Finite Group Databasebeta

← #14822402

Subgroups — #14822402

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#13073154C211yesmaximal, characteristic, complemented
2#13071685C211yesmaximal, characteristic
3#13070031C211yesmaximal, characteristic
4#13069989C211yesmaximal, characteristic
5#13069858C211yesmaximal, characteristic
6#13069858C211yesmaximal, characteristic
7#13069292C211yesmaximal, characteristic, complemented
8#13069251C211yesmaximal, characteristic, complemented
9#13069202C211yesmaximal, characteristic, complemented
10#13069195C211yesmaximal, characteristic, complemented
11#13068887C211yesmaximal, characteristic, complemented
12#13068880C211yesmaximal, characteristic
13#13068632C211yesmaximal, characteristic, complemented
14C4×#66885C211yesmaximal, characteristic
15C11×#1916C211yesmaximal, characteristic, complemented
16C2×#66928C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×#66885C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66881C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32#10622603—21no—
33#10622602—21no—
34#10622593—21no—
35#10622591—21no—
36#10622552C2211yescharacteristic
37#10622549C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40#10622542C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622282—21no—
46#10622279—21no—
47#10622271—21no—
48#10622263—21no—
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90#66928—22no—
91#66928—22no—
92C4×D44—22no—
93C4×D44—41no—
94C4×Dic22—22no—
95C4×Dic22—41no—
96C11×C4⋊C8—41no—
97C4×C8×C11—41no—
98C11×#95D411yescharacteristic
99C11×#95D411yescharacteristic
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110#66885—22no—
111#66885—22no—
112#66885—22no—
113#66885—41no—
114#66881—22no—
115#66881—22no—
116#66880—22no—
117#66880—22no—
118#66880—22no—
119#66880—41no—
120#26760—111nomaximal, Sylow
121C23×D11—21no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44#4112yes—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C4×D11—81no—
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—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—41no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171(C2×D11)⋊C4—24no—
172(C2×D11)⋊C4—24no—
173(C2×D11)⋊C4—42no—
174(C2×D11)⋊C4—42no—
175(C2×D11)⋊C4—81no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11#4112yes—
187C4⋊Dic11#4112yes—
188Dic11⋊C4—42no—
189Dic11⋊C4—42no—
190Dic11⋊C4—81no—
191Dic11⋊C4—81no—
192Dic11⋊C4—81no—
193C4×Dic11—42no—
194C4×Dic11—42no—
195C4×Dic11—81no—
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#1916D1111yescharacteristic, complemented
207#1865—111no—
208#1864—111no—
209#1805—111no—
210C4×#102—111no—
211C23×C11C22×D411yescharacteristic
212C22×D11—22no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11#13512yes—
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11H(5,𝔽2)11yescharacteristic
242C2×C4×C112−1+411yescharacteristic
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264D44—22no—
265D44—22no—
266D44—41no—
267D44—41no—
268C4×D11—84no—
269Dic22—22no—
270Dic22—22no—
271Dic22—41no—
272Dic22—41no—
273C8×C11—41no—
274C8×C11—41no—
275C8×C11—41no—
276C8×C11—41no—
277C2×#124—111no—
278C2×C4×Q8—111no—
279C2×C4×D4—111no—
280C2×#106—111no—
281C2×#106—111no—
282C2×C4⋊C8C2×D1111yescharacteristic
283C2×#103—111no—
284C2×#103—111no—
285C2×#103—111no—
286C2×#103—111no—
287C2×#102—111no—
288C2×#102—111no—
289C2×#102—111no—
290C2×#102—111no—
291C2×C4×C8C2×D1111yescharacteristic
292#400—221no—
293#398—221no—
294#391—111no—
295#390—111no—
296#389—111no—
297#389—111no—
298#389—111no—
299#389—111no—
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⋊C4C2×D1111yescharacteristic
309C4×C22⋊C4—221no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#336C2×D1111yescharacteristic
317#336C2×D1111yescharacteristic
318#336C2×D1111yescharacteristic
319#336C2×D1111yescharacteristic
320C22×C11#52511yescharacteristic
321C22×C11#54611yescharacteristic
322C22×C11#54811yescharacteristic
323C22×C11C2×#13511yescharacteristic
324C22×C11#57511yescharacteristic
325C22×C11#57711yescharacteristic
326C22×C11#57711yescharacteristic
327C2×D11—42no—
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C4×C11—22no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11#52911yescharacteristic
341C4×C11#53911yescharacteristic
342C4×C11#55211yescharacteristic
343C4×C11#55311yescharacteristic
344Dic11—42no—
345Dic11—42no—
346Dic11—42no—
347Dic11—81no—
348Dic11—81no—
