Finite Group Databasebeta

← #15633896

Subgroups — #15633896

Order 2816.

1730 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082483C211yesmaximal, characteristic
2#13081458C214yesmaximal, complemented
3#13081419C214yesmaximal, complemented
4#13081384C214yesmaximal, complemented
5#13081356C214yesmaximal, complemented
6#13078986C212yesmaximal, complemented
7#13078964C211yesmaximal, characteristic
8#13078474C212yesmaximal, complemented
9#13078417C211yesmaximal, characteristic, complemented
10#13078146C212yesmaximal, complemented
11#13078088C211yesmaximal, characteristic
12#13077557C211yesmaximal, characteristic, complemented
13#13077459C212yesmaximal, complemented
14C2×#10622643C211yesmaximal, characteristic, complemented
15C11×#3502C211yesmaximal, characteristic, complemented
16Q82×C11—21no—
17Q82×C11C2212yes—
18C11×#557—21no—
19C11×#557—22no—
20C11×#557C2214yes—
21C11×#557C2212yes—
22C11×#544—22no—
23C11×#544C2212yes—
24C11×#533—22no—
25C11×#533C2211yescharacteristic
26C11×#533C2211yescharacteristic
27C11×#519C2212yes—
28C2×C4×Q8×C11C2211yescharacteristic
29C22×#4326C2211yescharacteristic
30C2×#66995C2212yes—
31#10623263—21no—
32#10623261—21no—
33#10623225—22no—
34#10623176—22no—
35#10623155—22no—
36#10623116C2212yes—
37#10623115C2214yes—
38#10623101C2212yes—
39#10623057C2212yes—
40#10623054C2212yes—
41#10623008C2211yescharacteristic
42C2×C4×Dic22C2211yescharacteristic
43C2×#66899C2211yescharacteristic
44#10622707C2212yes—
45#10622707C2214yes—
46#10622706C2214yes—
47#10622704C2212yes—
48#10622702C2212yes—
49#10622702C2214yes—
50#10622702C2212yes—
51#10622697C2214yes—
52#10622682C2212yes—
53#10622682C2214yes—
54#10622681C2214yes—
55#10622680C2212yes—
56#10622679C2214yes—
57#10622676C2214yes—
58#10622676C2214yes—
59#10622644C2214yes—
60#10622644C2212yes—
61#10622644C2214yes—
62#10622643C2214yes—
63#10622643C2214yes—
64#10622643C2214yes—
65C4×#4326C2214yes—
66#10622641C2214yes—
67#10622641C2214yes—
68#10622641C2214yes—
69#10622640C2212yes—
70#10622639C2214yes—
71C4×#4325C2214yes—
72#10622637C2214yes—
73#10622637C2214yes—
74#10622617C2212yes—
75#10622615C2212yes—
76#10622615C2212yes—
77#10622612C2212yes—
78#10622610C2212yes—
79#10622608C2212yes—
80C2×#66874C2211yescharacteristic
81#10622579C2212yes—
82C2×#66872C2211yescharacteristic
83#10622537C2211yescharacteristic
84C2×#66867C2211yescharacteristic
85C22×Q8×C11C2311yescharacteristic
86C2×#4339C2312yes—
87C22×Dic22C2311yescharacteristic
88C11×C4⋊Q8—22no—
89C11×C4⋊Q8—24no—
90C11×C4⋊Q8—22no—
91C11×C4⋊Q8—24no—
92C11×C4⋊Q8—22no—
93C11×C4⋊Q8D411yescharacteristic
94C11×C4⋊Q8D411yescharacteristic
95C11×C4⋊Q8C2311yescharacteristic
96C11×C4⋊Q8C2311yescharacteristic
97C11×C4⋊Q8C2314yes—
98C11×#125—24no—
99C11×#125—24no—
100C11×#125—24no—
101C11×#125—22no—
102C11×#125D412yes—
103C11×#125C2312yes—
104C11×#125C2314yes—
105C11×C22⋊Q8—21no—
106C11×C22⋊Q8—21no—
107C11×C22⋊Q8—24no—
108C11×C22⋊Q8D412yes—
109C11×C22⋊Q8D412yes—
110C4×Q8×C11—22no—
111C4×Q8×C11—22no—
112C4×Q8×C11—22no—
113C4×Q8×C11—24no—
114C4×Q8×C11—22no—
115C4×Q8×C11—21no—
116C4×Q8×C11—21no—
