Finite Group Databasebeta

← #14726619

Subgroups — #14726619

Order 2816.

1166 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1166 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#13082387C211yesmaximal, characteristic
2#13078738C212yesmaximal, complemented
3#13067618C214yesmaximal, complemented
4#13067584C214yesmaximal, complemented
5#13067123C212yesmaximal, complemented
6#13066960C211yesmaximal, characteristic, complemented
7C11×#2399C211yesmaximal, characteristic, complemented
8C2×#67040—21no—
9C2×C4×Q8×C11C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11#10623108—22no—
12#10623107—24no—
13Q8×D44—22no—
14#10623041—21no—
15#10623041C2214yes—
16#10623008—22no—
17#10623008C2212yes—
18C11×#398—21no—
19C11×#398C2212yes—
20C11×#395—21no—
21C11×#395C2212yes—
22C4×C11×C4⋊C4—22no—
23C11×#376C2211yescharacteristic
24#10622840C2214yes—
25#10622640—22no—
26#10622639—24no—
27#10622634—22no—
28#10622580C2214yes—
29#10622539C2212yes—
30#10622166C2214yes—
31#10622089C2218yes—
32C22×Q8×C11D411yescharacteristic
33C22×Q8×C11C2311yescharacteristic
34#67040—48no—
35C2×#4343—24no—
36C2×Q8×D11—24no—
37C2×#4339—24no—
38C2×#4339—22no—
39C4×Q8×C11—22no—
40C4×Q8×C11—22no—
41C4×Q8×C11—22no—
42C4×Q8×C11—22no—
43C2×C11×C4⋊C4—22no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4C2311yescharacteristic
48C2×C11×C4⋊C4C2312yes—
49C2×C42×C11—21no—
50C2×C42×C11—21no—
51C2×C42×C11D412yes—
52C2×C42×C11C2311yescharacteristic
53C2×#4325—24no—
54#66983—22no—
55#66983—24no—
56#66983C2314yes—
57#66950—24no—
58#66950—28no—
59#66948—24no—
60#66948—28no—
61#66928—24no—
62#66928—22no—
63#66927—22no—
64#66927D412yes—
65C4×D44—24no—
66C4×D44—24no—
67C4×D44—22no—
68C4×D44D414yes—
69#66922—22no—
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#18187—111nomaximal, Sylow
82C2×Q8×C11—22no—
83C2×Q8×C11—24no—
84C2×Q8×C11—22no—
85C2×Q8×C11—42no—
86C22×C4×C11—22no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2411yescharacteristic
94C2×C22⋊D11—24no—
95#4343—416no—
96Q8×D11—416no—
97#4339—48no—
98#4339—48no—
99#4339—48no—
100C2×D44—24no—
101C2×D44—24no—
102C2×D44—22no—
103C2×D44—22no—
104C2×D44C2×D414yes—
105C2×C4×D11—28no—
106C2×C4×D11—24no—
107C2×Dic22—24no—
108C2×Dic22—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—44no—
113C11×C4⋊C4—42no—
114C11×C4⋊C4—44no—
115C42×C11—24no—
116C42×C11—22no—
117C42×C11—22no—
118C42×C11—41no—
119C42×C11—41no—
120C42×C11C2×D412yes—
121C42×C11C2×D412yes—
122#4325—48no—
123(C2×D11)⋊C4—28no—
124(C2×D11)⋊C4—24no—
125(C2×D11)⋊C4—24no—
126C4⋊Dic11—24no—
127C4⋊Dic11—22no—
128C4⋊Dic11C2×D414yes—
129C2×C11⋊C8—24no—
130#3497—111no—
131#3112—112no—
132#2399D1111yescharacteristic, complemented
133#1610—114no—
134#1604—114no—
135#1505—112no—
136#1467—111no—
137C23×C11C22×D411yescharacteristic
138C22×D11—24no—
139Q8×C11—28no—
140Q8×C11—24no—
141Q8×C11—42no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—24no—
147C2×C4×C11—22no—
148C2×C4×C11—22no—
149C2×C4×C11—41no—
150C2×C4×C11—42no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12012yes—
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11AGL(1,ℤ/8)14yes—
161C2×C4×C11C22×D412yes—
162C22⋊D11—48no—
163C2×Dic11—24no—
164D44—44no—
165D44—44no—
166D44—48no—
167D44—44no—
168D44—84no—
169C4×D11—48no—
170C4×D11—416no—
171Dic22—44no—
172Dic22—48no—
173C11⋊C8—44no—
174C2×2−1+4—221no—
175#550—222no—
176D4×Q8—222no—
177#548—224no—
178#537—114no—
179#537—221no—
180#532—112no—
181#532—222no—
182C2×C4×Q8C2×D1111yescharacteristic
183C2×C4×Q8C2×D1111yescharacteristic
184#480—114no—
185#477—222no—
186#460—222no—
187#448—114no—
188#440—224no—
189#432—112no—
190#398—21no—
191#398C2×D1112yes—
192#395—21no—
193#395C2×D1112yes—
194C4×C4⋊C4—22no—
195#376C2×D1111yescharacteristic
196#327—118no—
