Finite Group Databasebeta

← #15638538

Subgroups — #15638538

Order 2816.

2194 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082465C211yesmaximal, characteristic, complemented
2C2×#10623108C211yesmaximal, characteristic, complemented
3#13080568C214yesmaximal, complemented
4#13080552C214yesmaximal, complemented
5#13080371C214yesmaximal, complemented
6#13080347C214yesmaximal, complemented
7#13079559C211yesmaximal, characteristic, complemented
8#13079531C211yesmaximal, characteristic, complemented
9#13079380C214yesmaximal, complemented
10#13078655C211yesmaximal, characteristic, complemented
11#13077833C214yesmaximal, complemented
12#13077639C211yesmaximal, characteristic, complemented
13C11×#3103C211yesmaximal, characteristic, complemented
14C22×#4343C2212yes—
15C11×#532C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17#10623361—21no—
18#10623358—21no—
19C2×#66969C2218yescomplemented
20#10623263C2212yescomplemented
21#10623249C2212yescomplemented
22#10623212—22no—
23#10623148—22no—
24#10623137C2214yes—
25#10623108—22no—
26#10623108—22no—
27#10623108C2214yes—
28#10623108C2214yes—
29#10623096—22no—
30#10623094C2212yescomplemented
31#10623086C2212yescomplemented
32C2×#66948—22no—
33C2×#66948C2212yes—
34C2×#66927—21no—
35C2×#66927C2211yescharacteristic
36C2×C4×D44—21no—
37C2×C4×D44C2211yescharacteristic
38#10623001C2211yescharacteristic
39C11×#481C2212yes—
40C11×#475C2212yescomplemented
41C11×#460C2212yescomplemented
42C11×#448C2212yes—
43C4×C11×SD16C2214yescomplemented
44C11×#431C2211yescharacteristic
45#10622841C2212yes—
46#10622785C2218yescomplemented
47#10622701C2212yescomplemented
48#10622686C2212yescomplemented
49#10622649C2214yes—
50#10622644C2212yescomplemented
51C4×#4326C2214yescomplemented
52#10622634C2212yescomplemented
53#10622628C2214yescomplemented
54#10622583C2212yes—
55#10622538C2211yescharacteristic
56#10622479C2218yescomplemented
57#10622477C2218yescomplemented
58#10622461C2214yescomplemented
59#10622447C2214yescomplemented
60#10622423C2218yescomplemented
61#10622417C2218yescomplemented
62#10622394C2218yescomplemented
63#10622388C2218yescomplemented
64#10622344C2214yes—
65D11×C22⋊C8C2214yes—
66#10622307C2212yescomplemented
67#10622306C2212yescomplemented
68C8×D44C2214yescomplemented
69C2×C11×#41—21no—
70C22×Q8×C11C2311yescharacteristic
71C2×#4343—24no—
72C2×#4343—48no—
73C2×#4343C2318yes—
74C2×#4341C2314yes—
75C22×D44—22no—
76C22×D44—21no—
77C22×D44—22no—
78C22×D44—21no—
79C22×D44D411yescharacteristic
80C22×D44C2312yes—
81C22×C4×D11—22no—
82C22×C4×D11C2312yes—
83C2×C11×SD16C2314yes—
84C11×C4⋊Q8C2311yescharacteristic
85C11×#127C2311yescharacteristic
86C11×#124—21no—
87C11×#121—21no—
88C11×#121C2312yes—
89C4×Q8×C11—21no—
90C4×Q8×C11—21no—
91C4×Q8×C11C2312yes—
92C4×Q8×C11C2312yes—
93C4×D4×C11—21no—
94C4×D4×C11C2312yes—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C42×C11—21no—
98C2×C42×C11C2311yescharacteristic
99#67000—22no—
100Q8×Dic11—22no—
101C2×#4326C2314yes—
102#66993—22no—
103#66992—24no—
104#66991C2314yes—
105#66990—24no—
106D4×Dic11—24no—
107D4×Dic11—22no—
108C2×#4323C2318yes—
109#66983—22no—
110#66983—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4D412yes—
113#66979—21no—
114#66979—22no—
115C2×C4⋊Dic11—22no—
116C2×C4⋊Dic11D411yescharacteristic
117#66977—21no—
118#66977C2312yes—
119#66969—416no—
120C2×#4314C2318yes—
121C2×C8×D11C2318yes—
122#66951—24no—
123#66950C2314yes—
124#66948—24no—
125#66948—28no—
126#66948—28no—
127#66948C2318yes—
128#66945C2314yes—
