Finite Group Databasebeta

← #25087858

Subgroups — #25087858

Order 11008.

798 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146938C211yesmaximal, characteristic, complemented
2D4×#10621882C211yesmaximal, characteristic, complemented
3#19146196C211yesmaximal, characteristic, complemented
4#19134185C211yesmaximal, characteristic, complemented
5#19134060C211yesmaximal, characteristic, complemented
6#19134057C211yesmaximal, characteristic, complemented
7#19133982C211yesmaximal, characteristic, complemented
8#19133948C211yesmaximal, characteristic, complemented
9#19133774C211yesmaximal, characteristic, complemented
10#19133772C211yesmaximal, characteristic, complemented
11#19133684C211yesmaximal, characteristic, complemented
12#19133682C211yesmaximal, characteristic, complemented
13#19133478C211yesmaximal, characteristic, complemented
14D8×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3272C211yesmaximal, characteristic, complemented
16C2×#13063349—21no—
17C22×#10621882—21no—
18#14583553C2211yescharacteristic, complemented
19D4×D172C2211yescharacteristic
20#14583302C2211yescharacteristic, complemented
21#14583275C2211yescharacteristic
22#14583272C2211yescharacteristic, complemented
23#14583247C2211yescharacteristic, complemented
24#14583245C2211yescharacteristic, complemented
25#14583212—21no—
26#14583210—21no—
27#14583179C2211yescharacteristic, complemented
28#14583176C2211yescharacteristic, complemented
29#14583146—21no—
30#14583133—21no—
31#14583133—21no—
32#14583104C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583094C2211yescharacteristic, complemented
35#14583091C2211yescharacteristic
36#14583051—21no—
37#14583045—21no—
38#14583033—21no—
39#14583032—21no—
40C4×#10621882C2211yescharacteristic
41#14582978C2211yescharacteristic, complemented
42D4×C43⋊C8C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic, complemented
44C2×#13063258—21no—
45#14582652C2211yescharacteristic, complemented
46#14582651C2211yescharacteristic, complemented
47#14582646C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic, complemented
51D4⋊(C43⋊C8)C2211yescharacteristic
52D4⋊(C43⋊C8)C2211yescharacteristic, complemented
53D4⋊(C43⋊C8)C2211yescharacteristic, complemented
54#14582626C2211yescharacteristic, complemented
55C8×C43⋊C8C2211yescharacteristic, complemented
56C2×AGL(1,ℤ/8)×C43—21no—
57C43×#547C2211yescharacteristic, complemented
58D42×C43C2211yescharacteristic
59C43×#492C2211yescharacteristic, complemented
60C43×#468—21no—
61C43×#461C2211yescharacteristic
62C43×#459C2211yescharacteristic, complemented
63C43×#450—21no—
64C43×#449—21no—
65C4×D8×C43C2211yescharacteristic
66C43×#436C2211yescharacteristic, complemented
67C2×#10621900—21no—
68C22×D172—21no—
69C2×D4×D43—21no—
70#13063349—44no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621883—21no—
74C2×#10621882—21no—
75C2×#10621882—21no—
76C2×#10621882—21no—
77C2×#10621882—21no—
78C2×#10621882—21no—
79C2×#10621882—44no—
80C2×#10621882D411yescharacteristic
81C2×#10621872—21no—
82C22×C43⋊C8—21no—
83C22×C43⋊C8—21no—
84#13063325C2311yescharacteristic
