Finite Group Databasebeta

← #14781215

Subgroups — #14781215

Order 2816.

1164 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082021C211yesmaximal, characteristic, complemented
2C2×#10622853C211yesmaximal, characteristic
3C2×#10622853C211yesmaximal, characteristic
4#13069793C218yesmaximal, complemented
5#13068349C211yesmaximal, characteristic, complemented
6#13068348C211yesmaximal, characteristic, complemented
7#13068348C211yesmaximal, characteristic, complemented
8C2×C11×#410C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16#10623050—22no—
17#10623050—22no—
18#10623048—22no—
19#10623048—22no—
20#10623031—22no—
21#10623014C2214yes—
22#10623001—22no—
23C11×#410—22no—
24C11×#410—22no—
25C2×C11×#99C2214yes—
26#10622853—22no—
27#10622853—22no—
28#10622853—22no—
29#10622853—22no—
30C2×#66898C2214yes—
31C2×#66898C2214yes—
32#10622165C2214yes—
33#10622165C2214yes—
34#10622164C2214yes—
35C2×C11×#41—21no—
36C2×C11×#41—21no—
37C2×C11×#41—21no—
38C2×C11×#41—21no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C22×Q8×C11Q811yescharacteristic, complemented
48C22×D4×C11Q811yescharacteristic, complemented
49C22×D4×C11C2312yes—
50C23×C4×C11Q812yescomplemented
51C23×C4×C11C2311yescharacteristic
52C11×#117—21no—
53C11×#117—21no—
54C11×#117—21no—
55C11×#117—21no—
56C11×#117—21no—
57C11×#117—21no—
58C11×#117D412yes—
59C11×#117D412yes—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C22⋊C4C2312yes—
63C2×C11×C22⋊C4C2312yes—
64C2×C42×C11—21no—
65C2×C42×C11—21no—
66C2×C22⋊Dic11C2312yes—
67C2×C22⋊Dic11C2312yes—
68C2×C22⋊Dic11C2312yes—
69C2×C22⋊Dic11C2312yes—
70#66979—21no—
71#66979—21no—
72#66979—21no—
73#66979—21no—
74#66979—21no—
75#66979—21no—
76#66979—21no—
77#66979—21no—
78#66979—21no—
79#66979—21no—
80#66979—21no—
81#66979—21no—
82#66979D412yes—
83#66979D412yes—
84#66979D412yes—
85#66979D412yes—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90#66977—28no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95#66943—24no—
96#66943—24no—
97#66941—24no—
98#66941—24no—
99#66931—28no—
100#66931—28no—
101#66923—24no—
102#66922—24no—
103C4×Dic22—28no—
104C11×#99—28no—
105#66898—28no—
106#66898—28no—
107#23474—111nomaximal, Sylow
108C24×C11C2×Q812yes—
109C24×C11C2411yescharacteristic
110C11×#41—41no—
111C11×#41—41no—
112C11×#41—41no—
113C11×#41—41no—
114C11×#41—41no—
115C11×#41—41no—
116C11×#41—41no—
117C11×#41—41no—
118C11×#41—41no—
119C11×#41—41no—
120C11×#41—41no—
121C11×#41—41no—
122C11×#41—41no—
123C11×#41—41no—
124C11×#41—41no—
125C11×#41—41no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×Q812yes—
159C22×C4×C11C2×Q811yescharacteristic
160C22×C4×C11C2×Q811yescharacteristic
161C22×C4×C11#4111yescharacteristic
162C22×C4×C11#4111yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C22×C4×C11#4111yescharacteristic
165C22×C4×C11#4111yescharacteristic
166C22×C4×C11#4111yescharacteristic
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C2×Dic22—28no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4C2×D414yes—
180C42×C11—22no—
181C42×C11—22no—
182C42×C11—41no—
183C42×C11—41no—
184C22⋊Dic11—22no—
185C22⋊Dic11—22no—
186C22⋊Dic11—22no—
187C22⋊Dic11—22no—
