Finite Group Databasebeta

← #14810474

Subgroups — #14810474

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C211yesmaximal, characteristic
2C2×#10622316C211yesmaximal, characteristic, complemented
3C2×#10622294C211yesmaximal, characteristic, complemented
4#13074382C211yesmaximal, characteristic
5#13069768C212yesmaximal, complemented
6#13069758C212yesmaximal, complemented
7#13069589C211yesmaximal, characteristic, complemented
8#13069581C211yesmaximal, characteristic, complemented
9#13068926C212yesmaximal
10#13068921C212yesmaximal
11C11×#1750C211yesmaximal, characteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C2×#66977C2212yes—
16#10623050—24no—
17#10623050—24no—
18C2×#66943—21no—
19C2×#66941—21no—
20C2×#66931—21no—
21C2×#66931—21no—
22C2×#66923C2211yescharacteristic
23C2×#66923C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C2×C11×C22⋊C8C2212yes—
28C2×C11×#97C2211yescharacteristic
29C2×C4×C8×C11C2211yescharacteristic
30C2×#66880C2212yes—
31C2×#66880C2212yes—
32C2×#66880C2212yes—
33C2×#66880C2212yes—
34#10622596—21no—
35#10622596—21no—
36#10622566—21no—
37#10622566—21no—
38#10622549C2211yescharacteristic
39#10622542C2212yes—
40#10622316—24no—
41#10622294—24no—
42C11×#336C2212yes—
43#10622189C2212yes—
44#10622189C2212yes—
45#10622189C2212yes—
46#10622189C2212yes—
47C23×C4×C11C2311yescharacteristic
48C23×Dic11—21no—
49C22×Dic22—21no—
50C22×Dic22—21no—
51C22×Dic22C2312yes—
52C22×C8×C11C2312yes—
53C22×C8×C11C2312yes—
54C11×#117—22no—
55C11×#117—22no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C22⋊C4D411yescharacteristic
59C2×C11×C22⋊C4D411yescharacteristic
60C2×C42×C11C2311yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—21no—
63C2×C22⋊Dic11—22no—
64#66979—22no—
65#66979—22no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78#66977—28no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—22no—
84C2×C4×Dic11—21no—
85#66943—28no—
86#66941—28no—
87#66931—28no—
88#66931—28no—
89#66923—22no—
90#66923—22no—
91#66923—22no—
92#66923D414yes—
93#66922—22no—
94#66922—22no—
95#66922—22no—
96#66922—22no—
97#66922—22no—
98#66922D414yes—
99C11×C22⋊C8—24no—
100C11×#97—22no—
101C4×C8×C11—22no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106#66880—24no—
107#66880—24no—
108#66880—24no—
109#66880—24no—
110#25914—111nomaximal, Sylow
111C24×C11C2×D411yescharacteristic
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11#4114yes—
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—24no—
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—82no—
130C2×Dic22—24no—
131C2×Dic22—24no—
132C2×Dic22—22no—
133C2×Dic22—22no—
134C2×Dic22—24no—
135C2×Dic22—24no—
136C2×Dic22—82no—
137C2×Dic22—82no—
138C2×C8×C11—22no—
139C2×C8×C11—22no—
140C2×C8×C11—22no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C22⋊C4—22no—
147C11×C22⋊C4—22no—
148C42×C11—21no—
149C42×C11—21no—
150C42×C11C2×D412yes—
151C42×C11C2×D412yes—
152C22⋊Dic11—24no—
153C22⋊Dic11—44no—
154C4⋊Dic11—24no—
155C4⋊Dic11—24no—
156C4⋊Dic11—24no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—24no—
