Finite Group Databasebeta

← #14763223

Subgroups — #14763223

Order 2816.

1130 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623165C211yesmaximal, characteristic
2#13071213C211yesmaximal, characteristic
3#13071211C211yesmaximal, characteristic
4#13069602C211yesmaximal, characteristic, complemented
5#13069601C211yesmaximal, characteristic, complemented
6#13069600C211yesmaximal, characteristic, complemented
7#13069599C214yesmaximal, complemented
8#13068689C214yesmaximal
9C11×#1996C211yesmaximal, characteristic, complemented
10C2×C11×C22⋊Q8C2211yescharacteristic
11C2×#66999C412yescomplemented
12C22×(C2×D11)⋊C4C2211yescharacteristic
13C2×#66977C2211yescharacteristic
14#10623165—22no—
15#10623165—22no—
16#10623165—22no—
17#10623165—22no—
18C2×#66950C412yescomplemented
19C2×#66949C412yescomplemented
20C2×#66949C412yescomplemented
21C2×C22⋊C4×D11C2212yes—
22C2×#66931C2212yes—
23C11×#380C2211yescharacteristic
24C4×C11×C22⋊C4C2211yescharacteristic
25#10622825C2211yescharacteristic
26C4×C22⋊Dic11C2211yescharacteristic
27#10622603—22no—
28#10622568C2212yes—
29#10622568C2212yes—
30#10622555C2212yes—
31C22⋊C4×Dic11C2212yes—
32#10622553—22no—
33#10622283—22no—
34#10622282—22no—
35C11×#342C2214yes—
36#10622165C2214yes—
37#10622165C2214yes—
38#10622164C2214yes—
39C24×D11C2311yescharacteristic
40C22×Q8×C11C2×C411yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×Dic11C2311yescharacteristic
43C22×C4×D11C2×C412yes—
44C22×C4×D11C2×C412yes—
45C22×Dic22C2×C412yes—
46C22×Dic22C2×C411yescharacteristic
47C11×C22⋊Q8—21no—
48C11×C22⋊Q8—21no—
49C11×C22⋊Q8—21no—
50C11×C22⋊Q8—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2×C411yescharacteristic
53C2×C11×C4⋊C4C2×C412yes—
54C2×C11×C22⋊C4C2312yes—
55C2×C11×C22⋊C4C2312yes—
56C2×C11×C22⋊C4C2312yes—
57C2×C42×C11—21no—
58C2×C22⋊Dic11C2312yes—
59C2×C22⋊Dic11C2312yes—
60C2×C22⋊Dic11C2312yes—
61#66999—24no—
62#66999—24no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4C2×C412yes—
68C2×(C2×D11)⋊C4C2×C412yes—
69C2×(C2×D11)⋊C4C2×C412yes—
70C2×(C2×D11)⋊C4C2×C412yes—
71C2×(C2×D11)⋊C4D412yes—
72C2×(C2×D11)⋊C4D412yes—
73C2×(C2×D11)⋊C4D412yes—
74C2×(C2×D11)⋊C4D412yes—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2×C412yes—
77C2×C4⋊Dic11C2×C411yescharacteristic
78#66977—21no—
79#66977—21no—
80#66977—21no—
81#66977—21no—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4C2×C412yes—
84C2×Dic11⋊C4C2×C412yes—
85C2×Dic11⋊C4C2×C412yes—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—22no—
88#66950—24no—
89#66950—24no—
90#66949—24no—
91#66949—24no—
92#66949—24no—
93#66949—24no—
94C22⋊C4×D11—24no—
95C22⋊C4×D11—24no—
96#66931—24no—
97#66931—24no—
98C11×#95—21no—
99C11×#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104#21827—111nomaximal, Sylow
105C24×C11C2411yescharacteristic
106C23×D11—22no—
107C23×D11—22no—
108C23×D11—81no—
109C23×D11—81no—
110C23×D11C22×C412yes—
111C23×D11C2×D412yes—
112C23×D11C2×D412yes—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—81no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—81no—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—81no—
130C22×Dic11C22×C412yes—
131C22×Dic11C22×C412yes—
132C22×Dic11C22×C412yes—
133C22×Dic11C2×D412yes—
134C22×Dic11C2×D412yes—
135C2×C4×D11—24no—
136C2×C4×D11—24no—
137C2×C4×D11—82no—
138C2×C4×D11—82no—
139C2×Dic22—24no—
140C2×Dic22—21no—
141C2×Dic22—21no—
142C2×Dic22—81no—
143C2×Dic22—82no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—81no—
149C11×C22⋊C4—22no—
150C11×C22⋊C4—22no—
151C11×C22⋊C4—22no—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—22no—
154C42×C11—81no—
155C22⋊Dic11—22no—
156C22⋊Dic11—22no—
157C22⋊Dic11—24no—
158C22⋊Dic11—22no—
