Finite Group Databasebeta

← #14781205

Subgroups — #14781205

Order 2816.

1148 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082021C211yesmaximal, characteristic, complemented
2C2×#10622849C211yesmaximal, characteristic
3C2×#10622853C211yesmaximal, characteristic
4#13069788C218yesmaximal, complemented
5C2×#10622197C211yesmaximal, characteristic, complemented
6#13068326C211yesmaximal, characteristic, complemented
7C2×#10622195C211yesmaximal, characteristic, complemented
8C2×C11×#421C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16#10623050—22no—
17#10623050—22no—
18#10623048—22no—
19#10623048—22no—
20#10623031—22no—
21#10623014—22no—
22#10623001C2214yescomplemented
23C11×#421—22no—
24C11×#421—22no—
25C2×C11×#104C2214yes—
26#10622853—22no—
27#10622853C2214yes—
28#10622849—22no—
29#10622849C2214yes—
30C2×#66901—22no—
31C2×#66898—22no—
32#10622197C2214yescomplemented
33#10622195C2214yescomplemented
34#10622161C2214yescomplemented
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×#41Q812yescomplemented
46C2×C11×#41C2312yes—
47C22×Q8×C11Q811yescharacteristic, complemented
48C22×D4×C11—21no—
49C22×D4×C11Q811yescharacteristic, complemented
50C23×C4×C11—21no—
51C23×C4×C11C2311yescharacteristic
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16C2312yes—
58C22×C8×C11—21no—
59C11×#117—21no—
60C11×#117—21no—
61C11×#117D412yes—
62C11×#117D412yes—
63C2×C11×C4⋊C4—21no—
64C2×C11×C22⋊C4—21no—
65C2×C42×C11C2312yes—
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—21no—
68C2×C22⋊Dic11D412yes—
69#66979—21no—
70#66979—21no—
71#66979—21no—
72#66979—21no—
73#66979—21no—
74#66979—21no—
75#66979—21no—
76#66979D412yes—
77#66979D412yes—
78#66979C2312yes—
79#66979C2312yes—
80#66979C2312yes—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84#66977—28no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11D412yes—
88C2×#4318—21no—
89C2×#4318—21no—
90C2×#4318—21no—
91C2×#4318—21no—
92C2×#4318—21no—
93C2×#4318C2312yes—
94C22×C11⋊C8—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×#104—28no—
105#66901—28no—
106#66898—28no—
107#23472—111nomaximal, Sylow
108C24×C11—21no—
109C24×C11C2×D411yescharacteristic
110C11×#41—22no—
111C11×#41—22no—
112C11×#41—22no—
113C11×#41—22no—
114C11×#41—22no—
115C11×#41—22no—
116C11×#41—22no—
117C11×#41—22no—
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×C11C2×Q812yes—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—41no—
140C2×D4×C11—41no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C2×D4×C11C2×Q812yes—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—41no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×Q811yescharacteristic
158C22×C4×C11C2×Q811yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C22×C4×C11#4111yescharacteristic
161C22×C4×C11#4111yescharacteristic
162C22×C4×C11#4111yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C22×C4×C11#4111yescharacteristic
165C22×C4×C11C2411yescharacteristic
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—41no—
169C2×Dic22—28no—
170C11×M16—22no—
171C11×M16—22no—
172C11×M16—41no—
173C11×M16—41no—
174C2×C8×C11—22no—
175C2×C8×C11—41no—
176C2×C8×C11—41no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C42×C11—22no—
