Finite Group Databasebeta

← #14782466

Subgroups — #14782466

Order 2816.

1178 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622734C211yesmaximal, characteristic, complemented
2C2×#10622731C211yesmaximal, characteristic, complemented
3C2×#10622845C211yesmaximal, characteristic
4#13071107C211yesmaximal, characteristic
5C2×#10622586C211yesmaximal, characteristic, complemented
6#13070009C212yesmaximal, complemented
7#13070002C212yesmaximal, complemented
8#13069995C212yesmaximal, complemented
9#13069988C212yesmaximal, 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#10622845—24no—
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—
35#10622734—24no—
36#10622731—24no—
37C2×#66882C2212yes—
38C2×#66881C2212yes—
39C2×Dic11⋊C8C2212yes—
40C2×Dic11⋊C8C2212yes—
41#10622586—21no—
42#10622586—21no—
43#10622586C2212yes—
44#10622586C2212yes—
45#10622167C2212yes—
46#10622167C2212yes—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41Q814yes—
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11—21no—
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11—21no—
57C23×C4×C11—21no—
58C23×C4×C11C2311yescharacteristic
59C23×Dic11—21no—
60C23×Dic11D411yescharacteristic
61C23×Dic11D411yescharacteristic
62C2×C11×M16—22no—
63C2×C11×M16—22no—
64C2×C11×M16D414yes—
65C22×C8×C11C2312yes—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2312yes—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75#66979—22no—
76#66979—22no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11D414yes—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2312yes—
83C2×Dic11⋊C4—22no—
84C2×Dic11⋊C4—22no—
85C2×Dic11⋊C4—44no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C2×#4318—22no—
94C2×#4318—22no—
95C2×#4318—22no—
96C22×C11⋊C8C2312yes—
97C11×#103—24no—
98C11×#102—24no—
99#66899—24no—
100#66896—24no—
101C11⋊#95—22no—
102C11⋊#95—22no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107#66882—24no—
108#66881—24no—
109Dic11⋊C8—24no—
110Dic11⋊C8—24no—
111#23617—111nomaximal, Sylow
112C24×C11—21no—
113C24×C11C2×D411yescharacteristic
114C11×#41—28no—
115C11×#41—28no—
116C11×#41—44no—
117C11×#41—44no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11C2×Q812yes—
124C2×D4×C11—24no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—42no—
131C2×D4×C11—42no—
132C2×D4×C11C2×Q812yes—
133C22×C4×C11—21no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×Q812yes—
145C22×C4×C11#4112yes—
146C22×C4×C11#4112yes—
147C22×C4×C11#4112yes—
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—24no—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—41no—
158C22×Dic11—41no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C11×M16—28no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11C2×D414yes—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—42no—
172C22⋊Dic11—42no—
173C22⋊Dic11—42no—
174C22⋊Dic11—42no—
175C22⋊Dic11—42no—
176C22⋊Dic11—42no—
177C4⋊Dic11—24no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—22no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11C2×D414yes—
184Dic11⋊C4—44no—
185Dic11⋊C4—44no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—42no—
193#4318—44no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×#428—111no—
198C2×#423—111no—
199C2×#417—111no—
200C2×#417D1111yescharacteristic
201#2297—111no—
202C2×#389—111no—
203#2068—112no—
204#2067—112no—
205#2066—112no—
206#2065—112no—
207#1736—111no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—22no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11#12112yes—
220C23×C11#12112yes—
221C23×C11C22⋊Q812yes—
222C23×C11C22×D411yescharacteristic
