Finite Group Databasebeta

← #15624225

Subgroups — #15624225

Order 2816.

1886 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
1#13082502C211yesmaximal, characteristic, complemented
2#13079357C212yesmaximal, complemented
3#13079330C212yesmaximal, complemented
4#13079278C218yesmaximal, complemented
5#13079198C212yesmaximal, complemented
6#13079171C212yesmaximal, complemented
7#13079158C211yesmaximal, characteristic, complemented
8#13079076C211yesmaximal, characteristic, complemented
9#13078938C211yesmaximal, characteristic, complemented
10C2×#10622706C211yesmaximal, characteristic, complemented
11#13078309C214yesmaximal, complemented
12#13077455C214yesmaximal, complemented
13C4×#67001C211yesmaximal, characteristic, complemented
14C11×#3511C211yesmaximal, characteristic
15C11×#556—21no—
16C11×#555—21no—
17C11×#554—21no—
18C11×#553—22no—
19C11×#548—22no—
20C11×#547—21no—
21C11×#542C2214yes—
22C11×#537C2212yes—
23C11×#533C2212yes—
24C11×#532C2211yescharacteristic
25C11×#532C2212yes—
26C2×C11×C4⋊Q8C2211yescharacteristic
27C11×#520C2212yes—
28C4×C11×#41C2211yescharacteristic
29#10623356C2212yes—
30C2×#67004C2214yes—
31C2×#67001C2212yes—
32#10623098—21no—
33#10623098—21no—
34#10623073—21no—
35#10623073—21no—
36#10623072—22no—
37#10623072—22no—
38#10623049C2214yes—
39#10623047C2212yes—
40#10623001C2211yescharacteristic
41#10623001C2212yes—
42#10623001C2212yes—
43C2×#66922C2211yescharacteristic
44#10622846C2214yes—
45#10622706C2212yes—
46#10622706C2212yes—
47#10622706C2214yes—
48#10622705C2212yes—
49#10622694C2211yescharacteristic
50#10622694C2211yescharacteristic
51#10622693C2214yes—
52#10622692C2212yes—
53#10622691C2212yes—
54#10622689C2212yes—
55#10622683C2211yescharacteristic
56#10622683C2211yescharacteristic
57#10622673C2214yes—
58#10622669C2214yes—
59#10622665C2218yes—
60#10622664C2218yes—
61#10622655C2218yes—
62#10622654C2218yes—
63#10622643C2218yes—
64C4×#4326C2218yes—
65#10622631C2218yes—
66C4×#4324C2218yes—
67#10622610C2212yes—
68#10622610C2214yes—
69C2×#66874C2214yes—
70#10622577C2214yes—
71C4×#4318C2212yes—
72C4×#4318C2211yescharacteristic
73C2×C4×C11⋊C8C2212yes—
74C2×C4×C11⋊C8C2211yescharacteristic
75C2×C11×#41—22no—
76C2×C11×#41C2312yes—
77C2×C11×#41C2311yescharacteristic
78C22×Q8×C11—21no—
79C22×Dic22C2312yes—
80C11×C4⋊Q8—21no—
81C11×C4⋊Q8—21no—
82C11×C4⋊Q8C2311yescharacteristic
83C11×C4⋊Q8C2312yes—
84C11×C4⋊Q8C2312yes—
85C11×#127C2311yescharacteristic
86C11×#126—24no—
87C11×#125—22no—
88C11×#124—24no—
89C11×#124—22no—
90C11×#124C2312yes—
91C11×#123—24no—
92C11×C22⋊Q8—22no—
93C11×C22⋊Q8—22no—
94C11×C22⋊Q8—24no—
95C11×C22⋊Q8C2314yes—
96C11×#121—22no—
97C11×#121—24no—
98C11×#121—21no—
99C11×#121—21no—
100C11×#121—22no—
101C11×#121C2314yes—
102C4×Q8×C11—22no—
103C4×Q8×C11D411yescharacteristic
104C4×Q8×C11D411yescharacteristic
105C4×Q8×C11C2314yes—
106C4×D4×C11—24no—
107C4×D4×C11—21no—
108C4×D4×C11—22no—
109C4×D4×C11—21no—
110C4×D4×C11D412yes—
111C4×D4×C11D412yes—
112C4×D4×C11D411yescharacteristic