349Dic11—81no—
350Dic11—81no—
351C22×Q8—111no—
352C22×D4—111no—
353C23×C4—221no—
354C22×C8C22×D1111yescharacteristic
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357C22×C8C22×D1111yescharacteristic
358#124—222no—
359#124—222no—
360C4×Q8—222no—
361C4×Q8—441no—
362C4×D4—222no—
363C4×D4—441no—
364C2×C4⋊C4—111no—
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⋊C4—221no—
375C2×C4⋊C4D4411yescharacteristic
376C2×C4⋊C4D4411yescharacteristic
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C42—221no—
383C2×C42—221no—
384C2×C42—221no—
385C2×C42C22×D1111yescharacteristic
386C2×C42C22×D1111yescharacteristic
387C2×C42C22×D1111yescharacteristic
388#106—222no—
389#106—222no—
390C4⋊C8—41no—
391#103—222no—
392#103—222no—
393#103—222no—
394#103—441no—
395#102—222no—
396#102—222no—
397#102—222no—
398#102—441no—
399C4×C8—41no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95D4411yescharacteristic
411#95D4411yescharacteristic
412C2×C11#246011yescharacteristic
413C2×C11#310211yescharacteristic
414C2×C11#312511yescharacteristic
415C2×C11#329611yescharacteristic
416C2×C11#332111yescharacteristic
417C2×C11#336011yescharacteristic
418C2×C11#337111yescharacteristic
419D11—82no—
420C24—221no—
421C2×Q8—112no—
422C2×Q8—221no—
423C2×Q8—221no—
424C2×Q8—221no—
425C2×Q8—221no—
426C2×Q8—221no—
427C2×D4—112no—
428C2×D4—221no—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—221no—
432C2×D4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—442no—
441C22×C4—442no—
442C22×C4—881no—
443C22×C4C2×D4411yescharacteristic
444C22×C4C2×D4411yescharacteristic
445C22×C4C2×D4411yescharacteristic
446C22×C4C2×D4411yescharacteristic
447C22×C4C2×D4411yescharacteristic
448C22×C4C2×D4411yescharacteristic
449C22×C4C23×D1111yescharacteristic
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C4⋊C4—22no—
463C4⋊C4—41no—
464C4⋊C4—112no—
465C4⋊C4—112no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—442no—
477C4⋊C4—442no—
478C4⋊C4—881no—
479C4⋊C4—881no—
480C4⋊C4—881no—
481C22⋊C4—224no—
482C22⋊C4—224no—
483C22⋊C4—442no—
484C22⋊C4—442no—
485C22⋊C4—881no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—442no—
493C42—442no—
494C42—881no—
495C11#2676011yescharacteristic, complemented, Sylow
496C23—222no—
497C23—441no—
498C23—441no—
499C23—441no—
500C23—441no—
501C23—441no—
502C23—441no—
503C23C22×D4411yescharacteristic
504Q8—222no—
505Q8—222no—
506Q8—441no—
507Q8—441no—
508D4—222no—
509D4—222no—
510D4—441no—
511D4—441no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
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—884no—
551C2×C4#6695712yes—
552C2×C4#6703711yescharacteristic
553C2×C4#6704011yescharacteristic
554C2×C4#41×D1111yescharacteristic
555C2×C4#41×D1111yescharacteristic
556C2×C4#41×D1111yescharacteristic
557C2×C4#41×D1111yescharacteristic
558C8—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C22—442no—
563C22—442no—
564C22—442no—
565C22—881no—
566C22—881no—
567C22—881no—
568C22—881no—
569C22#1062305511yescharacteristic
570C22#1062308511yescharacteristic
571C22#1062310711yescharacteristic
572C22C2×#6695711yescharacteristic
573C22#1062327911yescharacteristic
574C22#1062328211yescharacteristic
575C22#1062328211yescharacteristic
576C4—22no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—442no—
583C4—442no—
584C4—442no—
585C4—881no—
586C4—881no—
587C4—881no—
588C4—881no—
589C4#1062316911yescharacteristic
590C4#1062319211yescharacteristic
591C4#1062322411yescharacteristic
592C4#1062323711yescharacteristic
593C2—882no—
594C2#1307256611yescharacteristic
595C2#1307863611yescharacteristic
596C2#1307889511yescharacteristic
597C2#1308045311yescharacteristic
598C2#1308080411yescharacteristic
599C2#1308126711yescharacteristic
600C2#1308138611yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1916C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1916D11
hypocenterC11#26760
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
1. #13073154C2semidirect
7. #13069292C2semidirect
8. #13069251C2semidirect
9. #13069202C2semidirect
10. #13069195C2semidirect
11. #13068887C2semidirect
13. #13068632C2semidirect
15. C11×#1916C2semidirect
206. #1916D11semidirect
495. C11#26760semidirect

Maximal subgroups

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

subgroupindex
#130731542
#130716852
#130700312
#130699892
#130698582
#130692922
#130692512
#130692022
#130691952
#130688872
#130688802
#130686322
C4×#668852
C11×#19162
#2676011