Finite Group Databasebeta

← #14822220

Subgroups — #14822220

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#13071641C211yesmaximal, characteristic, complemented
2#13069933C211yesmaximal, characteristic, complemented
3#13069819C211yesmaximal, characteristic, complemented
4#13069754C211yesmaximal, characteristic, complemented
5#13069619C211yesmaximal, characteristic
6#13069569C211yesmaximal, characteristic, complemented
7#13069316C211yesmaximal, characteristic, complemented
8#13069233C211yesmaximal, characteristic, complemented
9#13069231C211yesmaximal, characteristic, complemented
10#13069208C211yesmaximal, characteristic, complemented
11#13068974C211yesmaximal, characteristic, complemented
12#13068939C211yesmaximal, characteristic
13#13068708C211yesmaximal, characteristic, complemented
14#13068449C211yesmaximal, characteristic, complemented
15C11×#2491C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#124—21no—
18C2×C11×#121C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#394—21no—
24C11×#393—21no—
25C11×#390C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#388—21no—
28C11×#380C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622558—21no—
41#10622557—21no—
42C4×C4⋊Dic11C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47#10622265—21no—
48#10622262—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8—41no—
66C11×#124—44no—
67C11×#121—22no—
68C11×#121—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×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×#4324—22no—
87C2×#4324—41no—
88C2×#4324—41no—
89#66979—22no—
90#66979—41no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94#66977—22no—
95#66977—22no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C4×Dic22—22no—
107C4×Dic22—41no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95D411yescharacteristic
111C11×#95D411yescharacteristic
112#66896—22no—
113#66896—22no—
114#66896—41no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C22⋊(C11⋊C8)—41no—
120C22⋊(C11⋊C8)—41no—
121#66874—22no—
122#66874—22no—
123#66874—41no—
124#66871—22no—
125C4⋊(C11⋊C8)—41no—
126#66867—41no—
127#26748—111nomaximal, Sylow
128C24×C11—21no—
129C24×C11C2×D411yescharacteristic
130C2×Q8×C11—42no—
131C2×Q8×C11—42no—
132C2×Q8×C11—81no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—42no—
140C2×D4×C11—42no—
141C2×D4×C11—81no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22#4112yes—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4#4112yes—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—41no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—42no—
181C11×C22⋊C4—81no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—42no—
187C22⋊Dic11—24no—
188C22⋊Dic11—42no—
189#4324—44no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11#4112yes—
195C4⋊Dic11#4112yes—
196Dic11⋊C4—24no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199C4×Dic11—42no—
200C4×Dic11—42no—
201C4×Dic11—42no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214#2491D1111yescharacteristic
215#2362—111no—
216#2055—111no—
217#2036—111no—
218#2024—111no—
219#2000—111no—
220#1988—111no—
221#1936—111no—
222#1925—111no—
223#1924—111no—
224#1921—111no—
225#1880—111no—
226#1875—111no—
227#1825—111no—
228#1763—111no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11C22×D411yescharacteristic
244Q8×C11—84no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—84no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11AGL(1,ℤ/8)12yes—
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296Dic22—22no—
297Dic22—22no—
298Dic22—41no—
299Dic22—41no—
300C11⋊C8—41no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C22×SD16—111no—
305C2×C4⋊Q8C2×D1111yescharacteristic
306C2×#124—21no—
307C2×C22⋊Q8—111no—
308C2×#121C2×D1111yescharacteristic
309C2×C4×Q8—111no—
310C2×#117—111no—
311C2×#107—111no—
312C2×C4⋊C8—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#102—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×C22⋊C8—111no—
320C2×C22⋊C8—111no—
321C2×#97—111no—
322#394—21no—
323#393—21no—
324#391—111no—
325#390C2×D1111yescharacteristic
326#390C2×D1111yescharacteristic
327#389—111no—
328#388—21no—
329#388—221no—
330#388—221no—
331#387—221no—
332#380C2×D1111yescharacteristic
333C4×C4⋊C4—111no—
334C4×C4⋊C4—221no—
335C4×C4⋊C4C2×D1111yescharacteristic
336C4×C22⋊C4C2×D1111yescharacteristic
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#336—111no—
346#336—111no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—81no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11#52511yescharacteristic
362C22×C11#54611yescharacteristic
363C22×C11#54611yescharacteristic
364C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C11#57511yescharacteristic
366C22×C11#57711yescharacteristic
367C22×C11#57811yescharacteristic