117C4×Q8×C11—21no—
118C4×Q8×C11—21no—
119C4×Q8×C11C2312yes—
120C4×Q8×C11C2312yes—
121C4×Q8×C11C2314yes—
122C4×Q8×C11C2314yes—
123C4×Q8×C11C2312yes—
124C4×Q8×C11C2312yes—
125C11×#117—24no—
126C11×#117C2312yes—
127C11×#117C2312yes—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C42×C11—21no—
131C2×C42×C11C2311yescharacteristic
132#67000—22no—
133#66999—24no—
134Q8×Dic11—22no—
135C2×#4326—24no—
136C2×#4326C2314yes—
137C2×#4326C2314yes—
138#66995—28no—
139C2×#4325C2314yes—
140#66983—21no—
141#66983—21no—
142C2×C4⋊Dic11C2311yescharacteristic
143C2×Dic11⋊C4—21no—
144C2×C4×Dic11—21no—
145C2×#4318C2312yes—
146C22×C11⋊C8C2311yescharacteristic
147C22×C11⋊C8C2311yescharacteristic
148#66951—24no—
149#66951—24no—
150#66950—22no—
151#66950—22no—
152#66947—24no—
153#66946—22no—
154#66945—22no—
155#66945—24no—
156C4⋊C4×D11—22no—
157#66943—22no—
158#66943—24no—
159#66939—24no—
160(C22⋊D11)⋊C4—24no—
161#66928C2312yes—
162#66928C2314yes—
163#66927C2311yescharacteristic
164C4×D44—21no—
165C4×D44—21no—
166C4×D44C2314yes—
167#66922C2311yescharacteristic
168#66922C2314yes—
169C4×Dic22—21no—
170C4×Dic22—21no—
171C4×Dic22C2312yes—
172C4×Dic22C2312yes—
173C4×Dic22C2314yes—
174#66899C2314yes—
175#66874C2314yes—
176#66874C2314yes—
177#66874C2312yes—
178#66874C2312yes—
179#66874C2312yes—
180#66874C2312yes—
181#66874C2314yes—
182#66874C2314yes—
183#66873C2314yes—
184#66873C2312yes—
185#66873C2312yes—
186#66873C2312yes—
187#66873C2312yes—
188#66872C2314yes—
189#66872C2314yes—
190#66871C2314yes—
191C4⋊(C11⋊C8)C2312yes—
192C4⋊(C11⋊C8)C2312yes—
193C4⋊(C11⋊C8)C2314yes—
194C4⋊(C11⋊C8)C2314yes—
195#66867C2312yes—
196#66867C2312yes—
197#66867C2314yes—
198C4×C11⋊C8C2314yes—
199#61335—111nomaximal, Sylow
200C2×Q8×C11—21no—
201C2×Q8×C11—21no—
202C2×Q8×C11—21no—
203C2×Q8×C11—24no—
204C2×Q8×C11—22no—
205C2×Q8×C11C2×D412yes—
206C2×Q8×C11C2×D412yes—
207C2×Q8×C11#4114yes—
208C2×Q8×C11C2412yes—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2411yescharacteristic
214C2×C22⋊D11—22no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217#4339—24no—
218#4339—24no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44C2412yes—
222C2×C4×D11—22no—
223C2×C4×D11—24no—
224C2×Dic22—21no—
225C2×Dic22—22no—
226C2×Dic22—22no—
227C2×Dic22C2412yes—
228C2×Dic22C2412yes—
229C11×C4⋊C4—22no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—24no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—22no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—24no—
238C11×C4⋊C4—24no—
239C11×C4⋊C4—22no—
240C11×C4⋊C4—24no—
241C11×C4⋊C4C2×D412yes—
242C11×C4⋊C4C2×D414yes—
243C11×C4⋊C4C2×D412yes—
244C11×C4⋊C4C2×D412yes—
245C11×C4⋊C4C2×D414yes—
246C11×C4⋊C4C2×D412yes—
247C11×C4⋊C4C2412yes—
248C11×C4⋊C4C2412yes—
249C11×C4⋊C4C2412yes—
250C11×C22⋊C4—22no—
251C11×C22⋊C4C2×D414yes—
252C42×C11—22no—
253C42×C11—22no—
254C42×C11—24no—
255C42×C11—24no—
256C42×C11—22no—
257C42×C11C2×D411yescharacteristic
258C42×C11C2×D411yescharacteristic
259C42×C11C2414yes—
260C42×C11C2411yescharacteristic
261C42×C11C2411yescharacteristic
262#4326—28no—
263#4326—28no—