188C22⋊Dic11—22no—
189C22⋊Dic11—22no—
190C22⋊Dic11C2×D414yes—
191C22⋊Dic11C2×D414yes—
192C4⋊Dic11—28no—
193C4⋊Dic11—22no—
194C4⋊Dic11—22no—
195C4⋊Dic11—22no—
196C4⋊Dic11—22no—
197C4⋊Dic11—41no—
198C4⋊Dic11—41no—
199C4⋊Dic11—41no—
200C4⋊Dic11—41no—
201Dic11⋊C4—28no—
202Dic11⋊C4—28no—
203C4×Dic11—22no—
204C4×Dic11—22no—
205C4×Dic11—22no—
206C4×Dic11—22no—
207C4×Dic11—41no—
208C4×Dic11—41no—
209C4×Dic11—41no—
210C4×Dic11—41no—
211#3458—111no—
212C2×#410—111no—
213C2×#410—111no—
214C2×#410D1111yescharacteristic
215#2032—118no—
216#1740—111no—
217#1740—111no—
218#1740—111no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—81no—
223C23×C11—82no—
224C23×C11C22×D411yescharacteristic
225C23×C11C22×D411yescharacteristic
226C23×C11C22×D411yescharacteristic
227C23×C11C22×Q811yescharacteristic
228C23×C11C2×#4111yescharacteristic
229C23×C11C2×#4111yescharacteristic
230C23×C11C2×#4111yescharacteristic
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235D4×C11—42no—
236D4×C11—42no—
237D4×C11—42no—
238D4×C11—42no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—82no—
253C2×C4×C11—82no—
254C2×C4×C11#12011yescharacteristic
255C2×C4×C11#12011yescharacteristic
256C2×C4×C11#12011yescharacteristic
257C2×C4×C11#12011yescharacteristic
258C2×C4×C11C22⋊Q811yescharacteristic
259C2×C4×C11C22⋊Q811yescharacteristic
260C2×C4×C11C22⋊Q811yescharacteristic
261C2×C4×C11C22⋊Q811yescharacteristic
262C2×C4×C11C22⋊Q811yescharacteristic
263C2×C4×C11C22⋊Q811yescharacteristic
264C2×C4×C11C22⋊Q811yescharacteristic
265C2×C4×C11C22⋊Q811yescharacteristic
266C2×C4×C11C22⋊Q811yescharacteristic
267C2×C4×C11C22⋊Q811yescharacteristic
268C2×C4×C11C22⋊Q811yescharacteristic
269C2×C4×C11C22⋊Q811yescharacteristic
270C2×C4×C11#12411yescharacteristic
271C2×C4×C11#12411yescharacteristic
272C2×C4×C11#12411yescharacteristic
273C2×C4×C11#12411yescharacteristic
274C2×C4×C11#12411yescharacteristic
275C2×C4×C11#12411yescharacteristic
276C2×C4×C11#12411yescharacteristic
277C2×C4×C11#12411yescharacteristic
278C2×C4×C11#12411yescharacteristic
279C2×C4×C11#12411yescharacteristic
280C2×C4×C11#12411yescharacteristic
281C2×C4×C11#12411yescharacteristic
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—82no—
287C2×Dic11—82no—
288C2×Dic11—82no—
289C2×Dic11—82no—
290Dic22—88no—
291C22×#41C2×D1111yescharacteristic
292#544—222no—
293#544—222no—
294#544—222no—
295#543—114no—
296#533—222no—
297#533—222no—
298#533—222no—
299C2×#117—111no—
300C2×#117—111no—
301C2×#117—111no—
302C2×#117—111no—
303C2×#117C2×D1111yescharacteristic
304C2×#117C2×D1111yescharacteristic
305#410—22no—
306#410—22no—
307#410—222no—
308#410—222no—
309#410—222no—
310#410—222no—
311C2×#99—114no—
312C2×#99—114no—
313C2×#99C2×D1114yes—
314#342—114no—
315#342—114no—
316#342—114no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—42no—
325C22×C11—82no—
326C22×C11—82no—
327C22×C11—82no—
328C22×C11C2×#12011yescharacteristic
329C22×C11C2×C22⋊Q811yescharacteristic
330C22×C11C2×C22⋊Q811yescharacteristic
331C22×C11C2×C22⋊Q811yescharacteristic
332C22×C11C2×#12411yescharacteristic
333C22×C11C2×#12411yescharacteristic
334C22×C11C2×#12411yescharacteristic
