Finite Group Databasebeta

← #14781208

Subgroups — #14781208

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×#10622752C211yesmaximal, characteristic
3C2×#10622752C211yesmaximal, characteristic
4C2×#10622619C211yesmaximal, characteristic
5#13069791C218yesmaximal, complemented
6#13068327C211yesmaximal, characteristic, complemented
7C2×#10622195C211yesmaximal, characteristic, complemented
8C2×C11×#344C211yesmaximal, characteristic, complemented
9C22×#4339C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16#10623050—22no—
17#10623050—22no—
18#10623048—22no—
19#10623048C2214yescomplemented
20#10623031—22no—
21#10623014—22no—
22#10623001—22no—
23#10622752—22no—
24#10622752—22no—
25#10622752—22no—
26#10622752C2214yes—
27C2×#66889—22no—
28C2×#66889C2214yes—
29#10622619—22no—
30#10622619C2214yes—
31C2×#66870—22no—
32C11×#344C2214yescomplemented
33#10622195C2214yescomplemented
34#10622193C2214yescomplemented
35C23×C4×C11C2311yescharacteristic
36C22×C22⋊D11—21no—
37C2×#4339—21no—
38C2×#4339—21no—
39C2×#4339—21no—
40C2×#4339—21no—
41C2×#4339—21no—
42C2×#4339—21no—
43C2×#4339—21no—
44C2×#4339—21no—
45C2×#4339—21no—
46C2×#4339—21no—
47C2×#4339Q812yescomplemented
48C2×#4339C2312yes—
49C22×D44Q811yescharacteristic, complemented
50C22×C4×D11—21no—
51C22×Dic22Q811yescharacteristic, complemented
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16—21no—
61C2×C11×M16—21no—
62C2×C11×M16C2312yes—
63C2×C11×M16C2312yes—
64C22×C8×C11—21no—
65C22×C8×C11—21no—
66C11×#117—21no—
67C11×#117—21no—
68C11×#117D412yes—
69C11×#117C2312yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C22⋊C4D412yes—
72C2×C42×C11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76#66979—21no—
77#66979—21no—
78#66979—21no—
79#66979—21no—
80#66979—21no—
81#66979—21no—
82#66979—21no—
83#66979D412yes—
84#66979D412yes—
85#66979D412yes—
86#66979C2312yes—
87#66979C2312yes—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91#66977—28no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11D412yes—
94C2×C4×Dic11C2312yes—
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—
104#66889—28no—
105#66889—28no—
106#66870—28no—
107#23472—111nomaximal, Sylow
108C24×C11C2×D411yescharacteristic
109C23×D11—21no—
110C22×C4×C11—22no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×Q811yescharacteristic
117C22×C4×C11C2×Q811yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×C4×C11#4111yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C2×C22⋊D11—22no—
126C2×C22⋊D11—22no—
127C2×C22⋊D11—41no—
128C2×C22⋊D11—41no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131C22×Dic11—22no—
132C22×Dic11—21no—
133C22×Dic11—22no—
134C22×Dic11—41no—
135#4339—22no—
136#4339—22no—
137#4339—22no—
138#4339—22no—
139#4339—22no—
140#4339—22no—
141#4339—22no—
142#4339—22no—
143#4339—41no—
144#4339—41no—
145#4339—41no—
146#4339—41no—
147#4339—41no—
148#4339—41no—
149#4339—41no—
150#4339—41no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44C2×Q812yes—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—41no—
160C2×C4×D11—41no—
161C2×C4×D11—41no—
162C2×C4×D11—41no—
163C2×Dic22—28no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22C2×Q812yes—
170C11×M16—22no—
171C11×M16—22no—
172C11×M16—22no—
173C11×M16—22no—
174C11×M16—41no—
175C11×M16—41no—
176C11×M16—41no—
177C11×M16—41no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—41no—
181C2×C8×C11—41no—
182C2×C8×C11—41no—
183C2×C8×C11—41no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4C2×D414yes—
188C42×C11—22no—
189C42×C11—22no—
190C22⋊Dic11—22no—
191C22⋊Dic11—22no—
192C22⋊Dic11—22no—
193C22⋊Dic11—22no—
194C22⋊Dic11—22no—
195C22⋊Dic11—41no—
196C4⋊Dic11—28no—
197C4⋊Dic11—22no—
198C4⋊Dic11—22no—
199C4⋊Dic11—22no—
200C4⋊Dic11—22no—
201C4⋊Dic11—22no—
202C4⋊Dic11—41no—
203Dic11⋊C4—28no—
204Dic11⋊C4—28no—
205C4×Dic11—22no—
206C4×Dic11—22no—
207C4×Dic11—22no—
208C4×Dic11—41no—
209C4×Dic11C2×D414yes—
210C4×Dic11C2×D414yes—
211#3458—111no—
212C2×#421—111no—
213C2×#421—111no—
214C2×#410—111no—
215#2031—118no—
216C2×#344D1111yescharacteristic, complemented
217#1733—111no—
218C2×H(3,ℤ/4)—111no—
219C23×C11—81no—
220C23×C11#12011yescharacteristic
