Finite Group Databasebeta

← #14726884

Subgroups — #14726884

Order 2816.

1222 conjugacy classes of subgroups; only the 187 normal subgroups are shown.

normal subgroups only

This group has 1222 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#13082387C211yesmaximal, characteristic, complemented
2#13078616C212yesmaximal, complemented
3#13067618C214yesmaximal, complemented
4#13067550C214yesmaximal, complemented
5#13067175C212yesmaximal, complemented
6#13066940C211yesmaximal, characteristic, complemented
7C11×#2536C211yesmaximal, characteristic, complemented
8C2×#67040—21no—
9C2×C11×C22⋊Q8—21no—
10C2×C4×Q8×C11C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12#10623108—22no—
13#10623107—24no—
14Q8×D44—22no—
15#10623041—21no—
16#10623041C2214yes—
17#10623008—22no—
18#10623008C2212yes—
19C11×#398C2212yes—
20C11×#394C2212yes—
21C11×#388—22no—
22C11×#382C2211yescharacteristic
23C11×#380—21no—
24#10622830C2214yes—
25#10622628—22no—
26C4×#4323—24no—
27#10622620—22no—
28#10622580C2214yes—
29#10622538C2212yes—
30#10622166C2214yes—
31#10622089C2218yes—
32C22×Q8×C11D411yescharacteristic
33C22×D4×C11C2311yescharacteristic
34C23×C4×C11—21no—
35#67040—44no—
36#67040—44no—
37C2×#4343—24no—
38C2×Q8×D11—24no—
39C2×#4339—24no—
40C2×#4339—22no—
41C11×C22⋊Q8—44no—
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—22no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C4⋊C4C2312yes—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—22no—
54C2×C42×C11D412yes—
55C2×C42×C11C2311yescharacteristic
56C2×#4323—24no—
57#66983—22no—
58#66983—24no—
59#66983C2314yes—
60#66950—24no—
61#66950—28no—
62#66948—24no—
63#66948—28no—
64#66928—24no—
65#66928—22no—
66#66927—22no—
67#66927D412yes—
68C4×D44—24no—
69C4×D44—24no—
70C4×D44—22no—
71C4×D44D414yes—
72#66922—22no—
73#66922D412yes—
74C11×#95—22no—
75C11×#95—21no—
76C11×#95C2312yes—
77#66896—24no—
78C22⋊(C11⋊C8)C2314yes—
79#66873—24no—
80#66871—24no—
81C4⋊(C11⋊C8)—22no—
82C4×C11⋊C8—22no—
83#18218—111nomaximal, Sylow
84C24×C11—21no—
85C2×Q8×C11—22no—
86C2×Q8×C11—22no—
87C2×Q8×C11D814yescomplemented
88C2×D4×C11—22no—
89C2×D4×C11—42no—
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C2×C22⋊D11—24no—
101#4343—416no—
102Q8×D11—416no—
103#4339—48no—
104#4339—48no—
105#4339—44no—
106#4339—44no—
107C2×D44—24no—
108C2×D44—24no—
109C2×D44—22no—
110C2×D44—22no—
111C2×D44C2×D414yes—
112C2×C4×D11—28no—
113C2×C4×D11—24no—
114C2×Dic22—24no—
115C2×Dic22—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4—44no—
121C11×C22⋊C4—44no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—44no—
125C42×C11—22no—
126C42×C11—22no—
127C42×C11C2×D412yes—
128C42×C11C2×D412yes—
129#4323—48no—
130(C2×D11)⋊C4—28no—
131(C2×D11)⋊C4—24no—
132(C2×D11)⋊C4—24no—
133C4⋊Dic11—24no—
134C4⋊Dic11—22no—
135C4⋊Dic11C2×D414yes—
136C2×C11⋊C8—24no—
137#3497—111no—
138#3100—112no—
139#2536D1111yescharacteristic, complemented
140#1610—114no—
141#1598—114no—
142#1517—112no—
143#1461—111no—
144C23×C11—22no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11C22×D411yescharacteristic
152C22×D11—24no—
153Q8×C11—28no—
154D4×C11—24no—
155D4×C11—42no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—84no—
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12011yescharacteristic
171C2×C4×C11#12012yes—
172C2×C4×C11C2×D814yes—
173C2×C4×C11C2×D812yes—
174C2×C4×C11AGL(1,ℤ/8)12yes—
175C2×C4×C11C22×D412yes—
176C22⋊D11—44no—
177C22⋊D11—44no—
178C2×Dic11—24no—
179D44—44no—
180D44—44no—
181D44—48no—
182D44—44no—
183D44—84no—
184C4×D11—416no—
185C4×D11—48no—
186Dic22—48no—
187Dic22—44no—
188C11⋊C8—44no—
189C2×2−1+4—221no—
190#550—222no—
191D4×Q8—222no—
192#548—224no—
193#537—114no—
194#537—221no—
195#532—112no—
196#532—222no—
197C2×C22⋊Q8—21no—
198C2×C4×Q8C2×D1111yescharacteristic
199C2×C4×D4C2×D1111yescharacteristic
200#480—114no—
201#474—222no—
202#459—222no—
203#447—114no—
204C4×D8—224no—
205#431—112no—
206#398C2×D1112yes—
207#394C2×D1112yes—
208#388—22no—
209#382C2×D1111yescharacteristic
210#380—21no—
211#327—118no—
212#324—114no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11C2×#12011yescharacteristic
223C22×C11C22×D811yescharacteristic
