Finite Group Databasebeta

← #14960730

Subgroups — #14960730

Order 2816.

2406 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623148C211yesmaximal, characteristic
2C22×#66949C211yesmaximal, characteristic, complemented
3#13076907C212yesmaximal, complemented
4#13075207C214yesmaximal, complemented
5#13075187C214yesmaximal, complemented
6#13074965C214yesmaximal, complemented
7#13074952C214yesmaximal, complemented
8#13074393C212yesmaximal, complemented
9#13074097C211yesmaximal, characteristic, complemented
10#13073991C211yesmaximal, characteristic, complemented
11#13073962C212yesmaximal, complemented
12#13073090C211yesmaximal, characteristic, complemented
13#13071978C212yesmaximal, complemented
14#13071211C211yesmaximal, characteristic, complemented
15C11×#2504C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#66992C2212yes—
21C2×#66990C2212yes—
22C2×D4×Dic11C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C2×#66977C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28#10623148—28no—
29C2×#66951C2212yes—
30C2×#66949—28no—
31C2×#66949C2214yes—
32C2×#66949C2214yes—
33C2×#66939C2212yes—
34C2×#66938C2212yes—
35C2×#66936C2214yes—
36C2×#66931C2214yescomplemented
37C11×#397C2214yescomplemented
38C11×#390C2212yescomplemented
39C11×#386C2212yes—
40C11×#386C2212yes—
41C11×#382C2212yescomplemented
42C4×C11×C22⋊C4C2211yescharacteristic
43#10622835C2212yescomplemented
44#10622833C2212yes—
45#10622833C2212yes—
46#10622823C2212yes—
47#10622823C2212yes—
48C4×C22⋊Dic11C2211yescharacteristic
49#10622595C2212yescomplemented
50#10622593C2214yescomplemented
51#10622589C2212yescomplemented
52#10622587C2212yescomplemented
53#10622574C2214yes—
54#10622572C2214yes—
55#10622569C2214yes—
56#10622568C2212yes—
57#10622563C2212yes—
58#10622563C2212yes—
59#10622561C2214yescomplemented
60#10622560C2214yescomplemented
61#10622559C2214yescomplemented
62#10622558C2214yescomplemented
63#10622555C2212yes—
64#10622553C2214yes—
65#10622541C2214yescomplemented
66#10622288C2214yes—
67#10622287C2214yes—
68#10622282C2214yes—
69#10622281C2214yes—
70#10622277C2214yes—
71#10622274C2212yescomplemented
72#10622270C2214yescomplemented
73#10622269C2212yescomplemented
74#10622269C2214yescomplemented
75#10622267C2214yescomplemented
76#10622259C2214yescomplemented
77C24×D11C2311yescharacteristic
78C22×D4×C11C2312yes—
79C22×D4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11C2312yes—
84C22×C22⋊D11C2312yes—
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2312yes—
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C22×C4×D11—24no—
90C22×C4×D11—44no—
91C22×C4×D11C2314yes—
92C22×Dic22—24no—
93C22×Dic22—44no—
94C22×Dic22C2314yes—
95C22×Dic22C2311yescharacteristic
96C11×#121—24no—
97C2×C11×C4⋊C4—24no—
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C22⋊C4C2312yes—
102C2×C11×C22⋊C4C2312yes—
103C2×C11×C22⋊C4C2314yes—
104C2×C11×C22⋊C4C2314yes—
105C2×C42×C11C2312yes—
106C2×C22⋊Dic11C2314yes—
107C2×C22⋊Dic11C2312yes—
108C2×C22⋊Dic11C2312yes—
109C2×C22⋊Dic11C2312yes—
110C2×C22⋊Dic11C2314yes—
111#66992—28no—
112#66990—28no—
113D4×Dic11—28no—
114C2×(C2×D11)⋊C4—24no—
115C2×(C2×D11)⋊C4D418yes—
116C2×(C2×D11)⋊C4C2312yes—
117C2×(C2×D11)⋊C4C2312yes—
118C2×(C2×D11)⋊C4C2314yes—
119C2×(C2×D11)⋊C4C2314yes—
120C2×(C2×D11)⋊C4C2314yes—
121C2×(C2×D11)⋊C4C2312yes—
122C2×(C2×D11)⋊C4C2312yes—
123C2×C4⋊Dic11C2314yes—
