Finite Group Databasebeta

← #14769480

Subgroups — #14769480

Order 2816.

1818 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4323C211yesmaximal, characteristic
2C2×#10622627C212yesmaximal, complemented
3C22⋊C4×D44C211yesmaximal, characteristic, complemented
4#13069491C212yesmaximal, complemented
5#13068967C212yesmaximal, complemented
6#13068964C212yesmaximal, complemented
7#13068639C211yesmaximal, characteristic, complemented
8#13068547C211yesmaximal, characteristic, complemented
9#13068546C211yesmaximal, characteristic, complemented
10#13068394C211yesmaximal, characteristic, complemented
11D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C23×D44C2211yescharacteristic
14C2×C4×D4×C11C2212yescomplemented
15C22×C11×C22⋊C4—21no—
16C22×#4323—28no—
17C22×#4323C418yescomplemented
18C22×#4323C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C22×#4323C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C2×C22⋊C4×D11—21no—
24C2×C4×D44C2212yescomplemented
25C11×#390C2212yescomplemented
26C11×#386—22no—
27C11×#380C2211yescharacteristic
28C11×#379—21no—
29C4×C11×C22⋊C4C2211yescharacteristic
30C2×#66896C2212yescomplemented
31C2×#66896C2212yescomplemented
32#10622825C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34#10622627—28no—
35C2×#66873C2212yescomplemented
36C2×#66873C2212yescomplemented
37C2×#66872C2212yescomplemented
38#10622568—21no—
39#10622552C2212yescomplemented
40C2×#66867C2212yescomplemented
41#10622278—22no—
42#10622167C2212yescomplemented
43#10622162C2212yescomplemented
44C25×C11—21no—
45C24×D11—21no—
46C22×D4×C11—24no—
47C22×D4×C11—21no—
48C22×D4×C11—22no—
49C22×D4×C11—42no—
50C22×D4×C11C2×C414yescomplemented
51C22×D4×C11C2311yescharacteristic
52C22×D4×C11C2311yescharacteristic
53C23×C4×C11—22no—
54C23×C4×C11C2311yescharacteristic
55C22×D44—24no—
56C22×D44—21no—
57C22×D44—22no—
58C22×D44—42no—
59C22×D44C2×C414yescomplemented
60C22×D44C2311yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—22no—
63C4×D4×C11—24no—
64C4×D4×C11—42no—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—44no—
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C42×C11C2312yes—
74C2×C22⋊Dic11—21no—
75C2×#4323—24no—
76C2×#4323—24no—
77C2×#4323—232no—
78C2×#4323—24no—
79C2×#4323C2×C414yes—
80C2×#4323C2×C414yescomplemented
81C2×#4323C2×C414yescomplemented
82C2×#4323C2×C414yescomplemented
83C2×#4323D418yes—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×C4⋊Dic11C2312yes—
88C22×C11⋊C8—24no—
89C22×C11⋊C8C2×C414yescomplemented
90C22×C11⋊C8C2312yes—
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22⋊C4×D11—44no—
94C4×D44—24no—
95C4×D44—42no—
96C11×#95—21no—
97C11×#95D412yes—
98#66896—24no—
99#66896—42no—
100C11⋊#95—21no—
101C22⋊(C11⋊C8)—22no—
102#66873—24no—
103#66873—42no—
104#66872—24no—
105#66867—24no—
106#22436—111nomaximal, Sylow
107C24×C11—21no—
108C24×C11—21no—
109C24×C11—24no—
110C24×C11—44no—
111C24×C11—42no—
112C24×C11—42no—
113C24×C11—82no—
114C24×C11C2×D411yescharacteristic
115C23×D11—21no—
116C23×D11—21no—
117C23×D11—24no—
118C23×D11—44no—
119C23×D11—42no—
120C23×D11—42no—
121C23×D11—82no—
122C2×D4×C11—28no—
123C2×D4×C11—24no—
124C2×D4×C11—22no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—44no—
130C2×D4×C11—48no—
131C2×D4×C11—44no—
132C2×D4×C11C22×C412yes—
133C2×D4×C11C22×C412yes—
