Finite Group Databasebeta

← #14960729

Subgroups — #14960729

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
1C22×#66931C211yesmaximal, characteristic, complemented
2#13076906C212yesmaximal, complemented
3#13075208C214yesmaximal, complemented
4#13075184C214yesmaximal, complemented
5#13074962C214yesmaximal, complemented
6#13074953C214yesmaximal, complemented
7#13074391C212yesmaximal, complemented
8#13074097C211yesmaximal, characteristic, complemented
9#13073997C211yesmaximal, characteristic, complemented
10#13073959C212yesmaximal, complemented
11#13073109C211yesmaximal, characteristic, complemented
12#13073095C211yesmaximal, characteristic, complemented
13#13071981C212yesmaximal, 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×#121C2212yes—
24C2×C11×#121C2211yescharacteristic
25C2×C11×#120C2212yes—
26C2×C4×D4×C11C2212yes—
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C2×#66988C2214yes—
30C22×C4⋊Dic11C2211yescharacteristic
31C2×#66977C2214yescomplemented
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C2×#66931—28no—
35C2×#66931C2214yes—
36C2×#66931C2214yes—
37#10622860C2212yes—
38#10622843C2212yescomplemented
39#10622842C2212yescomplemented
40#10622835C2214yes—
41#10622835C2214yes—
42#10622835C2212yescomplemented
43#10622834C2212yescomplemented
44#10622833C2214yes—
45#10622833C2212yes—
46#10622833C2212yes—
47#10622833C2212yes—
48#10622833C2212yes—
49#10622825C2212yes—
50#10622823C2214yescomplemented
51C4×C22⋊Dic11C2211yescharacteristic
52C4×C22⋊Dic11C2211yescharacteristic
53#10622597C2214yescomplemented
54#10622596C2214yescomplemented
55#10622595C2212yescomplemented
56#10622593C2212yescomplemented
57#10622592C2214yescomplemented
58#10622590C2212yescomplemented
59#10622589C2212yescomplemented
60#10622585C2214yescomplemented
61#10622566C2214yescomplemented
62#10622565C2214yes—
63#10622565C2214yes—
64#10622564C2214yes—
65#10622564C2214yes—
66#10622561C2214yescomplemented
67#10622560C2214yescomplemented
68#10622559C2214yes—
69#10622559C2212yes—
70#10622559C2212yes—
71#10622559C2212yes—
72#10622559C2212yes—
73#10622558C2214yescomplemented
74#10622556C2214yes—
75#10622546C2214yescomplemented
76#10622542C2214yescomplemented
77C25×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11C2312yes—
80C22×D4×C11C2312yes—
81C22×D4×C11C2312yes—
82C22×D4×C11C2311yescharacteristic
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×Dic22C2314yes—
96C11×#126—28no—
97C11×#124—28no—
98C11×#123—28no—
99C11×C22⋊Q8—24no—
100C11×#121—24no—
101C11×#121—28no—
102C11×#120—28no—
103C4×D4×C11—28no—
104C2×C11×C4⋊C4C2312yes—
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2312yes—
108C2×C11×C22⋊C4D418yes—
109C2×C11×C22⋊C4C2312yes—
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×C42×C11C2312yes—
117C2×C22⋊Dic11—24no—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2312yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127#66988—48no—
128C2×C4⋊Dic11—24no—
129C2×C4⋊Dic11C2312yes—
130C2×C4⋊Dic11C2312yes—
131C2×C4⋊Dic11C2314yes—
132#66977—48no—
133C2×Dic11⋊C4—24no—
134C2×Dic11⋊C4—24no—
135C2×Dic11⋊C4C2314yes—
136C2×Dic11⋊C4C2312yes—
137C2×Dic11⋊C4C2312yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2314yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×C4×Dic11C2312yes—
143C2×C4×Dic11C2312yes—
144#66931—216no—
145#66931—216no—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2312yes—
156C11⋊#95C2312yes—
157#36716—111nomaximal, Sylow
158C24×C11—24no—
159C24×C11—42no—