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2312yes—
126C2×C4⋊Dic11C2314yes—
127#66977—24no—
128C2×Dic11⋊C4—24no—
129C2×Dic11⋊C4—24no—
130C2×Dic11⋊C4C2314yes—
131C2×Dic11⋊C4C2312yes—
132C2×Dic11⋊C4C2312yes—
133C2×Dic11⋊C4C2312yes—
134C2×Dic11⋊C4C2314yes—
135C2×Dic11⋊C4C2314yes—
136C2×Dic11⋊C4C2314yes—
137C2×C4×Dic11C2312yes—
138C2×C4×Dic11C2312yes—
139#66951—28no—
140#66949—216no—
141#66949—216no—
142#66939—28no—
143#66938—28no—
144#66936—48no—
145#66931—48no—
146C11×#95C2314yes—
147C11×#95C2314yes—
148C11×#95C2312yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2312yes—
157#36716—111nomaximal, Sylow
158C24×C11C2412yes—
159C24×C11C2411yescharacteristic
160C23×D11—24no—
161C23×D11—42no—
162C23×D11—42no—
163C23×D11C2×D414yes—
164C23×D11C2412yes—
165C2×D4×C11—24no—
166C2×D4×C11—28no—
167C2×D4×C11—22no—
168C2×D4×C11—42no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—42no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11C2×D414yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2414yes—
177C22×C4×C11C2412yes—
178C22×C4×C11C2412yes—
179C22×C4×C11C2411yescharacteristic
180C22×C4×C11C2411yescharacteristic
181C2×C22⋊D11—24no—
182C2×C22⋊D11—24no—
183C2×C22⋊D11—44no—
184C2×C22⋊D11—44no—
185C22×Dic11—24no—
186C22×Dic11—24no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—42no—
190C22×Dic11—42no—
191C22×Dic11—44no—
192C22×Dic11C2×D414yes—
193C22×Dic11C2414yes—
194C22×Dic11C2412yes—
195C22×Dic11C2412yes—
196C22×Dic11C2412yes—
197C22×Dic11C2412yes—
198C22×Dic11C2412yes—
199C2×C4×D11—28no—
200C2×C4×D11—28no—
201C2×C4×D11—44no—
202C2×C4×D11—416no—
203C2×Dic22—28no—
204C2×Dic22—28no—
205C2×Dic22—22no—
206C2×Dic22—44no—
207C2×Dic22—42no—
208C2×Dic22—416no—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4—22no—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—44no—
215C11×C22⋊C4—44no—
216C42×C11—42no—
217C22⋊Dic11—24no—
218C22⋊Dic11—28no—
219C22⋊Dic11—24no—
220C22⋊Dic11—24no—
221C22⋊Dic11—44no—
222(C2×D11)⋊C4—24no—
223(C2×D11)⋊C4—24no—
224(C2×D11)⋊C4—28no—
225(C2×D11)⋊C4—44no—
226(C2×D11)⋊C4—44no—
227(C2×D11)⋊C4C2×D418yes—
228(C2×D11)⋊C4C2×D418yes—
229C4⋊Dic11—24no—
230C4⋊Dic11—28no—
231C4⋊Dic11—22no—
232C4⋊Dic11—44no—
233Dic11⋊C4—28no—
234Dic11⋊C4—24no—
235Dic11⋊C4—24no—
236Dic11⋊C4—24no—
237Dic11⋊C4—44no—
238Dic11⋊C4—44no—
239Dic11⋊C4—44no—
240C4×Dic11—24no—
241C4×Dic11—42no—
242C2×#538—111no—
243C22×C22⋊Q8—111no—
244#2849—112no—
245#2700—114no—
246#2698—114no—
247#2681—114no—
248#2680—114no—
249#2622—112no—
250#2591—111no—
251#2583—111no—
252#2579—112no—
253#2504D1111yescharacteristic, complemented
254#2502—111no—
255#2409—112no—
256#2312—111no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—24no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11C22×D412yes—
264C23×C112−1+414yes—
265C23×C11C2511yescharacteristic
266C22×D11—28no—
267C22×D11—24no—
268C22×D11—24no—
269C22×D11—24no—
270C22×D11—44no—
271C22×D11—44no—
272C22×D11—416no—
273C22×D11C22×D414yes—
274D4×C11—48no—
275D4×C11—82no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—24no—
282C2×C4×C11—24no—
283C2×C4×C11—24no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—44no—
288C2×C4×C11—44no—
289C2×C4×C11—44no—
290C2×C4×C11C22×D412yes—
291C2×C4×C11C22×D412yes—
292C22⋊D11—84no—
293C22⋊D11—84no—
294C2×Dic11—28no—
295C2×Dic11—22no—
296C2×Dic11—24no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—22no—
300C2×Dic11—22no—