134C2×D4×C11C2×D414yes—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—44no—
139C22×C4×C11—44no—
140C22×C4×C11—82no—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11#4112yes—
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—22no—
148C2×D44—28no—
149C2×D44—24no—
150C2×D44—22no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—22no—
154C2×D44—22no—
155C2×D44—44no—
156C2×D44—44no—
157C2×D44—48no—
158C2×D44C22×C412yes—
159C2×D44C22×C412yes—
160C2×D44C2×D414yes—
161C2×C4×D11—44no—
162C2×C4×D11—44no—
163C2×C4×D11—82no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—44no—
169C11×C22⋊C4—44no—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—82no—
172C42×C11—22no—
173C42×C11—22no—
174C22⋊Dic11—42no—
175#4323—28no—
176#4323—28no—
177#4323—28no—
178#4323C22⋊C4116yescomplemented
179(C2×D11)⋊C4—44no—
180(C2×D11)⋊C4—44no—
181(C2×D11)⋊C4—82no—
182C4⋊Dic11—22no—
183C4⋊Dic11—22no—
184C2×C11⋊C8—28no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8C22×C412yes—
190C2×C11⋊C8C22×C412yes—
191C2×C11⋊C8C2×D414yes—
192C23×D8—111no—
193C2×#442—112no—
194D4×C22⋊C4—111no—
195D4×C22⋊C4D1111yescharacteristic, complemented
196#1972—112no—
197#1879—112no—
198#1879—112no—
199#1807—111no—
200#1786—111no—
201#1786—111no—
202#1752—111no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—24no—
207C23×C11—22no—
208C23×C11—48no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—42no—
216C23×C11—48no—
217C23×C11—84no—
218C23×C11—88no—
219C23×C11—88no—
220C23×C11C4×D412yes—
221C23×C11AGL(1,ℤ/8)12yes—
222C23×C11AGL(1,ℤ/8)12yes—
223C23×C11C22×D411yescharacteristic
224C22×D11—22no—
225C22×D11—24no—
226C22×D11—22no—
227C22×D11—48no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—42no—
235C22×D11—48no—
236C22×D11—84no—
237C22×D11—88no—
238C22×D11—88no—
239D4×C11—22no—
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—24no—
243D4×C11—48no—
244D4×C11—42no—
245D4×C11C2×C22⋊C414yescomplemented
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—88no—
260C2×C4×C11C4×D412yes—
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C22×D412yes—
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11H(5,𝔽2)12yes—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268D44—22no—
269D44—22no—
270D44—22no—
271D44—24no—
272D44—48no—
273D44—42no—
274D44C2×C22⋊C414yescomplemented
275C4×D11—88no—
276C11⋊C8—22no—
277C11⋊C8—42no—
278C11⋊C8C2×C22⋊C414yescomplemented
279C23×D4—111no—
280C23×D4C2×D1111yescharacteristic
281C22×D8—111no—
282C22×D8—111no—
283C22×D8—111no—
284C22×D8—111no—
285C22×D8—118no—
286C22×D8—228no—
287C23×C8—111no—
288C2×C4×D4—112no—
289C2×C4×D4C2×D1112yescomplemented
290C22×C22⋊C4—21no—
291C22×C22⋊C4—221no—
292#442—228no—
293C2×#106—112no—
294C2×#102—112no—
295C2×#102—112no—
296C2×#102—112no—
297C2×#102—112no—
298C2×C22⋊C8—111no—
299C2×#97—112no—
300#390—112no—
301#390C2×D1112yescomplemented
302#386—22no—
303#386—222no—
304#380—111no—
305#380C2×D1111yescharacteristic
306#379—21no—
307#379—221no—
308C4×C22⋊C4C2×D1111yescharacteristic
309#340—112no—
310#336—112no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—24no—
314C22×C11—24no—
315C22×C11—24no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—816no—
324C22×C11—82no—
325C22×C11—82no—
326C22×C11#44214yescomplemented
327C22×C11C2×C4×D411yescharacteristic
328C22×C11D4212yes—
329C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C11#57612yes—
