Finite Group Databasebeta

← #25081770

Subgroups — #25081770

Order 11008.

792 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145509C211yesmaximal, characteristic, complemented
2#19144054C211yesmaximal, characteristic, complemented
3#459×D43C211yesmaximal, characteristic, complemented
4#19143616C211yesmaximal, characteristic, complemented
5#19134033C211yesmaximal, characteristic, complemented
6#19134032C211yesmaximal, characteristic, complemented
7#19134031C211yesmaximal, characteristic, complemented
8#19134030C211yesmaximal, characteristic, complemented
9#19133949C211yesmaximal, characteristic, complemented
10#19133948C211yesmaximal, characteristic, complemented
11#19133947C211yesmaximal, characteristic, complemented
12#19133368C211yesmaximal, characteristic, complemented
13#19133261C211yesmaximal, characteristic, complemented
14#19133241C211yesmaximal, characteristic, complemented
15C43×#1667C211yesmaximal, characteristic, complemented
16C2×#13063349—21no—
17C2×D8×D43—21no—
18#14583447C2211yescharacteristic
19#127×D43C2211yescharacteristic
20C4×D4×D43C2211yescharacteristic
21#14583275C2211yescharacteristic, complemented
22#14583246C2211yescharacteristic, complemented
23#14583245C2211yescharacteristic, complemented
24#14583113—21no—
25#14583112—21no—
26#14583105C2211yescharacteristic, complemented
27#14583104C2211yescharacteristic, complemented
28#14583095C2211yescharacteristic
29#14583094C2211yescharacteristic
30#14583093—21no—
31#14583092—21no—
32#14583092—21no—
33#14583092—21no—
34#14583091C2211yescharacteristic
35#14583091C2211yescharacteristic, complemented
36#14583031—21no—
37#14583031—21no—
38C8×D172C2211yescharacteristic, complemented
39D4×C43⋊C8C2211yescharacteristic, complemented
40#14582964C2211yescharacteristic, complemented
41C8×C22⋊D43—21no—
42(C22⋊D43)⋊C8—21no—
43#14582951C2211yescharacteristic
44#14582950C2211yescharacteristic
45#14582921C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47#14582897—21no—
48#102×D43—21no—
49C2×(C2×D43)⋊C8—21no—
50C22⋊C8×D43—21no—
51#14582652C2211yescharacteristic, complemented
52#14582651C2211yescharacteristic, complemented
53#14582651C2211yescharacteristic, complemented
54#14582646C2211yescharacteristic, complemented
55#14582644C2211yescharacteristic, complemented
56#14582643C2211yescharacteristic, complemented
57#14582643C2211yescharacteristic, complemented
58#14582642C2211yescharacteristic, complemented
59#14582642C2211yescharacteristic, complemented
60C43×#493C2211yescharacteristic, complemented
61C43×#459C2211yescharacteristic
62C43×#459C2211yescharacteristic, complemented
63C8×D4×C43C2211yescharacteristic, complemented
64C43×#335C2211yescharacteristic, complemented
65C43×#331C2211yescharacteristic, complemented
66C43×#331C2211yescharacteristic, complemented
67C2×#10621900—21no—
68C2×D4×D43—21no—
69C2×D4×D43—21no—
70C2×D4×D43—21no—
71C2×D4×D43D411yescharacteristic
72C22×C4×D43—21no—
73#13063349—44no—
74C2×#10621873—21no—
75C2×#10621883—21no—
76C2×D344—21no—
77C2×#10621882—21no—
78C2×#10621882—21no—
79C2×#10621882—21no—
80C2×#10621882—21no—
81C2×#10621882—21no—
82D8×D43—44no—
83C2×#10621872—21no—
84C22×C43⋊C8—21no—
85C2×C8×D43—21no—
86C2×C8×D43—21no—
87C2×C8×D43—21no—
88#13063325C2311yescharacteristic
89#13063322C2311yescharacteristic
90#13063321—21no—
91#13063321—21no—
92#13063321—21no—
93#13063312—21no—
94#13063296—21no—
95#13063296—21no—
96C4×D172C2311yescharacteristic
97D4×Dic43—21no—
98D4×Dic43—21no—
99D4×Dic43D411yescharacteristic
