Finite Group Databasebeta

← #14776255

Subgroups — #14776255

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×#10622797C211yesmaximal, characteristic, complemented
2C2×SD16×Dic11C211yesmaximal, characteristic
3#13071691C211yesmaximal, characteristic
4Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
5#13069433C211yesmaximal, characteristic
6#13069380C211yesmaximal, characteristic, complemented
7#13069315C211yesmaximal, characteristic
8#13069294C211yesmaximal, characteristic, complemented
9#13068973C211yesmaximal, characteristic
10#13068959C211yesmaximal, characteristic, complemented
11#13068886C211yesmaximal, characteristic, complemented
12#13068879C211yesmaximal, characteristic
13#13068493C211yesmaximal, characteristic, complemented
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×Q8×Dic11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23C2×D4×Dic11C2211yescharacteristic
24C11×#464C418yescomplemented
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622834C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36#10622797—24no—
37SD16×Dic11—24no—
38C2×#66881C2211yescharacteristic
39C2×#66881C2211yescharacteristic
40C2×#66879C2211yescharacteristic
41C2×C8×Dic11C2211yescharacteristic
42#10622598—21no—
43#10622598—21no—
44#10622598C2211yescharacteristic
45#10622598C2211yescharacteristic
46#10622564—21no—
47#10622564—21no—
48#10622563—21no—
49C22⋊C4×Dic11—21no—
50#10622548—21no—
51#10622548C2211yescharacteristic
52C4×C4⋊Dic11—21no—
53C4×C4⋊Dic11C2211yescharacteristic
54C4×C4⋊Dic11C2211yescharacteristic
55C2×#66867C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C23×Dic11—21no—
66C2×C11×Q16—22no—
67C2×C11×Q16—22no—
68C2×C11×Q16C2×C414yescomplemented
69C2×C11×SD16—22no—
70C2×C11×SD16—22no—
71C2×C11×SD16C2×C414yes—
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×#124—22no—
75C11×#124C2×C414yes—
76C4×Q8×C11—22no—
77C4×Q8×C11C2×C414yescomplemented
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—22no—
89Q8×Dic11—22no—
90Q8×Dic11—41no—
91Q8×Dic11—41no—
92Q8×Dic11—41no—
93D4×Dic11—22no—
94D4×Dic11—41no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11D411yescharacteristic
103C2×C4⋊Dic11D411yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4×Dic11—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C11×C4⋊C8C2×C414yescomplemented
117C11×#103C2×C414yescomplemented
118C11×#102C2×C414yes—
119#66899—22no—
120#66899—22no—
121#66899—41no—
122#66899D414yes—
123#66896—22no—
124#66896—41no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95D411yescharacteristic
131C11⋊#95D411yescharacteristic
132#66881—22no—
133#66881—22no—
134#66879—22no—
135C8×Dic11—22no—
136#66867—22no—
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×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11C22×C412yes—
148C2×Q8×C11C22×C412yes—
149C2×Q8×C11C2×D412yes—
150C2×Q8×C11#4112yes—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11C22×C412yes—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2411yescharacteristic
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—42no—
168C22×Dic11—42no—
169C22×Dic11—81no—
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C11×Q16—28no—
175C11×SD16—28no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C22×C412yes—
181C2×C8×C11C22×C412yes—
182C11×C4⋊C4—24no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4C22×C412yes—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—24no—
187C42×C11—24no—
188C42×C11C22×C412yes—
189C42×C11#4112yes—
190C22⋊Dic11—42no—
191C22⋊Dic11—42no—
192C22⋊Dic11—81no—
193C4⋊Dic11—22no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—41no—
202C4⋊Dic11—42no—
203C4⋊Dic11—42no—
204C4⋊Dic11—42no—
205C4⋊Dic11—42no—
206C4⋊Dic11—81no—
207C4⋊Dic11—81no—
208C4⋊Dic11—81no—
209C4⋊Dic11C2×D412yes—
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⋊C8—21no—
223C2×C11⋊C8C2×D412yes—
224C2×#464D1111yescharacteristic
225C2×#441—111no—
226C2×C4×SD16—111no—
227#2367—111no—
228Q8×C4⋊C4—111no—
229#1959—111no—
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—22no—
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—41no—
253Q8×C11—41no—
254Q8×C11C4×D414yes—
255D4×C11—22no—
256D4×C11—22no—
257D4×C11—41no—
258D4×C11—41no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11C4×D412yes—
273C2×C4×C11C4×D412yes—
274C2×C4×C11C23×C411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C2×Dic11—21no—
281C2×Dic11—21no—
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—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—84no—
304C2×Dic11#13712yes—
305C8×C11—22no—
306C8×C11—22no—
307C11⋊C8—22no—
308C11⋊C8—41no—
309C22×Q16C2×D1111yescharacteristic
310C22×SD16C2×D1111yescharacteristic
311C2×#124C2×D1111yescharacteristic
312C2×C4×Q8—111no—
313C2×C4×Q8—111no—
314C2×C4×Q8—111no—
315C2×C4×Q8C2×D1111yescharacteristic
316C2×C4×D4—111no—
317#464Dic1118yescomplemented
318#441—224no—
319C4×SD16—224no—
320C2×#106—111no—
321C2×#106—111no—
322C2×C4⋊C8C2×D1111yescharacteristic
323C2×#103—111no—
324C2×#103—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103C2×D1111yescharacteristic
328C2×#102—111no—
329C2×#102—111no—
330C2×#102C2×D1111yescharacteristic
