Finite Group Databasebeta

← #14776257

Subgroups — #14776257

Order 2816.

954 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622667C211yesmaximal, characteristic
2C2×#10622402C211yesmaximal, characteristic, complemented
3C2×#10622371C211yesmaximal, characteristic
4#13071691C211yesmaximal, characteristic
5#13071528C211yesmaximal, characteristic, complemented
6#13069377C211yesmaximal, characteristic, complemented
7#13069310C211yesmaximal, characteristic
8#13069289C211yesmaximal, characteristic, complemented
9#13068968C211yesmaximal, characteristic
10#13068954C211yesmaximal, characteristic, complemented
11#13068882C211yesmaximal, characteristic, complemented
12#13068875C211yesmaximal, characteristic
13#13068488C211yesmaximal, characteristic, complemented
14#13068447C211yesmaximal, characteristic, complemented
15C11×#1959C211yesmaximal, characteristic
16C2×C11×#124C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#97C2211yescharacteristic
29C11×#384C2211yescharacteristic
30#10622843C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622834C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622667C418yescomplemented
39#10622589—21no—
40C4⋊C4×Dic11—21no—
41#10622586C2211yescharacteristic
42#10622586C2211yescharacteristic
43#10622585—21no—
44#10622585—21no—
45C2×#66872C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47#10622564—21no—
48#10622564—21no—
49#10622563—21no—
50C22⋊C4×Dic11—21no—
51C4×C4⋊Dic11C2211yescharacteristic
52C4×C4⋊Dic11C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54#10622402—24no—
55#10622371—24no—
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×#124—22no—
69C11×#124C2×C414yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80Q8×Dic11—22no—
81Q8×Dic11—41no—
82C2×#4326—22no—
83C2×#4326—22no—
84C2×#4326C2×C414yescomplemented
85D4×Dic11—22no—
86D4×Dic11—41no—
87C2×#4324—22no—
88C2×#4324—22no—
89C2×#4324C2×C414yes—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11D411yescharacteristic
92C2×C4⋊Dic11D411yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—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
110#66940—22no—
111#66940—22no—
112#66940—41no—
113#66940—41no—
114C4×Dic22—22no—
115C4×Dic22C2×C414yescomplemented
116C11×#103—22no—
117C11×#103—41no—
118C11×#102—22no—
119C11×#102—41no—
120C11×#97—22no—
121#66899C2×C414yescomplemented
122#66896C2×C414yes—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95D411yescharacteristic
129C11⋊#95D411yescharacteristic
130#66880—22no—
131#66880D414yes—
132#66879—22no—
133C8×Dic11—22no—
134#66872—22no—
135#66872—22no—
136C4⋊(C11⋊C8)C2×C414yescomplemented
137#23013—111nomaximal, Sylow
138C24×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11C22×C412yes—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11C22×C412yes—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—42no—
162C22×Dic11—42no—
163C22×Dic11—81no—
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22C22×C412yes—
172C2×Dic22C2×D412yes—
173C2×Dic22#4112yes—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11C2×D412yes—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4—81no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—24no—
188C42×C11C22×C412yes—
189C42×C11#4112yes—
190C22⋊Dic11—42no—
191C22⋊Dic11—42no—
192C22⋊Dic11—81no—
193#4326—28no—
194#4324—28no—
195C4⋊Dic11—22no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—41no—
201C4⋊Dic11—42no—
202C4⋊Dic11C22×C412yes—
203C4⋊Dic11C2×D412yes—
204Dic11⋊C4—24no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207Dic11⋊C4—81no—
208Dic11⋊C4—81no—
209C4×Dic11—24no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—42no—
215C4×Dic11—42no—
216C4×Dic11—42no—
217C4×Dic11—81no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8C22×C412yes—
223C2×C11⋊C8C22×C412yes—
224C2×#464—111no—
