Finite Group Databasebeta

← #15638522

Subgroups — #15638522

Order 2816.

2142 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623082C211yesmaximal, characteristic, complemented
2#13080538C214yesmaximal, complemented
3#13080527C214yesmaximal, complemented
4#13080346C214yesmaximal, complemented
5#13080334C214yesmaximal, complemented
6#13079561C211yesmaximal, characteristic, complemented
7#13079538C211yesmaximal, characteristic, complemented
8#13079393C214yesmaximal, complemented
9#13078620C211yesmaximal, characteristic, complemented
10#13078612C211yesmaximal, characteristic, complemented
11#13077832C214yesmaximal, complemented
12#13077640C211yesmaximal, characteristic, complemented
13C11×#3506C211yesmaximal, characteristic, complemented
14C22×#4339C2212yes—
15C11×#559—22no—
16C11×#556C2212yescomplemented
17C11×#555C2212yescomplemented
18C11×#553—22no—
19C11×#550C2212yescomplemented
20C11×#547C2212yescomplemented
21C11×#538—22no—
22C11×#535—21no—
23C11×#533C2211yescharacteristic
24C11×#532C2211yescharacteristic
25C11×#525C2214yes—
26C11×#520—21no—
27C2×C4×D4×C11C2211yescharacteristic
28C2×#67003C2218yescomplemented
29C2×#66991—21no—
30C2×#66977C2212yes—
31#10623082—22no—
32#10623082—22no—
33#10623082C2214yes—
34#10623082C2214yes—
35C2×C4⋊C4×D11—21no—
36C2×#66936—22no—
37C2×C4×D44C2211yescharacteristic
38C2×#66922C2211yescharacteristic
39#10622852C2218yescomplemented
40C2×C22⋊(C11⋊C8)C2214yes—
41#10622706C2212yescomplemented
42#10622706C2212yescomplemented
43#10622705C2212yescomplemented
44#10622700C2212yescomplemented
45#10622697C2212yescomplemented
46#10622696C2212yescomplemented
47#10622689C2212yescomplemented
48#10622685C2212yescomplemented
49#10622664C2218yescomplemented
50#10622663C2214yes—
51#10622660C2218yescomplemented
52#10622659C2212yes—
53#10622656C2212yes—
54#10622654C2218yescomplemented
55#10622653C2214yes—
56#10622650C2218yescomplemented
57#10622649C2212yes—
58#10622646C2212yes—
59#10622644C2214yescomplemented
60C4×#4325C2214yescomplemented
61#10622632C2214yescomplemented
62C4×#4323C2214yescomplemented
63D4×C11⋊C8C2214yescomplemented
64D4×C11⋊C8C2214yescomplemented
65#10622615C2218yescomplemented
66#10622609C2218yescomplemented
67#10622538C2211yescharacteristic
68#10622538C2211yescharacteristic
69C2×C11×#41—21no—
70C2×C11×#41C2314yes—
71C22×D4×C11D411yescharacteristic
72C23×C4×C11C2312yes—
73C22×C22⋊D11—22no—
74C2×#4339—24no—
75C2×#4339—48no—
76C2×#4339C2318yes—
77C22×D44C2311yescharacteristic
78C22×C4×D11—21no—
79C22×C4×D11—22no—
80C22×Dic22C2312yes—
81C11×C4⋊Q8C2311yescharacteristic
82C11×C4⋊Q8C2311yescharacteristic
83C11×C4⋊Q8C2311yescharacteristic
84C11×#127—22no—
85C11×#127C2311yescharacteristic
86C11×#126—24no—
87C11×#125—21no—
88C11×#124—22no—
89C11×#124—24no—
90C11×#124—21no—
91C11×#123—24no—
92C11×#123—24no—
93C11×C22⋊Q8—21no—
94C11×C22⋊Q8C2312yes—
95C11×C22⋊Q8C2314yes—
96C11×#121—22no—
97C11×#121—22no—
98C11×#121—21no—
99C11×#121—24no—
100C11×#121C2312yes—
101C11×#121C2314yes—
102C11×#120—24no—
103C4×Q8×C11—22no—
104C4×Q8×C11—21no—
105C4×Q8×C11C2312yes—
106C4×D4×C11—24no—
107C4×D4×C11—24no—
108C4×D4×C11—22no—
