Finite Group Databasebeta

← #14763227

Subgroups — #14763227

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623154C211yesmaximal, characteristic
2#13071218C211yesmaximal, characteristic
3#13071216C211yesmaximal, characteristic
4#13069602C211yesmaximal, characteristic
5#13069601C211yesmaximal, characteristic
6#13069600C211yesmaximal, characteristic
7#13069599C214yesmaximal
8#13068692C214yesmaximal
9C11×#1996C211yesmaximal, characteristic
10C2×C11×C22⋊Q8C2211yescharacteristic
11C2×#66997C412yescomplemented
12C2×#66977C2211yescharacteristic
13C22×Dic11⋊C4C2211yescharacteristic
14#10623154—22no—
15#10623154—22no—
16#10623154—22no—
17#10623154—22no—
18C2×#66942C412yescomplemented
19C2×#66942C412yescomplemented
20C2×#66941C412yescomplemented
21C2×#66931C2212yes—
22C2×#66930C2212yes—
23C11×#380C2211yescharacteristic
24C4×C11×C22⋊C4C2211yescharacteristic
25#10622825C2211yescharacteristic
26C4×C22⋊Dic11C2211yescharacteristic
27#10622591—22no—
28#10622556C2212yes—
29#10622556C2212yes—
30#10622555C2212yes—
31C22⋊C4×Dic11C2212yes—
32#10622546—22no—
33#10622268—22no—
34#10622265—22no—
35C11×#342C2214yes—
36#10622165C2214yes—
37#10622165C2214yes—
38#10622164C2214yes—
39C22×Q8×C11C2×C411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×Dic11C2311yescharacteristic
42C23×Dic11C2311yescharacteristic
43C22×Dic22C2×C412yes—
44C22×Dic22C2×C411yescharacteristic
45C11×C22⋊Q8—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8—21no—
48C11×C22⋊Q8—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4C2×C412yes—
51C2×C11×C4⋊C4C2×C411yescharacteristic
52C2×C11×C22⋊C4C2312yes—
53C2×C11×C22⋊C4C2312yes—
54C2×C11×C22⋊C4C2312yes—
55C2×C42×C11—21no—
56C2×C22⋊Dic11C2312yes—
57C2×C22⋊Dic11C2312yes—
58C2×C22⋊Dic11C2312yes—
59#66997—24no—
60#66997—24no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11C2×C412yes—
63C2×C4⋊Dic11C2×C411yescharacteristic
64#66977—21no—
65#66977—21no—
66#66977—21no—
67#66977—21no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4C2×C412yes—
70C2×Dic11⋊C4C2×C412yes—
71C2×Dic11⋊C4C2×C412yes—
72C2×Dic11⋊C4C2×C412yes—
73C2×Dic11⋊C4C2×C412yes—
74C2×Dic11⋊C4C2×C412yes—
75C2×Dic11⋊C4C2×C412yes—
76C2×Dic11⋊C4D412yes—
77C2×Dic11⋊C4D412yes—
78C2×Dic11⋊C4D412yes—
79C2×Dic11⋊C4D412yes—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11C2×C412yes—
83C2×C4×Dic11C2×C412yes—
84#66942—24no—
85#66942—24no—
86#66942—24no—
87#66942—24no—
88#66941—24no—
89#66941—24no—
90#66931—24no—
91#66931—24no—
92#66930—24no—
93#66930—24no—
94C11×#95—21no—
95C11×#95—21no—
96C11⋊#95—21no—
97C11⋊#95—21no—
98C11⋊#95—22no—
99C11⋊#95—24no—
100C11⋊#95—22no—
101C11⋊#95—24no—
102#21828—111nomaximal, Sylow
103C24×C11C2411yescharacteristic
104C2×Q8×C11—21no—
105C2×Q8×C11—21no—
106C2×Q8×C11—81no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—81no—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C22×C411yescharacteristic
113C22×C4×C11C22×C411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—81no—
123C22×Dic11C22×C412yes—
124C22×Dic11C22×C412yes—
125C22×Dic11C22×C412yes—
126C22×Dic11C22×C412yes—
127C22×Dic11C2×D412yes—
128C22×Dic11C2×D412yes—
129C22×Dic11C2×D412yes—
130C22×Dic11C2×D412yes—
131C2×Dic22—24no—
132C2×Dic22—21no—
133C2×Dic22—21no—
134C2×Dic22—81no—
