Finite Group Databasebeta

← #14960621

Subgroups — #14960621

Order 2816.

2422 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623154C211yesmaximal, characteristic, complemented
2C22×#66988C211yesmaximal, characteristic
3#13076901C212yesmaximal, complemented
4#13075135C214yesmaximal, complemented
5#13075131C214yesmaximal, complemented
6#13074899C214yesmaximal, complemented
7#13074891C214yesmaximal, complemented
8#13074425C212yesmaximal, complemented
9#13073997C211yesmaximal, characteristic, complemented
10#13073991C211yesmaximal, characteristic, complemented
11#13072887C212yesmaximal, complemented
12#13072887C212yesmaximal, complemented
13#13072263C211yesmaximal, characteristic
14#13071216C211yesmaximal, characteristic, complemented
15C11×#2435C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C2×C11×#124C2212yes—
19C2×C11×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C2×#66997C2212yescomplemented
24C2×#66989C2212yes—
25C2×#66988—28no—
26C2×#66988C2214yes—
27C2×#66988C2214yes—
28C2×#66977C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31#10623154—28no—
32C2×#66942C2212yescomplemented
33C2×#66942C2212yescomplemented
34C2×#66941C2212yescomplemented
35C2×#66931C2212yes—
36C2×#66931C2214yescomplemented
37C2×#66930C2212yes—
38C11×#394C2214yes—
39C11×#390C2212yes—
40C11×#379C2212yes—
41C11×#379C2212yes—
42C4×C11×C22⋊C4C2211yescharacteristic
43#10622860C2212yes—
44#10622860C2212yes—
45#10622842C2212yescomplemented
46#10622835C2214yes—
47#10622834C2212yes—
48C4×C22⋊Dic11C2211yescharacteristic
49#10622593C2212yescomplemented
50#10622585C2214yescomplemented
51#10622565C2214yescomplemented
52#10622565C2214yescomplemented
53#10622564C2214yescomplemented
54#10622564C2214yescomplemented
55#10622563C2212yes—
56#10622563C2212yes—
57#10622563C2214yescomplemented
58#10622562C2214yescomplemented
59#10622562C2214yescomplemented
60#10622562C2214yescomplemented
61#10622561C2214yescomplemented
62#10622561C2214yescomplemented
63#10622560C2214yescomplemented
64#10622559C2212yes—
65#10622559C2212yes—
66#10622559C2214yescomplemented
67#10622558C2214yescomplemented
68#10622558C2214yescomplemented
69#10622556C2212yes—
70#10622555C2212yes—
71#10622555C2214yescomplemented
72#10622546C2214yescomplemented
73#10622541C2214yescomplemented
74#10622274C2212yescomplemented
75#10622269C2212yescomplemented
76#10622265C2214yescomplemented
77C25×C11C2311yescharacteristic
78C25×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11—24no—
81C22×D4×C11—44no—
82C22×D4×C11C2312yes—
83C22×D4×C11C2312yes—
84C23×C4×C11C2311yescharacteristic
85C23×Dic11—24no—
86C23×Dic11—44no—
87C23×Dic11C2314yes—
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C22×Dic22C2312yes—
93C22×Dic22C2311yescharacteristic
94C11×#124—44no—
95C11×C22⋊Q8—24no—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4C2312yes—
99C2×C11×C22⋊C4C2314yes—
100C2×C11×C22⋊C4C2312yes—
101C2×C11×C22⋊C4C2314yes—
102C2×C11×C22⋊C4C2314yes—
103C2×C11×C22⋊C4C2314yes—
104C2×C42×C11C2312yes—
105C2×C22⋊Dic11—24no—
106C2×C22⋊Dic11—24no—
107C2×C22⋊Dic11—24no—
108C2×C22⋊Dic11C2312yes—
109C2×C22⋊Dic11C2314yes—
110C2×C22⋊Dic11C2312yes—
111C2×C22⋊Dic11C2314yes—
112C2×C22⋊Dic11C2314yes—
113C2×C22⋊Dic11C2314yes—
114C2×C22⋊Dic11C2314yes—
115C2×C22⋊Dic11C2314yes—
116C2×C22⋊Dic11C2314yes—
117#66997—28no—
118#66989—44no—
119#66988—216no—
120#66988—216no—
121C2×C4⋊Dic11C2312yes—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2314yes—
