Finite Group Databasebeta

← #14821918

Subgroups — #14821918

Order 2816.

782 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072957C211yesmaximal, characteristic, complemented
2#13069933C211yesmaximal, characteristic, complemented
3#13069802C211yesmaximal, characteristic
4#13069762C211yesmaximal, characteristic, complemented
5#13069619C211yesmaximal, characteristic
6#13069573C211yesmaximal, characteristic, complemented
7#13069291C211yesmaximal, characteristic, complemented
8#13069250C211yesmaximal, characteristic, complemented
9#13069224C211yesmaximal, characteristic, complemented
10#13069198C211yesmaximal, characteristic, complemented
11#13068950C211yesmaximal, characteristic, complemented
12#13068928C211yesmaximal, characteristic, complemented
13#13068711C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C11×#2363C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C11×#390—21no—
23C11×#390C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#388—21no—
26C11×#386—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C22⋊C4—21no—
29C4×C11×C22⋊C4C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40#10622565—21no—
41#10622557—21no—
42C4×C4⋊Dic11C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622542C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622271—21no—
48#10622263—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C11×#121—22no—
65C11×#121—22no—
66C4×D4×C11—22no—
67C4×D4×C11—41no—
68C11×#117—22no—
69C11×#117—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
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×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×#4324—22no—
88C2×#4324—41no—
89C2×#4324—41no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93#66977—22no—
94#66977—41no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66923—22no—
104#66923—41no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109#66896—22no—
110#66896—22no—
111#66896—41no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C22⋊(C11⋊C8)—41no—
119C22⋊(C11⋊C8)—41no—
120#66874—22no—
121#66874—22no—
122#66874—41no—
123#66872—22no—
124C4⋊(C11⋊C8)—41no—
125C4×C11⋊C8—41no—
126#26728—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11C2×D411yescharacteristic
129C2×D4×C11—24no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—81no—
136C2×D4×C11—81no—
137C2×D4×C11#4112yes—
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×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—81no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—81no—
171C11×C4⋊C4#4112yes—
172C11×C4⋊C4#4112yes—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—41no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—81no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—42no—
185C42×C11—81no—
186C22⋊Dic11—42no—
187C22⋊Dic11—42no—
188#4324—44no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11#4112yes—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198C4×Dic11—42no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
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—
211#2489—111no—
212#2363D1111yescharacteristic
213#2055—111no—
214#2034—111no—
215#2025—111no—
216#2000—111no—
217#1989—111no—
218#1933—111no—
219#1927—111no—
220#1923—111no—
221#1920—111no—
222#1877—111no—
223#1873—111no—
224#1825—111no—
225C4×#102—111no—
226C23×C11—22no—
227C23×C11—21no—
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×C11C22×D411yescharacteristic
241D4×C11—22no—
242D4×C11—22no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—84no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
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×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—84no—
274C2×C4×C11#13512yes—
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C2×Dic11—22no—
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—
292C2×Dic11—41no—
293Dic22—41no—
294Dic22—41no—
295Dic22—41no—
296Dic22—41no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C22×SD16—111no—
302C2×#125—111no—
303C2×C22⋊Q8—111no—
304C2×#121C2×D1111yescharacteristic
305C2×C4×D4C2×D1111yescharacteristic
306C2×#117C2×D1111yescharacteristic
307C2×#106—111no—
308C2×C4⋊C8—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#102—111no—
313C2×#102—111no—
314C2×#102—111no—
315C2×C22⋊C8—111no—
316C2×C22⋊C8—111no—
317C2×C4×C8—111no—
318#400—221no—
319#397—221no—
320#391—111no—
321#391—111no—
322#390—21no—
323#390C2×D1111yescharacteristic
324#389C2×D1111yescharacteristic
325#388—21no—
326#388—221no—
327#386—21no—
328#382—221no—
329#380—111no—
330C4×C4⋊C4—111no—
331C4×C4⋊C4C2×D1111yescharacteristic
332C4×C22⋊C4—21no—
333C4×C22⋊C4C2×D1111yescharacteristic
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#336—111no—
343#336—111no—
344C22×C11—41no—
345C22×C11—42no—
346C22×C11—41no—
347C22×C11—42no—
348C22×C11—41no—
349C22×C11—42no—
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#52511yescharacteristic
359C22×C11#54611yescharacteristic
360C22×C11#54611yescharacteristic
