Finite Group Databasebeta

← #14769165

Subgroups — #14769165

Order 2816.

1462 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623084C211yesmaximal, characteristic
2D4×#4318C211yesmaximal, characteristic, complemented
3C2×#10622745C212yesmaximal, complemented
4#13069456C211yesmaximal, characteristic, complemented
5#13069455C211yesmaximal, characteristic, complemented
6#13069079C212yesmaximal, complemented
7#13069077C212yesmaximal, complemented
8#13068609C211yesmaximal, characteristic, complemented
9#13068542C212yesmaximal, complemented
10C4×#66888C211yesmaximal, characteristic, complemented
11D4×C11×M16C211yesmaximal, characteristic, complemented
12C22×#4339C2212yes—
13C22×C11×M16C2212yes—
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66993C412yes—
16C2×#66983C2212yes—
17C22×#4318C2212yes—
18#10623084—21no—
19#10623084—22no—
20#10623084—21no—
21#10623084—21no—
22#10623084—22no—
23#10623084—21no—
24C2×#66946C412yes—
25C2×#66937C414yes—
26C2×#66927C2211yescharacteristic
27C2×C4×Dic22C2211yescharacteristic
28C11×#436—21no—
29C11×#435—22no—
30C8×D4×C11—21no—
31C11×#423C2211yescharacteristic
32C11×#407C2212yes—
33C4×C11×M16C2211yescharacteristic
34#10622820C2212yes—
35C2×#66888C2212yes—
36C2×#66888C2211yescharacteristic
37C2×#66888C2211yescharacteristic
38#10622745—28no—
39C2×#66887C2212yes—
40C2×#66887C2212yes—
41C2×#66887C2212yes—
42C2×#66887C2212yes—
43#10622625—21no—
44#10622624—22no—
45D4×C11⋊C8—21no—
46#10622537C2211yescharacteristic
47C4×#4318C2211yescharacteristic
48#10622192C2211yescharacteristic
49#10622192C2212yes—
50#10622192C2211yescharacteristic
51C22×D4×C11C2×C411yescharacteristic
52C23×C4×C11C2312yes—
53C22×C22⋊D11C2×C414yes—
54C22×C22⋊D11C2×C414yes—
55C2×#4339—22no—
56C2×#4339—22no—
57C2×#4339—22no—
58C2×#4339—22no—
59C2×#4339—24no—
60C2×#4339—24no—
61C2×#4339—42no—
62C2×#4339—42no—
63C22×D44C2×C412yes—
64C22×D44C2×C412yes—
65C22×D44C2312yes—
66C22×C4×D11C2×C414yes—
67C22×Dic22C2311yescharacteristic
68C2×C11×M16—22no—
69C2×C11×M16—24no—
70C2×C11×M16—42no—
71C2×C11×M16C2311yescharacteristic
72C2×C11×M16C2312yes—
73C2×C11×M16C2311yescharacteristic
74C22×C8×C11—22no—
75C4×D4×C11D411yescharacteristic
76C4×D4×C11D412yes—
77C4×D4×C11D411yescharacteristic
78C4×D4×C11D411yescharacteristic
79C4×D4×C11D412yes—
80C4×D4×C11D411yescharacteristic
81C2×C11×C4⋊C4C2×C411yescharacteristic
82C2×C11×C22⋊C4C2×C412yes—
83C2×C42×C11C2311yescharacteristic
84#66993—22no—
85#66993—22no—
86#66993—24no—
87#66983—22no—
88#66983—22no—
89#66983—22no—
90#66983—22no—
91C2×(C2×D11)⋊C4C2×C414yes—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4C2×C412yes—
94C2×C4×Dic11C2×C412yes—
95C2×#4318—22no—
96C2×#4318—24no—
97C2×#4318—42no—
98C2×#4318C2311yescharacteristic
99C2×#4318C2312yes—
100C2×#4318C2311yescharacteristic
101C22×C11⋊C8—22no—
102#66946—24no—
103#66946—22no—
104#66946—22no—
