
24. #10622830C22semidirect
28. #10622581C22semidirect
29. #10622539C22semidirect
30. #10622163C22semidirect
31. #10622089C22semidirect
70. #66927D4semidirect
72. C4×D44D4semidirect
73. #66922D4semidirect
140. #2397D11semidirect
203. C2×C4×D4C2×D11semidirect
211. #399C2×D11semidirect
213. #392C2×D11semidirect
214. #376C2×D11semidirect
355. C11#18178semidirect

Maximal subgroups

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

subgroupindex
#130823802
#130787072
#130676352
#130675332
#130671232
#130669572
C11×#23972
#1817811