Finite Group Databasebeta

← #14727953

Subgroups — #14727953

Order 2816.

1230 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1230 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
1C2×#10623041C211yesmaximal, characteristic
2#13079418C212yesmaximal, complemented
3#13067618C214yesmaximal, complemented
4#13067584C214yesmaximal, complemented
5#13067131C212yesmaximal, complemented
6#13066946C211yesmaximal, characteristic, complemented
7C11×#2583C211yesmaximal, characteristic, complemented
8C22×#4339—21no—
9C2×C11×C22⋊Q8C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C2×#66983—21no—
12C2×#66983C2212yes—
13#10623041—22no—
14#10623041—24no—
15#10623041C2214yes—
16C2×#66950—22no—
17C2×#66948—22no—
18C11×#398C2212yescomplemented
19C11×#395C2212yescomplemented
20C11×#389—22no—
21C11×#385—21no—
22C11×#385—21no—
23C4×C11×C22⋊C4C2211yescharacteristic
24#10622840C2214yescomplemented
25#10622820C2212yes—
26#10622662—24no—
27#10622659—22no—
28#10622657—22no—
29#10622580C2214yescomplemented
30#10622166C2214yescomplemented
31#10622089C2218yescomplemented
32C22×Q8×C11C2311yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11D411yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C22×C22⋊D11—22no—
37C2×#4339—24no—
38C2×#4339—24no—
39C2×#4339—48no—
40C22×D44—21no—
41C22×D44—21no—
42C22×D44D412yes—
43C22×C4×D11—22no—
44C22×Dic22—21no—
45C11×C22⋊Q8—22no—
46C11×C22⋊Q8—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4D412yes—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—21no—
57C2×C42×C11—21no—
58C2×#4325—24no—
59#66983—24no—
60#66983—22no—
61#66983—22no—
62#66983—24no—
63#66983D414yes—
64#66983C2314yes—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11D412yes—
69C2×#4318—22no—
70#66950—28no—
71#66950—28no—
72#66948—28no—
73#66948—28no—
74C11×#95—22no—
75C11×#95—22no—
76C11×#95C2312yes—
77#66899—24no—
78C22⋊(C11⋊C8)—22no—
79C22⋊(C11⋊C8)C2314yes—
80#66873—24no—
81#66871—24no—
82#18325—111nomaximal, Sylow
83C24×C11C2×D411yescharacteristic
84C23×D11—22no—
85C2×Q8×C11—22no—
86C2×Q8×C11—81no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—24no—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—81no—
96C22×C4×C11—81no—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2411yescharacteristic
103C2×C22⋊D11—24no—
104C2×C22⋊D11—24no—
105C2×C22⋊D11—48no—
106C22×Dic11—22no—
107#4339—416no—
108#4339—48no—
109#4339—48no—
110C2×D44—24no—
111C2×D44—24no—
112C2×D44—22no—
113C2×D44—44no—
114C2×D44—82no—
115C2×D44—82no—
116C2×D44C2×D414yes—
117C2×C4×D11—28no—
118C2×C4×D11—48no—
119C2×Dic22—24no—
120C2×Dic22—44no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—24no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—44no—
126C11×C4⋊C4—82no—
127C11×C22⋊C4—24no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C42×C11—81no—
131#4325—84no—
132(C2×D11)⋊C4—28no—
133(C2×D11)⋊C4—24no—
134(C2×D11)⋊C4—24no—
135C4⋊Dic11—24no—
136C4⋊Dic11—22no—
137C4⋊Dic11C2×D414yes—
138#4318—82no—
139C2×C11⋊C8—24no—
140C2×#537—111no—
141#3193—112no—
142#2583D1111yescharacteristic, complemented
143#1610—114no—
144#1604—114no—
145#1507—112no—
146#1463—111no—
147C23×C11—22no—
148C23×C11—22no—
149C23×C11—41no—
150C23×C11#12011yescharacteristic
151C23×C11#12011yescharacteristic
152C23×C11C22×D411yescharacteristic
153C22×D11—24no—
154C22×D11—44no—
155C22×D11—44no—
156C22×D11—44no—
157Q8×C11—44no—
158C2×C4×C11—24no—
159C2×C4×C11—24no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—24no—
163C2×C4×C11—22no—
164C2×C4×C11—42no—
165C2×C4×C11—41no—
166C2×C4×C11—42no—
167C2×C4×C11—41no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—81no—
177C2×C4×C11#12012yes—
178C2×C4×C11AGL(1,ℤ/8)14yes—
179C2×C4×C11C22×D412yes—
180C22⋊D11—48no—
181C22⋊D11—48no—
182C2×Dic11—24no—
183C2×Dic11—44no—
184D44—44no—
185D44—48no—
186D44—82no—
187D44—84no—
188C4×D11—416no—
189Dic22—48no—
190C11⋊C8—44no—
191C22×#41—221no—
192#537—114no—
193#537—224no—
194#537—222no—
195C2×C22⋊Q8—222no—
196C2×C22⋊Q8C2×D1111yescharacteristic
197C2×#121—112no—
198C2×#121—222no—
199C2×#121—221no—
200C22×C4⋊C4C2×D1111yescharacteristic
201#484—222no—
202#480—114no—
203#468—224no—
204#450—222no—
205#448—114no—
206#407—112no—
207#398C2×D1112yescomplemented
208#395C2×D1112yescomplemented
209#389—22no—
210#385—21no—
211#385—21no—
212C4×C22⋊C4C2×D1111yescharacteristic
213#327—118no—
214#324—114no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—44no—