124C2×C4⋊Dic11C2314yes—
125#66977—24no—
126C2×Dic11⋊C4—24no—
127C2×Dic11⋊C4D418yes—
128C2×Dic11⋊C4C2312yes—
129C2×Dic11⋊C4C2312yes—
130C2×Dic11⋊C4C2312yes—
131C2×Dic11⋊C4C2312yes—
132C2×Dic11⋊C4C2312yes—
133C2×Dic11⋊C4C2312yes—
134C2×Dic11⋊C4C2312yes—
135C2×Dic11⋊C4C2314yes—
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2312yes—
139C2×Dic11⋊C4C2312yes—
140C2×C4×Dic11C2312yes—
141C2×C4×Dic11C2312yes—
142C2×C4×Dic11C2312yes—
143#66942—28no—
144#66942—28no—
145#66941—28no—
146#66931—28no—
147#66931—48no—
148#66930—28no—
149C11×#95C2312yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2312yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158#36711—111nomaximal, Sylow
159C24×C11—22no—
160C24×C11—24no—
161C24×C11—22no—
162C24×C11—24no—
163C24×C11—24no—
164C24×C11—42no—
165C24×C11—42no—
166C24×C11—42no—
167C24×C11C2412yes—
168C24×C11C2412yes—
169C24×C11C2411yescharacteristic
170C2×Q8×C11—22no—
171C2×Q8×C11—42no—
172C2×D4×C11—24no—
173C2×D4×C11—24no—
174C2×D4×C11—24no—
175C2×D4×C11—24no—
176C2×D4×C11—42no—
177C2×D4×C11—42no—
178C2×D4×C11—416no—
179C22×C4×C11—42no—
180C22×C4×C11C2×D414yes—
181C22×C4×C11C2414yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C22×Dic11—28no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—28no—
190C22×Dic11—24no—
191C22×Dic11—42no—
192C22×Dic11—42no—
193C22×Dic11—44no—
194C22×Dic11—42no—
195C22×Dic11—416no—
196C22×Dic11C2×D414yes—
197C22×Dic11C2×D414yes—
198C22×Dic11C2414yes—
199C22×Dic11C2412yes—
200C22×Dic11C2412yes—
201C22×Dic11C2412yes—
202C22×Dic11C2412yes—
203C22×Dic11C2412yes—
204C22×Dic11C2412yes—
205C2×Dic22—24no—
206C2×Dic22—22no—
207C2×Dic22—44no—
208C2×Dic22—42no—
209C11×C4⋊C4—24no—
210C11×C4⋊C4—22no—
211C11×C22⋊C4—24no—
212C11×C22⋊C4—28no—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—44no—
215C11×C22⋊C4—44no—
216C11×C22⋊C4—44no—
217C42×C11—42no—
218C22⋊Dic11—28no—
219C22⋊Dic11—28no—
220C22⋊Dic11—28no—
221C22⋊Dic11—24no—
222C22⋊Dic11—28no—
223C22⋊Dic11—24no—
224C22⋊Dic11—44no—
225C22⋊Dic11—44no—
226C22⋊Dic11—44no—
227C4⋊Dic11—24no—
228C4⋊Dic11—22no—
229C4⋊Dic11—44no—
230C4⋊Dic11—44no—
231Dic11⋊C4—24no—
232Dic11⋊C4—24no—
233Dic11⋊C4—24no—
234Dic11⋊C4—24no—
235Dic11⋊C4—24no—
236Dic11⋊C4—24no—
237Dic11⋊C4—24no—
238Dic11⋊C4—44no—
239Dic11⋊C4—44no—
240Dic11⋊C4—44no—
241Dic11⋊C4C2×D418yes—
242Dic11⋊C4C2×D418yes—
243C4×Dic11—24no—
244C4×Dic11—24no—
245C4×Dic11—42no—
246C2×#544—111no—
247C22×#123—111no—
248#2848—112no—
249#2694—114no—
250#2694—114no—
251#2674—114no—
252#2674—114no—
253#2626—112no—
254#2583—111no—
255#2583—111no—
256#2482—112no—
257#2482—112no—
258#2435—111no—
259#2435D1111yescharacteristic
260#2313—111no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—28no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—24no—
267C23×C11—24no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—24no—
272C23×C11—24no—
273C23×C11—416no—
274C23×C11—44no—
275C23×C11—44no—
276C23×C11—44no—
277C23×C11—44no—
278C23×C11—44no—
279C23×C11—88no—
280C23×C11C22×D412yes—
281C23×C11H(5,𝔽2)14yes—
282C23×C112−1+414yes—
283C23×C11C2511yescharacteristic
284Q8×C11—82no—
285D4×C11—48no—
286D4×C11—48no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—44no—
297C2×C4×C11C22×D412yes—
298C2×C4×C11C22×D412yes—
299C2×Dic11—28no—
300C2×Dic11—24no—
301C2×Dic11—24no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—24no—
307C2×Dic11—24no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—22no—