331C2×#97—111no—
332C2×#97—111no—
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—111no—
344#384—221no—
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—24no—
370C4×C11—22no—
371C4×C11—22no—
372C4×C11—42no—
373C4×C11—42no—
374C4×C11C2×C4×D411yescharacteristic
375C4×C11#52011yescharacteristic
376C4×C11#54711yescharacteristic
377C4×C11#55311yescharacteristic
378Dic11—22no—
379Dic11—41no—
380Dic11—42no—
381Dic11—41no—
382Dic11—41no—
383Dic11—81no—
384Dic11—81no—
385Dic11—81no—
386C22×Q8C22×D1111yescharacteristic
387C22×Q8C22×D1111yescharacteristic
388C22×D4C22×D1111yescharacteristic
389C23×C4—221no—
390C2×Q16—22no—
391C2×Q16—22no—
392C2×Q16C2×Dic1114yescomplemented
393C2×SD16—22no—
394C2×SD16—22no—
395C2×SD16C2×Dic1114yes—
396C22×C8—111no—
397C22×C8—111no—
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400#124—22no—
401#124C2×Dic1114yes—
402C4×Q8—22no—
403C4×Q8—222no—
404C4×Q8—222no—
405C4×Q8—222no—
406C4×Q8—441no—
407C4×Q8—441no—
408C4×Q8—441no—
409C4×Q8C2×Dic1114yescomplemented
410C4×D4—222no—
411C4×D4—441no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—111no—
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⋊C4—221no—
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—21no—
433C2×C42—111no—
434C2×C42—111no—
435C2×C42—221no—
436C2×C42—221no—
437C2×C42—221no—
438C2×C42—221no—
439C2×C42C22×D1111yescharacteristic
440#106—222no—
441#106—222no—
442C4⋊C8C2×Dic1114yescomplemented
443#103—114no—
444#103—222no—
445#103—222no—
446#103—441no—
447#103C2×Dic1114yescomplemented
448#102—222no—
449#102—441no—
450#102C2×Dic1114yes—
451#97—222no—
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—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8D4×D1112yes—
479C2×Q8#434112yes—
480C2×Q8C22×Dic1112yes—
481C2×Q8C22×Dic1112yes—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4C22×Dic1112yes—
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—28no—
506SD16—28no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—112no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8C22×Dic1112yes—
518C2×C8C22×Dic1112yes—
519C4⋊C4—24no—
520C4⋊C4—21no—
521C4⋊C4—112no—
522C4⋊C4—222no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—441no—
531C4⋊C4—442no—
532C4⋊C4—442no—
533C4⋊C4—442no—
534C4⋊C4—442no—
535C4⋊C4—881no—
536C4⋊C4—881no—
537C4⋊C4—881no—
538C4⋊C4C22×Dic1112yes—
539C22⋊C4—24no—
540C22⋊C4—24no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—881no—
544C42—24no—
545C42—221no—
546C42—221no—
547C42—221no—
548C42—221no—
549C42—442no—
550C42—442no—
551C42—442no—
552C42—881no—
553C42#434112yes—
554C42C22×Dic1112yes—
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—22no—
567Q8—22no—
568Q8—22no—
569Q8—41no—
570Q8—41no—
571Q8D4×Dic1114yes—
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—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—112no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—222no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
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×C4D4×Dic1112yes—
615C2×C4D4×Dic1112yes—
616C2×C4C2×D4×D1111yescharacteristic
617C2×C4C2×#434111yescharacteristic
618C2×C4C2×#434111yescharacteristic
619C2×C4#6704211yescharacteristic
620C2×C4#6704311yescharacteristic
621C2×C4C23×Dic1111yescharacteristic
622C8—22no—
623C8—22no—
624C8—222no—
625C8—441no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22#1062312911yescharacteristic
634C22#1062314011yescharacteristic
635C22#1062330111yescharacteristic
636C22#1062330111yescharacteristic
637C22D11×#13711yescharacteristic
638C22#1062330811yescharacteristic
639C22C2×D4×Dic1111yescharacteristic
640C4—24no—
641C4—22no—
642C4—22no—
643C4—42no—
644C4—42no—
645C4—222no—
646C4—441no—
647C4—442no—
648C4—441no—
649C4—441no—
650C4—881no—
651C4—881no—
652C4—881no—
653C4#1062314211yescharacteristic
654C4#1062314911yescharacteristic
655C4C2×D4×Dic1111yescharacteristic
656C4#1062335811yescharacteristic
657C2—82no—
658C2#1307163611yescharacteristic
659C2#137×Dic1111yescharacteristic
660C2#1307750011yescharacteristic
661C2#1308012111yescharacteristic
662C2#1308020711yescharacteristic
663C2#1308135111yescharacteristic
664C2#1308138111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#464C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC2×#464D11
hypocenterC11#23013
LCSG ▷ C2×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×#10622797C2semidirect
4. Q8×C4⋊Dic11C2semidirect
6. #13069380C2semidirect
8. #13069294C2semidirect
10. #13068959C2semidirect
11. #13068886C2semidirect
13. #13068493C2semidirect
14. #13068446C2semidirect
24. C11×#464C4semidirect
68. C2×C11×Q16C2×C4semidirect
77. C4×Q8×C11C2×C4semidirect
116. C11×C4⋊C8C2×C4semidirect
117. C11×#103C2×C4semidirect
317. #464Dic11semidirect
392. C2×Q16C2×Dic11semidirect
409. C4×Q8C2×Dic11semidirect
442. C4⋊C8C2×Dic11semidirect
447. #103C2×Dic11semidirect
555. C11#23013semidirect

Maximal subgroups

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

subgroupindex
C2×#106227972
C2×SD16×Dic112
#130716912
Q8×C4⋊Dic112
#130694332
#130693802
#130693152
#130692942
#130689732
#130689592
#130688862
#130688792
#130684932
#130684462
C2×C11×#4642
#2301311