Finite Group Databasebeta

← #15624217

Subgroups — #15624217

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#13082527C211yesmaximal, characteristic
2#13079357C212yesmaximal, complemented
3#13079335C212yesmaximal, complemented
4#13079286C218yesmaximal, complemented
5#13079198C212yesmaximal, complemented
6#13079176C212yesmaximal, complemented
7#13079163C211yesmaximal, characteristic, complemented
8#13079073C211yesmaximal, characteristic, complemented
9#13078941C211yesmaximal, characteristic, complemented
10C2×#10622694C211yesmaximal, characteristic, complemented
11#13078303C214yesmaximal, complemented
12#13077459C214yesmaximal, complemented
13C4×#67001C211yesmaximal, characteristic, complemented
14C11×#3509C211yesmaximal, characteristic, complemented
15C11×#557—21no—
16C11×#557—21no—
17C11×#556—21no—
18C11×#556—21no—
19C11×#552—22no—
20C11×#552—22no—
21C11×#541C2214yes—
22C11×#536C2212yes—
23C11×#533C2212yes—
24C11×#533C2212yes—
25C11×#533C2211yescharacteristic
26C2×C11×C4⋊Q8C2211yescharacteristic
27C11×#519C2212yes—
28C4×C11×#41C2211yescharacteristic
29#10623364C2212yes—
30C2×#67001C2212yes—
31C2×#66995C2214yes—
32#10623115—21no—
33#10623110—21no—
34#10623096—22no—
35#10623094—21no—
36#10623083—22no—
37#10623082—21no—
38#10623065C2214yes—
39#10623054C2212yes—
40#10623008C2211yescharacteristic
41#10623008C2212yes—
42#10623001C2212yes—
43C2×#66922C2211yescharacteristic
44C2×#66899C2214yes—
45#10622706C2211yescharacteristic
46#10622706C2211yescharacteristic
47#10622705C2212yes—
48#10622701C2211yescharacteristic
49#10622701C2211yescharacteristic
50#10622699C2214yes—
51#10622698C2212yes—
52#10622694C2212yes—
53#10622694C2212yes—
54#10622694C2214yes—
55#10622692C2212yes—
56#10622691C2212yes—
57#10622681C2214yes—
58#10622678C2214yes—
59#10622665C2218yes—
60#10622664C2218yes—
61#10622662C2218yes—
62#10622661C2218yes—
63#10622643C2218yes—
64C4×#4326C2218yes—
65#10622639C2218yes—
66C4×#4325C2218yes—
67#10622615C2214yes—
68#10622610C2212yes—
69#10622610C2214yes—
70#10622608C2214yes—
71C4×#4318C2211yescharacteristic
72C4×#4318C2212yes—
73C2×C4×C11⋊C8C2212yes—
74C2×C4×C11⋊C8C2211yescharacteristic
75C2×C11×#41C2311yescharacteristic
76C22×Q8×C11C2312yes—
77C2×#4339—22no—
78C2×#4339C2312yes—
79C22×Dic22—21no—
80C11×C4⋊Q8—22no—
81C11×C4⋊Q8—21no—
82C11×C4⋊Q8—21no—
83C11×C4⋊Q8C2312yes—
84C11×C4⋊Q8C2312yes—
85C11×C4⋊Q8C2311yescharacteristic
86C11×C4⋊Q8C2311yescharacteristic
87C11×#126—24no—
88C11×#126—24no—
89C11×#125—24no—
90C11×#125—24no—
91C11×#125—22no—
92C11×#125—22no—
93C11×#125C2312yes—
94C11×#124—22no—
95C11×#123—24no—
96C11×C22⋊Q8—21no—
97C11×C22⋊Q8—21no—
98C11×C22⋊Q8—22no—
99C11×C22⋊Q8—22no—
100C11×C22⋊Q8C2314yes—
101C11×C22⋊Q8C2314yes—
102C4×Q8×C11—22no—
103C4×Q8×C11—22no—
104C4×Q8×C11—22no—
105C4×Q8×C11—22no—
106C4×Q8×C11—21no—
107C4×Q8×C11—21no—
108C4×Q8×C11D411yescharacteristic
109C4×Q8×C11D411yescharacteristic
110C4×Q8×C11C2314yes—
111C4×Q8×C11C2314yes—
112C4×D4×C11D411yescharacteristic
113C4×D4×C11D412yes—
114C4×D4×C11D411yescharacteristic
115C4×D4×C11D412yes—
116C11×#117—22no—
117C11×#117—22no—
118C11×#117—24no—
119C11×#117C2312yes—
120C11×#117C2311yescharacteristic
121C11×#117C2312yes—
122C2×C11×C4⋊C4—21no—
123C2×C11×C4⋊C4—21no—
124C2×C42×C11C2311yescharacteristic
125C2×C42×C11C2312yes—
126#67001—28no—