129#66939—24no—
130#66938—24no—
131#66936—24no—
132(C22⋊D11)⋊C4—24no—
133#66927—24no—
134#66927—24no—
135#66927—21no—
136#66927—21no—
137#66927C2312yes—
138#66927C2312yes—
139C4×D44—24no—
140C4×D44—24no—
141C4×D44D412yes—
142C4×D44D412yes—
143C4×D44C2312yes—
144C4×D44C2312yes—
145#66923—21no—
146#66922C2311yescharacteristic
147#66922C2311yescharacteristic
148C4×Dic22—21no—
149C4×Dic22C2312yes—
150C11×#106C2314yes—
151C11×C4⋊C8C2312yes—
152C11×#103C2314yes—
153C11×#102C2314yes—
154C11×C22⋊C8C2312yes—
155C4×C8×C11C2312yes—
156#66899C2314yes—
157C22⋊(C11⋊C8)C2312yes—
158#66885C2318yes—
159(C2×D11)⋊C8C2318yes—
160#66874C2314yes—
161#66873C2318yes—
162#66871C2314yes—
163C4⋊(C11⋊C8)C2312yes—
164C4×C11⋊C8C2312yes—
165#61566—111nomaximal, Sylow
166C23×D11—22no—
167C23×D11C2×D412yes—
168C11×#41—44no—
169C2×Q8×C11—24no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11C2412yes—
173C2×D4×C11—22no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11C2412yes—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—22no—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2411yescharacteristic
183C2×C22⋊D11—24no—
184C2×C22⋊D11—24no—
185C22×Dic11—24no—
186C22×Dic11C2×D412yes—
187#4343—216no—
188#4343—48no—
189#4343—416no—
190#4341—48no—
191C2×D44—28no—
192C2×D44—28no—
193C2×D44—24no—
194C2×D44—22no—
195C2×D44—22no—
196C2×D44—22no—
197C2×D44—22no—
198C2×D44—22no—
199C2×D44—44no—
200C2×D44—48no—
201C2×D44—44no—
202C2×D44—82no—
203C2×D44—84no—
204C2×D44C2×D412yes—
205C2×D44C2×D412yes—
206C2×D44C2414yes—
207C2×C4×D11—28no—
208C2×C4×D11—44no—
209C2×C4×D11—48no—
210C2×C4×D11C2×D414yes—
211C2×C4×D11C2414yes—
212C2×Dic22—21no—
213C2×Dic22C2412yes—
214C11×SD16—28no—
215C2×C8×C11C2414yes—
216C11×C4⋊C4—22no—
217C11×C4⋊C4—22no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4C2412yes—
221C11×C4⋊C4C2412yes—
222C11×C22⋊C4—22no—
223C11×C22⋊C4—22no—
224C42×C11—22no—
225C42×C11—22no—
226C42×C11C2×D411yescharacteristic
227C42×C11C2×D411yescharacteristic
228C42×C11C2411yescharacteristic
229C42×C11C2411yescharacteristic
230C22⋊Dic11—24no—
231C22⋊Dic11—22no—
232#4326—28no—
233#4323—48no—
234(C2×D11)⋊C4—28no—
235(C2×D11)⋊C4—24no—
236(C2×D11)⋊C4—24no—
237(C2×D11)⋊C4C2×D414yes—
238(C2×D11)⋊C4C2×D414yes—
239C4⋊Dic11—24no—
240C4⋊Dic11—21no—
241C4⋊Dic11—21no—
242C4⋊Dic11—21no—
243C4⋊Dic11C2×D412yes—
244C4⋊Dic11C2×D412yes—
245C4⋊Dic11C2412yes—
246Dic11⋊C4—22no—
247Dic11⋊C4—22no—
248C4×Dic11—24no—
249C4×Dic11—22no—
250C2×C11⋊C8C2414yes—
251#4314—48no—
252C8×D11—48no—
253#3506—111no—
254C2×#550—111no—
255#3305—114no—
256#3304—114no—
257#3287—114no—
258#3284—114no—
259#3208—111no—
260#3205—111no—
261#3188—114no—
262#3104—111no—
263#3103D1111yescharacteristic, complemented
264#3002—114no—
265#2972—111no—
266C23×C11—22no—
267C23×C11C22×D411yescharacteristic
268C22×D11—24no—
269C22×D11—24no—
270C22×D11—42no—
271C22×D11—42no—
272C22×D11—44no—
273C22×D11—44no—
274C22×D11—44no—
275C22×D11C22×D414yes—
276Q8×C11—24no—
277Q8×C11—22no—
278Q8×C11—42no—
279Q8×C11H(5,𝔽2)14yes—
280D4×C11—24no—
281D4×C11—44no—
282D4×C11—42no—
283D4×C11—81no—
284C2×C4×C11—24no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—41no—
290C2×C4×C11—42no—
291C2×C4×C11—44no—
292C2×C4×C11#13514yescomplemented
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C22×D411yescharacteristic
295C2×C4×C11C22×D411yescharacteristic
296C2×C4×C11C22×D411yescharacteristic
297C2×C4×C11C22×D411yescharacteristic
298C2×C4×C11C2511yescharacteristic
299C22⋊D11—84no—
