Finite Group Databasebeta

← #25967231

Subgroups — #25967231

Order 11008.

2362 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583409C212yesmaximal, complemented
2#19145431C214yesmaximal, complemented
3#19145424C214yesmaximal, complemented
4#19145419C211yesmaximal, characteristic, complemented
5#19145406C214yesmaximal, complemented
6#19145401C212yesmaximal, complemented
7#19144505C214yesmaximal, complemented
8#19144202C214yesmaximal, complemented
9#19143808C214yesmaximal, complemented
10#407×D43C211yesmaximal, characteristic, complemented
11C43×#3192C211yesmaximal, characteristic, complemented
12C22×#10621900C2212yescomplemented
13C23×C4×D43C2211yescharacteristic
14C2×#13063344C2214yescomplemented
15C2×M16×D43C2212yescomplemented
16#14583409—22no—
17#14583409—22no—
18#14583409—22no—
19#14583409—22no—
20#14583409C2214yes—
21#14583409C2214yes—
22#14583409C2214yescomplemented
23#14583409C2214yescomplemented
24C2×#13063307—22no—
25C2×#13063305C2212yescomplemented
26C2×#13063304C2212yes—
27C2×#13063296C2212yescomplemented
28C2×#13063293—22no—
29C2×D4×Dic43—22no—
30C2×(C22⋊D43)⋊C4—22no—
31C2×#13063283C2212yescomplemented
32#14583243C2218yescomplemented
33#14583234C2214yescomplemented
34#14583230C2214yescomplemented
35#14583222C2218yescomplemented
36#14583210C2214yescomplemented
37#14583158C2214yescomplemented
38#14583157C2214yescomplemented
39#14583149C2214yescomplemented
40#14583144C2218yescomplemented
41#14583143C2218yescomplemented
42#14583062C2218yescomplemented
43#14583057C2214yescomplemented
44#14583050C2214yescomplemented
45#14583041C2218yescomplemented
46#14583037C2214yescomplemented
47#14582934C2214yescomplemented
48#14582892C2218yescomplemented
49#14582863C2211yescharacteristic
50#14582862C2212yescomplemented
51#14582861C2214yescomplemented
52C22⋊C8×D43C2214yescomplemented
53C2×#121×C43C2212yes—
54C43×#481C2214yescomplemented
55C43×#469C2214yescomplemented
56C43×#447C2214yescomplemented
57C43×#407C2211yescharacteristic
58C24×D43D411yescharacteristic
59C2×#10621900—22no—
60C2×#10621900—22no—
61C2×#10621900—48no—
62C2×#10621900C2314yes—
63C2×#10621900C2314yes—
64C22×Dic86C2312yes—
65C22×C22⋊D43—22no—
66C22×C22⋊D43—22no—
67C23×Dic43—22no—
68C23×Dic43D411yescharacteristic
69C22×C4×D43—44no—
70C22×C4×D43D412yes—
71C22×C4×D43D412yes—
72C22×C4×D43D411yescharacteristic
73C22×C4×D43D411yescharacteristic
74C22×C4×D43C2312yes—
75C22×C4×D43C2311yescharacteristic
76C22×C4×D43C2312yes—
77C22×C4×D43C2311yescharacteristic
78#13063344—48no—
79C2×Dic172C2314yescomplemented
80C2×#10621883C2318yescomplemented
81C2×#10621877C2312yes—
82C2×#10621872C2314yes—
83M16×D43—44no—
84C2×C8×D43C2314yes—