162C4⋊Dic11—42no—
163C4⋊Dic11—42no—
164C4⋊Dic11C2×D412yes—
165C4⋊Dic11C2×D412yes—
166C4⋊Dic11C2×D412yes—
167C4⋊Dic11C2×D412yes—
168Dic11⋊C4—24no—
169Dic11⋊C4—24no—
170Dic11⋊C4—24no—
171Dic11⋊C4—24no—
172Dic11⋊C4—44no—
173C4×Dic11—24no—
174C2×#544—111no—
175C2×#491—111no—
176C2×#487—111no—
177#2621—111no—
178#2026—112no—
179#2024—112no—
180#1993—111no—
181#1991—111no—
182#1873—112no—
183#1872—112no—
184#1750D1111yescharacteristic
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11#12412yes—
190C23×C11C22×D411yescharacteristic
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11#12012yes—
202C2×C4×C11#12012yes—
203C2×C4×C11#12412yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C2×#4112yes—
207C2×C4×C112−1+412yes—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—84no—
223Dic22—44no—
224Dic22—44no—
225Dic22—84no—
226Dic22—84no—
227C8×C11—42no—
228C8×C11—42no—
229#544—224no—
230#544—224no—
231C2×C4⋊Q8—111no—
232C2×C4⋊Q8—111no—
233C2×C4⋊Q8—111no—
234C2×C4⋊Q8—221no—
235C2×#125—111no—
236C2×#125—111no—
237C2×#125—221no—
238C2×C22⋊Q8—112no—
239C2×C22⋊Q8—221no—
240C2×C22⋊Q8—221no—
241C2×#117—111no—
242C2×#117C2×D1111yescharacteristic
243C22×C4⋊C4—111no—
244#491—224no—
245#487—224no—
246C2×#103—112no—
247C2×#103—112no—
248C2×#103—112no—
249C2×#103—112no—
250C2×C22⋊C8C2×D1112yes—
251C2×#97C2×D1111yescharacteristic
252C2×C4×C8C2×D1111yescharacteristic
253#398—221no—
254#398—221no—
255#397—221no—
256#397—221no—
257#391—112no—
258#382—111no—
259#340—112no—
260#340—112no—
261#340—112no—
262#340—112no—
263#336C2×D1112yes—
264C22×C11—24no—
265C22×C11—22no—
266C22×C11—42no—
267C22×C11—41no—
268C22×C11—41no—
269C22×C11C2×#12011yescharacteristic
270C22×C11C2×#12411yescharacteristic
271C22×C11#53611yescharacteristic
272C22×C11#57712yes—
273C22×C11#57812yes—
274C4×C11—22no—
275C4×C11—22no—
276C4×C11—22no—
277C4×C11—41no—
278C4×C11—41no—
279C4×C11#54812yes—
280C4×C11#54812yes—
281Dic11—42no—
282Dic11—42no—
283Dic11—42no—
284Dic11—42no—
285Dic11—82no—
286Dic11—82no—
287C22×Q8—112no—
288C22×Q8—221no—
289C22×Q8—221no—
290C23×C4—221no—
291C23×C4C22×D1111yescharacteristic
292C22×C8C22×D1112yes—
293C22×C8C22×D1112yes—
294C4⋊Q8—114no—
295C4⋊Q8—222no—
296C4⋊Q8—222no—
297C4⋊Q8—228no—
298C4⋊Q8—222no—
299C4⋊Q8—222no—
300C4⋊Q8—222no—
301#125—114no—
302#125—222no—
303#125—222no—
304#125—228no—
305#125—222no—
306C22⋊Q8—228no—
307C22⋊Q8—228no—
308C22⋊Q8—228no—
309#117—22no—
310#117—22no—
311#117—222no—
312#117—222no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4—111no—
315C2×C4⋊C4—111no—
316C2×C4⋊C4—111no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4—222no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4D4411yescharacteristic
331C2×C4⋊C4D4411yescharacteristic
332C2×C22⋊C4—221no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4D4411yescharacteristic
335C2×C22⋊C4D4411yescharacteristic
336C2×C42—221no—
337C2×C42C22×D1111yescharacteristic
338C2×C42C22×D1111yescharacteristic
339#103—224no—
340#103—224no—
341#103—224no—
342#103—224no—
343C22⋊C8—24no—