368C4×C11—22no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—42no—
372C4×C11—41no—
373C4×C11—41no—
374C4×C11—81no—
375C4×C11—81no—
376C4×C11#52911yescharacteristic
377C4×C11#53811yescharacteristic
378C4×C11#55511yescharacteristic
379C4×C11#55911yescharacteristic
380Dic11—42no—
381Dic11—42no—
382Dic11—42no—
383Dic11—81no—
384C22×Q8—21no—
385C22×Q8—111no—
386C22×D4—21no—
387C22×D4C22×D1111yescharacteristic
388C23×C4C22×D1111yescharacteristic
389C2×SD16—222no—
390C2×SD16—441no—
391C2×SD16—441no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8—111no—
395C22×C8—111no—
396C4⋊Q8—22no—
397C4⋊Q8—41no—
398#124—44no—
399C22⋊Q8—222no—
400C22⋊Q8—222no—
401#121—22no—
402#121—41no—
403C4×Q8—222no—
404C4×Q8—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⋊C4—221no—
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4C22⋊D1111yescharacteristic
426C2×C22⋊C4C22⋊D1111yescharacteristic
427C2×C42—21no—
428C2×C42—221no—
429C2×C42—221no—
430C2×C42—221no—
431C2×C42C22×D1111yescharacteristic
432C2×C42C22×D1111yescharacteristic
433#107—222no—
434C4⋊C8—441no—
435#103—222no—
436#103—222no—
437#103—441no—
438#102—222no—
439#102—222no—
440#102—441no—
441C22⋊C8—441no—
442C22⋊C8—441no—
443#97—441no—
444#95—21no—
445#95—21no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95C22⋊D1111yescharacteristic
451#95C22⋊D1111yescharacteristic
452C2×C11—81no—
453C2×C11—161no—
454C2×C11#245911yescharacteristic
455C2×C11#311511yescharacteristic
456C2×C11#312111yescharacteristic
457C2×C11#331011yescharacteristic
458C2×C11#331311yescharacteristic
459C2×C11#332111yescharacteristic
460C2×C11#333011yescharacteristic
461C24—21no—
462C24C2×C22⋊D1111yescharacteristic
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—81no—
466C2×Q8—112no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—81no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C2×C22⋊D1111yescharacteristic
499C22×C4C23×D1111yescharacteristic
500SD16—444no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—42no—
519C4⋊C4—112no—
520C4⋊C4—112no—
521C4⋊C4—224no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—442no—
527C4⋊C4—442no—
528C4⋊C4#434112yes—
529C22⋊C4—22no—
530C22⋊C4—41no—
531C22⋊C4—42no—
532C22⋊C4—42no—
533C22⋊C4—42no—
534C22⋊C4—42no—
535C22⋊C4—42no—
536C22⋊C4—81no—
537C22⋊C4—224no—
538C22⋊C4—442no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—42no—
544C42—442no—
545C42—442no—
546C42—442no—
547C11#2674811yescharacteristic, complemented, Sylow
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23C22×C22⋊D1111yescharacteristic
563Q8—84no—
564Q8—222no—
565Q8—222no—
566Q8—441no—
567Q8—441no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—41no—
572D4—84no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—222no—
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—441no—
612C2×C4#6698512yes—
613C2×C4C2×#434111yescharacteristic
614C2×C4#6703711yescharacteristic
615C2×C4#41×D1111yescharacteristic
616C2×C4#41×D1111yescharacteristic
617C2×C4#41×D1111yescharacteristic
618C2×C4#6704211yescharacteristic
619C8—441no—
620C8—441no—
621C8—441no—
622C8—441no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22C2×#6698511yescharacteristic
638C22#1062333711yescharacteristic
639C22#1062335311yescharacteristic
640C22#1062335911yescharacteristic
641C22#1062336011yescharacteristic
642C22#1062336711yescharacteristic
643C22#1062336911yescharacteristic
644C4—22no—
645C4—42no—
646C4—41no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—81no—
651C4—81no—
652C4—442no—
653C4—442no—
654C4—442no—
655C4—881no—
656C4#1062320111yescharacteristic
657C4#1062320911yescharacteristic
658C4#1062321111yescharacteristic
659C4#1062321211yescharacteristic
660C2—81no—
661C2—161no—
662C2#1307254911yescharacteristic
663C2#1307876111yescharacteristic
664C2#1307883911yescharacteristic
665C2#1308063711yescharacteristic
666C2#1308068211yescharacteristic
667C2#1308079611yescharacteristic
668C2#1308091511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2491C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2491D11
hypocenterC11#26748
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2491

Complements

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

NH ≅ G/Ntype
1. #13071641C2semidirect
2. #13069933C2semidirect
3. #13069819C2semidirect
4. #13069754C2semidirect
6. #13069569C2semidirect
7. #13069316C2semidirect
8. #13069233C2semidirect
9. #13069231C2semidirect
10. #13069208C2semidirect
11. #13068974C2semidirect
13. #13068708C2semidirect
14. #13068449C2semidirect
547. C11#26748semidirect

Maximal subgroups

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

subgroupindex
#130716412
#130699332
#130698192
#130697542
#130696192
#130695692
#130693162
#130692332
#130692312
#130692082
#130689742
#130689392
#130687082
#130684492
C11×#24912
#2674811