85#13063307—24no—
86#13063307—24no—
87#13063307—24no—
88#13063307—24no—
89#13063305—22no—
90#13063305—22no—
91#13063305C2314yes—
92#13063305C2314yes—
93#13063304—22no—
94#13063304—22no—
95#13063304C2314yes—
96#13063304C2314yes—
97#13063296—22no—
98#13063296—22no—
99#13063296C2314yes—
100#13063296C2314yes—
101#13063293—24no—
102#13063293—24no—
103#13063293—24no—
104#13063293—24no—
105D4×Dic43—24no—
106D4×Dic43—24no—
107D4×Dic43—24no—
108D4×Dic43—24no—
109(C22⋊D43)⋊C4—24no—
110(C22⋊D43)⋊C4—24no—
111(C22⋊D43)⋊C4—24no—
112(C22⋊D43)⋊C4—24no—
113#13063283—22no—
114#13063283—22no—
115#13063283C2314yes—
116#13063283C2314yes—
117C2×C4⋊Dic43—22no—
118C2×C4⋊Dic43C2312yes—
119C2×Dic43⋊C4—22no—
120C2×C22⋊Dic43—22no—
121C2×C22⋊Dic43—22no—
122C2×(C2×D43)⋊C4—22no—
123C2×(C2×D43)⋊C4—22no—
124C2×C4×Dic43—22no—
125#13063258C2318yescomplemented
126#13063257C2314yescomplemented
127#13063250C2318yescomplemented
128#13063248C2318yescomplemented
129#13063246C2318yescomplemented
130C22⋊(C43⋊C8)C2314yes—
131(C2×D43)⋊C8C2318yes—
132C22×D4×C43—22no—
133C22×D4×C43C2312yes—
134C23×C4×C43C2311yescharacteristic
135C2×D8×C43C2314yescomplemented
136C2×M16×C43C2312yes—
137#121×C43—22no—
138#121×C43—22no—
139#121×C43C2314yes—
140#121×C43C2314yes—
141C2×C4⋊C4×C43C2312yes—
142C2×C22⋊C4×C43—22no—
143#106×C43C2314yescomplemented
144#102×C43C2318yescomplemented
145C22⋊C8×C43C2314yes—
146C24×C43—22no—
147C24×C43C2×D411yescharacteristic
148C23×D43—42no—
149C23×D43—44no—
150C23×D43C2×D412yes—
151C23×D43C2×D412yes—
152C23×D43C2×D411yescharacteristic
153C23×D43C2×D411yescharacteristic
154C2×D4×C43—22no—
155C2×D4×C43—24no—
156C2×D4×C43—24no—
157C2×D4×C43—48no—
158C2×D4×C43—44no—
159C2×D4×C43C2414yes—
160C22×C4×C43—22no—
161C22×C4×C43—42no—
162C22×C4×C43C2×D412yes—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2412yes—
165C22×C4×C43C2411yescharacteristic
166C2×C22⋊D43—24no—
167C2×C22⋊D43—24no—
168C2×C22⋊D43—24no—
169C2×C22⋊D43—24no—
170C2×C22⋊D43—48no—
171C2×C22⋊D43—48no—
172C22×Dic43—24no—
173C22×Dic43—24no—
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—42no—
177C22×Dic43—48no—
178C22×Dic43C2×D412yes—
179C22×Dic43C2×D411yescharacteristic
180C22×Dic43C2×D412yes—
181C22×Dic43C2×D411yescharacteristic
182#10621900—216no—
183#10621900—48no—
184#10621900—48no—
185#10621900—48no—
186C2×C4×D43—24no—
187C2×C4×D43—28no—
188C2×C4×D43—44no—
189C2×C4×D43—42no—
190C2×C4×D43—44no—
191C2×C4×D43—42no—
192C2×C4×D43—44no—
193C2×C4×D43—42no—
194C2×C4×D43C2×D412yes—
195C2×C4×D43C2×D412yes—
196C2×C4×D43C2×D411yescharacteristic
197C2×C4×D43C2×D411yescharacteristic
198C2×C4×D43C2×D412yes—
199C2×C4×D43C2×D412yes—
200C2×C4×D43C2×D412yes—
201C2×C4×D43C2412yes—
