Finite Group Databasebeta

← #14960542

Subgroups — #14960542

Order 2816.

2406 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C211yesmaximal, characteristic, complemented
2#13076906C212yesmaximal, complemented
3#13075061C214yesmaximal, complemented
4#13075031C214yesmaximal, complemented
5#13074891C214yesmaximal, complemented
6#13074861C214yesmaximal, complemented
7#13074391C212yesmaximal, complemented
8#13074097C211yesmaximal, characteristic, complemented
9#13073997C211yesmaximal, characteristic, complemented
10#13073959C212yesmaximal, complemented
11#13072933C212yesmaximal, complemented
12#13072275C211yesmaximal, characteristic, complemented
13#13072261C211yesmaximal, characteristic, complemented
14#13071214C211yesmaximal, characteristic, complemented
15C2×C11×#538C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C11×#538—28no—
19C2×C11×#126C2212yes—
20C2×C11×#124C2212yes—
21C2×C11×#123C2212yes—
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C11×#121C2212yes—
25C2×C11×#120C2212yes—
26C2×C4×D4×C11C2212yes—
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C2×#66997C2212yescomplemented
30C2×#66989C2212yescomplemented
31C2×#66988C2214yes—
32C22×C4⋊Dic11C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C2×#66931—28no—
36C2×#66931C2214yes—
37C2×#66931C2214yes—
38#10622860C2212yes—
39#10622842C2212yescomplemented
40#10622835C2214yes—
41#10622835C2214yes—
42#10622835C2212yescomplemented
43#10622833C2212yes—
44#10622833C2212yes—
45#10622833C2212yes—
46#10622833C2212yes—
47#10622833C2214yes—
48#10622825C2212yes—
49#10622825C2214yescomplemented
50#10622823C2214yescomplemented
51C4×C22⋊Dic11C2211yescharacteristic
52C4×C22⋊Dic11C2211yescharacteristic
53#10622599C2214yescomplemented
54#10622597C2214yescomplemented
55#10622595C2212yescomplemented
56#10622593C2212yescomplemented
57#10622592C2214yescomplemented
58#10622587C2212yescomplemented
59#10622587C2212yescomplemented
60#10622585C2214yescomplemented
61#10622565C2214yes—
62#10622565C2214yes—
63#10622564C2214yes—
64#10622564C2214yes—
65#10622562C2214yescomplemented
66#10622561C2214yescomplemented
67#10622560C2214yescomplemented
68#10622559C2212yes—
69#10622559C2212yes—
70#10622559C2212yes—
71#10622559C2212yes—
72#10622559C2214yes—
73#10622558C2214yescomplemented
74#10622556C2214yes—
75#10622546C2214yescomplemented
76#10622541C2214yescomplemented
77C25×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11C2312yes—
80C22×D4×C11C2312yes—
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2312yes—
83C23×C4×C11C2312yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×Dic11—24no—
87C23×Dic11—44no—
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2314yes—
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C22×Dic22—24no—
94C22×Dic22—44no—
95C22×Dic22C2312yes—
96C22×Dic22C2312yes—
97C11×#126—28no—
98C11×#124—28no—
99C11×#123—28no—
100C11×C22⋊Q8—24no—
101C11×#121—24no—
102C11×#121—28no—
103C11×#120—28no—
104C4×D4×C11—28no—
105C2×C11×C4⋊C4C2312yes—
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2312yes—
109C2×C11×C22⋊C4D418yes—
110C2×C11×C22⋊C4C2312yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2312yes—
114C2×C11×C22⋊C4C2312yes—
115C2×C11×C22⋊C4C2312yes—
116C2×C11×C22⋊C4C2312yes—
117C2×C42×C11C2312yes—
118C2×C22⋊Dic11—24no—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2312yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127C2×C22⋊Dic11C2314yes—
128#66997—44no—
