Finite Group Databasebeta

← #14821904

Subgroups — #14821904

Order 2816.

790 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#13072970C211yesmaximal, characteristic
2#13071625C211yesmaximal, characteristic, complemented
3#13069929C211yesmaximal, characteristic, complemented
4#13069816C211yesmaximal, characteristic, complemented
5#13069765C211yesmaximal, characteristic, complemented
6#13069572C211yesmaximal, characteristic, complemented
7#13069301C211yesmaximal, characteristic, complemented
8#13069239C211yesmaximal, characteristic, complemented
9#13069219C211yesmaximal, characteristic, complemented
10#13069211C211yesmaximal, characteristic, complemented
11#13068973C211yesmaximal, characteristic, complemented
12#13068934C211yesmaximal, characteristic
13#13068703C211yesmaximal, characteristic, complemented
14#103×Dic11C211yesmaximal, characteristic, complemented
15C11×#2000C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C2×#66943C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25#10622843C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28#10622835—21no—
29#10622834—21no—
30#10622834C2211yescharacteristic
31#10622834C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34#10622825C2211yescharacteristic
35C4×C22⋊Dic11C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39#10622598—21no—
40#10622598C2211yescharacteristic
41#10622594—21no—
42C4⋊C4×Dic11C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622566—21no—
46#10622563—21no—
47#10622558—21no—
48C22⋊C4×Dic11—21no—
49C11×#340C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—21no—
64C2×C11×SD16—22no—
65C2×C11×SD16—41no—
66C2×C11×SD16—41no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—22no—
71C11×#121—22no—
72C11×#121—41no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11D411yescharacteristic
84C2×C22⋊Dic11D411yescharacteristic
85Q8×Dic11—22no—
86Q8×Dic11—41no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—41no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66943—22no—
106#66943—41no—
107C11×#103—22no—
108C11×#102—22no—
109C11×C22⋊C8—41no—
110#66899—22no—
111#66899—41no—
112#66896—22no—
113#66896—41no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122C22⋊(C11⋊C8)—41no—
123Dic11⋊C8—41no—
124C8×Dic11—41no—
125#66871—22no—
126#26727—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11C2×D411yescharacteristic
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11#4112yes—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—42no—
142C2×D4×C11—42no—
143C2×D4×C11—81no—
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×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11—81no—
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C11×SD16—44no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4#4112yes—
177C11×C4⋊C4#4112yes—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—42no—
180C22⋊Dic11—22no—
181C22⋊Dic11—22no—
182C22⋊Dic11—42no—
183C22⋊Dic11—81no—
184C22⋊Dic11—81no—
185C22⋊Dic11—81no—
186C22⋊Dic11—81no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—42no—
195C4⋊Dic11—42no—
196C4⋊Dic11—42no—
197C4⋊Dic11—81no—
198C4⋊Dic11#4112yes—
199Dic11⋊C4—42no—
200C4×Dic11—21no—
201C4×Dic11—21no—
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#2490—111no—
214#2360—111no—
215#2055—111no—
216#2036—111no—
217#2026—111no—
218#2000D1111yescharacteristic
219#1989—111no—
220#1934—111no—
221#1925—111no—
222#1923—111no—
223#1921—111no—
224#1880—111no—
225#1874—111no—
226#1823—111no—
227C4×#103—111no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11#13512yes—
242C23×C11C22×D411yescharacteristic
243Q8×C11—22no—
244Q8×C11—22no—
245Q8×C11—41no—
246Q8×C11—41no—
247D4×C11—41no—
248D4×C11—41no—
249D4×C11—41no—
250D4×C11—41no—
251D4×C11—84no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
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—22no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
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—41no—
297C2×Dic11—84no—
298C2×Dic11#13712yes—
299C8×C11—41no—
300C8×C11—41no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C22×SD16C2×D1111yescharacteristic
304C2×#125—111no—
305C2×C22⋊Q8C2×D1111yescharacteristic
306C2×#121C2×D1111yescharacteristic
307C2×C4×Q8—111no—
308C22×C4⋊C4—111no—
309C2×#107—111no—
310C2×C4⋊C8—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103C2×D1111yescharacteristic
314C2×#102—111no—
315C2×#102—111no—
316C2×#102C2×D1111yescharacteristic
317C2×C22⋊C8—111no—
318C2×C22⋊C8C2×D1111yescharacteristic
319C2×C4×C8—111no—
320#397—221no—
321#394—221no—
322#391—111no—
323#390—111no—
324#390—111no—
325#390—221no—
326#389—111no—
327#389—221no—
328#388—221no—
329#387—221no—
330#385—221no—
331#380—111no—
332C4×C4⋊C4—111no—
333C4×C4⋊C4—111no—
334C4×C22⋊C4—111no—
