Finite Group Databasebeta

← #15633890

Subgroups — #15633890

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#13082421C211yesmaximal, characteristic, complemented
2#13081452C214yesmaximal, complemented
3#13081415C214yesmaximal, complemented
4#13081378C214yesmaximal, complemented
5#13081352C214yesmaximal, complemented
6#13078981C212yesmaximal, complemented
7#13078961C211yesmaximal, characteristic
8#13078478C212yesmaximal, complemented
9#13078421C211yesmaximal, characteristic, complemented
10#13078142C212yesmaximal, complemented
11#13078084C211yesmaximal, characteristic
12#13077557C211yesmaximal, characteristic, complemented
13#13077455C212yesmaximal, complemented
14C2×#10622643C211yesmaximal, characteristic, complemented
15C11×#3507C211yesmaximal, characteristic
16C11×#559C2212yes—
17C11×#557C2212yes—
18C11×#556—21no—
19C11×#556C2214yes—
20C11×#554—21no—
21C11×#552—22no—
22C11×#539—22no—
23C11×#536C2212yes—
24C11×#533C2211yescharacteristic
25C11×#532C2211yescharacteristic
26C11×#529—22no—
27C11×#520C2212yes—
28C2×C4×Q8×C11C2211yescharacteristic
29C2×#67004C2212yes—
30C22×#4326C2211yescharacteristic
31#10623253—21no—
32#10623252—21no—
33#10623216—22no—
34#10623154—22no—
35#10623153—22no—
36#10623098C2214yes—
37#10623098C2212yes—
38Q8×Dic22C2212yes—
39#10623050C2212yes—
40#10623047C2212yes—
41#10623001C2211yescharacteristic
42C2×C4×Dic22C2211yescharacteristic
43#10622846C2212yes—
44#10622846C2212yes—
45#10622845C2212yes—
46#10622838C2212yes—
47C2×#66899C2211yescharacteristic
48#10622703C2214yes—
49#10622703C2212yes—
50#10622703C2214yes—
51#10622695C2212yes—
52#10622695C2214yes—
53#10622694C2214yes—
54#10622688C2212yes—
55#10622684C2212yes—
56#10622669C2214yes—
57#10622668C2212yes—
58#10622668C2214yes—
59#10622668C2212yes—
60#10622667C2214yes—
61#10622667C2214yes—
62#10622667C2214yes—
63#10622643C2214yes—
64#10622643C2214yes—
65#10622643C2214yes—
66C4×#4326C2214yes—
67#10622637C2214yes—
68#10622637C2214yes—
69#10622635C2214yes—
70#10622635C2214yes—
71#10622634C2212yes—
72#10622633C2212yes—
73#10622633C2214yes—
74#10622631C2214yes—
75C4×#4324C2214yes—
76#10622622C2214yes—
77#10622621C2214yes—
78#10622612C2212yes—
79#10622610C2212yes—
80C2×#66874C2211yescharacteristic
81#10622577C2212yes—
82C2×#66872C2211yescharacteristic
83#10622537C2211yescharacteristic
84C2×#66867C2211yescharacteristic
85C2×C11×#41C2312yes—
86C22×Q8×C11C2311yescharacteristic
87C22×Dic22C2311yescharacteristic
88C11×C4⋊Q8D411yescharacteristic
89C11×C4⋊Q8D411yescharacteristic
90C11×C4⋊Q8C2311yescharacteristic
91C11×C4⋊Q8C2314yes—
92C11×#127C2311yescharacteristic
93C11×#126—24no—
94C11×#126—24no—
95C11×#125—22no—
96C11×#125—24no—
97C11×#125D412yes—
98C11×#124—22no—
99C11×#124C2312yes—
100C11×#124C2314yes—
101C11×#123—24no—
102C11×#123—24no—
103C11×C22⋊Q8—24no—
104C11×C22⋊Q8—22no—
105C11×C22⋊Q8—22no—
106C11×C22⋊Q8D412yes—
107C11×C22⋊Q8D412yes—
108C11×#121—21no—
109C11×#121—21no—
110C4×Q8×C11—22no—
111C4×Q8×C11—21no—
112C4×Q8×C11—21no—
113C4×Q8×C11C2312yes—
114C4×Q8×C11C2312yes—
115C4×Q8×C11C2314yes—
116C4×Q8×C11C2312yes—
117C4×Q8×C11C2312yes—
118C4×D4×C11—22no—
119C4×D4×C11—24no—
120C4×D4×C11—21no—
121C4×D4×C11—21no—
122C4×D4×C11C2314yes—
123C11×#117—22no—
124C11×#117—24no—
125C11×#117C2312yes—
126C2×C11×C4⋊C4—21no—
127C2×C11×C4⋊C4—22no—
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C42×C11—21no—
130C2×C42×C11C2311yescharacteristic
