Finite Group Databasebeta

← #14810416

Subgroups — #14810416

Order 2816.

1116 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C211yesmaximal, characteristic, complemented
2C2×#10622381C212yesmaximal, complemented
3#13076916C211yesmaximal, characteristic
4#13069768C211yesmaximal, characteristic, complemented
5#13069764C211yesmaximal, characteristic, complemented
6#13069762C211yesmaximal, characteristic, complemented
7#13069579C212yesmaximal, complemented
8#13068930C212yesmaximal
9#13068922C212yesmaximal, complemented
10#13068373C211yesmaximal, characteristic, complemented
11C11×#2025C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13C2×#66991C2211yescharacteristic
14C2×#66989C2211yescharacteristic
15D11×#125—28no—
16C2×#66950C2211yescharacteristic
17C2×C4⋊C4×D11—22no—
18C2×C4⋊C4×D11C2212yes—
19C2×#66943C2212yes—
20C2×#66942—22no—
21C2×C42×D11C2211yescharacteristic
22C2×#66923C2211yescharacteristic
23C2×C11×#102C2212yes—
24C11×#390C2211yescharacteristic
25C2×#66896C2212yes—
26C2×(C2×D11)⋊C8C2212yes—
27C2×#66880C2212yes—
28C2×C8×Dic11C2212yes—
29#10622590C2211yescharacteristic
30C2×#66874C2212yes—
31#10622569—22no—
32#10622564—22no—
33#10622542C2211yescharacteristic
34#10622381—28no—
35C11×#340C2212yes—
36C11×#336C2211yescharacteristic
37#10622189C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622162C2211yescharacteristic
41C22×D4×C11C2311yescharacteristic
42C22×C22⋊D11—21no—
43C22×C4×D11—22no—
44C22×C4×D11D412yes—
45C22×C4×D11C2311yescharacteristic
46C22×Dic22C2311yescharacteristic
47C22×C8×C11C2312yes—
48C11×#125—24no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C22⋊C4—22no—
53C2×C42×C11C2311yescharacteristic
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—21no—
56#66991—24no—
57#66989—24no—
58C2×(C2×D11)⋊C4—21no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2312yes—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×C4×Dic11D412yes—
67C2×C4×Dic11C2311yescharacteristic
68C22×C11⋊C8C2312yes—
69#66950—24no—
70C4⋊C4×D11—216no—
71C4⋊C4×D11—24no—
72C4⋊C4×D11—24no—
73#66943—24no—
74#66943D418yescomplemented
75#66942—216no—
76C42×D11—24no—
77#66923—24no—
78C11×#102—24no—
79#66896—24no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82(C2×D11)⋊C8—24no—
83#66880—24no—
84C8×Dic11—24no—
85#66874—24no—
86#25907—111nomaximal, Sylow
87C24×C11—21no—
88C23×D11C2×D411yescharacteristic
89C2×D4×C11—22no—
90C2×D4×C11—22no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—21no—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2411yescharacteristic
97C2×C22⋊D11—42no—
98C2×C22⋊D11—44no—
99C22×Dic11—22no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11C2×D412yes—
103C22×Dic11C2×D411yescharacteristic
104C2×C4×D11—28no—
105C2×C4×D11—24no—
106C2×C4×D11—24no—
107C2×C4×D11—22no—
108C2×C4×D11—21no—
109C2×C4×D11—21no—
110C2×C4×D11—42no—
111C2×C4×D11—44no—
112C2×C4×D11—44no—
113C2×C4×D11#4114yes—
114C2×Dic22—22no—
115C2×Dic22—22no—
116C2×Dic22—21no—
117C2×Dic22—21no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C11×C4⋊C4—28no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4C2×D414yes—
125C11×C22⋊C4—44no—
126C42×C11—22no—
127C22⋊Dic11—44no—
128C22⋊Dic11—42no—
129(C2×D11)⋊C4—42no—
