Finite Group Databasebeta

← #14767632

Subgroups — #14767632

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622699C211yesmaximal, characteristic
2#13071327C211yesmaximal, characteristic
3#13069425C211yesmaximal, characteristic
4#13069419C211yesmaximal, characteristic, complemented
5#13068971C212yesmaximal
6#13068960C212yesmaximal, complemented
7#13068957C212yesmaximal, complemented
8#13068953C212yesmaximal
9#13068749C211yesmaximal, characteristic, complemented
10#13068368C211yesmaximal, characteristic, complemented
11C11×#2327C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C22×#4326C2212yes—
15C22×#4325C2212yes—
16C2×#66928C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C11×#391C2212yes—
20C11×#387—22no—
21C11×#387—22no—
22C11×#382C2211yescharacteristic
23C11×#376C2211yescharacteristic
24C2×#66899C2212yes—
25C2×#66899C2212yes—
26#10622699C418yescomplemented
27C2×#66874C2212yes—
28C2×#66873C2212yes—
29#10622552C2211yescharacteristic
30#10622548C2211yescharacteristic
31#10622542C2211yescharacteristic
32C2×#66867C2211yescharacteristic
33C2×C4×C11⋊C8C2211yescharacteristic
34#10622283—22no—
35#10622281—22no—
36#10622167C2212yes—
37#10622167C2212yes—
38#10622162C2212yes—
39#10622162C2212yes—
40C22×Q8×C11C2312yes—
41C22×D44C2311yescharacteristic
42C22×C4×D11—21no—
43C22×Dic22C2311yescharacteristic
44C11×C4⋊Q8—22no—
45C11×C4⋊Q8C2×C414yescomplemented
46C4×Q8×C11—42no—
47C4×Q8×C11—42no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4C2312yes—
51C2×C42×C11—22no—
52C2×C42×C11C2311yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×#4326—42no—
56C2×#4326—42no—
57C2×#4326C2×C418yescomplemented
58C2×#4325—42no—
59C2×#4325—42no—
60C2×#4325C2×C418yes—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—21no—
63C2×(C2×D11)⋊C4—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×Dic11⋊C4—21no—
68C2×C4×Dic11—21no—
69C22×C11⋊C8C2312yes—
70C22×C11⋊C8C2312yes—
71#66928—22no—
72#66928C2×C414yes—
73C4×D44—42no—
74C4×Dic22—42no—
75C11×#95—22no—
76C11×#95—22no—
77C11×#95—22no—
78C11×#95D412yes—
79C11×#95D412yes—
80#66899—42no—
81#66899—42no—
82C11⋊#95—22no—
83#66874—42no—
84#66873—42no—
85#66867C2×C414yescomplemented
86C4×C11⋊C8—22no—
87#22278—111nomaximal, Sylow
88C23×D11—21no—
89C2×Q8×C11—22no—
90C2×Q8×C11—22no—
91C2×Q8×C11—22no—
92C2×Q8×C11—22no—
93C2×Q8×C11—22no—
94C2×Q8×C11C22×C414yes—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C2×D44—21no—
106C2×D44—22no—
107C2×D44—22no—
108C2×D44C22×C412yes—
109C2×C4×D11—42no—
110C2×C4×D11—82no—
111C2×Dic22—21no—
112C2×Dic22—22no—
113C2×Dic22—22no—
114C2×Dic22C22×C412yes—
115C11×C4⋊C4—28no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—44no—
119C42×C11—22no—
120C42×C11—22no—
121C42×C11—44no—
122C42×C11C22×C412yes—
123C42×C11#4112yes—
124#4326—48no—
125#4325—48no—
126(C2×D11)⋊C4—28no—
127(C2×D11)⋊C4—42no—
128(C2×D11)⋊C4—82no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11—82no—
132Dic11⋊C4—42no—
133C4×Dic11—42no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8C22×C414yes—
140C2×#497—111no—
141#2327D1111yescharacteristic, complemented
142#2326—111no—
143#1958—111no—
144#1956—111no—
145#1880—112no—
146#1878—112no—
147#1878—112no—
148#1877—112no—
149#1836—111no—
150#1746—111no—
151C23×C11C22×D411yescharacteristic
152C22×D11—22no—
153C22×D11—41no—
154C22×D11—41no—
155C22×D11—42no—
156C22×D11—42no—
157Q8×C11—24no—
158Q8×C11—24no—
159Q8×C11—42no—
160Q8×C11—42no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—24no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11C4×D414yes—
177C2×C4×C11C23×C411yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C2×C4×C11H(5,𝔽2)12yes—
180C2×C4×C11H(5,𝔽2)12yes—
181C2×Dic11—22no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188D44—24no—
189D44—42no—
190C4×D11—84no—
191Dic22—24no—
192Dic22—42no—
193C11⋊C8—24no—
194C11⋊C8—42no—
195C22×Q16—112no—
196C22×SD16—112no—
197C2×C4⋊Q8C2×D1111yescharacteristic
198C2×#124—111no—
199C2×C4×Q8—111no—
200C2×C4×Q8C2×D1112yes—
201C2×C4×D4—111no—
202#497—118no—
203C2×#103—112no—
204C2×#103—112no—
205C2×#103—112no—
206C2×#102—112no—
207C2×#97—111no—
208C2×C4×C8—111no—
209#391—111no—
210#391C2×D1112yes—
211#390—111no—
212#388—222no—
213#387—22no—
214#387—22no—
215#385—222no—
216#384—111no—
217#382C2×D1111yescharacteristic
218#376C2×D1111yescharacteristic
219#340—112no—
220#340—112no—
221#336—112no—
222#336—112no—