335C4×C11—44no—
336C4×C11—42no—
337C4×C11—82no—
338C4×C11#39311yescharacteristic
339C4×C11#39311yescharacteristic
340C4×C11#39311yescharacteristic
341C4×C11#39311yescharacteristic
342C4×C11#39311yescharacteristic
343C4×C11#39311yescharacteristic
344C4×C11#39311yescharacteristic
345C4×C11#39311yescharacteristic
346Dic11—44no—
347Dic11—44no—
348Dic11—82no—
349Dic11—82no—
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41—21no—
357C2×#41—21no—
358C2×#41—21no—
359C2×#41—21no—
360C2×#41—21no—
361C2×#41—21no—
362C22×Q8Dic2211yescharacteristic, complemented
363C22×D4Dic2211yescharacteristic, complemented
364C22×D4C22×D1112yes—
365C23×C4Dic2212yescomplemented
366C23×C4C22×D1111yescharacteristic
367C4⋊Q8—224no—
368C4⋊Q8—224no—
369C4⋊Q8—224no—
370#125—224no—
371#125—224no—
372#125—224no—
373C22⋊Q8—228no—
374C22⋊Q8—228no—
375C22⋊Q8—228no—
376C4×Q8—228no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—21no—
382#117—21no—
383#117—112no—
384#117—112no—
385#117—112no—
386#117—112no—
387#117—221no—
388#117—221no—
389#117—221no—
390#117—221no—
391#117—221no—
392#117—221no—
393#117—221no—
394#117—221no—
395#117—221no—
396#117—221no—
397#117—221no—
398#117—221no—
399#117C22⋊D1112yes—
400#117C22⋊D1112yes—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C22⋊C4—112no—
408C2×C22⋊C4—112no—
409C2×C22⋊C4—112no—
410C2×C22⋊C4—112no—
411C2×C22⋊C4C22×D1112yes—
412C2×C22⋊C4C22×D1112yes—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—221no—
416C2×C42—221no—
417C2×C42—221no—
418C2×C42—221no—
419#99—28no—
420#99—228no—
421#99—228no—
422C2×C11—21no—
423C2×C11—21no—
424C2×C11—21no—
425C2×C11—21no—
426C2×C11—21no—
427C2×C11—21no—
428C2×C11—21no—
429C2×C11—82no—
430C2×C11C2×#39311yescharacteristic
431C24C2×Dic2212yes—
432C24C23×D1111yescharacteristic
433#41—41no—
434#41—41no—
435#41—41no—
436#41—41no—
437#41—41no—
438#41—41no—
439#41—41no—
440#41—41no—
441#41—41no—
442#41—41no—
443#41—41no—
444#41—41no—
445#41—41no—
446#41—41no—
447#41—41no—
448#41—41no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—228no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4C2×Dic2212yes—
481C22×C4C2×Dic2211yescharacteristic
482C22×C4C2×Dic2211yescharacteristic
483C22×C4#433911yescharacteristic
484C22×C4#433911yescharacteristic
485C22×C4D4×D1111yescharacteristic
486C22×C4D4×D1111yescharacteristic
487C22×C4D4×D1111yescharacteristic
488C22×C4D4×D1111yescharacteristic
489C22×C4#434111yescharacteristic
490C22×C4#434111yescharacteristic
491C22×C4#434111yescharacteristic
492C22×C4#434111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—228no—
500C4⋊C4—228no—
501C4⋊C4—228no—
502C4⋊C4—222no—
503C4⋊C4—222no—
504C4⋊C4—222no—
505C4⋊C4—222no—
506C4⋊C4—441no—
507C4⋊C4—441no—
508C4⋊C4—441no—
509C4⋊C4—441no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—114no—
514C22⋊C4—114no—
515C22⋊C4—222no—
516C22⋊C4—222no—
517C22⋊C4—222no—
518C22⋊C4—222no—
519C22⋊C4—222no—
520C22⋊C4—222no—
521C22⋊C4C2×C22⋊D1114yes—
522C42—22no—
523C42—22no—
524C42—41no—
525C42—41no—
526C42—222no—
527C42—222no—
528C42—222no—
529C42—222no—
530C42—441no—
531C42—441no—
532C42—441no—
533C42—441no—
534C11#2347411yescharacteristic, complemented, Sylow