109C4×D4×C11—21no—
110C4×D4×C11D412yes—
111C4×D4×C11D412yes—
112C4×D4×C11C2312yes—
113C4×D4×C11C2312yes—
114C4×D4×C11C2312yes—
115C11×#117—21no—
116C11×#117—22no—
117C11×#117C2314yes—
118C2×C11×C4⋊C4—22no—
119C2×C11×C4⋊C4D411yescharacteristic
120C2×C11×C22⋊C4D412yes—
121C2×C42×C11C2311yescharacteristic
122C2×C22⋊Dic11—22no—
123#67003—416no—
124C2×#4326C2318yes—
125C2×#4325C2314yes—
126#66991—24no—
127#66991—24no—
128C2×#4324C2318yes—
129C2×#4323C2314yes—
130C2×(C2×D11)⋊C4—21no—
131C2×C4⋊Dic11—21no—
132C2×C4⋊Dic11—21no—
133C2×C4⋊Dic11C2311yescharacteristic
134#66977—24no—
135#66977C2318yes—
136C2×Dic11⋊C4—22no—
137C22×C11⋊C8C2318yes—
138C4⋊C4×D11—24no—
139C4⋊C4×D11—24no—
140#66936—28no—
141#66936—28no—
142C4×D44—21no—
143C4×D44—21no—
144C4×D44C2312yes—
145C4×D44C2312yes—
146#66922—21no—
147#66922—21no—
148#66922C2312yes—
149#66922C2312yes—
150#66899C2314yes—
151#66896C2314yes—
152C22⋊(C11⋊C8)C2312yes—
153C22⋊(C11⋊C8)C2312yes—
154C22⋊(C11⋊C8)C2318yes—
155#66874C2318yes—
156#66874C2318yes—
157#66873C2314yes—
158#66873C2314yes—
159#66872C2314yes—
160#66871C2314yes—
161C4⋊(C11⋊C8)C2312yes—
162C4⋊(C11⋊C8)C2312yes—
163C4×C11⋊C8C2312yes—
164C4×C11⋊C8C2312yes—
165#61565—111nomaximal, Sylow
166C24×C11C2×D412yes—
167C23×D11—21no—
168C11×#41—48no—
169C11×#41—44no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11C2412yes—
173C2×D4×C11—22no—
174C2×D4×C11—24no—
175C2×D4×C11—24no—
176C2×D4×C11—24no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11C2×D412yes—
180C2×D4×C11C2×D412yes—
181C2×D4×C11C2412yes—
182C22×C4×C11—22no—
183C22×C4×C11—24no—
184C22×C4×C11—44no—
185C22×C4×C11C2×D412yes—
186C22×C4×C11C2×D414yes—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2411yescharacteristic
190C22×C4×C11C2414yes—
191C2×C22⋊D11—28no—
192C2×C22⋊D11—48no—
193C22×Dic11—21no—
194C22×Dic11—22no—
195#4339—216no—
196#4339—48no—
197#4339—416no—
198C2×D44—24no—
199C2×D44—21no—
200C2×D44C2412yes—
201C2×C4×D11—22no—
202C2×C4×D11—22no—
203C2×C4×D11—28no—
204C2×C4×D11—48no—
205C2×C4×D11—44no—
206C2×Dic22—22no—
207C2×Dic22—44no—
208C2×Dic22C2414yes—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—22no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4C2×D412yes—
217C11×C4⋊C4C2×D412yes—
218C11×C4⋊C4C2412yes—
219C11×C4⋊C4C2412yes—
220C11×C22⋊C4—22no—
221C11×C22⋊C4—24no—
222C11×C22⋊C4—24no—
223C11×C22⋊C4—24no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4C2×D414yes—
227C11×C22⋊C4C2×D414yes—
228C42×C11—24no—
229C42×C11—22no—
230C42×C11C2×D411yescharacteristic
231C42×C11C2×D411yescharacteristic
232C42×C11C2411yescharacteristic
233C42×C11C2411yescharacteristic
234C22⋊Dic11—28no—
235#4326—48no—
236#4325—28no—
237#4324—48no—
238#4323—28no—
239(C2×D11)⋊C4—22no—
240(C2×D11)⋊C4—22no—
241C4⋊Dic11—22no—
242C4⋊Dic11—22no—
243C4⋊Dic11—22no—
244C4⋊Dic11—22no—
245C4⋊Dic11—21no—
246C4⋊Dic11C2412yes—
247Dic11⋊C4—28no—
248C2×C11⋊C8—48no—
249C2×C11⋊C8C2414yes—
250C2×C11⋊C8C2414yes—
251#3506D1111yescharacteristic, complemented
252C2×#547—111no—
253#3303—114no—
254#3302—114no—
255#3284—114no—
256#3283—114no—
257#3209—111no—
258#3206—111no—
259#3190—114no—
260#3101—111no—
261#3100—111no—