131#67004—28no—
132Q8×Dic11—22no—
133#66997—22no—
134#66997—24no—
135C2×#4326—24no—
136C2×#4326C2314yes—
137C2×#4326C2314yes—
138C2×#4324C2314yes—
139#66979C2312yes—
140C2×C4⋊Dic11C2311yescharacteristic
141#66977—21no—
142#66977—21no—
143C2×Dic11⋊C4—21no—
144C2×C4×Dic11—21no—
145C2×#4318C2312yes—
146C22×C11⋊C8C2311yescharacteristic
147C22×C11⋊C8C2311yescharacteristic
148#66943—22no—
149#66942—24no—
150#66942—24no—
151#66942—24no—
152#66941—22no—
153#66941—22no—
154#66941—24no—
155#66940—22no—
156#66940—22no—
157#66940—22no—
158#66940—24no—
159#66931—24no—
160#66930—24no—
161#66923C2312yes—
162#66923C2314yes—
163#66922C2311yescharacteristic
164#66922C2311yescharacteristic
165#66922C2314yes—
166C4×Dic22—21no—
167C4×Dic22—21no—
168C4×Dic22—21no—
169C4×Dic22—21no—
170C4×Dic22C2312yes—
171C4×Dic22C2312yes—
172C4×Dic22C2314yes—
173C4×Dic22C2314yes—
174#66899C2314yes—
175#66899C2314yes—
176#66899C2314yes—
177#66899C2314yes—
178#66899C2312yes—
179#66899C2312yes—
180#66899C2312yes—
181#66899C2312yes—
182#66896C2314yes—
183#66896C2312yes—
184#66896C2312yes—
185#66896C2312yes—
186#66896C2312yes—
187#66874C2314yes—
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
200C11×#41—24no—
201C11×#41—24no—
202C2×Q8×C11—21no—
203C2×Q8×C11—22no—
204C2×Q8×C11—22no—
205C2×Q8×C11C2×D412yes—
206C2×Q8×C11C2×D412yes—
207C2×Q8×C11C2412yes—
208C2×Q8×C11C2412yes—
209C2×D4×C11—22no—
210C2×D4×C11—21no—
211C2×D4×C11—21no—
212C2×D4×C11C2412yes—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—22no—
216C22×C4×C11—24no—
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2411yescharacteristic
220C22×Dic11—21no—
221C22×Dic11—21no—
222C2×Dic22—21no—
223C2×Dic22—21no—
224C2×Dic22—21no—
225C2×Dic22—24no—
226C2×Dic22—22no—
227C2×Dic22#4114yes—
228C2×Dic22C2412yes—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—24no—
231C11×C4⋊C4—22no—
232C11×C4⋊C4—22no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—24no—
237C11×C4⋊C4C2×D412yes—
238C11×C4⋊C4C2×D412yes—
239C11×C4⋊C4C2×D414yes—
240C11×C4⋊C4C2×D412yes—
241C11×C4⋊C4C2×D414yes—
242C11×C4⋊C4C2×D412yes—
243C11×C4⋊C4C2412yes—
244C11×C22⋊C4—22no—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—22no—
248C11×C22⋊C4—24no—
249C11×C22⋊C4C2×D414yes—
250C42×C11—22no—
251C42×C11—22no—
252C42×C11—24no—
253C42×C11C2×D411yescharacteristic
254C42×C11C2×D411yescharacteristic
255C42×C11C2414yes—
256C42×C11C2411yescharacteristic
257C42×C11C2411yescharacteristic
258C22⋊Dic11—22no—
259#4326—28no—
260#4326—28no—
261#4324—28no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—24no—
266C4⋊Dic11C2412yes—
267C4⋊Dic11C2412yes—
268C4⋊Dic11C2412yes—
269Dic11⋊C4—22no—
270Dic11⋊C4—22no—
271Dic11⋊C4—22no—
272Dic11⋊C4—22no—
273Dic11⋊C4—24no—
274Dic11⋊C4—24no—
275Dic11⋊C4—24no—
276Dic11⋊C4—24no—
277C4×Dic11—22no—
278C4×Dic11—22no—
279C4×Dic11—22no—
280C4×Dic11—24no—
281C4×Dic11—24no—
282#4318—24no—
283C2×C11⋊C8—22no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8C2412yes—
286C2×C11⋊C8C2414yes—
287C2×C11⋊C8C2412yes—
288#3507D1111yescharacteristic
289#3502—111no—
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×C11—22no—
304C23×C11C22×D411yescharacteristic
305Q8×C11—22no—
306Q8×C11—22no—
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—42no—
310Q8×C11—42no—
311Q8×C11—42no—
312D4×C11—22no—
313D4×C11—22no—
314D4×C11—42no—
315D4×C11—44no—
316D4×C11—81no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—42no—