129#66989—44no—
130#66988—48no—
131C2×C4⋊Dic11—24no—
132C2×C4⋊Dic11C2314yes—
133C2×C4⋊Dic11C2314yes—
134C2×Dic11⋊C4—24no—
135C2×Dic11⋊C4—24no—
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2312yes—
138C2×Dic11⋊C4C2312yes—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×C4×Dic11C2312yes—
144C2×C4×Dic11C2312yes—
145#66931—216no—
146#66931—216no—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2312yes—
157C11⋊#95C2312yes—
158#36705—111nomaximal, Sylow
159C24×C11—24no—
160C24×C11—42no—
161C24×C11—42no—
162C24×C11C2×D414yes—
163C24×C11C2412yes—
164C24×C11C2412yes—
165C24×C11C2411yescharacteristic
166C2×Q8×C11—22no—
167C2×Q8×C11—42no—
168C2×D4×C11—24no—
169C2×D4×C11—28no—
170C2×D4×C11—24no—
171C2×D4×C11—24no—
172C2×D4×C11—22no—
173C2×D4×C11—44no—
174C2×D4×C11—42no—
175C2×D4×C11—44no—
176C22×C4×C11—24no—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11—44no—
180C22×C4×C11C2×D414yes—
181C22×C4×C11C2×D414yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2412yes—
185C22×C4×C11C2411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C22×C4×C11C2412yes—
188C22×Dic11—24no—
189C22×Dic11—28no—
190C22×Dic11—22no—
191C22×Dic11—28no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—42no—
196C22×Dic11—42no—
197C22×Dic11—44no—
198C22×Dic11—42no—
199C22×Dic11—416no—
200C22×Dic11C2414yes—
201C22×Dic11C2414yes—
202C22×Dic11C2412yes—
203C22×Dic11C2412yes—
204C22×Dic11C2412yes—
205C22×Dic11C2412yes—
206C2×Dic22—24no—
207C2×Dic22—24no—
208C2×Dic22—24no—
209C2×Dic22—24no—
210C2×Dic22—42no—
211C2×Dic22—42no—
212C2×Dic22—416no—
213C11×C4⋊C4—24no—
214C11×C4⋊C4—24no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—22no—
217C11×C22⋊C4—24no—
218C11×C22⋊C4—24no—
219C11×C22⋊C4—24no—
220C11×C22⋊C4—24no—
221C11×C22⋊C4—24no—
222C11×C22⋊C4C2×D418yes—
223C11×C22⋊C4C2×D418yes—
224C42×C11—24no—
225C22⋊Dic11—28no—
226C22⋊Dic11—28no—
227C22⋊Dic11—24no—
228C22⋊Dic11—24no—
229C22⋊Dic11—44no—
230C22⋊Dic11—44no—
231C22⋊Dic11—44no—
232C22⋊Dic11—44no—
233C22⋊Dic11—44no—
234C4⋊Dic11—28no—
235C4⋊Dic11—44no—
236Dic11⋊C4—28no—
237Dic11⋊C4—28no—
238Dic11⋊C4—24no—
239Dic11⋊C4—24no—
240Dic11⋊C4—44no—
241Dic11⋊C4—44no—
242Dic11⋊C4—44no—
243C4×Dic11—42no—
244C4×Dic11—42no—
245C2×#538D1111yescharacteristic
246C22×C22⋊Q8—111no—
247#2849—112no—
248#2689—114no—
249#2687—114no—
250#2674—114no—
251#2672—114no—
252#2622—112no—
253#2591—111no—
254#2583—111no—
255#2579—112no—
256#2487—112no—
257#2436—111no—
258#2434—111no—
259#2312—111no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—28no—
263C23×C11—24no—
264C23×C11—24no—
265C23×C11—24no—
266C23×C11—22no—
267C23×C11—24no—
268C23×C11—24no—
269C23×C11—24no—
270C23×C11—44no—
271C23×C11—44no—
272C23×C11—416no—
273C23×C11C22×D414yes—
274C23×C11C22×D412yes—
275C23×C112−1+414yes—
276C23×C11C2511yescharacteristic
277Q8×C11—82no—
278D4×C11—48no—
279D4×C11—82no—
280D4×C11—84no—
281D4×C11—84no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—24no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—24no—
289C2×C4×C11—24no—
290C2×C4×C11—24no—
291C2×C4×C11—44no—
292C2×C4×C11—44no—
293C2×C4×C11—84no—
294C2×C4×C11C22×D414yes—
295C2×C4×C11C22×D412yes—
296C2×C4×C11C22×D412yes—
297C2×Dic11—28no—
298C2×Dic11—22no—
299C2×Dic11—22no—
300C2×Dic11—22no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—24no—
304C2×Dic11—24no—
305C2×Dic11—22no—
306C2×Dic11—24no—
307C2×Dic11—22no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—22no—