135C2×Dic22—82no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—81no—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—24no—
145C11×C22⋊C4—22no—
146C42×C11—81no—
147C22⋊Dic11—22no—
148C22⋊Dic11—22no—
149C22⋊Dic11—24no—
150C22⋊Dic11—22no—
151C22⋊Dic11—22no—
152C4⋊Dic11—24no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—81no—
156Dic11⋊C4—24no—
157Dic11⋊C4—24no—
158Dic11⋊C4—24no—
159Dic11⋊C4—24no—
160Dic11⋊C4—22no—
161Dic11⋊C4—22no—
162Dic11⋊C4—82no—
163Dic11⋊C4C22⋊C414yes—
164Dic11⋊C4C22⋊C414yes—
165Dic11⋊C4C22⋊C414yes—
166Dic11⋊C4C22⋊C414yes—
167C4×Dic11—24no—
168C4×Dic11—24no—
169C4×Dic11—81no—
170C4×Dic11—82no—
171C2×#544—111no—
172#2313—111no—
173#2313—111no—
174#1996—111no—
175#1996—111no—
176#1996—114no—
177#1996—111no—
178#1996D1111yescharacteristic
179#1820—114no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11C23×C411yescharacteristic
183C23×C11C22×D411yescharacteristic
184C23×C11C22×D411yescharacteristic
185C23×C112−1+412yes—
186C23×C112−1+412yes—
187Q8×C11—81no—
188Q8×C11—81no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11C2×C22⋊C411yescharacteristic
206C2×C4×C11C2×C22⋊C411yescharacteristic
207C2×C4×C11C2×C22⋊C411yescharacteristic
208C2×C4×C11C2×C22⋊C411yescharacteristic
209C2×Dic11—24no—
210C2×Dic11—22no—
211C2×Dic11—24no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11C2×C22⋊C414yes—
227C2×Dic11C2×C22⋊C414yes—
228Dic22—84no—
229Dic22—81no—
230Dic22—81no—
231#544—222no—
232#544—222no—
233#544—222no—
234#544—222no—
235C2×C4⋊Q8—112no—
236C2×C4⋊Q8—112no—
237C2×#125—112no—
238C2×#125—112no—
239C2×C22⋊Q8—111no—
240C2×C22⋊Q8—112no—
241C2×C22⋊Q8C2×D1111yescharacteristic
242C2×#117—112no—
243C22×C4⋊C4—111no—
244#387—222no—
245#387—222no—
246#387—222no—
247#387—222no—
248#381—112no—
249#381—112no—
250#380—111no—
251#380—112no—
252#380C2×D1111yescharacteristic
253C4×C22⋊C4—111no—
254C4×C22⋊C4—112no—
255C4×C22⋊C4C2×D1111yescharacteristic
256#342—114no—
257#342—114no—
258#342—114no—
259#342C2×D1114yes—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11C22×C22⋊C411yescharacteristic
269C22×C11#51912yes—
270C22×C11#53611yescharacteristic
271C22×C11#53612yes—
272C22×C11#53611yescharacteristic
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—42no—
278C4×C11—42no—
279C4×C11—82no—
280C4×C11—82no—
281Dic11—24no—
282Dic11—24no—
283Dic11—42no—
284Dic11—42no—
285Dic11—82no—
286Dic11—82no—
287C22×Q8—112no—
288C22×Q8—111no—
289C22×Q8C4×D1111yescharacteristic
290C23×C4—111no—
291C23×C4—111no—
292C23×C4C22×D1111yescharacteristic
293C4⋊Q8—224no—
294C4⋊Q8—224no—
295C4⋊Q8—224no—
296C4⋊Q8—224no—
297#125—224no—
298#125—224no—
299#125—224no—
300#125—224no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—224no—
306C22⋊Q8—224no—
307C22⋊Q8—221no—
308C22⋊Q8—221no—
309C22⋊Q8—221no—
310C22⋊Q8—221no—
311#117—224no—
312#117—224no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—112no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—112no—
319C2×C4⋊C4—112no—
320C2×C4⋊C4—112no—
321C2×C4⋊C4—112no—
322C2×C4⋊C4—112no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—112no—
325C2×C4⋊C4—112no—
326C2×C4⋊C4—112no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4C4×D1111yescharacteristic
330C2×C4⋊C4C4×D1112yes—
331C2×C22⋊C4—112no—
332C2×C22⋊C4—112no—
333C2×C22⋊C4—112no—
334C2×C22⋊C4C22×D1112yes—
335C2×C22⋊C4C22×D1112yes—
336C2×C22⋊C4C22×D1112yes—
