Finite Group Databasebeta

← #14826627

Subgroups — #14826627

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073039C211yesmaximal, characteristic
2#13071639C211yesmaximal, characteristic
3#13070027C211yesmaximal, characteristic, complemented
4#13070007C211yesmaximal, characteristic, complemented
5#13069818C211yesmaximal, characteristic
6#13069817C211yesmaximal, characteristic
7#13069373C211yesmaximal, characteristic, complemented
8#13069346C211yesmaximal, characteristic, complemented
9#13069220C211yesmaximal, characteristic
10#13069203C211yesmaximal, characteristic, complemented
11#13069188C211yesmaximal, characteristic, complemented
12#13068814C211yesmaximal, characteristic
13#13068709C211yesmaximal, characteristic
14C4×#66899C211yesmaximal, characteristic, complemented
15C11×#1865C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C2×#66951—21no—
19C2×#66945C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C11×#389C2211yescharacteristic
24#10622843C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31#10622603—21no—
32#10622600C2211yescharacteristic
33#10622600C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622591—21no—
36#10622591—21no—
37#10622589C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622553—21no—
42C4×(C2×D11)⋊C4C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44C4×Dic11⋊C4—21no—
45#10622541C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622288—21no—
48#10622273—21no—
49C11×#340C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×C4×D11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C4×Q8×C11—22no—
64C4×Q8×C11—41no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72#66999—22no—
73#66999—22no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4D411yescharacteristic
79C2×(C2×D11)⋊C4D411yescharacteristic
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×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95#66951—44no—
96#66945—22no—
97#66945—41no—
98C11×#106—22no—
99C11×#103—22no—
100C11×#103—41no—
101C11×#95—21no—
102#66899—22no—
103#66899—22no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114(C2×D11)⋊C8—22no—
115(C2×D11)⋊C8—41no—
116#66882—22no—
117Dic11⋊C8—22no—
118#66871—22no—
119#66871—41no—
120C4×C11⋊C8—41no—
121#27043—111nomaximal, Sylow
122C23×D11C2×D411yescharacteristic
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11#4112yes—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C2×C4×D11—21no—
144C2×C4×D11—21no—
145C2×C4×D11—21no—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—42no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4#4112yes—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—42no—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—22no—
168(C2×D11)⋊C4—22no—
169(C2×D11)⋊C4—42no—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4—42no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—42no—
180C4⋊Dic11#4112yes—
181Dic11⋊C4—24no—
182Dic11⋊C4—42no—
183Dic11⋊C4—42no—
184Dic11⋊C4—42no—
185C4×Dic11—21no—
186C4×Dic11—21no—
187C4×Dic11—42no—
188C4×Dic11—42no—
189C4×Dic11—42no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8#4112yes—
196#2496—111no—
197#2362—111no—
198#2072—111no—
199#2068—111no—
200#2036—111no—
201#2036—111no—
202#1947—111no—
203#1942—111no—
204#1923—111no—
205#1920—111no—
206#1918—111no—
207#1865D1111yescharacteristic, complemented
208#1854—111no—
209#1825—111no—
210C4×#103—111no—
211C23×C11C22×D411yescharacteristic
212C22×D11—21no—
213C22×D11—21no—
214C22×D11—21no—
215C22×D11—21no—
216C22×D11—21no—
217C22×D11—21no—
218C22×D11—21no—
219Q8×C11—22no—
220Q8×C11—22no—
221Q8×C11—41no—
222Q8×C11—41no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
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—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11AGL(1,ℤ/8)12yes—
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11H(5,𝔽2)11yescharacteristic
246C2×C4×C112−1+411yescharacteristic
247C2×Dic11—21no—
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—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
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#13512yes—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—41no—
271C4×D11—41no—
272C8×C11—41no—
273C8×C11—41no—
274C11⋊C8—22no—
275C11⋊C8—41no—
276C2×#126—221no—
277C2×C22⋊Q8—111no—
278C2×C4×Q8C2×D1111yescharacteristic
279C2×#117—111no—
280C2×#107—111no—
281C2×#107—111no—
282C2×#107—111no—
283C2×#106C2×D1111yescharacteristic
284C2×C4⋊C8—111no—
285C2×#103—111no—
286C2×#103—111no—
287C2×#103C2×D1111yescharacteristic
288C2×#103C2×D1111yescharacteristic
289C2×C22⋊C8—111no—
290C2×C22⋊C8—111no—
291C2×C4×C8—111no—
292#400—221no—
293#397—221no—
294#391—111no—
295#389—111no—
296#389—111no—
297#389C2×D1111yescharacteristic
298#388—221no—
299#388—221no—
300#387—221no—
301#387—221no—
302#384—111no—
303#380—111no—
304#380—111no—
305C4×C4⋊C4—111no—
306C4×C4⋊C4—111no—
307C4×C4⋊C4—221no—
308C4×C22⋊C4—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340C2×D1111yescharacteristic
