Finite Group Databasebeta

← #15644171

Subgroups — #15644171

Order 2816.

1704 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13083016C211yesmaximal, characteristic
2#13081555C214yesmaximal, complemented
3#13081522C212yesmaximal, complemented
4#13081487C212yesmaximal, complemented
5#13081345C214yesmaximal, complemented
6#13081345C212yesmaximal, complemented
7#13081287C212yesmaximal, complemented
8#13079869C214yesmaximal, complemented
9#13079814C211yesmaximal, characteristic, complemented
10#13079752C211yesmaximal, characteristic, complemented
11#13078907C214yesmaximal, complemented
12#13078738C211yesmaximal, characteristic, complemented
13#13078647C211yesmaximal, characteristic, complemented
14#13077711C211yesmaximal, characteristic, complemented
15C11×#3502C211yesmaximal, characteristic, complemented
16Q82×C11—21no—
17Q82×C11C2212yes—
18C11×#557—21no—
19C11×#557—22no—
20C11×#557C2212yes—
21C11×#557C2214yes—
22C11×#544—22no—
23C11×#544C2212yes—
24C11×#533—22no—
25C11×#533C2211yescharacteristic
26C11×#533C2211yescharacteristic
27C11×#519C2212yes—
28C2×C4×Q8×C11C2211yescharacteristic
29#10623257—21no—
30#10623257—21no—
31#10623231—22no—
32#10623160—22no—
33#10623160—22no—
34#10623110C2212yes—
35#10623110C2212yes—
36#10623108C2212yes—
37#10623108C2212yes—
38#10623066C2214yes—
39#10623008C2211yescharacteristic
40#10623008C2211yescharacteristic
41#10622840C2212yes—
42#10622840C2212yes—
43#10622701C2211yescharacteristic
44#10622701C2214yes—
45#10622701C2211yescharacteristic
46#10622700C2212yes—
47#10622700C2214yes—
48#10622697C2212yes—
49#10622697C2214yes—
50#10622693C2214yes—
51#10622692C2211yescharacteristic
52#10622691C2211yescharacteristic
53#10622680C2212yes—
54#10622680C2214yes—
55#10622679C2214yes—
56#10622679C2214yes—
57#10622679C2214yes—
58#10622678C2212yes—
59#10622677C2214yes—
60#10622640C2212yes—
61#10622640C2214yes—
62#10622640C2214yes—
63#10622640C2212yes—
64#10622639C2214yes—
65#10622639C2214yes—
66#10622639C2214yes—
67C4×#4325C2212yes—
68C4×#4325C2214yes—
69C4×#4325C2212yes—
70C4×#4325C2214yes—
71#10622637C2212yes—
72#10622637C2214yes—
73Q8×C11⋊C8C2212yes—
74#10622635C2214yes—
75#10622635C2214yes—
76#10622634C2212yes—
77#10622633C2212yes—
78#10622616C2214yes—
79#10622616C2214yes—
80#10622613C2214yes—
81#10622581C2212yes—
82#10622580C2212yes—
83#10622539C2211yescharacteristic
84#10622538C2211yescharacteristic
85C22×Q8×C11C2311yescharacteristic
86C2×#4343—22no—
87C2×#4343—22no—
88C2×#4339—21no—
89C2×#4339—21no—
90C11×C4⋊Q8—22no—
91C11×C4⋊Q8—24no—
92C11×C4⋊Q8—22no—
93C11×C4⋊Q8—24no—
94C11×C4⋊Q8—22no—
95C11×C4⋊Q8D411yescharacteristic
96C11×C4⋊Q8D411yescharacteristic
97C11×C4⋊Q8C2311yescharacteristic
98C11×C4⋊Q8C2311yescharacteristic
99C11×C4⋊Q8C2314yes—
100C11×#125—24no—
101C11×#125—24no—
102C11×#125—24no—
103C11×#125—22no—
104C11×#125D412yes—
105C11×#125C2312yes—
106C11×#125C2314yes—
107C11×C22⋊Q8—21no—
108C11×C22⋊Q8—21no—
109C11×C22⋊Q8—24no—
110C11×C22⋊Q8D412yes—
111C11×C22⋊Q8D412yes—
112C4×Q8×C11—22no—
113C4×Q8×C11—22no—
114C4×Q8×C11—22no—