311C2×Dic11—24no—
312C2×Dic11—24no—
313C2×Dic11—22no—
314C2×Dic11—416no—
315C2×Dic11—44no—
316C2×Dic11—44no—
317C2×Dic11—44no—
318C2×Dic11H(5,𝔽2)14yes—
319Dic22—48no—
320Dic22—48no—
321C23×Q8—111no—
322C24×C4—111no—
323#538—28no—
324C2×C4⋊Q8—112no—
325C2×#126C2×D1112yes—
326C2×#124—112no—
327C2×#124C2×D1112yes—
328C2×#123—114no—
329C2×#123C2×D1112yes—
330C2×C22⋊Q8—114no—
331C2×C22⋊Q8—114no—
332C2×C22⋊Q8—228no—
333C2×C22⋊Q8C2×D1111yescharacteristic
334C2×#121C2×D1111yescharacteristic
335C2×#121C2×D1112yes—
336C2×#120C2×D1112yes—
337C2×C4×D4C2×D1112yes—
338C22×C4⋊C4—111no—
339C22×C4⋊C4—111no—
340C22×C4⋊C4—111no—
341C22×C22⋊C4—111no—
342C22×C22⋊C4C2×D1111yescharacteristic
343#400—112no—
344#400—114no—
345#399—114no—
346#398—114no—
347#398—112no—
348#397—114no—
349#397—114no—
350#396—114no—
351#395—112no—
352#395—114no—
353#394—112no—
354#394—114no—
355#394—114no—
356#393—114no—
357#391—112no—
358#391—112no—
359#389—114no—
360#389—114no—
361#388—114no—
362#388—114no—
363#388—114no—
364#387—114no—
365#386—112no—
366#386—112no—
367#386—112no—
368#386—114no—
369#386—112no—
370#385—114no—
371#385—112no—
372#385—112no—
373#385—112no—
374#385—114no—
375#385—112no—
376#381—114no—
377#380—112no—
378#380—114no—
379#379—112no—
380C4×C22⋊C4—111no—
381C4×C22⋊C4—111no—
382C22×C11—22no—
383C22×C11—22no—
384C22×C11—28no—
385C22×C11—24no—
386C22×C11—24no—
387C22×C11—24no—
388C22×C11—416no—
389C22×C11—48no—
390C22×C11—42no—
391C22×C11—42no—
392C22×C11—42no—
393C22×C11—48no—
394C22×C11#53614yes—
395C22×C11C23×D411yescharacteristic
396C22×C11C2×H(5,𝔽2)12yes—
397C22×C11C2×2−1+412yes—
398C22×C11#58512yes—
399C4×C11—22no—
400C4×C11—22no—
401C4×C11—24no—
402C4×C11—42no—
403C4×C11—42no—
404C4×C11—42no—
405Dic11—24no—
406Dic11—42no—
407Dic11—42no—
408Dic11—42no—
409Dic11—44no—
410Dic11—44no—
411C25C22×D1111yescharacteristic
412C22×Q8—112no—
413C22×Q8—112no—
414C22×Q8—224no—
415C22×Q8—444no—
416C22×Q8C22×D1111yescharacteristic
417C22×D4C22×D1112yes—
418C22×D4C22×D1112yes—
419C22×D4C22×D1112yes—
420C22×D4C22×D1111yescharacteristic
421C23×C4—111no—
422C23×C4—114no—
423C23×C4—111no—
424C23×C4—111no—
425C23×C4—111no—
426C23×C4—224no—
427C23×C4—444no—
428C23×C4C22×D1112yes—
429C23×C4C22×D1111yescharacteristic
430C23×C4C22×D1111yescharacteristic
431C4⋊Q8—444no—
432#126—28no—
433#124—28no—
434#124—444no—
435#123—28no—
436#123—448no—
437C22⋊Q8—24no—
438C22⋊Q8—2216no—
439C22⋊Q8—2216no—
440#121—24no—
441#121—28no—
442#120—28no—
443C4×D4—28no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4—114no—
446C2×C4⋊C4—112no—
447C2×C4⋊C4—112no—
448C2×C4⋊C4—114no—
449C2×C4⋊C4—114no—
450C2×C4⋊C4—114no—
451C2×C4⋊C4—114no—
452C2×C4⋊C4—114no—
453C2×C4⋊C4—224no—
454C2×C4⋊C4—224no—
455C2×C4⋊C4—224no—
456C2×C4⋊C4C22×D1112yes—
457C2×C4⋊C4C22×D1112yes—
458C2×C4⋊C4C22×D1111yescharacteristic
459C2×C4⋊C4C22×D1111yescharacteristic
460C2×C22⋊C4—114no—
461C2×C22⋊C4—114no—
462C2×C22⋊C4—112no—
463C2×C22⋊C4—112no—
464C2×C22⋊C4—114no—
465C2×C22⋊C4—114no—
466C2×C22⋊C4—114no—
467C2×C22⋊C4—114no—
468C2×C22⋊C4—114no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4C22⋊D1118yes—
471C2×C22⋊C4C22×D1112yes—
472C2×C22⋊C4C22×D1112yes—
473C2×C22⋊C4C22×D1112yes—
474C2×C22⋊C4C22×D1112yes—
475C2×C22⋊C4C22×D1112yes—
476C2×C22⋊C4C22×D1112yes—
477C2×C22⋊C4C22×D1112yes—
478C2×C42—112no—
479C2×C42—112no—
480C2×C42C22×D1112yes—
481#95—112no—
482#95—112no—
483#95—114no—
484#95—114no—
485#95—114no—
486#95—114no—
487#95—114no—
488#95—114no—