535C23—22no—
536C23—22no—
537C23—22no—
538C23—81no—
539C23—82no—
540C23C22×Dic2211yescharacteristic
541C23C2×#433911yescharacteristic
542C23C2×D4×D1111yescharacteristic
543C23C2×D4×D1111yescharacteristic
544C23C2×#434111yescharacteristic
545C23C2×#434111yescharacteristic
546C23C22×C22⋊D1111yescharacteristic
547Q8—41no—
548Q8—41no—
549Q8—41no—
550Q8—41no—
551Q8—888no—
552D4—42no—
553D4—42no—
554D4—42no—
555D4—42no—
556D4—41no—
557D4—41no—
558D4—41no—
559D4—41no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—882no—
576C2×C4—882no—
577C2×C4—882no—
578C2×C4—882no—
579C2×C4#6693111yescharacteristic
580C2×C4#6693111yescharacteristic
581C2×C4#6693111yescharacteristic
582C2×C4#6693111yescharacteristic
583C2×C4#6693111yescharacteristic
584C2×C4#6693111yescharacteristic
585C2×C4#6693111yescharacteristic
586C2×C4#6693111yescharacteristic
587C2×C4#6693811yescharacteristic
588C2×C4#6693811yescharacteristic
589C2×C4#6693811yescharacteristic
590C2×C4#6693811yescharacteristic
591C2×C4#6693811yescharacteristic
592C2×C4#6693811yescharacteristic
593C2×C4#6693811yescharacteristic
594C2×C4#6693811yescharacteristic
595C2×C4#6697711yescharacteristic
596C2×C4#6697711yescharacteristic
597C2×C4#6697711yescharacteristic
598C2×C4#6697711yescharacteristic
599C2×C4#6698911yescharacteristic
600C2×C4#6698911yescharacteristic
601C2×C4#6698911yescharacteristic
602C2×C4#6698911yescharacteristic
603C2×C4#6699011yescharacteristic
604C2×C4#6699011yescharacteristic
605C2×C4#6699011yescharacteristic
606C2×C4#6699011yescharacteristic
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—42no—
615C22—82no—
616C22—82no—
617C22—82no—
618C22C2×#6693111yescharacteristic
619C22C2×#6693111yescharacteristic
620C22C2×#6693811yescharacteristic
621C22C2×#6693811yescharacteristic
622C22C2×#6697711yescharacteristic
623C22C2×#6698911yescharacteristic
624C22C2×#6699011yescharacteristic
625C4—44no—
626C4—42no—
627C4—82no—
628C4—444no—
629C4—444no—
630C4—882no—
631C4—882no—
632C4#1062256011yescharacteristic
633C4#1062256011yescharacteristic
634C4#1062256011yescharacteristic
635C4#1062256011yescharacteristic
636C4#1062256011yescharacteristic
637C4#1062256011yescharacteristic
638C4#1062256011yescharacteristic
639C4#1062256011yescharacteristic
640C2—21no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—21no—
645C2—21no—
646C2—21no—
647C2—82no—
648C2C2×#1062256011yescharacteristic
subgroupG/H
centerC4#10622560
commutator, cosocleC24×C11C24
FrattiniC24C23×D11
FittingC2×C11×#410C2
socleC2×C11C2×#393
prime radicalC22×C11×#41C22
hypercenterC2×#410D11
hypocenterC11#23474
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
1. #13082021C2semidirect
4. #13069793C2semidirect
5. #13068349C2semidirect
6. #13068348C2semidirect
7. #13068348C2semidirect
47. C22×Q8×C11Q8semidirect
48. C22×D4×C11Q8semidirect
50. C23×C4×C11Q8semidirect
362. C22×Q8Dic22semidirect
363. C22×D4Dic22semidirect
365. C23×C4Dic22semidirect
534. C11#23474semidirect

Maximal subgroups

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

subgroupindex
#130820212
C2×#106228532
#130697932
#130683492
#130683482
C2×C11×#4102
#2347411