300C22⋊D11—84no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—42no—
304C2×Dic11—84no—
305C2×Dic11C22×D414yes—
306D44—24no—
307D44—24no—
308D44—28no—
309D44—416no—
310D44—44no—
311D44—44no—
312D44—44no—
313D44—82no—
314D44—82no—
315D44—88no—
316C4×D11—28no—
317C4×D11—44no—
318C4×D11—416no—
319Dic22—24no—
320Dic22—81no—
321C8×C11—24no—
322C11⋊C8—24no—
323C22×#41—112no—
324C2×#135—118no—
325#559—222no—
326#556—112no—
327#555—112no—
328#553—222no—
329#550—112no—
330#550—114no—
331#550—114no—
332#550—222no—
333#550—222no—
334#547—112no—
335#538—222no—
336#535—221no—
337#533—111no—
338#532C2×D1111yescharacteristic
339C2×#127—111no—
340C2×#127—221no—
341#525—114no—
342C2×#121—112no—
343C2×#121—222no—
344#520—221no—
345C2×C4×Q8C2×D1111yescharacteristic
346C2×C4×D4—111no—
347C2×C4×D4—221no—
348#493—112no—
349#492—112no—
350#486—112no—
351#486—112no—
352#484—112no—
353#482—118no—
354#481C2×D1112yes—
355#477—112no—
356#475C2×D1112yescomplemented
357#466—118no—
358#465—118no—
359#462—112no—
360#460—114no—
361#460C2×D1112yescomplemented
362#459—114no—
363#452—118no—
364#451—112no—
365#450—114no—
366#449—118no—
367#449—118no—
368#448C2×D1112yes—
369#447—114no—
370C4×Q16—114no—
371C4×SD16C2×D1114yescomplemented
372C8×D4—114no—
373C8×D4—114no—
374#431—111no—
375#431C2×D1111yescharacteristic
376#416—118no—
377C2×C22⋊C8—114no—
378C22×C11—21no—
379C22×C11—21no—
380C22×C11—42no—
381C22×C11—42no—
382C22×C11—42no—
383C22×C11C2×#13512yes—
384C22×C11C23×D411yescharacteristic
385C2×D11—24no—
386C2×D11—24no—
387C2×D11—24no—
388C2×D11—44no—
389C2×D11—44no—
390C2×D11—44no—
391C2×D11—84no—
392C2×D11—88no—
393C4×C11—21no—
394C4×C11—21no—
395C4×C11—24no—
396C4×C11—21no—
397C4×C11—42no—
398C4×C11—42no—
399C4×C11C2×#13512yes—
400C4×C11C2×#13512yes—
401C4×C11C2×H(5,𝔽2)12yes—
402Dic11—24no—
403Dic11—42no—
404Dic11—42no—
405C2×#41—21no—
406C2×#41—118no—
407C2×#41—114no—
408C2×#41—224no—
409C2×#41—448no—
410C22×Q8C22×D1111yescharacteristic
411C22×D4—111no—
412C22×D4—112no—
413C22×D4—222no—
414C22×D4—222no—
415C22×D4—221no—
416C22×D4—221no—
417C23×C4—112no—
418C23×C4—222no—
419#135—4416no—
420C2×Q16—114no—
421C2×SD16—118no—
422C2×SD16C22×D1114yes—
423C2×D8—118no—
424C22×C8—118no—
425C4⋊Q8—111no—
426C4⋊Q8—111no—
427C4⋊Q8C22×D1111yescharacteristic
428#127—112no—
429#127—112no—
430#127—224no—
431#127—224no—
432#127—222no—
433#127—221no—
434#127—221no—
435#127C22×D1111yescharacteristic
436#126—224no—
437#125—221no—
438#124—21no—
439#124—224no—
440#124—222no—
441#123—224no—
442#123—224no—
443C22⋊Q8—112no—
444C22⋊Q8—114no—
445C22⋊Q8—221no—
446#121—21no—
447#121—114no—
448#121—118no—
449#121—228no—
450#121—228no—
451#121—224no—
452#121—224no—
453#121—222no—
454#121—222no—
455#121C22×D1112yes—
456#120—224no—
457C4×Q8—21no—
458C4×Q8—21no—
459C4×Q8—112no—
460C4×Q8—222no—
461C4×Q8—221no—
462C4×Q8C22×D1112yes—
463C4×Q8C22×D1112yes—
464C4×D4—21no—
465C4×D4—112no—
466C4×D4—112no—
467C4×D4—112no—
468C4×D4—112no—
469C4×D4—224no—
470C4×D4—224no—
471C4×D4—224no—
472C4×D4—222no—
473C4×D4—224no—
474C4×D4C22×D1112yes—
475#117—114no—
476#117—222no—
477#117—221no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—111no—
480C2×C4⋊C4—222no—
481C2×C4⋊C4C22×D1111yescharacteristic
482C2×C22⋊C4—112no—
483C2×C22⋊C4—222no—
484C2×C42—21no—
485C2×C42C22×D1111yescharacteristic
486#107—114no—
487#106C22×D1114yes—
488C4⋊C8—112no—
489C4⋊C8C22×D1112yes—
490#103—114no—
491#103—114no—
492#103C22×D1114yes—
493#102—118no—
494#102—118no—
495#102C22×D1114yes—
496C22⋊C8—112no—
