Finite Group Databasebeta

← #14821972

Subgroups — #14821972

Order 2816.

798 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072993C211yesmaximal, characteristic, complemented
2#13071659C211yesmaximal, characteristic
3#13069933C211yesmaximal, characteristic, complemented
4#13069797C211yesmaximal, characteristic
5#13069620C211yesmaximal, characteristic
6#13069569C211yesmaximal, characteristic, complemented
7#13069290C211yesmaximal, characteristic, complemented
8#13069258C211yesmaximal, characteristic, complemented
9#13069223C211yesmaximal, characteristic, complemented
10#13069207C211yesmaximal, characteristic, complemented
11#13068948C211yesmaximal, characteristic, complemented
12#13068927C211yesmaximal, characteristic, complemented
13#13068709C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic, complemented
15C11×#2023C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×#66991C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C2×#66950C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C11×#390C2211yescharacteristic
25#10622844—21no—
26#10622843—21no—
27C2×#66896C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622603—21no—
35#10622600C2211yescharacteristic
36#10622599—21no—
37C4⋊C4×Dic11C2211yescharacteristic
38#10622587C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41#10622571—21no—
42#10622570—21no—
43#10622558—21no—
44C22⋊C4×Dic11—21no—
45C4×(C2×D11)⋊C4C2211yescharacteristic
46C4×C4⋊Dic11C2211yescharacteristic
47#10622542C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C23×Dic11—21no—
63C22×C4×D11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8—41no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78#66991—22no—
79#66991—22no—
80D4×Dic11—22no—
81D4×Dic11—41no—
82C2×#4324—22no—
83C2×#4324—41no—
84C2×#4324—41no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4D411yescharacteristic
89C2×(C2×D11)⋊C4D411yescharacteristic
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66950—22no—
102#66950—41no—
103#66945—22no—
104#66945—41no—
105C11×#102—22no—
106C11×#102—41no—
107#66896—22no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95D411yescharacteristic
117C11⋊#95D411yescharacteristic
118(C2×D11)⋊C8—41no—
119(C2×D11)⋊C8—41no—
120#66882—22no—
121#66880—22no—
122#66880—22no—
123C8×Dic11—41no—
124#66874—41no—
125C4⋊(C11⋊C8)—41no—
126#26731—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11C2×D411yescharacteristic
129C2×Q8×C11—42no—
130C2×Q8×C11—42no—
131C2×Q8×C11—81no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11#4112yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11—24no—
145C2×C22⋊D11—81no—
146C2×C22⋊D11—81no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11—81no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4#4112yes—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—81no—
184C42×C11—21no—
185C42×C11—21no—
186C22⋊Dic11—24no—
187C22⋊Dic11—42no—
188#4324—44no—
189(C2×D11)⋊C4—22no—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—81no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—42no—
199C4⋊Dic11#4112yes—
200C4⋊Dic11#4112yes—
201Dic11⋊C4—81no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—42no—
205C4×Dic11—81no—
206C4×Dic11—81no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213#2492—111no—
214#2363—111no—
215#2055—111no—
216#2033—111no—
217#2023D1111yescharacteristic, complemented
218#2000—111no—
219#1988—111no—
220#1933—111no—
221#1928—111no—
222#1923—111no—
223#1921—111no—
224#1877—111no—
225#1873—111no—
226#1825—111no—
227C4×#102—111no—
228C23×C11—22no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11C22×D411yescharacteristic
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243Q8×C11—84no—
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—41no—
247D4×C11—41no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11#13512yes—
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C22⋊D11—84no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—22no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—22no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—84no—
291C2×Dic11#13712yes—
292C4×D11—41no—
293C4×D11—41no—
294C4×D11—41no—
295C4×D11—41no—
296Dic22—41no—
297Dic22—41no—
298Dic22—41no—
299Dic22—41no—
300C8×C11—41no—
301C8×C11—41no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C22×SD16—111no—
305C2×C4⋊Q8C2×D1111yescharacteristic
306C2×C22⋊Q8—111no—
307C2×#121—111no—
308C2×C4×D4—111no—
309C2×#117—111no—
310C2×#107—111no—
311C2×C4⋊C8—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#102—111no—
316C2×#102C2×D1111yescharacteristic
317C2×#102C2×D1111yescharacteristic
318C2×C22⋊C8—111no—
319C2×C22⋊C8—111no—
320C2×C4×C8—111no—
321#400—221no—
322#393—221no—
323#391—111no—
324#391—111no—
325#391—221no—
326#390—221no—
327#390C2×D1111yescharacteristic
328#389—111no—
329#388—221no—
330#388—221no—
331#386—221no—
332#380—111no—
333C4×C4⋊C4—111no—
334C4×C4⋊C4—111no—
335C4×C22⋊C4—111no—
336C4×C22⋊C4—221no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340C2×D1111yescharacteristic
344#340C2×D1111yescharacteristic
345#336—111no—
346#336C2×D1111yescharacteristic
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11#52511yescharacteristic
355C22×C11#54611yescharacteristic
356C22×C11#54611yescharacteristic