202C2×C4×D43C2411yescharacteristic
203C2×C4×D43C2411yescharacteristic
204C2×Dic86—22no—
205C2×Dic86—44no—
206C2×Dic86C2414yes—
207D8×C43—44no—
208M16×C43—42no—
209C2×C8×C43C2414yes—
210C4⋊C4×C43—22no—
211C4⋊C4×C43C2414yes—
212C22⋊C4×C43—24no—
213C22⋊C4×C43—24no—
214C22⋊Dic43—24no—
215C22⋊Dic43—24no—
216C22⋊Dic43—24no—
217C22⋊Dic43—24no—
218#10621883—48no—
219(C2×D43)⋊C4—24no—
220(C2×D43)⋊C4—24no—
221(C2×D43)⋊C4—24no—
222(C2×D43)⋊C4—24no—
223C4⋊Dic43—22no—
224C4⋊Dic43—24no—
225C4⋊Dic43—24no—
226C4⋊Dic43C2414yes—
227Dic43⋊C4—24no—
228Dic43⋊C4—24no—
229C4×Dic43—24no—
230C4×Dic43—24no—
231#10621877—42no—
232C2×C43⋊C8C2414yes—
233Dic172—44no—
234#10621872—44no—
235C8×D43—28no—
236C23×C43—24no—
237C23×C43—24no—
238C23×C43—41no—
239C23×C43—44no—
240C23×C43—44no—
241C23×C43—44no—
242C23×C43C22×D411yescharacteristic
243C23×C43C22×D412yes—
244C22×D43—24no—
245C22×D43—24no—
246C22×D43—24no—
247C22×D43—22no—
248C22×D43—42no—
249C22×D43—41no—
250C22×D43—42no—
251C22×D43—42no—
252C22×D43—42no—
253C22×D43—42no—
254C22×D43—416no—
255C22×D43C22×D411yescharacteristic
256C22×D43C22×D412yes—
257C22×D43C22×D411yescharacteristic
258D4×C43—28no—
259D4×C43—44no—
260D4×C43—48no—
261D4×C43—48no—
262C2×C4×C43—22no—
263C2×C4×C43—24no—
264C2×C4×C43—24no—
265C2×C4×C43—41no—
266C2×C4×C43—42no—
267C2×C4×C43—44no—
268C2×C4×C43C22×D411yescharacteristic
269C2×C4×C43C22×D412yes—
270C2×C4×C43C2511yescharacteristic
271C22⋊D43—48no—
272C22⋊D43—48no—
273C22⋊D43—48no—
274C22⋊D43—48no—
275C2×Dic43—24no—
276C2×Dic43—22no—
277C2×Dic43—24no—
278C2×Dic43—24no—
279C2×Dic43—41no—
280C2×Dic43—42no—
281C2×Dic43—48no—
282C2×Dic43—44no—
283C2×Dic43—44no—
284C2×Dic43—48no—
285C2×Dic43C22×D412yes—
286C2×Dic43C22×D411yescharacteristic
287C2×Dic43C22×D411yescharacteristic
288C4×D43—22no—
289C4×D43—24no—
290C4×D43—22no—
291C4×D43—24no—
292C4×D43—22no—
293C4×D43—24no—
294C4×D43—42no—
295C4×D43—42no—
296C4×D43—42no—
297C4×D43H(5,𝔽2)14yes—
298Dic86—28no—
299Dic86—44no—
300C8×C43—24no—
301C43⋊C8—24no—
302#60741—431nomaximal, Sylow
303C22×C43—22no—
304C22×C43—22no—
305C22×C43—21no—
306C22×C43—22no—
307C22×C43—44no—
308C22×C43—44no—
309C22×C43—44no—
310C22×C43—44no—
311C22×C43—88no—
312C22×C43#57514yes—
313C22×C43C23×D411yescharacteristic
314C2×D43—22no—
315C2×D43—21no—
316C2×D43—22no—
317C2×D43—22no—
318C2×D43—22no—
319C2×D43—22no—
320C2×D43—48no—
321C2×D43—44no—
322C2×D43—48no—
323C2×D43—44no—
324C2×D43#53412yes—
325C4×C43—22no—
326C4×C43—21no—
327C4×C43—44no—
328C4×C43C2×H(5,𝔽2)12yes—
329Dic43—22no—
330Dic43—21no—
331Dic43—44no—
332Dic43—44no—
333Dic43#53412yes—
334C2×#525—432no—
335#3197—434no—
336#3196—434no—
337#3195—431no—
338#3194—434no—