301C2×Dic11—24no—
302C2×Dic11—24no—
303C2×Dic11—24no—
304C2×Dic11—24no—
305C2×Dic11—24no—
306C2×Dic11—24no—
307C2×Dic11—44no—
308C2×Dic11—44no—
309C2×Dic11—84no—
310C2×Dic11C22×D414yes—
311C2×Dic11H(5,𝔽2)14yes—
312C4×D11—416no—
313Dic22—416no—
314Dic22—82no—
315C23×Q8—111no—
316C24×C4—111no—
317#538—228no—
318C2×#126—112no—
319C2×#124—112no—
320C2×#123—112no—
321C2×#123—114no—
322C2×C22⋊Q8—111no—
323C2×C22⋊Q8—114no—
324C2×C22⋊Q8—114no—
325C2×C22⋊Q8—114no—
326C2×C22⋊Q8—228no—
327C2×#121—112no—
328C2×#121C2×D1111yescharacteristic
329C2×#120—112no—
330C2×C4×D4—112no—
331C22×C4⋊C4—111no—
332C22×C4⋊C4—111no—
333C22×C4⋊C4C2×D1111yescharacteristic
334C22×C22⋊C4—111no—
335C22×C22⋊C4—111no—
336#400—112no—
337#398—114no—
338#398—114no—
339#398—112no—
340#397—114no—
341#397—114no—
342#397C2×D1114yescomplemented
343#396—114no—
344#395—112no—
345#395—114no—
346#394—112no—
347#394—114no—
348#394—114no—
349#393—114no—
350#391—112no—
351#391—114no—
352#390C2×D1112yescomplemented
353#389—114no—
354#388—114no—
355#388—114no—
356#388—114no—
357#387—114no—
358#386—112no—
359#386—112no—
360#386—114no—
361#386C2×D1112yes—
362#386C2×D1112yes—
363#385—112no—
364#385—112no—
365#385—112no—
366#385—114no—
367#385—112no—
368#385—114no—
369#384—112no—
370#382C2×D1112yescomplemented
371#381—114no—
372#380—112no—
373#379—112no—
374C4×C22⋊C4—111no—
375C4×C22⋊C4C2×D1111yescharacteristic
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—28no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—48no—
383C22×C11#53614yes—
384C22×C11C23×D411yescharacteristic
385C22×C11C2×H(5,𝔽2)12yes—
386C22×C11C2×2−1+412yes—
387C22×C11#58512yes—
388C2×D11—24no—
389C2×D11—24no—
390C2×D11—24no—
391C2×D11—416no—
392C2×D11—48no—
393C4×C11—22no—
394C4×C11—22no—
395C4×C11—42no—
396C4×C11—42no—
397C4×C11—42no—
398C4×C11—44no—
399Dic11—24no—
400Dic11—24no—
401Dic11—42no—
402Dic11—42no—
403Dic11—42no—
404Dic11—44no—
405C25—111no—
406C22×Q8—114no—
407C22×Q8—111no—
408C22×Q8—224no—
409C22×Q8—444no—
410C22×D4—112no—
411C22×D4—112no—
412C22×D4C22×D1112yes—
413C22×D4C22×D1111yescharacteristic
414C23×C4—111no—
415C23×C4—111no—
416C23×C4—111no—
417C23×C4—112no—
418C23×C4—114no—
419C23×C4—224no—
420C23×C4—444no—
421C23×C4C22×D1111yescharacteristic
422C23×C4C22×D1111yescharacteristic
423C23×C4C22×D1111yescharacteristic
424#126—228no—
425#124—228no—
426#123—228no—
427#123—448no—
428C22⋊Q8—2216no—
429C22⋊Q8—2216no—
430C22⋊Q8—224no—
431C22⋊Q8—448no—
432#121—24no—
433#121—228no—
434#120—228no—
435C4×D4—228no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—114no—
438C2×C4⋊C4—112no—
439C2×C4⋊C4—112no—
440C2×C4⋊C4—112no—
441C2×C4⋊C4—112no—
442C2×C4⋊C4—111no—
443C2×C4⋊C4—114no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4—114no—
446C2×C4⋊C4—114no—
447C2×C4⋊C4—114no—
448C2×C4⋊C4—224no—
449C2×C4⋊C4—224no—
450C2×C4⋊C4C22×D1112yes—
451C2×C4⋊C4C22×D1112yes—
452C2×C4⋊C4C22×D1111yescharacteristic
453C2×C22⋊C4—118no—
454C2×C22⋊C4—112no—
455C2×C22⋊C4—112no—
456C2×C22⋊C4—112no—
457C2×C22⋊C4—112no—
458C2×C22⋊C4—114no—
459C2×C22⋊C4—112no—
460C2×C22⋊C4—114no—
461C2×C22⋊C4—112no—
462C2×C22⋊C4—112no—
463C2×C22⋊C4—114no—
464C2×C22⋊C4—114no—
465C2×C22⋊C4—114no—
466C2×C22⋊C4—224no—
467C2×C22⋊C4C22×D1112yes—
468C2×C22⋊C4C22×D1112yes—
469C2×C22⋊C4C22×D1114yes—
470C2×C22⋊C4C22×D1114yes—
471C2×C42—112no—
472C2×C42—112no—
473C2×C42C22×D1112yes—
474#95—112no—
475#95—114no—