489#95—114no—
490#95—114no—
491#95—114no—
492C2×C11—24no—
493C2×C11—44no—
494C2×C11—82no—
495C2×C11C2×#53611yescharacteristic
496C2×C11#348411yescharacteristic
497C2×C11#348511yescharacteristic
498C2×C11#354114yes—
499C24—24no—
500C24—42no—
501C24—42no—
502C24C2×C22⋊D1114yes—
503C24C23×D1112yes—
504C24C23×D1112yes—
505C24C23×D1111yescharacteristic
506C2×Q8—22no—
507C2×Q8—42no—
508C2×Q8—224no—
509C2×Q8—224no—
510C2×Q8—224no—
511C2×Q8—224no—
512C2×Q8—442no—
513C2×Q8—442no—
514C2×Q8—4416no—
515C2×D4—28no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—24no—
519C2×D4—22no—
520C2×D4—44no—
521C2×D4—42no—
522C2×D4—44no—
523C22×C4—24no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—44no—
527C22×C4—112no—
528C22×C4—114no—
529C22×C4—114no—
530C22×C4—112no—
531C22×C4—112no—
532C22×C4—112no—
533C22×C4—224no—
534C22×C4—228no—
535C22×C4—222no—
536C22×C4—222no—
537C22×C4—222no—
538C22×C4—222no—
539C22×C4—228no—
540C22×C4—444no—
541C22×C4—442no—
542C22×C4—442no—
543C22×C4—442no—
544C22×C4—4416no—
545C22×C4C2×C22⋊D1114yes—
546C22×C4C2×C22⋊D1114yes—
547C22×C4C23×D1112yes—
548C22×C4C23×D1112yes—
549C22×C4C23×D1112yes—
550C22×C4C23×D1111yescharacteristic
551C22×C4C23×D1111yescharacteristic
552C22×C4C23×D1112yes—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—228no—
558C4⋊C4—228no—
559C4⋊C4—224no—
560C4⋊C4—224no—
561C4⋊C4—228no—
562C4⋊C4—444no—
563C4⋊C4—444no—
564C4⋊C4—444no—
565C4⋊C4—444no—
566C22⋊C4—24no—
567C22⋊C4—24no—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—24no—
571C22⋊C4—228no—
572C22⋊C4—224no—
573C22⋊C4—224no—
574C22⋊C4—228no—
575C22⋊C4—444no—
576C22⋊C4—444no—
577C22⋊C4—444no—
578C22⋊C4—444no—
579C22⋊C4—444no—
580C22⋊C4C2×C22⋊D1118yes—
581C22⋊C4C2×C22⋊D1118yes—
582C42—24no—
583C42—442no—
584C42—442no—
585C11#3670511yescharacteristic, complemented, Sylow
586C23—22no—
587C23—22no—
588C23—28no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—22no—
596C23—44no—
597C23—44no—
598C23—416no—
599C23#6704314yes—
600C23C22×C22⋊D1114yes—
601C23C22×C22⋊D1112yes—
602C23C24×D1111yescharacteristic
603Q8—82no—
604Q8—448no—
605Q8—448no—
606D4—48no—
607D4—82no—
608D4—84no—
609D4—84no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—84no—
622C2×C4—114no—
623C2×C4—228no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—224no—
627C2×C4—224no—
628C2×C4—224no—
629C2×C4—224no—
630C2×C4—222no—
631C2×C4—224no—
632C2×C4—222no—
633C2×C4—224no—
634C2×C4—222no—
635C2×C4—224no—
636C2×C4—222no—
637C2×C4—222no—
638C2×C4—222no—
639C2×C4—222no—
640C2×C4—4416no—
641C2×C4—444no—
642C2×C4—444no—
643C2×C4—444no—
644C2×C4C22×C22⋊D1114yes—
645C2×C4C22×C22⋊D1112yes—
646C2×C4C22×C22⋊D1112yes—
647C22—28no—
648C22—22no—
649C22—22no—
650C22—24no—
651C22—24no—
652C22—24no—
653C22—416no—
654C22—48no—
655C22—48no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22#1062335614yes—
660C22C2×#6704312yes—
661C22D11×H(5,𝔽2)12yes—
662C22#1062345512yes—
663C22C23×C22⋊D1111yescharacteristic
664C4—22no—
665C4—22no—
666C4—24no—
667C4—42no—
668C4—42no—
669C4—42no—
670C4—224no—
671C4—444no—
672C4—444no—
673C4—442no—
674C4—442no—
675C4—442no—
676C2—24no—
677C2—44no—
678C2—82no—
679C2C2×#1062335611yescharacteristic
680C2#1308224711yescharacteristic
681C2#1308225611yescharacteristic
682C2#1308289614yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
Fitting, prime radicalC2×C11×#538C2
hypercenterC2×#538D11
hypocenterC11#36705
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#538