127#66999—22no—
128C2×#4326C2318yes—
129#66995—216no—
130C2×#4325C2318yes—
131#66992—24no—
132#66991—22no—
133#66983—21no—
134#66983—22no—
135#66983—21no—
136#66983C2314yes—
137#66979—22no—
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11C2312yes—
140#66977—22no—
141#66977C2314yes—
142C2×#4318C2314yes—
143C2×#4318C2312yes—
144C22×C11⋊C8C2312yes—
145C22×C11⋊C8C2314yes—
146#66951—24no—
147#66949—24no—
148#66945—22no—
149C4⋊C4×D11—22no—
150#66938—24no—
151#66936—24no—
152(C22⋊D11)⋊C4—24no—
153#66928—22no—
154#66928C2312yes—
155#66927C2311yescharacteristic
156C4×D44—21no—
157C4×D44—21no—
158C4×D44—22no—
159C4×D44C2314yes—
160#66923—22no—
161#66922—21no—
162#66922—21no—
163#66922C2311yescharacteristic
164#66922C2312yes—
165#66922C2312yes—
166C4×Dic22—22no—
167C4×Dic22C2314yes—
168#66899C2318yes—
169#66899C2318yes—
170#66874C2314yes—
171#66874C2314yes—
172#66873C2314yes—
173#66873C2314yes—
174#66872C2318yes—
175#66871C2318yes—
176#66867C2314yes—
177#66867C2312yes—
178C4×C11⋊C8C2311yescharacteristic
179C4×C11⋊C8C2312yes—
180C4×C11⋊C8C2311yescharacteristic
181C4×C11⋊C8C2314yes—
182C4×C11⋊C8C2312yes—
183#60723—111nomaximal, Sylow
184C11×#41—24no—
185C2×Q8×C11—21no—
186C2×Q8×C11—21no—
187C2×Q8×C11—22no—
188C2×Q8×C11—28no—
189C2×Q8×C11C2×D411yescharacteristic
190C2×Q8×C11C2414yes—
191C2×D4×C11C2×D411yescharacteristic
192C2×D4×C11C2×D412yes—
193C22×C4×C11—22no—
194C22×C4×C11C2×D412yes—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2412yes—
199C22×C4×C11C2411yescharacteristic
200C2×C22⋊D11—22no—
201C2×C22⋊D11—24no—
202C22×Dic11—22no—
203#4339—28no—
204#4339—84no—
205C2×D44—21no—
206C2×D44—21no—
207C2×D44C2412yes—
208C2×C4×D11—22no—
209C2×C4×D11—24no—
210C2×Dic22—22no—
211C2×Dic22—22no—
212C2×Dic22—82no—
213C2×Dic22C2412yes—
214C11×C4⋊C4—22no—
215C11×C4⋊C4—22no—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—22no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—24no—
221C11×C4⋊C4—24no—
222C11×C4⋊C4—22no—
223C11×C4⋊C4—22no—
224C11×C4⋊C4—24no—
225C11×C4⋊C4—24no—
226C11×C4⋊C4C2×D411yescharacteristic
227C11×C4⋊C4C2×D411yescharacteristic
228C11×C4⋊C4C2×D412yes—
229C11×C4⋊C4C2×D412yes—
230C11×C4⋊C4C2412yes—
231C11×C4⋊C4C2412yes—
232C11×C22⋊C4—22no—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4C2×D412yes—
236C11×C22⋊C4C2×D412yes—
237C11×C22⋊C4C2×D412yes—
238C42×C11—24no—
239C42×C11—24no—
240C42×C11—22no—
241C42×C11C2×D412yes—
242C42×C11C2×D411yescharacteristic
243C42×C11C2×D411yescharacteristic
244C42×C11C2×D412yes—
245C42×C11C2411yescharacteristic
246C42×C11C2412yes—
247C42×C11C2411yescharacteristic
248C22⋊Dic11—24no—
249#4326—216no—
250#4325—216no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—22no—
253(C2×D11)⋊C4—22no—
254(C2×D11)⋊C4—24no—
255C4⋊Dic11—21no—
256C4⋊Dic11—22no—
257C4⋊Dic11—22no—
258C4⋊Dic11—22no—
259C4⋊Dic11—21no—
260C4⋊Dic11C2414yes—
261Dic11⋊C4—24no—
262Dic11⋊C4—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#3511—111no—
272#3509D1111yescharacteristic, complemented
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×C11C22×D412yes—
286C23×C11C22×D411yescharacteristic
287C22×D11—22no—
288Q8×C11—22no—
289Q8×C11—28no—
290Q8×C11—44no—
291Q8×C11—42no—
292Q8×C11—42no—
293D4×C11—24no—
294D4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—24no—