339#3193—432no—
340#3192D4311yescharacteristic, complemented
341#3091—434no—
342#3054—434no—
343#3002—434no—
344C2×#407—431no—
345C2×C43—24no—
346C2×C43—41no—
347C2×C43—84no—
348C2×C43C2×#53411yescharacteristic
349C2×C43C2×#57512yes—
350D43—22no—
351D43—41no—
352D43—42no—
353C22×#41—432no—
354C24×C4—431no—
355C2×#135—434no—
356C22×M16—432no—
357#525—434no—
358#525—434no—
359#525—434no—
360#525—434no—
361#525—862no—
362#525—862no—
363#525—862no—
364#525—862no—
365C2×#123—862no—
366C2×C22⋊Q8—432no—
367C2×C22⋊Q8—432no—
368C2×#121—432no—
369C2×#121C2×D4312yes—
370C2×#120—862no—
371C2×C4×D4—862no—
372C2×C4×D4—862no—
373C2×#117—432no—
374#485—438no—
375#484—434no—
376#483—434no—
377#482—438no—
378#481C2×D4314yescomplemented
379#480—434no—
380#470—434no—
381#470—434no—
382#469—434no—
383#469C2×D4314yescomplemented
384#468—438no—
385#468—438no—
386#452—438no—
387#451—434no—
388#450—434no—
389#449—438no—
390#448—434no—
391#447C2×D4314yescomplemented
392#427—434no—
393#416—438no—
394#407—431no—
395#407—432no—
396#407—434no—
397#407C2×D4311yescharacteristic
398C2×C22⋊C8—434no—
399C43#6074111yescharacteristic, complemented, Sylow
400C25—431no—
401C2×#41—434no—
402C2×#41—434no—
403C2×#41—862no—
404C2×#41—862no—
405C2×#41—1728no—
406C22×Q8—432no—
407C22×D4—22no—
408C22×D4—862no—
409C22×D4—862no—
410C22×D4C22×D4312yes—
411C23×C4—431no—
412C23×C4—432no—
413C23×C4—431no—
414C23×C4—432no—
415C23×C4—432no—
416C23×C4—431no—
417C23×C4—431no—
418C23×C4—432no—
419C23×C4—431no—
420C23×C4—862no—
421C23×C4—1724no—
422C23×C4C22×D4311yescharacteristic
423#135—1728no—
424C2×Q16—434no—
425C2×SD16—438no—
426C2×D8C22×D4314yescomplemented
427C2×M16—432no—
428C2×M16—434no—
429C2×M16—1724no—
430C2×M16C22×D4312yes—
431C22×C8—434no—
432#123—864no—
433#123—864no—
434#123—864no—
435#123—864no—
436C22⋊Q8—434no—
437C22⋊Q8—434no—
438C22⋊Q8—434no—
439C22⋊Q8—434no—
440C22⋊Q8—862no—
441C22⋊Q8—862no—
442C22⋊Q8—862no—
443C22⋊Q8—862no—
444#121—22no—
445#121—22no—
446#121—434no—
447#121—434no—
448#121—862no—
449#121—862no—
450#121C22×D4314yes—
451#121C22×D4314yes—
452#120—864no—
453#120—864no—
454#120—864no—
455#120—864no—
456C4×D4—864no—
457C4×D4—864no—
458C4×D4—864no—
459C4×D4—864no—
460C4×D4—864no—
461C4×D4—864no—
462C4×D4—864no—
463C4×D4—864no—
464#117—434no—
465#117—434no—
466#117—862no—
467#117—862no—
468C2×C4⋊C4—432no—
469C2×C4⋊C4—862no—
470C2×C4⋊C4—862no—
471C2×C4⋊C4C22×D4312yes—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—862no—
474C2×C22⋊C4—862no—
475C2×C22⋊C4—862no—
476C2×C22⋊C4—862no—
477C2×C42—862no—
478#107—438no—
479#106—434no—
480#106C22×D4314yescomplemented
481#103—438no—
482#103—438no—
483#102—438no—