223C22×C11#45612yes—
224C22×C11C2×#12011yescharacteristic
225C22×C11C2×AGL(1,ℤ/8)12yes—
226C2×D11—44no—
227C2×D11—44no—
228C2×D11—44no—
229C2×D11—88no—
230C4×C11—24no—
231C4×C11—22no—
232C4×C11—22no—
233C4×C11—44no—
234C4×C11—42no—
235C4×C11—81no—
236C4×C11—81no—
237Dic11—44no—
238C2×#41—224no—
239C2×#41—224no—
240C2×#41—448no—
241C22×Q8—221no—
242C22×Q8C22×D1111yescharacteristic
243C22×D4—112no—
244C22×D4—221no—
245C22×D4—221no—
246C22×D4—222no—
247C23×C4—222no—
248C23×C4C22⋊D1111yescharacteristic
249C23×C4C22⋊D1111yescharacteristic
250C23×C4C22×D1111yescharacteristic
251C2×SD16—224no—
252C2×M16—222no—
253C22⋊Q8—22no—
254C22⋊Q8—22no—
255C22⋊Q8—228no—
256C22⋊Q8—228no—
257#121—114no—
258#121—114no—
259#121—228no—
260#121—228no—
261#121—224no—
262#121—222no—
263#121—222no—
264#121—224no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—112no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4C22⋊D1112yes—
273C2×C4⋊C4C22×D1111yescharacteristic
274C2×C4⋊C4C22×D1112yes—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—222no—
278C2×C22⋊C4—222no—
279C2×C42—21no—
280#107—224no—
281#103—224no—
282#102—224no—
283C22⋊C8—114no—
284C22⋊C8—222no—
285#95—22no—
286#95—22no—
287#95C22×D1112yes—
288C2×C11—22no—
289C2×C11—22no—
290C2×C11—41no—
291C2×C11#300311yescharacteristic
292C2×C11C2×#45611yescharacteristic
293C2×C11#302611yescharacteristic
294D11—84no—
295C24—222no—
296C24C2×C22⋊D1111yescharacteristic
297#41—4416no—
298#41—448no—
299#41—448no—
300C2×Q8—22no—
301C2×Q8—81no—
302C2×Q8—224no—
303C2×Q8—444no—
304C2×D4—114no—
305C2×D4—224no—
306C2×D4—224no—
307C2×D4—224no—
308C2×D4—224no—
309C2×D4—222no—
310C2×D4—444no—
311C2×D4—448no—
312C2×D4—882no—
313C2×D4—882no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—24no—
317C22×C4—21no—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—81no—
323C22×C4—81no—
324C22×C4—228no—
325C22×C4—222no—
326C22×C4—448no—
327C22×C4D4×D1112yes—
328C22×C4D4×D1112yes—
329C22×C4C2×C22⋊D1112yes—
330C22×C4C2×C22⋊D1112yes—
331C22×C4C2×C22⋊D1111yescharacteristic
332C22×C4C23×D1111yescharacteristic
333SD16—884no—
334M16—882no—
335C2×C8—224no—
336C4⋊C4—24no—
337C4⋊C4—24no—
338C4⋊C4—22no—
339C4⋊C4—42no—
340C4⋊C4—44no—
341C4⋊C4—82no—
342C4⋊C4—114no—
343C4⋊C4—224no—
344C4⋊C4—222no—
345C22⋊C4—24no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—228no—
349C22⋊C4—224no—
350C22⋊C4—224no—
351C42—81no—
352C11#1832511yescharacteristic, complemented, Sylow
353C23—22no—
354C23—22no—
355C23—41no—
356C23—224no—
357C23—444no—
358C23—444no—
359C23—444no—
360C23#6699011yescharacteristic
361C23#6699011yescharacteristic
362C23C22×C22⋊D1111yescharacteristic
363Q8—44no—
364Q8—448no—
365D4—444no—
366D4—448no—
367D4—448no—
368D4—448no—
369D4—882no—
370D4—884no—
371C2×C4—24no—
372C2×C4—24no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—24no—
376C2×C4—22no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—81no—
390C2×C4—224no—
391C2×C4—4416no—
392C2×C4—444no—
393C2×C4#6699012yes—
394C2×C4#6700214yes—
395C2×C4C2×D4×D1112yes—
396C8—444no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—44no—
405C22—444no—
406C22—444no—
407C22—444no—
408C22—888no—
409C22#1062270812yes—
410C22C2×#6699011yescharacteristic
411C22C2×#6700212yes—
412C4—24no—
413C4—22no—
414C4—22no—
415C4—44no—
416C4—42no—
417C4—81no—
418C4—81no—
419C4—444no—
420C2—22no—
421C2—22no—
422C2—41no—
423C2—884no—
424C2#1307784211yescharacteristic
425C2C2×#1062270811yescharacteristic
426C2#1307801211yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2583C2
socleC22×C11C2×#120
prime radicalC2×#10623041C2
hypercenter#2583D11
hypocenterC11#18325
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2583

Complements

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

NH ≅ G/Ntype
2. #13079418C2semidirect
3. #13067618C2semidirect
4. #13067584C2semidirect
5. #13067131C2semidirect
6. #13066946C2semidirect
7. C11×#2583C2semidirect
18. C11×#398C22semidirect
19. C11×#395C22semidirect
24. #10622840C22semidirect
29. #10622580C22semidirect
30. #10622166C22semidirect
31. #10622089C22semidirect
142. #2583D11semidirect
207. #398C2×D11semidirect
208. #395C2×D11semidirect
352. C11#18325semidirect

Maximal subgroups

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

subgroupindex
C2×#106230412
#130794182
#130676182
#130675842
#130671312
#130669462
C11×#25832
#1832511