Finite Group Databasebeta

← #14770922

Subgroups — #14770922

Order 2816.

1002 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66880C211yesmaximal, characteristic
2#13071487C211yesmaximal, characteristic
3#13071448C211yesmaximal, characteristic
4#13069290C212yesmaximal, complemented
5#13069249C212yesmaximal, complemented
6#13068881C212yesmaximal, complemented
7#13068700C211yesmaximal, characteristic
8#13068550C211yesmaximal, characteristic
9#13068435C212yesmaximal, complemented
10C8×C22⋊Dic11C211yesmaximal, characteristic
11C11×#1807C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C2×#66940C2212yes—
16C2×#66930—21no—
17C2×C11×#106C2212yes—
18C11×#380C2211yescharacteristic
19C11×#380C2211yescharacteristic
20C4×C22⋊Dic11C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2211yescharacteristic
22C2×#66880C418yescomplemented
23C2×#66880C2211yescharacteristic
24C2×#66880C2211yescharacteristic
25C2×#66880C2211yescharacteristic
26C2×#66880C2211yescharacteristic
27C2×C8×Dic11C2212yes—
28C4⋊C4×Dic11C2212yes—
29#10622587C2212yes—
30#10622586C2212yes—
31C2×#66874C2212yes—
32C2×#66874C2212yes—
33#10622556—21no—
34#10622555—21no—
35C22⋊C4×Dic11—21no—
36#10622267—22no—
37#10622259—22no—
38C11×#340C2212yes—
39#10622188C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C23×C4×C11C2311yescharacteristic
43C23×Dic11—21no—
44C23×Dic11—21no—
45C22×Dic22—24no—
46C22×Dic22—21no—
47C22×Dic22—22no—
48C22×Dic22—42no—
49C22×Dic22C2×C414yes—
50C22×Dic22C2311yescharacteristic
51C22×Dic22C2311yescharacteristic
52C22×C8×C11—42no—
53C22×C8×C11C2×C414yes—
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—21no—
60C2×C22⋊Dic11D411yescharacteristic
61C2×C22⋊Dic11D411yescharacteristic
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11C2×C414yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11—22no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11C2312yes—
72C22×C11⋊C8C2312yes—
73#66940—24no—
74#66940—42no—
75#66930—44no—
76C11×#106—42no—
77C11×#95—21no—
78C11×#95—21no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95D412yes—
84C22⋊(C11⋊C8)—22no—
85#66880C2×C414yes—
86#66880C2×C414yes—
87#66880C2×C414yes—
88#66880C2×C414yes—
89C8×Dic11—42no—
90#66874—24no—
91#66874—42no—
92#22571—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11C22×C412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4112yes—
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—24no—
103C22×Dic11—24no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—44no—
109C22×Dic11—42no—
110C22×Dic11—42no—
111C22×Dic11C2×D412yes—
112C22×Dic11C2×D412yes—
113C2×Dic22—28no—
114C2×Dic22—24no—
115C2×Dic22—21no—
116C2×Dic22—22no—
117C2×Dic22—21no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22—44no—
121C2×Dic22—48no—
122C2×Dic22—44no—
123C2×Dic22C22×C412yes—
124C2×Dic22C22×C412yes—
125C2×Dic22#4114yes—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—44no—
129C2×C8×C11C22×C412yes—
130C2×C8×C11C22×C412yes—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C22⋊C4—42no—
136C11×C22⋊C4—42no—
137C22⋊Dic11—22no—
138C22⋊Dic11SD1614yes—
139C4⋊Dic11—24no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11C22×C412yes—
143C4⋊Dic11C22×C412yes—
144Dic11⋊C4—44no—
145Dic11⋊C4—44no—
146C4×Dic11—22no—
147C4×Dic11—22no—
148C4×Dic11—44no—
149C4×Dic11—44no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C22×#103—111no—
154#2344—111no—
155Q8×C22⋊C4—111no—
156#1933—112no—
157#1927—112no—
158#1865—112no—
159#1823—111no—
160#1807D1111yescharacteristic
161#1787—111no—
162C4×#103—112no—
163C8×C22⋊C4—111no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11C4×D412yes—
167C23×C11C2×SD1612yes—
168C23×C11#13512yes—
169C23×C11C22×D411yescharacteristic
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11C4×D412yes—
181C2×C4×C11C23×C411yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C2×C4×C11C2×#4112yes—
184C2×C4×C11H(5,𝔽2)12yes—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—24no—
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—48no—
196C2×Dic11—42no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—48no—
202C2×Dic11C2×SD1614yes—
203Dic22—22no—
204Dic22—24no—
205Dic22—22no—
206Dic22—22no—
207Dic22—48no—
208Dic22—42no—
209Dic22#11714yescomplemented
210C8×C11—22no—
211C8×C11—22no—
212C11⋊C8—42no—
213C23×Q8—111no—
214C23×C8C2×D1111yescharacteristic
215C2×C4×Q8—112no—
216C2×#117—221no—
217C22×C4⋊C4—111no—
218C2×#106C2×D1112yes—
219C2×#103—111no—
220C2×#103—111no—
221C2×#103—111no—
222C2×#103—111no—
223C2×#103—118no—
224C2×#103—112no—
225C2×#103—112no—
226C2×C22⋊C8—111no—
227C2×C4×C8—112no—
228#391—112no—
229#391—222no—
230#389—112no—
231#387—222no—
232#381—221no—
233#380—221no—
234#380C2×D1111yescharacteristic
235#380C2×D1111yescharacteristic