85#13063322C2311yescharacteristic
86#13063309—41no—
87#13063305—21no—
88#13063300—21no—
89#13063299—21no—
90#13063299—21no—
91#13063295—41no—
92C4×D172C2311yescharacteristic
93C2×C4⋊Dic43—21no—
94#13063258—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258—21no—
98#13063258D411yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102#13063248—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—41no—
106#13063246D411yescharacteristic
107#13063245—21no—
108#13063245—21no—
109#13063245—21no—
110#13063245—41no—
111#13063245D411yescharacteristic
112C22⋊(C43⋊C8)—21no—
113C22⋊(C43⋊C8)—21no—
114(C2×D43)⋊C8—21no—
115C4×C43⋊C8C2311yescharacteristic
116C4×C43⋊C8C2311yescharacteristic
117C2×#41×C43—21no—
118C22×D4×C43—21no—
119C22×D4×C43—21no—
120AGL(1,ℤ/8)×C43—44no—
121C2×SD16×C43—21no—
122C2×SD16×C43—21no—
123C2×SD16×C43—21no—
124C2×D8×C43—21no—
125C2×D8×C43D411yescharacteristic
126C2×M16×C43—21no—
127C4⋊Q8×C43C2311yescharacteristic
128#127×C43C2311yescharacteristic
129#123×C43—41no—
130C22⋊Q8×C43—21no—
131#121×C43—21no—
132#121×C43—21no—
133#121×C43—21no—
134#120×C43—41no—
135C4×D4×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137C4×D4×C43C2311yescharacteristic
138C2×C4⋊C4×C43—21no—
139#107×C43D411yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#103×C43—21no—
142#102×C43—21no—
143#102×C43D411yescharacteristic
144#102×C43D411yescharacteristic
145C22⋊C8×C43—21no—
146C4×C8×C43C2311yescharacteristic
147C24×C43—41no—
148C23×D43—41no—
149#41×C43—42no—
150#41×C43—81no—
151C2×Q8×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43—81no—
161C2×D4×C43—81no—
162C2×D4×C43C2×D411yescharacteristic
163C2×D4×C43C2×D411yescharacteristic
164C2×D4×C43C2×D411yescharacteristic
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—41no—
169C2×C22⋊D43—41no—
170C2×C22⋊D43—41no—
171C22×Dic43—41no—
172#10621900—42no—
173#10621900—81no—
174D4×D43—42no—
175D4×D43—81no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—41no—
180C2×D172—42no—
181C2×D172—81no—
182C2×D172C2×D411yescharacteristic
183C2×C4×D43—21no—
184C2×Dic86—21no—
185SD16×C43—42no—
186SD16×C43—42no—
187SD16×C43—81no—
188D8×C43—42no—
189D8×C43D814yescomplemented
190M16×C43—42no—
191C2×C8×C43—21no—
192C2×C8×C43C2×D411yescharacteristic
193C2×C8×C43C2×D411yescharacteristic
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—41no—
197C4⋊C4×C43C2×D411yescharacteristic
198C4⋊C4×C43C2×D411yescharacteristic
199C4⋊C4×C43C2×D411yescharacteristic
200C22⋊C4×C43—21no—
201C22⋊C4×C43—21no—
202C22⋊C4×C43—21no—
203C22⋊C4×C43—41no—
204C22⋊C4×C43—41no—
205C42×C43C2411yescharacteristic
206#10621883—42no—
207#10621882—22no—
208#10621882—42no—
209#10621882—42no—
210#10621882—42no—
211#10621882—42no—
212#10621882—81no—
213(C2×D43)⋊C4—21no—
214(C2×D43)⋊C4—41no—
215(C2×D43)⋊C4—41no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—41no—
219C4⋊Dic43C2×D411yescharacteristic
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—42no—
225C2×C43⋊C8—42no—
226C2×C43⋊C8C2×D411yescharacteristic
227C2×C43⋊C8C2×D411yescharacteristic
228#10621873—42no—
229#10621873—81no—
230#10621872—42no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—41no—
