Finite Group Databasebeta

← #15638648

Subgroups — #15638648

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082419C211yesmaximal, characteristic, complemented
2#13080727C218yesmaximal, complemented
3#13080182C218yesmaximal, complemented
4#13079619C212yesmaximal, complemented
5#13079437C212yesmaximal, complemented
6#13079373C212yesmaximal, complemented
7#13078746C212yesmaximal, complemented
8#13077876C212yesmaximal, complemented
9C2×#10622841C212yesmaximal, complemented
10#13077645C211yesmaximal, characteristic, complemented
11C2×C11×#548C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C23×Q8×C11C2211yescharacteristic
14C11×#548—24no—
15C11×#548C2218yes—
16C2×C11×#124—21no—
17C2×C11×#124C2211yescharacteristic
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C11×#121—21no—
21C2×C11×#121C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C2×#67004C2214yescomplemented
26C22×#4326C2214yescomplemented
27#10623329—21no—
28C2×#66977C2212yes—
29C2×#66977C2212yes—
30#10623074C2214yescomplemented
31#10623070—24no—
32D4×Dic22C2214yescomplemented
33#10623031—21no—
34#10623014—21no—
35#10623014—21no—
36#10623001C2212yes—
37#10622852C2218yescomplemented
38#10622845C2214yescomplemented
39#10622841C2214yes—
40#10622841C2214yes—
41#10622841C2218yescomplemented
42C2×#66899C2214yescomplemented
43#10622831C2214yes—
44#10622820C2212yes—
45C2×C22⋊(C11⋊C8)C2212yes—
46#10622673C2214yescomplemented
47#10622668C2214yescomplemented
48#10622667C2218yescomplemented
49#10622665C2218yescomplemented
50#10622663C2214yescomplemented
51#10622656C2214yescomplemented
52#10622654C2218yescomplemented
53#10622653C2214yescomplemented
54#10622647C2214yescomplemented
55#10622644C2214yescomplemented
56#10622643C2218yescomplemented
57#10622633C2214yescomplemented
58#10622624C2218yescomplemented
59#10622584C2214yes—
60#10622539C2212yes—
61C2×C11×#41—22no—
62C2×C11×#41—44no—
63C2×C11×#41C2314yes—
64C22×Q8×C11—21no—
65C22×Q8×C11—22no—
66C22×Q8×C11—44no—
67C22×Q8×C11C2311yescharacteristic
68C22×Q8×C11C2314yes—
69C22×Q8×C11C2311yescharacteristic
70C22×D4×C11—21no—
71C22×D4×C11—21no—
72C22×D4×C11D411yescharacteristic
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11—21no—
75C23×C4×C11—21no—
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C22×Dic22C2312yes—
79C22×Dic22C2312yes—
80C11×#124—28no—
81C11×#124—22no—
82C11×#124C2314yes—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—28no—
85C11×C22⋊Q8C2314yes—
86C11×#121—28no—
87C11×#121—22no—
88C11×#121C2314yes—
89C4×Q8×C11—22no—
90C4×Q8×C11C2314yes—
91C4×D4×C11—28no—
92C4×D4×C11D414yes—
93C4×D4×C11C2314yes—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C42×C11—21no—
105C2×C42×C11C2311yescharacteristic
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—22no—
108#67004—48no—
109C2×#4326—48no—