262#3002—114no—
263#2972—111no—
264C23×C11—24no—
265C23×C11—22no—
266C23×C11—42no—
267C23×C11—42no—
268C23×C11C22×D414yes—
269C23×C11C22×D411yescharacteristic
270C22×D11—24no—
271C22×D11—22no—
272C22×D11—42no—
273C22×D11—42no—
274Q8×C11—24no—
275Q8×C11—42no—
276Q8×C11—81no—
277D4×C11—24no—
278D4×C11—24no—
279D4×C11—24no—
280D4×C11—44no—
281D4×C11—42no—
282D4×C11—81no—
283D4×C11—84no—
284D4×C11—84no—
285C2×C4×C11—28no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—42no—
291C2×C4×C11—44no—
292C2×C4×C11—41no—
293C2×C4×C11—44no—
294C2×C4×C11—84no—
295C2×C4×C11#13514yescomplemented
296C2×C4×C11C22×D414yes—
297C2×C4×C11C22×D411yescharacteristic
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C22×D411yescharacteristic
300C2×C4×C11C22×D411yescharacteristic
301C2×C4×C11C22×D411yescharacteristic
302C2×C4×C11C2511yescharacteristic
303C22⋊D11—416no—
304C2×Dic11—22no—
305C2×Dic11—24no—
306C2×Dic11—44no—
307C2×Dic11—42no—
308D44—24no—
309D44—22no—
310D44H(5,𝔽2)14yes—
311C4×D11—416no—
312C4×D11—44no—
313C4×D11—44no—
314Dic22—28no—
315Dic22—44no—
316C11⋊C8—24no—
317C11⋊C8—24no—
318C22×#41—112no—
319C2×#135—118no—
320#559—22no—
321#556C2×D1112yescomplemented
322#555C2×D1112yescomplemented
323#553—22no—
324#550C2×D1112yescomplemented
325#547—114no—
326#547—114no—
327#547—222no—
328#547—222no—
329#547C2×D1112yescomplemented
330#538—22no—
331#535—21no—
332#533C2×D1111yescharacteristic
333#532C2×D1111yescharacteristic
334C2×C4⋊Q8—111no—
335#525C2×D1114yes—
336C2×#123—222no—
337C2×C22⋊Q8—112no—
338C2×#121—221no—
339#520—21no—
340C2×C4×D4—111no—
341C2×C4×D4C2×D1111yescharacteristic
342C22×C4⋊C4—221no—
343#494—112no—
344#492—112no—
345#487—112no—
346#487—112no—
347#485—118no—
348#483—112no—
349#480—112no—
350#476—112no—
351#474—112no—
352#467—118no—
353#465—118no—
354#462—114no—
355#461—112no—
356#461—114no—
357#459—112no—
358#452—118no—
359#452—118no—
360#451—114no—
361#450—112no—
362#449—118no—
363#448—114no—
364#447—112no—
365C4×SD16—114no—
366C4×D8—114no—
367C8×D4—114no—
368C8×D4—114no—
369#431—111no—
370#431—111no—
371#416—118no—
372C2×C22⋊C8—114no—
373C22×C11—21no—
374C22×C11—21no—
375C22×C11—24no—
376C22×C11—24no—
377C22×C11—24no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—42no—
381C22×C11—84no—
382C22×C11C2×#13512yes—
383C22×C11C23×D411yescharacteristic
384C2×D11—24no—
385C2×D11—48no—
386C2×D11—42no—
387C2×D11—42no—
388C4×C11—21no—
389C4×C11—21no—
390C4×C11—21no—
391C4×C11—24no—
392C4×C11—42no—
393C4×C11—42no—
394C4×C11—42no—
395C4×C11C2×#13512yes—
396C4×C11C2×#13512yes—
397C4×C11C2×H(5,𝔽2)12yes—
398Dic11—44no—
399Dic11—42no—
400C2×#41—21no—
401C2×#41—118no—
402C2×#41—224no—
403C2×#41—448no—
404C2×#41C22×D1114yes—
405C22×Q8—112no—
406C22×D4—111no—
407C22×D4—222no—
408C22×D4C22⋊D1111yescharacteristic
409C23×C4—221no—
410C23×C4—222no—
411C23×C4C22×D1112yes—
412#135—4416no—
413C2×Q16—118no—
414C2×SD16—114no—
415C2×SD16—118no—
416C2×D8—114no—
417C22×C8—118no—
418C4⋊Q8—112no—
419C4⋊Q8—112no—
420C4⋊Q8—221no—
421C4⋊Q8—221no—
422C4⋊Q8C22×D1111yescharacteristic
423C4⋊Q8C22×D1111yescharacteristic
424C4⋊Q8C22×D1111yescharacteristic
425#127—22no—