335C4×C22⋊C4—221no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340C2×D1111yescharacteristic
344#336—111no—
345#336—111no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
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#54611yescharacteristic
363C22×C11C2×#13511yescharacteristic
364C22×C11C2×#13711yescharacteristic
365C22×C11#57611yescharacteristic
366C22×C11#57711yescharacteristic
367C4×C11—42no—
368C4×C11—41no—
369C4×C11—42no—
370C4×C11—42no—
371C4×C11#52911yescharacteristic
372C4×C11#53811yescharacteristic
373C4×C11#55511yescharacteristic
374C4×C11#55911yescharacteristic
375Dic11—22no—
376Dic11—41no—
377Dic11—41no—
378Dic11—41no—
379Dic11—42no—
380Dic11—81no—
381Dic11—81no—
382Dic11—81no—
383C22×Q8C22×D1111yescharacteristic
384C22×D4—21no—
385C22×D4C22×D1111yescharacteristic
386C23×C4—221no—
387C23×C4C22×D1111yescharacteristic
388C2×SD16—22no—
389C2×SD16—41no—
390C2×SD16—41no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395#125—222no—
396#125—441no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399#121—22no—
400#121—41no—
401C4×Q8—222no—
402C4×Q8—441no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—222no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—441no—
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—111no—
420C2×C22⋊C4—111no—
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—
431#107—222no—
432C4⋊C8—441no—
433#103—22no—
434#103—222no—
435#103—441no—
436#102—22no—
437#102—222no—
438#102—441no—
439C22⋊C8—41no—
440C22⋊C8—441no—
441C4×C8—441no—
442#95—111no—
443#95—111no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450C2×C11—42no—
451C2×C11—161no—
452C2×C11#245911yescharacteristic
453C2×C11#310811yescharacteristic
454C2×C11#311911yescharacteristic
455C2×C11#329611yescharacteristic
456C2×C11#329711yescharacteristic
457C2×C11#332011yescharacteristic
458C2×C11#333311yescharacteristic
459C24—21no—
460C24D4×D1111yescharacteristic
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8#434112yes—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—81no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—442no—
494C22×C4—442no—
495C22×C4—881no—
496C22×C4D4×D1111yescharacteristic
497C22×C4C23×D1111yescharacteristic
498SD16—44no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C4⋊C4—24no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—112no—
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—442no—
526C4⋊C4—881no—
527C4⋊C4#434112yes—
528C4⋊C4#434112yes—
529C22⋊C4—24no—
530C22⋊C4—42no—
531C22⋊C4—222no—
532C22⋊C4—222no—
533C22⋊C4—442no—
534C22⋊C4—881no—
535C22⋊C4—881no—
536C22⋊C4—881no—
537C22⋊C4—881no—
538C42—221no—
539C42—221no—
540C42—221no—
541C42—221no—
542C42—442no—
543C42—881no—
544C42—881no—
545C11#2672711yescharacteristic, complemented, Sylow
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23#6696912yes—
560C23C2×D4×D1111yescharacteristic
561Q8—22no—
562Q8—22no—
563Q8—41no—
564Q8—41no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—84no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—41no—
577C2×C4—41no—
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—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—41no—
618C8—41no—
619C8—441no—
620C8—441no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22#1062311711yescharacteristic
636C22#1062312211yescharacteristic
637C22#1062314111yescharacteristic
638C22C2×#6696911yescharacteristic
639C22#1062330011yescharacteristic
640C22#1062330611yescharacteristic
641C22D11×#13711yescharacteristic
642C4—42no—
643C4—42no—
644C4—41no—
645C4—42no—
646C4—222no—
647C4—441no—
648C4—441no—
649C4—441no—
650C4—442no—
651C4—881no—
652C4—881no—
653C4—881no—
654C4#1062312411yescharacteristic
655C4#1062313111yescharacteristic
656C4#1062314711yescharacteristic
657C4#1062324411yescharacteristic
658C2—42no—
659C2—161no—
660C2#1307254811yescharacteristic
661C2#1307869111yescharacteristic
662C2#1307880811yescharacteristic
663C2#1308045511yescharacteristic
664C2#1308047211yescharacteristic
665C2#1308078211yescharacteristic
666C2#1308094711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2000C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2000D11
hypocenterC11#26727
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
2. #13071625C2semidirect
3. #13069929C2semidirect
4. #13069816C2semidirect
5. #13069765C2semidirect
6. #13069572C2semidirect
7. #13069301C2semidirect
8. #13069239C2semidirect
9. #13069219C2semidirect
10. #13069211C2semidirect
11. #13068973C2semidirect
13. #13068703C2semidirect
14. #103×Dic11C2semidirect
545. C11#26727semidirect

Maximal subgroups

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

subgroupindex
#130729702
#130716252
#130699292
#130698162
#130697652
#130695722
#130693012
#130692392
#130692192
#130692112
#130689732
#130689342
#130687032
#103×Dic112
C11×#20002
#2672711