264#4325—28no—
265(C2×D11)⋊C4—22no—
266(C2×D11)⋊C4—22no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269(C2×D11)⋊C4—24no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11—24no—
274C4⋊Dic11—24no—
275C4⋊Dic11C2412yes—
276Dic11⋊C4—22no—
277Dic11⋊C4—22no—
278Dic11⋊C4—24no—
279C4×Dic11—22no—
280C4×Dic11—22no—
281C4×Dic11—24no—
282#4318—24no—
283C2×C11⋊C8—22no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8C2412yes—
286C2×C11⋊C8C2414yes—
287C2×C11⋊C8C2412yes—
288#3507—111no—
289#3502D1111yescharacteristic, complemented
290#3377—114no—
291#3374—114no—
292#3371—114no—
293#3369—114no—
294#3137—112no—
295#3135—111no—
296#3084—112no—
297#3078—111no—
298#3044—112no—
299#3037—111no—
300#2961—111no—
301#2947—112no—
302C2×#441—111no—
303C23×C11C22×D411yescharacteristic
304C22×D11—22no—
305Q8×C11—24no—
306Q8×C11—22no—
307Q8×C11—42no—
308Q8×C11—42no—
309Q8×C11—42no—
310Q8×C11—81no—
311Q8×C11—84no—
312Q8×C11C2×#4114yes—
313C2×C4×C11—24no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—81no—
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C22×D411yescharacteristic
323C2×C4×C11C22×D414yes—
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11C22×D414yes—
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C2×#4112yes—
329C2×C4×C112−1+412yes—
330C2×C4×C11C2511yescharacteristic
331C22⋊D11—44no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—42no—
336C2×Dic11—81no—
337D44—22no—
338D44—22no—
339D44—42no—
340D44—81no—
341C4×D11—44no—
342C4×D11—84no—
343Dic22—22no—
344Dic22—22no—
345Dic22—22no—
346Dic22—22no—
347Dic22—42no—
348C11⋊C8—22no—
349C11⋊C8—24no—
350C11⋊C8—22no—
351C2×#137—112no—
352C22×Q16—111no—
353#559—112no—
354Q82—21no—
355Q82C2×D1112yes—
356#557—21no—
357#557—22no—
358#557—112no—
359#557C2×D1114yes—
360#557C2×D1112yes—
361#556—114no—
362#556—221no—
363#554—221no—
364#552—222no—
365#544—22no—
366#544C2×D1112yes—
367#539—222no—
368#536—112no—
369#533—22no—
370#533C2×D1111yescharacteristic
371#533C2×D1111yescharacteristic
372#532—111no—
373#529—222no—
374#520—112no—
375#519C2×D1112yes—
376C2×C4×Q8—111no—
377C2×C4×Q8C2×D1111yescharacteristic
378#491—112no—
379#491—114no—
380#490—112no—
381#489—112no—
382#489—114no—
383#489—112no—
384#488—114no—
385#487—114no—
386#479—114no—
387#479—114no—
388#478—114no—
389#477—112no—
390#476—114no—
391#475—112no—
392#475—114no—
393#464—114no—
394#464—114no—
395#464—114no—
396#462—114no—
397#462—112no—
398#462—114no—
399#460—112no—
400#446—114no—
401#446—114no—
402#441—114no—
403#441—114no—
404#441—114no—
405#440—114no—
406C4×Q16—114no—
407C4×SD16—114no—
408#428—112no—
409C2×#106—111no—
410#424—112no—
411#423—111no—
412#419—112no—
413#417—112no—
414#416—112no—
415#416—112no—
416C2×#103—111no—
417C2×#103—111no—
418#405—112no—
419C2×#97—111no—
420C22×C11—21no—
421C22×C11—21no—
422C22×C11#54812yes—
423C22×C11C23×D411yescharacteristic
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—42no—
427C4×C11—21no—
428C4×C11—21no—
429C4×C11—21no—
430C4×C11—21no—
431C4×C11—24no—
432C4×C11—24no—
433C4×C11—24no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11—42no—