426#127C22×D1111yescharacteristic
427#126—24no—
428#125—21no—
429#124—22no—
430#124—24no—
431#124—21no—
432#123—24no—
433#123—24no—
434#123—228no—
435#123—228no—
436C22⋊Q8—21no—
437C22⋊Q8—118no—
438C22⋊Q8—224no—
439C22⋊Q8C22×D1112yes—
440C22⋊Q8C22×D1114yes—
441#121—22no—
442#121—22no—
443#121—21no—
444#121—24no—
445#121—224no—
446#121—224no—
447#121C22×D1112yes—
448#121C22×D1114yes—
449#120—24no—
450C4×Q8—22no—
451C4×Q8—21no—
452C4×Q8C22×D1112yes—
453C4×D4—24no—
454C4×D4—24no—
455C4×D4—22no—
456C4×D4—21no—
457C4×D4—112no—
458C4×D4—112no—
459C4×D4—221no—
460C4×D4—221no—
461C4×D4C22⋊D1112yes—
462C4×D4C22⋊D1112yes—
463C4×D4C22×D1112yes—
464C4×D4C22×D1112yes—
465C4×D4C22×D1112yes—
466#117—21no—
467#117—22no—
468#117C22×D1114yes—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—221no—
472C2×C4⋊C4—222no—
473C2×C4⋊C4—221no—
474C2×C4⋊C4—224no—
475C2×C4⋊C4—224no—
476C2×C4⋊C4C22⋊D1111yescharacteristic
477C2×C22⋊C4—222no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4C22⋊D1112yes—
480C2×C42C22×D1111yescharacteristic
481#107—114no—
482#106—114no—
483C4⋊C8—112no—
484C4⋊C8—112no—
485#103—114no—
486#103—118no—
487#103—118no—
488#102—114no—
489#102—114no—
490#102—114no—
491C22⋊C8—112no—
492C22⋊C8—112no—
493C22⋊C8—118no—
494C4×C8—112no—
495C4×C8—112no—
496C2×C11—22no—
497C2×C11—44no—
498C2×C11—82no—
499C2×C11#348411yescharacteristic
500C2×C11C22×#13511yescharacteristic
501C2×C11#358611yescharacteristic
502D11—44no—
503C24—221no—
504C24C2×C22⋊D1112yes—
505#41—48no—
506#41—44no—
507#41—2216no—
508#41—448no—
509#41—4416no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—114no—
513C2×Q8—222no—
514C2×Q8—444no—
515C2×Q8C23×D1112yes—
516C2×D4—22no—
517C2×D4—24no—
518C2×D4—24no—
519C2×D4—24no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—112no—
523C2×D4—224no—
524C2×D4—228no—
525C2×D4—221no—
526C2×D4—448no—
527C2×D4C2×C22⋊D1112yes—
528C2×D4C2×C22⋊D1112yes—
529C2×D4C23×D1112yes—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—44no—
533C22×C4—221no—
534C22×C4—222no—
535C22×C4—222no—
536C22×C4—222no—
537C22×C4—228no—
538C22×C4—448no—
539C22×C4—444no—
540C22×C4C2×C22⋊D1111yescharacteristic
541C22×C4C2×C22⋊D1112yes—
542C22×C4C2×C22⋊D1114yes—
543C22×C4C2×C22⋊D1111yescharacteristic
544C22×C4C23×D1111yescharacteristic
545C22×C4C23×D1114yes—
546Q16—448no—
547SD16—228no—
548SD16—448no—
549D8—228no—
550C2×C8—114no—
551C2×C8—114no—
552C2×C8—448no—
553C4⋊C4—21no—
554C4⋊C4—24no—
555C4⋊C4—21no—
556C4⋊C4—22no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—22no—
560C4⋊C4—112no—
561C4⋊C4—221no—
562C4⋊C4—222no—
563C4⋊C4—222no—
564C4⋊C4—228no—
565C4⋊C4—222no—
566C4⋊C4—222no—
567C4⋊C4C2×C22⋊D1112yes—
568C4⋊C4C2×C22⋊D1112yes—
569C4⋊C4C23×D1112yes—
570C4⋊C4C23×D1112yes—
571C22⋊C4—22no—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—228no—
578C22⋊C4—222no—
579C22⋊C4—222no—
580C22⋊C4C2×C22⋊D1114yes—
581C22⋊C4C2×C22⋊D1114yes—
582C42—24no—
583C42—22no—
584C42C2×C22⋊D1111yescharacteristic
585C42C2×C22⋊D1111yescharacteristic
586C42C23×D1111yescharacteristic
587C42C23×D1111yescharacteristic
588C11#6156511yescharacteristic, complemented, Sylow
589C23—24no—
590C23—22no—