235C23×C43—82no—
236C23×C43—82no—
237C23×C43—161no—
238C22×D43—21no—
239C22×D43—41no—
240C22×D43—82no—
241C22×D43—82no—
242C22×D43—161no—
243Q8×C43—41no—
244Q8×C43—41no—
245D4×C43—21no—
246D4×C43—21no—
247D4×C43—21no—
248D4×C43—21no—
249D4×C43—41no—
250D4×C43—41no—
251D4×C43—41no—
252D4×C43—41no—
253D4×C43—81no—
254D4×C43—82no—
255D4×C43—82no—
256D4×C43—82no—
257D4×C43C2×D812yes—
258D4×C43C2×D812yescomplemented
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—82no—
270C2×C4×C43C22×D411yescharacteristic
271C2×C4×C43C22×D411yescharacteristic
272C2×C4×C43H(5,𝔽2)11yescharacteristic
273C22⋊D43—82no—
274C22⋊D43—82no—
275C2×Dic43—21no—
276C2×Dic43—41no—
277C2×Dic43—82no—
278D172—21no—
279D172—21no—
280D172—41no—
281D172—41no—
282D172—41no—
283D172—41no—
284D172—81no—
285D172—82no—
286C4×D43—41no—
287C4×D43—41no—
288Dic86—41no—
289Dic86—41no—
290C8×C43—21no—
291C8×C43—41no—
292C8×C43C2×D812yescomplemented
293C43⋊C8—21no—
294C43⋊C8—41no—
295C43⋊C8—41no—
296C43⋊C8—41no—
297C43⋊C8—41no—
298C43⋊C8AGL(1,ℤ/8)12yescomplemented
299#19883—431nomaximal, Sylow
300C22×C43—22no—
301C22×C43—22no—
302C22×C43—41no—
303C22×C43—41no—
304C22×C43—41no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43—81no—
312C22×C43—164no—
313C22×C43D4211yescharacteristic
314C2×D43—41no—
315C2×D43—41no—
316C2×D43—41no—
317C2×D43—81no—
318C2×D43—81no—
319C2×D43—81no—
320C2×D43—164no—
321C4×C43—21no—
322C4×C43—41no—
323C4×C43—41no—
324C4×C43—41no—
325C4×C43—81no—
326C4×C43C22×D811yescharacteristic
327C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
328C4×C43#57611yescharacteristic
329C4×C43#57711yescharacteristic
330Dic43—41no—
331Dic43—81no—
332#3334—431no—
333D4×D8—431no—
334#3272—431no—
335#3272D4311yescharacteristic, complemented
336#1706—431no—
337#1685—431no—
338#1685—431no—
339#1673—431no—
340#1667—431no—
341#1639—431no—
342#1639—431no—
343#1625—431no—
344#1625—431no—
345#1589—431no—
346C8×D8—431no—
347C2×C43—42no—
348C2×C43—42no—
349C2×C43—81no—
350C2×C43—161no—
351C2×C43#327211yescharacteristic
352C2×C43D4×D811yescharacteristic
353C2×C43#329011yescharacteristic
354D43—81no—
355D43—161no—
356C2×AGL(1,ℤ/8)—21no—
357C2×AGL(1,ℤ/8)—861no—
358C22×D8—861no—
359#547—431no—
360#547C2×D4311yescharacteristic, complemented
361D42—431no—
362D42C2×D4311yescharacteristic
363#500—431no—
364#493—431no—
365#492—431no—
366#492C2×D4311yescharacteristic, complemented
367#486—431no—
368#486—431no—
369#480—861no—
370#480—861no—
371#474—431no—
372#474—431no—
373#468—21no—
374#468—861no—
375#466—861no—
376#466—861no—
377#461—431no—
378#461C2×D4311yescharacteristic
379#459—431no—
380#459—431no—
381#459—431no—
382#459C2×D4311yescharacteristic, complemented
383#450—21no—
384#450—861no—
385#449—21no—
386#449—861no—
387#447—861no—
388#447—861no—
389C4×D8—431no—
390C4×D8C2×D4311yescharacteristic
391#436—431no—
392#436C2×D4311yescharacteristic, complemented
393C8×D4—431no—
394C8×D4—431no—
395C2×#107—861no—
396#335—431no—
397#335—431no—
398#332—431no—
399#332—431no—
400#331—431no—
401#331—431no—
402D4⋊C8—431no—
403D4⋊C8—431no—
404D4⋊C8—431no—
