Finite Group Databasebeta

← #14803873

Subgroups — #14803873

Order 2816.

824 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622668C211yesmaximal, characteristic
2#13073828C211yesmaximal, characteristic, complemented
3#13071691C211yesmaximal, characteristic
4#13070037C211yesmaximal, characteristic, complemented
5#13070032C211yesmaximal, characteristic
6#13069936C211yesmaximal, characteristic, complemented
7#13069929C211yesmaximal, characteristic
8#13069563C211yesmaximal, characteristic, complemented
9#13069337C211yesmaximal, characteristic, complemented
10#13068959C211yesmaximal, characteristic, complemented
11#13068952C211yesmaximal, characteristic
12#13068629C211yesmaximal, characteristic, complemented
13#13068624C211yesmaximal, characteristic
14#13068446C211yesmaximal, characteristic, complemented
15C2×C11×#464C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×D4×Dic11C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C11×#464—24no—
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27#10622843C2211yescharacteristic
28#10622843C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34#10622834C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39#10622668—24no—
40#10622599—21no—
41#10622599—21no—
42#10622590C2211yescharacteristic
43#10622590C2211yescharacteristic
44#10622564—21no—
45#10622564—21no—
46#10622563—21no—
47C22⋊C4×Dic11—21no—
48C4×C4⋊Dic11C2211yescharacteristic
49C4×C4⋊Dic11C2211yescharacteristic
50#10622542—21no—
51#10622542—21no—
52C2×#66867C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C22×Dic22—21no—
66C2×C11×Q16—22no—
67C2×C11×Q16—22no—
68C2×C11×Q16—41no—
69C2×C11×SD16—22no—
70C2×C11×SD16—22no—
71C2×C11×SD16—41no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×#124—22no—
75C11×#124D414yes—
76C4×Q8×C11—22no—
77C4×Q8×C11—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87Q8×Dic11—22no—
88Q8×Dic11—41no—
89D4×Dic11—22no—
90D4×Dic11—41no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11D411yescharacteristic
94C2×C4⋊Dic11D411yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66922—22no—
106#66922—22no—
107C11×C4⋊C8—22no—
108C11×#103—22no—
109C11×#102—22no—
110#66899—22no—
111#66899—22no—
112#66899—22no—
113#66899—22no—
114#66896—22no—
115#66896—22no—
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—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95D411yescharacteristic
128C11⋊#95D411yescharacteristic
129Dic11⋊C8—41no—
130Dic11⋊C8—41no—
131#66867—22no—
132#25337—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×C11C2×D412yes—
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×C11C2×D412yes—
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×Dic11—42no—
163C22×Dic11—42no—
164C22×Dic11—81no—
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C2×Dic22—42no—
170C2×Dic22—42no—
171C2×Dic22—42no—
172C11×Q16—44no—
173C11×SD16—44no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—42no—
183C11×C22⋊C4—24no—
184C11×C22⋊C4—24no—
185C42×C11—42no—
186C42×C11C2×D412yes—
187C42×C11#4112yes—
188C22⋊Dic11—42no—
189C22⋊Dic11—42no—
190C22⋊Dic11—81no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—41no—
199C4⋊Dic11—41no—
200C4⋊Dic11—42no—
201C4⋊Dic11—42no—
202C4⋊Dic11#4112yes—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—42no—
208C4×Dic11—81no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×#489—111no—
216C2×#464D1111yescharacteristic
217#2568—111no—
218#2367—111no—
219#2074—111no—
220#2073—111no—
221#2056—111no—
222#2055—111no—
223#1987—111no—
224#1940—111no—
225#1878—111no—
226#1877—111no—
227#1805—111no—
228#1804—111no—
229#1763—111no—
230C23×C11—22no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11C22×D411yescharacteristic
238Q8×C11—22no—
239Q8×C11—22no—
240Q8×C11—22no—
241Q8×C11—22no—
242Q8×C11—41no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11—41no—
246D4×C11—22no—
247D4×C11—22no—
248D4×C11—41no—
249D4×C11—41no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
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×C11—41no—
263C2×C4×C11#12112yes—
264C2×C4×C11#12112yes—
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×C4×C112−1+411yescharacteristic
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—22no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
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—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—84no—
296Dic22—84no—
297C8×C11—41no—
298C8×C11—41no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C22×Q16C2×D1111yescharacteristic
302C22×SD16C2×D1111yescharacteristic
303C2×C4⋊Q8—111no—
304C2×#124C2×D1111yescharacteristic
305C2×C4×Q8—111no—
306C2×C4×Q8C2×D1111yescharacteristic
307C2×C4×D4—111no—
308#489—224no—
309#464—24no—
310C2×C4⋊C8—111no—
311C2×C4⋊C8—111no—
312C2×C4⋊C8C2×D1111yescharacteristic
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103C2×D1111yescharacteristic
318C2×#102—111no—
319C2×#102—111no—
320C2×#102C2×D1111yescharacteristic
321C2×#97—111no—
322#400—221no—
323#400—221no—
324#391—111no—
325#391—111no—
326#391—111no—
327#391—221no—
328#391—221no—
329#390—111no—
330#388—221no—