323C2×C4×C11—44no—
324C2×C4×C11—84no—
325C2×C4×C11—81no—
326C2×C4×C11C22×D411yescharacteristic
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C22×D414yes—
329C2×C4×C11C22×D414yes—
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C2×#4112yes—
334C2×C4×C112−1+412yes—
335C2×C4×C11C2511yescharacteristic
336C2×Dic11—24no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—81no—
342Dic22—24no—
343Dic22—22no—
344Dic22—42no—
345Dic22—81no—
346Dic22—84no—
347Dic22C2×#4114yes—
348C11⋊C8—22no—
349C11⋊C8—24no—
350C11⋊C8—22no—
351C2×#137—112no—
352C22×Q16—111no—
353#559C2×D1112yes—
354Q82—112no—
355Q82—221no—
356#557—114no—
357#557—112no—
358#557—221no—
359#557—222no—
360#557C2×D1112yes—
361#556—21no—
362#556C2×D1114yes—
363#554—21no—
364#552—22no—
365#544—112no—
366#544—222no—
367#539—22no—
368#536C2×D1112yes—
369#533—111no—
370#533—222no—
371#533C2×D1111yescharacteristic
372#532C2×D1111yescharacteristic
373#529—22no—
374#520C2×D1112yes—
375#519—112no—
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—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11#54812yes—
426C22×C11C23×D411yescharacteristic
427C4×C11—21no—
428C4×C11—21no—
429C4×C11—21no—
430C4×C11—21no—
431C4×C11—24no—
432C4×C11—24no—
433C4×C11—42no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11#54812yes—
437C4×C11C22×#4111yescharacteristic
438C4×C11C2×2−1+411yescharacteristic
439Dic11—24no—
440Dic11—42no—
441Dic11—42no—
442Dic11—42no—
443C2×#41C22×D1112yes—
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—111no—
455C4⋊Q8—111no—
456C4⋊Q8—114no—
457C4⋊Q8—222no—
458C4⋊Q8—224no—
459C4⋊Q8—222no—
460C4⋊Q8—222no—
461C4⋊Q8—224no—
462C4⋊Q8C22⋊D1111yescharacteristic
463C4⋊Q8C22⋊D1111yescharacteristic
464C4⋊Q8C22×D1111yescharacteristic
465C4⋊Q8C22×D1114yes—
466#127C22×D1111yescharacteristic
467#126—24no—
468#126—24no—
469#125—22no—
470#125—24no—
471#125—112no—
472#125—114no—
473#125—224no—
474#125—222no—
475#125—224no—
476#125—224no—
477#125C22⋊D1112yes—
478#124—22no—
479#124C22×D1112yes—
480#124C22×D1114yes—
481#123—24no—
482#123—24no—
483C22⋊Q8—24no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—221no—
487C22⋊Q8—221no—
488C22⋊Q8—224no—
489C22⋊Q8C22⋊D1112yes—
490C22⋊Q8C22⋊D1112yes—
491#121—21no—
492#121—21no—
493C4×Q8—22no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—112no—
497C4×Q8—112no—
498C4×Q8—114no—
499C4×Q8—114no—
500C4×Q8—222no—
501C4×Q8—222no—
502C4×Q8—222no—
503C4×Q8—224no—
504C4×Q8—222no—
505C4×Q8—221no—
506C4×Q8—221no—
507C4×Q8—221no—
508C4×Q8—221no—
509C4×Q8C22×D1112yes—
510C4×Q8C22×D1112yes—
511C4×Q8C22×D1114yes—
512C4×Q8C22×D1112yes—
513C4×Q8C22×D1112yes—
514C4×D4—22no—
515C4×D4—24no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4C22×D1114yes—
519#117—22no—
520#117—24no—
521#117—112no—
522#117—224no—
523#117C22×D1112yes—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—221no—
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—112no—
541#103—112no—
542#103—112no—
543#103—112no—
544#103—114no—
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×C11—82no—
559C2×C11C2×#54811yescharacteristic
560C2×C11#358611yescharacteristic
561C2×C11#358611yescharacteristic
562#41—24no—
563#41—24no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—114no—
568C2×Q8—112no—
569C2×Q8—222no—
570C2×Q8—221no—
571C2×Q8—221no—
572C2×Q8—221no—
573C2×Q8—224no—
574C2×Q8C2×C22⋊D1112yes—
575C2×Q8C2×C22⋊D1112yes—