484#102C22×D4318yescomplemented
485C22⋊C8—434no—
486C22⋊C8—438no—
487C22⋊C8C22×D4314yes—
488C24—22no—
489C24—432no—
490C24—432no—
491C24—431no—
492C24—431no—
493C24—1724no—
494C24—1722no—
495C24D4×D4311yescharacteristic
496#41—8616no—
497#41—1728no—
498#41—1728no—
499#41—1728no—
500C2×Q8—434no—
501C2×Q8—862no—
502C2×Q8—1724no—
503C2×D4—24no—
504C2×D4—24no—
505C2×D4—22no—
506C2×D4—44no—
507C2×D4—48no—
508C2×D4—864no—
509C2×D4—864no—
510C2×D4—864no—
511C2×D4—864no—
512C2×D4—1728no—
513C2×D4—1728no—
514C2×D4C23×D4314yes—
515C22×C4—22no—
516C22×C4—42no—
517C22×C4—431no—
518C22×C4—432no—
519C22×C4—431no—
520C22×C4—432no—
521C22×C4—431no—
522C22×C4—432no—
523C22×C4—432no—
524C22×C4—431no—
525C22×C4—431no—
526C22×C4—432no—
527C22×C4—431no—
528C22×C4—432no—
529C22×C4—432no—
530C22×C4—432no—
531C22×C4—864no—
532C22×C4—868no—
533C22×C4—864no—
534C22×C4—864no—
535C22×C4—862no—
536C22×C4—862no—
537C22×C4—1722no—
538C22×C4—1724no—
539C22×C4—1722no—
540C22×C4—1724no—
541C22×C4—1722no—
542C22×C4—1724no—
543C22×C4—1722no—
544C22×C4—1728no—
545C22×C4D4×D4312yes—
546C22×C4D4×D4311yescharacteristic
547C22×C4C23×D4312yes—
548C22×C4C23×D4311yescharacteristic
549Q16—1724no—
550SD16—1728no—
551D8—44no—
552M16—42no—
553M16—1724no—
554M16—1722no—
555C2×C8—434no—
556C2×C8—868no—
557C2×C8C23×D4314yes—
558C4⋊C4—22no—
559C4⋊C4—434no—
560C4⋊C4—864no—
561C4⋊C4—864no—
562C4⋊C4—862no—
563C4⋊C4—864no—
564C4⋊C4—864no—
565C4⋊C4C23×D4314yes—
566C22⋊C4—24no—
567C22⋊C4—24no—
568C22⋊C4—864no—
569C22⋊C4—864no—
570C22⋊C4—864no—
571C22⋊C4—864no—
572C22⋊C4—864no—
573C22⋊C4—864no—
574C22⋊C4—864no—
575C22⋊C4—864no—
576C42—864no—
577C42—864no—
578C23—24no—
579C23—24no—
580C23—41no—
581C23—44no—
582C23—44no—
583C23—44no—
584C23—431no—
585C23—431no—
586C23—432no—
587C23—864no—
588C23—862no—
589C23—864no—
590C23—864no—
591C23—1722no—
592C23—1721no—
593C23—1722no—
594C23—1722no—
595C23—1722no—
596C23—1722no—
597C23—17216no—
598C23C2×D4×D4311yescharacteristic
599C23C2×D4×D4312yes—
600Q8—868no—
601Q8—1724no—
602D4—28no—
603D4—44no—
604D4—48no—
605D4—48no—
606D4—1728no—
607D4—1728no—
608D4—1728no—
609D4—1728no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—44no—
616C2×C4—431no—
617C2×C4—434no—
618C2×C4—432no—
619C2×C4—431no—
620C2×C4—864no—
621C2×C4—862no—
622C2×C4—864no—
623C2×C4—862no—
624C2×C4—864no—
625C2×C4—862no—
626C2×C4—862no—
627C2×C4—864no—
628C2×C4—864no—
629C2×C4—864no—
630C2×C4—1722no—
631C2×C4—1722no—
632C2×C4—1722no—
633C2×C4—1728no—
634C2×C4—1721no—
635C2×C4—1722no—
636C2×C4—1728no—
637C2×C4—1724no—
638C2×C4—1724no—
639C2×C4C2×D4×D4311yescharacteristic
640C2×C4C2×D4×D4312yes—
641C2×C4C24×D4311yescharacteristic
642C8—24no—