100#13063287D411yescharacteristic
101C4×C22⋊D43—21no—
102(C22⋊D43)⋊C4—21no—
103C4⋊C4×D43D411yescharacteristic
104C22⋊C4×D43—21no—
105C42×D43C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8D411yescharacteristic
112Dic43⋊C8D411yescharacteristic
113#13063250—21no—
114#13063248—21no—
115#13063247—21no—
116#13063247—21no—
117#13063247—21no—
118#13063246—21no—
119#13063246—21no—
120#13063246—21no—
121#13063246—21no—
122#13063245—21no—
123C22⋊(C43⋊C8)—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127(C2×D43)⋊C8D411yescharacteristic
128(C2×D43)⋊C8D411yescharacteristic
129C4×C43⋊C8C2311yescharacteristic
130C8×Dic43—21no—
131C2×D8×C43—21no—
132C2×D8×C43—21no—
133C2×D8×C43—21no—
134C2×D8×C43—21no—
135C22×C8×C43—21no—
136#127×C43C2311yescharacteristic
137#127×C43C2311yescharacteristic
138C4×D4×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142#102×C43—21no—
143#102×C43—21no—
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C23×D43—21no—
147C23×D43—41no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
156C2×C22⋊D43—21no—
157C2×C22⋊D43—41no—
158C2×C22⋊D43—41no—
159C2×C22⋊D43—41no—
160C2×C22⋊D43—41no—
161C22×Dic43—21no—
162C22×Dic43—41no—
163#10621900—42no—
164#10621900—42no—
165D4×D43—22no—
166D4×D43—42no—
167D4×D43—42no—
168D4×D43—81no—
169D4×D43—81no—
170D4×D43—82no—
171D4×D43D814yescomplemented
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172C2×D411yescharacteristic
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—81no—
180C2×C4×D43—81no—
181C2×C4×D43C2×D411yescharacteristic
182C2×C4×D43C2×D411yescharacteristic
183C2×C4×D43#4111yescharacteristic
184C2×Dic86—21no—
185D8×C43—42no—
186D8×C43—42no—
187D8×C43—81no—
188D8×C43—81no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—81no—
193C2×C8×C43C2×D411yescharacteristic
194C2×C8×C43C2×D411yescharacteristic
195C4⋊C4×C43C2×D411yescharacteristic
196C22⋊C4×C43—21no—
197C42×C43C2411yescharacteristic
198C22⋊Dic43—21no—
199C22⋊Dic43—41no—
200C22⋊Dic43—41no—
201#10621883—42no—
202#10621882—42no—
203#10621882—42no—
204#10621882—42no—
205#10621882—81no—
206#10621882—81no—
207(C2×D43)⋊C4—21no—
208(C2×D43)⋊C4—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43C2×D411yescharacteristic
212Dic43⋊C4—21no—
213C4×Dic43C2×D411yescharacteristic
214C4×Dic43C2×D411yescharacteristic
215C4×Dic43#4111yescharacteristic
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—81no—
220C2×C43⋊C8C2×D411yescharacteristic
221C2×C43⋊C8C2×D411yescharacteristic
222D344—42no—
223#10621873—42no—
224#10621872—42no—
225C8×D43—42no—
226C8×D43—81no—
227C8×D43—81no—
228C23×C43—21no—
229C23×C43—41no—
230C23×C43—41no—
231C22×D43—21no—
232C22×D43—24no—
233C22×D43—41no—
234C22×D43—81no—
235C22×D43—81no—
236C22×D43—82no—
237C22×D43—82no—
238C22×D43—82no—
239C22×D43#12111yescharacteristic
240D4×C43—21no—
241D4×C43—41no—
242D4×C43—41no—
243D4×C43—41no—
244D4×C43—41no—
245D4×C43—41no—
246D4×C43—41no—
247D4×C43—41no—
248D4×C43—41no—
249D4×C43—81no—
250D4×C43—81no—
251D4×C43C2×D812yes—
252C2×C4×C43—21no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C22⋊D43—24no—
259C22⋊D43—82no—
260C22⋊D43—82no—
261C22⋊D43—82no—
262C22⋊D43—82no—
263C2×Dic43—21no—
264C2×Dic43—41no—
265C2×Dic43—81no—
266C2×Dic43—82no—
267C2×Dic43#12111yescharacteristic
268C2×Dic43#12111yescharacteristic
269C2×Dic43#12111yescharacteristic
270D172—21no—
271D172—41no—
272D172—41no—
273D172—41no—
274D172—41no—
275D172—81no—
276D172C2×D812yes—
277C4×D43—21no—
278C4×D43—21no—
279C4×D43—41no—
280C4×D43—41no—