437C4×C11#54812yes—
438C4×C11C22×#4111yescharacteristic
439C4×C11C2×2−1+411yescharacteristic
440Dic11—42no—
441Dic11—42no—
442Dic11—42no—
443C2×#41—112no—
444C22×Q8—111no—
445C22×Q8C22×D1111yescharacteristic
446#137—228no—
447C2×Q16—114no—
448C2×Q16—114no—
449C2×Q16—224no—
450C2×SD16—114no—
451C2×M16—112no—
452C22×C8—111no—
453C22×C8—111no—
454C4⋊Q8—22no—
455C4⋊Q8—24no—
456C4⋊Q8—22no—
457C4⋊Q8—24no—
458C4⋊Q8—22no—
459C4⋊Q8—111no—
460C4⋊Q8—114no—
461C4⋊Q8C22⋊D1111yescharacteristic
462C4⋊Q8C22⋊D1111yescharacteristic
463C4⋊Q8C22×D1111yescharacteristic
464C4⋊Q8C22×D1111yescharacteristic
465C4⋊Q8C22×D1114yes—
466#127—111no—
467#126—224no—
468#126—224no—
469#125—24no—
470#125—24no—
471#125—24no—
472#125—22no—
473#125—222no—
474#125—224no—
475#125C22⋊D1112yes—
476#125C22×D1112yes—
477#125C22×D1114yes—
478#124—112no—
479#124—114no—
480#124—222no—
481#123—224no—
482#123—224no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8—24no—
486C22⋊Q8—224no—
487C22⋊Q8—222no—
488C22⋊Q8—222no—
489C22⋊Q8C22⋊D1112yes—
490C22⋊Q8C22⋊D1112yes—
491#121—221no—
492#121—221no—
493C4×Q8—22no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×Q8—24no—
497C4×Q8—22no—
498C4×Q8—21no—
499C4×Q8—21no—
500C4×Q8—21no—
501C4×Q8—21no—
502C4×Q8—112no—
503C4×Q8—112no—
504C4×Q8—114no—
505C4×Q8—222no—
506C4×Q8—221no—
507C4×Q8—221no—
508C4×Q8C22×D1112yes—
509C4×Q8C22×D1112yes—
510C4×Q8C22×D1114yes—
511C4×Q8C22×D1114yes—
512C4×Q8C22×D1112yes—
513C4×Q8C22×D1112yes—
514C4×D4—114no—
515C4×D4—222no—
516C4×D4—224no—
517C4×D4—221no—
518C4×D4—221no—
519#117—24no—
520#117—222no—
521#117—224no—
522#117C22×D1112yes—
523#117C22×D1112yes—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—221no—
527C2×C4⋊C4—222no—
528C2×C4⋊C4C22×D1111yescharacteristic
529C2×C42—21no—
530C2×C42—221no—
531C2×C42C22×D1111yescharacteristic
532#107—114no—
533#106—114no—
534#106—114no—
535C4⋊C8—112no—
536C4⋊C8—112no—
537C4⋊C8—114no—
538C4⋊C8—114no—
539#103—114no—
540#103—114no—
541#103—112no—
542#103—112no—
543#103—112no—
544#103—112no—
545#103—114no—
546#103—114no—
547#103—114no—
548#102—112no—
549#102—112no—
550#102—112no—
551#102—112no—
552#102—114no—
553#97—112no—
554#97—112no—
555#97—114no—
556C4×C8—114no—
557C2×C11—22no—
558C2×C11C2×#54811yescharacteristic
559C2×C11#358611yescharacteristic
560C2×C11#358611yescharacteristic
561D11—82no—
562#41—224no—
563#41—224no—
564C2×Q8—22no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—24no—
569C2×Q8—112no—
570C2×Q8—112no—
571C2×Q8—221no—
572C2×Q8—222no—
573C2×Q8—222no—
574C2×Q8#434314yes—
575C2×Q8C2×C22⋊D1112yes—
576C2×Q8C2×C22⋊D1112yes—
577C2×Q8C23×D1112yes—
578C2×D4—112no—
579C2×D4—222no—
580C2×D4—221no—
581C2×D4—221no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—222no—
587C22×C4—224no—
588C22×C4C2×C22⋊D1111yescharacteristic
589C22×C4C2×C22⋊D1111yescharacteristic
590C22×C4C23×D1111yescharacteristic
591Q16—228no—
592Q16—228no—
593SD16—228no—
594M16—224no—
595C2×C8—112no—
596C2×C8—114no—
597C2×C8—112no—
598C2×C8—222no—
599C2×C8—222no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—22no—
