Finite Group Databasebeta

← #15638543

Subgroups — #15638543

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#13082470C211yesmaximal, characteristic, complemented
2C2×#10623108C211yesmaximal, characteristic, complemented
3#13080563C214yesmaximal, complemented
4#13080557C214yesmaximal, complemented
5#13080375C214yesmaximal, complemented
6#13080341C214yesmaximal, complemented
7#13079554C211yesmaximal, characteristic, complemented
8#13079536C211yesmaximal, characteristic, complemented
9#13079386C214yesmaximal, complemented
10#13078647C211yesmaximal, characteristic, complemented
11#13077839C214yesmaximal, complemented
12#13077639C211yesmaximal, characteristic, complemented
13C11×#3104C211yesmaximal, characteristic, complemented
14C22×#4343C2212yes—
15C11×#533C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66972C2218yescomplemented
18#10623265C2212yescomplemented
19#10623257C2212yescomplemented
20#10623226—22no—
21#10623175—22no—
22#10623158C2214yes—
23#10623116—22no—
24#10623115C2212yescomplemented
25#10623108—22no—
26#10623108—22no—
27#10623108C2214yes—
28#10623108C2214yes—
29#10623108C2212yescomplemented
30#10623056—21no—
31#10623054—21no—
32C2×#66948—22no—
33C2×#66948C2212yes—
34#10623008C2211yescharacteristic
35C2×#66927—21no—
36C2×#66927C2211yescharacteristic
37C2×C4×D44—21no—
38C2×C4×D44C2211yescharacteristic
39C11×#484C2212yes—
40C11×#477C2212yescomplemented
41C11×#462C2212yescomplemented
42C11×#451C2212yes—
43C4×C11×Q16C2214yescomplemented
44C11×#431C2211yescharacteristic
45#10622840C2212yes—
46#10622800C2218yescomplemented
47#10622701C2212yescomplemented
48#10622698C2212yescomplemented
49#10622659C2214yes—
50#10622640C2214yescomplemented
51#10622640C2212yescomplemented
52C4×#4325C2214yescomplemented
53#10622633C2212yescomplemented
54#10622581C2212yes—
55#10622538C2211yescharacteristic
56#10622498C2218yescomplemented
57#10622496C2218yescomplemented
58#10622456C2214yescomplemented
59#10622447C2214yescomplemented
60#10622424C2218yescomplemented
61#10622424C2218yescomplemented
62#10622420C2218yescomplemented
63#10622417C2218yescomplemented
64#10622345C2214yes—
65D11×C22⋊C8C2214yes—
66#10622308C2212yescomplemented
67#10622307C2212yescomplemented
68C8×D44C2214yescomplemented
69C22×Q8×C11C2311yescharacteristic
70C2×#4343—24no—
71C2×#4343—48no—
72C2×#4343C2318yes—
73C2×#4343C2314yes—
74C2×#4339—21no—
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×Q16C2314yes—
84C11×C4⋊Q8C2311yescharacteristic
85C11×C4⋊Q8C2311yescharacteristic
86C11×#125—21no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8C2312yes—
89C4×Q8×C11—21no—
90C4×Q8×C11—21no—
91C4×Q8×C11—21no—
92C4×Q8×C11C2312yes—
93C4×Q8×C11C2312yes—
94C4×Q8×C11C2312yes—
95C11×#117—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C42×C11—21no—
99C2×C42×C11C2311yescharacteristic
100#67000—24no—
101#66999C2314yes—
102C2×#4325C2314yes—
103C2×#4325C2318yes—
104#66983—21no—
105#66983C2312yes—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4D412yes—
108C2×C4⋊Dic11D411yescharacteristic
109#66972—416no—
110C2×D88C2318yes—
111C2×C8×D11C2318yes—
112#66951—24no—
113#66948—22no—
114#66948—22no—
115#66948—24no—
116#66948—28no—
117#66948—28no—
118#66948—24no—
119#66948C2314yes—
120#66948C2318yes—
121#66947—24no—
122#66947—24no—
123#66946—24no—
124#66945—22no—
125#66945C2314yes—
126C4⋊C4×D11—22no—
127#66935—24no—
128(C22⋊D11)⋊C4—24no—
129#66928—22no—
130#66928—21no—
131#66927—24no—
132#66927—24no—
133#66927—22no—
134#66927—21no—
135#66927—21no—
136#66927C2312yes—
137#66927C2312yes—
138#66927C2311yescharacteristic
139C4×D44—21no—
140C4×D44—24no—
141C4×D44—24no—
142C4×D44—22no—
143C4×D44D412yes—
144C4×D44D412yes—
145C4×D44C2312yes—
146C4×D44C2312yes—
147C4×D44C2312yes—
148#66922C2311yescharacteristic
149C4×Dic22—22no—
150C11×#107C2314yes—
151C11×C4⋊C8C2312yes—
152C11×#103C2314yes—
153C11×#103C2314yes—
154C11×C22⋊C8C2312yes—
155C4×C8×C11C2312yes—
156#66899C2314yes—
157C22⋊(C11⋊C8)C2312yes—
158#66885C2318yes—
159(C2×D11)⋊C8C2318yes—
160#66873C2314yes—
161#66873C2318yes—
162#66872C2314yes—
163C4⋊(C11⋊C8)C2312yes—
164C4×C11⋊C8C2312yes—
165#61566—111nomaximal, Sylow
