Finite Group Databasebeta

← #14822406

Subgroups — #14822406

Order 2816.

704 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073155C211yesmaximal, characteristic, complemented
2#13071689C211yesmaximal, characteristic
3#13070032C211yesmaximal, characteristic
4#13069988C211yesmaximal, characteristic
5#13069856C211yesmaximal, characteristic
6#13069855C211yesmaximal, characteristic
7#13069291C211yesmaximal, characteristic, complemented
8#13069251C211yesmaximal, characteristic, complemented
9#13069203C211yesmaximal, characteristic, complemented
10#13069193C211yesmaximal, characteristic, complemented
11#13069171C211yesmaximal, characteristic, complemented
12#13068881C211yesmaximal, characteristic, complemented
13#13068630C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic
15C11×#1864C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66989C2211yescharacteristic
18C2×#66940C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C11×#389C2211yescharacteristic
23#10622834C2211yescharacteristic
24C2×#66896C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26#10622823—21no—
27C4×C22⋊Dic11—21no—
28C2×#66881C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32#10622598C2211yescharacteristic
33#10622597—21no—
34#10622595—21no—
35#10622590C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41#10622558—21no—
42#10622557—21no—
43C4×C4⋊Dic11C2211yescharacteristic
44C4×Dic11⋊C4C2211yescharacteristic
45#10622542C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622266—21no—
48#10622263—21no—
49C11×#340C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C4×D4×C11—22no—
65C4×D4×C11—41no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76#66989—22no—
77#66989—22no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4D411yescharacteristic
86C2×Dic11⋊C4D411yescharacteristic
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94#66940—22no—
95#66940—41no—
96C11×#106—22no—
97C11×#102—22no—
98C11×#102—41no—
99C11×#95—21no—
100#66896—22no—
101#66896—22no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95D411yescharacteristic
112C11⋊#95D411yescharacteristic
113#66881—22no—
114#66880—22no—
115#66880—22no—
116Dic11⋊C8—41no—
117#66874—22no—
118#66874—41no—
119C4×C11⋊C8—41no—
120#26760—111nomaximal, Sylow
121C24×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11#4112yes—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—81no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22#4112yes—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—81no—
163C11×C4⋊C4#4112yes—
164C11×C22⋊C4—42no—
165C42×C11—21no—
166C42×C11—21no—
167C22⋊Dic11—24no—
168C22⋊Dic11—24no—
169C22⋊Dic11—42no—
170C22⋊Dic11—81no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—42no—
177C4⋊Dic11#4112yes—
178Dic11⋊C4—22no—
179Dic11⋊C4—41no—
180Dic11⋊C4—42no—
181Dic11⋊C4—81no—
182Dic11⋊C4—81no—
183C4×Dic11—21no—
184C4×Dic11—21no—
185C4×Dic11—21no—
186C4×Dic11—21no—
187C4×Dic11—42no—
188C4×Dic11—42no—
189C4×Dic11—81no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196#2508—111no—
197#2367—111no—
198#2073—111no—
199#2065—111no—
200#2042—111no—
201#2042—111no—
202#1933—111no—
203#1927—111no—
204#1920—111no—
205#1919—111no—
206#1916—111no—
207#1865—111no—
208#1864D1111yescharacteristic
209#1805—111no—
210C4×#102—111no—
211C23×C11—22no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11C22×D411yescharacteristic
219D4×C11—22no—
220D4×C11—22no—
221D4×C11—41no—
222D4×C11—41no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—84no—
238C2×C4×C11#13512yes—
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×C4×C112−1+411yescharacteristic
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—22no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—22no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269Dic22—22no—
270Dic22—22no—
271Dic22—41no—
272Dic22—41no—
273C8×C11—41no—
274C8×C11—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C2×#124—111no—
278C2×C4×Q8—111no—
279C2×C4×D4C2×D1111yescharacteristic
280C2×#106—111no—
281C2×#106C2×D1111yescharacteristic
282C2×C4⋊C8—111no—
283C2×#103—111no—
284C2×#103—111no—
285C2×#103—111no—
286C2×#103—111no—
287C2×#102—111no—
288C2×#102—111no—
289C2×#102C2×D1111yescharacteristic
290C2×#102C2×D1111yescharacteristic
291C2×C4×C8—111no—
292#400—221no—
293#398—221no—
294#391—111no—
295#390—111no—
296#389—111no—
297#389—111no—
298#389—111no—
299#389C2×D1111yescharacteristic
300#388—221no—
301#388—221no—
302#387—221no—
303#385—221no—
304#382—111no—
305#382—221no—
306C4×C4⋊C4—111no—
307C4×C4⋊C4—111no—
308C4×C4⋊C4—111no—
309C4×C22⋊C4—221no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340C2×D1111yescharacteristic
316#336—111no—
317#336—111no—
318#336—111no—
319#336C2×D1111yescharacteristic