497C22⋊C8—118no—
498C22⋊C8C22×D1112yes—
499C4×C8—112no—
500C4×C8C22×D1112yes—
501C2×C11—22no—
502C2×C11—82no—
503C2×C11#348411yescharacteristic
504C2×C11C22×#13511yescharacteristic
505C2×C11#358511yescharacteristic
506D11—44no—
507D11—84no—
508C24—112no—
509C24—222no—
510#41—44no—
511#41—2216no—
512#41—448no—
513#41—448no—
514#41—4416no—
515C2×Q8—24no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—112no—
519C2×Q8—221no—
520C2×Q8C23×D1112yes—
521C2×D4—22no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—112no—
525C2×D4—112no—
526C2×D4—114no—
527C2×D4—228no—
528C2×D4—228no—
529C2×D4—224no—
530C2×D4—224no—
531C2×D4—224no—
532C2×D4—222no—
533C2×D4—222no—
534C2×D4—222no—
535C2×D4—222no—
536C2×D4—222no—
537C2×D4—444no—
538C2×D4—448no—
539C2×D4—444no—
540C2×D4—882no—
541C2×D4—884no—
542C2×D4C23×D1112yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—112no—
547C22×C4—114no—
548C22×C4—114no—
549C22×C4—228no—
550C22×C4—224no—
551C22×C4—444no—
552C22×C4—448no—
553C22×C4D4×D1111yescharacteristic
554C22×C4D4×D1111yescharacteristic
555C22×C4C23×D1111yescharacteristic
556Q16—228no—
557SD16—28no—
558SD16—448no—
559D8—448no—
560C2×C8—114no—
561C2×C8—448no—
562C2×C8C23×D1114yes—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—112no—
568C4⋊C4—112no—
569C4⋊C4—112no—
570C4⋊C4—224no—
571C4⋊C4—221no—
572C4⋊C4—221no—
573C4⋊C4—222no—
574C4⋊C4—222no—
575C4⋊C4—221no—
576C4⋊C4C23×D1112yes—
577C4⋊C4C23×D1112yes—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—114no—
581C22⋊C4—114no—
582C22⋊C4—228no—
583C22⋊C4—224no—
584C22⋊C4—224no—
585C22⋊C4—224no—
586C22⋊C4—222no—
587C42—22no—
588C42—22no—
589C42—224no—
590C42—222no—
591C42D4×D1111yescharacteristic
592C42D4×D1111yescharacteristic
593C42C23×D1111yescharacteristic
594C42C23×D1111yescharacteristic
595C11#6156611yescharacteristic, complemented, Sylow
596C23—22no—
597C23—114no—
598C23—224no—
599C23—224no—
600C23—442no—
601C23—442no—
602C23—444no—
603C23—444no—
604C23—444no—
605C23C2×D4×D1111yescharacteristic
606Q8—24no—
607Q8—22no—
608Q8—42no—
609Q8—224no—
610Q8—881no—
611Q8#6704214yes—
612D4—24no—
613D4—44no—
614D4—42no—
615D4—81no—
616D4—224no—
617D4—224no—
618D4—228no—
619D4—4416no—
620D4—444no—
621D4—444no—
622D4—444no—
623D4—882no—
624D4—882no—
625D4—888no—
626D4—884no—
627D4—884no—
628C2×C4—24no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—44no—
636C2×C4—114no—
637C2×C4—228no—
638C2×C4—222no—
639C2×C4—222no—
640C2×C4—444no—
641C2×C4—4416no—
642C2×C4—442no—
643C2×C4—884no—
644C2×C4#6696914yescomplemented
645C2×C4C2×D4×D1111yescharacteristic
646C2×C4C2×D4×D1111yescharacteristic
647C2×C4C2×D4×D1111yescharacteristic
648C2×C4C2×D4×D1111yescharacteristic
649C2×C4C2×D4×D1111yescharacteristic
650C2×C4C24×D1111yescharacteristic
651C8—24no—
652C8—224no—
653C22—21no—
654C22—21no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—224no—
659C22—224no—
660C22—224no—
661C22—444no—
662C22—444no—
663C22—444no—
664C22—884no—
665C22—888no—
666C22C2×#6696912yes—
667C22C22×D4×D1111yescharacteristic
668C4—21no—
669C4—21no—
670C4—24no—
671C4—21no—
672C4—42no—
673C4—42no—
674C4—224no—
675C4—442no—
676C4—442no—
677C4C2×#6696912yes—
678C4C2×#6696912yes—
679C4C2×#6704212yes—
680C2—22no—
681C2—82no—
682C2—444no—
683C2—884no—
684C2#1308224911yescharacteristic
685C2C22×#6696911yescharacteristic
686C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3103C2
socleC22×C11C23×D4
hypercenter#3103D11
hypocenterC11#61566
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3103