160C24×C11—42no—
161C24×C11C2×D414yes—
162C24×C11C2412yes—
163C24×C11C2412yes—
164C24×C11C2411yescharacteristic
165C2×Q8×C11—22no—
166C2×Q8×C11—42no—
167C2×D4×C11—24no—
168C2×D4×C11—28no—
169C2×D4×C11—24no—
170C2×D4×C11—24no—
171C2×D4×C11—22no—
172C2×D4×C11—44no—
173C2×D4×C11—42no—
174C2×D4×C11—44no—
175C22×C4×C11—24no—
176C22×C4×C11—42no—
177C22×C4×C11—42no—
178C22×C4×C11—44no—
179C22×C4×C11C2×D414yes—
180C22×C4×C11C2×D414yes—
181C22×C4×C11C2412yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C22×C4×C11C2412yes—
187C22×Dic11—24no—
188C22×Dic11—28no—
189C22×Dic11—22no—
190C22×Dic11—28no—
191C22×Dic11—22no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—42no—
195C22×Dic11—42no—
196C22×Dic11—44no—
197C22×Dic11—42no—
198C22×Dic11—416no—
199C22×Dic11C2414yes—
200C22×Dic11C2414yes—
201C22×Dic11C2412yes—
202C22×Dic11C2412yes—
203C22×Dic11C2412yes—
204C22×Dic11C2412yes—
205C2×Dic22—28no—
206C2×Dic22—28no—
207C2×Dic22—44no—
208C2×Dic22—416no—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4—22no—
212C11×C4⋊C4—22no—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—24no—
215C11×C22⋊C4—24no—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—24no—
218C11×C22⋊C4C2×D418yes—
219C11×C22⋊C4C2×D418yes—
220C42×C11—24no—
221C22⋊Dic11—28no—
222C22⋊Dic11—28no—
223C22⋊Dic11—24no—
224C22⋊Dic11—24no—
225C22⋊Dic11—44no—
226C22⋊Dic11—44no—
227C22⋊Dic11—44no—
228C22⋊Dic11—44no—
229C22⋊Dic11—44no—
230C4⋊Dic11—24no—
231C4⋊Dic11—24no—
232C4⋊Dic11—44no—
233Dic11⋊C4—28no—
234Dic11⋊C4—24no—
235Dic11⋊C4—24no—
236Dic11⋊C4—28no—
237Dic11⋊C4—44no—
238Dic11⋊C4—44no—
239Dic11⋊C4—44no—
240C4×Dic11—42no—
241C4×Dic11—42no—
242C2×#538D1111yescharacteristic
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#2504—111no—
254#2502—111no—
255#2409—112no—
256#2312—111no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—28no—
260C23×C11—24no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11—22no—
264C23×C11—24no—
265C23×C11—24no—
266C23×C11—24no—
267C23×C11—44no—
268C23×C11—44no—
269C23×C11—416no—
270C23×C11C22×D414yes—
271C23×C11C22×D412yes—
272C23×C112−1+414yes—
273C23×C11C2511yescharacteristic
274Q8×C11—82no—
275D4×C11—48no—
276D4×C11—82no—
277D4×C11—84no—
278D4×C11—84no—
279C2×C4×C11—24no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—44no—
289C2×C4×C11—44no—
290C2×C4×C11—84no—
291C2×C4×C11C22×D412yes—
292C2×C4×C11C22×D412yes—
293C2×C4×C11C22×D414yes—
294C2×Dic11—28no—
295C2×Dic11—22no—
296C2×Dic11—22no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—22no—
300C2×Dic11—24no—
301C2×Dic11—24no—
302C2×Dic11—24no—
303C2×Dic11—24no—
304C2×Dic11—24no—
305C2×Dic11—24no—
306C2×Dic11—24no—
307C2×Dic11—24no—
308C2×Dic11—24no—
309C2×Dic11—416no—
310C2×Dic11—44no—
311C2×Dic11—44no—
312C2×Dic11—44no—
313C2×Dic11H(5,𝔽2)14yes—
314Dic22—416no—
315C23×Q8—111no—
316C24×C4—111no—
317#538—28no—
318C2×#126C2×D1112yes—
319C2×#124C2×D1112yes—
320C2×#123—114no—
321C2×#123C2×D1112yes—
322C2×C22⋊Q8—114no—
323C2×C22⋊Q8—114no—
324C2×C22⋊Q8—114no—
325C2×C22⋊Q8—228no—
326C2×C22⋊Q8C2×D1111yescharacteristic
327C2×#121C2×D1111yescharacteristic
328C2×#121C2×D1112yes—
329C2×#120C2×D1112yes—
330C2×C4×D4C2×D1112yes—
331C22×C4⋊C4—111no—
332C22×C4⋊C4—111no—
333C22×C4⋊C4—111no—
334C22×C22⋊C4—111no—
335C22×C22⋊C4C2×D1111yescharacteristic
336#400—112no—
337#398—114no—
338#398—112no—
339#398—114no—
340#397—114no—
341#397—114no—
342#397—114no—
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#390—112no—
353#389—114no—
354#388—114no—
355#388—114no—
