Finite Group Databasebeta

← #14727713

Subgroups — #14727713

Order 2816.

1084 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079388C211yesmaximal, characteristic, complemented
2#13079373C211yesmaximal, characteristic, complemented
3#13074421C211yesmaximal, characteristic, complemented
4#13067664C214yesmaximal, complemented
5#13067596C214yesmaximal, complemented
6#13067188C211yesmaximal, characteristic, complemented
7#13067184C211yesmaximal, characteristic, complemented
8C2×#10622163C211yesmaximal, characteristic, complemented
9C2×C11×#538C211yesmaximal, characteristic
10C11×#538—22no—
11C11×#538—22no—
12C11×#538—22no—
13C11×#538C2214yes—
14C2×C11×#126—21no—
15C2×C11×#124—21no—
16C2×C11×#123—21no—
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#121—21no—
19C2×C11×#121C2211yescharacteristic
20C2×C11×#120—21no—
21C2×C4×D4×C11—21no—
22C22×C11×C22⋊C4C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24#10622860—21no—
25#10622841—21no—
26#10622831—21no—
27#10622825C2211yescharacteristic
28#10622823—21no—
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31#10622664—22no—
32#10622663C2212yescomplemented
33#10622657C2212yescomplemented
34#10622654—22no—
35#10622653C2212yescomplemented
36#10622647C2212yescomplemented
37#10622584—21no—
38#10622583—21no—
39#10622562C2212yescomplemented
40#10622561—22no—
41#10622560C2212yescomplemented
42#10622176C2214yescomplemented
43#10622175C2214yescomplemented
44#10622163C2214yescomplemented
45C25×C11D411yescharacteristic
46C22×Q8×C11D411yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11D411yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C22×Dic22C2311yescharacteristic
55C11×#126—24no—
56C11×#126—24no—
57C11×#124—24no—
58C11×#124—24no—
59C11×#123—24no—
60C11×#123—24no—
61C11×C22⋊Q8—21no—
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8D412yes—
64C11×C22⋊Q8C2312yes—
65C11×#121—24no—
66C11×#121—24no—
67C11×#121—21no—
68C11×#121—21no—
69C11×#121D412yes—
70C11×#121C2312yes—
71C11×#120—24no—
72C11×#120—24no—
73C4×D4×C11—24no—
74C4×D4×C11—24no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4D412yes—
89C2×C11×C22⋊C4C2312yes—
90C2×C42×C11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×#4326—22no—
96C2×#4324—22no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11C2311yescharacteristic
99#66977—21no—
100#66977—21no—
101#66977—21no—
102#66977—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—22no—
105C22×C11⋊C8—21no—
106C22×C11⋊C8—21no—
107#66899—22no—
108#66896—22no—
109C11⋊#95—22no—
110C11⋊#95C2312yes—
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)C2312yes—
114C22⋊(C11⋊C8)C2312yes—
115#66874—22no—
116#66874—22no—
117#66872—22no—
118#66871—22no—
119#18297—111nomaximal, Sylow
120C24×C11—21no—
121C24×C11—21no—
122C24×C11—21no—
123C24×C11—22no—
124C24×C11—22no—
125C24×C11—81no—
126C24×C11—81no—
127C24×C11C2×D412yes—
128C24×C11C2×D411yescharacteristic
129C2×Q8×C11—21no—
130C2×Q8×C11—81no—
131C2×Q8×C11C2×D412yes—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—24no—
135C2×D4×C11—24no—
136C2×D4×C11—21no—
137C2×D4×C11—42no—
138C2×D4×C11—42no—
139C2×D4×C11—81no—
140C2×D4×C11—82no—
141C2×D4×C11—82no—
142C2×D4×C11C2×D412yes—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—24no—
148C22×C4×C11—21no—
149C22×C4×C11—81no—
150C22×C4×C11—81no—
151C22×C4×C11—82no—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—81no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4C2×D412yes—
171C11×C4⋊C4C2×D412yes—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C42×C11—24no—
184C22⋊Dic11—41no—
185C22⋊Dic11—41no—
186C22⋊Dic11—42no—
187C22⋊Dic11—82no—
