Finite Group Databasebeta

← #14776256

Subgroups — #14776256

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×#10622798C211yesmaximal, characteristic
2C2×#10622401C211yesmaximal, characteristic
3#13071683C211yesmaximal, characteristic
4Q8×Dic11⋊C4C211yesmaximal, characteristic, complemented
5#13069429C211yesmaximal, characteristic
6#13069376C211yesmaximal, characteristic, complemented
7#13069313C211yesmaximal, characteristic
8#13069289C211yesmaximal, characteristic, complemented
9#13068971C211yesmaximal, characteristic
10#13068959C211yesmaximal, characteristic, complemented
11#13068884C211yesmaximal, characteristic, complemented
12#13068874C211yesmaximal, characteristic
13#13068492C211yesmaximal, characteristic, complemented
14#13068448C211yesmaximal, characteristic, complemented
15C2×C11×#441C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#67000C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C2×#66946C2211yescharacteristic
24C11×#441—24no—
25C2×C11×#106C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C11×#97C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33#10622798C418yescomplemented
34C2×#66885C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39#10622603—21no—
40#10622602—21no—
41#10622589—21no—
42#10622589C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44#10622586—21no—
45#10622586C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48#10622553—21no—
49#10622552C2211yescharacteristic
50C4×(C2×D11)⋊C4—21no—
51C4×Dic11⋊C4—21no—
52C4×Dic11⋊C4C2211yescharacteristic
53#10622541—21no—
54#10622541C2211yescharacteristic
55#10622401—24no—
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C2×C11×Q16—22no—
67C2×C11×Q16—22no—
68C2×C11×Q16C2×C414yescomplemented
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C4×Q8×C11—22no—
72C4×Q8×C11—22no—
73C4×Q8×C11—41no—
74C4×Q8×C11—41no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82#67000—22no—
83#67000C2×C414yes—
84Q8×Dic11—22no—
85Q8×Dic11—22no—
86Q8×Dic11—41no—
87Q8×Dic11C2×C414yescomplemented
88C2×#4325—22no—
89C2×#4325—22no—
90C2×#4325C2×C414yes—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4D411yescharacteristic
106C2×Dic11⋊C4D411yescharacteristic
107C2×C4×Dic11—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11C2311yescharacteristic
111C2×C4×Dic11C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114#66946—22no—
115#66946—41no—
116C11×#106—22no—
117C11×#103—22no—
118C11×#103D414yes—
119C11×#97—22no—
120#66899—22no—
121#66899—41no—
122#66899C2×C414yescomplemented
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95D411yescharacteristic
129C11⋊#95D411yescharacteristic
130#66885—22no—
131#66885C2×C414yes—
132#66879—22no—
133Dic11⋊C8C2×C414yescomplemented
134C8×Dic11—22no—
135#66873—41no—
136#66872—22no—
137#23013—111nomaximal, Sylow
138C23×D11—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—
151C22×C4×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×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44C22×C412yes—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—81no—
174C11×Q16—28no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11C22×C412yes—
180C2×C8×C11C2×D412yes—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4—42no—
186C11×C4⋊C4C2×D412yes—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—42no—
190C42×C11—42no—
191#4325—28no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—24no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—81no—
197C4⋊Dic11—24no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—42no—
204C4⋊Dic11C22×C412yes—
205Dic11⋊C4—22no—
206Dic11⋊C4—41no—
207Dic11⋊C4—42no—
