Finite Group Databasebeta

← #14756475

Subgroups — #14756475

Order 2816.

1198 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622845C211yesmaximal, characteristic
2C2×M16×Dic11C211yesmaximal, characteristic, complemented
3#13071107C211yesmaximal, characteristic
4C2×#10622586C211yesmaximal, characteristic, complemented
5#13069310C212yesmaximal, complemented
6#13069303C212yesmaximal, complemented
7#13069296C212yesmaximal, complemented
8#13069289C212yesmaximal, complemented
9#13068336C211yesmaximal, characteristic, complemented
10#13068335C211yesmaximal, characteristic, complemented
11C2×C11×#417C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×Dic11⋊C4—21no—
18C22×C4×Dic11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C11×#417—24no—
21C2×C11×#103C2212yes—
22C2×C11×#102C2212yes—
23#10622845C418yescomplemented
24#10622843C2211yescharacteristic
25#10622843C2211yescharacteristic
26C2×#66899C2212yes—
27#10622834C2211yescharacteristic
28#10622834C2211yescharacteristic
29#10622833—21no—
30#10622833—21no—
31C2×#66896C2212yes—
32C4×C22⋊Dic11—21no—
33C4×C22⋊Dic11—21no—
34C2×C11⋊#95—21no—
35M16×Dic11—24no—
36C2×#66879C2212yes—
37C2×C8×Dic11C2212yes—
38#10622586—21no—
39#10622586—21no—
40#10622586C2212yes—
41#10622586C2212yes—
42#10622189C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41C2×C414yes—
52C22×Q8×C11C2311yescharacteristic
53C22×D4×C11—21no—
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11—21no—
57C23×C4×C11C2311yescharacteristic
58C23×Dic11—21no—
59C23×Dic11D411yescharacteristic
60C23×Dic11D411yescharacteristic
61C2×C11×M16—22no—
62C2×C11×M16—22no—
63C2×C11×M16D414yes—
64C22×C8×C11C2312yes—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2312yes—
69C2×C22⋊Dic11—21no—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74#66979—22no—
75#66979—22no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11C2×C414yes—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2312yes—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4—22no—
84C2×Dic11⋊C4—44no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11D411yescharacteristic
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×#4318—22no—
93C2×#4318—22no—
94C2×#4318C2×C414yes—
95C22×C11⋊C8C2312yes—
96C11×#103—24no—
97C11×#102—24no—
98#66899C2×C418yescomplemented
99#66896C2×C418yescomplemented
100C11⋊#95—22no—
101C11⋊#95—22no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106#66879—24no—
107C8×Dic11—24no—
108#21093—111nomaximal, Sylow
109C24×C11—21no—
110C24×C11C2×D411yescharacteristic
111C11×#41—28no—
112C11×#41—28no—
113C11×#41—44no—
114C11×#41—44no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11C22×C412yes—
121C2×D4×C11—24no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11C22×C412yes—
130C22×C4×C11—21no—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—42no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D412yes—
141C22×C4×C11#4112yes—
142C22×C4×C11#4112yes—
143C22×C4×C11#4112yes—
144C22×C4×C11#4112yes—
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—41no—
155C22×Dic11—41no—
156C22×Dic11—42no—
157C22×Dic11—42no—
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C11×M16—28no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11C2×D414yes—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—42no—
169C22⋊Dic11—42no—
170C22⋊Dic11—42no—
171C22⋊Dic11—42no—
172C22⋊Dic11—42no—
173C22⋊Dic11—42no—
174C4⋊Dic11—24no—
175C4⋊Dic11—22no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11C22×C414yes—
181Dic11⋊C4—44no—
182Dic11⋊C4—44no—
183C4×Dic11—22no—
184C4×Dic11—22no—
185C4×Dic11—21no—
186C4×Dic11—21no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—42no—
190#4318—28no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8C22×C414yes—
194C2×#417—111no—
195C2×#417D1111yescharacteristic
196C2×C4×M16—111no—
