Finite Group Databasebeta

← #15644164

Subgroups — #15644164

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#13082421C211yesmaximal, characteristic, complemented
2#13081561C214yesmaximal, complemented
3#13081526C212yesmaximal, complemented
4#13081491C212yesmaximal, complemented
5#13081341C212yesmaximal, complemented
6#13081341C214yesmaximal, complemented
7#13081283C212yesmaximal, complemented
8#13079863C214yesmaximal, complemented
9#13079810C211yesmaximal, characteristic, complemented
10#13079748C211yesmaximal, characteristic, complemented
11#13078902C214yesmaximal, complemented
12#13078734C211yesmaximal, characteristic, complemented
13#13078643C211yesmaximal, characteristic, complemented
14#13077711C211yesmaximal, characteristic, complemented
15C11×#3548C211yesmaximal, characteristic
16C11×#562—22no—
17C11×#554C2212yes—
18C11×#554C2212yes—
19C11×#550C2212yes—
20C11×#550C2212yes—
21C11×#547—21no—
22C11×#547—21no—
23C11×#540C2214yes—
24C11×#537—22no—
25C11×#537—22no—
26C11×#533C2211yescharacteristic
27C11×#532C2211yescharacteristic
28C11×#532C2211yescharacteristic
29#10623253—21no—
30#10623252—21no—
31#10623216—22no—
32#10623154—22no—
33#10623153—22no—
34#10623098C2212yes—
35#10623098C2214yes—
36Q8×Dic22C2212yes—
37#10623050C2212yes—
38#10623047C2212yes—
39#10623001C2211yescharacteristic
40C2×C4×Dic22C2211yescharacteristic
41#10622707C2212yes—
42#10622704C2212yes—
43#10622693C2212yes—
44#10622692C2211yescharacteristic
45#10622691C2211yescharacteristic
46#10622688C2212yes—
47#10622688C2214yes—
48#10622688C2214yes—
49#10622688C2212yes—
50#10622684C2212yes—
51#10622684C2214yes—
52#10622683C2214yes—
53#10622683C2211yescharacteristic
54#10622683C2211yescharacteristic
55#10622678C2214yes—
56#10622677C2214yes—
57#10622676C2214yes—
58#10622676C2214yes—
59#10622653C2212yes—
60#10622653C2212yes—
61#10622648C2214yes—
62#10622648C2214yes—
63#10622647C2212yes—
64#10622646C2212yes—
65#10622637C2212yes—
66#10622637C2214yes—
67Q8×C11⋊C8C2212yes—
68#10622631C2214yes—
69#10622631C2214yes—
70#10622631C2214yes—
71C4×#4324C2212yes—
72C4×#4324C2212yes—
73C4×#4324C2214yes—
74C4×#4324C2214yes—
75#10622622C2214yes—
76#10622622C2214yes—
77#10622622C2214yes—
78#10622621C2212yes—
79#10622621C2214yes—
80#10622620C2212yes—
81#10622620C2214yes—
82#10622613C2214yes—
83#10622539C2211yescharacteristic
84#10622538C2211yescharacteristic
85C2×C11×#41—22no—
86C2×C11×#41—22no—
87C2×C11×#41—21no—
88C2×C11×#41—21no—
89C22×Dic22C2311yescharacteristic
90C11×C4⋊Q8D411yescharacteristic
91C11×C4⋊Q8D411yescharacteristic
92C11×C4⋊Q8C2311yescharacteristic
93C11×C4⋊Q8C2311yescharacteristic
94C11×#127C2311yescharacteristic
95C11×#127C2311yescharacteristic
96C11×#127C2314yes—
97C11×#125D412yes—
98C11×#125C2314yes—
99C11×#124—21no—
100C11×#124—21no—
101C11×#123—24no—
102C11×#123—24no—
103C11×C22⋊Q8—22no—
104C11×C22⋊Q8—22no—
105C11×C22⋊Q8—24no—
106C11×C22⋊Q8—24no—
107C11×C22⋊Q8D412yes—
108C11×C22⋊Q8D412yes—
109C11×#121—21no—
110C11×#121—21no—
111C11×#121—22no—
112C11×#121—22no—
113C11×#121—24no—
114C11×#121—24no—
115C11×#121—24no—
116C11×#121—24no—
117C11×#121C2312yes—
118C11×#121C2312yes—
119C4×Q8×C11C2312yes—
120C4×Q8×C11C2312yes—
121C4×D4×C11—21no—
122C4×D4×C11—21no—
123C4×D4×C11C2312yes—
124C4×D4×C11C2314yes—
125C4×D4×C11C2314yes—