311C2×Dic11—24no—
312C2×Dic11—22no—
313C2×Dic11—24no—
314C2×Dic11—44no—
315C2×Dic11—416no—
316C2×Dic11—44no—
317C2×Dic11—44no—
318C2×Dic11C22×D414yes—
319C2×Dic11C22×D414yes—
320Dic22—84no—
321Dic22—82no—
322C23×D4C2×D1111yescharacteristic
323C24×C4—111no—
324#544—228no—
325C2×C4⋊Q8—112no—
326C2×C4⋊Q8—112no—
327C2×#125—112no—
328C2×#125—112no—
329C2×#124—112no—
330C2×#124C2×D1112yes—
331C2×#123—114no—
332C2×#123—114no—
333C2×#123—228no—
334C2×C22⋊Q8—111no—
335C2×C22⋊Q8—112no—
336C2×C22⋊Q8—114no—
337C2×C22⋊Q8C2×D1111yescharacteristic
338C2×#117—112no—
339C22×C4⋊C4—111no—
340C22×C4⋊C4—111no—
341C22×C22⋊C4—111no—
342C22×C22⋊C4—111no—
343C22×C22⋊C4—111no—
344#399—114no—
345#399—114no—
346#399—114no—
347#398—112no—
348#398—112no—
349#397—114no—
350#397—114no—
351#396—114no—
352#396—114no—
353#395—112no—
354#395—112no—
355#394—114no—
356#394C2×D1114yes—
357#393—114no—
358#390—112no—
359#390C2×D1112yes—
360#389—114no—
361#389—114no—
362#388—114no—
363#388—114no—
364#388—114no—
365#388—114no—
366#387—114no—
367#387—114no—
368#385—112no—
369#385—112no—
370#385—112no—
371#385—112no—
372#385—114no—
373#385—114no—
374#381—112no—
375#380—112no—
376#380—114no—
377#379—112no—
378#379—112no—
379#379C2×D1112yes—
380#379C2×D1112yes—
381C4×C22⋊C4—111no—
382C4×C22⋊C4C2×D1111yescharacteristic
383C22×C11—22no—
384C22×C11—22no—
385C22×C11—28no—
386C22×C11—24no—
387C22×C11—28no—
388C22×C11—416no—
389C22×C11—42no—
390C22×C11—42no—
391C22×C11—44no—
392C22×C11—42no—
393C22×C11—42no—
394C22×C11—42no—
395C22×C11—44no—
396C22×C11—44no—
397C22×C11—88no—
398C22×C11#53614yes—
399C22×C11C23×D411yescharacteristic
400C22×C11C2×H(5,𝔽2)12yes—
401C22×C11C2×2−1+412yes—
402C22×C11#58512yes—
403C4×C11—22no—
404C4×C11—22no—
405C4×C11—42no—
406C4×C11—42no—
407C4×C11—44no—
408Dic11—24no—
409Dic11—24no—
410Dic11—42no—
411Dic11—42no—
412Dic11—42no—
413Dic11—42no—
414Dic11—44no—
415C25C22×D1111yescharacteristic
416C25C22×D1111yescharacteristic
417C22×Q8—112no—
418C22×Q8—111no—
419C22×Q8C22×D1111yescharacteristic
420C22×D4—24no—
421C22×D4—44no—
422C22×D4C22×D1112yes—
423C22×D4C22×D1112yes—
424C23×C4—111no—
425C23×C4—111no—
426C23×C4—114no—
427C23×C4—111no—
428C23×C4—111no—
429C23×C4—224no—
430C23×C4—444no—
431C23×C4C22×D1111yescharacteristic
432C4⋊Q8—228no—
433C4⋊Q8—228no—
434#125—228no—
435#125—228no—
436#124—44no—
437#124—444no—
438#123—2216no—
439#123—2216no—
440C22⋊Q8—24no—
441C22⋊Q8—228no—
442C22⋊Q8—224no—
443C22⋊Q8—448no—
444#117—228no—
445C2×C4⋊C4—118no—
446C2×C4⋊C4—112no—
447C2×C4⋊C4—112no—
448C2×C4⋊C4—112no—
449C2×C4⋊C4—112no—
450C2×C4⋊C4—112no—
451C2×C4⋊C4—112no—
452C2×C4⋊C4—112no—
453C2×C4⋊C4—111no—
454C2×C4⋊C4—112no—
455C2×C4⋊C4—112no—
456C2×C4⋊C4—112no—
457C2×C4⋊C4—114no—
458C2×C4⋊C4—114no—
459C2×C4⋊C4—114no—
460C2×C4⋊C4—114no—
461C2×C4⋊C4—114no—
462C2×C4⋊C4—224no—
463C2×C4⋊C4C22×D1111yescharacteristic
464C2×C4⋊C4C22×D1112yes—
465C2×C22⋊C4—114no—
466C2×C22⋊C4—114no—
467C2×C22⋊C4—114no—
468C2×C22⋊C4—112no—
469C2×C22⋊C4—114no—
470C2×C22⋊C4—112no—
471C2×C22⋊C4—114no—
472C2×C22⋊C4—114no—
473C2×C22⋊C4—114no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4C22×D1112yes—
478C2×C22⋊C4C22×D1114yes—
479C2×C22⋊C4C22×D1112yes—
480C2×C22⋊C4C22×D1114yes—
481C2×C22⋊C4C22×D1114yes—
482C2×C22⋊C4C22×D1114yes—
483C2×C42—112no—
484C2×C42—112no—
485C2×C42—112no—
486C2×C42C22×D1112yes—
487#95—112no—
488#95—114no—
489#95—114no—
490#95—114no—
491#95—114no—
492#95—114no—
493#95—114no—