115C4×Q8×C11—24no—
116C4×Q8×C11—22no—
117C4×Q8×C11—21no—
118C4×Q8×C11—21no—
119C4×Q8×C11—21no—
120C4×Q8×C11—21no—
121C4×Q8×C11C2312yes—
122C4×Q8×C11C2312yes—
123C4×Q8×C11C2314yes—
124C4×Q8×C11C2314yes—
125C4×Q8×C11C2312yes—
126C4×Q8×C11C2312yes—
127C11×#117—24no—
128C11×#117C2312yes—
129C11×#117C2312yes—
130C2×C11×C4⋊C4—21no—
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C42×C11—21no—
133C2×C42×C11C2311yescharacteristic
134#66999—22no—
135#66999—22no—
136C2×#4325C2312yes—
137C2×#4325C2312yes—
138C2×#4325C2314yes—
139#66983—21no—
140#66983—21no—
141#66983C2312yes—
142#66983C2312yes—
143#66949—24no—
144#66949—24no—
145#66948—22no—
146#66948—22no—
147#66948—24no—
148#66948—24no—
149#66947—24no—
150#66947—24no—
151C4⋊C4×D11—22no—
152C4⋊C4×D11—22no—
153#66937—24no—
154#66937—24no—
155#66928—21no—
156#66928—21no—
157#66927C2311yescharacteristic
158#66927C2311yescharacteristic
159#66927C2314yes—
160C4×D44—21no—
161C4×D44—21no—
162C4×D44C2312yes—
163C4×D44C2312yes—
164C4×D44C2314yes—
165C4×D44C2314yes—
166#66923C2314yes—
167#66922C2311yescharacteristic
168#66922C2311yescharacteristic
169#66899C2312yes—
170#66899C2312yes—
171#66899C2314yes—
172C22⋊(C11⋊C8)C2312yes—
173C22⋊(C11⋊C8)C2312yes—
174#66873C2314yes—
175#66873C2312yes—
176#66873C2312yes—
177#66873C2314yes—
178#66873C2314yes—
179#66873C2314yes—
180#66873C2314yes—
181#66872C2312yes—
182#66872C2312yes—
183#66872C2314yes—
184#66872C2314yes—
185#66871C2314yes—
186#66871C2314yes—
187#66871C2314yes—
188C4⋊(C11⋊C8)C2312yes—
189C4⋊(C11⋊C8)C2312yes—
190C4⋊(C11⋊C8)C2314yes—
191C4⋊(C11⋊C8)C2314yes—
192#66867C2312yes—
193#66867C2314yes—
194C4×C11⋊C8C2311yescharacteristic
195C4×C11⋊C8C2311yescharacteristic
196C4×C11⋊C8C2314yes—
197#61851—111nomaximal, Sylow
198C2×Q8×C11—24no—
199C2×Q8×C11—21no—
200C2×Q8×C11—21no—
201C2×Q8×C11—21no—
202C2×Q8×C11—24no—
203C2×Q8×C11C2×D412yes—
204C2×Q8×C11C2×D412yes—
205C2×Q8×C11C2412yes—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2411yescharacteristic
211C2×C22⋊D11—22no—
212C2×C22⋊D11—22no—
213#4343—84no—
214#4343—84no—
215#4339—82no—
216#4339—82no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44—24no—
222C2×D44—24no—
223C2×D44C2412yes—
224C2×D44C2412yes—
225C2×C4×D11—22no—
226C2×C4×D11—22no—
227C2×C4×D11—24no—
228C2×C4×D11—24no—
229C2×Dic22—21no—
230C2×Dic22—21no—
231C11×C4⋊C4—22no—
232C11×C4⋊C4—22no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—24no—
235C11×C4⋊C4—24no—
236C11×C4⋊C4—22no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—24no—
240C11×C4⋊C4—24no—
241C11×C4⋊C4—22no—
242C11×C4⋊C4—24no—
243C11×C4⋊C4C2×D412yes—
244C11×C4⋊C4C2×D412yes—
245C11×C4⋊C4C2×D412yes—
246C11×C4⋊C4C2×D412yes—
247C11×C4⋊C4C2×D414yes—
248C11×C4⋊C4C2×D414yes—
249C11×C4⋊C4C2412yes—
250C11×C4⋊C4C2412yes—
251C11×C4⋊C4C2412yes—
252C11×C22⋊C4—22no—
253C11×C22⋊C4C2×D414yes—
254C42×C11—22no—
255C42×C11—22no—
256C42×C11—24no—
257C42×C11—24no—
258C42×C11—22no—
259C42×C11C2×D411yescharacteristic
260C42×C11C2×D411yescharacteristic
261C42×C11C2411yescharacteristic
262C42×C11C2414yes—