126C4×D4×C11C2312yes—
127C11×#117C2312yes—
128C2×C11×C4⋊C4—22no—
129C2×C11×C4⋊C4—22no—
130C2×C42×C11C2311yescharacteristic
131Q8×Dic11—22no—
132#66997—22no—
133#66997—24no—
134C2×#4324C2312yes—
135C2×#4324C2312yes—
136C2×#4324C2314yes—
137#66979C2312yes—
138C2×C4⋊Dic11C2311yescharacteristic
139#66977—21no—
140#66977—21no—
141C2×Dic11⋊C4—21no—
142C2×C4×Dic11—21no—
143#66943—22no—
144#66942—24no—
145#66942—24no—
146#66942—24no—
147#66941—22no—
148#66941—22no—
149#66941—24no—
150#66940—22no—
151#66940—22no—
152#66940—22no—
153#66940—24no—
154#66931—24no—
155#66930—24no—
156#66923C2312yes—
157#66923C2314yes—
158#66922C2311yescharacteristic
159#66922C2311yescharacteristic
160#66922C2314yes—
161C4×Dic22—21no—
162C4×Dic22—21no—
163C4×Dic22—21no—
164C4×Dic22—21no—
165C4×Dic22C2312yes—
166C4×Dic22C2312yes—
167C4×Dic22C2314yes—
168C4×Dic22C2314yes—
169#66896C2312yes—
170#66896C2314yes—
171#66896C2314yes—
172#66896C2314yes—
173#66896C2314yes—
174#66896C2312yes—
175#66896C2314yes—
176C22⋊(C11⋊C8)C2312yes—
177C22⋊(C11⋊C8)C2312yes—
178#66874C2312yes—
179#66874C2314yes—
180#66874C2312yes—
181#66872C2312yes—
182#66872C2314yes—
183#66872C2312yes—
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
198C11×#41—82no—
199C11×#41—82no—
200C11×#41—84no—
201C11×#41—84no—
202C2×Q8×C11—21no—
203C2×Q8×C11—21no—
204C2×Q8×C11C2×D412yes—
205C2×Q8×C11C2×D412yes—
206C2×D4×C11—22no—
207C2×D4×C11—22no—
208C2×D4×C11—21no—
209C2×D4×C11—21no—
210C2×D4×C11—24no—
211C2×D4×C11—24no—
212C2×D4×C11—21no—
213C2×D4×C11—21no—
214C2×D4×C11C2412yes—
215C2×D4×C11C2412yes—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—24no—
219C22×C4×C11—24no—
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2411yescharacteristic
223C22×Dic11—21no—
224C22×Dic11—21no—
225C2×Dic22—24no—
226C2×Dic22—21no—
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—24no—
230C2×Dic22C2412yes—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—24no—
235C11×C4⋊C4C2×D412yes—
236C11×C4⋊C4C2×D412yes—
237C11×C4⋊C4C2×D414yes—
238C11×C4⋊C4C2×D412yes—
239C11×C4⋊C4C2×D414yes—
240C11×C4⋊C4C2×D412yes—
241C11×C4⋊C4C2412yes—
242C11×C4⋊C4C2412yes—
243C11×C22⋊C4—22no—
244C11×C22⋊C4—22no—
245C11×C22⋊C4—24no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—22no—
248C11×C22⋊C4—22no—
249C11×C22⋊C4C2×D414yes—
250C42×C11C2×D411yescharacteristic
251C42×C11C2×D411yescharacteristic
252C42×C11C2411yescharacteristic
253C42×C11C2414yes—
254C42×C11C2411yescharacteristic
255C22⋊Dic11—22no—
256#4324—24no—
257#4324—24no—
258#4324—28no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—24no—
263C4⋊Dic11C2412yes—
264C4⋊Dic11C2412yes—
265C4⋊Dic11C2412yes—
266Dic11⋊C4—22no—
267Dic11⋊C4—22no—
268Dic11⋊C4—22no—
269Dic11⋊C4—22no—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274C4×Dic11—22no—
275C4×Dic11—22no—
276C4×Dic11—22no—
277C4×Dic11—24no—
278C4×Dic11—24no—
279C2×C11⋊C8C2412yes—
280C2×C11⋊C8C2412yes—
281C2×C11⋊C8C2414yes—
282#3548D1111yescharacteristic
283#3502—111no—
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×C11—22no—
298C23×C11—22no—
299C23×C11C22×D411yescharacteristic
300Q8×C11—24no—
301Q8×C11—42no—
302Q8×C11—81no—
303Q8×C11—81no—
304D4×C11—22no—
305D4×C11—22no—
306D4×C11—24no—
307D4×C11—42no—
308D4×C11—42no—
309D4×C11—81no—
310D4×C11—84no—
311D4×C11—81no—