476#95—114no—
477#95—114no—
478#95—114no—
479#95—114no—
480#95—114no—
481#95—114no—
482#95C22×D1112yes—
483#95C22×D1114yes—
484#95C22×D1114yes—
485C2×C11—24no—
486C2×C11—82no—
487C2×C11C2×#53611yescharacteristic
488C2×C11#348411yescharacteristic
489C2×C11#348511yescharacteristic
490C2×C11#354114yes—
491D11—44no—
492C24—112no—
493C24—114no—
494C24—224no—
495C24—442no—
496C24—442no—
497C24C23×D1112yes—
498C24C23×D1111yescharacteristic
499C2×Q8—228no—
500C2×Q8—228no—
501C2×Q8—222no—
502C2×Q8—444no—
503C2×Q8—442no—
504C2×Q8—4416no—
505C2×D4—24no—
506C2×D4—28no—
507C2×D4—22no—
508C2×D4—42no—
509C2×D4—224no—
510C2×D4—224no—
511C2×D4—444no—
512C2×D4—444no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—112no—
519C22×C4—112no—
520C22×C4—114no—
521C22×C4—114no—
522C22×C4—112no—
523C22×C4—112no—
524C22×C4—112no—
525C22×C4—228no—
526C22×C4—228no—
527C22×C4—224no—
528C22×C4—224no—
529C22×C4—222no—
530C22×C4—222no—
531C22×C4—444no—
532C22×C4—4416no—
533C22×C4—442no—
534C22×C4—442no—
535C22×C4—444no—
536C22×C4D4×D1114yes—
537C22×C4C23×D1112yes—
538C22×C4C23×D1114yes—
539C22×C4C23×D1112yes—
540C22×C4C23×D1112yes—
541C22×C4C23×D1111yescharacteristic
542C22×C4C23×D1111yescharacteristic
543C4⋊C4—24no—
544C4⋊C4—24no—
545C4⋊C4—22no—
546C4⋊C4—228no—
547C4⋊C4—224no—
548C4⋊C4—228no—
549C4⋊C4—224no—
550C4⋊C4—224no—
551C4⋊C4—224no—
552C4⋊C4—222no—
553C4⋊C4—444no—
554C4⋊C4—444no—
555C4⋊C4—444no—
556C4⋊C4—444no—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C22⋊C4—44no—
560C22⋊C4—44no—
561C22⋊C4—118no—
562C22⋊C4—118no—
563C22⋊C4—228no—
564C22⋊C4—224no—
565C22⋊C4—224no—
566C22⋊C4—224no—
567C22⋊C4—228no—
568C22⋊C4—224no—
569C22⋊C4—224no—
570C22⋊C4—444no—
571C22⋊C4—444no—
572C22⋊C4—444no—
573C42—42no—
574C42—224no—
575C42—442no—
576C11#3671611yescharacteristic, complemented, Sylow
577C23—22no—
578C23—22no—
579C23—22no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—114no—
584C23—224no—
585C23—224no—
586C23—224no—
587C23—228no—
588C23—444no—
589C23—444no—
590C23—4416no—
591C23C2×D4×D1112yes—
592C23#6704314yes—
593C23C24×D1111yescharacteristic
594Q8—4416no—
595Q8—882no—
596D4—48no—
597D4—82no—
598D4—884no—
599D4—884no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—44no—
612C2×C4—44no—
613C2×C4—44no—
614C2×C4—114no—
615C2×C4—114no—
616C2×C4—228no—
617C2×C4—222no—
618C2×C4—224no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—224no—
624C2×C4—224no—
625C2×C4—224no—
626C2×C4—224no—
627C2×C4—224no—
628C2×C4—224no—
629C2×C4—4416no—
630C2×C4—444no—
631C2×C4—444no—
632C2×C4—884no—
633C2×C4C2×D4×D1112yes—
634C2×C4C2×D4×D1112yes—
635C22—28no—
636C22—22no—
637C22—22no—
638C22—48no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—224no—
643C22—224no—
644C22—224no—
645C22—4416no—
646C22—448no—
647C22#1062320614yes—
648C22C22×D4×D1111yescharacteristic
649C22C2×#6704312yes—
650C22#1062345312yes—
651C22D11×H(5,𝔽2)12yes—
652C4—22no—
653C4—22no—
654C4—44no—
655C4—42no—
656C4—42no—
657C4—42no—
658C4—224no—
659C4—224no—
660C4—444no—
661C4—442no—
662C4—442no—
663C4—442no—
664C2—24no—
665C2—82no—
666C2—444no—
667C2C2×#1062320611yescharacteristic
668C2#1308225011yescharacteristic
669C2#1308225411yescharacteristic
670C2#1308289414yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2504C2
prime radicalC2×#10623148C2
hypercenter#2504D11
hypocenterC11#36716
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2504