Complements

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

NH ≅ G/Ntype
1. #13082465C2semidirect
2. C2×#10623108C2semidirect
3. #13080568C2semidirect
4. #13080552C2semidirect
5. #13080371C2semidirect
6. #13080347C2semidirect
7. #13079559C2semidirect
8. #13079531C2semidirect
9. #13079380C2semidirect
10. #13078655C2semidirect
11. #13077833C2semidirect
12. #13077639C2semidirect
13. C11×#3103C2semidirect
19. C2×#66969C22semidirect
20. #10623263C22semidirect
21. #10623249C22semidirect
30. #10623094C22semidirect
31. #10623086C22semidirect
40. C11×#475C22semidirect
41. C11×#460C22semidirect
43. C4×C11×SD16C22semidirect
46. #10622785C22semidirect
47. #10622701C22semidirect
48. #10622686C22semidirect
50. #10622644C22semidirect
51. C4×#4326C22semidirect
52. #10622634C22semidirect
53. #10622628C22semidirect
56. #10622479C22semidirect
57. #10622477C22semidirect
58. #10622461C22semidirect
59. #10622447C22semidirect
60. #10622423C22semidirect
61. #10622417C22semidirect
62. #10622394C22semidirect
63. #10622388C22semidirect
66. #10622307C22semidirect
67. #10622306C22semidirect
68. C8×D44C22semidirect
263. #3103D11semidirect
292. C2×C4×C11#135semidirect
356. #475C2×D11semidirect
361. #460C2×D11semidirect
371. C4×SD16C2×D11semidirect
595. C11#61566semidirect
644. C2×C4#66969semidirect

Maximal subgroups

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

subgroupindex
#130824652
C2×#106231082
#130805682
#130805522
#130803712
#130803472
#130795592
#130795312
#130793802
#130786552
#130778332
#130776392
C11×#31032
#6156611