312D4×C11—84no—
313D4×C11—82no—
314D4×C11—82no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—41no—
320C2×C4×C11—44no—
321C2×C4×C11—44no—
322C2×C4×C11—84no—
323C2×C4×C11—84no—
324C2×C4×C11C22×D411yescharacteristic
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11C22×D414yes—
327C2×C4×C11C22×D414yes—
328C2×C4×C11C22×D411yescharacteristic
329C2×C4×C11C22×D411yescharacteristic
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C2511yescharacteristic
332C2×Dic11—24no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—81no—
338Dic22—24no—
339Dic22—22no—
340Dic22—42no—
341Dic22—81no—
342Dic22—84no—
343Dic222−1+414yes—
344C11⋊C8—22no—
345C11⋊C8—22no—
346C11⋊C8—24no—
347#562—22no—
348Q82—112no—
349Q82—221no—
350#557—112no—
351#557—114no—
352#557—221no—
353#557—222no—
354#554C2×D1112yes—
355#554C2×D1112yes—
356#550C2×D1112yes—
357#550C2×D1112yes—
358#547—21no—
359#547—21no—
360#544—112no—
361#544—222no—
362#540C2×D1114yes—
363#537—22no—
364#537—22no—
365#533—111no—
366#533—222no—
367#533C2×D1111yescharacteristic
368#532C2×D1111yescharacteristic
369#532C2×D1111yescharacteristic
370#519—112no—
371C2×C4×Q8—111no—
372#501—112no—
373#501—114no—
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×C11—42no—
420C22×C11—42no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11C23×D411yescharacteristic
426C4×C11—21no—
427C4×C11—21no—
428C4×C11—24no—
429C4×C11—21no—
430C4×C11—21no—
431C4×C11—24no—
432C4×C11—42no—
433C4×C11—42no—
434C4×C11#57712yes—
435C4×C11C2×2−1+412yes—
436Dic11—24no—
437Dic11—42no—
438Dic11—42no—
439Dic11—42no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—21no—
443C2×#41—21no—
444C22×Q8—111no—
445C2×SD16—112no—
446C2×SD16—112no—
447C2×SD16—114no—
448C4⋊Q8—111no—
449C4⋊Q8—111no—
450C4⋊Q8—114no—
451C4⋊Q8—222no—
452C4⋊Q8—224no—
453C4⋊Q8—222no—
454C4⋊Q8—222no—
455C4⋊Q8—224no—
456C4⋊Q8C22⋊D1111yescharacteristic
457C4⋊Q8C22⋊D1111yescharacteristic
458C4⋊Q8C22×D1111yescharacteristic
459C4⋊Q8C22×D1111yescharacteristic
460#127C22×D1111yescharacteristic
461#127C22×D1111yescharacteristic
462#127C22×D1114yes—
463#125—112no—
464#125—114no—
465#125—224no—
466#125—222no—
467#125—224no—
468#125—224no—
469#125C22⋊D1112yes—
470#125C22×D1114yes—
471#124—21no—
472#124—21no—
473#123—24no—
474#123—24no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8—24no—
478C22⋊Q8—24no—
479C22⋊Q8—221no—
480C22⋊Q8—221no—
481C22⋊Q8—224no—
482C22⋊Q8C22⋊D1112yes—
483C22⋊Q8C22⋊D1112yes—
484#121—21no—
485#121—21no—
486#121—22no—
487#121—22no—
488#121—24no—
489#121—24no—
490#121—24no—
491#121—24no—
492#121C22×D1112yes—
493#121C22×D1112yes—
494C4×Q8—112no—
495C4×Q8—112no—
496C4×Q8—114no—
497C4×Q8—114no—
498C4×Q8—222no—
499C4×Q8—222no—
500C4×Q8—222no—
501C4×Q8—224no—
502C4×Q8—222no—
503C4×Q8—221no—
504C4×Q8—221no—
505C4×Q8—221no—
506C4×Q8—221no—
507C4×Q8C22×D1112yes—
508C4×Q8C22×D1112yes—
509C4×D4—21no—
510C4×D4—21no—
511C4×D4C22×D1112yes—
512C4×D4C22×D1112yes—
513C4×D4C22×D1114yes—
514C4×D4C22×D1114yes—
515#117—112no—
516#117—224no—
517#117C22×D1112yes—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—111no—
521C2×C4⋊C4—221no—
522C2×C42—221no—
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—82no—
554C2×C11—82no—
555C2×C11#348611yescharacteristic
556C2×C11C2×#57711yescharacteristic
