Finite Group Databasebeta

← #14853509

Subgroups — #14853509

Order 2816.

742 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076975C211yesmaximal, characteristic, complemented
2#124×Dic11C211yesmaximal, characteristic
3#13070185C211yesmaximal, characteristic, complemented
4#13070184C211yesmaximal, characteristic, complemented
5#13069852C211yesmaximal, characteristic
6#13069315C211yesmaximal, characteristic
7#13069310C211yesmaximal, characteristic
8#13069308C211yesmaximal, characteristic, complemented
9#13069303C211yesmaximal, characteristic, complemented
10#13068619C211yesmaximal, characteristic, complemented
11#13068619C211yesmaximal, characteristic, complemented
12#13068614C211yesmaximal, characteristic
13#13068614C211yesmaximal, characteristic
14#13068468C211yesmaximal, characteristic, complemented
15C11×#2042C211yesmaximal, characteristic
16C2×C11×#124C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×#66942—21no—
20C2×C11×#103C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C11×#389C2211yescharacteristic
25#10622843C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28#10622834C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622589C2211yescharacteristic
37#10622589C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622585—21no—
40#10622564—21no—
41#10622564—21no—
42C22⋊C4×Dic11—21no—
43C22⋊C4×Dic11—21no—
44#10622549C2211yescharacteristic
45C42×Dic11C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622263—21no—
48#10622260—21no—
49C11×#336C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×Dic11—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×#124—22no—
65C11×#124—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75Q8×Dic11—22no—
76Q8×Dic11—22no—
77D4×Dic11—22no—
78D4×Dic11—22no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11D411yescharacteristic
94C2×C4×Dic11D411yescharacteristic
95C2×C4×Dic11D411yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100#66942—44no—
101C11×#103—22no—
102C11×#103—41no—
103C11×#102—22no—
104C11×#102—41no—
105C11×#95—21no—
106#66899—22no—
107#66899—41no—
108#66896—22no—
109#66896—41no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117#66879—41no—
118#66879—41no—
119Dic11⋊C8—22no—
120Dic11⋊C8—22no—
121#29131—111nomaximal, Sylow
122C24×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11#4112yes—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11#4112yes—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—42no—
146C22×Dic11—42no—
147C22×Dic11—42no—
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—42no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C42×C11—21no—
166C42×C11—21no—
167C22⋊Dic11—42no—
168C22⋊Dic11—42no—
169C22⋊Dic11—42no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—42no—
179C4⋊Dic11—42no—
180Dic11⋊C4—42no—
181Dic11⋊C4—42no—
182Dic11⋊C4—42no—
183Dic11⋊C4—42no—
184Dic11⋊C4—42no—
185Dic11⋊C4—42no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—41no—
191C4×Dic11—41no—
192C4×Dic11—42no—
193C4×Dic11#4112yes—
194C4×Dic11#4112yes—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201#2859—111no—
202C4×#124—111no—
203#2101—111no—
204#2101—111no—
205#2042—111no—
206#2042D1111yescharacteristic
207#1936—111no—
208#1936—111no—
209#1935—111no—
210#1935—111no—
211#1803—111no—
212#1803—111no—
213#1802—111no—
214#1802—111no—
215#1767—111no—
216C23×C11—22no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11C22×D411yescharacteristic
224Q8×C11—22no—
225Q8×C11—22no—
226Q8×C11—41no—
227Q8×C11—41no—
228D4×C11—22no—
229D4×C11—22no—
230D4×C11—41no—
231D4×C11—41no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×C4×C112−1+411yescharacteristic
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—84no—
274C2×Dic11#12412yes—
275C2×Dic11#12412yes—
276C2×Dic11AGL(1,ℤ/8)12yes—
277C2×Dic11#13712yes—
278C8×C11—41no—
279C8×C11—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C2×#125—221no—
283C2×#124C2×D1111yescharacteristic
284C2×C4×Q8—111no—
285C2×C4×D4—111no—
286C2×C4⋊C8—111no—
287C2×C4⋊C8—111no—
288C2×#103—111no—
289C2×#103—111no—
290C2×#103C2×D1111yescharacteristic
291C2×#103C2×D1111yescharacteristic
292C2×#102—111no—
293C2×#102—111no—
294C2×#102C2×D1111yescharacteristic
295C2×#102C2×D1111yescharacteristic
296C2×#97—111no—
297C2×#97—111no—
298#391—111no—
299#390—111no—
300#389—111no—
301#389—111no—
302#389—111no—
303#389—221no—
304#389—221no—
305#389C2×D1111yescharacteristic
306#388—221no—
307#388—221no—
308#384—111no—
309#384—111no—
310#382—111no—
311#382—221no—
312C4×C22⋊C4—221no—
313C4×C22⋊C4—221no—
314C43—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#336—111no—
324#336C2×D1111yescharacteristic
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11#52511yescharacteristic