197#324—114no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11C2×#12011yescharacteristic
201C22×C11C2×AGL(1,ℤ/8)12yes—
202C2×D11—44no—
203C2×D11—44no—
204C2×D11—44no—
205C4×C11—22no—
206C4×C11—24no—
207C4×C11—21no—
208C4×C11—22no—
209C4×C11—44no—
210C4×C11—42no—
211C4×C11—42no—
212C4×C11—81no—
213C4×C11#45612yes—
214Dic11—44no—
2152−1+4—448no—
216C2×#41—224no—
217C2×#41—222no—
218C2×#41—224no—
219C22×Q8—224no—
220C22×Q8C22⋊D1111yescharacteristic
221C22×Q8C22×D1111yescharacteristic
222C2×SD16—224no—
223C4⋊Q8—112no—
224C4⋊Q8—222no—
225#127—112no—
226#127—222no—
227#124—224no—
228#124—222no—
229C22⋊Q8—228no—
230C22⋊Q8—224no—
231#121—114no—
232#121—228no—
233#121—224no—
234#121—222no—
235#121—224no—
236C4×Q8—22no—
237C4×Q8—22no—
238C4×Q8—22no—
239C4×Q8—22no—
240C4×D4—114no—
241C4×D4—224no—
242C4×D4—224no—
243C4×D4—222no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4C22⋊D1111yescharacteristic
248C2×C4⋊C4C22×D1111yescharacteristic
249C2×C4⋊C4C22×D1112yes—
250C2×C42—21no—
251C2×C42—21no—
252C2×C42C22⋊D1112yes—
253C2×C42C22×D1111yescharacteristic
254#107—224no—
255C4⋊C8—222no—
256#103—224no—
257#102—224no—
258C22⋊C8—114no—
259#97—222no—
260#95—21no—
261#95—22no—
262#95—22no—
263#95C22×D1112yes—
264C2×C11—22no—
265C2×C11#300311yescharacteristic
266C2×C11C2×#45611yescharacteristic
267C2×C11#302511yescharacteristic
268D11—84no—
269#41—448no—
270#41—448no—
271#41—4416no—
272#41—448no—
273C2×Q8—22no—
274C2×Q8—24no—
275C2×Q8—22no—
276C2×Q8—42no—
277C2×Q8—224no—
278C2×Q8—222no—
279C2×Q8—4416no—
280C2×D4—114no—
281C2×D4—224no—
282C2×D4—224no—
283C2×D4—224no—
284C2×D4—222no—
285C2×D4—222no—
286C22×C4—22no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—228no—
290C22×C4—224no—
291C22×C4C2×C22⋊D1111yescharacteristic
292C22×C4C2×C22⋊D1111yescharacteristic
293C22×C4C2×C22⋊D1112yes—
294C22×C4C2×C22⋊D1112yes—
295C22×C4C23×D1111yescharacteristic
296SD16—448no—
297C2×C8—224no—
298C4⋊C4—22no—
299C4⋊C4—24no—
300C4⋊C4—22no—
301C4⋊C4—44no—
302C4⋊C4—42no—
303C4⋊C4—44no—
304C4⋊C4—114no—
305C4⋊C4—224no—
306C4⋊C4—222no—
307C22⋊C4—228no—
308C22⋊C4—224no—
309C22⋊C4—224no—
310C42—24no—
311C42—22no—
312C42—22no—
313C42—41no—
314C42—41no—
315C42D4×D1112yes—
316C42D4×D1112yes—
317C11#1818711yescharacteristic, complemented, Sylow
318C23—224no—
319C23C22×C22⋊D1111yescharacteristic
320Q8—28no—
321Q8—24no—
322Q8—42no—
323Q8—444no—
324Q8—448no—
325D4—444no—
326D4—444no—
327D4—448no—
328D4—448no—
329D4—444no—
330D4—884no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—24no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—224no—
347C2×C4—448no—
348C2×C4—4416no—
349C2×C4#6699011yescharacteristic
350C2×C4#6699012yes—
351C2×C4#6699011yescharacteristic
352C2×C4#6700214yes—
353C2×C4C2×D4×D1112yes—
354C8—444no—
355C22—21no—
356C22—21no—
357C22—444no—
358C22—444no—
359C22—444no—
360C22C2×#6699011yescharacteristic
361C22C2×#6700212yes—
362C4—22no—
363C4—24no—
364C4—21no—
365C4—22no—
366C4—44no—
367C4—42no—
368C4—42no—
369C4—81no—
370C4—444no—
371C4#1062270812yes—
372C2—22no—
373C2—884no—
374C2#1307784211yescharacteristic
375C2C2×#1062270811yescharacteristic
376C2#1307800711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2399C2
socleC22×C11C2×#120
prime radical#13082387C2
hypercenter#2399D11
hypocenterC11#18187
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2399

Complements

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

NH ≅ G/Ntype
2. #13078738C2semidirect
3. #13067618C2semidirect
4. #13067584C2semidirect
5. #13067123C2semidirect
6. #13066960C2semidirect
7. C11×#2399C2semidirect
132. #2399D11semidirect
317. C11#18187semidirect

Maximal subgroups

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

subgroupindex
#130823872
#130787382
#130676182
#130675842
#130671232
#130669602
C11×#23992
#1818711