405D4⋊C8—431no—
406C82—431no—
407C43#1988311yescharacteristic, complemented, Sylow
408C2×#41—21no—
409C2×#41—861no—
410C22×D4—21no—
411C22×D4—21no—
412C22×D4—861no—
413C22×D4—861no—
414AGL(1,ℤ/8)—44no—
415AGL(1,ℤ/8)—1724no—
416C2×SD16—21no—
417C2×SD16—21no—
418C2×SD16—21no—
419C2×SD16—861no—
420C2×SD16—861no—
421C2×SD16—861no—
422C2×D8—21no—
423C2×D8—431no—
424C2×D8—861no—
425C2×D8—861no—
426C2×D8—861no—
427C2×D8—861no—
428C2×D8—861no—
429C2×D8—1724no—
430C2×D8C22⋊D4311yescharacteristic
431C2×M16—21no—
432C2×M16—861no—
433C22×C8—861no—
434C22×C8—861no—
435C4⋊Q8—431no—
436C4⋊Q8C22×D4311yescharacteristic
437#127—431no—
438#127C22×D4311yescharacteristic
439#123—41no—
440#123—1721no—
441C22⋊Q8—21no—
442C22⋊Q8—861no—
443#121—21no—
444#121—21no—
445#121—21no—
446#121—861no—
447#121—861no—
448#121—861no—
449#120—41no—
450#120—1721no—
451C4×D4—431no—
452C4×D4C22×D4311yescharacteristic
453C4×D4C22×D4311yescharacteristic
454C4×D4C22×D4311yescharacteristic
455C2×C4⋊C4—21no—
456C2×C4⋊C4—861no—
457#107—431no—
458#107—861no—
459#107—861no—
460#107—861no—
461#107—861no—
462#107C22⋊D4311yescharacteristic
463C4⋊C8—431no—
464C4⋊C8—431no—
465C4⋊C8—431no—
466C4⋊C8C22×D4311yescharacteristic
467#103—21no—
468#103—861no—
469#102—21no—
470#102—431no—
471#102—431no—
472#102—861no—
473#102—861no—
474#102—861no—
475#102—861no—
476#102—861no—
477#102—1721no—
478#102—1721no—
479#102C22⋊D4311yescharacteristic
480#102C22⋊D4311yescharacteristic
481C22⋊C8—21no—
482C22⋊C8—861no—
483C22⋊C8—861no—
484C22⋊C8—861no—
485C4×C8—431no—
486C4×C8—431no—
487C4×C8C22×D4311yescharacteristic
488C24—41no—
489C24—1721no—
490#41—42no—
491#41—81no—
492#41—3441no—
493#41—1722no—
494C2×Q8—21no—
495C2×Q8—861no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—41no—
500C2×D4—41no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—41no—
504C2×D4—81no—
505C2×D4—81no—
506C2×D4—431no—
507C2×D4—861no—
508C2×D4—861no—
509C2×D4—861no—
510C2×D4—3441no—
511C2×D4—3441no—
512C2×D4—1721no—
513C2×D4—1722no—
514C2×D4—1721no—
515C2×D4—1721no—
516C2×D4—1722no—
517C2×D4D4×D4311yescharacteristic
518C2×D4C2×C22⋊D4311yescharacteristic
519C2×D4C2×C22⋊D4311yescharacteristic
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—41no—
524C22×C4—861no—
525C22×C4—1721no—
526SD16—42no—
527SD16—42no—
528SD16—81no—
529SD16—3441no—
530SD16—1722no—
531SD16—1722no—
532D8—42no—
533D8—862no—
534D8—3441no—
535D8—1722no—
536D8—1722no—
537D8—1722no—
538D8—1722no—
539D8#1062188214yescomplemented
540M16—42no—
541M16—1722no—
542C2×C8—21no—
543C2×C8—431no—
544C2×C8—431no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—1722no—
550C2×C8—1722no—
551C2×C8C2×C22⋊D4311yescharacteristic
552C2×C8C2×C22⋊D4311yescharacteristic
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—41no—
556C4⋊C4—431no—
557C4⋊C4—861no—
558C4⋊C4—861no—
559C4⋊C4—1721no—
560C4⋊C4D4×D4311yescharacteristic
561C4⋊C4C2×C22⋊D4311yescharacteristic
562C4⋊C4C2×C22⋊D4311yescharacteristic
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—21no—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C22⋊C4—861no—
569C22⋊C4—1721no—
570C22⋊C4—1721no—