188C22⋊Dic11—82no—
189#4326—82no—
190#4324—82no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—81no—
194Dic11⋊C4—41no—
195Dic11⋊C4—41no—
196Dic11⋊C4—82no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—81no—
200C2×C11⋊C8—81no—
201C2×#538D1111yescharacteristic
202#3189—111no—
203#3187—111no—
204#2626—111no—
205#1618—114no—
206#1606—114no—
207#1520—111no—
208#1519—111no—
209C2×#323—111no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—81no—
226C23×C11—81no—
227C23×C11—84no—
228C23×C11—84no—
229C23×C11#12011yescharacteristic
230C23×C11#12011yescharacteristic
231C23×C11#13512yes—
232C23×C11#13712yes—
233C23×C11C22×D411yescharacteristic
234Q8×C11—42no—
235Q8×C11—81no—
236D4×C11—42no—
237D4×C11—42no—
238D4×C11—42no—
239D4×C11—44no—
240D4×C11—81no—
241D4×C11—84no—
242D4×C11—84no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—81no—
259C2×C4×C11—84no—
260C2×C4×C11#12011yescharacteristic
261C2×C4×C11#12011yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—42no—
271Dic22—42no—
272Dic22—42no—
273C11⋊C8—42no—
274C11⋊C8—42no—
275#538—22no—
276#538—22no—
277#538—22no—
278#538C2×D1114yes—
279C2×#126—21no—
280C2×#124—21no—
281C2×#123—21no—
282C2×C22⋊Q8—111no—
283C2×C22⋊Q8C2×D1111yescharacteristic
284C2×#121—21no—
285C2×#121C2×D1111yescharacteristic
286C2×#120—21no—
287C2×C4×D4—21no—
288C22×C22⋊C4C2×D1111yescharacteristic
289#484—112no—
290#484—221no—
291#483—221no—
292#481—112no—
293#467—222no—
294#465—222no—
295#451—112no—
296#451—221no—
297#450—221no—
298#448—112no—
299C2×C22⋊C8—111no—
300C2×C22⋊C8—111no—
301#399—112no—
302#396—222no—
303#393—112no—
304#385—221no—
305#380—111no—
306#379—221no—
307#328—114no—
308#327—114no—
309#323—114no—
310C22×C11—21no—
311C22×C11—21no—
312C22×C11—21no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—44no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—82no—
326C22×C11—84no—
327C22×C11—84no—
328C22×C11—84no—
329C22×C11#45212yes—
330C22×C11#45212yes—
331C22×C11C2×#12011yescharacteristic
332C22×C11C2×#13511yescharacteristic
333C22×C11C2×#13711yescharacteristic
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—42no—
339C4×C11—42no—
340C4×C11—42no—
341C4×C11—42no—
342Dic11—82no—
343Dic11—81no—
344Dic11—81no—
345C25C22⋊D1111yescharacteristic
346C22×Q8—111no—
347C22×Q8C22⋊D1111yescharacteristic
348C22×D4—21no—
349C22×D4—21no—
350C22×D4—21no—
351C22×D4C22⋊D1111yescharacteristic
352C23×C4—21no—
353C23×C4C22⋊D1111yescharacteristic
354C23×C4C22×D1111yescharacteristic
355C2×Q16—222no—
356C2×SD16—222no—
357C22×C8—221no—
358C22×C8—221no—
359#126—24no—
360#126—24no—
361#124—24no—
362#124—24no—
363#123—24no—
364#123—24no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—221no—
368C22⋊Q8—221no—
369C22⋊Q8—221no—
370C22⋊Q8—221no—
371C22⋊Q8C22⋊D1112yes—
372C22⋊Q8C22×D1112yes—
373#121—24no—
374#121—24no—
375#121—21no—
376#121—21no—
377#121C22⋊D1112yes—
378#121C22×D1112yes—
379#120—24no—
380#120—24no—
381C4×D4—24no—
382C4×D4—24no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—222no—
389C2×C4⋊C4C22⋊D1111yescharacteristic
390C2×C4⋊C4C22⋊D1111yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—222no—
403C2×C22⋊C4—222no—
404C2×C22⋊C4C22⋊D1112yes—
405C2×C22⋊C4C22×D1112yes—
406C2×C42—21no—
407#107—222no—
408#106—222no—
409#103—222no—
410#103—222no—
411#103—222no—
412#102—222no—
413C22⋊C8—112no—
414C22⋊C8—112no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417#95—112no—
418#95—222no—
419C2×C11—21no—
420C2×C11—21no—
421C2×C11—22no—
422C2×C11—22no—
423C2×C11—82no—
424C2×C11—82no—
425C2×C11C2×#45211yescharacteristic
426C2×C11#301911yescharacteristic
427C2×C11#302611yescharacteristic
