Finite Group Databasebeta

← #14810391

Subgroups — #14810391

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623219C211yesmaximal, characteristic
2C2×#10622405C212yesmaximal, complemented
3#13076965C211yesmaximal, characteristic
4#13069768C211yesmaximal, characteristic, complemented
5#13069767C211yesmaximal, characteristic, complemented
6#13069764C211yesmaximal, characteristic, complemented
7#13069575C212yesmaximal, complemented
8#13068927C212yesmaximal
9#13068925C212yesmaximal
10#13068373C211yesmaximal, characteristic
11C11×#2026C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13C2×#66999C2211yescharacteristic
14C2×#66997C2211yescharacteristic
15#10623219—28no—
16C2×#66950C2211yescharacteristic
17C2×#66949—22no—
18C2×#66945C2212yes—
19C2×#66941C2212yes—
20C2×#66940—22no—
21C2×C42×D11C2211yescharacteristic
22C2×#66923C2211yescharacteristic
23C2×C11×#103C2212yes—
24C11×#391C2211yescharacteristic
25C2×#66899C2212yes—
26C2×(C2×D11)⋊C8C2212yes—
27C2×#66880C2212yes—
28C2×C8×Dic11C2212yes—
29#10622589C2211yescharacteristic
30C2×#66874C2212yes—
31#10622542C2211yescharacteristic
32#10622405—28no—
33#10622280—22no—
34#10622260—22no—
35C11×#340C2212yes—
36C11×#336C2211yescharacteristic
37#10622189C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622162C2211yescharacteristic
41C22×Q8×C11C2311yescharacteristic
42C22×C4×D11D412yes—
43C22×C4×D11C2311yescharacteristic
44C22×Dic22—22no—
45C22×Dic22C2311yescharacteristic
46C22×C8×C11C2312yes—
47C11×#125—24no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4C2311yescharacteristic
50C2×C11×C4⋊C4C2312yes—
51C2×C42×C11C2311yescharacteristic
52#66999—24no—
53#66997—24no—
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11C2311yescharacteristic
59C2×C4⋊Dic11C2312yes—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—21no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11D412yes—
67C2×C4×Dic11C2311yescharacteristic
68C22×C11⋊C8C2312yes—
69#66950—24no—
70#66949—216no—
71#66945—24no—
72#66945—24no—
73#66941—24no—
74#66941D418yes—
75#66940—216no—
76C42×D11—24no—
77#66923—24no—
78C11×#103—24no—
79C11×#95—22no—
80#66899—24no—
81C11⋊#95—22no—
82(C2×D11)⋊C8—24no—
83#66880—24no—
84C8×Dic11—24no—
85#66874—24no—
86#25904—111nomaximal, Sylow
87C23×D11C2×D411yescharacteristic
88C2×Q8×C11—22no—
89C2×Q8×C11—22no—
90C2×Q8×C11—21no—
91C2×Q8×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2411yescharacteristic
97C22×Dic11—22no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11C2×D411yescharacteristic
101C22×Dic11C2×D412yes—
102C2×C4×D11—24no—
103C2×C4×D11—24no—
104C2×C4×D11—24no—
105C2×C4×D11—22no—
106C2×C4×D11—21no—
107C2×C4×D11—21no—
108C2×C4×D11#4114yes—
109C2×Dic22—28no—
110C2×Dic22—22no—
111C2×Dic22—22no—
112C2×Dic22—21no—
113C2×Dic22—21no—
114C2×Dic22—44no—
115C2×Dic22—44no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C11×C4⋊C4—28no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4C2×D414yes—
123C42×C11—22no—
124(C2×D11)⋊C4—28no—
125(C2×D11)⋊C4—42no—