494#95—114no—
495#95C22×D1112yes—
496C2×C11—24no—
497C2×C11—44no—
498C2×C11—82no—
499C2×C11C2×#53611yescharacteristic
500C2×C11#348411yescharacteristic
501C2×C11#348711yescharacteristic
502C2×C11#353514yes—
503C24—22no—
504C24—24no—
505C24—22no—
506C24—24no—
507C24—24no—
508C24—42no—
509C24—42no—
510C24—42no—
511C24C23×D1112yes—
512C24C23×D1112yes—
513C24C23×D1111yescharacteristic
514C2×Q8—22no—
515C2×Q8—42no—
516C2×Q8—224no—
517C2×Q8—222no—
518C2×Q8—444no—
519C2×Q8—442no—
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—24no—
523C2×D4—24no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—416no—
527C22×C4—42no—
528C22×C4—114no—
529C22×C4—112no—
530C22×C4—112no—
531C22×C4—114no—
532C22×C4—114no—
533C22×C4—112no—
534C22×C4—112no—
535C22×C4—112no—
536C22×C4—112no—
537C22×C4—228no—
538C22×C4—224no—
539C22×C4—222no—
540C22×C4—222no—
541C22×C4—228no—
542C22×C4—442no—
543C22×C4—444no—
544C22×C4—442no—
545C22×C4—442no—
546C22×C4—4416no—
547C22×C4D4×D1114yes—
548C22×C4C23×D1114yes—
549C22×C4C23×D1112yes—
550C22×C4C23×D1112yes—
551C22×C4C23×D1111yescharacteristic
552C22×C4C23×D1111yescharacteristic
553C4⋊C4—22no—
554C4⋊C4—24no—
555C4⋊C4—118no—
556C4⋊C4—118no—
557C4⋊C4—224no—
558C4⋊C4—224no—
559C4⋊C4—224no—
560C4⋊C4—224no—
561C4⋊C4—224no—
562C4⋊C4—224no—
563C4⋊C4—224no—
564C4⋊C4—222no—
565C4⋊C4—224no—
566C4⋊C4—444no—
567C4⋊C4—444no—
568C4⋊C4—444no—
569C4⋊C4—444no—
570C4⋊C4—444no—
571C22⋊C4—24no—
572C22⋊C4—28no—
573C22⋊C4—24no—
574C22⋊C4—44no—
575C22⋊C4—44no—
576C22⋊C4—44no—
577C22⋊C4—228no—
578C22⋊C4—228no—
579C22⋊C4—228no—
580C22⋊C4—224no—
581C22⋊C4—228no—
582C22⋊C4—224no—
583C22⋊C4—444no—
584C22⋊C4—444no—
585C22⋊C4—444no—
586C42—42no—
587C42—224no—
588C42—224no—
589C42—442no—
590C11#3671111yescharacteristic, complemented, Sylow
591C23—22no—
592C23—22no—
593C23—28no—
594C23—22no—
595C23—22no—
596C23—24no—
597C23—24no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—416no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23—44no—
609C23—88no—
610C23C2×D4×D1112yes—
611C23#6703714yes—
612C23#6704314yes—
613C23C24×D1111yescharacteristic
614Q8—82no—
615Q8—882no—
616Q8—884no—
617D4—48no—
618D4—48no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—44no—
629C2×C4—114no—
630C2×C4—114no—
631C2×C4—224no—
632C2×C4—224no—
633C2×C4—228no—
634C2×C4—222no—
635C2×C4—222no—
636C2×C4—222no—
637C2×C4—222no—
638C2×C4—224no—
639C2×C4—224no—
640C2×C4—224no—
641C2×C4—224no—
642C2×C4—224no—
643C2×C4—224no—
644C2×C4—222no—
645C2×C4—222no—
646C2×C4—444no—
647C2×C4—4416no—
648C2×C4—444no—
649C2×C4—444no—
650C2×C4C2×D4×D1112yes—
651C2×C4C2×D4×D1112yes—
652C22—22no—
653C22—22no—
654C22—28no—
655C22—24no—
656C22—28no—
657C22—416no—
658C22—42no—
659C22—42no—
660C22—44no—
661C22—42no—
662C22—42no—
663C22—42no—
664C22—44no—
665C22—44no—
666C22—88no—
667C22#1062320614yes—
668C22C22×D4×D1111yescharacteristic
669C22C2×#6703712yes—
670C22C2×#6704312yes—
671C22#1062345512yes—
672C4—22no—
673C4—22no—
674C4—42no—
675C4—42no—
676C4—44no—
677C4—224no—
678C4—224no—
679C4—442no—
680C4—442no—
681C4—442no—
682C4—442no—
683C4—444no—
684C2—24no—
685C2—44no—
686C2—82no—
687C2C2×#1062320611yescharacteristic
688C2#1308224511yescharacteristic
689C2#1308227211yescharacteristic
690C2#1308281314yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2435C2
prime radicalC23×D4×C11C22
hypercenter#2435D11
hypocenterC11#36711
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2435