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—21no—
433C24—81no—
434C24—81no—
435C24C2×C22⋊D1112yes—
436C24C2×C22⋊D1111yescharacteristic
437C2×Q8—21no—
438C2×Q8—81no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8—881no—
442C2×Q8C2×C22⋊D1112yes—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—24no—
446C2×D4—24no—
447C2×D4—21no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—81no—
451C2×D4—82no—
452C2×D4—82no—
453C2×D4C2×C22⋊D1112yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—24no—
459C22×C4—21no—
460C22×C4—81no—
461C22×C4—81no—
462C22×C4—82no—
463C22×C4—222no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4C2×C22⋊D1112yes—
467C22×C4C2×C22⋊D1111yescharacteristic
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C23×D1111yescharacteristic
473Q16—882no—
474SD16—882no—
475C2×C8—222no—
476C2×C8—222no—
477C2×C8—881no—
478C2×C8—881no—
479C4⋊C4—24no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—441no—
487C4⋊C4—441no—
488C4⋊C4—882no—
489C4⋊C4—881no—
490C4⋊C4C2×C22⋊D1112yes—
491C4⋊C4C2×C22⋊D1112yes—
492C22⋊C4—24no—
493C22⋊C4—24no—
494C22⋊C4—24no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—442no—
504C22⋊C4—441no—
505C22⋊C4—441no—
506C22⋊C4—882no—
507C22⋊C4—882no—
508C42—24no—
509C11#1829711yescharacteristic, complemented, Sylow
510C23—22no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—41no—
515C23—41no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—81no—
526C23—81no—
527C23—84no—
528C23—84no—
529C23#6700312yes—
530C23#6700412yes—
531C23#6700611yescharacteristic
532C23#6700611yescharacteristic
533C23C22×C22⋊D1111yescharacteristic
534Q8—42no—
535Q8—81no—
536Q8—442no—
537Q8—442no—
538D4—42no—
539D4—42no—
540D4—42no—
541D4—44no—
542D4—81no—
543D4—84no—
544D4—84no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—81no—
561C2×C4—84no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4#6700611yescharacteristic
570C2×C4#6700611yescharacteristic
571C2×C4C22×C22⋊D1111yescharacteristic
572C2×C4C22×C22⋊D1111yescharacteristic
573C8—442no—
574C8—442no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—42no—
582C22—42no—
583C22—44no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—82no—
591C22—84no—
592C22—84no—
593C22—84no—
594C22#1062285212yes—
595C22#1062285212yes—
596C22C2×#6700311yescharacteristic
597C22C2×#6700411yescharacteristic
598C22C2×#6700611yescharacteristic
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—42no—
604C4—42no—
605C4—42no—
606C4—42no—
607C4—882no—
608C4—881no—
609C4—881no—
610C2—21no—
611C2—21no—
612C2—22no—
613C2—22no—
614C2—82no—
615C2—82no—
616C2C2×#1062285211yescharacteristic
617C2#1307797311yescharacteristic
618C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#538C2
socleC22×C11C2×#120
hypercenterC2×#538D11
hypocenterC11#18297
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#538

Complements

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

NH ≅ G/Ntype
1. #13079388C2semidirect
2. #13079373C2semidirect
3. #13074421C2semidirect
4. #13067664C2semidirect
5. #13067596C2semidirect
6. #13067188C2semidirect
7. #13067184C2semidirect
8. C2×#10622163C2semidirect
32. #10622663C22semidirect
33. #10622657C22semidirect
35. #10622653C22semidirect
36. #10622647C22semidirect
39. #10622562C22semidirect
41. #10622560C22semidirect
42. #10622176C22semidirect
43. #10622175C22semidirect
44. #10622163C22semidirect
509. C11#18297semidirect

Maximal subgroups

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

subgroupindex
#130793882
#130793732
#130744212
#130676642
#130675962
#130671882
#130671842
C2×#106221632
C2×C11×#5382
#1829711