576C2×Q8C23×D1112yes—
577C2×Q8C23×D1112yes—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4C23×D1112yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—221no—
587C22×C4—221no—
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—21no—
601C4⋊C4—24no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—24no—
608C4⋊C4—112no—
609C4⋊C4—112no—
610C4⋊C4—112no—
611C4⋊C4—221no—
612C4⋊C4—222no—
613C4⋊C4—222no—
614C4⋊C4—224no—
615C4⋊C4—224no—
616C4⋊C4—222no—
617C4⋊C4—221no—
618C4⋊C4—224no—
619C4⋊C4—222no—
620C4⋊C4—224no—
621C4⋊C4—221no—
622C4⋊C4—224no—
623C4⋊C4C2×C22⋊D1112yes—
624C4⋊C4C2×C22⋊D1112yes—
625C4⋊C4C2×C22⋊D1114yes—
626C4⋊C4C2×C22⋊D1112yes—
627C4⋊C4C2×C22⋊D1114yes—
628C4⋊C4C2×C22⋊D1112yes—
629C4⋊C4C23×D1112yes—
630C22⋊C4—22no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—22no—
634C22⋊C4—24no—
635C22⋊C4—222no—
636C22⋊C4C2×C22⋊D1114yes—
637C42—22no—
638C42—22no—
639C42—24no—
640C42—222no—
641C42—222no—
642C42—222no—
643C42—224no—
644C42—224no—
645C42C2×C22⋊D1111yescharacteristic
646C42C2×C22⋊D1111yescharacteristic
647C42C23×D1114yes—
648C42C23×D1111yescharacteristic
649C42C23×D1111yescharacteristic
650C11#6133511yescharacteristic, complemented, Sylow
651C23—22no—
652C23C22×C22⋊D1111yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—22no—
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—114no—
661Q8—224no—
662Q8—222no—
663Q8—442no—
664Q8—881no—
665Q8—884no—
666D4—22no—
667D4—22no—
668D4—42no—
669D4—44no—
670D4—81no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—44no—
678C2×C4—84no—
679C2×C4—81no—
680C2×C4—224no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—881no—
686C2×C4#41×D1112yes—
687C2×C4#6704312yes—
688C2×C4C22×C22⋊D1111yescharacteristic
689C2×C4C22×C22⋊D1111yescharacteristic
690C2×C4C22×C22⋊D1114yes—
691C2×C4C22×C22⋊D1111yescharacteristic
692C2×C4C22×C22⋊D1111yescharacteristic
693C2×C4C22×C22⋊D1114yes—
694C2×C4C22×C22⋊D1111yescharacteristic
695C2×C4C24×D1111yescharacteristic
696C8—222no—
697C8—224no—
698C8—222no—
699C22—21no—
700C22—21no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22#1062336212yes—
705C22C23×C22⋊D1111yescharacteristic
706C4—21no—
707C4—21no—
708C4—24no—
709C4—21no—
710C4—21no—
711C4—24no—
712C4—42no—
713C4—42no—
714C4—42no—
715C4—224no—
716C4—442no—
717C4—442no—
718C4—442no—
719C4#1062336212yes—
720C4C2×#41×D1111yescharacteristic
721C4C2×#6704311yescharacteristic
722C2—22no—
723C2—82no—
724C2C2×#1062336211yescharacteristic
725C2#1308340211yescharacteristic
726C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3507C2
socleC22×C11C23×D4
prime radicalC11×#532C22
hypercenter#3507D11
hypocenterC11#61335
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #533 ◁ #3507

Complements

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

NH ≅ G/Ntype
1. #13082421C2semidirect
2. #13081452C2semidirect
3. #13081415C2semidirect
4. #13081378C2semidirect
5. #13081352C2semidirect
6. #13078981C2semidirect
8. #13078478C2semidirect
9. #13078421C2semidirect
10. #13078142C2semidirect
12. #13077557C2semidirect
13. #13077455C2semidirect
14. C2×#10622643C2semidirect
650. C11#61335semidirect

Maximal subgroups

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

subgroupindex
#130824212
#130814522
#130814152
#130813782
#130813522
#130789812
#130789612
#130784782
#130784212
#130781422
#130780842
#130775572
#130774552
C2×#106226432
C11×#35072
#6133511