110C2×#4326C2318yes—
111C2×#4326C2318yes—
112D4×Dic11—24no—
113D4×Dic11—24no—
114C2×#4324C2318yes—
115#66979—22no—
116C2×C4⋊Dic11C2312yes—
117C2×C4⋊Dic11C2312yes—
118#66977—22no—
119#66977—22no—
120#66977—22no—
121#66977—22no—
122#66977—22no—
123#66977C2314yes—
124#66977C2314yes—
125#66977C2314yes—
126C2×Dic11⋊C4—22no—
127C2×Dic11⋊C4—22no—
128C2×#4318C2314yes—
129C22×C11⋊C8C2314yes—
130#66943—24no—
131#66941—24no—
132#66931—24no—
133#66931—24no—
134#66931—24no—
135#66931—24no—
136#66923—22no—
137#66922C2312yes—
138#66922C2312yes—
139C4×Dic22—22no—
140C4×Dic22C2314yes—
141#66899C2318yes—
142#66899C2318yes—
143#66896C2318yes—
144C22⋊(C11⋊C8)C2314yes—
145C22⋊(C11⋊C8)C2314yes—
146C22⋊(C11⋊C8)C2314yes—
147#66874C2318yes—
148#66872C2318yes—
149C4⋊(C11⋊C8)C2314yes—
150#66867C2314yes—
151#61573—111nomaximal, Sylow
152C24×C11—21no—
153C24×C11C2×D411yescharacteristic
154C24×C11C2×D411yescharacteristic
155C11×#41—28no—
156C11×#41—44no—
157C11×#41—48no—
158C2×Q8×C11—24no—
159C2×Q8×C11—21no—
160C2×Q8×C11—24no—
161C2×Q8×C11—21no—
162C2×Q8×C11—28no—
163C2×Q8×C11—44no—
164C2×Q8×C11—42no—
165C2×Q8×C11—44no—
166C2×Q8×C11—48no—
167C2×Q8×C11C2412yes—
168C2×Q8×C11C2412yes—
169C2×D4×C11—24no—
170C2×D4×C11—24no—
171C2×D4×C11—24no—
172C2×D4×C11—21no—
173C2×D4×C11—42no—
174C2×D4×C11—44no—
175C2×D4×C11—44no—
176C2×D4×C11C2×D414yes—
177C2×D4×C11C2412yes—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—24no—
182C22×C4×C11—24no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11—44no—
186C22×C4×C11—44no—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2411yescharacteristic
194C22×C4×C11C2412yes—
195C22×C4×C11C2412yes—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C2×Dic22—22no—
201C2×Dic22—22no—
202C2×Dic22—22no—
203C2×Dic22—44no—
204C2×Dic22—44no—
205C2×Dic22C2414yes—
206C11×C4⋊C4—24no—
207C11×C4⋊C4—24no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4C2×D414yes—
210C11×C4⋊C4C2412yes—
211C11×C22⋊C4—24no—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—24no—
215C11×C22⋊C4C2×D414yes—
216C11×C22⋊C4C2×D414yes—
217C42×C11—24no—
218C42×C11C2×D412yes—
219C42×C11C2412yes—
220C22⋊Dic11—24no—
221C22⋊Dic11—24no—
222C22⋊Dic11—24no—
223#4326—216no—
224#4326—48no—
225#4324—48no—
226C4⋊Dic11—22no—
227C4⋊Dic11—22no—
228C4⋊Dic11—22no—
229C4⋊Dic11—22no—
230C4⋊Dic11—22no—
231C4⋊Dic11C2414yes—
232Dic11⋊C4—24no—
233Dic11⋊C4—24no—
234Dic11⋊C4—24no—
235Dic11⋊C4—24no—
236C4×Dic11—24no—
237#4318—44no—
238C2×C11⋊C8—44no—
239C2×C11⋊C8C2418yes—
240#3501—111no—
241C2×#548D1111yescharacteristic
242#3316—118no—
243#3270—118no—
244#3215—112no—
245#3195—112no—
246#3187—112no—
247#3113—112no—
248#3007—112no—
249C2×#451—112no—
250#2973—111no—
251C23×C11—22no—
252C23×C11—22no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—42no—
258C23×C11—42no—
259C23×C11—42no—