263C42×C11C2411yescharacteristic
264#4325—24no—
265#4325—24no—
266#4325—28no—
267(C2×D11)⋊C4—22no—
268(C2×D11)⋊C4—22no—
269(C2×D11)⋊C4—22no—
270(C2×D11)⋊C4—22no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273C4⋊Dic11—21no—
274C4⋊Dic11—21no—
275C4⋊Dic11C2412yes—
276C4⋊Dic11C2412yes—
277Dic11⋊C4—24no—
278Dic11⋊C4—24no—
279C2×C11⋊C8C2412yes—
280C2×C11⋊C8C2412yes—
281C2×C11⋊C8C2414yes—
282#3548—111no—
283#3502D1111yescharacteristic, complemented
284#3388—114no—
285#3385—112no—
286#3381—112no—
287#3368—112no—
288#3368—114no—
289#3362—112no—
290#3241—114no—
291#3235—111no—
292#3228—111no—
293#3126—114no—
294#3112—111no—
295#3103—111no—
296#2985—111no—
297C23×C11C22×D411yescharacteristic
298C22×D11—22no—
299C22×D11—22no—
300Q8×C11—24no—
301Q8×C11—24no—
302Q8×C11—22no—
303Q8×C11—42no—
304Q8×C11—42no—
305Q8×C11—81no—
306Q8×C11—84no—
307Q8×C112−1+414yes—
308C2×C4×C11—24no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—41no—
316C2×C4×C11—81no—
317C2×C4×C11C22×D414yes—
318C2×C4×C11C22×D414yes—
319C2×C4×C11C22×D411yescharacteristic
320C2×C4×C11C22×D411yescharacteristic
321C2×C4×C11C22×D411yescharacteristic
322C2×C4×C11C22×D411yescharacteristic
323C2×C4×C11C22×D411yescharacteristic
324C2×C4×C11C2511yescharacteristic
325C22⋊D11—82no—
326C22⋊D11—82no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329D44—22no—
330D44—24no—
331D44—22no—
332D44—42no—
333D44—42no—
334D44—81no—
335D44—81no—
336D44—84no—
337D44—84no—
338C4×D11—44no—
339C4×D11—44no—
340C4×D11—84no—
341C4×D11—84no—
342Dic22—81no—
343Dic22—81no—
344C11⋊C8—22no—
345C11⋊C8—22no—
346C11⋊C8—24no—
347#562—222no—
348Q82—21no—
349Q82C2×D1112yes—
350#557—21no—
351#557—22no—
352#557C2×D1112yes—
353#557C2×D1114yes—
354#554—112no—
355#554—112no—
356#550—112no—
357#550—112no—
358#547—221no—
359#547—221no—
360#544—22no—
361#544C2×D1112yes—
362#540—114no—
363#537—222no—
364#537—222no—
365#533—22no—
366#533C2×D1111yescharacteristic
367#533C2×D1111yescharacteristic
368#532—111no—
369#532—111no—
370#519C2×D1112yes—
371C2×C4×Q8C2×D1111yescharacteristic
372#501—114no—
373#501—112no—
374#500—111no—
375#499—114no—
376#498—111no—
377#490—112no—
378#490—114no—
379#486—111no—
380#486—114no—
381#486—111no—
382#482—114no—
383#482—114no—
384#481—112no—
385#480—112no—
386#479—114no—
387#479—114no—
388#478—114no—
389#478—114no—
390#478—114no—
391#477—112no—
392#476—112no—
393#476—114no—
394#475—112no—
395#474—112no—
396#474—114no—
397#460—112no—
398#460—112no—
399#460—114no—
400#460—114no—
401#448—112no—
402#448—112no—
403#446—112no—
404#446—114no—
405C8×Q8—112no—
406#440—114no—
407#440—114no—
408#440—114no—
409C4×SD16—112no—
410C4×SD16—112no—
411C4×SD16—114no—
412C4×SD16—114no—
413#433—114no—
414#432—111no—
415#431—111no—
416C22×C11—21no—
417C22×C11—21no—
418C22×C11—21no—
419C22×C11C23×D411yescharacteristic
420C2×D11—42no—
421C2×D11—42no—
422C2×D11—42no—
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C4×C11—21no—
427C4×C11—21no—
428C4×C11—24no—
429C4×C11—24no—
430C4×C11—21no—
431C4×C11—21no—
432C4×C11—24no—
433C4×C11—42no—