105#66937—24no—
106#66937—24no—
107#66937—24no—
108#66937—24no—
109#66927—21no—
110#66927—21no—
111#66927—21no—
112#66927—21no—
113C4×Dic22—21no—
114C4×Dic22—21no—
115C4×Dic22—21no—
116C4×Dic22—21no—
117C11×C4⋊C8—21no—
118C11×C4⋊C8—21no—
119C11×C22⋊C8—22no—
120C11×C22⋊C8—22no—
121C11×#97—21no—
122C4×C8×C11—21no—
123C22⋊(C11⋊C8)—22no—
124C22⋊(C11⋊C8)—22no—
125#66888—24no—
126#66888—22no—
127#66888D414yescomplemented
128#66887—24no—
129#66887—24no—
130#66887—42no—
131#66887—42no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)—21no—
134#66867—21no—
135C4×C11⋊C8—21no—
136#22412—111nomaximal, Sylow
137C24×C11C22×C412yes—
138C23×D11C22×C414yes—
139C2×D4×C11—42no—
140C2×D4×C11C22⋊C411yescharacteristic
141C2×D4×C11C22⋊C411yescharacteristic
142C2×D4×C11C22⋊C412yes—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C22×C412yes—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—28no—
156C2×C22⋊D11—24no—
157C2×C22⋊D11—24no—
158C2×C22⋊D11—24no—
159C2×C22⋊D11—24no—
160C2×C22⋊D11—44no—
161C2×C22⋊D11—84no—
162C22×Dic11C22×C412yes—
163C22×Dic11C22×C412yes—
164#4339—44no—
165#4339—44no—
166#4339—44no—
167#4339—44no—
168#4339—44no—
169#4339—44no—
170#4339—44no—
171#4339—44no—
172C2×D44—22no—
173C2×D44—22no—
174C2×D44—22no—
175C2×D44—22no—
176C2×D44—22no—
177C2×D44—22no—
178C2×D44—22no—
179C2×D44—22no—
180C2×D44—22no—
181C2×D44—22no—
182C2×D44—44no—
183C2×D44—82no—
184C2×C4×D11—28no—
185C2×C4×D11—24no—
186C2×C4×D11—24no—
187C2×C4×D11—44no—
188C2×Dic22—21no—
189C2×Dic22—21no—
190C2×Dic22—21no—
191C2×Dic22—21no—
192C2×Dic22C2×D412yes—
193C2×Dic22#4112yes—
194C11×M16—22no—
195C11×M16—21no—
196C11×M16—21no—
197C11×M16—21no—
198C11×M16—22no—
199C11×M16—44no—
200C11×M16C2×D412yes—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—22no—
204C2×C8×C11—44no—
205C11×C4⋊C4C22⋊C412yes—
206C11×C4⋊C4C22⋊C411yescharacteristic
207C11×C4⋊C4C22⋊C411yescharacteristic
208C11×C22⋊C4C22⋊C412yes—
209C11×C22⋊C4C22⋊C412yes—
210C11×C22⋊C4C22⋊C412yes—
211C11×C22⋊C4C22⋊C412yes—
212C42×C11C2×D411yescharacteristic
213C42×C11C2×D411yescharacteristic
214C42×C11C2×D411yescharacteristic
215C42×C11C2×D411yescharacteristic
216(C2×D11)⋊C4—24no—
217(C2×D11)⋊C4—24no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220Dic11⋊C4—22no—
221Dic11⋊C4—22no—
222C4×Dic11—22no—
223C4×Dic11—22no—
224#4318—22no—
225#4318—21no—
226#4318—21no—
227#4318—21no—
228#4318—22no—
229#4318—44no—
230#4318C2×D412yes—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—22no—
234C2×C11⋊C8—44no—
235C2×#550—111no—
236D4×M16—111no—
237D4×M16D1111yescharacteristic, complemented
238C2×#413—112no—
239#1965—111no—
240#1965—111no—
241#1900—112no—
242#1900—112no—
243#1801—111no—
244#1785—112no—
245C4×#101—111no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11C2×C22⋊C412yes—
251C23×C11C2×C22⋊C412yes—
252C23×C11C23×C411yescharacteristic
253C22×D11—24no—