197#2297—111no—
198C2×#389—111no—
199#1936—112no—
200#1935—112no—
201#1934—112no—
202#1933—112no—
203#1736—111no—
204#1736—111no—
205C23×C11—21no—
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—22no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11C4×D412yes—
217C23×C11#12112yes—
218C23×C11#12412yes—
219C23×C11C22×D411yescharacteristic
220Q8×C11—22no—
221Q8×C11—22no—
222Q8×C11—41no—
223Q8×C11—41no—
224D4×C11—22no—
225D4×C11—22no—
226D4×C11—48no—
227D4×C11—41no—
228D4×C11—41no—
229C2×C4×C11—22no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—48no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—84no—
237C2×C4×C11#11714yes—
238C2×C4×C11C4×D412yes—
239C2×C4×C11C4×D414yes—
240C2×C4×C11#12112yes—
241C2×C4×C11#12314yes—
242C2×C4×C11#12412yes—
243C2×C4×C11#12614yes—
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—24no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—44no—
262C2×Dic11—44no—
263C2×Dic11—48no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11AGL(1,ℤ/8)12yes—
273C2×Dic11#13712yes—
274C8×C11—24no—
275C11⋊C8—24no—
276C22×#41C2×D1111yescharacteristic
277C22×M16—111no—
278C22×M16C2×D1111yescharacteristic
279C2×#117—111no—
280C22×C4⋊C4—111no—
281C22×C4⋊C4—221no—
282C22×C4⋊C4C2×D1111yescharacteristic
283C22×C42—111no—
284#417—24no—
285#417—118no—
286C2×#103—112no—
287C2×#103C2×D1112yes—
288C2×#102—112no—
289C2×#102C2×D1112yes—
290C4×M16—224no—
291C2×#97—112no—
292C2×C4×C8—112no—
293#391—111no—
294#391—111no—
295#390—111no—
296#390—111no—
297#389—112no—
298#389—112no—
299#389—221no—
300#389—221no—
301#386—221no—
302#386—221no—
303C4×C22⋊C4—221no—
304C4×C22⋊C4—221no—
305C2×#95—221no—
306#340—112no—
307#340—112no—
308#340—112no—
309#340—112no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11#38814yes—
324C22×C11C2×C4×D411yescharacteristic
325C22×C11C2×#12111yescharacteristic
326C22×C11C2×#12411yescharacteristic
327C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
328C22×C11C2×#13711yescharacteristic
329C22×C11#57511yescharacteristic
330C22×C11#57511yescharacteristic
331C4×C11—42no—
332C4×C11—82no—
333C4×C11#38814yes—
334C4×C11C2×#11711yescharacteristic
335C4×C11C2×C4×D411yescharacteristic
336C4×C11C2×#12311yescharacteristic
337C4×C11C2×#12611yescharacteristic
338Dic11—22no—
339Dic11—22no—
340Dic11—44no—
341Dic11—41no—
342Dic11—41no—
343Dic11—81no—
344Dic11—81no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41—22no—
348C2×#41—22no—
349C2×#41—22no—
350C2×#41C4×D1114yes—
351C22×Q8C22×D1111yescharacteristic
352C22×D4—21no—
353C22×D4C22×D1111yescharacteristic
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—111no—
357C23×C4—111no—
358C23×C4—221no—
359C23×C4C22×D1111yescharacteristic
360C2×M16—22no—
361C2×M16—22no—
362C2×M16—114no—
363C2×M16—222no—
364C2×M16—222no—
365C2×M16C22⋊D1114yes—
366C22×C8—112no—
367C22×C8C22×D1112yes—
368#117—222no—
369#117—222no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—114no—
374C2×C4⋊C4—112no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—444no—
382C2×C4⋊C4C22×D1112yes—
383C2×C22⋊C4—221no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C22⋊C4—221no—
387C2×C22⋊C4—221no—
388C2×C42—111no—
389C2×C42—111no—
390C2×C42—111no—
391C2×C42—111no—
392C2×C42—222no—
393C2×C42—222no—
394C2×C42—221no—
395#103—24no—
396#103—118no—
397#102—24no—
398#102—118no—
399#97—224no—
400C4×C8—224no—
401#95—222no—
402#95—222no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407C2×C11—24no—
408C2×C11—82no—
409C2×C11C2×#38811yescharacteristic
410C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
411C2×C11C4×#13711yescharacteristic
412C2×C11#305511yescharacteristic
413C2×C11#305611yescharacteristic
414C2×C11#314111yescharacteristic
415C2×C11#314211yescharacteristic
416C24—21no—
417C24D4×D1111yescharacteristic
418#41—28no—
419#41—28no—