Complements

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

NH ≅ G/Ntype
1. C22×#66931C2semidirect
2. #13076906C2semidirect
3. #13075061C2semidirect
4. #13075031C2semidirect
5. #13074891C2semidirect
6. #13074861C2semidirect
7. #13074391C2semidirect
8. #13074097C2semidirect
9. #13073997C2semidirect
10. #13073959C2semidirect
11. #13072933C2semidirect
12. #13072275C2semidirect
13. #13072261C2semidirect
14. #13071214C2semidirect
29. C2×#66997C22semidirect
30. C2×#66989C22semidirect
39. #10622842C22semidirect
42. #10622835C22semidirect
49. #10622825C22semidirect
50. #10622823C22semidirect
53. #10622599C22semidirect
54. #10622597C22semidirect
55. #10622595C22semidirect
56. #10622593C22semidirect
57. #10622592C22semidirect
58. #10622587C22semidirect
59. #10622587C22semidirect
60. #10622585C22semidirect
65. #10622562C22semidirect
66. #10622561C22semidirect
67. #10622560C22semidirect
73. #10622558C22semidirect
75. #10622546C22semidirect
76. #10622541C22semidirect
585. C11#36705semidirect

Maximal subgroups

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

subgroupindex
C22×#669312
#130769062
#130750612
#130750312
#130748912
#130748612
#130743912
#130740972
#130739972
#130739592
#130729332
#130722752
#130722612
#130712142
C2×C11×#5382
#3670511