159C22⋊Dic11—22no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—82no—
163(C2×D11)⋊C4—82no—
164(C2×D11)⋊C4—82no—
165(C2×D11)⋊C4—82no—
166(C2×D11)⋊C4C22⋊C414yes—
167(C2×D11)⋊C4C22⋊C414yes—
168(C2×D11)⋊C4C22⋊C414yes—
169(C2×D11)⋊C4C22⋊C414yes—
170C4⋊Dic11—24no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—81no—
174Dic11⋊C4—24no—
175Dic11⋊C4—24no—
176Dic11⋊C4—22no—
177Dic11⋊C4—22no—
178Dic11⋊C4—82no—
179C4×Dic11—81no—
180C4×Dic11—82no—
181C2×#543—111no—
182#2312—111no—
183#2312—111no—
184#1996—111no—
185#1996—111no—
186#1996—114no—
187#1996—111no—
188#1996D1111yescharacteristic, complemented
189#1819—114no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11C23×C411yescharacteristic
193C23×C11C22×D411yescharacteristic
194C23×C11C22×D411yescharacteristic
195C23×C112−1+412yes—
196C23×C112−1+412yes—
197C22×D11—24no—
198C22×D11—22no—
199C22×D11—24no—
200C22×D11—22no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206C22×D11—42no—
207C22×D11—84no—
208C22×D11—84no—
209C22×D11C2×C22⋊C414yes—
210Q8×C11—81no—
211Q8×C11—81no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11C2×C22⋊C411yescharacteristic
229C2×C4×C11C2×C22⋊C411yescharacteristic
230C2×C4×C11C2×C22⋊C411yescharacteristic
231C2×C4×C11C2×C22⋊C411yescharacteristic
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11C2×C22⋊C414yes—
246C4×D11—84no—
247C4×D11—84no—
248Dic22—84no—
249Dic22—81no—
250Dic22—81no—
251#543—222no—
252#543—222no—
253#543—222no—
254#543—222no—
255C2×C22⋊Q8—112no—
256C2×C22⋊Q8—111no—
257C2×C22⋊Q8—112no—
258C2×C22⋊Q8—112no—
259C2×C22⋊Q8—112no—
260C2×C22⋊Q8—112no—
261C2×C22⋊Q8C2×D1111yescharacteristic
262C22×C22⋊C4—111no—
263C22×C22⋊C4—112no—
264#388—222no—
265#388—222no—
266#388—222no—
267#388—222no—
268#380—111no—
269#380—112no—
270#380C2×D1111yescharacteristic
271#379—112no—
272#379—112no—
273C4×C22⋊C4—111no—
274C4×C22⋊C4—112no—
275C4×C22⋊C4C2×D1111yescharacteristic
276#342—114no—
277#342—114no—
278#342—114no—
279#342C2×D1114yes—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11C22×C22⋊C411yescharacteristic
289C22×C11#51912yes—
290C22×C11#53611yescharacteristic
291C22×C11#53612yes—
292C22×C11#53611yescharacteristic
293C2×D11—24no—
294C2×D11—24no—
295C2×D11—24no—
296C2×D11—48no—
297C2×D11—82no—
298C2×D11—84no—
299C2×D11—82no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—82no—
307C4×C11—82no—
308Dic11—24no—
309Dic11—42no—
310Dic11—42no—
311Dic11—82no—
312Dic11—82no—
313C25—111no—
314C22×Q8—112no—
315C22×Q8—111no—
316C22×Q8C4×D1111yescharacteristic
317C23×C4—111no—
318C23×C4—112no—
319C23×C4—112no—
320C23×C4C22×D1111yescharacteristic
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8—224no—
326C22⋊Q8—224no—
327C22⋊Q8—224no—
328C22⋊Q8—224no—
329C22⋊Q8—224no—
330C22⋊Q8—224no—
331C22⋊Q8—224no—
332C22⋊Q8—224no—
333C22⋊Q8—224no—
334C22⋊Q8—224no—
335C22⋊Q8—221no—
336C22⋊Q8—221no—
337C22⋊Q8—221no—
338C22⋊Q8—221no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—112no—
341C2×C4⋊C4—112no—
342C2×C4⋊C4—112no—
343C2×C4⋊C4—112no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4C4×D1112yes—
348C2×C4⋊C4C4×D1111yescharacteristic
349C2×C22⋊C4—112no—
350C2×C22⋊C4—112no—
351C2×C22⋊C4—112no—
352C2×C22⋊C4—112no—
353C2×C22⋊C4—112no—
354C2×C22⋊C4—112no—
355C2×C22⋊C4—112no—
356C2×C22⋊C4—112no—
357C2×C22⋊C4—112no—
358C2×C22⋊C4—112no—
359C2×C22⋊C4—112no—
360C2×C22⋊C4—224no—
361C2×C22⋊C4—224no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4—222no—
364C2×C22⋊C4—222no—
365C2×C22⋊C4—222no—
366C2×C22⋊C4C22×D1112yes—
367C2×C22⋊C4C22×D1112yes—
368C2×C22⋊C4C22×D1112yes—
369C2×C42—21no—
370C2×C42—222no—
371C2×C42—221no—
372#95—21no—
373#95—21no—
374#95—222no—
375#95—222no—
376#95—221no—
377#95—221no—