223Q8×C11—22no—
224Q8×C11—22no—
225Q8×C11—41no—
226Q8×C11—41no—
227D4×C11—22no—
228D4×C11—22no—
229D4×C11—48no—
230D4×C11—41no—
231D4×C11—41no—
232C2×C4×C11—22no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—48no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—84no—
240C2×C4×C11#12112yes—
241C2×C4×C11#12112yes—
242C2×C4×C11#12114yes—
243C2×C4×C11C22⋊Q814yes—
244C2×C4×C11C22⋊Q812yes—
245C2×C4×C11C22⋊Q814yes—
246C2×C4×C11#12614yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×Q811yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—24no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—44no—
265C2×Dic11—44no—
266C2×Dic11—48no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11AGL(1,ℤ/8)12yes—
276C2×Dic11#13712yes—
277C8×C11—24no—
278C11⋊C8—42no—
279C22×#41C2×D1111yescharacteristic
280C22×M16—111no—
281C22×M16C2×D1111yescharacteristic
282C2×#117—111no—
283C22×C4⋊C4—111no—
284C22×C4⋊C4—221no—
285C22×C4⋊C4C2×D1111yescharacteristic
286C22×C42—111no—
287#428—224no—
288C2×#107—112no—
289C2×#106—112no—
290#423—224no—
291C2×C4⋊C8—112no—
292C2×C4⋊C8—112no—
293#417—24no—
294#417—224no—
295C2×#103—112no—
296C2×#103C2×D1112yes—
297C2×#102—112no—
298C2×#102C2×D1112yes—
299#391—111no—
300#391—111no—
301#390—111no—
302#390—111no—
303#389—112no—
304#389—112no—
305#389—221no—
306#389—221no—
307#386—221no—
308#386—221no—
309C4×C22⋊C4—221no—
310C4×C22⋊C4—221no—
311C2×#95—221no—
312#340—112no—
313#340—112no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—22no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11#39614yes—
328C22×C11C2×#12111yescharacteristic
329C22×C11C2×#12111yescharacteristic
330C22×C11C2×C22⋊Q811yescharacteristic
331C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C11C2×#13711yescharacteristic
333C22×C11#57511yescharacteristic
334C22×C11#57511yescharacteristic
335C4×C11—42no—
336C4×C11—82no—
337C4×C11#39614yes—
338C4×C11C2×#12111yescharacteristic
339C4×C11C2×C22⋊Q811yescharacteristic
340C4×C11C2×C22⋊Q811yescharacteristic
341C4×C11C2×#12611yescharacteristic
342Dic11—22no—
343Dic11—22no—
344Dic11—44no—
345Dic11—41no—
346Dic11—41no—
347Dic11—81no—
348Dic11—81no—
349C2×#41—22no—
350C2×#41—22no—
351C2×#41—22no—
352C2×#41—22no—
353C2×#41—22no—
354C2×#41Dic2214yes—
355C22×Q8C22×D1111yescharacteristic
356C22×D4—21no—
357C22×D4C22×D1111yescharacteristic
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—111no—
361C23×C4—111no—
362C23×C4—221no—
363C23×C4C22×D1111yescharacteristic
364C2×M16—22no—
365C2×M16—22no—
366C2×M16—222no—
367C2×M16—222no—
368C2×M16—222no—
369C2×M16C22⋊D1114yes—
370C22×C8—112no—
371C22×C8C22×D1112yes—
372#117—222no—
373#117—222no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—114no—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—222no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—444no—
386C2×C4⋊C4C22×D1112yes—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—222no—
397C2×C42—222no—
398C2×C42—221no—
399#107—224no—
400#106—224no—
401C4⋊C8—224no—
402C4⋊C8—224no—
403#103—24no—
404#103—224no—
405#102—24no—
406#102—224no—
407#95—222no—
408#95—222no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413C2×C11—24no—
414C2×C11—82no—
415C2×C11C2×#39611yescharacteristic
416C2×C11#303611yescharacteristic
417C2×C11#303711yescharacteristic
418C2×C11#305511yescharacteristic
419C2×C11#305611yescharacteristic
420C2×C11#307911yescharacteristic
421C2×C11#308011yescharacteristic
422C24—21no—
423C24D4×D1111yescharacteristic
424#41—28no—
425#41—28no—
426#41—44no—
427#41—44no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8C2×Dic2212yes—
