Finite Group Databasebeta

← #14827040

Subgroups — #14827040

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073200C211yesmaximal, characteristic, complemented
2#13071691C211yesmaximal, characteristic, complemented
3#13070147C211yesmaximal, characteristic, complemented
4#13069924C211yesmaximal, characteristic
5#13069852C211yesmaximal, characteristic, complemented
6#13069472C211yesmaximal, characteristic, complemented
7#13069253C211yesmaximal, characteristic, complemented
8#13069240C211yesmaximal, characteristic, complemented
9#13069202C211yesmaximal, characteristic, complemented
10#13069172C211yesmaximal, characteristic, complemented
11#13068973C211yesmaximal, characteristic, complemented
12#13068966C211yesmaximal, characteristic
13#13068619C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic, complemented
15C11×#2012C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×#66932—21no—
22C2×C11×#103C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C11×#390C2211yescharacteristic
25#10622843C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28#10622834C2211yescharacteristic
29#10622834C2211yescharacteristic
30#10622834C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622589C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41#10622565—21no—
42#10622564—21no—
43#10622564—21no—
44#10622563—21no—
45#10622561—21no—
46#10622558—21no—
47C22⋊C4×Dic11—21no—
48C4×C4⋊Dic11C2211yescharacteristic
49C4×C4⋊Dic11C2211yescharacteristic
50#10622541C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C2×C11×SD16—22no—
64C2×C11×SD16—22no—
65C2×C11×SD16—41no—
66C2×C11×D8—22no—
67C2×C11×D8—41no—
68C2×C11×D8—41no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×#124—22no—
72C11×#124—22no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86Q8×Dic11—22no—
87Q8×Dic11—41no—
88D4×Dic11—22no—
89D4×Dic11—41no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11D411yescharacteristic
92C2×C4⋊Dic11D411yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66932—44no—
108C11×#103—41no—
109C11×#102—22no—
110#66899—22no—
111#66899—41no—
112#66896—22no—
113#66896—22no—
114#66896—41no—
115#66896—41no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123#66881—22no—
124Dic11⋊C8—41no—
125C8×Dic11—41no—
126#66872—41no—
127#27071—111nomaximal, Sylow
128C24×C11—21no—
129C24×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11#4112yes—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11#4112yes—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—42no—
158C22×Dic11—42no—
159C22×Dic11—81no—
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C11×SD16—44no—
165C11×D8—44no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11#4112yes—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—24no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—81no—
178C42×C11—21no—
179C42×C11—21no—
180C22⋊Dic11—42no—
181C22⋊Dic11—42no—
182C22⋊Dic11—42no—
183C22⋊Dic11—42no—
184C22⋊Dic11—42no—
185C22⋊Dic11—81no—
186C22⋊Dic11—81no—
187C4⋊Dic11—22no—
188C4⋊Dic11—22no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—42no—
197C4⋊Dic11#4112yes—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200Dic11⋊C4—81no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—42no—
206C4×Dic11—42no—
207C4×Dic11—81no—
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#2512—111no—
215#2367—111no—
216#2094—111no—
217#2054—111no—
218#2042—111no—
219#2012D1111yescharacteristic
220#1968—111no—
221#1927—111no—
222#1926—111no—
223#1920—111no—
224#1916—111no—
225#1880—111no—
226#1879—111no—
227#1803—111no—
228C4×#102—111no—
229C23×C11—22no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
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—22no—
245Q8×C11—22no—
246Q8×C11—41no—
247Q8×C11—41no—
248D4×C11—22no—
249D4×C11—22no—
250D4×C11—41no—
251D4×C11—41no—
252D4×C11—41no—
253D4×C11—41no—
254D4×C11—41no—
255D4×C11—41no—
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—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—22no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—41no—
286C2×Dic11—41no—
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—
296C2×Dic11—84no—
297C2×Dic11#13512yes—
298C2×Dic11AGL(1,ℤ/8)12yes—
299C8×C11—22no—
300C8×C11—41no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C22×SD16C2×D1111yescharacteristic
304C22×D8C2×D1111yescharacteristic
305C2×#126—221no—
306C2×#124C2×D1111yescharacteristic
307C2×C4×Q8—111no—
308C2×C4×D4—111no—
309C2×#106—111no—
310C2×#106—111no—
311C2×C4⋊C8—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103C2×D1111yescharacteristic
315C2×#102—111no—
316C2×#102—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×#102C2×D1111yescharacteristic
320C2×C4×C8—111no—
321#397—221no—
322#396—221no—
323#391—111no—
324#390—111no—
325#390—111no—
326#390—111no—
327#390C2×D1111yescharacteristic
328#389—111no—
329#388—221no—
330#388—221no—
331#388—221no—
332#385—221no—
333#384—111no—
334C4×C4⋊C4—111no—
335C4×C4⋊C4—111no—
336C4×C4⋊C4—111no—
337C4×C22⋊C4—221no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#336—111no—
343#336—111no—
344#336—111no—
345#336C2×D1111yescharacteristic
