Finite Group Databasebeta

← #14802007

Subgroups — #14802007

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622648C211yesmaximal, characteristic
2#13073070C211yesmaximal, characteristic, complemented
3#13071658C211yesmaximal, characteristic
4#13070095C211yesmaximal, characteristic, complemented
5#13070032C211yesmaximal, characteristic, complemented
6#13070007C211yesmaximal, characteristic, complemented
7#13069929C211yesmaximal, characteristic, complemented
8#13069385C211yesmaximal, characteristic, complemented
9#13069253C211yesmaximal, characteristic, complemented
10#13068952C211yesmaximal, characteristic, complemented
11#13068929C211yesmaximal, characteristic, complemented
12#13068794C211yesmaximal, characteristic, complemented
13#13068614C211yesmaximal, characteristic, complemented
14#13068333C211yesmaximal, characteristic, complemented
15C2×C11×#465C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C11×#465—24no—
24C2×C11×#106C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27#10622843C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31#10622834—21no—
32#10622834C2211yescharacteristic
33#10622833—21no—
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C4×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40#10622648—24no—
41#10622598C2211yescharacteristic
42#10622591—21no—
43#10622591—21no—
44#10622590C2211yescharacteristic
45#10622589C2211yescharacteristic
46C4⋊C4×Dic11C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622565—21no—
50#10622565—21no—
51#10622564—21no—
52C22⋊C4×Dic11—21no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C2×C11×SD16—22no—
67C2×C11×SD16—22no—
68C2×C11×SD16—41no—
69C22×C8×C11—22no—
70C22×C8×C11—22no—
71C22×C8×C11—41no—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—22no—
76C11×#121—22no—
77C11×#121D414yes—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11D411yescharacteristic
89C2×C22⋊Dic11D411yescharacteristic
90D4×Dic11—22no—
91D4×Dic11—41no—
92#66979—22no—
93#66979—22no—
94#66979—22no—
95#66979—41no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C11×#106—22no—
111C11×#103—22no—
112C11×#102—22no—
113#66899—22no—
114#66899—41no—
115#66896—22no—
116#66896—22no—
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⋊#95D411yescharacteristic
126C11⋊#95D411yescharacteristic
127C22⋊(C11⋊C8)—22no—
128Dic11⋊C8—22no—
129Dic11⋊C8—41no—
130#66872—22no—
131#66871—22no—
132#25205—111nomaximal, Sylow
133C24×C11—21no—
134C24×C11C2×D411yescharacteristic
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×D4×C11—24no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—81no—
148C2×D4×C11—81no—
149C2×D4×C11C2×D412yes—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11#4112yes—
160C22×C4×C11C2411yescharacteristic
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—42no—
166C22×Dic11—42no—
167C22×Dic11—81no—
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C11×SD16—44no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—44no—
179C2×C8×C11#4112yes—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4C2×D412yes—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—42no—
187C22⋊Dic11—22no—
188C22⋊Dic11—41no—
189C22⋊Dic11—42no—
190C22⋊Dic11—42no—
191C22⋊Dic11—42no—
192C22⋊Dic11—42no—
193C22⋊Dic11—81no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—81no—
202C4⋊Dic11#4112yes—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—42no—
210C4×Dic11—42no—
211C4×Dic11—81no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×#482—111no—
219C2×#465D1111yescharacteristic
220#2499—111no—
221#2363—111no—
222#2084—111no—
223#2073—111no—
224#2068—111no—
225#2055—111no—
226#1949—111no—
227#1927—111no—
228#1877—111no—
229#1873—111no—
230#1850—111no—
231#1802—111no—
232#1735—111no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—22no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11#12112yes—
247C23×C11C22×D411yescharacteristic
248Q8×C11—41no—
249Q8×C11—41no—
250Q8×C11—41no—
251Q8×C11—41no—
252D4×C11—22no—
253D4×C11—22no—
254D4×C11—41no—
255D4×C11—41no—
256D4×C11—84no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
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#12112yes—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C112−1+411yescharacteristic
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—22no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—84no—
303C2×Dic11#13512yes—
304C8×C11—22no—
305C8×C11—41no—
306C11⋊C8—41no—
307C11⋊C8—41no—
308C22×SD16C2×D1111yescharacteristic
309C23×C8C2×D1111yescharacteristic
310C2×C22⋊Q8C2×D1111yescharacteristic
311C2×#121C2×D1111yescharacteristic
312C2×C4×D4—111no—
313C2×#117—111no—
314C2×#117—111no—
315#482—224no—
316#465—24no—
317C2×#107—111no—
318C2×#106—111no—
319C2×#106C2×D1111yescharacteristic
320C2×C4⋊C8—111no—
321C2×C4⋊C8—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#103C2×D1111yescharacteristic
325C2×#102—111no—
326C2×#102—111no—
327C2×#102C2×D1111yescharacteristic
328C2×C22⋊C8—111no—
329#397—221no—
330#397—221no—
331#391—111no—
332#391—111no—
333#390—111no—
334#390—221no—
335#389—111no—
336#388—221no—
337#387—221no—
338#387—221no—
339#386—221no—
340#384—111no—
341#382—111no—
342C4×C4⋊C4—111no—
343C4×C22⋊C4—111no—
344C4×C22⋊C4—221no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#336—111no—
352#336—111no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11C2×#12111yescharacteristic