113C4×D4×C11D411yescharacteristic
114C4×D4×C11C2314yes—
115C11×#117—22no—
116C11×#117—22no—
117C11×#117C2311yescharacteristic
118C11×#117C2312yes—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4—22no—
121C2×C11×C4⋊C4C2312yes—
122C2×C42×C11C2311yescharacteristic
123C2×C42×C11C2312yes—
124#67004—216no—
125#67001—28no—
126#66997—22no—
127C2×#4326C2318yes—
128#66989—22no—
129#66988—24no—
130C2×#4324C2318yes—
131#66979—22no—
132#66979—22no—
133#66979C2312yes—
134C2×C4⋊Dic11—21no—
135C2×C4⋊Dic11—21no—
136#66977—21no—
137#66977—21no—
138#66977—22no—
139#66977—22no—
140#66977C2314yes—
141#66977C2314yes—
142C2×#4318C2314yes—
143C2×#4318C2312yes—
144C22×C11⋊C8C2312yes—
145C22×C11⋊C8C2314yes—
146#66942—24no—
147#66942—24no—
148#66940—22no—
149#66940—22no—
150#66932—24no—
151#66932—24no—
152#66930—24no—
153#66923—22no—
154#66923—22no—
155#66923C2312yes—
156#66922—21no—
157#66922—21no—
158#66922C2312yes—
159#66922C2312yes—
160#66922C2311yescharacteristic
161#66922C2311yescharacteristic
162C4×Dic22—22no—
163C4×Dic22—22no—
164C4×Dic22—21no—
165C4×Dic22—21no—
166C4×Dic22C2314yes—
167C4×Dic22C2314yes—
168#66899C2314yes—
169#66899C2314yes—
170#66896C2314yes—
171#66896C2314yes—
172#66874C2318yes—
173#66874C2318yes—
174#66872C2318yes—
175#66871C2318yes—
176#66867C2314yes—
177#66867C2312yes—
178C4×C11⋊C8C2311yescharacteristic
179C4×C11⋊C8C2311yescharacteristic
180C4×C11⋊C8C2312yes—
181C4×C11⋊C8C2314yes—
182C4×C11⋊C8C2312yes—
183#60723—111nomaximal, Sylow
184C11×#41—24no—
185C11×#41—28no—
186C11×#41—84no—
187C2×Q8×C11—22no—
188C2×Q8×C11—22no—
189C2×Q8×C11—82no—
190C2×Q8×C11C2×D411yescharacteristic
191C2×Q8×C11C2412yes—
192C2×D4×C11—22no—
193C2×D4×C11—24no—
194C2×D4×C11—21no—
195C2×D4×C11—21no—
196C2×D4×C11C2×D412yes—
197C2×D4×C11C2×D411yescharacteristic
198C2×D4×C11C2412yes—
199C22×C4×C11—22no—
200C22×C4×C11—22no—
201C22×C4×C11—24no—
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D412yes—
205C22×C4×C11C2×D412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2411yescharacteristic
208C22×Dic11—22no—
209C2×Dic22—21no—
210C2×Dic22—21no—
211C2×Dic22—22no—
212C2×Dic22—28no—
213C2×Dic22C2414yes—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—24no—
217C11×C4⋊C4—22no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—24no—
221C11×C4⋊C4C2×D411yescharacteristic
222C11×C4⋊C4C2×D411yescharacteristic
223C11×C4⋊C4C2×D412yes—
224C11×C4⋊C4C2×D412yes—
225C11×C4⋊C4C2414yes—
226C11×C22⋊C4—24no—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—24no—
229C11×C22⋊C4—22no—
230C11×C22⋊C4—22no—
231C11×C22⋊C4C2×D412yes—
232C11×C22⋊C4C2×D412yes—
233C11×C22⋊C4C2×D412yes—
234C42×C11—24no—
235C42×C11C2×D411yescharacteristic
236C42×C11C2×D411yescharacteristic
237C42×C11C2×D412yes—
238C42×C11C2×D412yes—
239C42×C11C2411yescharacteristic
240C42×C11C2412yes—
241C42×C11C2411yescharacteristic
242C22⋊Dic11—22no—
243C22⋊Dic11—24no—
244C22⋊Dic11—24no—
245#4326—216no—
246#4324—216no—
247C4⋊Dic11—22no—
248C4⋊Dic11—22no—
249C4⋊Dic11—21no—