166C23×D11—22no—
167C23×D11C2×D412yes—
168C2×Q8×C11—24no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11C2412yes—
172C2×Q8×C11C2412yes—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2411yescharacteristic
178C2×C22⋊D11—22no—
179C22×Dic11C2×D412yes—
180#4343—216no—
181#4343—48no—
182#4343—48no—
183#4343—416no—
184#4339—44no—
185C2×D44—28no—
186C2×D44—28no—
187C2×D44—24no—
188C2×D44—24no—
189C2×D44—24no—
190C2×D44—22no—
191C2×D44—22no—
192C2×D44—21no—
193C2×D44—22no—
194C2×D44—21no—
195C2×D44—22no—
196C2×D44—22no—
197C2×D44—44no—
198C2×D44—48no—
199C2×D44—44no—
200C2×D44—82no—
201C2×D44—84no—
202C2×D44C2×D412yes—
203C2×D44C2×D412yes—
204C2×D44C2414yes—
205C2×D44C2412yes—
206C2×C4×D11—28no—
207C2×C4×D11—24no—
208C2×C4×D11—22no—
209C2×C4×D11—44no—
210C2×C4×D11—48no—
211C2×C4×D11C2×D414yes—
212C2×C4×D11C2414yes—
213C2×Dic22—21no—
214C11×Q16—28no—
215C2×C8×C11C2414yes—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—22no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—22no—
221C11×C4⋊C4—22no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—22no—
224C11×C4⋊C4C2412yes—
225C11×C4⋊C4C2412yes—
226C11×C22⋊C4—22no—
227C42×C11—22no—
228C42×C11—22no—
229C42×C11—22no—
230C42×C11C2×D411yescharacteristic
231C42×C11C2×D411yescharacteristic
232C42×C11C2411yescharacteristic
233C42×C11C2411yescharacteristic
234#4325—28no—
235#4325—48no—
236(C2×D11)⋊C4—28no—
237(C2×D11)⋊C4—24no—
238(C2×D11)⋊C4—24no—
239(C2×D11)⋊C4—24no—
240(C2×D11)⋊C4—22no—
241(C2×D11)⋊C4—22no—
242(C2×D11)⋊C4C2×D414yes—
243(C2×D11)⋊C4C2×D414yes—
244C4⋊Dic11—21no—
245C4⋊Dic11C2×D412yes—
246C4⋊Dic11C2×D412yes—
247C4⋊Dic11C2412yes—
248Dic11⋊C4—24no—
249C4×Dic11—24no—
250C2×C11⋊C8C2414yes—
251D88—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#3104D1111yescharacteristic, complemented
263#3103—111no—
264#3002—114no—
265#2972—111no—
266C23×C11C22×D411yescharacteristic
267C22×D11—24no—
268C22×D11—22no—
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—24no—
279Q8×C11—81no—
280Q8×C11H(5,𝔽2)14yes—
281C2×C4×C11—24no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—41no—
288C2×C4×C11—42no—
289C2×C4×C11#13514yescomplemented
290C2×C4×C11C22×D411yescharacteristic
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C22×D411yescharacteristic
295C2×C4×C11C2511yescharacteristic
296C22⋊D11—44no—
297C2×Dic11—22no—
298C2×Dic11—42no—
299C2×Dic11C22×D414yes—
300D44—24no—
301D44—24no—
302D44—24no—
303D44—28no—
304D44—416no—
305D44—44no—
306D44—44no—
307D44—44no—
308D44—42no—
309D44—81no—
310D44—82no—
311D44—82no—
312D44—84no—
313D44—88no—
314D44—84no—
315C4×D11—28no—
316C4×D11—44no—
317C4×D11—416no—
318C4×D11—44no—
319C4×D11—84no—
320Dic22—42no—
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—114no—
330#550—114no—
331#550—112no—
332#550—222no—
333#550—222no—
334#547—112no—
335#538—222no—
336#535—221no—
337#533C2×D1111yescharacteristic
338#532—111no—
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#484C2×D1112yes—
353#482—118no—
354#481—112no—
355#477C2×D1112yescomplemented
356#475—112no—
357#466—118no—
358#465—118no—
359#462C2×D1112yescomplemented
360#460—112no—
361#460—114no—
362#459—114no—
363#452—118no—
364#451C2×D1112yes—
365#450—114no—
366#449—118no—
367#449—118no—
368#448—112no—
369#447—114no—
370C4×Q16C2×D1114yescomplemented
371C4×SD16—114no—
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×C11C2×#13512yes—
381C22×C11C23×D411yescharacteristic
382C2×D11—24no—
383C2×D11—24no—
384C2×D11—24no—
385C2×D11—44no—
386C2×D11—42no—
387C2×D11—44no—
388C2×D11—42no—
389C2×D11—44no—
390C2×D11—42no—
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×C11—42no—
400C4×C11C2×#13512yes—
401C4×C11C2×#13512yes—
402C4×C11C2×H(5,𝔽2)12yes—
403Dic11—24no—
404Dic11—42no—
405C2×#41—118no—
406C2×#41—114no—
407C2×#41—224no—
408C2×#41—221no—
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×Q16C22×D1114yes—
421C2×SD16—114no—
422C2×SD16—118no—
423C2×D8—118no—
424C22×C8—118no—
425C4⋊Q8—111no—
426C4⋊Q8C22×D1111yescharacteristic
427C4⋊Q8C22×D1111yescharacteristic
428#127—112no—
429#127—112no—
430#127—111no—
431#127—224no—
432#127—224no—
433#127—222no—
434#127—221no—