434C2×D4—24no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—42no—
441C2×D4—42no—
442C2×D4C2×Dic2212yes—
443C22×C4—21no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—224no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—441no—
464C22×C4—441no—
465C22×C4—442no—
466C22×C4—442no—
467C22×C4C2×Dic2212yes—
468C22×C4#433912yes—
469C22×C4D4×D1111yescharacteristic
470C22×C4D4×D1112yes—
471C22×C4#434112yes—
472C22×C4#434112yes—
473C22×C4C2×C22⋊D1112yes—
474C22×C4C23×D1111yescharacteristic
475M16—28no—
476M16—444no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—222no—
480C2×C8—222no—
481C2×C8—222no—
482C2×C8C2×C22⋊D1114yes—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—42no—
486C4⋊C4—114no—
487C4⋊C4—224no—
488C4⋊C4—222no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—444no—
494C4⋊C4—444no—
495C22⋊C4—442no—
496C22⋊C4—442no—
497C22⋊C4—442no—
498C22⋊C4—442no—
499C22⋊C4—442no—
500C42—222no—
501C42—222no—
502C42—221no—
503C42—221no—
504C42—221no—
505C42—221no—
506C42—442no—
507C11#2361711yescharacteristic, complemented, Sylow
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—22no—
513C23—41no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23#6693112yes—
520C23#6693712yes—
521C23#6699112yes—
522C23C2×D4×D1111yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—41no—
526Q8—41no—
527D4—22no—
528D4—22no—
529D4—48no—
530D4—41no—
531D4—41no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—48no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—84no—
540C2×C4—112no—
541C2×C4—112no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—224no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—444no—
554C2×C4—444no—
555C2×C4—448no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4#6693114yes—
565C2×C4#6693112yes—
566C2×C4#6693214yes—
567C2×C4#6693712yes—
568C2×C4#6697714yes—
569C2×C4#6699112yes—
570C2×C4#6699214yes—
571C2×C4C22×Dic2211yescharacteristic
572C2×C4C2×#433911yescharacteristic
573C2×C4C2×D4×D1111yescharacteristic
574C2×C4C2×#434111yescharacteristic
575C2×C4C2×#434111yescharacteristic
576C2×C4C22×C22⋊D1111yescharacteristic
577C8—24no—
578C8—442no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22#1062256114yes—
593C22C2×#6693111yescharacteristic
594C22C2×#6693711yescharacteristic
595C22D11×AGL(1,ℤ/8)11yescharacteristic
596C22#1062330411yescharacteristic
597C22D11×#13711yescharacteristic
598C22#1062330811yescharacteristic
599C22C2×#6699111yescharacteristic
600C4—42no—
601C4—82no—
602C4—222no—
603C4—222no—
604C4—444no—
605C4—441no—
606C4—441no—
607C4—881no—
608C4—881no—
609C4#1062256114yes—
610C4C2×#6693111yescharacteristic
611C4C2×#6693211yescharacteristic
612C4C2×#6697711yescharacteristic
613C4C2×#6699211yescharacteristic
614C2—24no—
615C2—82no—
616C2C2×#1062256111yescharacteristic
617C2#1307807911yescharacteristic
618C2#1307808711yescharacteristic
619C2#1307822911yescharacteristic
620C2#1307824011yescharacteristic
621C2#1307842711yescharacteristic
622C2#1307843611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenterC2×#417D11
hypocenterC11#23617
LCSG ▷ C22×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
1. C2×#10622734C2semidirect
2. C2×#10622731C2semidirect
5. C2×#10622586C2semidirect
6. #13070009C2semidirect
7. #13070002C2semidirect
8. #13069995C2semidirect
9. #13069988C2semidirect
10. #13068335C2semidirect
507. C11#23617semidirect

Maximal subgroups

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

subgroupindex
C2×#106227342
C2×#106227312
C2×#106228452
#130711072
C2×#106225862
#130700092
#130700022
#130699952
#130699882
#130683352
C2×C11×#4172
#2361711