Finite Group Databasebeta

← #14822268

Subgroups — #14822268

Order 2816.

762 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072970C211yesmaximal, characteristic
2#13071643C211yesmaximal, characteristic, complemented
3#13069932C211yesmaximal, characteristic, complemented
4#13069813C211yesmaximal, characteristic, complemented
5#13069766C211yesmaximal, characteristic, complemented
6#13069619C211yesmaximal, characteristic
7#13069572C211yesmaximal, characteristic, complemented
8#13069310C211yesmaximal, characteristic, complemented
9#13069245C211yesmaximal, characteristic, complemented
10#13069232C211yesmaximal, characteristic, complemented
11#13069200C211yesmaximal, characteristic, complemented
12#13068968C211yesmaximal, characteristic, complemented
13#13068711C211yesmaximal, characteristic, complemented
14#13068445C211yesmaximal, characteristic, complemented
15C11×#1875C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×#4324C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C2×#66943C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25#10622835—21no—
26#10622834—21no—
27#10622834C2211yescharacteristic
28#10622834C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30#10622825C2211yescharacteristic
31C4×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40#10622587C2211yescharacteristic
41#10622586C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43#10622566—21no—
44#10622558—21no—
45#10622558—21no—
46#10622557—21no—
47#10622546—21no—
48C4×Dic11⋊C4—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×#121—22no—
66C11×#121—41no—
67C11×#117—22no—
68C11×#117—41no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C42×C11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11D411yescharacteristic
82C2×C22⋊Dic11D411yescharacteristic
83C2×#4324—22no—
84C2×#4324—41no—
85C2×#4324—41no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90#66977—22no—
91#66977—22no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66943—22no—
104#66943—41no—
105#66940—22no—
106#66940—41no—
107C11×#102—22no—
108C11×#102—41no—
109C11×C22⋊C8—41no—
110#66896—22no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95D411yescharacteristic
118C11⋊#95D411yescharacteristic
119C22⋊(C11⋊C8)—41no—
120#66881—22no—
121#66880—22no—
122#66880—41no—
123#66879—41no—
124Dic11⋊C8—41no—
125#66874—22no—
126#26751—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11C2×D411yescharacteristic
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—42no—
136C2×D4×C11—42no—
137C2×D4×C11—81no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22#4112yes—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4#4112yes—
174C11×C4⋊C4#4112yes—
175C11×C22⋊C4—42no—
176C11×C22⋊C4—42no—
177C42×C11—42no—
178C22⋊Dic11—24no—
179C22⋊Dic11—41no—
180C22⋊Dic11—41no—
181C22⋊Dic11—42no—
182C22⋊Dic11—81no—
183C22⋊Dic11—81no—
184C22⋊Dic11—81no—
185C22⋊Dic11—81no—
186#4324—44no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—42no—
193C4⋊Dic11#4112yes—
194Dic11⋊C4—24no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—42no—
203C4×Dic11—42no—
204C4×Dic11—81no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211#2490—111no—
212#2362—111no—
213#2055—111no—
214#2035—111no—
215#2026—111no—
216#2000—111no—
217#1989—111no—
218#1936—111no—
219#1926—111no—
220#1924—111no—
221#1920—111no—
222#1880—111no—
223#1875D1111yescharacteristic
224#1825—111no—
225#1763—111no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11C22×D411yescharacteristic
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—84no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
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×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
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—41no—
291C2×Dic11—41no—
292Dic22—22no—
293Dic22—22no—
294Dic22—41no—
295Dic22—41no—
296C8×C11—41no—
297C8×C11—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C22×SD16—111no—
301C2×#125—111no—
302C2×C22⋊Q8—111no—
303C2×#121C2×D1111yescharacteristic
304C2×C4×Q8—111no—
305C2×#117C2×D1111yescharacteristic
306C2×#106—111no—
307C2×C4⋊C8—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#102—111no—
312C2×#102C2×D1111yescharacteristic
313C2×#102C2×D1111yescharacteristic
314C2×C22⋊C8—111no—
315C2×C22⋊C8C2×D1111yescharacteristic
316C2×#97—111no—
317#397—221no—
318#394—221no—
319#391—111no—
320#390—111no—
321#390—111no—
322#390—221no—
323#389—111no—
324#388—221no—
325#388—221no—
326#388—221no—
327#387—221no—
328#380—111no—
329C4×C4⋊C4—111no—
330C4×C4⋊C4—111no—
331C4×C4⋊C4—221no—
332C4×C22⋊C4—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340C2×D1111yescharacteristic
340#340C2×D1111yescharacteristic
341#336—111no—
342#336—111no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11—81no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11#52511yescharacteristic