182C42×C11C2×D414yes—
183C22⋊Dic11—22no—
184C22⋊Dic11—22no—
185C22⋊Dic11—22no—
186C22⋊Dic11—22no—
187C22⋊Dic11—41no—
188C22⋊Dic11C2×D414yes—
189C4⋊Dic11—28no—
190C4⋊Dic11—22no—
191C4⋊Dic11—22no—
192C4⋊Dic11—22no—
193C4⋊Dic11—22no—
194C4⋊Dic11—22no—
195C4⋊Dic11—41no—
196Dic11⋊C4—28no—
197Dic11⋊C4—28no—
198C4×Dic11—22no—
199C4×Dic11—22no—
200C4×Dic11—22no—
201C4×Dic11—22no—
202C4×Dic11—41no—
203C4×Dic11C2×D414yes—
204#4318—22no—
205#4318—22no—
206#4318—41no—
207#4318—41no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—41no—
210C2×C11⋊C8—41no—
211#3458—111no—
212C2×#421—111no—
213C2×#421D1111yescharacteristic
214C2×#410—111no—
215#2031—118no—
216C2×#344—111no—
217#1733—111no—
218C2×H(3,ℤ/4)—111no—
219C23×C11—22no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—81no—
223C23×C11—82no—
224C23×C11#12011yescharacteristic
225C23×C11#12011yescharacteristic
226C23×C11C22⋊Q811yescharacteristic
227C23×C11C22⋊Q811yescharacteristic
228C23×C11#12411yescharacteristic
229C23×C11#12411yescharacteristic
230C23×C11C22×D411yescharacteristic
231Q8×C11—22no—
232Q8×C11—22no—
233Q8×C11—41no—
234Q8×C11—41no—
235D4×C11—22no—
236D4×C11—22no—
237D4×C11—42no—
238D4×C11—42no—
239D4×C11—42no—
240D4×C11—42no—
241D4×C11—41no—
242D4×C11—41no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—82no—
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11C22⋊Q811yescharacteristic
255C2×C4×C11C22⋊Q811yescharacteristic
256C2×C4×C11C22⋊Q811yescharacteristic
257C2×C4×C11C22⋊Q811yescharacteristic
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×C11#12411yescharacteristic
265C2×C4×C11#12411yescharacteristic
266C2×C4×C11#12411yescharacteristic
267C2×C4×C11#12411yescharacteristic
268C2×C4×C11#12411yescharacteristic
269C2×C4×C11#12411yescharacteristic
270C2×C4×C11#12411yescharacteristic
271C2×C4×C11#12411yescharacteristic
272C2×C4×C11#12411yescharacteristic
273C2×C4×C11#12411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×Q811yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—42no—
283C2×Dic11—82no—
284C2×Dic11—82no—
285C2×Dic11—82no—
286Dic22—88no—
287C8×C11—42no—
288C11⋊C8—42no—
289C22×#41C2×D1111yescharacteristic
290C22×M16—111no—
291C22×M16C2×D1111yescharacteristic
292#544—222no—
293#544—222no—
294#544—222no—
295#543—222no—
296#533—114no—
297#533—222no—
298#533—222no—
299C2×#117—111no—
300C2×#117—111no—
301C2×#117—111no—
302C2×#117C2×D1111yescharacteristic
303#421—22no—
304#421—22no—
305#421—114no—
306#421—222no—
307C2×#104—222no—
308C2×#104C2×D1114yes—
309#410—114no—
310#410—222no—
311C2×#99—222no—
312#344—114no—
313#339—114no—
314H(3,ℤ/4)—114no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—42no—
323C22×C11—82no—
324C22×C11—82no—
325C22×C11—82no—
326C22×C11#39311yescharacteristic
327C22×C11#39311yescharacteristic
328C22×C11#39311yescharacteristic
329C22×C11#39311yescharacteristic
330C22×C11C2×#12011yescharacteristic
331C22×C11C2×C22⋊Q811yescharacteristic
332C22×C11C2×#12411yescharacteristic
333C4×C11—44no—
334C4×C11—42no—
335C4×C11#39311yescharacteristic
336C4×C11#39311yescharacteristic
337C4×C11#39311yescharacteristic
338C4×C11#39311yescharacteristic
339C4×C11C2×C22⋊Q811yescharacteristic
340C4×C11C2×C22⋊Q811yescharacteristic