224C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
225C2×D11—44no—
226C2×D11—44no—
227C2×D11—44no—
228C4×C11—24no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—22no—
232C4×C11—42no—
233C4×C11—82no—
234C4×C11—81no—
235C4×C11#44714yes—
236Dic11—44no—
2372−1+4—444no—
2382−1+4—444no—
239C2×#41—224no—
240C2×#41—222no—
241C2×#41—224no—
242C22×Q8—224no—
243C22×Q8C22⋊D1111yescharacteristic
244C22×D4C22×D1111yescharacteristic
245C23×C4—21no—
246C2×D8—224no—
247C4⋊Q8—112no—
248C4⋊Q8—222no—
249#127—112no—
250#127—222no—
251#124—224no—
252#124—222no—
253C22⋊Q8—44no—
254C22⋊Q8—228no—
255C22⋊Q8—224no—
256#121—114no—
257#121—228no—
258#121—224no—
259#121—222no—
260#121—224no—
261C4×Q8—22no—
262C4×Q8—22no—
263C4×D4—22no—
264C4×D4—22no—
265C4×D4—114no—
266C4×D4—224no—
267C4×D4—224no—
268C4×D4—222no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4C22⋊D1111yescharacteristic
272C2×C4⋊C4C22×D1111yescharacteristic
273C2×C4⋊C4C22×D1112yes—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C42C22⋊D1112yes—
278C2×C42C22×D1111yescharacteristic
279#107—224no—
280C4⋊C8—222no—
281#102—224no—
282#102—224no—
283C22⋊C8—114no—
284C4×C8—222no—
285#95—22no—
286#95—21no—
287#95C22×D1112yes—
288C2×C11—21no—
289C2×C11—21no—
290C2×C11—82no—
291C2×C11C2×#44711yescharacteristic
292C2×C11#302011yescharacteristic
293C2×C11#302511yescharacteristic
294D11—84no—
295C24—21no—
296#41—448no—
297#41—4416no—
298#41—448no—
299#41—444no—
300#41—444no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—224no—
304C2×Q8—222no—
305C2×Q8—4416no—
306C2×Q8#432314yescomplemented
307C2×D4—22no—
308C2×D4—42no—
309C2×D4—114no—
310C2×D4—224no—
311C2×D4—224no—
312C2×D4—224no—
313C2×D4—222no—
314C2×D4—222no—
315C22×C4—22no—
316C22×C4—21no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—228no—
321C22×C4—224no—
322C22×C4C2×C22⋊D1112yes—
323C22×C4C2×C22⋊D1112yes—
324C22×C4C2×C22⋊D1111yescharacteristic
325C22×C4C2×C22⋊D1111yescharacteristic
326C22×C4C23×D1111yescharacteristic
327D8—448no—
328C2×C8—224no—
329C4⋊C4—22no—
330C4⋊C4—24no—
331C4⋊C4—22no—
332C4⋊C4—42no—
333C4⋊C4—44no—
334C4⋊C4—114no—
335C4⋊C4—224no—
336C4⋊C4—222no—
337C22⋊C4—44no—
338C22⋊C4—44no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—228no—
342C22⋊C4—224no—
343C22⋊C4—224no—
344C42—22no—
345C42—22no—
346C42D4×D1112yes—
347C42D4×D1112yes—
348C11#1821811yescharacteristic, complemented, Sylow
349C23—22no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—224no—
357C23C22×C22⋊D1111yescharacteristic
358Q8—28no—
359Q8—448no—
360Q8—444no—
361D4—24no—
362D4—42no—
363D4—444no—
364D4—448no—
365D4—444no—
366D4—444no—
367D4—444no—
368D4—444no—
369D4—884no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—84no—
383C2×C4—224no—
384C2×C4—4416no—
385C2×C4—448no—
386C2×C4C2×#432314yes—
387C2×C4C2×#432312yes—
388C2×C4#6699011yescharacteristic
389C2×C4#6699011yescharacteristic
390C2×C4#6699012yes—
391C2×C4#6700212yes—
392C2×C4C2×D4×D1112yes—
393C8—444no—
394C22—21no—
395C22—21no—
396C22—42no—
397C22—42no—
398C22—42no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—444no—
404C22—444no—
405C22—444no—
406C22C22×#432311yescharacteristic
407C22C2×#6699011yescharacteristic
408C22C2×#6700211yescharacteristic
409C4—24no—
410C4—21no—
411C4—21no—
412C4—22no—
413C4—42no—
414C4—82no—
415C4—81no—
416C4—444no—
417C4#1062264914yes—
418C2—21no—
419C2—21no—
420C2—82no—
421C2—884no—
422C2C2×#1062264911yescharacteristic
423C2#1307797911yescharacteristic
424C2#1307800711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2536C2
socleC22×C11C2×#120
hypercenter#2536D11
hypocenterC11#18218
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2536

Complements

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

NH ≅ G/Ntype
1. #13082387C2semidirect
2. #13078616C2semidirect
3. #13067618C2semidirect
4. #13067550C2semidirect
5. #13067175C2semidirect
6. #13066940C2semidirect
7. C11×#2536C2semidirect
87. C2×Q8×C11D8semidirect
139. #2536D11semidirect
306. C2×Q8#4323semidirect
348. C11#18218semidirect

Maximal subgroups

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

subgroupindex
#130823872
#130786162
#130676182
#130675502
#130671752
#130669402
C11×#25362
#1821811