332C2×D11—24no—
333C2×D11—42no—
334C2×D11—42no—
335C2×D11—44no—
336C2×D11—44no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—42no—
340C2×D11—816no—
341C2×D11—82no—
342C2×D11—82no—
343C4×C11—22no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11—82no—
347C4×C11C22×C22⋊C411yescharacteristic
348C4×C11#51811yescharacteristic
349C4×C11#54612yes—
350Dic11—82no—
351C25—21no—
352C25—221no—
353C22×D4—24no—
354C22×D4—22no—
355C22×D4—21no—
356C22×D4—42no—
357C22×D4—114no—
358C22×D4—111no—
359C22×D4—111no—
360C22×D4—224no—
361C22×D4—222no—
362C22×D4—221no—
363C22×D4—442no—
364C22×D4C4×D1114yescomplemented
365C22×D4C22×D1111yescharacteristic
366C22×D4C22×D1111yescharacteristic
367C23×C4—22no—
368C23×C4—222no—
369C23×C4C22×D1111yescharacteristic
370C2×D8—114no—
371C2×D8—118no—
372C2×D8—114no—
373C2×D8—114no—
374C2×D8—114no—
375C2×D8—224no—
376C2×D8—2232no—
377C2×D8—224no—
378C2×D8—224no—
379C22×C8—111no—
380C22×C8—114no—
381C22×C8—111no—
382C22×C8—112no—
383C22×C8—224no—
384C4×D4—24no—
385C4×D4—42no—
386C4×D4—224no—
387C4×D4—442no—
388C2×C4⋊C4—112no—
389C2×C4⋊C4C22×D1112yes—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—222no—
397C2×C22⋊C4—222no—
398C2×C22⋊C4—222no—
399C2×C22⋊C4—444no—
400C2×C22⋊C4C22⋊D1111yescharacteristic
401C2×C22⋊C4C22⋊D1111yescharacteristic
402C2×C42C22×D1112yes—
403#106—224no—
404#102—224no—
405#102—224no—
406#102—442no—
407#102—442no—
408C22⋊C8—222no—
409#97—224no—
410#95—21no—
411#95—221no—
412#95C22⋊D1112yes—
413C2×C11—24no—
414C2×C11—44no—
415C2×C11—82no—
416C2×C11D4×C22⋊C411yescharacteristic
417C2×C11C2×#44211yescharacteristic
418C2×C11#294811yescharacteristic
419C2×C11#326412yes—
420C2×C11#326412yes—
421D11—44no—
422D11—82no—
423C24—21no—
424C24—21no—
425C24—24no—
426C24—44no—
427C24—42no—
428C24—42no—
429C24—82no—
430C24—221no—
431C24—221no—
432C24—224no—
433C24—444no—
434C24—442no—
435C24—442no—
436C24—882no—
437C24C2×C22⋊D1111yescharacteristic
438C2×D4—28no—
439C2×D4—24no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—44no—
448C2×D4—112no—
449C2×D4—112no—
450C2×D4—114no—
451C2×D4—228no—
452C2×D4—224no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—222no—
456C2×D4—222no—
457C2×D4—222no—
458C2×D4—444no—
459C2×D4—448no—
460C2×D4—444no—
461C2×D4C2×C4×D1112yes—
462C2×D4C2×C4×D1112yes—
463C2×D4D4×D1114yes—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—44no—
468C22×C4—44no—
469C22×C4—82no—
470C22×C4—222no—
471C22×C4—444no—
472C22×C4—444no—
473C22×C4—882no—
474C22×C4C2×C4×D1112yes—
475C22×C4#433912yes—
476C22×C4C2×C22⋊D1112yes—
477C22×C4C2×C22⋊D1112yes—
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C23×D1111yescharacteristic
480D8—1116no—
481D8—228no—
482D8—228no—
483D8—228no—
484C2×C8—112no—
485C2×C8—114no—
486C2×C8—112no—
487C2×C8—228no—
488C2×C8—222no—
489C2×C8—222no—
490C2×C8—222no—
491C2×C8—222no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—222no—
495C4⋊C4—222no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—44no—
499C22⋊C4—44no—
500C22⋊C4—42no—
501C22⋊C4—82no—
502C22⋊C4—444no—
503C22⋊C4—444no—
504C22⋊C4—442no—
505C22⋊C4—882no—
506C42—22no—
507C42—22no—
508C11#2243611yescharacteristic, complemented, Sylow
509C23—22no—
510C23—22no—
511C23—22no—
512C23—24no—
513C23—22no—
514C23—48no—
515C23—41no—
516C23—41no—
517C23—42no—
518C23—41no—
519C23—42no—