378C2×C11—21no—
379C2×C11—22no—
380C2×C11—21no—
381C2×C11—22no—
382C2×C11#231011yescharacteristic
383C2×C11#288311yescharacteristic
384C2×C11#288311yescharacteristic
385D11—44no—
386C24—112no—
387C24—112no—
388C24—112no—
389C24—222no—
390C24—222no—
391C24—881no—
392C24—881no—
393C24C23×D1111yescharacteristic
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—81no—
397C2×Q8—224no—
398C2×Q8—221no—
399C2×Q8—221no—
400C2×Q8—881no—
401C2×Q8—882no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—81no—
405C22×C4—112no—
406C22×C4—112no—
407C22×C4—112no—
408C22×C4—112no—
409C22×C4—112no—
410C22×C4—224no—
411C22×C4—224no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—882no—
415C22×C4—882no—
416C22×C4—881no—
417C22×C4C2×C4×D1112yes—
418C22×C4C2×C4×D1112yes—
419C22×C4C2×C4×D1111yescharacteristic
420C22×C4C2×C4×D1111yescharacteristic
421C22×C4D4×D1111yescharacteristic
422C22×C4D4×D1111yescharacteristic
423C22×C4D4×D1111yescharacteristic
424C22×C4D4×D1111yescharacteristic
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—81no—
430C4⋊C4—224no—
431C4⋊C4—224no—
432C4⋊C4—224no—
433C4⋊C4—222no—
434C4⋊C4—222no—
435C4⋊C4—221no—
436C4⋊C4—221no—
437C4⋊C4—882no—
438C4⋊C4—881no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—24no—
444C22⋊C4—114no—
445C22⋊C4—114no—
446C22⋊C4—114no—
447C22⋊C4—114no—
448C22⋊C4—224no—
449C22⋊C4—224no—
450C22⋊C4—222no—
451C22⋊C4—222no—
452C22⋊C4—224no—
453C22⋊C4—222no—
454C22⋊C4—222no—
455C22⋊C4—882no—
456C22⋊C4—882no—
457C22⋊C4—882no—
458C22⋊C4—882no—
459C42—81no—
460C42—881no—
461C42—882no—
462C11#2182711yescharacteristic, complemented, Sylow
463C23—41no—
464C23—41no—
465C23—114no—
466C23—224no—
467C23—222no—
468C23—224no—
469C23—222no—
470C23—442no—
471C23—442no—
472C23—442no—
473C23—442no—
474C23—442no—
475C23—442no—
476C23—884no—
477C23—884no—
478C23C22×C4×D1111yescharacteristic
479C23C2×D4×D1111yescharacteristic
480C23C2×D4×D1111yescharacteristic
481C23#6704012yes—
482C23#6704312yes—
483Q8—81no—
484Q8—81no—
485Q8—881no—
486Q8—881no—
487Q8—884no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—114no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—884no—
519C2×C4—884no—
520C2×C4C22⋊C4×D1111yescharacteristic
521C2×C4C22⋊C4×D1111yescharacteristic
522C2×C4C22⋊C4×D1111yescharacteristic
523C2×C4C22⋊C4×D1111yescharacteristic
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—42no—
531C22—42no—
532C22—224no—
533C22—224no—
534C22—224no—
535C22—448no—
536C22—882no—
537C22—884no—
538C22—882no—
539C22C2×C22⋊C4×D1111yescharacteristic
540C22#1062310312yes—
541C22#1062315912yes—
542C22#1062320611yescharacteristic
543C22#1062325511yescharacteristic
544C4—21no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—42no—
549C4—42no—
550C4—82no—
551C4—82no—
552C4—224no—
553C4—442no—
554C4—442no—
555C4—882no—
556C4—882no—
557C2—21no—
558C2—22no—
559C2—21no—
560C2—22no—
561C2—444no—
562C2#1307119911yescharacteristic
563C2#1307707411yescharacteristic
564C2#1307707511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#1996C2
socleC22×C11C22×C22⋊C4
prime radicalC24×D11C23
cosocleC24×C11C24
hypercenter#1996D11
hypocenterC11#21827
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
4. #13069602C2semidirect
5. #13069601C2semidirect
6. #13069600C2semidirect
7. #13069599C2semidirect
9. C11×#1996C2semidirect
11. C2×#66999C4semidirect
18. C2×#66950C4semidirect
19. C2×#66949C4semidirect
20. C2×#66949C4semidirect
188. #1996D11semidirect
462. C11#21827semidirect

Maximal subgroups

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

subgroupindex
C2×#106231652
#130712132
#130712112
#130696022
#130696012
#130696002
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