341C4×C11C2×#12411yescharacteristic
342C4×C11C2×#12411yescharacteristic
343Dic11—44no—
344Dic11—44no—
345Dic11—82no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41—21no—
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41—21no—
355C2×#41—21no—
356C2×#41Dic2212yescomplemented
357C2×#41C22×D1112yes—
358C22×Q8Dic2211yescharacteristic, complemented
359C22×D4—21no—
360C22×D4Dic2211yescharacteristic, complemented
361C23×C4—21no—
362C23×C4C22×D1111yescharacteristic
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—112no—
369C2×M16—221no—
370C2×M16—221no—
371C2×M16—221no—
372C2×M16—221no—
373C2×M16—221no—
374C2×M16C22×D1112yes—
375C22×C8—21no—
376C22×C8—221no—
377C4⋊Q8—224no—
378C4⋊Q8—224no—
379C4⋊Q8—224no—
380#125—224no—
381#125—224no—
382#125—224no—
383C22⋊Q8—228no—
384C22⋊Q8—228no—
385C22⋊Q8—228no—
386C4×Q8—228no—
387#117—21no—
388#117—21no—
389#117—112no—
390#117—112no—
391#117—112no—
392#117—112no—
393#117—112no—
394#117—221no—
395#117—221no—
396#117—221no—
397#117—221no—
398#117—221no—
399#117—221no—
400#117—221no—
401#117C22⋊D1112yes—
402#117C22⋊D1112yes—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—112no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C42—112no—
412C2×C42—221no—
413C2×C42—221no—
414C2×C42C22×D1112yes—
415#104—28no—
416#104—228no—
417#99—228no—
418C2×C11—21no—
419C2×C11—21no—
420C2×C11—21no—
421C2×C11—21no—
422C2×C11—21no—
423C2×C11—21no—
424C2×C11—21no—
425C2×C11—82no—
426C2×C11C2×#39311yescharacteristic
427C24—21no—
428C24D4×D1111yescharacteristic
429#41—22no—
430#41—22no—
431#41—22no—
432#41—22no—
433#41—22no—
434#41—22no—
435#41—22no—
436#41—22no—
437#41—41no—
438#41—41no—
439#41—41no—
440#41—41no—
441#41—41no—
442#41—41no—
443#41—41no—
444#41—41no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—228no—
451C2×Q8C2×Dic2212yes—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4C2×Dic2212yes—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—441no—
475C22×C4C2×Dic2211yescharacteristic
476C22×C4C2×Dic2211yescharacteristic
477C22×C4#433911yescharacteristic
478C22×C4#433911yescharacteristic
479C22×C4D4×D1111yescharacteristic
480C22×C4D4×D1111yescharacteristic
481C22×C4D4×D1111yescharacteristic
482C22×C4#434111yescharacteristic
483C22×C4#434111yescharacteristic
484C22×C4#434111yescharacteristic
485C22×C4#434111yescharacteristic
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489M16—22no—
490M16—22no—
491M16—41no—
492M16—41no—
493M16—222no—
494M16—222no—
495M16—441no—
496M16—441no—
497C2×C8—22no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—222no—
501C2×C8—441no—
502C2×C8—441no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—228no—
506C4⋊C4—228no—
507C4⋊C4—228no—
508C4⋊C4—222no—
509C4⋊C4—222no—
510C4⋊C4—222no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4—441no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—114no—
517C22⋊C4—222no—
518C22⋊C4—222no—
519C22⋊C4—222no—
520C22⋊C4—222no—
521C22⋊C4—441no—
522C42—22no—
523C42—114no—
524C42—222no—
525C42—222no—
526C42—222no—
527C42—222no—
528C42—441no—
529C42C2×C22⋊D1114yes—
530C11#2347211yescharacteristic, complemented, Sylow
531C23—22no—
532C23—41no—
533C23—41no—
534C23—81no—
535C23—82no—
536C23#6693111yescharacteristic