126(C2×D11)⋊C4—42no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—42no—
130C4⋊Dic11C2×D414yes—
131Dic11⋊C4—28no—
132Dic11⋊C4—28no—
133Dic11⋊C4—44no—
134Dic11⋊C4—42no—
135Dic11⋊C4—44no—
136C4×Dic11—28no—
137C4×Dic11—24no—
138C4×Dic11C2×D414yes—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142C2×#533—111no—
143C2×#487—112no—
144#2857—111no—
145#2026—111no—
146#2026—111no—
147#2026—111no—
148#2026D1111yescharacteristic, complemented
149#1990—112no—
150#1873—112no—
151#1873—112no—
152C4×C22⋊C8—111no—
153C23×C11C22×D411yescharacteristic
154C22×D11—21no—
155C22×D11—21no—
156C22×D11—22no—
157C22×D11—22no—
158C22×D11#12412yes—
159Q8×C11—42no—
160Q8×C11—42no—
161C2×C4×C11—22no—
162C2×C4×C11—24no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11C22×D412yes—
173C2×C4×C11C2×#4112yes—
174C2×C4×C112−1+411yescharacteristic
175C2×C4×C112−1+411yescharacteristic
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—24no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—42no—
186C2×Dic11#12014yes—
187C2×Dic11#12412yes—
188C2×Dic11#13514yes—
189C2×Dic11#13714yes—
190C4×D11—24no—
191C4×D11—24no—
192C4×D11—48no—
193Dic22—416no—
194Dic22—42no—
195Dic22—42no—
196C8×C11—42no—
197C11⋊C8—42no—
198#533—228no—
199C2×C4⋊Q8—112no—
200C2×C4⋊Q8—111no—
201C2×#125—111no—
202C2×#125C2×D1111yescharacteristic
203C2×C22⋊Q8—111no—
204C2×C22⋊Q8—111no—
205C2×C22⋊Q8—222no—
206C2×C4×Q8—222no—
207C2×#117—112no—
208C22×C42—111no—
209#487—228no—
210C2×#103—112no—
211C2×#103—112no—
212C2×#103—112no—
213C2×#103C2×D1112yes—
214C2×C22⋊C8—112no—
215C2×C4×C8—112no—
216#391—111no—
217#391C2×D1111yescharacteristic
218#389—222no—
219#384—111no—
220#380—222no—
221#340—112no—
222#340—112no—
223#340—112no—
224#340C2×D1112yes—
225#336—111no—
226#336C2×D1111yescharacteristic
227C22×C11C2×#12011yescharacteristic
228C22×C11C2×#12411yescharacteristic
229C22×C11#53611yescharacteristic
230C22×C11C2×#13512yes—
231C22×C11C2×#13712yes—
232C2×D11—22no—
233C2×D11—22no—
234C2×D11—22no—
235C2×D11—42no—
236C2×D11—42no—
237C4×C11—42no—
238C4×C11—44no—
239C4×C11—81no—
240C4×C11—81no—
241C4×C11#54812yes—
242C4×C11#54812yes—
243Dic11—22no—
244Dic11—44no—
245Dic11—81no—
246Dic11—81no—
247Dic11#45218yes—
248C22×Q8—111no—
249C22×Q8—222no—
250C22×Q8C22×D1111yescharacteristic
251C23×C4—111no—
252C23×C4—112no—
253C22×C8—112no—
254C22×C8C22×D1112yes—
255C4⋊Q8—118no—
256C4⋊Q8—224no—
257C4⋊Q8—224no—
258#125—24no—
259#125—224no—
260C22⋊Q8—2216no—
261C22⋊Q8—224no—
262C22⋊Q8—224no—
263C4×Q8—2216no—
264#117—224no—
265#117—224no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—112no—
268C2×C4⋊C4—111no—
269C2×C4⋊C4—222no—
270C2×C4⋊C4—222no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—222no—
274C2×C4⋊C4—222no—
275C2×C4⋊C4C22×D1111yescharacteristic
276C2×C4⋊C4C22×D1112yes—
277C2×C22⋊C4—222no—
278C2×C22⋊C4—221no—
279C2×C22⋊C4—221no—
280C2×C42—111no—
281C2×C42—112no—
282C2×C42—224no—
283C2×C42—222no—
284C2×C42C22×D1111yescharacteristic
285#103—24no—
286#103—224no—
287#103—224no—
288#103—224no—
289C22⋊C8—224no—
290C4×C8—224no—
291#95—22no—