337C2×C42—21no—
338C2×C42—112no—
339C2×C42—112no—
340C2×C42—222no—
341C2×C42—221no—
342#95—21no—
343#95—21no—
344#95—222no—
345#95—222no—
346#95—224no—
347#95—224no—
348#95—221no—
349#95—221no—
350C2×C11—21no—
351C2×C11—22no—
352C2×C11—21no—
353C2×C11—22no—
354C2×C11#231011yescharacteristic
355C2×C11#288311yescharacteristic
356C2×C11#288411yescharacteristic
357C24C23×D1111yescharacteristic
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—81no—
361C2×Q8—224no—
362C2×Q8—221no—
363C2×Q8—221no—
364C2×Q8—881no—
365C2×Q8—882no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—81no—
369C22×C4—112no—
370C22×C4—112no—
371C22×C4—112no—
372C22×C4—112no—
373C22×C4—112no—
374C22×C4—112no—
375C22×C4—112no—
376C22×C4—112no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—881no—
382C22×C4C2×C4×D1112yes—
383C22×C4C2×C4×D1112yes—
384C22×C4C2×C4×D1111yescharacteristic
385C22×C4C2×C4×D1111yescharacteristic
386C22×C4D4×D1111yescharacteristic
387C22×C4D4×D1111yescharacteristic
388C22×C4D4×D1111yescharacteristic
389C22×C4D4×D1111yescharacteristic
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—81no—
395C4⋊C4—114no—
396C4⋊C4—114no—
397C4⋊C4—114no—
398C4⋊C4—114no—
399C4⋊C4—224no—
400C4⋊C4—224no—
401C4⋊C4—224no—
402C4⋊C4—224no—
403C4⋊C4—224no—
404C4⋊C4—221no—
405C4⋊C4—221no—
406C4⋊C4—222no—
407C4⋊C4—222no—
408C4⋊C4—882no—
409C4⋊C4—881no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—22no—
414C22⋊C4—24no—
415C22⋊C4—222no—
416C22⋊C4—222no—
417C22⋊C4—224no—
418C22⋊C4—222no—
419C22⋊C4—222no—
420C42—81no—
421C42—224no—
422C42—224no—
423C42—881no—
424C42—882no—
425C11#2182811yescharacteristic, complemented, Sylow
426C23—41no—
427C23—41no—
428C23C22×C4×D1111yescharacteristic
429C23C2×D4×D1111yescharacteristic
430C23C2×D4×D1111yescharacteristic
431C23#6704012yes—
432C23#6704312yes—
433Q8—81no—
434Q8—81no—
435Q8—881no—
436Q8—881no—
437Q8—884no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—114no—
455C2×C4—114no—
456C2×C4—222no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—222no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4C22⋊C4×D1111yescharacteristic
474C2×C4C22⋊C4×D1111yescharacteristic
475C2×C4C22⋊C4×D1111yescharacteristic
476C2×C4C22⋊C4×D1111yescharacteristic
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—42no—
484C22—42no—
485C22C2×C22⋊C4×D1111yescharacteristic
486C22#1062310312yes—
487C22#1062315912yes—
488C22#1062320611yescharacteristic
489C22#1062325511yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—42no—
495C4—42no—
496C4—82no—
497C4—82no—
498C4—224no—
499C4—224no—
500C4—442no—
501C4—442no—
502C4—882no—
503C4—882no—
504C2—21no—
505C2—22no—
506C2—21no—
507C2—22no—
508C2#1307119911yescharacteristic
509C2#1307707411yescharacteristic
510C2#1307707811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#1996C2
socleC22×C11C22×C22⋊C4
prime radical, cosocleC24×C11C24
hypercenter#1996D11
hypocenterC11#21828
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
11. C2×#66997C4semidirect
18. C2×#66942C4semidirect
19. C2×#66942C4semidirect
20. C2×#66941C4semidirect
425. C11#21828semidirect

Maximal subgroups

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

subgroupindex
C2×#106231542
#130712182
#130712162
#130696022
#130696012
#130696002
#130695992
#130686922
C11×#19962
#2182811