Complements

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

NH ≅ G/Ntype
2. C22×#66949C2semidirect
3. #13076907C2semidirect
4. #13075207C2semidirect
5. #13075187C2semidirect
6. #13074965C2semidirect
7. #13074952C2semidirect
8. #13074393C2semidirect
9. #13074097C2semidirect
10. #13073991C2semidirect
11. #13073962C2semidirect
12. #13073090C2semidirect
13. #13071978C2semidirect
14. #13071211C2semidirect
15. C11×#2504C2semidirect
36. C2×#66931C22semidirect
37. C11×#397C22semidirect
38. C11×#390C22semidirect
41. C11×#382C22semidirect
43. #10622835C22semidirect
49. #10622595C22semidirect
50. #10622593C22semidirect
51. #10622589C22semidirect
52. #10622587C22semidirect
59. #10622561C22semidirect
60. #10622560C22semidirect
61. #10622559C22semidirect
62. #10622558C22semidirect
65. #10622541C22semidirect
71. #10622274C22semidirect
72. #10622270C22semidirect
73. #10622269C22semidirect
74. #10622269C22semidirect
75. #10622267C22semidirect
76. #10622259C22semidirect
253. #2504D11semidirect
342. #397C2×D11semidirect
352. #390C2×D11semidirect
370. #382C2×D11semidirect
576. C11#36716semidirect

Maximal subgroups

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

subgroupindex
C2×#106231482
C22×#669492
#130769072
#130752072
#130751872
#130749652
#130749522
#130743932
#130740972
#130739912
#130739622
#130730902
#130719782
#130712112
C11×#25042
#3671611