358C22×C11#54611yescharacteristic
359C22×C11#54611yescharacteristic
360C22×C11#57511yescharacteristic
361C22×C11#57511yescharacteristic
362C22×C11#57711yescharacteristic
363C22×C11#57711yescharacteristic
364C4×C11—41no—
365C4×C11—42no—
366C4×C11—42no—
367C4×C11—81no—
368C4×C11#52911yescharacteristic
369C4×C11#53811yescharacteristic
370C4×C11#55511yescharacteristic
371C4×C11#55911yescharacteristic
372Dic11—42no—
373Dic11—42no—
374Dic11—41no—
375Dic11—41no—
376Dic11—41no—
377Dic11—41no—
378Dic11—81no—
379Dic11—81no—
380C22×Q8—111no—
381C22×D4—21no—
382C22×D4C22×D1111yescharacteristic
383C23×C4C22×D1111yescharacteristic
384C2×SD16—222no—
385C2×SD16—441no—
386C2×SD16—441no—
387C22×C8—111no—
388C22×C8—111no—
389C22×C8C22×D1111yescharacteristic
390C22×C8C22×D1111yescharacteristic
391#125—222no—
392#125—441no—
393C22⋊Q8—222no—
394C22⋊Q8—222no—
395#121—22no—
396#121—41no—
397C4×Q8—222no—
398C4×Q8—441no—
399#117—22no—
400#117—41no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—111no—
415C2×C22⋊C4—111no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C42—21no—
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—221no—
426C2×C42—221no—
427C2×C42—221no—
428#106—222no—
429C4⋊C8—441no—
430#103—222no—
431#103—222no—
432#103—441no—
433#102—22no—
434#102—41no—
435#102—222no—
436C22⋊C8—41no—
437C22⋊C8—441no—
438#97—441no—
439#95—111no—
440#95—111no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447C2×C11—81no—
448C2×C11—161no—
449C2×C11#245911yescharacteristic
450C2×C11#311111yescharacteristic
451C2×C11#312611yescharacteristic
452C2×C11#330711yescharacteristic
453C2×C11#331111yescharacteristic
454C2×C11#331711yescharacteristic
455C2×C11#332611yescharacteristic
456C24—21no—
457C24D4×D1111yescharacteristic
458C2×Q8—112no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—81no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
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×C4D4×D1111yescharacteristic
491C22×C4C23×D1111yescharacteristic
492SD16—444no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—112no—
510C4⋊C4—224no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4—442no—
519C4⋊C4—442no—
520C4⋊C4#433912yes—
521C4⋊C4#434112yes—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C22⋊C4—224no—
525C22⋊C4—441no—
526C22⋊C4—441no—
527C22⋊C4—442no—
528C22⋊C4—881no—
529C22⋊C4—881no—
530C22⋊C4—881no—
531C22⋊C4—881no—
532C42—42no—
533C42—221no—
534C42—221no—
535C42—221no—
536C42—221no—
537C42—442no—
538C42—442no—
539C42—881no—
540C11#2675111yescharacteristic, complemented, Sylow
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23C2×D4×D1111yescharacteristic
556Q8—222no—
557Q8—222no—
558Q8—441no—
559Q8—441no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—41no—
564D4—84no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—441no—
596C2×C4—441no—
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×C4C2×#433911yescharacteristic
606C2×C4C2×#434111yescharacteristic
607C2×C4#6703711yescharacteristic
608C2×C4#6703711yescharacteristic
609C2×C4#41×D1111yescharacteristic
610C2×C4#41×D1111yescharacteristic
611C8—41no—
612C8—41no—
613C8—441no—
614C8—441no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22#1062302111yescharacteristic
630C22#1062312211yescharacteristic
631C22#1062318711yescharacteristic
632C22#1062329911yescharacteristic
633C22#1062330111yescharacteristic
634C22#1062330411yescharacteristic
635C22#1062330611yescharacteristic
636C4—42no—
637C4—42no—
638C4—41no—
639C4—81no—
640C4—441no—
641C4—441no—
642C4—441no—
643C4—441no—
644C4—442no—
645C4—442no—
646C4—881no—
647C4—881no—
648C4#1062308811yescharacteristic
649C4#1062309011yescharacteristic
650C4#1062314411yescharacteristic
651C4#1062314711yescharacteristic
652C2—81no—
653C2—161no—
654C2#1307255211yescharacteristic
655C2#1307872011yescharacteristic
656C2#1307890311yescharacteristic
657C2#1308059611yescharacteristic
658C2#1308065311yescharacteristic
659C2#1308073811yescharacteristic
660C2#1308086211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1875C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#1875D11
hypocenterC11#26751
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
2. #13071643C2semidirect
3. #13069932C2semidirect
4. #13069813C2semidirect
5. #13069766C2semidirect
7. #13069572C2semidirect
8. #13069310C2semidirect
9. #13069245C2semidirect
10. #13069232C2semidirect
11. #13069200C2semidirect
12. #13068968C2semidirect
13. #13068711C2semidirect
14. #13068445C2semidirect
540. C11#26751semidirect

Maximal subgroups

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

subgroupindex
#130729702
#130716432
#130699322
#130698132
#130697662
#130696192
#130695722
#130693102
#130692452
#130692322
#130692002
#130689682
#130687112
#130684452
C11×#18752
#2675111