254C22×D11—24no—
255C22×D11—24no—
256C22×D11—44no—
257C22×D11—44no—
258D4×C11—22no—
259D4×C11—22no—
260D4×C11—42no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—41no—
273C2×C4×C11C2×C22⋊C411yescharacteristic
274C2×C4×C11C2×C22⋊C411yescharacteristic
275C2×C4×C11C2×C22⋊C411yescharacteristic
276C2×C4×C11C2×C22⋊C412yes—
277C2×C4×C11C2×C22⋊C412yes—
278C2×C4×C11C2×C22⋊C411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C22⋊D11—48no—
286C22⋊D11—48no—
287C22⋊D11—84no—
288C22⋊D11—84no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—42no—
293C2×Dic11C4×D414yes—
294D44—44no—
295D44—42no—
296D44—42no—
297D44—42no—
298D44—42no—
299D44—44no—
300D44—82no—
301D44—82no—
302C4×D11—48no—
303C4×D11—48no—
304Dic22—22no—
305Dic22—22no—
306Dic22—22no—
307Dic22—22no—
308C8×C11—22no—
309C8×C11—42no—
310C8×C11—41no—
311C11⋊C8—22no—
312C11⋊C8—42no—
313C11⋊C8—41no—
314C22×#41—112no—
315C22×M16—112no—
316C22×M16C2×D1112yes—
317#550—221no—
318#550—222no—
319#550—221no—
320#550—221no—
321#550—222no—
322#550—221no—
323C2×#127—112no—
324C2×#127—111no—
325C2×#121—112no—
326C2×#121—114no—
327C2×C4×Q8—111no—
328C2×C4×D4—112no—
329C2×C4×D4C2×D1111yescharacteristic
330#436—21no—
331#436—221no—
332#435—22no—
333#435—222no—
334C8×D4—21no—
335C8×D4—221no—
336#423—111no—
337#423C2×D1111yescharacteristic
338#413—228no—
339C2×#101—111no—
340C2×#101—112no—
341C2×#101—111no—
342C2×#100—112no—
343C2×#100—112no—
344C2×#100—112no—
345C2×#100—112no—
346#407—112no—
347#407C2×D1112yes—
348C4×M16—111no—
349C4×M16C2×D1111yescharacteristic
350#343—112no—
351#343—111no—
352#343—111no—
353C22×C11—21no—
354C22×C11—21no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—82no—
362C22×C11—82no—
363C22×C11C22×C22⋊C411yescharacteristic
364C22×C11C2×C4×D411yescharacteristic
365C22×C11#51811yescharacteristic
366C2×D11—44no—
367C2×D11—44no—
368C2×D11—44no—
369C2×D11—84no—
370C2×D11—84no—
371C4×C11—22no—
372C4×C11—22no—
373C4×C11—21no—
374C4×C11—21no—
375C4×C11—21no—
376C4×C11#41312yescomplemented
377C4×C11D4211yescharacteristic
378C4×C11D4211yescharacteristic
379C4×C11#54611yescharacteristic
380C4×C11#54611yescharacteristic
381Dic11—24no—
382Dic11—42no—
383C2×#41—224no—
384C2×#41—224no—
385C2×#41—222no—
386C2×#41—222no—
387C2×#41—222no—
388C2×#41—222no—
389C2×#41—442no—
390C2×#41—442no—
391C22×Q8—111no—
392C22×D4—114no—
393C22×D4—114no—
394C22×D4—112no—
395C22×D4—112no—
396C22×D4—112no—
397C22×D4C4×D1111yescharacteristic
398C23×C4—114no—
399C23×C4C22×D1112yes—
400C2×M16—22no—
401C2×M16—24no—
402C2×M16—42no—
403C2×M16—111no—
404C2×M16—112no—
405C2×M16—111no—
406C2×M16—222no—
407C2×M16—224no—
408C2×M16—442no—
409C2×M16C22×D1112yes—
410C2×M16C22×D1111yescharacteristic
411C2×M16C22×D1111yescharacteristic
412C22×C8—22no—
413C22×C8—222no—
414#127—222no—
415#127—222no—
416#127—224no—
417#127—221no—
418#127—221no—
419#127—221no—