333C22×C11C2×#12411yescharacteristic
334C22×C11#53711yescharacteristic
335C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
336C22×C11C2×#13711yescharacteristic
337C22×C11#57511yescharacteristic
338C22×C11#57511yescharacteristic
339C4×C11—42no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—81no—
343C4×C11—81no—
344C4×C11#55211yescharacteristic
345C4×C11#55211yescharacteristic
346C4×C11#55311yescharacteristic
347C4×C11#55311yescharacteristic
348Dic11—22no—
349Dic11—41no—
350Dic11—41no—
351Dic11—81no—
352Dic11—81no—
353Dic11—81no—
354Dic11—81no—
355Dic11#48914yes—
356C22×Q8C22×D1111yescharacteristic
357C22×D4C22×D1111yescharacteristic
358C23×C4—221no—
359C22×C8—111no—
360C22×C8—111no—
361C22×C8C22×D1111yescharacteristic
362C22×C8C22×D1111yescharacteristic
363#125—444no—
364#124—22no—
365#124—22no—
366C4×Q8—222no—
367C4×Q8—222no—
368C4×D4—222no—
369C4×D4—222no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C42—111no—
391C2×C42—111no—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—221no—
397C2×C42C22×D1111yescharacteristic
398C4⋊C8—222no—
399C4⋊C8—222no—
400#103—22no—
401#103—41no—
402#103—222no—
403#103—441no—
404#102—22no—
405#102—41no—
406#102—222no—
407#102—441no—
408#97—441no—
409#97—441no—
410#95—21no—
411#95—221no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418C2×C11—82no—
419C2×C11#256211yescharacteristic
420C2×C11#311511yescharacteristic
421C2×C11#311611yescharacteristic
422C2×C11C2×#48911yescharacteristic
423C2×C11#314211yescharacteristic
424C2×C11#325111yescharacteristic
425C2×C11#325211yescharacteristic
426C24—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8#434112yes—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4#434112yes—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—442no—
451C22×C4—442no—
452C22×C4—442no—
453C22×C4D4×D1111yescharacteristic
454C22×C4D4×D1111yescharacteristic
455C22×C4C23×D1111yescharacteristic
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—42no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—442no—
482C4⋊C4—442no—
483C4⋊C4—442no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C4⋊C4—442no—
487C4⋊C4—442no—
488C4⋊C4—442no—
489C22⋊C4—24no—
490C22⋊C4—24no—
491C22⋊C4—442no—
492C22⋊C4—442no—
493C22⋊C4—442no—
494C42—21no—
495C42—21no—
496C42—112no—
497C42—112no—
498C42—222no—
499C42—222no—
500C42—221no—
501C42—221no—
502C42—441no—
503C42—441no—
504C42—442no—
505C11#2913111yescharacteristic, complemented, Sylow
506C23—22no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23C2×D4×D1111yescharacteristic
514Q8—22no—
515Q8—22no—
516Q8—41no—
517Q8—41no—
518D4—22no—
519D4—22no—
520D4—41no—
521D4—41no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—112no—
538C2×C4—112no—
539C2×C4—112no—
540C2×C4—112no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—884no—
562C2×C4C2×#434111yescharacteristic
563C2×C4C2×#434111yescharacteristic
564C2×C4#6703711yescharacteristic
565C2×C4#41×D1111yescharacteristic
566C2×C4#41×D1111yescharacteristic
567C2×C4#6704311yescharacteristic
568C8—41no—
569C8—41no—
570C8—441no—
571C8—441no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22#1062311711yescharacteristic
580C22#1062313911yescharacteristic
581C22D11×#12411yescharacteristic
582C22#1062329911yescharacteristic
583C22#1062329911yescharacteristic
584C22D11×AGL(1,ℤ/8)11yescharacteristic
585C22D11×#13711yescharacteristic
586C4—42no—
587C4—41no—
588C4—41no—
589C4—81no—
590C4—81no—
591C4—114no—
592C4—222no—
593C4—441no—
594C4—441no—
595C4—881no—
596C4—881no—
597C4—881no—
598C4—881no—
599C4#1062313211yescharacteristic
600C4#1062313211yescharacteristic
601C4#1062318111yescharacteristic
602C4#1062318111yescharacteristic
603C2—82no—
604C2#1307377611yescharacteristic
605C2#1307876011yescharacteristic
606C2#1307877111yescharacteristic
607C2D11×#48911yescharacteristic
608C2#1307901311yescharacteristic
609C2#1307997511yescharacteristic
610C2#1307998611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2042C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2042D11
hypocenterC11#29131
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2042

Complements

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

NH ≅ G/Ntype
1. #13076975C2semidirect
3. #13070185C2semidirect
4. #13070184C2semidirect
8. #13069308C2semidirect
9. #13069303C2semidirect
10. #13068619C2semidirect
11. #13068619C2semidirect
14. #13068468C2semidirect
505. C11#29131semidirect

Maximal subgroups

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

subgroupindex
#130769752
#124×Dic112
#130701852
#130701842
#130698522
#130693152
#130693102
#130693082
#130693032
#130686192
#130686142
#130684682
C11×#20422
#2913111