434C4×C11—42no—
435C4×C11—42no—
436C4×C11#57712yes—
437C4×C11C2×2−1+412yes—
438Dic11—42no—
439Dic11—42no—
440C2×#41—222no—
441C2×#41—222no—
442C2×#41—221no—
443C2×#41—221no—
444C22×Q8C22×D1111yescharacteristic
445C2×SD16—112no—
446C2×SD16—112no—
447C2×SD16—114no—
448C4⋊Q8—22no—
449C4⋊Q8—24no—
450C4⋊Q8—22no—
451C4⋊Q8—24no—
452C4⋊Q8—22no—
453C4⋊Q8—111no—
454C4⋊Q8—111no—
455C4⋊Q8C22⋊D1111yescharacteristic
456C4⋊Q8C22⋊D1111yescharacteristic
457C4⋊Q8C22×D1111yescharacteristic
458C4⋊Q8C22×D1111yescharacteristic
459C4⋊Q8C22×D1114yes—
460#127—111no—
461#127—111no—
462#127—114no—
463#125—24no—
464#125—24no—
465#125—24no—
466#125—22no—
467#125—114no—
468#125C22⋊D1112yes—
469#125C22×D1112yes—
470#125C22×D1114yes—
471#124—221no—
472#124—221no—
473#123—224no—
474#123—224no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8—24no—
478C22⋊Q8—222no—
479C22⋊Q8—222no—
480C22⋊Q8—224no—
481C22⋊Q8—224no—
482C22⋊Q8C22⋊D1112yes—
483C22⋊Q8C22⋊D1112yes—
484#121—112no—
485#121—112no—
486#121—221no—
487#121—221no—
488#121—222no—
489#121—222no—
490#121—224no—
491#121—224no—
492#121—224no—
493#121—224no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×Q8—22no—
497C4×Q8—24no—
498C4×Q8—22no—
499C4×Q8—21no—
500C4×Q8—21no—
501C4×Q8—21no—
502C4×Q8—21no—
503C4×Q8C22×D1112yes—
504C4×Q8C22×D1112yes—
505C4×Q8C22×D1114yes—
506C4×Q8C22×D1114yes—
507C4×Q8C22×D1112yes—
508C4×Q8C22×D1112yes—
509C4×D4—112no—
510C4×D4—112no—
511C4×D4—114no—
512C4×D4—114no—
513C4×D4—221no—
514C4×D4—221no—
515#117—24no—
516#117C22×D1112yes—
517#117C22×D1112yes—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—222no—
520C2×C4⋊C4—222no—
521C2×C4⋊C4C22×D1111yescharacteristic
522C2×C42—21no—
523C2×C42C22×D1111yescharacteristic
524#107—114no—
525#107—114no—
526#107—114no—
527#106—112no—
528#106—112no—
529#106—114no—
530#106—114no—
531C4⋊C8—112no—
532C4⋊C8—112no—
533C4⋊C8—114no—
534C4⋊C8—114no—
535#103—112no—
536#103—112no—
537#103—114no—
538#102—112no—
539#102—114no—
540#102—114no—
541#102—112no—
542#102—114no—
543#102—114no—
544#102—114no—
545C22⋊C8—112no—
546C22⋊C8—112no—
547#97—112no—
548#97—114no—
549C4×C8—111no—
550C4×C8—111no—
551C4×C8—114no—
552C2×C11—41no—
553C2×C11#348611yescharacteristic
554C2×C11C2×#57711yescharacteristic
555C2×C11#358511yescharacteristic
556D11—82no—
557D11—82no—
558#41—882no—
559#41—882no—
560#41—884no—
561#41—884no—
562C2×Q8—24no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—24no—
567C2×Q8—221no—
568C2×Q8—221no—
569C2×Q8C2×C22⋊D1112yes—
570C2×Q8C2×C22⋊D1112yes—
571C2×Q8C23×D1112yes—
572C2×D4—112no—
573C2×D4—112no—
574C2×D4—222no—
575C2×D4—222no—
576C2×D4—221no—
577C2×D4—221no—
578C2×D4—224no—
579C2×D4—224no—
580C2×D4—221no—
581C2×D4—221no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—224no—
587C22×C4—224no—
588C22×C4C2×C22⋊D1111yescharacteristic
589C22×C4C2×C22⋊D1111yescharacteristic
590C22×C4C23×D1111yescharacteristic
591SD16—224no—
592SD16—224no—
593SD16—228no—
594C2×C8—112no—
595C2×C8—112no—