357C22×C11C2×#13511yescharacteristic
358C22×C11C2×#13711yescharacteristic
359C22×C11#57611yescharacteristic
360C22×C11#57711yescharacteristic
361C2×D11—41no—
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—41no—
365C2×D11—41no—
366C2×D11—41no—
367C2×D11—41no—
368C4×C11—22no—
369C4×C11—41no—
370C4×C11—42no—
371C4×C11—81no—
372C4×C11—81no—
373C4×C11#52911yescharacteristic
374C4×C11#53811yescharacteristic
375C4×C11#55511yescharacteristic
376C4×C11#55911yescharacteristic
377Dic11—22no—
378Dic11—42no—
379Dic11—41no—
380Dic11—41no—
381Dic11—42no—
382Dic11—81no—
383Dic11—81no—
384C22×Q8—21no—
385C22×Q8—111no—
386C22×D4—221no—
387C22×D4C22×D1111yescharacteristic
388C23×C4—111no—
389C23×C4—221no—
390C2×SD16—222no—
391C2×SD16—441no—
392C2×SD16—441no—
393C22×C8—111no—
394C22×C8—111no—
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397C4⋊Q8—22no—
398C4⋊Q8—41no—
399C22⋊Q8—222no—
400C22⋊Q8—441no—
401#121—222no—
402#121—222no—
403C4×D4—222no—
404C4×D4—441no—
405#117—222no—
406#117—441no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—111no—
419C2×C22⋊C4—111no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C42—111no—
426C2×C42—221no—
427C2×C42—221no—
428C2×C42—221no—
429C2×C42C22×D1111yescharacteristic
430#107—222no—
431C4⋊C8—441no—
432#103—222no—
433#103—222no—
434#103—441no—
435#102—22no—
436#102—41no—
437#102—222no—
438C22⋊C8—441no—
439C22⋊C8—441no—
440C4×C8—441no—
441#95—111no—
442#95—111no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451C2×C11—82no—
452C2×C11#245911yescharacteristic
453C2×C11#310711yescharacteristic
454C2×C11#311811yescharacteristic
455C2×C11#329711yescharacteristic
456C2×C11#330411yescharacteristic
457C2×C11#331411yescharacteristic
458C2×C11#332911yescharacteristic
459D11—81no—
460C24—21no—
461C24—111no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—81no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—224no—
477C2×D4—881no—
478C2×D4—881no—
479C2×D4#434312yes—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—442no—
497C22×C4—442no—
498C22×C4—881no—
499C22×C4D4×D1111yescharacteristic
500C22×C4D4×D1111yescharacteristic
501C22×C4C23×D1111yescharacteristic
502SD16—444no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—112no—
522C4⋊C4—112no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—442no—
528C4⋊C4—881no—
529C4⋊C4#434112yes—
530C22⋊C4—42no—
531C22⋊C4—81no—
532C22⋊C4—222no—
533C22⋊C4—224no—
534C22⋊C4—222no—
535C22⋊C4—442no—
536C22⋊C4—442no—
537C22⋊C4—442no—
538C22⋊C4—881no—
539C42—21no—
540C42—21no—
541C42—221no—
542C42—221no—
543C42—442no—
544C42—881no—
545C42—881no—
546C11#2673111yescharacteristic, complemented, Sylow
547C23—22no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—221no—
555C23—221no—
556C23—221no—
557C23—221no—
558C23—221no—
559C23—221no—
560C23—221no—
561C23C2×D4×D1111yescharacteristic
562Q8—84no—
563Q8—441no—
564Q8—441no—
565Q8—441no—
566Q8—441no—
567D4—22no—
568D4—22no—
569D4—41no—
570D4—41no—
571D4—884no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—112no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—222no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—222no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—884no—
612C2×C4#6696512yes—
613C2×C4C2×#434111yescharacteristic
614C2×C4#6703711yescharacteristic
615C2×C4C2×#434311yescharacteristic
616C2×C4#41×D1111yescharacteristic
617C2×C4#41×D1111yescharacteristic
618C2×C4#6704211yescharacteristic
619C8—41no—
620C8—41no—
621C8—441no—
622C8—441no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—441no—
631C22—441no—
632C22—441no—
633C22—441no—
634C22—441no—
635C22—441no—
636C22—441no—
637C22#1062312211yescharacteristic
638C22#1062315811yescharacteristic
639C22#1062320711yescharacteristic
640C22C2×#6696511yescharacteristic
641C22#1062329311yescharacteristic
642C22#1062330511yescharacteristic
643C22D11×#13711yescharacteristic
644C4—22no—
645C4—41no—
646C4—42no—
647C4—81no—
648C4—81no—
649C4—222no—
650C4—442no—
651C4—442no—
652C4—441no—
653C4—441no—
654C4—881no—
655C4—881no—
656C4#1062315511yescharacteristic
657C4#1062317511yescharacteristic
658C4#1062320111yescharacteristic
659C4#1062321211yescharacteristic
660C2—82no—
661C2—881no—
662C2#1307255611yescharacteristic
663C2#1307868911yescharacteristic
664C2#1307880511yescharacteristic
665C2#1308047011yescharacteristic
666C2#1308055411yescharacteristic
667C2#1308069611yescharacteristic
668C2#1308090311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2023C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenter#2023D11
hypocenterC11#26731
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
1. #13072993C2semidirect
3. #13069933C2semidirect
6. #13069569C2semidirect
7. #13069290C2semidirect
8. #13069258C2semidirect
9. #13069223C2semidirect
10. #13069207C2semidirect
11. #13068948C2semidirect
12. #13068927C2semidirect
13. #13068709C2semidirect
14. #102×Dic11C2semidirect
15. C11×#2023C2semidirect
217. #2023D11semidirect
546. C11#26731semidirect

Maximal subgroups

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

subgroupindex
#130729932
#130716592
#130699332
#130697972
#130696202
#130695692
#130692902
#130692582
#130692232
#130692072
#130689482
#130689272
#130687092
#102×Dic112
C11×#20232
#2673111