208Dic11⋊C4—81no—
209Dic11⋊C4—81no—
210Dic11⋊C4—81no—
211C4×Dic11—24no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—42no—
215C4×Dic11—81no—
216C4×Dic11C22×C412yes—
217C4×Dic11#4112yes—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8C22×C412yes—
224C2×#464—111no—
225C2×#441D1111yescharacteristic, complemented
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×C11C22×D411yescharacteristic
240C22×D11—22no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247Q8×C11—22no—
248Q8×C11—22no—
249Q8×C11—22no—
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—41no—
253Q8×C11—41no—
254Q8×C11C4×D414yes—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
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—41no—
273C2×C4×C11C23×C411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
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—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11C4×D412yes—
298C2×Dic11C4×D412yes—
299C2×Dic11#13712yes—
300D44—22no—
301D44—22no—
302D44—41no—
303D44—41no—
304C4×D11—84no—
305C8×C11—22no—
306C8×C11—22no—
307C11⋊C8—22no—
308C11⋊C8—41no—
309C22×Q16C2×D1111yescharacteristic
310C22×SD16—111no—
311C2×#124—111no—
312C2×C4×Q8—111no—
313C2×C4×Q8—111no—
314C2×C4×Q8C2×D1111yescharacteristic
315C2×C4×Q8C2×D1111yescharacteristic
316C2×C4×D4—111no—
317#464—118no—
318#441—24no—
319C4×SD16—224no—
320C2×#106—111no—
321C2×#106C2×D1111yescharacteristic
322C2×C4⋊C8—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#103—111no—
326C2×#103C2×D1111yescharacteristic
327C2×#103C2×D1111yescharacteristic
328C2×#102—111no—
329C2×#102—111no—
330C2×#102—111no—
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—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×C11C2×C4×D411yescharacteristic
356C22×C11D4211yescharacteristic
357C22×C11#54811yescharacteristic
358C22×C11C2×#13711yescharacteristic
359C22×C11#57511yescharacteristic
360C22×C11#57711yescharacteristic
361C22×C11#57711yescharacteristic
362C2×D11—42no—
363C2×D11—42no—
364C2×D11—42no—
365C2×D11—81no—
366C2×D11—81no—
367C2×D11—81no—
368C2×D11—81no—
369C4×C11—24no—
370C4×C11—42no—
371C4×C11—41no—
372C4×C11—42no—
373C4×C11—41no—
374C4×C11—81no—
375C4×C11C2×C4×D411yescharacteristic
376C4×C11#52011yescharacteristic
377C4×C11#54711yescharacteristic
378C4×C11#55311yescharacteristic
379Dic11—22no—
380Dic11—22no—
381Dic11—22no—
382Dic11—42no—
383Dic11—41no—
384Dic11—81no—
385Dic11—81no—
386C22×Q8C22×D1111yescharacteristic
387C22×Q8C22×D1111yescharacteristic
388C22×D4—111no—
389C23×C4—221no—
390C2×Q16—22no—
391C2×Q16—22no—
392C2×Q16C4×D1114yescomplemented
393C2×SD16—114no—
394C2×SD16—222no—
395C2×SD16—222no—
396C22×C8—111no—
397C22×C8—111no—
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400#124—114no—
401#124—222no—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8—41no—
405C4×Q8—41no—
406C4×Q8—114no—
407C4×Q8—222no—
408C4×Q8—222no—
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—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—111no—
435C2×C42—111no—
436C2×C42—221no—
437C2×C42—221no—
438C2×C42—221no—
439C2×C42C22×D1111yescharacteristic
440#106—22no—
441#106—222no—
442C4⋊C8—114no—
443#103—22no—
444#103—114no—
445#103—222no—
446#103—441no—
447#103C22⋊D1114yes—
448#102—114no—
449#102—222no—
450#102—441no—
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#236111yescharacteristic
462C2×C11C4×#13711yescharacteristic
463C2×C11#295211yescharacteristic
464C2×C11#326611yescharacteristic
465C2×C11#327111yescharacteristic
466C2×C11#336911yescharacteristic
467C2×C11#337111yescharacteristic
468D11—82no—
469C24—221no—