Complements

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

NH ≅ G/Ntype
1. C2×#10623154C2semidirect
3. #13076901C2semidirect
4. #13075135C2semidirect
5. #13075131C2semidirect
6. #13074899C2semidirect
7. #13074891C2semidirect
8. #13074425C2semidirect
9. #13073997C2semidirect
10. #13073991C2semidirect
11. #13072887C2semidirect
12. #13072887C2semidirect
14. #13071216C2semidirect
23. C2×#66997C22semidirect
32. C2×#66942C22semidirect
33. C2×#66942C22semidirect
34. C2×#66941C22semidirect
36. C2×#66931C22semidirect
45. #10622842C22semidirect
49. #10622593C22semidirect
50. #10622585C22semidirect
51. #10622565C22semidirect
52. #10622565C22semidirect
53. #10622564C22semidirect
54. #10622564C22semidirect
57. #10622563C22semidirect
58. #10622562C22semidirect
59. #10622562C22semidirect
60. #10622562C22semidirect
61. #10622561C22semidirect
62. #10622561C22semidirect
63. #10622560C22semidirect
66. #10622559C22semidirect
67. #10622558C22semidirect
68. #10622558C22semidirect
71. #10622555C22semidirect
72. #10622546C22semidirect
73. #10622541C22semidirect
74. #10622274C22semidirect
75. #10622269C22semidirect
76. #10622265C22semidirect
590. C11#36711semidirect

Maximal subgroups

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

subgroupindex
C2×#106231542
C22×#669882
#130769012
#130751352
#130751312
#130748992
#130748912
#130744252
#130739972
#130739912
#130728872
#130722632
#130712162
C11×#24352
#3671111