297C2×C4×C11—22no—
298C2×C4×C11—24no—
299C2×C4×C11—24no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—24no—
303C2×C4×C11—44no—
304C2×C4×C11C22×D412yes—
305C2×C4×C11C22×D412yes—
306C2×C4×C11C22×D412yes—
307C2×C4×C11C22×D411yescharacteristic
308C2×C4×C11C22×D411yescharacteristic
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C22×D411yescharacteristic
311C2×C4×C11C22×D411yescharacteristic
312C2×C4×C11C2×#4114yes—
313C2×C4×C11C2511yescharacteristic
314C22⋊D11—44no—
315C22⋊D11—84no—
316C2×Dic11—22no—
317C2×Dic11—24no—
318C2×Dic11—82no—
319D44—24no—
320D44—42no—
321D44—42no—
322C4×D11—44no—
323C4×D11—84no—
324Dic22—24no—
325Dic22—44no—
326Dic22—82no—
327C11⋊C8—22no—
328C11⋊C8—22no—
329C11⋊C8C2×#4118yes—
330C2×#137—114no—
331C2×#131—112no—
332#557—21no—
333#557—21no—
334#556—21no—
335#556—21no—
336#556—221no—
337#555—221no—
338#554—221no—
339#553—222no—
340#552—22no—
341#552—22no—
342#548—222no—
343#547—221no—
344#542—114no—
345#541C2×D1114yes—
346#537—112no—
347#536C2×D1112yes—
348#533—112no—
349#533C2×D1112yes—
350#533C2×D1112yes—
351#533C2×D1111yescharacteristic
352#532—112no—
353#532—111no—
354C2×C4⋊Q8—111no—
355C2×C4⋊Q8C2×D1111yescharacteristic
356#520—112no—
357#519C2×D1112yes—
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#53212yes—
396C22×C11C23×D411yescharacteristic
397C2×D11—42no—
398C2×D11—42no—
399C2×D11—42no—
400C4×C11—22no—
401C4×C11—21no—
402C4×C11—22no—
403C4×C11—22no—
404C4×C11—21no—
405C4×C11—44no—
406C4×C11—42no—
407C4×C11—42no—
408C4×C11#53212yes—
409C4×C11#57712yes—
410C4×C11#57812yes—
411C4×C11C22×#4112yes—
412Dic11—42no—
413Dic11—44no—
414C2×#41—112no—
415C2×#41—222no—
416C2×#41C22×D1111yescharacteristic
417C22×Q8—221no—
418C22×Q8C22×D1112yes—
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—22no—
428C4⋊Q8—21no—
429C4⋊Q8—21no—
430C4⋊Q8—112no—
431C4⋊Q8—112no—
432C4⋊Q8—111no—
433C4⋊Q8—221no—
434C4⋊Q8—221no—
435C4⋊Q8C22×D1112yes—
436C4⋊Q8C22×D1112yes—
437C4⋊Q8C22×D1111yescharacteristic
438C4⋊Q8C22×D1111yescharacteristic
439#127—111no—
440#126—24no—
441#126—24no—
442#126—224no—
443#125—24no—
444#125—24no—
445#125—22no—
446#125—22no—
447#125—222no—
448#125C22×D1112yes—
449#124—22no—
450#124—112no—
451#124—224no—
452#124—222no—
453#123—24no—
454#123—224no—
455C22⋊Q8—21no—
456C22⋊Q8—21no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—114no—
460C22⋊Q8—222no—
461C22⋊Q8—222no—
462C22⋊Q8—224no—
463C22⋊Q8C22×D1114yes—
464C22⋊Q8C22×D1114yes—
465#121—114no—
466#121—222no—
467#121—224no—
468#121—221no—
469#121—221no—
470#121—222no—
471C4×Q8—22no—
472C4×Q8—22no—
473C4×Q8—22no—
474C4×Q8—22no—
475C4×Q8—21no—
476C4×Q8—21no—
477C4×Q8—114no—
478C4×Q8—222no—
479C4×Q8C22⋊D1111yescharacteristic
480C4×Q8C22⋊D1111yescharacteristic
481C4×Q8C22×D1114yes—
482C4×Q8C22×D1114yes—
483C4×D4—114no—
484C4×D4—224no—
485C4×D4—221no—
486C4×D4—222no—
487C4×D4—221no—
488C4×D4C22⋊D1111yescharacteristic
489C4×D4C22⋊D1112yes—
490C4×D4C22⋊D1112yes—
491C4×D4C22⋊D1111yescharacteristic
492#117—22no—
493#117—22no—
494#117—24no—
495#117—222no—
496#117—222no—
497#117C22×D1112yes—
498#117C22×D1111yescharacteristic
499#117C22×D1112yes—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—112no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4—222no—
505C2×C42C22×D1111yescharacteristic
506C2×C42C22×D1112yes—