260C23×C11#13714yescomplemented
261C23×C11C22×D412yes—
262C23×C11C22×D411yescharacteristic
263C23×C11C22×D412yes—
264Q8×C11—24no—
265Q8×C11—22no—
266Q8×C11—24no—
267Q8×C11—48no—
268Q8×C11—42no—
269Q8×C11H(5,𝔽2)14yes—
270D4×C11—28no—
271D4×C11—24no—
272D4×C11—48no—
273D4×C11—42no—
274D4×C11—48no—
275C2×C4×C11—24no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—41no—
284C2×C4×C11—42no—
285C2×C4×C11—41no—
286C2×C4×C11—42no—
287C2×C4×C11—41no—
288C2×C4×C11—48no—
289C2×C4×C11—48no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11C22×D412yes—
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C22×D412yes—
295C2×C4×C11C22×D412yes—
296C2×C4×C11C22×D412yes—
297C2×C4×C11C2511yescharacteristic
298C2×Dic11—24no—
299C2×Dic11—24no—
300C2×Dic11—82no—
301C2×Dic11—82no—
302C2×Dic11—82no—
303C2×Dic11—82no—
304Dic22—28no—
305Dic22—82no—
306Dic22—82no—
307Dic22—82no—
308C11⋊C8—28no—
309C22×#41C2×D1111yescharacteristic
310C23×Q8C2×D1111yescharacteristic
311C2×#137—114no—
312C22×Q16—114no—
313#554—114no—
314#554—224no—
315D4×Q8—114no—
316#548—24no—
317#548C2×D1118yes—
318#544—221no—
319#543—221no—
320#543—221no—
321#533—112no—
322C2×#124—21no—
323C2×#124C2×D1111yescharacteristic
324C2×C22⋊Q8—21no—
325C2×C22⋊Q8—112no—
326C2×C22⋊Q8—112no—
327C2×C22⋊Q8C2×D1111yescharacteristic
328C2×#121—21no—
329C2×#121C2×D1111yescharacteristic
330#518—221no—
331C2×C4×Q8C2×D1111yescharacteristic
332C2×C4×D4—21no—
333C2×C4×D4C2×D1111yescharacteristic
334#497—114no—
335#489—114no—
336#483—114no—
337#483—114no—
338#481—114no—
339#475—114no—
340#470—118no—
341#465—118no—
342#464—118no—
343#462—114no—
344#452—118no—
345#451—114no—
346#451—114no—
347#451—118no—
348#451—114no—
349#450—114no—
350#448—114no—
351#441—118no—
352#435—118no—
353#432—112no—
354#417—114no—
355C2×#103—114no—
356#407—112no—
357C2×C22⋊C8—112no—
358C22×C11—21no—
359C22×C11—22no—
360C22×C11—21no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—44no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11—82no—
370C22×C11—84no—
371C22×C11C2×#13712yes—
372C22×C11C2×#13714yes—
373C22×C11C23×D411yescharacteristic
374C4×C11—22no—
375C4×C11—24no—
376C4×C11—22no—
377C4×C11—21no—
378C4×C11—22no—
379C4×C11—22no—
380C4×C11—42no—
381C4×C11—42no—
382C4×C11C2×H(5,𝔽2)12yes—
383Dic11—44no—
384Dic11—44no—
385C2×#41—22no—
386C2×#41—44no—
387C2×#41C22×D1114yes—
388C22×Q8—21no—
389C22×Q8—22no—
390C22×Q8—44no—
391C22×Q8—112no—
392C22×Q8—112no—
393C22×Q8C22×D1111yescharacteristic
394C22×Q8C22×D1114yes—
395C22×Q8C22×D1111yescharacteristic
396C22×D4—21no—
397C22×D4—21no—
398C22×D4C22⋊D1111yescharacteristic
399C22×D4C22×D1111yescharacteristic
400C23×C4—21no—
401C23×C4—21no—
402C23×C4C22×D1111yescharacteristic
403C23×C4C22×D1111yescharacteristic
404#137—448no—
405C2×Q16—118no—
406C2×Q16—118no—
407C2×Q16—448no—