435#127—221no—
436#126—224no—
437#125—21no—
438#124—222no—
439#124—224no—
440#124—221no—
441#123—224no—
442#123—224no—
443C22⋊Q8—21no—
444C22⋊Q8—114no—
445C22⋊Q8C22×D1112yes—
446#121—112no—
447#121—118no—
448#121—114no—
449#121—228no—
450#121—228no—
451#121—224no—
452#121—224no—
453#121—222no—
454#121—222no—
455#121—221no—
456#120—224no—
457C4×Q8—21no—
458C4×Q8—21no—
459C4×Q8—21no—
460C4×Q8—222no—
461C4×Q8C22×D1112yes—
462C4×Q8C22×D1112yes—
463C4×Q8C22×D1112yes—
464C4×D4—112no—
465C4×D4—112no—
466C4×D4—112no—
467C4×D4—112no—
468C4×D4—112no—
469C4×D4—224no—
470C4×D4—224no—
471C4×D4—222no—
472C4×D4—224no—
473C4×D4—224no—
474C4×D4—221no—
475#117—21no—
476#117—114no—
477#117—222no—
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#107C22×D1114yes—
487#106—114no—
488C4⋊C8—112no—
489C4⋊C8C22×D1112yes—
490#103—114no—
491#103C22×D1114yes—
492#103C22×D1114yes—
493#102—118no—
494#102—118no—
495#102—114no—
496C22⋊C8—112no—
497C22⋊C8—118no—
498C22⋊C8C22×D1112yes—
499C4×C8—112no—
500C4×C8C22×D1112yes—
501C2×C11—22no—
502C2×C11#348411yescharacteristic
503C2×C11C22×#13511yescharacteristic
504C2×C11#358511yescharacteristic
505D11—44no—
506D11—82no—
507D11—84no—
508C24—112no—
509C24—222no—
510#41—2216no—
511#41—448no—
512#41—448no—
513#41—4416no—
514#41—444no—
515C2×Q8—24no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—221no—
519C2×Q8C23×D1112yes—
520C2×Q8C23×D1112yes—
521C2×D4—112no—
522C2×D4—112no—
523C2×D4—114no—
524C2×D4—112no—
525C2×D4—228no—
526C2×D4—224no—
527C2×D4—224no—
528C2×D4—228no—
529C2×D4—222no—
530C2×D4—224no—
531C2×D4—221no—
532C2×D4—222no—
533C2×D4—222no—
534C2×D4—222no—
535C2×D4—221no—
536C2×D4—222no—
537C2×D4—222no—
538C2×D4—444no—
539C2×D4—448no—
540C2×D4—444no—
541C2×D4—882no—
542C2×D4—884no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—112no—
546C22×C4—114no—
547C22×C4—114no—
548C22×C4—228no—
549C22×C4—224no—
550C22×C4—222no—
551C22×C4—444no—
552C22×C4—448no—
553C22×C4D4×D1111yescharacteristic
554C22×C4D4×D1111yescharacteristic
555C22×C4C23×D1111yescharacteristic
556Q16—28no—
557SD16—228no—
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—21no—
568C4⋊C4—22no—
569C4⋊C4—21no—
570C4⋊C4—22no—
571C4⋊C4—112no—
572C4⋊C4—112no—
573C4⋊C4—112no—
574C4⋊C4—224no—
575C4⋊C4—221no—
576C4⋊C4C23×D1112yes—
577C4⋊C4C23×D1112yes—
578C22⋊C4—22no—
579C22⋊C4—114no—
580C22⋊C4—114no—
581C22⋊C4—228no—
582C22⋊C4—224no—
583C22⋊C4—224no—
584C22⋊C4—224no—
585C22⋊C4—222no—
586C22⋊C4—222no—
587C42—22no—
588C42—22no—
589C42—22no—
590C42—224no—
591C42D4×D1111yescharacteristic
592C42D4×D1111yescharacteristic
593C42C23×D1111yescharacteristic
594C42C23×D1111yescharacteristic
595C11#6156611yescharacteristic, complemented, Sylow
596C23—114no—
597C23—224no—
598C23—222no—
599C23—224no—
600C23—442no—
601C23—442no—
602C23—444no—
603C23—444no—
604C23—444no—
605C23C2×D4×D1111yescharacteristic
606Q8—24no—
607Q8—22no—
608Q8—24no—
609Q8—81no—
610Q8—442no—
611Q8#6704214yes—
612D4—224no—
613D4—224no—
614D4—224no—
615D4—228no—
616D4—4416no—
617D4—444no—
618D4—444no—
619D4—444no—
620D4—444no—
621D4—442no—
622D4—882no—
623D4—882no—
624D4—881no—
625D4—888no—
626D4—884no—
627D4—884no—
628C2×C4—24no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—41no—
635C2×C4—42no—
636C2×C4—114no—
637C2×C4—228no—
638C2×C4—222no—
639C2×C4—444no—
640C2×C4—4416no—
641C2×C4—442no—
642C2×C4—444no—
643C2×C4—884no—
644C2×C4#6697214yescomplemented
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—224no—
656C22—224no—
657C22—224no—
658C22—444no—
659C22—442no—
660C22—444no—
661C22—442no—
662C22—442no—
663C22—444no—
664C22—884no—
665C22—888no—
666C22C2×#6697212yes—
667C22C22×D4×D1111yescharacteristic
668C4—21no—
669C4—21no—
670C4—24no—
671C4—21no—
672C4—42no—
673C4—42no—
674C4—42no—
675C4—224no—
676C4—442no—
677C4C2×#6697212yes—
678C4C2×#6697212yes—
679C4C2×#6704212yes—
680C2—22no—
681C2—444no—
682C2—884no—
683C2—882no—
684C2#1308224911yescharacteristic
685C2C22×#6697211yescharacteristic
686C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3104C2
socleC22×C11C23×D4
hypercenter#3104D11
hypocenterC11#61566
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3104