591C23—42no—
592C23—42no—
593C23—224no—
594C23—222no—
595C23—442no—
596C23—442no—
597C23C22×C22⋊D1114yes—
598C23C22×C22⋊D1111yescharacteristic
599Q8—24no—
600Q8—42no—
601Q8—81no—
602Q8—228no—
603Q8—444no—
604D4—24no—
605D4—24no—
606D4—24no—
607D4—44no—
608D4—42no—
609D4—81no—
610D4—84no—
611D4—84no—
612D4—114no—
613D4—224no—
614D4—222no—
615D4—4416no—
616C2×C4—28no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—42no—
622C2×C4—44no—
623C2×C4—41no—
624C2×C4—44no—
625C2×C4—84no—
626C2×C4—222no—
627C2×C4—224no—
628C2×C4—4416no—
629C2×C4—444no—
630C2×C4—442no—
631C2×C4—444no—
632C2×C4—444no—
633C2×C4#6700314yescomplemented
634C2×C4C22×C22⋊D1114yes—
635C2×C4C22×C22⋊D1111yescharacteristic
636C2×C4C22×C22⋊D1111yescharacteristic
637C2×C4C22×C22⋊D1111yescharacteristic
638C2×C4C22×C22⋊D1111yescharacteristic
639C2×C4C22×C22⋊D1111yescharacteristic
640C2×C4C24×D1111yescharacteristic
641C8—224no—
642C8—224no—
643C22—21no—
644C22—21no—
645C22—24no—
646C22—24no—
647C22—24no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—84no—
652C22—224no—
653C22—448no—
654C22—442no—
655C22—442no—
656C22C2×#6700312yes—
657C22C23×C22⋊D1111yescharacteristic
658C4—21no—
659C4—21no—
660C4—21no—
661C4—24no—
662C4—42no—
663C4—42no—
664C4—42no—
665C4—444no—
666C4—442no—
667C4C2×#6700312yes—
668C4C2×#6700312yes—
669C4D11×H(5,𝔽2)12yes—
670C2—22no—
671C2—44no—
672C2—82no—
673C2—444no—
674C2#1308224711yescharacteristic
675C2C22×#6700311yescharacteristic
676C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3506C2
socleC22×C11C23×D4
hypercenter#3506D11
hypocenterC11#61565
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. C2×#10623082C2semidirect
2. #13080538C2semidirect
3. #13080527C2semidirect
4. #13080346C2semidirect
5. #13080334C2semidirect
6. #13079561C2semidirect
7. #13079538C2semidirect
8. #13079393C2semidirect
9. #13078620C2semidirect
10. #13078612C2semidirect
11. #13077832C2semidirect
12. #13077640C2semidirect
13. C11×#3506C2semidirect
16. C11×#556C22semidirect
17. C11×#555C22semidirect
19. C11×#550C22semidirect
20. C11×#547C22semidirect
28. C2×#67003C22semidirect
39. #10622852C22semidirect
41. #10622706C22semidirect
42. #10622706C22semidirect
43. #10622705C22semidirect
44. #10622700C22semidirect
45. #10622697C22semidirect
46. #10622696C22semidirect
47. #10622689C22semidirect
48. #10622685C22semidirect
49. #10622664C22semidirect
51. #10622660C22semidirect
54. #10622654C22semidirect
56. #10622650C22semidirect
59. #10622644C22semidirect
60. C4×#4325C22semidirect
61. #10622632C22semidirect
62. C4×#4323C22semidirect
63. D4×C11⋊C8C22semidirect
64. D4×C11⋊C8C22semidirect
65. #10622615C22semidirect
66. #10622609C22semidirect
251. #3506D11semidirect
295. C2×C4×C11#135semidirect
321. #556C2×D11semidirect
322. #555C2×D11semidirect
324. #550C2×D11semidirect
329. #547C2×D11semidirect
588. C11#61565semidirect
633. C2×C4#67003semidirect

Maximal subgroups

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

subgroupindex
C2×#106230822
#130805382
#130805272
#130803462
#130803342
#130795612
#130795382
#130793932
#130786202
#130786122
#130778322
#130776402
C11×#35062
#6156511