408C2×SD16—118no—
409C2×M16—114no—
410C22×C8—114no—
411C4⋊Q8—112no—
412C4⋊Q8—112no—
413C4⋊Q8—224no—
414#125—224no—
415#125—222no—
416#124—28no—
417#124—22no—
418#124C22×D1114yes—
419C22⋊Q8—22no—
420C22⋊Q8—28no—
421C22⋊Q8—114no—
422C22⋊Q8—114no—
423C22⋊Q8—114no—
424C22⋊Q8—222no—
425C22⋊Q8—222no—
426C22⋊Q8—222no—
427C22⋊Q8—222no—
428C22⋊Q8—222no—
429C22⋊Q8—224no—
430C22⋊Q8—224no—
431C22⋊Q8—224no—
432C22⋊Q8—224no—
433C22⋊Q8C22×D1114yes—
434#121—28no—
435#121—22no—
436#121C22×D1114yes—
437C4×Q8—22no—
438C4×Q8—114no—
439C4×Q8—222no—
440C4×Q8C22×D1114yes—
441C4×D4—28no—
442C4×D4—224no—
443C4×D4—224no—
444C4×D4C22⋊D1114yes—
445C4×D4C22×D1114yes—
446#117—222no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—112no—
450C2×C4⋊C4—112no—
451C2×C4⋊C4—222no—
452C2×C4⋊C4—222no—
453C2×C4⋊C4C22⋊D1111yescharacteristic
454C2×C4⋊C4C22×D1111yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—222no—
460C2×C22⋊C4—222no—
461C2×C22⋊C4C22⋊D1111yescharacteristic
462C2×C22⋊C4C22⋊D1111yescharacteristic
463C2×C42—21no—
464C2×C42C22×D1111yescharacteristic
465#106—118no—
466C4⋊C8—114no—
467#103—118no—
468#103—118no—
469#103—118no—
470#102—118no—
471C22⋊C8—114no—
472C22⋊C8—114no—
473C22⋊C8—114no—
474#97—114no—
475C2×C11—22no—
476C2×C11—24no—
477C2×C11—42no—
478C2×C11—82no—
479C2×C11#348411yescharacteristic
480C2×C11C22×#13711yescharacteristic
481C2×C11#358611yescharacteristic
482C24—21no—
483C24C2×C22⋊D1111yescharacteristic
484C24C2×C22⋊D1111yescharacteristic
485#41—28no—
486#41—44no—
487#41—48no—
488C2×Q8—24no—
489C2×Q8—21no—
490C2×Q8—24no—
491C2×Q8—21no—
492C2×Q8—28no—
493C2×Q8—44no—
494C2×Q8—42no—
495C2×Q8—44no—
496C2×Q8—48no—
497C2×Q8—114no—
498C2×Q8—222no—
499C2×Q8—222no—
500C2×Q8—222no—
501C2×Q8—444no—
502C2×Q8—444no—
503C2×Q8C23×D1112yes—
504C2×Q8C23×D1112yes—
505C2×D4—24no—
506C2×D4—24no—
507C2×D4—24no—
508C2×D4—21no—
509C2×D4—42no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4C2×C22⋊D1114yes—
513C2×D4C23×D1112yes—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4C2×C22⋊D1111yescharacteristic
528C22×C4C2×C22⋊D1111yescharacteristic
529C22×C4C2×C22⋊D1111yescharacteristic
530C22×C4C2×C22⋊D1111yescharacteristic
531C22×C4C2×C22⋊D1112yes—
532C22×C4C2×C22⋊D1112yes—
533C22×C4C23×D1111yescharacteristic
534C22×C4C23×D1112yes—
535C22×C4C23×D1112yes—
536Q16—2216no—
537Q16—448no—
538SD16—448no—
539M16—444no—
540C2×C8—118no—
541C2×C8—444no—
542C4⋊C4—24no—
543C4⋊C4—24no—
544C4⋊C4—21no—
545C4⋊C4—114no—
546C4⋊C4—222no—
547C4⋊C4—222no—
548C4⋊C4—224no—
549C4⋊C4—224no—
550C4⋊C4—224no—
551C4⋊C4—222no—
552C4⋊C4—222no—
553C4⋊C4—224no—
554C4⋊C4—222no—
555C4⋊C4C2×C22⋊D1114yes—
556C4⋊C4C23×D1112yes—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C22⋊C4—24no—
560C22⋊C4—24no—
561C22⋊C4—224no—
562C22⋊C4—224no—
563C22⋊C4—224no—
564C22⋊C4C2×C22⋊D1114yes—
565C22⋊C4C2×C22⋊D1114yes—