420#127—221no—
421#121—222no—
422#121—222no—
423#121—222no—
424#121—222no—
425#121—224no—
426#121—224no—
427#121—224no—
428#121—224no—
429C4×Q8—221no—
430C4×Q8—221no—
431C4×Q8—221no—
432C4×Q8—221no—
433C4×D4—224no—
434C4×D4—222no—
435C4×D4—222no—
436C4×D4D4411yescharacteristic
437C4×D4D4412yes—
438C4×D4D4411yescharacteristic
439C4×D4C22⋊D1111yescharacteristic
440C4×D4C22⋊D1112yes—
441C4×D4C22⋊D1111yescharacteristic
442C2×C4⋊C4—112no—
443C2×C4⋊C4—111no—
444C2×C4⋊C4C4×D1111yescharacteristic
445C2×C22⋊C4—114no—
446C2×C22⋊C4C4×D1112yes—
447C2×C42—112no—
448C2×C42C22×D1111yescharacteristic
449C4⋊C8—21no—
450C4⋊C8—21no—
451C4⋊C8—221no—
452C4⋊C8—221no—
453#101—114no—
454#101—222no—
455#101—224no—
456#100—224no—
457#100—224no—
458#100—442no—
459#100—442no—
460C22⋊C8—22no—
461C22⋊C8—22no—
462C22⋊C8—222no—
463C22⋊C8—222no—
464#97—21no—
465#97—221no—
466C4×C8—21no—
467C4×C8—221no—
468C2×C11—21no—
469C2×C11—21no—
470C2×C11—42no—
471C2×C11—42no—
472C2×C11D4×C22⋊C411yescharacteristic
473C2×C11C2×#41311yescharacteristic
474C2×C11#288811yescharacteristic
475D11—84no—
476C24—114no—
477C24C2×C4×D1112yes—
478#41—444no—
479#41—444no—
480#41—444no—
481#41—444no—
482#41—444no—
483#41—444no—
484#41—444no—
485#41—444no—
486C2×Q8—112no—
487C2×Q8—112no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×Q8—221no—
491C2×Q8—221no—
492C2×D4—42no—
493C2×D4—228no—
494C2×D4—224no—
495C2×D4—224no—
496C2×D4—224no—
497C2×D4—224no—
498C2×D4—222no—
499C2×D4—222no—
500C2×D4—222no—
501C2×D4—222no—
502C2×D4—222no—
503C2×D4—222no—
504C2×D4—222no—
505C2×D4—222no—
506C2×D4—222no—
507C2×D4—222no—
508C2×D4—444no—
509C2×D4—444no—
510C2×D4—882no—
511C2×D4—884no—
512C2×D4(C2×D11)⋊C411yescharacteristic
513C2×D4(C2×D11)⋊C411yescharacteristic
514C2×D4(C2×D11)⋊C412yes—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—112no—
520C22×C4—112no—
521C22×C4—228no—
522C22×C4—224no—
523C22×C4—224no—
524C22×C4—444no—
525C22×C4C2×C4×D1111yescharacteristic
526C22×C4C2×C4×D1112yes—
527C22×C4C2×C4×D1111yescharacteristic
528C22×C4C2×D4412yes—
529C22×C4C2×D4412yes—
530C22×C4C2×C22⋊D1112yes—
531C22×C4C2×C22⋊D1112yes—
532C22×C4C23×D1111yescharacteristic
533M16—21no—
534M16—22no—
535M16—22no—
536M16—21no—
537M16—21no—
538M16—44no—
539M16—112no—
540M16—221no—
541M16—222no—
542M16—221no—
543M16—221no—
544M16—222no—
545M16—444no—
546M16D4×D1112yes—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—22no—
550C2×C8—44no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8—222no—
554C2×C8—444no—
555C4⋊C4—222no—
556C4⋊C4—222no—
557C4⋊C4—221no—
558C4⋊C4—221no—
559C4⋊C4(C2×D11)⋊C412yes—
560C4⋊C4(C2×D11)⋊C411yescharacteristic
561C4⋊C4(C2×D11)⋊C411yescharacteristic
562C22⋊C4—224no—
563C22⋊C4—224no—
564C22⋊C4(C2×D11)⋊C412yes—
565C22⋊C4(C2×D11)⋊C412yes—
566C22⋊C4(C2×D11)⋊C412yes—
567C22⋊C4(C2×D11)⋊C412yes—
568C42—222no—
569C42—222no—
570C42C2×D4411yescharacteristic