225C2×#441—111no—
226C2×C4×SD16—111no—
227#2367—111no—
228Q8×C4⋊C4—111no—
229#1959D1111yescharacteristic
230#1948—111no—
231#1936—111no—
232#1933—111no—
233#1880—111no—
234#1878—111no—
235#1865—111no—
236#1864—111no—
237#1771—111no—
238#1763—111no—
239C23×C11—22no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11C22×D411yescharacteristic
247Q8×C11—22no—
248Q8×C11—22no—
249Q8×C11—41no—
250Q8×C11—41no—
251D4×C11—22no—
252D4×C11—22no—
253D4×C11—41no—
254D4×C11—41no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
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×C11C4×D412yes—
269C2×C4×C11C4×D412yes—
270C2×C4×C11C23×C411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C2×Dic11—22no—
277C2×Dic11—21no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—21no—
281C2×Dic11—22no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—84no—
300C2×Dic11#13712yes—
301Dic22—22no—
302Dic22—22no—
303Dic22—22no—
304Dic22C4×D414yes—
305C8×C11—22no—
306C8×C11—41no—
307C11⋊C8—22no—
308C11⋊C8—22no—
309C22×Q16—111no—
310C22×SD16—111no—
311C2×#124C2×D1111yescharacteristic
312C2×C4×Q8—111no—
313C2×C4×Q8—111no—
314C2×C4×Q8—111no—
315C2×C4×Q8—111no—
316C2×C4×D4—111no—
317#464—118no—
318#441—224no—
319C4×SD16—224no—
320C2×#106—111no—
321C2×#106—111no—
322C2×C4⋊C8—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#103—111no—
326C2×#103C2×D1111yescharacteristic
327C2×#103C2×D1111yescharacteristic
328C2×#102—111no—
329C2×#102C2×D1111yescharacteristic
330C2×#102C2×D1111yescharacteristic
331C2×#97—111no—
332C2×#97C2×D1111yescharacteristic
333C2×C4×C8—111no—
334#391—111no—
335#390—111no—
336#389—111no—
337#389—111no—
338#389—221no—
339#389—221no—
340#388—221no—
341#388—221no—
342#385—221no—
343#384—221no—
344#384C2×D1111yescharacteristic
345C4×C4⋊C4—111no—
346C4×C4⋊C4—111no—
347C4×C4⋊C4—221no—
348C4×C22⋊C4—221no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#336—111no—
354#336—111no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11—81no—
362C22×C11C2×C4×D411yescharacteristic
363C22×C11D4211yescharacteristic
364C22×C11#54811yescharacteristic
365C22×C11C2×#13711yescharacteristic
366C22×C11#57511yescharacteristic
367C22×C11#57711yescharacteristic
368C22×C11#57711yescharacteristic
369C4×C11—22no—
370C4×C11—22no—
371C4×C11—42no—
372C4×C11—81no—
373C4×C11—81no—
374C4×C11C2×C4×D411yescharacteristic
375C4×C11#52011yescharacteristic
376C4×C11#54711yescharacteristic
377C4×C11#55311yescharacteristic
378Dic11—24no—
379Dic11—22no—
380Dic11—42no—
381Dic11—41no—
382Dic11—42no—
383Dic11—41no—
384Dic11—41no—
385Dic11—81no—
386C22×Q8—111no—
387C22×Q8C22×D1111yescharacteristic
388C22×D4C22×D1111yescharacteristic
389C23×C4—221no—
390C2×Q16—114no—
391C2×Q16—222no—
392C2×Q16—222no—
393C2×SD16—114no—
394C2×SD16—222no—
395C2×SD16—222no—
396C22×C8—111no—
397C22×C8—111no—
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400#124—22no—
401#124C4×D1114yes—
402C4×Q8—114no—
403C4×Q8—222no—
404C4×Q8—222no—
405C4×Q8—222no—
406C4×Q8—222no—
407C4×Q8—441no—
408C4×Q8—441no—
409C4×Q8—441no—
410C4×D4—222no—
411C4×D4—441no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4C22×D1111yescharacteristic
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C42—111no—
433C2×C42—111no—
434C2×C42—221no—
435C2×C42—221no—
436C2×C42—221no—
437C2×C42—221no—
438C2×C42—221no—
439C2×C42C22×D1111yescharacteristic
440#106—222no—
441#106—222no—
442C4⋊C8—114no—
443#103—22no—
444#103—41no—
445#103—114no—
446#103—114no—
447#103—222no—
448#102—22no—
449#102—41no—
450#102—114no—
451#97—22no—
452#97—222no—
453C4×C8—222no—
454#95—111no—
455#95—111no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461C2×C11—82no—
462C2×C11#236111yescharacteristic
463C2×C11C4×#13711yescharacteristic
464C2×C11#295211yescharacteristic
465C2×C11#326611yescharacteristic