236C4×C4⋊C4—112no—
237C4×C22⋊C4—111no—
238C4×C22⋊C4—221no—
239#340—112no—
240#340—112no—
241#340C2×D1112yes—
242#336—112no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—24no—
246C22×C11—24no—
247C22×C11C4×SD1614yes—
248C22×C11C2×C4×D411yescharacteristic
249C22×C11#54612yes—
250C22×C11C22×SD1611yescharacteristic
251C22×C11C2×#13511yescharacteristic
252C22×C11#57812yes—
253C4×C11—22no—
254C4×C11—82no—
255C4×C11—82no—
256C4×C11C2×#11711yescharacteristic
257C4×C11#51811yescharacteristic
258C4×C11#55112yes—
259Dic11—24no—
260Dic11—24no—
261Dic11—42no—
262Dic11—42no—
263Dic11—42no—
264Dic11—42no—
265C22×Q8—114no—
266C22×Q8—111no—
267C22×Q8—111no—
268C22×Q8—224no—
269C22×Q8—221no—
270C22×Q8—222no—
271C22×Q8—442no—
272C23×C4—221no—
273C23×C4—221no—
274C23×C4C22×D1111yescharacteristic
275C22×C8—42no—
276C22×C8—112no—
277C22×C8C4×D1114yes—
278C22×C8C22×D1111yescharacteristic
279C22×C8C22×D1111yescharacteristic
280C4×Q8—224no—
281C4×Q8—442no—
282#117—444no—
283C2×C4⋊C4—114no—
284C2×C4⋊C4—111no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4—222no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4C22×D1112yes—
291C2×C4⋊C4C22×D1112yes—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—111no—
295C2×C22⋊C4—111no—
296C2×C42—112no—
297C2×C42—222no—
298C2×C42—222no—
299#106—42no—
300#103—114no—
301#103—114no—
302#103—114no—
303#103—114no—
304#103—224no—
305#103—442no—
306C22⋊C8—222no—
307C4×C8—442no—
308#95—21no—
309#95—21no—
310#95—112no—
311#95—222no—
312#95—222no—
313#95—222no—
314#95—222no—
315C2×C11—24no—
316C2×C11#234211yescharacteristic
317C2×C11C2×C4×SD1611yescharacteristic
318C2×C11#295011yescharacteristic
319C2×C11#329812yes—
320C2×C11#330012yes—
321C24D4×D1111yescharacteristic
322C2×Q8—112no—
323C2×Q8—112no—
324C2×Q8—114no—
325C2×Q8—228no—
326C2×Q8—224no—
327C2×Q8—222no—
328C2×Q8—221no—
329C2×Q8—221no—
330C2×Q8—222no—
331C2×Q8—222no—
332C2×Q8—444no—
333C2×Q8—444no—
334C2×Q8—448no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—112no—
340C22×C4—112no—
341C22×C4—221no—
342C22×C4—224no—
343C22×C4—224no—
344C22×C4—221no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4—444no—
348C22×C4—442no—
349C22×C4—442no—
350C22×C4C2×C4×D1112yes—
351C22×C4D4×D1111yescharacteristic
352C22×C4#434312yes—
353C22×C4C23×D1111yescharacteristic
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—44no—
357C2×C8—222no—
358C2×C8—222no—
359C2×C8—222no—
360C2×C8C2×C4×D1112yes—
361C2×C8C2×C4×D1112yes—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—112no—
367C4⋊C4—112no—
368C4⋊C4—224no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—444no—
372C4⋊C4—444no—
373C22⋊C4—42no—
374C22⋊C4—42no—
375C22⋊C4—114no—
376C22⋊C4—222no—
377C42—222no—
378C42—222no—
379C42—444no—
380C42—444no—
381C11#2257111yescharacteristic, complemented, Sylow
382C23—22no—
383C23—22no—
384C23#6694612yes—
385C23SD16×D1112yes—
386C23#6696912yes—
387C23C2×D4×D1111yescharacteristic
388Q8—114no—
389Q8—222no—
390Q8—224no—
391Q8—222no—
392Q8—222no—
393Q8—448no—
394Q8—442no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—114no—
406C2×C4—222no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—224no—
410C2×C4—222no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—448no—
417C2×C4—448no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—442no—
423C2×C4#6694612yes—
424C2×C4C22×C4×D1111yescharacteristic
425C2×C4#6703712yes—
426C2×C4C2×#434311yescharacteristic
427C2×C4#41×D1112yes—
428C8—22no—
429C8—22no—
430C8—442no—
431C22—22no—
432C22—24no—
433C22—24no—
434C22—22no—
435C22#1062246514yes—
436C22C2×#6694611yescharacteristic
437C22#1062314112yes—
438C22C2×SD16×D1111yescharacteristic
439C22C2×#6696911yescharacteristic
440C22#1062330212yes—
441C4—22no—
442C4—82no—
443C4—82no—
444C4—224no—
445C4—224no—
446C4—442no—
447C4—442no—
448C4—442no—
449C4—442no—
450C4#1062301711yescharacteristic
451C4D11×#11711yescharacteristic
452C4#1062316812yes—
453C2—24no—
454C2#1307146211yescharacteristic
455C2C2×#1062246511yescharacteristic
456C2#1307748311yescharacteristic
457C2#1308047612yes—
458C2#1308050912yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1807C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1807D11
hypocenterC11#22571
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1807

Complements

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

NH ≅ G/Ntype
4. #13069290C2semidirect
5. #13069249C2semidirect
6. #13068881C2semidirect
9. #13068435C2semidirect
22. C2×#66880C4semidirect
209. Dic22#117semidirect
381. C11#22571semidirect

Maximal subgroups

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

subgroupindex
C22×#668802
#130714872
#130714482
#130692902
#130692492
#130688812
#130687002
#130685502
#130684352
C8×C22⋊Dic112
C11×#18072
#2257111