331#388—221no—
332#385—221no—
333#382—111no—
334#382—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#340—111no—
343#340—111no—
344#336—111no—
345#336—111no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11C2×#12111yescharacteristic
354C22×C11#54611yescharacteristic
355C22×C11#54811yescharacteristic
356C22×C11#57511yescharacteristic
357C22×C11#57511yescharacteristic
358C22×C11#57711yescharacteristic
359C22×C11#57811yescharacteristic
360C4×C11—22no—
361C4×C11—22no—
362C4×C11—42no—
363C4×C11—42no—
364C4×C11—81no—
365C4×C11#52911yescharacteristic
366C4×C11#54211yescharacteristic
367C4×C11#54611yescharacteristic
368C4×C11#54711yescharacteristic
369Dic11—41no—
370Dic11—41no—
371Dic11—42no—
372Dic11—41no—
373Dic11—41no—
374Dic11—81no—
375Dic11—81no—
376Dic11—81no—
377C22×Q8—221no—
378C22×Q8C22×D1111yescharacteristic
379C22×Q8C22×D1111yescharacteristic
380C22×D4C22×D1111yescharacteristic
381C23×C4—221no—
382C2×Q16—22no—
383C2×Q16—22no—
384C2×Q16—41no—
385C2×SD16—22no—
386C2×SD16—22no—
387C2×SD16—41no—
388C22×C8—111no—
389C22×C8—111no—
390C22×C8C22×D1111yescharacteristic
391C22×C8C22×D1111yescharacteristic
392C4⋊Q8—222no—
393C4⋊Q8—222no—
394#124—22no—
395#124C22⋊D1114yes—
396C4×Q8—22no—
397C4×Q8—22no—
398C4×Q8—222no—
399C4×Q8—441no—
400C4×D4—222no—
401C4×D4—441no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C42—21no—
418C2×C42—111no—
419C2×C42—111no—
420C2×C42—221no—
421C2×C42—221no—
422C2×C42C22×D1111yescharacteristic
423C4⋊C8—22no—
424C4⋊C8—441no—
425C4⋊C8—441no—
426#103—22no—
427#103—222no—
428#103—222no—
429#103—222no—
430#103—222no—
431#102—22no—
432#102—222no—
433#102—222no—
434#97—222no—
435#95—111no—
436#95—111no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448C2×C11—82no—
449C2×C11#242711yescharacteristic
450C2×C11#304011yescharacteristic
451C2×C11#304611yescharacteristic
452C2×C11#331111yescharacteristic
453C2×C11#331311yescharacteristic
454C2×C11#337111yescharacteristic
455C2×C11#337711yescharacteristic
456C24—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—21no—
466C2×Q8—21no—
467C2×Q8—442no—
468C2×Q8—442no—
469C2×Q8—442no—
470C2×Q8#434112yes—
471C2×Q8C2×C22⋊D1112yes—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4C2×C22⋊D1112yes—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4—881no—
492C22×C4D4×D1111yescharacteristic
493C22×C4D4×D1111yescharacteristic
494C22×C4C23×D1111yescharacteristic
495Q16—44no—
496SD16—44no—
497C2×C8—21no—
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—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—42no—
512C4⋊C4—112no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—441no—
521C4⋊C4—441no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C22⋊C4—24no—
525C22⋊C4—24no—
526C22⋊C4—442no—
527C22⋊C4—442no—
528C22⋊C4—881no—
529C42—42no—
530C42—221no—
531C42—221no—
532C42—221no—
533C42—221no—
534C42—442no—
535C42—881no—
536C42#434112yes—
537C42C2×C22⋊D1112yes—
538C11#2533711yescharacteristic, complemented, Sylow
539C23—22no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23C2×D4×D1111yescharacteristic
547Q8—22no—
548Q8—22no—
549Q8—22no—
550Q8—22no—
551Q8—41no—
552Q8—41no—
553Q8—41no—
554Q8—41no—
555Q8—884no—
556D4—22no—
557D4—22no—
558D4—41no—
559D4—41no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—222no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—884no—
598C2×C4#6699212yes—
599C2×C4#6699212yes—
600C2×C4C2×#434111yescharacteristic
601C2×C4C2×#434111yescharacteristic
602C2×C4#6703711yescharacteristic
603C2×C4#41×D1111yescharacteristic
604C2×C4#6704311yescharacteristic
605C2×C4C22×C22⋊D1111yescharacteristic
606C8—41no—
607C8—41no—
608C8—441no—
609C8—441no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22#1062312911yescharacteristic
618C22#1062314311yescharacteristic
619C22#1062330111yescharacteristic
620C22#1062330211yescharacteristic
621C22#1062330811yescharacteristic
622C22#1062330811yescharacteristic
623C22C2×#6699211yescharacteristic
624C4—22no—
625C4—22no—
626C4—42no—
627C4—42no—
628C4—81no—
629C4—441no—
630C4—441no—
631C4—442no—
632C4—441no—
633C4—441no—
634C4—881no—
635C4—881no—
636C4—881no—
637C4#1062313111yescharacteristic
638C4#1062313411yescharacteristic
639C4#1062333711yescharacteristic
640C4#1062335511yescharacteristic
641C2—82no—
642C2#1307219511yescharacteristic
643C2#1307811211yescharacteristic
644C2#1307816411yescharacteristic
645C2#1308065911yescharacteristic
646C2#1308068911yescharacteristic
647C2#1308138111yescharacteristic
648C2#1308145511yescharacteristic
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#25337
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
2. #13073828C2semidirect
4. #13070037C2semidirect
6. #13069936C2semidirect
8. #13069563C2semidirect
9. #13069337C2semidirect
10. #13068959C2semidirect
12. #13068629C2semidirect
14. #13068446C2semidirect
538. C11#25337semidirect

Maximal subgroups

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

subgroupindex
C2×#106226682
#130738282
#130716912
#130700372
#130700322
#130699362
#130699292
#130695632
#130693372
#130689592
#130689522
#130686292
#130686242
#130684462
C2×C11×#4642
#2533711