130C4⋊Dic11—28no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133C4⋊Dic11—42no—
134C4⋊Dic11C2×D414yes—
135Dic11⋊C4—28no—
136Dic11⋊C4—28no—
137Dic11⋊C4—28no—
138C4×Dic11—24no—
139C4×Dic11C2×D414yes—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C22×#125—111no—
144C2×#488—112no—
145#2850—111no—
146#2026—111no—
147#2026—111no—
148#2025—111no—
149#2025D1111yescharacteristic, complemented
150#1991—112no—
151#1874—112no—
152#1872—112no—
153C4×C22⋊C8—111no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—42no—
158C23×C11—42no—
159C23×C11C22×D411yescharacteristic
160C22×D11—21no—
161C22×D11—21no—
162C22×D11—22no—
163C22×D11#12412yes—
164C22×D11#13514yes—
165D4×C11—42no—
166D4×C11—42no—
167C2×C4×C11—22no—
168C2×C4×C11—24no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11C22×D412yes—
176C2×C4×C11C2×#4112yes—
177C2×C4×C112−1+411yescharacteristic
178C2×C4×C112−1+411yescharacteristic
179C22⋊D11—84no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—24no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—42no—
192C2×Dic11#12014yes—
193C2×Dic11#12412yes—
194C4×D11—24no—
195C4×D11—24no—
196C4×D11—48no—
197C4×D11—416no—
198Dic22—42no—
199Dic22—42no—
200C8×C11—42no—
201C11⋊C8—42no—
202C2×#125—112no—
203C2×#125—111no—
204C2×#125—222no—
205C2×#125—228no—
206C2×#125C2×D1111yescharacteristic
207C2×#124—111no—
208C2×C22⋊Q8—111no—
209C2×#121—111no—
210C22×C4⋊C4—112no—
211C22×C4⋊C4—222no—
212C22×C42—111no—
213#488—228no—
214C2×#103—112no—
215C2×#103—112no—
216C2×#102—112no—
217C2×#102C2×D1112yes—
218C2×C22⋊C8—112no—
219C2×C4×C8—112no—
220#391—111no—
221#390C2×D1111yescharacteristic
222#388—222no—
223#386—222no—
224#382—111no—
225#340—112no—
226#340—112no—
227#340—112no—
228#340C2×D1112yes—
229#336—111no—
230#336C2×D1111yescharacteristic
231C22×C11—81no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—82no—
235C22×C11—82no—
236C22×C11C2×#12011yescharacteristic
237C22×C11C2×#12411yescharacteristic
238C22×C11#53611yescharacteristic
239C22×C11C2×#13512yes—
240C22×C11#57512yes—
241C2×D11—22no—
242C2×D11—22no—
243C2×D11—24no—
244C2×D11—24no—
245C2×D11#48814yescomplemented
246C4×C11—42no—
247C4×C11—44no—
248C4×C11—81no—
249C4×C11#54812yes—
250C4×C11#54812yes—
251Dic11—22no—
252Dic11—24no—
253Dic11—44no—
254Dic11—81no—
255Dic11—81no—
256C22×Q8—111no—
257C22×D4—221no—
258C22×D4C22×D1111yescharacteristic
259C23×C4—111no—
260C23×C4—112no—
261C23×C4—222no—
262C22×C8—112no—
263C22×C8C22×D1112yes—
264#125—24no—
265#125—118no—
266#125—224no—
267#125—224no—
268#125—2216no—
269#124—224no—
270C22⋊Q8—224no—
271#121—224no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—112no—
274C2×C4⋊C4—111no—
275C2×C4⋊C4—224no—
276C2×C4⋊C4—2216no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4—222no—
279C2×C4⋊C4—222no—
280C2×C4⋊C4—222no—
281C2×C4⋊C4—224no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4C22×D1111yescharacteristic
284C2×C4⋊C4C22×D1112yes—
285C2×C22⋊C4—22no—
286C2×C22⋊C4—221no—
287C2×C22⋊C4—221no—
288C2×C22⋊C4—222no—
289C2×C42—111no—
290C2×C42—112no—
291C2×C42—224no—
292C2×C42C22×D1111yescharacteristic
293#103—224no—
294#103—224no—
295#102—24no—
296#102—224no—
297C22⋊C8—224no—
298C4×C8—224no—
299#95—222no—
300#95—222no—
301C2×C11—161no—
302C2×C11#243611yescharacteristic