566C42—24no—
567C42—224no—
568C42C2×C22⋊D1112yes—
569C42C23×D1112yes—
570C11#6157311yescharacteristic, complemented, Sylow
571C23—22no—
572C23—22no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23#6700414yescomplemented
581C23C22×C22⋊D1112yes—
582C23C22×C22⋊D1111yescharacteristic
583C23C22×C22⋊D1112yes—
584Q8—24no—
585Q8—22no—
586Q8—24no—
587Q8—48no—
588Q8—42no—
589Q8—228no—
590Q8—882no—
591Q8—882no—
592Q8—882no—
593Q8#6703714yes—
594D4—28no—
595D4—24no—
596D4—48no—
597D4—42no—
598D4—48no—
599C2×C4—24no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—41no—
610C2×C4—42no—
611C2×C4—41no—
612C2×C4—48no—
613C2×C4—48no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—224no—
617C2×C4—224no—
618C2×C4—882no—
619C2×C4—882no—
620C2×C4—882no—
621C2×C4—882no—
622C2×C4C22×C22⋊D1112yes—
623C2×C4C22×C22⋊D1112yes—
624C2×C4C22×C22⋊D1111yescharacteristic
625C2×C4C22×C22⋊D1112yes—
626C2×C4C22×C22⋊D1112yes—
627C2×C4C24×D1111yescharacteristic
628C8—228no—
629C22—21no—
630C22—22no—
631C22—21no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—44no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—82no—
641C22—84no—
642C22C2×#6700412yes—
643C22C2×#6700414yes—
644C22C23×C22⋊D1111yescharacteristic
645C4—22no—
646C4—24no—
647C4—22no—
648C4—21no—
649C4—22no—
650C4—22no—
651C4—42no—
652C4—42no—
653C4—444no—
654C4—444no—
655C4C2×#6703712yes—
656C2—22no—
657C2—24no—
658C2—42no—
659C2—82no—
660C2#1308225111yescharacteristic
661C2C22×#6700411yescharacteristic
662C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#548C2
socleC22×C11C23×D4
hypercenterC2×#548D11
hypocenterC11#61573
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. #13082419C2semidirect
2. #13080727C2semidirect
3. #13080182C2semidirect
4. #13079619C2semidirect
5. #13079437C2semidirect
6. #13079373C2semidirect
7. #13078746C2semidirect
8. #13077876C2semidirect
9. C2×#10622841C2semidirect
10. #13077645C2semidirect
25. C2×#67004C22semidirect
26. C22×#4326C22semidirect
30. #10623074C22semidirect
32. D4×Dic22C22semidirect
37. #10622852C22semidirect
38. #10622845C22semidirect
41. #10622841C22semidirect
42. C2×#66899C22semidirect
46. #10622673C22semidirect
47. #10622668C22semidirect
48. #10622667C22semidirect
49. #10622665C22semidirect
50. #10622663C22semidirect
51. #10622656C22semidirect
52. #10622654C22semidirect
53. #10622653C22semidirect
54. #10622647C22semidirect
55. #10622644C22semidirect
56. #10622643C22semidirect
57. #10622633C22semidirect
58. #10622624C22semidirect
260. C23×C11#137semidirect
570. C11#61573semidirect
580. C23#67004semidirect

Maximal subgroups

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

subgroupindex
#130824192
#130807272
#130801822
#130796192
#130794372
#130793732
#130787462
#130778762
C2×#106228412
#130776452
C2×C11×#5482
#6157311