Finite Group Databasebeta

← #14803329

Subgroups — #14803329

Order 2816.

800 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622443C211yesmaximal, characteristic, complemented
2#13074105C211yesmaximal, characteristic
3#13073978C211yesmaximal, characteristic, complemented
4#13070002C211yesmaximal, characteristic
5#13069995C211yesmaximal, characteristic, complemented
6#13069936C211yesmaximal, characteristic, complemented
7#13069929C211yesmaximal, characteristic
8#13069478C211yesmaximal, characteristic, complemented
9#13069472C211yesmaximal, characteristic
10#13069428C211yesmaximal, characteristic
11#13069386C211yesmaximal, characteristic, complemented
12#13069296C211yesmaximal, characteristic
13#13069289C211yesmaximal, characteristic, complemented
14C4×#66899C211yesmaximal, characteristic, complemented
15C2×C11×#464C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C11×#464—24no—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25#10622843C2211yescharacteristic
26#10622843C2211yescharacteristic
27#10622843C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622834C2211yescharacteristic
34#10622834C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66882C2211yescharacteristic
38C2×#66881C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×C8×Dic11C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43#10622599—21no—
44#10622592—21no—
45#10622586C2211yescharacteristic
46#10622586C2211yescharacteristic
47#10622566—21no—
48#10622560—21no—
49#10622558—21no—
50#10622558—21no—
51#10622549C2211yescharacteristic
52C4×C4⋊Dic11C2211yescharacteristic
53#10622546—21no—
54#10622546—21no—
55C2×C4×C11⋊C8C2211yescharacteristic
56#10622443—24no—
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C22×Dic22D411yescharacteristic
65C2×C11×Q16—22no—
66C2×C11×Q16—22no—
67C2×C11×Q16—41no—
68C2×C11×SD16—22no—
69C2×C11×SD16—22no—
70C2×C11×SD16—41no—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#124—22no—
74C11×#124—22no—
75C4×Q8×C11—22no—
76C4×Q8×C11—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C4⋊Dic11D411yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4D411yescharacteristic
95C2×Dic11⋊C4D411yescharacteristic
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C4×Dic22—22no—
102C4×Dic22—22no—
103C11×C4⋊C8D414yes—
104C11×#103—22no—
105C11×#102—22no—
106#66899—22no—
107#66899—22no—
108#66899—22no—
109#66899—41no—
110#66896—22no—
111#66896—41no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125#66882—41no—
126#66881—41no—
127Dic11⋊C8—22no—
128Dic11⋊C8—22no—
129C8×Dic11—22no—
130C8×Dic11—22no—
131C4×C11⋊C8—22no—
132#25297—111nomaximal, Sylow
133C24×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11#4112yes—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C2×Dic22—22no—
167C2×Dic22—22no—
168C2×Dic22—22no—
169C11×Q16—44no—
170C11×SD16—44no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11C2×D412yes—
176C2×C8×C11C2×D412yes—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—42no—
180C11×C22⋊C4—42no—
181C11×C22⋊C4—42no—
182C42×C11—42no—
183C42×C11C2×D412yes—
184C42×C11#4112yes—
185C22⋊Dic11—42no—
186C22⋊Dic11—42no—
187C22⋊Dic11—81no—
188C22⋊Dic11—81no—
189C4⋊Dic11—22no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198Dic11⋊C4—22no—
199Dic11⋊C4—22no—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
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#4112yes—
213C2×#464D1111yescharacteristic
214C2×C8×Q8—111no—
215#2592—111no—
216#2581—111no—
217#2067—111no—
218#2066—111no—
219#2056—111no—
220#2055—111no—
221#1969—111no—
222#1968—111no—
223#1958—111no—
224#1949—111no—
225#1934—111no—
226#1933—111no—
227C4×#103—111no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11C22×D411yescharacteristic
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—41no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
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#12112yes—
262C2×C4×C11#12112yes—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×C4×C112−1+411yescharacteristic
269C2×Dic11—21no—
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—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
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#13512yes—
292C2×Dic11#13512yes—
293Dic22—28no—
294C8×C11—22no—
295C8×C11—22no—
296C11⋊C8—22no—
297C11⋊C8—41no—
298C22×Q16C2×D1111yescharacteristic
299C22×SD16C2×D1111yescharacteristic
300C2×#124C2×D1111yescharacteristic
301C2×C4×Q8—111no—
302C2×C4×Q8C2×D1111yescharacteristic
303#464—24no—
304C8×Q8—224no—
305C2×#107—111no—
306C2×#106—111no—
307C2×C4⋊C8—111no—
308C2×C4⋊C8—111no—
309C2×C4⋊C8C2×D1111yescharacteristic
310C2×#103—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103C2×D1111yescharacteristic
315C2×#102—111no—
316C2×#102—111no—
317C2×#102C2×D1111yescharacteristic
318C2×C4×C8—111no—
319C2×C4×C8—111no—
320C2×C4×C8—111no—
321#400—221no—
322#397—221no—
323#395—221no—
324#393—221no—
325#391—111no—
326#391—111no—
327#391—111no—
328#391—111no—
329#390—111no—
330#390—111no—