356#388—114no—
357#387—114no—
358#386—112no—
359#386—112no—
360#386—112no—
361#386—114no—
362#386—112no—
363#385—114no—
364#385—112no—
365#385—112no—
366#385—112no—
367#385—114no—
368#385—112no—
369#384—112no—
370#382—112no—
371#381—114no—
372#380—112no—
373#379—112no—
374C4×C22⋊C4—111no—
375C4×C22⋊C4—111no—
376C22×C11—22no—
377C22×C11—22no—
378C22×C11—28no—
379C22×C11—24no—
380C22×C11—24no—
381C22×C11—24no—
382C22×C11—416no—
383C22×C11—48no—
384C22×C11—42no—
385C22×C11—42no—
386C22×C11—42no—
387C22×C11—48no—
388C22×C11#53614yes—
389C22×C11C23×D411yescharacteristic
390C22×C11C2×H(5,𝔽2)12yes—
391C22×C11C2×2−1+412yes—
392C22×C11#58512yes—
393C4×C11—24no—
394C4×C11—22no—
395C4×C11—22no—
396C4×C11—42no—
397C4×C11—42no—
398C4×C11—42no—
399Dic11—24no—
400Dic11—42no—
401Dic11—42no—
402Dic11—42no—
403Dic11—44no—
404Dic11—44no—
405C25C22×D1111yescharacteristic
406C22×Q8—114no—
407C22×Q8—224no—
408C22×Q8—444no—
409C22×Q8C22×D1111yescharacteristic
410C22×D4C22×D1112yes—
411C22×D4C22×D1112yes—
412C22×D4C22×D1112yes—
413C22×D4C22×D1111yescharacteristic
414C23×C4—111no—
415C23×C4—114no—
416C23×C4—111no—
417C23×C4—111no—
418C23×C4—111no—
419C23×C4—224no—
420C23×C4—444no—
421C23×C4C22×D1112yes—
422C23×C4C22×D1111yescharacteristic
423C23×C4C22×D1111yescharacteristic
424#126—28no—
425#124—28no—
426#123—28no—
427#123—448no—
428C22⋊Q8—24no—
429C22⋊Q8—2216no—
430C22⋊Q8—2216no—
431C22⋊Q8—448no—
432#121—24no—
433#121—28no—
434#120—28no—
435C4×D4—28no—
436C2×C4⋊C4—112no—
437C2×C4⋊C4—112no—
438C2×C4⋊C4—114no—
439C2×C4⋊C4—112no—
440C2×C4⋊C4—112no—
441C2×C4⋊C4—114no—
442C2×C4⋊C4—114no—
443C2×C4⋊C4—114no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4—114no—
446C2×C4⋊C4—224no—
447C2×C4⋊C4—224no—
448C2×C4⋊C4—224no—
449C2×C4⋊C4C22×D1112yes—
450C2×C4⋊C4C22×D1112yes—
451C2×C4⋊C4C22×D1111yescharacteristic
452C2×C4⋊C4C22×D1111yescharacteristic
453C2×C22⋊C4—114no—
454C2×C22⋊C4—114no—
455C2×C22⋊C4—112no—
456C2×C22⋊C4—112no—
457C2×C22⋊C4—114no—
458C2×C22⋊C4—114no—
459C2×C22⋊C4—114no—
460C2×C22⋊C4—114no—
461C2×C22⋊C4—114no—
462C2×C22⋊C4—224no—
463C2×C22⋊C4C22⋊D1118yes—
464C2×C22⋊C4C22×D1112yes—
465C2×C22⋊C4C22×D1112yes—
466C2×C22⋊C4C22×D1112yes—
467C2×C22⋊C4C22×D1112yes—
468C2×C22⋊C4C22×D1112yes—
469C2×C22⋊C4C22×D1112yes—
470C2×C22⋊C4C22×D1112yes—
471C2×C42—112no—
472C2×C42—112no—
473C2×C42C22×D1112yes—
474#95—112no—
475#95—112no—
476#95—114no—
477#95—114no—
478#95—114no—
479#95—114no—
480#95—114no—
481#95—114no—
482#95—114no—
483#95—114no—
484#95—114no—
485C2×C11—24no—
486C2×C11—44no—
487C2×C11—82no—
488C2×C11C2×#53611yescharacteristic
489C2×C11#348411yescharacteristic
490C2×C11#348511yescharacteristic
491C2×C11#354114yes—
492C24—24no—
493C24—42no—
494C24—42no—
495C24C2×C22⋊D1114yes—
496C24C23×D1112yes—
497C24C23×D1112yes—
498C24C23×D1111yescharacteristic
499C2×Q8—22no—
500C2×Q8—42no—
501C2×Q8—228no—
502C2×Q8—228no—
503C2×Q8—444no—
504C2×Q8—4416no—
505C2×D4—28no—
506C2×D4—24no—
507C2×D4—24no—
508C2×D4—24no—
509C2×D4—22no—
510C2×D4—44no—
511C2×D4—42no—
512C2×D4—44no—
513C22×C4—24no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—44no—
517C22×C4—112no—
518C22×C4—114no—
519C22×C4—114no—
520C22×C4—112no—
521C22×C4—112no—
522C22×C4—112no—
523C22×C4—224no—
524C22×C4—228no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4—222no—
529C22×C4—228no—
530C22×C4—444no—
531C22×C4—442no—
532C22×C4—442no—
533C22×C4—442no—
534C22×C4—4416no—
535C22×C4C2×C22⋊D1114yes—
536C22×C4C2×C22⋊D1114yes—
537C22×C4C23×D1112yes—
538C22×C4C23×D1112yes—