317#336—111no—
318#336C2×D1111yescharacteristic
319C22×C11#52511yescharacteristic
320C22×C11#54611yescharacteristic
321C22×C11#54711yescharacteristic
322C22×C11C2×#13511yescharacteristic
323C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
324C22×C11#57811yescharacteristic
325C22×C11#57811yescharacteristic
326C2×D11—41no—
327C2×D11—41no—
328C2×D11—41no—
329C2×D11—41no—
330C2×D11—41no—
331C2×D11—41no—
332C2×D11—41no—
333C4×C11—22no—
334C4×C11—42no—
335C4×C11—41no—
336C4×C11—42no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11#52911yescharacteristic
340C4×C11#53911yescharacteristic
341C4×C11#55311yescharacteristic
342C4×C11#55611yescharacteristic
343Dic11—22no—
344Dic11—41no—
345Dic11—42no—
346Dic11—41no—
347Dic11—81no—
348Dic11—81no—
349Dic11—81no—
350C22×Q8C22×D1111yescharacteristic
351C23×C4—111no—
352C22×C8—111no—
353C22×C8—111no—
354C22×C8C22×D1111yescharacteristic
355C22×C8C22×D1111yescharacteristic
356#126—444no—
357C22⋊Q8—222no—
358C22⋊Q8—222no—
359C4×Q8—22no—
360C4×Q8—41no—
361#117—222no—
362#117—441no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—221no—
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—111no—
378C2×C22⋊C4—111no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C42—21no—
384C2×C42—111no—
385C2×C42—221no—
386C2×C42—221no—
387C2×C42—221no—
388C2×C42C22×D1111yescharacteristic
389#107—222no—
390#107—222no—
391#107—441no—
392#106—22no—
393C4⋊C8—222no—
394#103—22no—
395#103—41no—
396#103—222no—
397#103—222no—
398C22⋊C8—222no—
399C22⋊C8—441no—
400C4×C8—441no—
401#95—21no—
402#95—111no—
403#95—111no—
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#246611yescharacteristic
413C2×C11#310611yescharacteristic
414C2×C11#312711yescharacteristic
415C2×C11#330211yescharacteristic
416C2×C11#330811yescharacteristic
417C2×C11#333611yescharacteristic
418C2×C11#335311yescharacteristic
419D11—81no—
420C24—111no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8#433912yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4D4×D1111yescharacteristic
445C22×C4D4×D1111yescharacteristic
446C22×C4C23×D1111yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—112no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—42no—
465C4⋊C4—42no—
466C4⋊C4—112no—
467C4⋊C4—224no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—442no—
476C4⋊C4—442no—
477C4⋊C4—442no—
478C4⋊C4—442no—
479C4⋊C4#434112yes—
480C22⋊C4—222no—
481C22⋊C4—224no—
482C22⋊C4—222no—
483C22⋊C4—442no—
484C22⋊C4—442no—
485C22⋊C4—442no—
486C42—21no—
487C42—21no—
488C42—42no—
489C42—221no—
490C42—221no—
491C42—442no—
492C42—442no—
493C42—442no—
494C11#2704311yescharacteristic, complemented, Sylow
495C23—221no—
496C23—221no—
497C23—221no—
498C23—221no—
499C23—221no—
500C23—221no—
501C23—221no—
502C23C2×D4×D1111yescharacteristic
503Q8—22no—
504Q8—22no—
505Q8—41no—
506Q8—41no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—112no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—222no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
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#6696712yes—
550C2×C4C2×#433911yescharacteristic
551C2×C4C2×#434111yescharacteristic
552C2×C4#6703711yescharacteristic
553C2×C4#6704011yescharacteristic
554C2×C4#41×D1111yescharacteristic
555C2×C4#41×D1111yescharacteristic
556C8—41no—
557C8—41no—
558C8—222no—
559C8—441no—
560C22—441no—
561C22—441no—
562C22—441no—
563C22—441no—
564C22—441no—
565C22—441no—
566C22—441no—
567C22#1062307811yescharacteristic
568C22#1062312211yescharacteristic
569C22#1062316211yescharacteristic
570C22C2×#6696711yescharacteristic
571C22D11×#13511yescharacteristic
572C22#1062331011yescharacteristic
573C22#1062331011yescharacteristic
574C4—22no—
575C4—42no—
576C4—41no—
577C4—42no—
578C4—81no—
579C4—81no—
580C4—222no—
581C4—441no—
582C4—441no—
583C4—442no—
584C4—881no—
585C4—881no—
586C4—881no—
587C4#1062304611yescharacteristic
588C4#1062306911yescharacteristic
589C4#1062317211yescharacteristic
590C4#1062319211yescharacteristic
591C2—881no—
592C2#1307265411yescharacteristic
593C2#1307867411yescharacteristic
594C2#1307891511yescharacteristic
595C2#1308052611yescharacteristic
596C2#1308061111yescharacteristic
597C2#1308098111yescharacteristic
598C2#1308120311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1865C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1865D11
hypocenterC11#27043
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
3. #13070027C2semidirect
4. #13070007C2semidirect
7. #13069373C2semidirect
8. #13069346C2semidirect
10. #13069203C2semidirect
11. #13069188C2semidirect
14. C4×#66899C2semidirect
15. C11×#1865C2semidirect
207. #1865D11semidirect
494. C11#27043semidirect

Maximal subgroups

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

subgroupindex
#130730392
#130716392
#130700272
#130700072
#130698182
#130698172
#130693732
#130693462
#130692202
#130692032
#130691882
#130688142
#130687092
C4×#668992
C11×#18652
#2704311