331#389—111no—
332#389—111no—
333#388—221no—
334#388—221no—
335#387—221no—
336#387—221no—
337#382—111no—
338C4×C4⋊C4—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11C2×#12111yescharacteristic
351C22×C11#54811yescharacteristic
352C22×C11#55011yescharacteristic
353C22×C11C2×#13511yescharacteristic
354C22×C11C2×#13511yescharacteristic
355C22×C11#57711yescharacteristic
356C22×C11#57811yescharacteristic
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—42no—
360C4×C11—81no—
361C4×C11—81no—
362C4×C11#52911yescharacteristic
363C4×C11#54211yescharacteristic
364C4×C11#54611yescharacteristic
365C4×C11#54811yescharacteristic
366Dic11—22no—
367Dic11—22no—
368Dic11—41no—
369Dic11—41no—
370Dic11—81no—
371Dic11—81no—
372Dic11—81no—
373Dic11—81no—
374C22×Q8—111no—
375C22×Q8C22×D1111yescharacteristic
376C22×Q8C22×D1111yescharacteristic
377C22×D4C22×D1111yescharacteristic
378C2×Q16—22no—
379C2×Q16—22no—
380C2×Q16—41no—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—41no—
384C22×C8—111no—
385C22×C8—111no—
386C22×C8C22×D1111yescharacteristic
387C22×C8C22×D1111yescharacteristic
388#124—22no—
389#124—22no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—222no—
393C4×Q8—222no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C42—21no—
412C2×C42—111no—
413C2×C42—111no—
414C2×C42—221no—
415C2×C42C22×D1111yescharacteristic
416#107—441no—
417#106—441no—
418C4⋊C8—222no—
419C4⋊C8—222no—
420C4⋊C8C22⋊D1114yes—
421#103—22no—
422#103—222no—
423#103—222no—
424#103—222no—
425#103—441no—
426#102—22no—
427#102—222no—
428#102—441no—
429C4×C8—222no—
430C4×C8—222no—
431C4×C8—222no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445C2×C11—161no—
446C2×C11#242611yescharacteristic
447C2×C11#305011yescharacteristic
448C2×C11#306311yescharacteristic
449C2×C11#336411yescharacteristic
450C2×C11#336511yescharacteristic
451C2×C11#339311yescharacteristic
452C2×C11#339411yescharacteristic
453C24—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—222no—
466C2×Q8—222no—
467C2×Q8—222no—
468C2×Q8#434112yes—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4D4×D1111yescharacteristic
487C22×C4D4×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489Q16—44no—
490SD16—44no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—112no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8C2×C22⋊D1112yes—
502C2×C8C2×C22⋊D1112yes—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—42no—
506C4⋊C4—222no—
507C4⋊C4—222no—
508C4⋊C4—222no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—442no—
518C4⋊C4—442no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C22⋊C4—442no—
522C22⋊C4—442no—
523C22⋊C4—881no—
524C22⋊C4—881no—
525C42—42no—
526C42—221no—
527C42—221no—
528C42—221no—
529C42—221no—
530C42—881no—
531C42#434112yes—
532C42C2×C22⋊D1112yes—
533C11#2529711yescharacteristic, complemented, Sylow
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23C2×D4×D1111yescharacteristic
542Q8—22no—
543Q8—22no—
544Q8—41no—
545Q8—41no—
546Q8—41no—
547Q8—41no—
548Q8—41no—
549Q8—41no—
550Q8—228no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—112no—
569C2×C4—112no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4#6699112yes—
593C2×C4#6699112yes—
594C2×C4C2×#434111yescharacteristic
595C2×C4C2×#434111yescharacteristic
596C2×C4#6703711yescharacteristic
597C2×C4#41×D1111yescharacteristic
598C2×C4#6704311yescharacteristic
599C2×C4C22×C22⋊D1111yescharacteristic
600C8—22no—
601C8—22no—
602C8—222no—
603C8—441no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22#1062312911yescharacteristic
612C22#1062313011yescharacteristic
613C22D11×#13511yescharacteristic
614C22D11×#13511yescharacteristic
615C22#1062330911yescharacteristic
616C22#1062331011yescharacteristic
617C22C2×#6699111yescharacteristic
618C4—22no—
619C4—22no—
620C4—42no—
621C4—81no—
622C4—81no—
623C4—222no—
624C4—222no—
625C4—441no—
626C4—441no—
627C4—881no—
628C4—881no—
629C4—881no—
630C4—881no—
631C4#1062313111yescharacteristic
632C4#1062313411yescharacteristic
633C4#1062333711yescharacteristic
634C4#1062336211yescharacteristic
635C2—161no—
636C2#1307217811yescharacteristic
637C2#1307819311yescharacteristic
638C2#1307830111yescharacteristic
639C2#1308129611yescharacteristic
640C2#1308130711yescharacteristic
641C2#1308159911yescharacteristic
642C2#1308160711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#464C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#464D11
hypocenterC11#25297
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#10622443C2semidirect
3. #13073978C2semidirect
5. #13069995C2semidirect
6. #13069936C2semidirect
8. #13069478C2semidirect
11. #13069386C2semidirect
13. #13069289C2semidirect
14. C4×#66899C2semidirect
533. C11#25297semidirect

Maximal subgroups

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

subgroupindex
C2×#106224432
#130741052
#130739782
#130700022
#130699952
#130699362
#130699292
#130694782
#130694722
#130694282
#130693862
#130692962
#130692892
C4×#668992
C2×C11×#4642
#2529711