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×Q8C2×C4×D1112yes—
479C2×Q8C2×C4×D1112yes—
480C2×Q8#433912yes—
481C2×Q8C2×C22⋊D1112yes—
482C2×D4—112no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C2×D4—221no—
487C2×D4—221no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—111no—
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—228no—
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×C8C2×C4×D1112yes—
518C2×C8C2×C22⋊D1112yes—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4—112no—
525C4⋊C4—222no—
526C4⋊C4—224no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—441no—
533C4⋊C4—442no—
534C4⋊C4—442no—
535C4⋊C4—881no—
536C4⋊C4—881no—
537C4⋊C4—881no—
538C4⋊C4C2×C22⋊D1112yes—
539C22⋊C4—224no—
540C22⋊C4—224no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—881no—
544C42—21no—
545C42—21no—
546C42—42no—
547C42—42no—
548C42—112no—
549C42—112no—
550C42—224no—
551C42—221no—
552C42—221no—
553C42—442no—
554C42—881no—
555C11#2301311yescharacteristic, complemented, Sylow
556C23—222no—
557C23—441no—
558C23—441no—
559C23—441no—
560C23—441no—
561C23—441no—
562C23—441no—
563C23C2×D4×D1111yescharacteristic
564Q8—22no—
565Q8—22no—
566Q8—22no—
567Q8—22no—
568Q8—22no—
569Q8—41no—
570Q8—41no—
571Q8C4×C22⋊D1114yes—
572D4—222no—
573D4—222no—
574D4—441no—
575D4—441no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
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—112no—
595C2×C4—112no—
596C2×C4—112no—
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—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—884no—
616C2×C4C22×C4×D1111yescharacteristic
617C2×C4C2×#433911yescharacteristic
618C2×C4#6703711yescharacteristic
619C2×C4#41×D1111yescharacteristic
620C2×C4#6704311yescharacteristic
621C2×C4C22×C22⋊D1111yescharacteristic
622C8—22no—
623C8—22no—
624C8—222no—
625C8—441no—
626C22—442no—
627C22—442no—
628C22—442no—
629C22—881no—
630C22—881no—
631C22—881no—
632C22—881no—
633C22C4×D4×D1111yescharacteristic
634C22#1062308311yescharacteristic
635C22D11×#13711yescharacteristic
636C22#1062330811yescharacteristic
637C22#1062330911yescharacteristic
638C22#1062330911yescharacteristic
639C22D4×C22⋊D1111yescharacteristic
640C4—24no—
641C4—42no—
642C4—41no—
643C4—42no—
644C4—41no—
645C4—81no—
646C4—222no—
647C4—222no—
648C4—222no—
649C4—441no—
650C4—442no—
651C4—881no—
652C4—881no—
653C4#1062307111yescharacteristic
654C4#1062307711yescharacteristic
655C4C2×C4×C22⋊D1111yescharacteristic
656C4#1062335511yescharacteristic
657C2—882no—
658C2#1307163311yescharacteristic
659C2#1307743211yescharacteristic
660C2#1307749611yescharacteristic
661C2#1308012011yescharacteristic
662C2#1308019511yescharacteristic
663C2#1308135711yescharacteristic
664C2#1308138511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#441C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenterC2×#441D11
hypocenterC11#23013
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
4. Q8×Dic11⋊C4C2semidirect
6. #13069376C2semidirect
8. #13069289C2semidirect
10. #13068959C2semidirect
11. #13068884C2semidirect
13. #13068492C2semidirect
14. #13068448C2semidirect
15. C2×C11×#441C2semidirect
33. #10622798C4semidirect
68. C2×C11×Q16C2×C4semidirect
87. Q8×Dic11C2×C4semidirect
122. #66899C2×C4semidirect
133. Dic11⋊C8C2×C4semidirect
225. C2×#441D11semidirect
392. C2×Q16C4×D11semidirect
555. C11#23013semidirect

Maximal subgroups

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

subgroupindex
C2×#106227982
C2×#106224012
#130716832
Q8×Dic11⋊C42
#130694292
#130693762
#130693132
#130692892
#130689712
#130689592
#130688842
#130688742
#130684922
#130684482
C2×C11×#4412
#2301311