303C2×C11#300212yes—
304C2×C11C2×#48811yescharacteristic
305C2×C11#314211yescharacteristic
306C2×C11#323212yes—
307D11—24no—
308C24—21no—
309C24—111no—
310C2×Q8—222no—
311C2×Q8—221no—
312C2×Q8—222no—
313C2×Q8—221no—
314C2×D4—22no—
315C2×D4—21no—
316C2×D4—22no—
317C2×D4—21no—
318C2×D4—442no—
319C2×D4—444no—
320C22×C4—22no—
321C22×C4—21no—
322C22×C4—112no—
323C22×C4—111no—
324C22×C4—114no—
325C22×C4—224no—
326C22×C4—224no—
327C22×C4—228no—
328C22×C4—222no—
329C22×C4—221no—
330C22×C4—221no—
331C22×C4—222no—
332C22×C4—221no—
333C22×C4—221no—
334C22×C4—442no—
335C22×C4—444no—
336C22×C4—444no—
337C22×C4D4×D1112yes—
338C22×C4C23×D1111yescharacteristic
339C2×C8—22no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—222no—
343C2×C8—222no—
344C2×C8—222no—
345C4⋊C4—28no—
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—114no—
349C4⋊C4—228no—
350C4⋊C4—228no—
351C4⋊C4—228no—
352C4⋊C4—228no—
353C4⋊C4—222no—
354C4⋊C4—222no—
355C4⋊C4—442no—
356C4⋊C4D4×D1114yes—
357C22⋊C4—44no—
358C22⋊C4—442no—
359C22⋊C4—442no—
360C22⋊C4—444no—
361C42—22no—
362C42—114no—
363C42—224no—
364C11#2590711yescharacteristic, complemented, Sylow
365C23—42no—
366C23—42no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—114no—
371C23—112no—
372C23—222no—
373C23—221no—
374C23—221no—
375C23C2×D4×D1111yescharacteristic
376Q8—442no—
377Q8—442no—
378D4—42no—
379D4—42no—
380D4—884no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—24no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—114no—
390C2×C4—112no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—221no—
394C2×C4—221no—
395C2×C4—224no—
396C2×C4—224no—
397C2×C4—224no—
398C2×C4—448no—
399C2×C4—4416no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4C2×D4×D1112yes—
408C2×C4#6704011yescharacteristic
409C2×C4#41×D1112yes—
410C2×C4#6704311yescharacteristic
411C8—42no—
412C8—442no—
413C22—82no—
414C22—81no—
415C22—81no—
416C22—82no—
417C22—81no—
418C22—114no—
419C22—224no—
420C22—222no—
421C22—224no—
422C22—222no—
423C22D11×#12011yescharacteristic
424C22#1062315911yescharacteristic
425C22D11×#12411yescharacteristic
426C22D11×#13512yes—
427C22#1062330412yes—
428C4—42no—
429C4—44no—
430C4—81no—
431C4—224no—
432C4—222no—
433C4—444no—
434C4—881no—
435C4—881no—
436C4#1062316412yes—
437C4#1062320812yes—
438C2—161no—
439C2—224no—
440C2#1307226911yescharacteristic
441C2#1307783112yes—
442C2D11×#48811yescharacteristic
443C2#1307901511yescharacteristic
444C2#1307978212yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2025C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenter#2025D11
hypocenterC11#25907
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2025

Complements

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

NH ≅ G/Ntype
1. C2×D11×#125C2semidirect
2. C2×#10622381C2semidirect
4. #13069768C2semidirect
5. #13069764C2semidirect
6. #13069762C2semidirect
7. #13069579C2semidirect
9. #13068922C2semidirect
10. #13068373C2semidirect
11. C11×#2025C2semidirect
74. #66943D4semidirect
149. #2025D11semidirect
245. C2×D11#488semidirect
364. C11#25907semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
C2×#106223812
#130769162
#130697682
#130697642
#130697622
#130695792
#130689302
#130689222
#130683732
C11×#20252
#2590711