221C23×C11#12011yescharacteristic
222C23×C11C22⋊Q811yescharacteristic
223C23×C11C22⋊Q811yescharacteristic
224C23×C11#12411yescharacteristic
225C23×C11#12411yescharacteristic
226C23×C11C22×D411yescharacteristic
227C22×D11—22no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—82no—
231C2×C4×C11—24no—
232C2×C4×C11—82no—
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11#12011yescharacteristic
235C2×C4×C11C22⋊Q811yescharacteristic
236C2×C4×C11C22⋊Q811yescharacteristic
237C2×C4×C11C22⋊Q811yescharacteristic
238C2×C4×C11C22⋊Q811yescharacteristic
239C2×C4×C11C22⋊Q811yescharacteristic
240C2×C4×C11C22⋊Q811yescharacteristic
241C2×C4×C11C22⋊Q811yescharacteristic
242C2×C4×C11C22⋊Q811yescharacteristic
243C2×C4×C11C22⋊Q811yescharacteristic
244C2×C4×C11C22⋊Q811yescharacteristic
245C2×C4×C11#12411yescharacteristic
246C2×C4×C11#12411yescharacteristic
247C2×C4×C11#12411yescharacteristic
248C2×C4×C11#12411yescharacteristic
249C2×C4×C11#12411yescharacteristic
250C2×C4×C11#12411yescharacteristic
251C2×C4×C11#12411yescharacteristic
252C2×C4×C11#12411yescharacteristic
253C2×C4×C11#12411yescharacteristic
254C2×C4×C11#12411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×Q811yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C22⋊D11—42no—
262C22⋊D11—42no—
263C22⋊D11—42no—
264C22⋊D11—42no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—22no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—42no—
271C2×Dic11—82no—
272C2×Dic11—82no—
273C2×Dic11—82no—
274D44—22no—
275D44—22no—
276D44—41no—
277D44—41no—
278C4×D11—42no—
279C4×D11—42no—
280C4×D11—42no—
281C4×D11—42no—
282Dic22—22no—
283Dic22—22no—
284Dic22—41no—
285Dic22—41no—
286Dic22—88no—
287C8×C11—42no—
288C8×C11—42no—
289C22×#41—111no—
290C22×M16C2×D1111yescharacteristic
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—114no—
304#421—222no—
305#421—222no—
306#421—222no—
307C2×#104—114no—
308C2×#104—222no—
309#410—114no—
310#410—222no—
311C2×#99—222no—
312#344C2×D1114yescomplemented
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#39311yescharacteristic
323C22×C11#39311yescharacteristic
324C22×C11#39311yescharacteristic
325C22×C11#39311yescharacteristic
326C22×C11C2×#12011yescharacteristic
327C22×C11C2×C22⋊Q811yescharacteristic
328C22×C11C2×#12411yescharacteristic
329C2×D11—42no—
330C2×D11—82no—
331C2×D11—82no—
332C2×D11—82no—
333C4×C11—44no—
334C4×C11#39311yescharacteristic
335C4×C11#39311yescharacteristic
336C4×C11#39311yescharacteristic
337C4×C11#39311yescharacteristic
338C4×C11C2×C22⋊Q811yescharacteristic
339C4×C11C2×C22⋊Q811yescharacteristic
340C4×C11C2×#12411yescharacteristic
341C4×C11C2×#12411yescharacteristic
342Dic11—44no—
343Dic11—44no—
344Dic11—42no—
345Dic11—82no—
346C2×#41—112no—
347C2×#41—112no—
348C2×#41—221no—
349C2×#41—221no—
350C2×#41—221no—
351C2×#41—221no—
352C2×#41—221no—
353C2×#41—221no—
354C2×#41—221no—
355C2×#41—221no—
356C2×#41—221no—
357C2×#41—221no—
358C22×Q8—111no—
359C22×D4—111no—
360C22×D4—221no—
361C23×C4—221no—
362C23×C4C22×D1111yescharacteristic
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16C22×D1112yes—
374C2×M16C22×D1112yes—
375C22×C8—21no—
376C22×C8—21no—
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#117D4412yes—
402#117C22×D1112yes—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4D4412yes—
411C2×C42—21no—
412C2×C42—112no—
413C2×C42—112no—
414C2×C42—221no—
415#104—228no—
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×C11C2×#39311yescharacteristic
426D11—82no—
427C24—221no—
428C24C2×D4411yescharacteristic
429#41—222no—
430#41—222no—
431#41—222no—
432#41—222no—
433#41—222no—
434#41—222no—
435#41—222no—
436#41—222no—
437#41—441no—
438#41—441no—
439#41—441no—
440#41—441no—
441#41—441no—
442#41—441no—
443#41—441no—
444#41—441no—
445C2×Q8—112no—
446C2×Q8—228no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×D4—112no—
453C2×D4—222no—
454C2×D4—222no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—441no—
461C2×D4—441no—
462C2×D4—441no—
463C2×D4—441no—
464C22×C4—22no—
465C22×C4—221no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—441no—
471C22×C4—441no—
472C22×C4—441no—
473C22×C4—441no—
474C22×C4—441no—
475C22×C4C2×D4411yescharacteristic