292#95—222no—
293C2×C11#243611yescharacteristic
294C2×C11C2×#45212yes—
295C2×C11#313111yescharacteristic
296C2×C11#313911yescharacteristic
297C2×C11#323112yes—
298D11—42no—
299C24—111no—
300C2×Q8—22no—
301C2×Q8—21no—
302C2×Q8—22no—
303C2×Q8—21no—
304C2×Q8—228no—
305C2×Q8—222no—
306C2×Q8—221no—
307C2×Q8—222no—
308C2×Q8—221no—
309C2×Q8—444no—
310C2×Q8—444no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—112no—
315C22×C4—111no—
316C22×C4—114no—
317C22×C4—224no—
318C22×C4—224no—
319C22×C4—224no—
320C22×C4—222no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—222no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4D4×D1112yes—
327C22×C4C23×D1111yescharacteristic
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—222no—
332C2×C8—222no—
333C2×C8—222no—
334C4⋊C4—28no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—114no—
338C4⋊C4—228no—
339C4⋊C4—228no—
340C4⋊C4—222no—
341C4⋊C4—222no—
342C4⋊C4—442no—
343C4⋊C4—442no—
344C4⋊C4—444no—
345C4⋊C4—444no—
346C4⋊C4D4×D1114yes—
347C22⋊C4—228no—
348C22⋊C4—442no—
349C22⋊C4—442no—
350C42—22no—
351C42—114no—
352C42—224no—
353C42—228no—
354C11#2590411yescharacteristic, complemented, Sylow
355C23—112no—
356C23—222no—
357C23—222no—
358C23—221no—
359C23—221no—
360C23C2×D4×D1111yescharacteristic
361Q8—42no—
362Q8—42no—
363Q8—4416no—
364Q8—442no—
365Q8—442no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—24no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—114no—
378C2×C4—114no—
379C2×C4—114no—
380C2×C4—112no—
381C2×C4—221no—
382C2×C4—221no—
383C2×C4—224no—
384C2×C4—224no—
385C2×C4—224no—
386C2×C4—448no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4C2×D4×D1112yes—
395C2×C4#6704011yescharacteristic
396C2×C4#41×D1112yes—
397C2×C4#6704311yescharacteristic
398C8—42no—
399C8—442no—
400C22—222no—
401C22—222no—
402C22—222no—
403C22—442no—
404C22—442no—
405C22D11×#12011yescharacteristic
406C22#1062315911yescharacteristic
407C22D11×#12411yescharacteristic
408C22D11×#13512yes—
409C22D11×#13712yes—
410C4—42no—
411C4—44no—
412C4—81no—
413C4—81no—
414C4—118no—
415C4—222no—
416C4—444no—
417C4—881no—
418C4—881no—
419C4#1062316412yes—
420C4#1062320812yes—
421C2—442no—
422C2#1307226911yescharacteristic
423C2D11×#45212yes—
424C2#1307893711yescharacteristic
425C2#1307899511yescharacteristic
426C2#1307977412yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2026C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2026D11
hypocenterC11#25904
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2026

Complements

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

NH ≅ G/Ntype
2. C2×#10622405C2semidirect
4. #13069768C2semidirect
5. #13069767C2semidirect
6. #13069764C2semidirect
7. #13069575C2semidirect
11. C11×#2026C2semidirect
148. #2026D11semidirect
354. C11#25904semidirect

Maximal subgroups

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

subgroupindex
C2×#106232192
C2×#106224052
#130769652
#130697682
#130697672
#130697642
#130695752
#130689272
#130689252
#130683732
C11×#20262
#2590411