250C4⋊Dic11—21no—
251C4⋊Dic11—22no—
252C4⋊Dic11—22no—
253C4⋊Dic11C2412yes—
254C4⋊Dic11C2412yes—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257Dic11⋊C4—22no—
258Dic11⋊C4—22no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261C4×Dic11—22no—
262C4×Dic11—24no—
263C4×Dic11—24no—
264#4318—28no—
265#4318#4118yescomplemented
266C2×C11⋊C8—28no—
267C2×C11⋊C8—24no—
268C2×C11⋊C8C2412yes—
269C2×C11⋊C8C2412yes—
270C2×C11⋊C8C2414yes—
271#3511D1111yescharacteristic
272#3509—111no—
273#3185—112no—
274#3182—112no—
275#3178—118no—
276#3170—112no—
277#3167—112no—
278#3165—111no—
279#3152—111no—
280#3131—111no—
281C2×#487—111no—
282#3063—114no—
283#2947—114no—
284C4×#131—111no—
285C23×C11—22no—
286C23×C11C22×D412yes—
287C23×C11C22×D411yescharacteristic
288Q8×C11—22no—
289Q8×C11—24no—
290Q8×C11—44no—
291Q8×C11—82no—
292D4×C11—24no—
293D4×C11—22no—
294D4×C11—24no—
295D4×C11—44no—
296D4×C11—42no—
297D4×C11—42no—
298D4×C11—84no—
299C2×C4×C11—22no—
300C2×C4×C11—24no—
301C2×C4×C11—22no—
302C2×C4×C11—24no—
303C2×C4×C11—24no—
304C2×C4×C11—22no—
305C2×C4×C11—24no—
306C2×C4×C11—44no—
307C2×C4×C11—84no—
308C2×C4×C11—82no—
309C2×C4×C11C22×D412yes—
310C2×C4×C11C22×D412yes—
311C2×C4×C11C22×D412yes—
312C2×C4×C11C22×D411yescharacteristic
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11C22×D411yescharacteristic
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C2×#4114yes—
318C2×C4×C11C2511yescharacteristic
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—24no—
322C2×Dic11—44no—
323Dic22—28no—
324Dic22—44no—
325Dic22—42no—
326Dic22—42no—
327C11⋊C8—22no—
328C11⋊C8—22no—
329C11⋊C8C2×#4118yes—
330C2×#137—114no—
331C2×#131—112no—
332#557—221no—
333#557—221no—
334#556—21no—
335#556—221no—
336#556—221no—
337#555—21no—
338#554—21no—
339#553—22no—
340#552—222no—
341#552—222no—
342#548—22no—
343#547—21no—
344#542C2×D1114yes—
345#541—114no—
346#537C2×D1112yes—
347#536—112no—
348#533—111no—
349#533—112no—
350#533—112no—
351#533C2×D1112yes—
352#532C2×D1111yescharacteristic
353#532C2×D1112yes—
354C2×C4⋊Q8—111no—
355C2×C4⋊Q8C2×D1111yescharacteristic
356#520C2×D1112yes—
357#519—112no—
358C4×#41C2×D1111yescharacteristic
359#501—114no—
360#500—112no—
361#498—112no—
362#497—114no—
363#494—112no—
364#492—112no—
365#488—114no—
366#487—112no—
367#487—114no—
368#487—112no—
369#487—111no—
370#487—111no—
371#486—111no—
372#486—111no—
373#470—118no—
374#468—118no—
375#467—118no—
376#465—118no—
377#441—118no—
378#440—118no—
379C4×Q16—118no—
380C4×SD16—118no—
381#428—114no—
382#416—114no—
383C2×#103—114no—
384#405—114no—
385#405—112no—
386C4×M16—111no—
387C4×M16—112no—
388C2×C4×C8—111no—
389C2×C4×C8—112no—
390C22×C11—21no—
391C22×C11—21no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11#53212yes—
399C22×C11C23×D411yescharacteristic
400C4×C11—22no—
401C4×C11—22no—
402C4×C11—21no—
403C4×C11—22no—
404C4×C11—21no—
405C4×C11—42no—
406C4×C11—44no—
407C4×C11#53212yes—
408C4×C11#57712yes—
409C4×C11#57812yes—
410C4×C11C22×#4112yes—