466C2×C11#327111yescharacteristic
467C2×C11#336911yescharacteristic
468C2×C11#337111yescharacteristic
469C24—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—112no—
476C2×Q8—112no—
477C2×Q8—112no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×Q8—221no—
481C2×Q8C2×C4×D1112yes—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4C2×C4×D1112yes—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4—881no—
502C22×C4D4×D1111yescharacteristic
503C22×C4D4×D1111yescharacteristic
504C22×C4C23×D1111yescharacteristic
505Q16—228no—
506SD16—228no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—112no—
513C2×C8—112no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8D4×D1112yes—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—42no—
524C4⋊C4—81no—
525C4⋊C4—112no—
526C4⋊C4—112no—
527C4⋊C4—222no—
528C4⋊C4—224no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—441no—
534C4⋊C4—442no—
535C4⋊C4—442no—
536C4⋊C4—442no—
537C4⋊C4—881no—
538C4⋊C4—881no—
539C22⋊C4—24no—
540C22⋊C4—24no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—881no—
544C42—224no—
545C42—221no—
546C42—221no—
547C42—221no—
548C42—221no—
549C42—442no—
550C42—442no—
551C42—442no—
552C42—881no—
553C42C2×C4×D1112yes—
554C42#434112yes—
555C11#2301311yescharacteristic, complemented, Sylow
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23C2×D4×D1111yescharacteristic
564Q8—22no—
565Q8—22no—
566Q8—41no—
567Q8—41no—
568Q8—114no—
569Q8—222no—
570Q8—222no—
571Q8—222no—
572D4—22no—
573D4—22no—
574D4—41no—
575D4—41no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—112no—
590C2×C4—221no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—221no—
594C2×C4—222no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—884no—
614C2×C4(C22⋊D11)⋊C412yes—
615C2×C4(C22⋊D11)⋊C412yes—
616C2×C4C22×C4×D1111yescharacteristic
617C2×C4C2×D4×D1111yescharacteristic
618C2×C4C2×#434111yescharacteristic
619C2×C4#6703711yescharacteristic
620C2×C4#41×D1111yescharacteristic
621C2×C4#6704311yescharacteristic
622C8—22no—
623C8—41no—
624C8—222no—
625C8—222no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22C2×(C22⋊D11)⋊C411yescharacteristic
634C22#1062320811yescharacteristic
635C22#1062324811yescharacteristic
636C22#1062330411yescharacteristic
637C22#1062330611yescharacteristic
638C22D11×#13711yescharacteristic
639C22#1062330911yescharacteristic
640C4—22no—
641C4—22no—
642C4—42no—
643C4—81no—
644C4—81no—
645C4—224no—
646C4—222no—
647C4—441no—
648C4—442no—
649C4—441no—
650C4—441no—
651C4—442no—
652C4—881no—
653C4C4×D4×D1111yescharacteristic
654C4#1062307711yescharacteristic
655C4#1062314211yescharacteristic
656C4#1062314511yescharacteristic
657C2—82no—
658C2#1307163711yescharacteristic
659C2#1307744011yescharacteristic
660C2#1307749511yescharacteristic
661C2#1308012511yescharacteristic
662C2#1308020011yescharacteristic
663C2#1308135311yescharacteristic
664C2#1308138311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1959C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1959D11
hypocenterC11#23013
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1959

Complements

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

NH ≅ G/Ntype
2. C2×#10622402C2semidirect
5. #13071528C2semidirect
6. #13069377C2semidirect
8. #13069289C2semidirect
10. #13068954C2semidirect
11. #13068882C2semidirect
13. #13068488C2semidirect
14. #13068447C2semidirect
38. #10622667C4semidirect
84. C2×#4326C2×C4semidirect
115. C4×Dic22C2×C4semidirect
121. #66899C2×C4semidirect
136. C4⋊(C11⋊C8)C2×C4semidirect
555. C11#23013semidirect

Maximal subgroups

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

subgroupindex
C2×#106226672
C2×#106224022
C2×#106223712
#130716912
#130715282
#130693772
#130693102
#130692892
#130689682
#130689542
#130688822
#130688752
#130684882
#130684472
C11×#19592
#2301311