507#107—118no—
508#106—118no—
509#103—118no—
510#103—118no—
511#103—114no—
512#103—114no—
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×C11C2×#53211yescharacteristic
525C2×C11C2×#57711yescharacteristic
526C2×C11C2×#57811yescharacteristic
527D11—82no—
528#41—24no—
529#41—228no—
530#41—884no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—22no—
534C2×Q8—28no—
535C2×Q8—112no—
536C2×Q8—222no—
537C2×Q8—222no—
538C2×Q8—882no—
539C2×Q8C2×C22⋊D1111yescharacteristic
540C2×Q8C23×D1114yes—
541C2×D4—112no—
542C2×D4—222no—
543C2×D4—224no—
544C2×D4—221no—
545C2×D4—221no—
546C2×D4C2×C22⋊D1112yes—
547C2×D4C2×C22⋊D1111yescharacteristic
548C22×C4—22no—
549C22×C4—222no—
550C22×C4—222no—
551C22×C4—224no—
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—22no—
570C4⋊C4—22no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—114no—
580C4⋊C4—222no—
581C4⋊C4—222no—
582C4⋊C4—224no—
583C4⋊C4—222no—
584C4⋊C4—221no—
585C4⋊C4—221no—
586C4⋊C4—224no—
587C4⋊C4C2×C22⋊D1111yescharacteristic
588C4⋊C4C2×C22⋊D1111yescharacteristic
589C4⋊C4C2×C22⋊D1112yes—
590C4⋊C4C2×C22⋊D1112yes—
591C4⋊C4C23×D1112yes—
592C4⋊C4C23×D1112yes—
593C22⋊C4—22no—
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—224no—
597C22⋊C4—224no—
598C22⋊C4—224no—
599C22⋊C4—222no—
600C22⋊C4—222no—
601C22⋊C4C2×C22⋊D1112yes—
602C22⋊C4C2×C22⋊D1112yes—
603C22⋊C4C2×C22⋊D1112yes—
604C42—24no—
605C42—24no—
606C42—22no—
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—222no—
617C23C22×C22⋊D1112yes—
618C23C22×C22⋊D1111yescharacteristic
619Q8—22no—
620Q8—28no—
621Q8—44no—
622Q8—42no—
623Q8—42no—
624Q8—224no—
625Q8—444no—
626Q8—882no—
627D4—24no—
628D4—22no—
629D4—224no—
630D4—444no—
631D4—442no—
632D4—442no—
633D4—884no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—44no—
643C2×C4—222no—
644C2×C4—224no—
645C2×C4—444no—
646C2×C4—884no—
647C2×C4—882no—
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—442no—
667C22—442no—
668C22—442no—
669C22#1062336312yes—
670C22C23×C22⋊D1111yescharacteristic
671C4—22no—
672C4—22no—
673C4—21no—
674C4—22no—
675C4—21no—
676C4—44no—
677C4—42no—
678C4—42no—
679C4—442no—
680C4—444no—
681C4#1062336312yes—
682C4#1062336812yes—
683C4#1062336912yes—
684C4C2×#41×D1112yes—
685C2—22no—
686C2—42no—
687C2—882no—
688C2C2×#1062336311yescharacteristic
689C2C2×#1062336811yescharacteristic
690C2C2×#1062336911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3509C2
socleC22×C11C23×D4
prime radical#13082527C2
hypercenter#3509D11
hypocenterC11#60723
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3509

Complements

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

NH ≅ G/Ntype
2. #13079357C2semidirect
3. #13079335C2semidirect
4. #13079286C2semidirect
5. #13079198C2semidirect
6. #13079176C2semidirect
7. #13079163C2semidirect
8. #13079073C2semidirect
9. #13078941C2semidirect
10. C2×#10622694C2semidirect
11. #13078303C2semidirect
12. #13077459C2semidirect
13. C4×#67001C2semidirect
14. C11×#3509C2semidirect
265. #4318#41semidirect
272. #3509D11semidirect
615. C11#60723semidirect

Maximal subgroups

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

subgroupindex
#130825272
#130793572
#130793352
#130792862
#130791982
#130791762
#130791632
#130790732
#130789412
C2×#106226942
#130783032
#130774592
C4×#670012
C11×#35092
#6072311