Complements

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

NH ≅ G/Ntype
1. #13082470C2semidirect
2. C2×#10623108C2semidirect
3. #13080563C2semidirect
4. #13080557C2semidirect
5. #13080375C2semidirect
6. #13080341C2semidirect
7. #13079554C2semidirect
8. #13079536C2semidirect
9. #13079386C2semidirect
10. #13078647C2semidirect
11. #13077839C2semidirect
12. #13077639C2semidirect
13. C11×#3104C2semidirect
17. C2×#66972C22semidirect
18. #10623265C22semidirect
19. #10623257C22semidirect
24. #10623115C22semidirect
29. #10623108C22semidirect
40. C11×#477C22semidirect
41. C11×#462C22semidirect
43. C4×C11×Q16C22semidirect
46. #10622800C22semidirect
47. #10622701C22semidirect
48. #10622698C22semidirect
50. #10622640C22semidirect
51. #10622640C22semidirect
52. C4×#4325C22semidirect
53. #10622633C22semidirect
56. #10622498C22semidirect
57. #10622496C22semidirect
58. #10622456C22semidirect
59. #10622447C22semidirect
60. #10622424C22semidirect
61. #10622424C22semidirect
62. #10622420C22semidirect
63. #10622417C22semidirect
66. #10622308C22semidirect
67. #10622307C22semidirect
68. C8×D44C22semidirect
262. #3104D11semidirect
289. C2×C4×C11#135semidirect
355. #477C2×D11semidirect
359. #462C2×D11semidirect
370. C4×Q16C2×D11semidirect
595. C11#61566semidirect
644. C2×C4#66972semidirect

Maximal subgroups

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

subgroupindex
#130824702
C2×#106231082
#130805632
#130805572
#130803752
#130803412
#130795542
#130795362
#130793862
#130786472
#130778392
#130776392
C11×#31042
#6156611