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11—81no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11#52511yescharacteristic
361C22×C11#54611yescharacteristic
362C22×C11#55011yescharacteristic
363C22×C11C2×#13511yescharacteristic
364C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C11#57711yescharacteristic
366C22×C11#57711yescharacteristic
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—42no—
370C4×C11—81no—
371C4×C11#52911yescharacteristic
372C4×C11#53811yescharacteristic
373C4×C11#55111yescharacteristic
374C4×C11#55311yescharacteristic
375Dic11—22no—
376Dic11—22no—
377Dic11—41no—
378Dic11—41no—
379Dic11—42no—
380Dic11—81no—
381Dic11—81no—
382Dic11—81no—
383C22×Q8C22×D1111yescharacteristic
384C22×D4C22×D1111yescharacteristic
385C22×D4C22×D1111yescharacteristic
386C23×C4—221no—
387C2×SD16—22no—
388C2×SD16—22no—
389C2×SD16—41no—
390C2×D8—22no—
391C2×D8—41no—
392C2×D8—41no—
393C22×C8—111no—
394C22×C8—111no—
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397#126—444no—
398#124—22no—
399#124—22no—
400C4×Q8—222no—
401C4×Q8—441no—
402C4×D4—222no—
403C4×D4—441no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C42—111no—
427C2×C42—111no—
428C2×C42—221no—
429C2×C42—221no—
430C2×C42—221no—
431C2×C42C22×D1111yescharacteristic
432#106—222no—
433#106—441no—
434C4⋊C8—441no—
435#103—41no—
436#103—222no—
437#103—441no—
438#102—22no—
439#102—222no—
440#102—222no—
441#102—441no—
442#102—441no—
443C4×C8—441no—
444#95—111no—
445#95—111no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451C2×C11—82no—
452C2×C11—161no—
453C2×C11#246711yescharacteristic
454C2×C11#310611yescharacteristic
455C2×C11#312511yescharacteristic
456C2×C11#330111yescharacteristic
457C2×C11#330611yescharacteristic
458C2×C11#339411yescharacteristic
459C2×C11#339711yescharacteristic
460C24—21no—
461C24—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8#434112yes—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4#434112yes—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4—881no—
493C22×C4D4×D1111yescharacteristic
494C22×C4D4×D1111yescharacteristic
495C22×C4C23×D1111yescharacteristic
496SD16—44no—
497D8—44no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8#434112yes—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—112no—
513C4⋊C4—222no—
514C4⋊C4—222no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4—881no—
526C22⋊C4—24no—
527C22⋊C4—24no—
528C22⋊C4—42no—
529C22⋊C4—81no—
530C22⋊C4—442no—
531C22⋊C4—442no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C22⋊C4—442no—
535C22⋊C4—881no—
536C22⋊C4—881no—
537C42—21no—
538C42—21no—
539C42—221no—
540C42—221no—
541C42—221no—
542C42—221no—
543C42—442no—
544C42—442no—
545C42—881no—
546C11#2707111yescharacteristic, complemented, Sylow
547C23—22no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23C2×D4×D1111yescharacteristic
562Q8—22no—
563Q8—22no—
564Q8—41no—
565Q8—41no—
566D4—22no—
567D4—22no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—41no—
572D4—41no—
573D4—41no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—112no—
587C2×C4—112no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—222no—
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—884no—
611C2×C4C2×#434111yescharacteristic
612C2×C4C2×#434111yescharacteristic
613C2×C4C2×#434111yescharacteristic
614C2×C4#6703711yescharacteristic
615C2×C4#6703711yescharacteristic
616C2×C4#41×D1111yescharacteristic
617C8—22no—
618C8—41no—
619C8—441no—
620C8—441no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22#1062311711yescharacteristic
636C22#1062314311yescharacteristic
637C22#1062324911yescharacteristic
638C22D11×#13511yescharacteristic
639C22#1062330111yescharacteristic
640C22D11×AGL(1,ℤ/8)11yescharacteristic
641C22#1062330611yescharacteristic
642C4—42no—
643C4—41no—
644C4—41no—
645C4—81no—
646C4—222no—
647C4—222no—
648C4—441no—
649C4—442no—
650C4—441no—
651C4—881no—
652C4—881no—
653C4—881no—
654C4#1062311811yescharacteristic
655C4#1062312411yescharacteristic
656C4#1062313111yescharacteristic
657C4#1062313211yescharacteristic
658C2—82no—
659C2—161no—
660C2#1307266211yescharacteristic
661C2#1307866911yescharacteristic
662C2#1307889411yescharacteristic
663C2#1308052511yescharacteristic
664C2#1308058411yescharacteristic
665C2#1308160911yescharacteristic
666C2#1308163311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2012C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
hypercenter#2012D11
hypocenterC11#27071
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2012

Complements

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

NH ≅ G/Ntype
1. #13073200C2semidirect
2. #13071691C2semidirect
3. #13070147C2semidirect
5. #13069852C2semidirect
6. #13069472C2semidirect
7. #13069253C2semidirect
8. #13069240C2semidirect
9. #13069202C2semidirect
10. #13069172C2semidirect
11. #13068973C2semidirect
13. #13068619C2semidirect
14. #102×Dic11C2semidirect
546. C11#27071semidirect

Maximal subgroups

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

subgroupindex
#130732002
#130716912
#130701472
#130699242
#130698522
#130694722
#130692532
#130692402
#130692022
#130691722
#130689732
#130689662
#130686192
#102×Dic112
C11×#20122
#2707111