411Dic11—44no—
412Dic11—42no—
413Dic11—42no—
414C2×#41—22no—
415C2×#41C22×D1112yes—
416C2×#41C22×D1111yescharacteristic
417C22×Q8—21no—
418C22×Q8—112no—
419#137—2216no—
420C2×Q16—118no—
421C2×SD16—118no—
422#131—228no—
423C2×M16—112no—
424C2×M16—114no—
425C22×C8—112no—
426C22×C8—114no—
427C4⋊Q8—21no—
428C4⋊Q8—21no—
429C4⋊Q8—111no—
430C4⋊Q8—111no—
431C4⋊Q8—112no—
432C4⋊Q8—112no—
433C4⋊Q8—222no—
434C4⋊Q8—221no—
435C4⋊Q8—221no—
436C4⋊Q8C22×D1111yescharacteristic
437C4⋊Q8C22×D1112yes—
438C4⋊Q8C22×D1112yes—
439#127C22×D1111yescharacteristic
440#126—24no—
441#126—224no—
442#126—224no—
443#125—22no—
444#125—112no—
445#125—224no—
446#125—224no—
447#125—222no—
448#125—222no—
449#124—24no—
450#124—22no—
451#124—222no—
452#124C22×D1112yes—
453#123—24no—
454#123—224no—
455C22⋊Q8—22no—
456C22⋊Q8—22no—
457C22⋊Q8—24no—
458C22⋊Q8—114no—
459C22⋊Q8—114no—
460C22⋊Q8—221no—
461C22⋊Q8—221no—
462C22⋊Q8—222no—
463C22⋊Q8—222no—
464C22⋊Q8C22×D1114yes—
465#121—22no—
466#121—24no—
467#121—21no—
468#121—21no—
469#121—22no—
470#121C22×D1114yes—
471C4×Q8—22no—
472C4×Q8—114no—
473C4×Q8—114no—
474C4×Q8—222no—
475C4×Q8—222no—
476C4×Q8—222no—
477C4×Q8—222no—
478C4×Q8—221no—
479C4×Q8—221no—
480C4×Q8C22⋊D1111yescharacteristic
481C4×Q8C22⋊D1111yescharacteristic
482C4×Q8C22×D1114yes—
483C4×D4—24no—
484C4×D4—21no—
485C4×D4—22no—
486C4×D4—21no—
487C4×D4C22⋊D1111yescharacteristic
488C4×D4C22⋊D1112yes—
489C4×D4C22⋊D1112yes—
490C4×D4C22⋊D1111yescharacteristic
491C4×D4C22×D1114yes—
492#117—22no—
493#117—22no—
494#117—112no—
495#117—222no—
496#117—222no—
497#117—224no—
498#117C22×D1111yescharacteristic
499#117C22×D1112yes—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4C22×D1112yes—
505C2×C42C22×D1111yescharacteristic
506C2×C42C22×D1112yes—
507#107—118no—
508#106—118no—
509#103—114no—
510#103—114no—
511#103—118no—
512#103—118no—
513#102—114no—
514#102—114no—
515#97—114no—
516#97—112no—
517C4×C8—111no—
518C4×C8—111no—
519C4×C8—112no—
520C4×C8—114no—
521C4×C8—112no—
522C2×C11—22no—
523C2×C11—42no—
524C2×C11—82no—
525C2×C11C2×#53211yescharacteristic
526C2×C11C2×#57711yescharacteristic
527C2×C11C2×#57811yescharacteristic
528#41—24no—
529#41—28no—
530#41—84no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—82no—
534C2×Q8—114no—
535C2×Q8—221no—
536C2×Q8—221no—
537C2×Q8—222no—
538C2×Q8—228no—
539C2×Q8C2×C22⋊D1111yescharacteristic
540C2×Q8C23×D1112yes—
541C2×D4—22no—
542C2×D4—24no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4C2×C22⋊D1112yes—
546C2×D4C2×C22⋊D1111yescharacteristic
547C2×D4C23×D1112yes—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—222no—
552C22×C4C2×C22⋊D1111yescharacteristic
553C22×C4C2×C22⋊D1111yescharacteristic
554C22×C4C2×C22⋊D1112yes—
555C22×C4C2×C22⋊D1112yes—
556C22×C4C23×D1112yes—
557C22×C4C23×D1111yescharacteristic
558Q16—2216no—
559SD16—2216no—
560M16—118no—
561M16—228no—
562C2×C8—114no—
563C2×C8—112no—
564C2×C8—112no—
565C2×C8—228no—
566C2×C8—224no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—24no—