520C23—41no—
521C23—42no—
522C23—48no—
523C23—84no—
524C23—88no—
525C23—88no—
526C23—222no—
527C23—224no—
528C23—222no—
529C23—448no—
530C23—441no—
531C23—441no—
532C23—442no—
533C23—441no—
534C23—442no—
535C23—441no—
536C23—442no—
537C23—448no—
538C23—884no—
539C23—888no—
540C23—888no—
541C23C4×C22⋊D1112yes—
542C23#6698512yes—
543C23#6700212yes—
544C23C22×C22⋊D1111yescharacteristic
545D4—22no—
546D4—22no—
547D4—22no—
548D4—24no—
549D4—48no—
550D4—42no—
551D4—114no—
552D4—222no—
553D4—222no—
554D4—222no—
555D4—224no—
556D4—448no—
557D4—442no—
558D4C22⋊C4×D1114yescomplemented
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—88no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—888no—
577C2×C4C4×C22⋊D1112yes—
578C2×C4C22×C4×D1111yescharacteristic
579C2×C4C2×#433911yescharacteristic
580C2×C4C2×D4×D1112yes—
581C2×C4#6703712yes—
582C8—114no—
583C8—222no—
584C8—442no—
585C22—24no—
586C22—24no—
587C22—22no—
588C22—22no—
589C22—24no—
590C22—44no—
591C22—44no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—42no—
597C22—816no—
598C22—82no—
599C22—82no—
600C22—224no—
601C22—444no—
602C22—444no—
603C22—442no—
604C22—442no—
605C22—442no—
606C22—442no—
607C22—442no—
608C22—8816no—
609C22—882no—
610C22—882no—
611C22#1062262714yescomplemented
612C22C2×C4×C22⋊D1111yescharacteristic
613C22C2×#6698511yescharacteristic
614C22D4×C22⋊D1112yes—
615C22C2×#6700211yescharacteristic
616C22#1062336612yes—
617C4—22no—
618C4—42no—
619C4—42no—
620C4—82no—
621C4—882no—
622C4C2×C22⋊C4×D1111yescharacteristic
623C4#1062301711yescharacteristic
624C4#1062302112yes—
625C2—24no—
626C2—44no—
627C2—82no—
628C2—444no—
629C2—882no—
630C2C22⋊C4×C22⋊D1111yescharacteristic
631C2C2×#1062262711yescharacteristic
632C2#1307746611yescharacteristic
633C2#1308009212yes—
634C2#1308009712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC23×#4323C2
cosocleC22×C4×C11C24
hypercenterD4×C22⋊C4D11
hypocenterC11#22436
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622627C2semidirect
3. C22⋊C4×D44C2semidirect
4. #13069491C2semidirect
5. #13068967C2semidirect
6. #13068964C2semidirect
7. #13068639C2semidirect
8. #13068547C2semidirect
9. #13068546C2semidirect
10. #13068394C2semidirect
11. D4×C11×C22⋊C4C2semidirect
14. C2×C4×D4×C11C22semidirect
17. C22×#4323C4semidirect
24. C2×C4×D44C22semidirect
25. C11×#390C22semidirect
30. C2×#66896C22semidirect
31. C2×#66896C22semidirect
35. C2×#66873C22semidirect
36. C2×#66873C22semidirect
37. C2×#66872C22semidirect
39. #10622552C22semidirect
40. C2×#66867C22semidirect
42. #10622167C22semidirect
43. #10622162C22semidirect
50. C22×D4×C11C2×C4semidirect
59. C22×D44C2×C4semidirect
80. C2×#4323C2×C4semidirect
81. C2×#4323C2×C4semidirect
82. C2×#4323C2×C4semidirect
89. C22×C11⋊C8C2×C4semidirect
178. #4323C22⋊C4semidirect
195. D4×C22⋊C4D11semidirect
245. D4×C11C2×C22⋊C4semidirect
274. D44C2×C22⋊C4semidirect
278. C11⋊C8C2×C22⋊C4semidirect
289. C2×C4×D4C2×D11semidirect
301. #390C2×D11semidirect
326. C22×C11#442semidirect
364. C22×D4C4×D11semidirect
508. C11#22436semidirect
558. D4C22⋊C4×D11semidirect
611. C22#10622627semidirect

Maximal subgroups

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

subgroupindex
C23×#43232
C2×#106226272
C22⋊C4×D442
#130694912
#130689672
#130689642
#130686392
#130685472
#130685462
#130683942
D4×C11×C22⋊C42
#2243611