281C4×D43—41no—
282C4×D43—81no—
283C4×D43—81no—
284C4×D43C2×D812yes—
285C4×D43#13512yes—
286Dic86—41no—
287Dic86—41no—
288C8×C43—21no—
289C8×C43—21no—
290C8×C43—41no—
291C8×C43—41no—
292C8×C43—41no—
293C43⋊C8—21no—
294C43⋊C8—21no—
295C43⋊C8—41no—
296C43⋊C8—41no—
297C43⋊C8—41no—
298#19386—431nomaximal, Sylow
299C22×C43—22no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43C2×#12111yescharacteristic
309C2×D43—21no—
310C2×D43—21no—
311C2×D43—22no—
312C2×D43—41no—
313C2×D43—41no—
314C2×D43—84no—
315C2×D43—81no—
316C2×D43—81no—
317C2×D43—81no—
318C2×D43—164no—
319C2×D43#46612yes—
320C4×C43—21no—
321C4×C43—41no—
322C4×C43C22×D811yescharacteristic
323C4×C43C2×#13511yescharacteristic
324C4×C43#57611yescharacteristic
325C4×C43#57611yescharacteristic
326Dic43—21no—
327Dic43—21no—
328Dic43—41no—
329Dic43—81no—
330Dic43#46612yes—
331#3205—431no—
332#3036—431no—
333C2×#459—431no—
334#2972—431no—
335#1681—431no—
336#1681—431no—
337#1681—431no—
338#1681—431no—
339#1667—431no—
340#1667—431no—
341#1667—431no—
342#1667D4311yescharacteristic, complemented
343#1571—431no—
344#1545—431no—
345#1540—431no—
346C2×C43—42no—
347C2×C43—161no—
348C2×C43—161no—
349C2×C43#304111yescharacteristic
350C2×C43C2×#46611yescharacteristic
351C2×C43#306811yescharacteristic
352D43—22no—
353D43—42no—
354D43—161no—
355C2×AGL(1,ℤ/8)—861no—
356C22×D8—861no—
357#532—431no—
358C2×#127—431no—
359C2×C4×D4—431no—
360#493—431no—
361#493C2×D4311yescharacteristic, complemented
362#486—431no—
363#486—431no—
364#463—861no—
365#463—861no—
366#461—431no—
367#461—431no—
368#459—431no—
369#459—431no—
370#459—431no—
371#459—431no—
372#459—861no—
373#459—861no—
374#459—861no—
375#459—861no—
376#459C2×D4311yescharacteristic
377#459C2×D4311yescharacteristic, complemented
378#447—861no—
379#447—861no—
380C8×D4—431no—
381C8×D4—431no—
382C8×D4—431no—
383C8×D4—861no—
384C8×D4—861no—
385C8×D4C2×D4311yescharacteristic, complemented
386#431—431no—
387#431—431no—
388#423—431no—
389C2×C4⋊C8—431no—
390#417—861no—
391C2×#102—861no—
392C2×C22⋊C8—861no—
393C2×C22⋊C8—861no—
394#335—431no—
395#335—431no—
396#335—431no—
397#335C2×D4311yescharacteristic, complemented
398#332—431no—
399#332—431no—
400#331—431no—
401#331—431no—
402#331—431no—
403#331—431no—
404#331C2×D4311yescharacteristic, complemented
405#331C2×D4311yescharacteristic, complemented
406C43#1938611yescharacteristic, complemented, Sylow
407C2×#41—861no—
408C22×D4—431no—
409C22×D4—861no—
410C22×D4—861no—
411C22×D4—861no—
412C23×C4—861no—
413AGL(1,ℤ/8)—1724no—
414C2×SD16—861no—
415C2×SD16—861no—
416C2×D8—21no—
417C2×D8—21no—
418C2×D8—21no—
419C2×D8—21no—
420C2×D8—861no—
421C2×D8—861no—
422C2×D8—861no—
423C2×D8—861no—
424C2×D8—861no—
425C2×D8—861no—
426C2×D8—1724no—
427C2×M16—861no—
428C22×C8—21no—
429C22×C8—861no—
430C22×C8—861no—
431C22×C8—861no—
432C22×C8—861no—
433C4⋊Q8—431no—
434#127—431no—
435#127—861no—
436#127—861no—
437#127—861no—
438#127C22×D4311yescharacteristic
439#127C22×D4311yescharacteristic
440#124—861no—
441#121—861no—
442#121—861no—
443C4×D4—431no—
444C4×D4—431no—
445C4×D4—431no—
446C4×D4—861no—
447C4×D4—861no—
448C4×D4—861no—
449C4×D4—861no—
450C4×D4C22×D4311yescharacteristic
451C2×C4⋊C4—431no—
452C2×C22⋊C4—861no—
453C2×C42—431no—
454C4⋊C8—431no—
455C4⋊C8—431no—
456C4⋊C8—431no—
457C4⋊C8—431no—
458C4⋊C8—431no—
459C4⋊C8—861no—
460C4⋊C8—861no—
461C4⋊C8C22×D4311yescharacteristic
462C4⋊C8C22×D4311yescharacteristic
463C4⋊C8C22×D4311yescharacteristic
464#103—861no—
465#103—861no—
466#102—21no—
467#102—21no—