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11#52511yescharacteristic
328C22×C11#54611yescharacteristic
329C22×C11#54811yescharacteristic
330C22×C11C2×#13511yescharacteristic
331C22×C11#57511yescharacteristic
332C22×C11#57711yescharacteristic
333C22×C11#57711yescharacteristic
334C4×C11—22no—
335C4×C11—42no—
336C4×C11—41no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11#52911yescharacteristic
340C4×C11#53911yescharacteristic
341C4×C11#55211yescharacteristic
342C4×C11#55311yescharacteristic
343Dic11—41no—
344Dic11—42no—
345Dic11—41no—
346Dic11—42no—
347Dic11—41no—
348Dic11—41no—
349Dic11—81no—
350Dic11—81no—
351C22×Q8—111no—
352C22×D4C22×D1111yescharacteristic
353C23×C4—21no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8C22×D1111yescharacteristic
357C22×C8C22×D1111yescharacteristic
358#124—222no—
359#124—222no—
360C4×Q8—222no—
361C4×Q8—441no—
362C4×D4—22no—
363C4×D4—41no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C42—111no—
383C2×C42—111no—
384C2×C42—221no—
385C2×C42—221no—
386C2×C42—221no—
387C2×C42C22×D1111yescharacteristic
388#106—22no—
389#106—222no—
390C4⋊C8—441no—
391#103—222no—
392#103—222no—
393#103—222no—
394#103—441no—
395#102—22no—
396#102—41no—
397#102—222no—
398#102—222no—
399C4×C8—441no—
400#95—21no—
401#95—111no—
402#95—111no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412C2×C11—82no—
413C2×C11#246011yescharacteristic
414C2×C11#310211yescharacteristic
415C2×C11#312511yescharacteristic
416C2×C11#329611yescharacteristic
417C2×C11#332111yescharacteristic
418C2×C11#336011yescharacteristic
419C2×C11#337111yescharacteristic
420C24—21no—
421C2×Q8—112no—
422C2×Q8—221no—
423C2×Q8—221no—
424C2×Q8—221no—
425C2×Q8—221no—
426C2×Q8—221no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4#433912yes—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—81no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4D4×D1111yescharacteristic
448C22×C4D4×D1111yescharacteristic
449C22×C4C23×D1111yescharacteristic
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—81no—
468C4⋊C4—112no—
469C4⋊C4—222no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—441no—
476C4⋊C4—442no—
477C4⋊C4—442no—
478C4⋊C4—881no—
479C4⋊C4—881no—
480C4⋊C4#434112yes—
481C22⋊C4—42no—
482C22⋊C4—224no—
483C22⋊C4—224no—
484C22⋊C4—442no—
485C22⋊C4—881no—
486C42—21no—
487C42—21no—
488C42—221no—
489C42—221no—
490C42—221no—
491C42—221no—
492C42—442no—
493C42—442no—
494C42—881no—
495C11#2676011yescharacteristic, complemented, Sylow
496C23—22no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23C2×D4×D1111yescharacteristic
504Q8—222no—
505Q8—222no—
506Q8—441no—
507Q8—441no—
508D4—22no—
509D4—22no—
510D4—41no—
511D4—41no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—84no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—222no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—222no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4#6696912yes—
552C2×C4C2×#433911yescharacteristic
553C2×C4C2×#434111yescharacteristic
554C2×C4#6703711yescharacteristic
555C2×C4#6704011yescharacteristic
556C2×C4#41×D1111yescharacteristic
557C2×C4#41×D1111yescharacteristic
558C8—41no—
559C8—41no—
560C8—441no—
561C8—441no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22#1062307811yescharacteristic
570C22#1062312211yescharacteristic
571C22#1062316411yescharacteristic
572C22C2×#6696911yescharacteristic
573C22#1062329911yescharacteristic
574C22#1062330611yescharacteristic
575C22#1062330611yescharacteristic
576C4—22no—
577C4—42no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4—441no—
582C4—441no—
583C4—441no—
584C4—442no—
585C4—442no—
586C4—441no—
587C4—881no—
588C4—881no—
589C4#1062304611yescharacteristic
590C4#1062306911yescharacteristic
591C4#1062317011yescharacteristic
592C4#1062319211yescharacteristic
593C2—82no—
594C2#1307257011yescharacteristic
595C2#1307863811yescharacteristic
596C2#1307889711yescharacteristic
597C2#1308045511yescharacteristic
598C2#1308080611yescharacteristic
599C2#1308126411yescharacteristic
600C2#1308138211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1864C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#1864D11
hypocenterC11#26760
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
1. #13073155C2semidirect
7. #13069291C2semidirect
8. #13069251C2semidirect
9. #13069203C2semidirect
10. #13069193C2semidirect
11. #13069171C2semidirect
12. #13068881C2semidirect
13. #13068630C2semidirect
495. C11#26760semidirect

Maximal subgroups

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

subgroupindex
#130731552
#130716892
#130700322
#130699882
#130698562
#130698552
#130692912
#130692512
#130692032
#130691932
#130691712
#130688812
#130686302
C4×#668962
C11×#18642
#2676011