574C4⋊C4—112no—
575C4⋊C4—112no—
576C4⋊C4—222no—
577C4⋊C4—222no—
578C4⋊C4—222no—
579C4⋊C4—222no—
580C4⋊C4—221no—
581C4⋊C4—221no—
582C4⋊C4—224no—
583C4⋊C4—224no—
584C4⋊C4—224no—
585C4⋊C4—224no—
586C4⋊C4—222no—
587C4⋊C4—222no—
588C4⋊C4C2×C22⋊D1111yescharacteristic
589C4⋊C4C2×C22⋊D1111yescharacteristic
590C4⋊C4C2×C22⋊D1112yes—
591C4⋊C4C2×C22⋊D1112yes—
592C4⋊C4C23×D1114yes—
593C22⋊C4—24no—
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—222no—
599C22⋊C4—224no—
600C22⋊C4—224no—
601C22⋊C4C2×C22⋊D1112yes—
602C22⋊C4C2×C22⋊D1112yes—
603C22⋊C4C2×C22⋊D1112yes—
604C42—24no—
605C42—222no—
606C42—224no—
607C42—224no—
608C42C2×C22⋊D1112yes—
609C42C2×C22⋊D1111yescharacteristic
610C42C2×C22⋊D1111yescharacteristic
611C42C2×C22⋊D1112yes—
612C42C23×D1111yescharacteristic
613C42C23×D1112yes—
614C42C23×D1111yescharacteristic
615C11#6072311yescharacteristic, complemented, Sylow
616C23—22no—
617C23C22×C22⋊D1112yes—
618C23C22×C22⋊D1111yescharacteristic
619Q8—22no—
620Q8—24no—
621Q8—44no—
622Q8—82no—
623Q8—228no—
624Q8—444no—
625Q8—442no—
626Q8—442no—
627D4—24no—
628D4—22no—
629D4—24no—
630D4—44no—
631D4—42no—
632D4—42no—
633D4—84no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—22no—
640C2×C4—24no—
641C2×C4—44no—
642C2×C4—84no—
643C2×C4—82no—
644C2×C4—222no—
645C2×C4—222no—
646C2×C4—224no—
647C2×C4—444no—
648C2×C4#41×D1114yes—
649C2×C4C22×C22⋊D1112yes—
650C2×C4C22×C22⋊D1112yes—
651C2×C4C22×C22⋊D1112yes—
652C2×C4C22×C22⋊D1111yescharacteristic
653C2×C4C22×C22⋊D1111yescharacteristic
654C2×C4C22×C22⋊D1111yescharacteristic
655C2×C4C22×C22⋊D1111yescharacteristic
656C2×C4C22×C22⋊D1111yescharacteristic
657C2×C4C24×D1111yescharacteristic
658C8—118no—
659C8—222no—
660C8—222no—
661C22—21no—
662C22—21no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22#1062336312yes—
670C22C23×C22⋊D1111yescharacteristic
671C4—22no—
672C4—22no—
673C4—21no—
674C4—22no—
675C4—21no—
676C4—42no—
677C4—44no—
678C4—444no—
679C4—442no—
680C4—442no—
681C4#1062336312yes—
682C4#1062336712yes—
683C4#1062336912yes—
684C4C2×#41×D1112yes—
685C2—22no—
686C2—42no—
687C2—82no—
688C2C2×#1062336311yescharacteristic
689C2C2×#1062336711yescharacteristic
690C2C2×#1062336911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC11×#3511C2
socleC22×C11C23×D4
hypercenter#3511D11
hypocenterC11#60723
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #13082502C2semidirect
2. #13079357C2semidirect
3. #13079330C2semidirect
4. #13079278C2semidirect
5. #13079198C2semidirect
6. #13079171C2semidirect
7. #13079158C2semidirect
8. #13079076C2semidirect
9. #13078938C2semidirect
10. C2×#10622706C2semidirect
11. #13078309C2semidirect
12. #13077455C2semidirect
13. C4×#67001C2semidirect
265. #4318#41semidirect
615. C11#60723semidirect

Maximal subgroups

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

subgroupindex
#130825022
#130793572
#130793302
#130792782
#130791982
#130791712
#130791582
#130790762
#130789382
C2×#106227062
#130783092
#130774552
C4×#670012
C11×#35112
#6072311