344#97—22no—
345C4×C8—22no—
346#95—221no—
347#95—221no—
348#95—222no—
349#95—222no—
350C2×C11—42no—
351C2×C11#243611yescharacteristic
352C2×C11#300911yescharacteristic
353C2×C11#301111yescharacteristic
354C2×C11#313712yes—
355C2×C11#324212yes—
356C24C2×D4411yescharacteristic
357C2×Q8—224no—
358C2×Q8—224no—
359C2×Q8—224no—
360C2×Q8—222no—
361C2×Q8—222no—
362C2×Q8—224no—
363C2×Q8—882no—
364C2×Q8—882no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—221no—
369C22×C4—221no—
370C22×C4—221no—
371C22×C4—221no—
372C22×C4—224no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4—882no—
376C22×C4C2×D4411yescharacteristic
377C22×C4C2×D4411yescharacteristic
378C22×C4C2×D4411yescharacteristic
379C22×C4C2×D4411yescharacteristic
380C22×C4C2×D4411yescharacteristic
381C22×C4#433914yes—
382C22×C4C23×D1111yescharacteristic
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—112no—
392C4⋊C4—112no—
393C4⋊C4—112no—
394C4⋊C4—112no—
395C4⋊C4—224no—
396C4⋊C4—224no—
397C4⋊C4—224no—
398C4⋊C4—224no—
399C4⋊C4—224no—
400C4⋊C4—224no—
401C4⋊C4—224no—
402C4⋊C4—221no—
403C4⋊C4—221no—
404C4⋊C4—221no—
405C4⋊C4—221no—
406C4⋊C4—224no—
407C4⋊C4—444no—
408C4⋊C4—442no—
409C4⋊C4—442no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—224no—
413C22⋊C4—444no—
414C42—21no—
415C42—21no—
416C42—224no—
417C42D4×D1112yes—
418C42D4×D1112yes—
419C11#2591411yescharacteristic, complemented, Sylow
420C23—21no—
421C23—22no—
422C23—22no—
423C23—21no—
424C23#6692812yes—
425C23C22×D4411yescharacteristic
426Q8—444no—
427Q8—444no—
428Q8—884no—
429Q8—884no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—222no—
443C2×C4—222no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—884no—
455C2×C4#6692812yes—
456C2×C4#6693512yes—
457C2×C4#6693512yes—
458C2×C4C2×#433912yes—
459C2×C4C2×D4×D1111yescharacteristic
460C2×C4C2×D4×D1111yescharacteristic
461C2×C4#6704312yes—
462C8—42no—
463C8—42no—
464C22—22no—
465C22—24no—
466C22—42no—
467C22—41no—
468C22—41no—
469C22C2×#6692811yescharacteristic
470C22C2×#6693511yescharacteristic
471C22#1062305711yescharacteristic
472C22#1062328212yes—
473C22#1062328412yes—
474C4—22no—
475C4—22no—
476C4—22no—
477C4—41no—
478C4—41no—
479C4—442no—
480C4—442no—
481C4—442no—
482C4—442no—
483C4—882no—
484C4—882no—
485C4#1062308312yes—
486C4#1062308312yes—
487C2—42no—
488C2#1307227411yescharacteristic
489C2#1307789511yescharacteristic
490C2#1307791311yescharacteristic
491C2#1307898312yes—
492C2#1307988612yes—
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1750C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1750D11
hypocenterC11#25914
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. C2×#10622316C2semidirect
3. C2×#10622294C2semidirect
5. #13069768C2semidirect
6. #13069758C2semidirect
7. #13069589C2semidirect
8. #13069581C2semidirect
419. C11#25914semidirect

Maximal subgroups

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

subgroupindex
C2×#106230502
C2×#106223162
C2×#106222942
#130743822
#130697682
#130697582
#130695892
#130695812
#130689262
#130689212
C11×#17502
#2591411