571C42C2×D4411yescharacteristic
572C42C2×C22⋊D1111yescharacteristic
573C42C2×C22⋊D1111yescharacteristic
574C11#2241211yescharacteristic, complemented, Sylow
575C23—22no—
576C23—22no—
577C23—42no—
578C23—42no—
579C23—224no—
580C23—224no—
581C23—224no—
582C23—444no—
583C23—444no—
584C23C2×(C2×D11)⋊C412yes—
585C23C2×(C2×D11)⋊C412yes—
586C23C22×C4×D1111yescharacteristic
587Q8—222no—
588Q8—222no—
589Q8—222no—
590Q8—222no—
591D4—22no—
592D4—22no—
593D4—42no—
594D4—444no—
595D4—448no—
596D4—448no—
597D4—444no—
598D4—442no—
599D4—442no—
600D4—442no—
601D4—442no—
602D4—882no—
603D4—882no—
604D4—884no—
605D4—884no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—41no—
618C2×C4—114no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—448no—
623C2×C4—448no—
624C2×C4—442no—
625C2×C4C2×(C2×D11)⋊C411yescharacteristic
626C2×C4C2×(C2×D11)⋊C411yescharacteristic
627C2×C4C2×(C2×D11)⋊C411yescharacteristic
628C2×C4C2×(C2×D11)⋊C412yes—
629C2×C4C2×(C2×D11)⋊C412yes—
630C2×C4C2×(C2×D11)⋊C411yescharacteristic
631C2×C4C22×D4411yescharacteristic
632C2×C4C2×D4×D1111yescharacteristic
633C2×C4#6703711yescharacteristic
634C2×C4#41×D1111yescharacteristic
635C2×C4#6704211yescharacteristic
636C2×C4C22×C22⋊D1111yescharacteristic
637C8—22no—
638C8—42no—
639C8—41no—
640C8—222no—
641C8—442no—
642C8—441no—
643C22—21no—
644C22—21no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—82no—
652C22—82no—
653C22—444no—
654C22—444no—
655C22—444no—
656C22—884no—
657C22—884no—
658C22C4×D4×D1111yescharacteristic
659C22#1062307611yescharacteristic
660C22C22×(C2×D11)⋊C411yescharacteristic
661C4—22no—
662C4—22no—
663C4—21no—
664C4—21no—
665C4—21no—
666C4—224no—
667C4—442no—
668C4#1062274512yescomplemented
669C4D4×D4411yescharacteristic
670C4#1062308511yescharacteristic
671C4D4×C22⋊D1111yescharacteristic
672C4#1062336011yescharacteristic
673C2—21no—
674C2—21no—
675C2—42no—
676C2—42no—
677C2—884no—
678C2D4×(C2×D11)⋊C411yescharacteristic
679C2C2×#1062274511yescharacteristic
680C2#1307709411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×M16C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623084C2
cosocleC22×C4×C11C24
hypercenterD4×M16D11
hypocenterC11#22412
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. D4×#4318C2semidirect
3. C2×#10622745C2semidirect
4. #13069456C2semidirect
5. #13069455C2semidirect
6. #13069079C2semidirect
7. #13069077C2semidirect
8. #13068609C2semidirect
9. #13068542C2semidirect
10. C4×#66888C2semidirect
11. D4×C11×M16C2semidirect
127. #66888D4semidirect
237. D4×M16D11semidirect
376. C4×C11#413semidirect
574. C11#22412semidirect
668. C4#10622745semidirect

Maximal subgroups

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

subgroupindex
C2×#106230842
D4×#43182
C2×#106227452
#130694562
#130694552
#130690792
#130690772
#130686092
#130685422
C4×#668882
D4×C11×M162
#2241211