537C23#6693111yescharacteristic
538C23#6693811yescharacteristic
539C23#6693811yescharacteristic
540C23#6699011yescharacteristic
541C23#6699011yescharacteristic
542C23C2×D4×D1111yescharacteristic
543Q8—22no—
544Q8—22no—
545Q8—41no—
546Q8—41no—
547Q8—888no—
548D4—22no—
549D4—22no—
550D4—42no—
551D4—42no—
552D4—42no—
553D4—42no—
554D4—41no—
555D4—41no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—82no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—442no—
568C2×C4—882no—
569C2×C4—882no—
570C2×C4—882no—
571C2×C4#6693111yescharacteristic
572C2×C4#6693111yescharacteristic
573C2×C4#6693111yescharacteristic
574C2×C4#6693111yescharacteristic
575C2×C4#6693111yescharacteristic
576C2×C4#6693111yescharacteristic
577C2×C4#6693811yescharacteristic
578C2×C4#6693811yescharacteristic
579C2×C4#6693811yescharacteristic
580C2×C4#6693811yescharacteristic
581C2×C4#6693811yescharacteristic
582C2×C4#6693811yescharacteristic
583C2×C4#6697711yescharacteristic
584C2×C4#6697711yescharacteristic
585C2×C4#6697711yescharacteristic
586C2×C4#6697711yescharacteristic
587C2×C4#6698911yescharacteristic
588C2×C4#6698911yescharacteristic
589C2×C4#6698911yescharacteristic
590C2×C4#6698911yescharacteristic
591C2×C4#6699011yescharacteristic
592C2×C4#6699011yescharacteristic
593C2×C4C22×Dic2211yescharacteristic
594C2×C4C2×#433911yescharacteristic
595C2×C4C2×D4×D1111yescharacteristic
596C2×C4C2×#434111yescharacteristic
597C2×C4C2×#434111yescharacteristic
598C2×C4C22×C22⋊D1111yescharacteristic
599C8—42no—
600C8—442no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—42no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22#1062256011yescharacteristic
613C22#1062256011yescharacteristic
614C22#1062256011yescharacteristic
615C22#1062256011yescharacteristic
616C22C2×#6693111yescharacteristic
617C22C2×#6693811yescharacteristic
618C22C2×#6699011yescharacteristic
619C4—44no—
620C4—42no—
621C4—444no—
622C4—444no—
623C4—882no—
624C4#1062256011yescharacteristic
625C4#1062256011yescharacteristic
626C4#1062256011yescharacteristic
627C4#1062256011yescharacteristic
628C4C2×#6693111yescharacteristic
629C4C2×#6693811yescharacteristic
630C4C2×#6697711yescharacteristic
631C4C2×#6698911yescharacteristic
632C2—21no—
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—21no—
638C2—21no—
639C2—82no—
640C2C2×#1062256011yescharacteristic
subgroupG/H
centerC4C2×#66938
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#421C2
socleC2×C11C2×#393
prime radicalC22×C11×#41C22
hypercenterC2×#421D11
hypocenterC11#23472
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
1. #13082021C2semidirect
4. #13069788C2semidirect
5. C2×#10622197C2semidirect
6. #13068326C2semidirect
7. C2×#10622195C2semidirect
22. #10623001C22semidirect
32. #10622197C22semidirect
33. #10622195C22semidirect
34. #10622161C22semidirect
45. C2×C11×#41Q8semidirect
47. C22×Q8×C11Q8semidirect
49. C22×D4×C11Q8semidirect
356. C2×#41Dic22semidirect
358. C22×Q8Dic22semidirect
360. C22×D4Dic22semidirect
530. C11#23472semidirect

Maximal subgroups

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

subgroupindex
#130820212
C2×#106228492
C2×#106228532
#130697882
C2×#106221972
#130683262
C2×#106221952
C2×C11×#4212
#2347211