420#41—44no—
421#41—44no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8C2×C4×D1112yes—
428C2×D4—24no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—42no—
435C2×D4—42no—
436C2×D4C2×C4×D1112yes—
437C22×C4—21no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—224no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—441no—
458C22×C4—441no—
459C22×C4—442no—
460C22×C4—442no—
461C22×C4C2×C4×D1112yes—
462C22×C4#433912yes—
463C22×C4D4×D1111yescharacteristic
464C22×C4#434112yes—
465C22×C4#434112yes—
466C22×C4#434112yes—
467C22×C4C2×C22⋊D1112yes—
468C22×C4C23×D1111yescharacteristic
469M16—28no—
470M16—228no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—114no—
474C2×C8—222no—
475C2×C8—222no—
476C2×C8C2×C22⋊D1114yes—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—42no—
480C4⋊C4—114no—
481C4⋊C4—224no—
482C4⋊C4—222no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—444no—
488C4⋊C4—444no—
489C22⋊C4—442no—
490C22⋊C4—442no—
491C22⋊C4—442no—
492C22⋊C4—442no—
493C22⋊C4—442no—
494C42—222no—
495C42—222no—
496C42—221no—
497C42—221no—
498C42—221no—
499C42—221no—
500C42—442no—
501C11#2109311yescharacteristic, complemented, Sylow
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—22no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23(C22⋊D11)⋊C412yes—
514C23#6693812yes—
515C23#6699112yes—
516C23C2×D4×D1111yescharacteristic
517Q8—22no—
518Q8—22no—
519Q8—41no—
520Q8—41no—
521D4—22no—
522D4—22no—
523D4—48no—
524D4—41no—
525D4—41no—
526C2×C4—22no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—48no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—84no—
534C2×C4—112no—
535C2×C4—112no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—224no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—444no—
548C2×C4—444no—
549C2×C4—448no—
550C2×C4—442no—
551C2×C4—442no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4#6693014yes—
559C2×C4#6693214yes—
560C2×C4(C22⋊D11)⋊C412yes—
561C2×C4#6693812yes—
562C2×C4C4×C22⋊D1114yes—
563C2×C4#6698814yes—
564C2×C4#6699112yes—
565C2×C4C22×C4×D1111yescharacteristic
566C2×C4C2×#433911yescharacteristic
567C2×C4C2×#434111yescharacteristic
568C2×C4C2×#434111yescharacteristic
569C2×C4C2×#434111yescharacteristic
570C2×C4C22×C22⋊D1111yescharacteristic
571C8—24no—
572C8—224no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22#1062255714yes—
587C22C2×(C22⋊D11)⋊C411yescharacteristic
588C22C2×#6693811yescharacteristic
589C22D11×AGL(1,ℤ/8)11yescharacteristic
590C22#1062330411yescharacteristic
591C22D11×#13711yescharacteristic
592C22#1062330811yescharacteristic
593C22C2×#6699111yescharacteristic
594C4—42no—
595C4—82no—
596C4—222no—
597C4—222no—
598C4—444no—
599C4—441no—
600C4—441no—
601C4—881no—
602C4—881no—
603C4#1062255714yes—
604C4C2×#6693011yescharacteristic
605C4C2×#6693211yescharacteristic
606C4C2×C4×C22⋊D1111yescharacteristic
607C4C2×#6698811yescharacteristic
608C2—24no—
609C2—82no—
610C2C2×#1062255711yescharacteristic
611C2#1307742911yescharacteristic
612C2#1307744011yescharacteristic
613C2#1307822911yescharacteristic
614C2#1307824011yescharacteristic
615C2#1307900711yescharacteristic
616C2#1307901411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC2×#417D11
hypocenterC11#21093
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×M16×Dic11C2semidirect
4. C2×#10622586C2semidirect
5. #13069310C2semidirect
6. #13069303C2semidirect
7. #13069296C2semidirect
8. #13069289C2semidirect
9. #13068336C2semidirect
10. #13068335C2semidirect
23. #10622845C4semidirect
98. #66899C2×C4semidirect
99. #66896C2×C4semidirect
501. C11#21093semidirect

Maximal subgroups

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

subgroupindex
C2×#106228452
C2×M16×Dic112
#130711072
C2×#106225862
#130693102
#130693032
#130692962
#130692892
#130683362
#130683352
C2×C11×#4172
#2109311