476C22×C4#433911yescharacteristic
477C22×C4#433911yescharacteristic
478C22×C4#433911yescharacteristic
479C22×C4#433911yescharacteristic
480C22×C4D4×D1111yescharacteristic
481C22×C4D4×D1111yescharacteristic
482C22×C4D4×D1111yescharacteristic
483C22×C4D4×D1111yescharacteristic
484C22×C4#434111yescharacteristic
485C22×C4#434111yescharacteristic
486C22×C4Q8×D1111yescharacteristic
487C22×C4Q8×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489M16—22no—
490M16—22no—
491M16—22no—
492M16—22no—
493M16—41no—
494M16—41no—
495M16—41no—
496M16—41no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
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—222no—
516C22⋊C4—222no—
517C22⋊C4—222no—
518C22⋊C4—222no—
519C22⋊C4—222no—
520C22⋊C4—441no—
521C22⋊C4C2×D4414yes—
522C42—22no—
523C42—22no—
524C42—114no—
525C42—114no—
526C42—222no—
527C42—222no—
528C42—222no—
529C42—441no—
530C11#2347211yescharacteristic, complemented, Sylow
531C23—81no—
532C23—222no—
533C23—441no—
534C23—441no—
535C23—882no—
536C23#6692811yescharacteristic
537C23#6692811yescharacteristic
538C23#6693511yescharacteristic
539C23#6693511yescharacteristic
540C23#6695011yescharacteristic
541C23#6695011yescharacteristic
542C23C22×D4411yescharacteristic
543Q8—222no—
544Q8—222no—
545Q8—441no—
546Q8—441no—
547Q8—888no—
548D4—222no—
549D4—222no—
550D4—442no—
551D4—442no—
552D4—442no—
553D4—442no—
554D4—441no—
555D4—441no—
556C2×C4—24no—
557C2×C4—82no—
558C2×C4—224no—
559C2×C4—224no—
560C2×C4—222no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4—442no—
568C2×C4—882no—
569C2×C4—882no—
570C2×C4—882no—
571C2×C4#6692811yescharacteristic
572C2×C4#6692811yescharacteristic
573C2×C4#6693511yescharacteristic
574C2×C4#6693511yescharacteristic
575C2×C4#6693811yescharacteristic
576C2×C4#6693811yescharacteristic
577C2×C4#6693811yescharacteristic
578C2×C4#6693811yescharacteristic
579C2×C4#6693811yescharacteristic
580C2×C4#6693811yescharacteristic
581C2×C4#6693811yescharacteristic
582C2×C4#6693811yescharacteristic
583C2×C4#6694911yescharacteristic
584C2×C4#6694911yescharacteristic
585C2×C4#6694911yescharacteristic
586C2×C4#6694911yescharacteristic
587C2×C4#6694911yescharacteristic
588C2×C4#6694911yescharacteristic
589C2×C4#6694911yescharacteristic
590C2×C4#6694911yescharacteristic
591C2×C4#6695011yescharacteristic
592C2×C4#6695011yescharacteristic
593C2×C4C2×#433911yescharacteristic
594C2×C4C2×#433911yescharacteristic
595C2×C4C2×D4×D1111yescharacteristic
596C2×C4C2×D4×D1111yescharacteristic
597C2×C4C2×#434111yescharacteristic
598C2×C4C2×Q8×D1111yescharacteristic
599C8—42no—
600C8—42no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—442no—
609C22—882no—
610C22—882no—
611C22—882no—
612C22#1062228611yescharacteristic
613C22#1062228611yescharacteristic
614C22#1062228611yescharacteristic
615C22#1062228611yescharacteristic
616C22C2×#6692811yescharacteristic
617C22C2×#6693511yescharacteristic
618C22C2×#6695011yescharacteristic
619C4—44no—
620C4—444no—
621C4—444no—
622C4—442no—
623C4—882no—
624C4#1062228611yescharacteristic
625C4#1062228611yescharacteristic
626C4#1062228611yescharacteristic
627C4#1062228611yescharacteristic
628C4C2×#6693811yescharacteristic
629C4C2×#6693811yescharacteristic
630C4C2×#6694911yescharacteristic
631C4C2×#6694911yescharacteristic
632C2—21no—
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—21no—
638C2—21no—
639C2—882no—
640C2C2×#1062228611yescharacteristic
subgroupG/H
centerC4C2×#66938
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#344C2
socleC2×C11C2×#393
prime radicalC22×#4339C22
hypercenterC2×#344D11
hypocenterC11#23472
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. #13082021C2semidirect
5. #13069791C2semidirect
6. #13068327C2semidirect
7. C2×#10622195C2semidirect
8. C2×C11×#344C2semidirect
19. #10623048C22semidirect
32. C11×#344C22semidirect
33. #10622195C22semidirect
34. #10622193C22semidirect
47. C2×#4339Q8semidirect
49. C22×D44Q8semidirect
51. C22×Dic22Q8semidirect
216. C2×#344D11semidirect
312. #344C2×D11semidirect
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×#106227522
C2×#106226192
#130697912
#130683272
C2×#106221952
C2×C11×#3442
#2347211