468#102—861no—
469#102—861no—
470#102—861no—
471#102—861no—
472#102—861no—
473#102—861no—
474#102—861no—
475#102—861no—
476C22⋊C8—21no—
477C22⋊C8—431no—
478C22⋊C8—431no—
479C22⋊C8—861no—
480C22⋊C8—861no—
481C22⋊C8—861no—
482C22⋊C8—861no—
483C4×C8—431no—
484C4×C8—861no—
485C4×C8C22×D4311yescharacteristic
486C24—861no—
487C24—1721no—
488#41—1722no—
489#41—1722no—
490C2×Q8—861no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—434no—
498C2×D4—431no—
499C2×D4—862no—
500C2×D4—861no—
501C2×D4—861no—
502C2×D4—861no—
503C2×D4—861no—
504C2×D4—3441no—
505C2×D4—3441no—
506C2×D4—3442no—
507C2×D4—1722no—
508C2×D4—1722no—
509C2×D4—1721no—
510C2×D4—1721no—
511C2×D4—1721no—
512C2×D4—1721no—
513C2×D4D4×D4311yescharacteristic
514C22×C4—21no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—3441no—
523C22×C4—3441no—
524C22×C4—1721no—
525SD16—1722no—
526SD16—1722no—
527D8—42no—
528D8—42no—
529D8—81no—
530D8—81no—
531D8—3441no—
532D8—3441no—
533D8—1722no—
534D8—1722no—
535D8—1722no—
536D8—1722no—
537M16—1722no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—81no—
542C2×C8—431no—
543C2×C8—431no—
544C2×C8—861no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—3441no—
548C2×C8—3441no—
549C2×C8—3441no—
550C2×C8—1722no—
551C2×C8D4×D4311yescharacteristic
552C2×C8D4×D4311yescharacteristic
553C4⋊C4—431no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4D4×D4311yescharacteristic
558C22⋊C4—21no—
559C22⋊C4—861no—
560C22⋊C4—861no—
561C22⋊C4—861no—
562C22⋊C4—1721no—
563C22⋊C4—1721no—
564C42—431no—
565C42—431no—
566C42—431no—
567C42C23×D4311yescharacteristic
568C23—21no—
569C23—41no—
570C23—41no—
571C23—431no—
572C23—864no—
573C23—861no—
574C23—3441no—
575C23—3441no—
576C23—3442no—
577C23—3442no—
578C23—3442no—
579C23—1721no—
580Q8—1721no—
581Q8—1721no—
582D4—21no—
583D4—41no—
584D4—41no—
585D4—41no—
586D4—41no—
587D4—41no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—81no—
592D4—81no—
593D4—432no—
594D4—864no—
595D4—861no—
596D4—3441no—
597D4—3442no—
598D4—3442no—
599D4—3442no—
600D4—3442no—
601D4—1721no—
602D4—1721no—
603D4—1721no—
604D4—1721no—
605D4D8×D4312yes—
606C2×C4—21no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—431no—
610C2×C4—432no—
611C2×C4—432no—
612C2×C4—431no—
613C2×C4—431no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—3441no—
618C2×C4—3441no—
619C2×C4—3442no—
620C2×C4—3441no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4C2×D4×D4311yescharacteristic
626C2×C4C2×D4×D4311yescharacteristic
627C2×C4#41×D4311yescharacteristic
628C8—21no—
629C8—21no—
630C8—41no—
631C8—41no—
632C8—41no—
633C8—861no—
634C8—861no—
635C8—1721no—
636C8—1721no—
637C8—1721no—
638C22—22no—
639C22—41no—
640C22—41no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—432no—
648C22—861no—
649C22—861no—
650C22—862no—
651C22—3444no—
652C22—3441no—
653C22—3441no—
654C22—3441no—
655C22—1721no—
656C22—1721no—
657C22—6884no—
658C22#121×D4311yescharacteristic
659C4—21no—
660C4—41no—
661C4—432no—
662C4—861no—
663C4—861no—
664C4—3441no—
665C4—1721no—
666C4C2×D8×D4311yescharacteristic
667C4#135×D4311yescharacteristic
668C4#1458370011yescharacteristic
669C4#1458370311yescharacteristic
670C2—42no—
671C2—161no—
672C2—161no—
673C2—862no—
674C2—1722no—
675C2—6881no—
676C2#1914409311yescharacteristic
677C2#466×D4311yescharacteristic
678C2#1914432111yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1667C2
socleC22×C43C2×#121
hypercenter#1667D43
hypocenterC43#19386
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1667