368C22×C11#54611yescharacteristic
369C22×C11#54711yescharacteristic
370C22×C11C2×#13511yescharacteristic
371C22×C11#57511yescharacteristic
372C22×C11#57711yescharacteristic
373C22×C11#57711yescharacteristic
374C4×C11—22no—
375C4×C11—42no—
376C4×C11—81no—
377C4×C11—81no—
378C4×C11#52911yescharacteristic
379C4×C11#53911yescharacteristic
380C4×C11#54611yescharacteristic
381C4×C11#54711yescharacteristic
382Dic11—22no—
383Dic11—41no—
384Dic11—41no—
385Dic11—42no—
386Dic11—41no—
387Dic11—81no—
388Dic11—81no—
389Dic11—81no—
390C22×Q8C22×D1111yescharacteristic
391C22×D4—21no—
392C22×D4C22×D1111yescharacteristic
393C23×C4—221no—
394C23×C4C22×D1111yescharacteristic
395C2×SD16—22no—
396C2×SD16—22no—
397C2×SD16—41no—
398C22×C8—22no—
399C22×C8—22no—
400C22×C8—41no—
401C22×C8—111no—
402C22×C8—111no—
403C22×C8C22×D1111yescharacteristic
404C22×C8C22×D1111yescharacteristic
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407#121—22no—
408#121C22⋊D1114yes—
409C4×D4—222no—
410C4×D4—441no—
411#117—222no—
412#117—222no—
413#117—222no—
414#117—441no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—111no—
428C2×C22⋊C4—111no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C42—111no—
435C2×C42—111no—
436C2×C42—221no—
437C2×C42—221no—
438C2×C42—221no—
439#107—222no—
440#106—22no—
441#106—222no—
442C4⋊C8—222no—
443C4⋊C8—441no—
444#103—22no—
445#103—222no—
446#103—441no—
447#102—22no—
448#102—222no—
449#102—222no—
450C22⋊C8—222no—
451#95—111no—
452#95—111no—
453#95—221no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461C2×C11—42no—
462C2×C11—82no—
463C2×C11#242511yescharacteristic
464C2×C11#303511yescharacteristic
465C2×C11#304211yescharacteristic
466C2×C11#329611yescharacteristic
467C2×C11#331711yescharacteristic
468C2×C11#334011yescharacteristic
469C2×C11#335011yescharacteristic
470C24—21no—
471C24D4×D1111yescharacteristic
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×D4—24no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—81no—
485C2×D4—81no—
486C2×D4C2×C22⋊D1112yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—111no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—442no—
503C22×C4—442no—
504C22×C4—881no—
505C22×C4D4×D1111yescharacteristic
506C22×C4#434112yes—
507C22×C4C2×C22⋊D1112yes—
508C22×C4C23×D1111yescharacteristic
509SD16—44no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—44no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8#434112yes—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—42no—
527C4⋊C4—112no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—442no—
536C4⋊C4—442no—
537C4⋊C4—881no—
538C4⋊C4C2×C22⋊D1112yes—
539C22⋊C4—24no—
540C22⋊C4—42no—
541C22⋊C4—222no—
542C22⋊C4—441no—
543C22⋊C4—442no—
544C22⋊C4—442no—
545C22⋊C4—442no—
546C22⋊C4—442no—
547C22⋊C4—881no—
548C42—221no—
549C42—221no—
550C42—221no—
551C42—221no—
552C42—442no—
553C42—442no—
554C42—881no—
555C11#2520511yescharacteristic, complemented, Sylow
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—22no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23#6699212yes—
570C23C2×D4×D1111yescharacteristic
571Q8—41no—
572Q8—41no—
573Q8—41no—
574Q8—41no—
575D4—22no—
576D4—22no—
577D4—41no—
578D4—41no—
579D4—84no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—112no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—222no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—884no—
620C2×C4#6699212yes—
621C2×C4C2×#434111yescharacteristic
622C2×C4C2×#434111yescharacteristic
623C2×C4#6703711yescharacteristic
624C2×C4#41×D1111yescharacteristic
625C2×C4#6704311yescharacteristic
626C2×C4C22×C22⋊D1111yescharacteristic
627C8—22no—
628C8—41no—
629C8—441no—
630C8—441no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22#1062314111yescharacteristic
646C22#1062314211yescharacteristic
647C22#1062329311yescharacteristic
648C22#1062329311yescharacteristic
649C22D11×#13511yescharacteristic
650C22#1062329911yescharacteristic
651C22C2×#6699211yescharacteristic
652C4—22no—
653C4—42no—
654C4—81no—
655C4—81no—
656C4—222no—
657C4—441no—
658C4—442no—
659C4—441no—
660C4—441no—
661C4—881no—
662C4—881no—
663C4—881no—
664C4#1062313111yescharacteristic
665C4#1062313311yescharacteristic
666C4#1062333711yescharacteristic
667C4#1062335511yescharacteristic
668C2—42no—
669C2—82no—
670C2#1307217311yescharacteristic
671C2#1307806711yescharacteristic
672C2#1307812511yescharacteristic
673C2#1308044611yescharacteristic
674C2#1308074811yescharacteristic
675C2#1308102411yescharacteristic
676C2#1308116711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#465C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenterC2×#465D11
hypocenterC11#25205
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
2. #13073070C2semidirect
4. #13070095C2semidirect
5. #13070032C2semidirect
6. #13070007C2semidirect
7. #13069929C2semidirect
8. #13069385C2semidirect
9. #13069253C2semidirect
10. #13068952C2semidirect
11. #13068929C2semidirect
12. #13068794C2semidirect
13. #13068614C2semidirect
14. #13068333C2semidirect
555. C11#25205semidirect

Maximal subgroups

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

subgroupindex
C2×#106226482
#130730702
#130716582
#130700952
#130700322
#130700072
#130699292
#130693852
#130692532
#130689522
#130689292
#130687942
#130686142
#130683332
C2×C11×#4652
#2520511