557C2×C11#358511yescharacteristic
558#41—82no—
559#41—82no—
560#41—84no—
561#41—84no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—112no—
565C2×Q8—224no—
566C2×Q8—221no—
567C2×Q8—221no—
568C2×Q8—221no—
569C2×Q8—224no—
570C2×Q8C2×C22⋊D1112yes—
571C2×Q8C2×C22⋊D1112yes—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—24no—
577C2×D4—24no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4C23×D1112yes—
581C2×D4C23×D1112yes—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—221no—
587C22×C4—221no—
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—21no—
598C4⋊C4—21no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—112no—
602C4⋊C4—112no—
603C4⋊C4—112no—
604C4⋊C4—221no—
605C4⋊C4—222no—
606C4⋊C4—222no—
607C4⋊C4—224no—
608C4⋊C4—224no—
609C4⋊C4—222no—
610C4⋊C4—221no—
611C4⋊C4—224no—
612C4⋊C4—222no—
613C4⋊C4—224no—
614C4⋊C4—221no—
615C4⋊C4—224no—
616C4⋊C4C2×C22⋊D1112yes—
617C4⋊C4C2×C22⋊D1112yes—
618C4⋊C4C2×C22⋊D1112yes—
619C4⋊C4C2×C22⋊D1112yes—
620C4⋊C4C2×C22⋊D1114yes—
621C4⋊C4C2×C22⋊D1114yes—
622C4⋊C4C23×D1112yes—
623C4⋊C4C23×D1112yes—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—222no—
631C22⋊C4C2×C22⋊D1114yes—
632C42—222no—
633C42—222no—
634C42—222no—
635C42—224no—
636C42—224no—
637C42C2×C22⋊D1111yescharacteristic
638C42C2×C22⋊D1111yescharacteristic
639C42C23×D1111yescharacteristic
640C42C23×D1114yes—
641C42C23×D1111yescharacteristic
642C11#6185111yescharacteristic, complemented, Sylow
643C23—22no—
644C23—22no—
645C23C22×C22⋊D1111yescharacteristic
646Q8—24no—
647Q8—42no—
648Q8—81no—
649Q8—81no—
650Q8—114no—
651Q8—224no—
652Q8—222no—
653Q8—442no—
654Q8—881no—
655Q8—884no—
656D4—22no—
657D4—22no—
658D4—24no—
659D4—42no—
660D4—42no—
661D4—81no—
662D4—84no—
663D4—81no—
664D4—84no—
665D4—82no—
666D4—82no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—41no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—84no—
675C2×C4—84no—
676C2×C4—224no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—881no—
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—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22C23×C22⋊D1111yescharacteristic
703C4—21no—
704C4—21no—
705C4—24no—
706C4—21no—
707C4—21no—
708C4—24no—
709C4—42no—
710C4—42no—
711C4—224no—
712C4—442no—
713C4—442no—
714C4—442no—
715C4#1062336712yes—
716C4D11×2−1+412yes—
717C2—41no—
718C2—82no—
719C2—82no—
720C2#1308226411yescharacteristic
721C2C2×#1062336711yescharacteristic
722C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC11×#3548C2
socleC22×C11C23×D4
hypercenter#3548D11
hypocenterC11#61851
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #533 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #13082421C2semidirect
2. #13081561C2semidirect
3. #13081526C2semidirect
4. #13081491C2semidirect
5. #13081341C2semidirect
6. #13081341C2semidirect
7. #13081283C2semidirect
8. #13079863C2semidirect
9. #13079810C2semidirect
10. #13079748C2semidirect
11. #13078902C2semidirect
12. #13078734C2semidirect
13. #13078643C2semidirect
14. #13077711C2semidirect
642. C11#61851semidirect

Maximal subgroups

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

subgroupindex
#130824212
#130815612
#130815262
#130814912
#130813412
#130812832
#130798632
#130798102
#130797482
#130789022
#130787342
#130786432
#130777112
C11×#35482
#6185111