611C4⋊C4—24no—
612C4⋊C4—112no—
613C4⋊C4—221no—
614C4⋊C4—224no—
615C4⋊C4—222no—
616C4⋊C4—222no—
617C4⋊C4—224no—
618C4⋊C4—221no—
619C4⋊C4—221no—
620C4⋊C4—224no—
621C4⋊C4C2×C22⋊D1112yes—
622C4⋊C4C2×C22⋊D1112yes—
623C4⋊C4C2×C22⋊D1114yes—
624C4⋊C4C2×C22⋊D1112yes—
625C4⋊C4C2×C22⋊D1114yes—
626C4⋊C4C2×C22⋊D1112yes—
627C4⋊C4C23×D1112yes—
628C4⋊C4C23×D1112yes—
629C4⋊C4C23×D1112yes—
630C22⋊C4—22no—
631C22⋊C4—222no—
632C22⋊C4—224no—
633C22⋊C4—224no—
634C22⋊C4—222no—
635C22⋊C4—224no—
636C22⋊C4C2×C22⋊D1114yes—
637C42—22no—
638C42—22no—
639C42—24no—
640C42—24no—
641C42—22no—
642C42—222no—
643C42—222no—
644C42—224no—
645C42C2×C22⋊D1111yescharacteristic
646C42C2×C22⋊D1111yescharacteristic
647C42C23×D1114yes—
648C42C23×D1111yescharacteristic
649C42C23×D1111yescharacteristic
650C11#6133511yescharacteristic, complemented, Sylow
651C23—222no—
652C23C22×C22⋊D1111yescharacteristic
653Q8—24no—
654Q8—22no—
655Q8—42no—
656Q8—42no—
657Q8—42no—
658Q8—81no—
659Q8—84no—
660Q8—222no—
661Q8—222no—
662Q8—222no—
663Q8—222no—
664Q8—442no—
665Q8C2×#434314yes—
666D4—222no—
667D4—222no—
668D4—442no—
669D4—444no—
670D4—881no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—81no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—442no—
683C2×C4—444no—
684C2×C4—884no—
685C2×C4—881no—
686C2×C4C2×#434312yes—
687C2×C4#6704012yes—
688C2×C4C22×C22⋊D1111yescharacteristic
689C2×C4C22×C22⋊D1111yescharacteristic
690C2×C4C22×C22⋊D1114yes—
691C2×C4C22×C22⋊D1114yes—
692C2×C4C22×C22⋊D1111yescharacteristic
693C2×C4C22×C22⋊D1111yescharacteristic
694C2×C4C22×C22⋊D1111yescharacteristic
695C2×C4C24×D1111yescharacteristic
696C8—222no—
697C8—224no—
698C8—222no—
699C22—21no—
700C22—21no—
701C22—442no—
702C22—442no—
703C22—442no—
704C22#1062334812yes—
705C22C23×C22⋊D1111yescharacteristic
706C4—21no—
707C4—21no—
708C4—24no—
709C4—21no—
710C4—21no—
711C4—24no—
712C4—24no—
713C4—42no—
714C4—42no—
715C4—42no—
716C4—442no—
717C4—442no—
718C4—442no—
719C4#1062334812yes—
720C4C22×#434311yescharacteristic
721C4C2×#6704011yescharacteristic
722C2—22no—
723C2—882no—
724C2C2×#1062334811yescharacteristic
725C2#1308340211yescharacteristic
726C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3502C2
socleC22×C11C23×D4
prime radical#10623008C22
hypercenter#3502D11
hypocenterC11#61335
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #533 ◁ #3502

Complements

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

NH ≅ G/Ntype
2. #13081458C2semidirect
3. #13081419C2semidirect
4. #13081384C2semidirect
5. #13081356C2semidirect
6. #13078986C2semidirect
8. #13078474C2semidirect
9. #13078417C2semidirect
10. #13078146C2semidirect
12. #13077557C2semidirect
13. #13077459C2semidirect
14. C2×#10622643C2semidirect
15. C11×#3502C2semidirect
289. #3502D11semidirect
650. C11#61335semidirect

Maximal subgroups

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

subgroupindex
#130824832
#130814582
#130814192
#130813842
#130813562
#130789862
#130789642
#130784742
#130784172
#130781462
#130780882
#130775572
#130774592
C2×#106226432
C11×#35022
#6133511