223C22×C11C2×C4×D411yescharacteristic
224C22×C11#53511yescharacteristic
225C22×C11#53511yescharacteristic
226C22×C11#57712yes—
227C22×C11#57812yes—
228C2×D11—42no—
229C2×D11—44no—
230C2×D11—81no—
231C2×D11—81no—
232C2×D11—82no—
233C4×C11—24no—
234C4×C11—44no—
235C4×C11—41no—
236C4×C11—41no—
237C4×C11—42no—
238C4×C11—82no—
239C4×C11#51812yes—
240C4×C11#54012yes—
241Dic11—42no—
242Dic11—81no—
243Dic11—81no—
244C22×Q8—111no—
245C22×Q8C22×D1112yes—
246C22×D4—111no—
247C23×C4—221no—
248C2×Q16—118no—
249C2×Q16—442no—
250C2×Q16—442no—
251C2×SD16—118no—
252C2×SD16—442no—
253C2×SD16—442no—
254C22×C8—112no—
255C22×C8—112no—
256C4⋊Q8—22no—
257C4⋊Q8C4×D1114yescomplemented
258#124—114no—
259#124—222no—
260C4×Q8—42no—
261C4×Q8—42no—
262C4×Q8—442no—
263C4×D4—442no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—111no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—222no—
270C2×C4⋊C4C22×D1112yes—
271C2×C22⋊C4—222no—
272C2×C22⋊C4—221no—
273C2×C22⋊C4—222no—
274C2×C42—22no—
275C2×C42—221no—
276C2×C42C22×D1111yescharacteristic
277C2×C42C22×D1111yescharacteristic
278C2×C42C22×D1111yescharacteristic
279#103—442no—
280#103—442no—
281#103—442no—
282#102—442no—
283#97—114no—
284C4×C8—222no—
285#95—22no—
286#95—22no—
287#95—22no—
288#95—222no—
289#95C22⋊D1112yes—
290#95C22⋊D1112yes—
291C2×C11#232811yescharacteristic
292C2×C11#294712yes—
293C2×C11#322211yescharacteristic
294C2×C11#322311yescharacteristic
295C2×C11#322512yes—
296D11—82no—
297C24—221no—
298C2×Q8—22no—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—112no—
304C2×Q8—221no—
305C2×Q8—222no—
306C2×Q8—222no—
307C2×Q8C2×C4×D1114yes—
308C2×D4—112no—
309C2×D4—221no—
310C2×D4—222no—
311C2×D4—222no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—442no—
318C22×C4—882no—
319C22×C4C2×C22⋊D1111yescharacteristic
320C22×C4C2×C22⋊D1111yescharacteristic
321C22×C4C2×C22⋊D1112yes—
322C22×C4C2×C22⋊D1112yes—
323C22×C4C23×D1111yescharacteristic
324Q16—448no—
325SD16—448no—
326C2×C8—114no—
327C2×C8—222no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8—222no—
331C2×C8—222no—
332C4⋊C4—28no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—44no—
336C4⋊C4—222no—
337C4⋊C4—222no—
338C4⋊C4—442no—
339C4⋊C4—882no—
340C22⋊C4—228no—
341C22⋊C4—442no—
342C22⋊C4—882no—
343C42—22no—
344C42—22no—
345C42—44no—
346C42—442no—
347C42C2×C4×D1112yes—
348C42#433912yes—
349C11#2227811yescharacteristic, complemented, Sylow
350C23—222no—
351C23—441no—
352C23—441no—
353C23—442no—
354C23—442no—
355C23C22×C22⋊D1111yescharacteristic
356Q8—24no—
357Q8—24no—
358Q8—42no—
359Q8—42no—
360Q8—224no—
361Q8—442no—
362D4—224no—
363D4—442no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—24no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—222no—
380C2×C4—441no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—442no—
385C2×C4—442no—
386C2×C4—884no—
387C2×C4C4×C22⋊D1114yes—
388C2×C4C22×C4×D1111yescharacteristic
389C2×C4C2×#433911yescharacteristic
390C2×C4#6703712yes—
391C2×C4#6704212yes—
392C8—224no—
393C8—442no—
394C22—444no—
395C22—442no—
396C22—881no—
397C22—881no—
398C22—882no—
399C22C2×C4×C22⋊D1111yescharacteristic
400C22#1062333611yescharacteristic
401C22#1062336111yescharacteristic
402C22#1062336812yes—
403C22#1062336912yes—
404C4—24no—
405C4—41no—
406C4—41no—
407C4—42no—
408C4—44no—
409C4—82no—
410C4—442no—
411C4—881no—
412C4—881no—
413C4#1062307612yes—
414C4#1062309312yes—
415C2—882no—
416C2#1307133811yescharacteristic
417C2#1307745912yes—
418C2#1307968211yescharacteristic
419C2#1307969311yescharacteristic
420C2#1307972512yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2327C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#2327D11
hypocenterC11#22278
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2327

Complements

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

NH ≅ G/Ntype
4. #13069419C2semidirect
6. #13068960C2semidirect
7. #13068957C2semidirect
9. #13068749C2semidirect
10. #13068368C2semidirect
11. C11×#2327C2semidirect
26. #10622699C4semidirect
45. C11×C4⋊Q8C2×C4semidirect
57. C2×#4326C2×C4semidirect
85. #66867C2×C4semidirect
141. #2327D11semidirect
257. C4⋊Q8C4×D11semidirect
349. C11#22278semidirect

Maximal subgroups

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

subgroupindex
C2×#106226992
#130713272
#130694252
#130694192
#130689712
#130689602
#130689572
#130689532
#130687492
#130683682
C11×#23272
#2227811