539C22×C4C23×D1112yes—
540C22×C4C23×D1111yescharacteristic
541C22×C4C23×D1111yescharacteristic
542C22×C4C23×D1112yes—
543C4⋊C4—24no—
544C4⋊C4—24no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—228no—
548C4⋊C4—224no—
549C4⋊C4—224no—
550C4⋊C4—228no—
551C4⋊C4—224no—
552C4⋊C4—224no—
553C4⋊C4—444no—
554C4⋊C4—444no—
555C4⋊C4—444no—
556C4⋊C4—444no—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C22⋊C4—24no—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C22⋊C4—228no—
563C22⋊C4—224no—
564C22⋊C4—224no—
565C22⋊C4—228no—
566C22⋊C4—444no—
567C22⋊C4—444no—
568C22⋊C4—444no—
569C22⋊C4—444no—
570C22⋊C4—444no—
571C22⋊C4C2×C22⋊D1118yes—
572C22⋊C4C2×C22⋊D1118yes—
573C42—24no—
574C42—442no—
575C42—442no—
576C11#3671611yescharacteristic, complemented, Sylow
577C23—22no—
578C23—22no—
579C23—28no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—22no—
587C23—44no—
588C23—44no—
589C23—416no—
590C23#6704314yes—
591C23C22×C22⋊D1114yes—
592C23C22×C22⋊D1112yes—
593C23C24×D1111yescharacteristic
594Q8—82no—
595Q8—4416no—
596D4—48no—
597D4—82no—
598D4—84no—
599D4—84no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—84no—
612C2×C4—114no—
613C2×C4—228no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—224no—
617C2×C4—224no—
618C2×C4—224no—
619C2×C4—224no—
620C2×C4—224no—
621C2×C4—224no—
622C2×C4—224no—
623C2×C4—224no—
624C2×C4—224no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—4416no—
629C2×C4—444no—
630C2×C4—444no—
631C2×C4—444no—
632C2×C4C22×C22⋊D1114yes—
633C2×C4C22×C22⋊D1112yes—
634C2×C4C22×C22⋊D1112yes—
635C22—28no—
636C22—22no—
637C22—22no—
638C22—24no—
639C22—24no—
640C22—24no—
641C22—416no—
642C22—48no—
643C22—48no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22#1062335614yes—
648C22C2×#6704312yes—
649C22D11×H(5,𝔽2)12yes—
650C22#1062345512yes—
651C22C23×C22⋊D1111yescharacteristic
652C4—24no—
653C4—22no—
654C4—22no—
655C4—42no—
656C4—42no—
657C4—42no—
658C4—224no—
659C4—444no—
660C4—444no—
661C4—442no—
662C4—442no—
663C4—442no—
664C2—24no—
665C2—44no—
666C2—82no—
667C2C2×#1062335611yescharacteristic
668C2#1308224711yescharacteristic
669C2#1308225611yescharacteristic
670C2#1308290414yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
Fitting, prime radicalC2×C11×#538C2
hypercenterC2×#538D11
hypocenterC11#36716
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. #13075208C2semidirect
4. #13075184C2semidirect
5. #13074962C2semidirect
6. #13074953C2semidirect
7. #13074391C2semidirect
8. #13074097C2semidirect
9. #13073997C2semidirect
10. #13073959C2semidirect
11. #13073109C2semidirect
12. #13073095C2semidirect
13. #13071981C2semidirect
14. #13071214C2semidirect
31. C2×#66977C22semidirect
38. #10622843C22semidirect
39. #10622842C22semidirect
42. #10622835C22semidirect
43. #10622834C22semidirect
50. #10622823C22semidirect
53. #10622597C22semidirect
54. #10622596C22semidirect
55. #10622595C22semidirect
56. #10622593C22semidirect
57. #10622592C22semidirect
58. #10622590C22semidirect
59. #10622589C22semidirect
60. #10622585C22semidirect
61. #10622566C22semidirect
66. #10622561C22semidirect
67. #10622560C22semidirect
73. #10622558C22semidirect
75. #10622546C22semidirect
76. #10622542C22semidirect
576. C11#36716semidirect

Maximal subgroups

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

subgroupindex
C22×#669312
#130769062
#130752082
#130751842
#130749622
#130749532
#130743912
#130740972
#130739972
#130739592
#130731092
#130730952
#130719812
#130712142
C2×C11×#5382
#3671611