Complements

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

NH ≅ G/Ntype
1. #19145509C2semidirect
2. #19144054C2semidirect
3. #459×D43C2semidirect
4. #19143616C2semidirect
5. #19134033C2semidirect
6. #19134032C2semidirect
7. #19134031C2semidirect
8. #19134030C2semidirect
9. #19133949C2semidirect
10. #19133948C2semidirect
11. #19133947C2semidirect
12. #19133368C2semidirect
13. #19133261C2semidirect
14. #19133241C2semidirect
15. C43×#1667C2semidirect
21. #14583275C22semidirect
22. #14583246C22semidirect
23. #14583245C22semidirect
26. #14583105C22semidirect
27. #14583104C22semidirect
35. #14583091C22semidirect
38. C8×D172C22semidirect
39. D4×C43⋊C8C22semidirect
40. #14582964C22semidirect
51. #14582652C22semidirect
52. #14582651C22semidirect
53. #14582651C22semidirect
54. #14582646C22semidirect
55. #14582644C22semidirect
56. #14582643C22semidirect
57. #14582643C22semidirect
58. #14582642C22semidirect
59. #14582642C22semidirect
60. C43×#493C22semidirect
62. C43×#459C22semidirect
63. C8×D4×C43C22semidirect
64. C43×#335C22semidirect
65. C43×#331C22semidirect
66. C43×#331C22semidirect
171. D4×D43D8semidirect
342. #1667D43semidirect
361. #493C2×D43semidirect
377. #459C2×D43semidirect
385. C8×D4C2×D43semidirect
397. #335C2×D43semidirect
404. #331C2×D43semidirect
405. #331C2×D43semidirect
406. C43#19386semidirect

Maximal subgroups

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

subgroupindex
#191455092
#191440542
#459×D432
#191436162
#191340332
#191340322
#191340312
#191340302
#191339492
#191339482
#191339472
#191333682
#191332612
#191332412
C43×#16672
#1938643