643C8—864no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—21no—
648C22—44no—
649C22—44no—
650C22—44no—
651C22—44no—
652C22—88no—
653C22—432no—
654C22—862no—
655C22—862no—
656C22—862no—
657C22—862no—
658C22—862no—
659C22—861no—
660C22—1728no—
661C22—1728no—
662C22—1724no—
663C22—1724no—
664C22#1458369514yes—
665C22C22×D4×D4311yescharacteristic
666C4—22no—
667C4—21no—
668C4—44no—
669C4—432no—
670C4—862no—
671C4—861no—
672C4—1724no—
673C4—1724no—
674C4H(5,𝔽2)×D4312yes—
675C2—24no—
676C2—41no—
677C2—84no—
678C2—862no—
679C2—1721no—
680C2—1722no—
681C2#534×D4311yescharacteristic
682C2C2×#1458369512yes—
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3192C2
socleC22×C43C23×D4
hypercenter#3192D43
hypocenterC43#60741
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3192

Complements

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

NH ≅ G/Ntype
1. C2×#14583409C2semidirect
2. #19145431C2semidirect
3. #19145424C2semidirect
4. #19145419C2semidirect
5. #19145406C2semidirect
6. #19145401C2semidirect
7. #19144505C2semidirect
8. #19144202C2semidirect
9. #19143808C2semidirect
10. #407×D43C2semidirect
11. C43×#3192C2semidirect
12. C22×#10621900C22semidirect
14. C2×#13063344C22semidirect
15. C2×M16×D43C22semidirect
22. #14583409C22semidirect
23. #14583409C22semidirect
25. C2×#13063305C22semidirect
27. C2×#13063296C22semidirect
31. C2×#13063283C22semidirect
32. #14583243C22semidirect
33. #14583234C22semidirect
34. #14583230C22semidirect
35. #14583222C22semidirect
36. #14583210C22semidirect
37. #14583158C22semidirect
38. #14583157C22semidirect
39. #14583149C22semidirect
40. #14583144C22semidirect
41. #14583143C22semidirect
42. #14583062C22semidirect
43. #14583057C22semidirect
44. #14583050C22semidirect
45. #14583041C22semidirect
46. #14583037C22semidirect
47. #14582934C22semidirect
48. #14582892C22semidirect
50. #14582862C22semidirect
51. #14582861C22semidirect
52. C22⋊C8×D43C22semidirect
54. C43×#481C22semidirect
55. C43×#469C22semidirect
56. C43×#447C22semidirect
79. C2×Dic172C23semidirect
80. C2×#10621883C23semidirect
125. #13063258C23semidirect
126. #13063257C23semidirect
127. #13063250C23semidirect
128. #13063248C23semidirect
129. #13063246C23semidirect
135. C2×D8×C43C23semidirect
143. #106×C43C23semidirect
144. #102×C43C23semidirect
340. #3192D43semidirect
378. #481C2×D43semidirect
383. #469C2×D43semidirect
391. #447C2×D43semidirect
399. C43#60741semidirect
426. C2×D8C22×D43semidirect
480. #106C22×D43semidirect
484. #102C22×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834092
#191454312
#191454242
#191454192
#191454062
#191454012
#191445052
#191442022
#191438082
#407×D432
C43×#31922
#6074143