361C22×C11C2×#13511yescharacteristic
362C22×C11#57511yescharacteristic
363C22×C11#57711yescharacteristic
364C22×C11#57711yescharacteristic
365C4×C11—22no—
366C4×C11—42no—
367C4×C11—41no—
368C4×C11—42no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11—81no—
373C4×C11#52911yescharacteristic
374C4×C11#53811yescharacteristic
375C4×C11#55511yescharacteristic
376C4×C11#55911yescharacteristic
377Dic11—42no—
378Dic11—81no—
379Dic11—81no—
380Dic11—81no—
381C22×Q8—111no—
382C22×D4—21no—
383C22×D4C22×D1111yescharacteristic
384C23×C4—21no—
385C23×C4C22×D1111yescharacteristic
386C2×SD16—222no—
387C2×SD16—441no—
388C2×SD16—441no—
389C22×C8—111no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—111no—
393#125—222no—
394#125—441no—
395C22⋊Q8—222no—
396C22⋊Q8—441no—
397#121—22no—
398#121—22no—
399C4×D4—22no—
400C4×D4—41no—
401#117—22no—
402#117—41no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4C22⋊D1111yescharacteristic
421C2×C22⋊C4C22⋊D1111yescharacteristic
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—221no—
425C2×C42C22×D1111yescharacteristic
426C2×C42C22×D1111yescharacteristic
427#106—222no—
428C4⋊C8—441no—
429#103—222no—
430#103—222no—
431#103—441no—
432#102—222no—
433#102—222no—
434#102—441no—
435C22⋊C8—441no—
436C22⋊C8—441no—
437C4×C8—441no—
438#95—21no—
439#95—21no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95C22⋊D1111yescharacteristic
447#95C22⋊D1111yescharacteristic
448C2×C11—81no—
449C2×C11—82no—
450C2×C11#245911yescharacteristic
451C2×C11#310211yescharacteristic
452C2×C11#312311yescharacteristic
453C2×C11#329611yescharacteristic
454C2×C11#330311yescharacteristic
455C2×C11#331711yescharacteristic
456C2×C11#332611yescharacteristic
457C24—21no—
458C24C2×C22⋊D1111yescharacteristic
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×D4—24no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—81no—
472C2×D4—81no—
473C2×D4#433912yes—
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—21no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—81no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C23×D1111yescharacteristic
496SD16—444no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—81no—
514C4⋊C4—112no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—442no—
521C4⋊C4—442no—
522C4⋊C4—442no—
523C4⋊C4#433912yes—
524C4⋊C4#434112yes—
525C22⋊C4—24no—
526C22⋊C4—22no—
527C22⋊C4—41no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—42no—
531C22⋊C4—81no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—42no—
539C42—81no—
540C42—442no—
541C11#2672811yescharacteristic, complemented, Sylow
542C23—22no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23C22×C22⋊D1111yescharacteristic
557Q8—441no—
558Q8—441no—
559Q8—441no—
560Q8—441no—
561D4—22no—
562D4—22no—
563D4—41no—
564D4—41no—
565D4—84no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—84no—
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×C4—441no—
606C2×C4#6700312yes—
607C2×C4C2×#433911yescharacteristic
608C2×C4C2×#433911yescharacteristic
609C2×C4C2×#434111yescharacteristic
610C2×C4#6703711yescharacteristic
611C2×C4#41×D1111yescharacteristic
612C2×C4#6704211yescharacteristic
613C8—441no—
614C8—441no—
615C8—441no—
616C8—441no—
617C22—41no—
618C22—41no—
619C22—42no—
620C22—41no—
621C22—42no—
622C22—41no—
623C22—41no—
624C22—42no—
625C22—41no—
626C22—41no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22#1062332211yescharacteristic
632C22#1062333711yescharacteristic
633C22C2×#6700311yescharacteristic
634C22#1062335311yescharacteristic
635C22#1062336011yescharacteristic
636C22#1062336711yescharacteristic
637C22#1062336711yescharacteristic
638C4—22no—
639C4—41no—
640C4—42no—
641C4—42no—
642C4—41no—
643C4—41no—
644C4—41no—
645C4—81no—
646C4—442no—
647C4—881no—
648C4—881no—
649C4—881no—
650C4#1062306911yescharacteristic
651C4#1062309011yescharacteristic
652C4#1062309111yescharacteristic
653C4#1062309411yescharacteristic
654C2—81no—
655C2—82no—
656C2#1307254711yescharacteristic
657C2#1307863411yescharacteristic
658C2#1307886811yescharacteristic
659C2#1308045111yescharacteristic
660C2#1308053811yescharacteristic
661C2#1308074211yescharacteristic
662C2#1308086311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2363C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2363D11
hypocenterC11#26728
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
1. #13072957C2semidirect
2. #13069933C2semidirect
4. #13069762C2semidirect
6. #13069573C2semidirect
7. #13069291C2semidirect
8. #13069250C2semidirect
9. #13069224C2semidirect
10. #13069198C2semidirect
11. #13068950C2semidirect
12. #13068928C2semidirect
13. #13068711C2semidirect
14. C4×#66896C2semidirect
541. C11#26728semidirect

Maximal subgroups

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

subgroupindex
#130729572
#130699332
#130698022
#130697622
#130696192
#130695732
#130692912
#130692502
#130692242
#130691982
#130689502
#130689282
#130687112
C4×#668962
C11×#23632
#2672811