596C2×C8—114no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—21no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—22no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—22no—
608C4⋊C4—24no—
609C4⋊C4—112no—
610C4⋊C4—112no—
611C4⋊C4—221no—
612C4⋊C4—221no—
613C4⋊C4—224no—
614C4⋊C4—224no—
615C4⋊C4C2×C22⋊D1112yes—
616C4⋊C4C2×C22⋊D1112yes—
617C4⋊C4C2×C22⋊D1112yes—
618C4⋊C4C2×C22⋊D1112yes—
619C4⋊C4C2×C22⋊D1114yes—
620C4⋊C4C2×C22⋊D1114yes—
621C4⋊C4C23×D1112yes—
622C4⋊C4C23×D1112yes—
623C4⋊C4C23×D1112yes—
624C22⋊C4—22no—
625C22⋊C4—224no—
626C22⋊C4—224no—
627C22⋊C4—222no—
628C22⋊C4—222no—
629C22⋊C4—222no—
630C22⋊C4—222no—
631C22⋊C4C2×C22⋊D1114yes—
632C42—22no—
633C42—22no—
634C42—24no—
635C42—24no—
636C42—22no—
637C42C2×C22⋊D1111yescharacteristic
638C42C2×C22⋊D1111yescharacteristic
639C42C23×D1111yescharacteristic
640C42C23×D1114yes—
641C42C23×D1111yescharacteristic
642C11#6185111yescharacteristic, complemented, Sylow
643C23—222no—
644C23—222no—
645C23C22×C22⋊D1111yescharacteristic
646Q8—24no—
647Q8—24no—
648Q8—22no—
649Q8—42no—
650Q8—42no—
651Q8—81no—
652Q8—84no—
653Q8—881no—
654Q8—881no—
655Q8#6704014yes—
656D4—222no—
657D4—222no—
658D4—224no—
659D4—442no—
660D4—442no—
661D4—881no—
662D4—884no—
663D4—881no—
664D4—884no—
665D4—882no—
666D4—882no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—41no—
675C2×C4—81no—
676C2×C4—222no—
677C2×C4—222no—
678C2×C4—444no—
679C2×C4—444no—
680C2×C4—884no—
681C2×C4—884no—
682C2×C4C22×C22⋊D1111yescharacteristic
683C2×C4C22×C22⋊D1111yescharacteristic
684C2×C4C22×C22⋊D1114yes—
685C2×C4C22×C22⋊D1114yes—
686C2×C4C22×C22⋊D1111yescharacteristic
687C2×C4C22×C22⋊D1111yescharacteristic
688C2×C4C22×C22⋊D1111yescharacteristic
689C2×C4C24×D1111yescharacteristic
690C8—222no—
691C8—222no—
692C8—224no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—442no—
697C22—442no—
698C22—442no—
699C22—442no—
700C22—442no—
701C22—442no—
702C22C23×C22⋊D1111yescharacteristic
703C4—21no—
704C4—21no—
705C4—24no—
706C4—24no—
707C4—21no—
708C4—21no—
709C4—24no—
710C4—42no—
711C4—42no—
712C4—42no—
713C4—442no—
714C4—442no—
715C4#1062336812yes—
716C4C2×#6704012yes—
717C2—41no—
718C2—882no—
719C2—882no—
720C2#1308226711yescharacteristic
721C2C2×#1062336811yescharacteristic
722C2#1308339511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3502C2
socleC22×C11C23×D4
prime radical#13083016C2
hypercenter#3502D11
hypocenterC11#61851
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. #13081555C2semidirect
3. #13081522C2semidirect
4. #13081487C2semidirect
5. #13081345C2semidirect
6. #13081345C2semidirect
7. #13081287C2semidirect
8. #13079869C2semidirect
9. #13079814C2semidirect
10. #13079752C2semidirect
11. #13078907C2semidirect
12. #13078738C2semidirect
13. #13078647C2semidirect
14. #13077711C2semidirect
15. C11×#3502C2semidirect
283. #3502D11semidirect
642. C11#61851semidirect

Maximal subgroups

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

subgroupindex
#130830162
#130815552
#130815222
#130814872
#130813452
#130812872
#130798692
#130798142
#130797522
#130789072
#130787382
#130786472
#130777112
C11×#35022
#6185111