571C42C23×D4311yescharacteristic
572C23—21no—
573C23—21no—
574C23—21no—
575C23—41no—
576C23—82no—
577C23—82no—
578C23—161no—
579C23—861no—
580C23—3442no—
581C23—3442no—
582C23—1721no—
583C23—6881no—
584Q8—41no—
585Q8—41no—
586Q8—1721no—
587Q8—1721no—
588D4—21no—
589D4—21no—
590D4—21no—
591D4—21no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—81no—
597D4—82no—
598D4—82no—
599D4—82no—
600D4—861no—
601D4—861no—
602D4—3441no—
603D4—3442no—
604D4—3442no—
605D4—3442no—
606D4—1721no—
607D4—1721no—
608D4—1721no—
609D4—1721no—
610D4C2×#1062188212yes—
611D4C2×#1062188212yescomplemented
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—82no—
623C2×C4—861no—
624C2×C4—3442no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4C2×D4×D4311yescharacteristic
629C2×C4C22×C22⋊D4311yescharacteristic
630C2×C4#1306337011yescharacteristic
631C8—21no—
632C8—41no—
633C8—432no—
634C8—861no—
635C8—1721no—
636C8—1721no—
637C8—1721no—
638C8—1721no—
639C8C2×#1062188212yescomplemented
640C22—22no—
641C22—22no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—164no—
653C22—3441no—
654C22—3441no—
655C22—3441no—
656C22—1721no—
657C22—1721no—
658C22—1721no—
659C22—6884no—
660C22D4×C22⋊D4311yescharacteristic
661C4—21no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—81no—
666C4—3441no—
667C4—1721no—
668C4C22×#1062188211yescharacteristic
669C4AGL(1,ℤ/8)×D4311yescharacteristic
670C4#1458370211yescharacteristic
671C4#1458370911yescharacteristic
672C2—42no—
673C2—42no—
674C2—81no—
675C2—161no—
676C2—3441no—
677C2—6881no—
678C2#1914618911yescharacteristic
679C2D4×#1062188211yescharacteristic
680C2#1914637511yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3272C2
socleC22×C43D42
hypercenter#3272D43
hypocenterC43#19883
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3272

Complements

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

NH ≅ G/Ntype
1. #19146938C2semidirect
2. D4×#10621882C2semidirect
3. #19146196C2semidirect
4. #19134185C2semidirect
5. #19134060C2semidirect
6. #19134057C2semidirect
7. #19133982C2semidirect
8. #19133948C2semidirect
9. #19133774C2semidirect
10. #19133772C2semidirect
11. #19133684C2semidirect
12. #19133682C2semidirect
13. #19133478C2semidirect
14. D8×C43⋊C8C2semidirect
15. C43×#3272C2semidirect
18. #14583553C22semidirect
20. #14583302C22semidirect
22. #14583272C22semidirect
23. #14583247C22semidirect
24. #14583245C22semidirect
27. #14583179C22semidirect
28. #14583176C22semidirect
34. #14583094C22semidirect
41. #14582978C22semidirect
43. D4×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582651C22semidirect
47. #14582646C22semidirect
48. #14582645C22semidirect
49. #14582643C22semidirect
50. #14582642C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. C8×C43⋊C8C22semidirect
57. C43×#547C22semidirect
59. C43×#492C22semidirect
62. C43×#459C22semidirect
66. C43×#436C22semidirect
189. D8×C43D8semidirect
258. D4×C43C2×D8semidirect
292. C8×C43C2×D8semidirect
298. C43⋊C8AGL(1,ℤ/8)semidirect
335. #3272D43semidirect
360. #547C2×D43semidirect
366. #492C2×D43semidirect
382. #459C2×D43semidirect
392. #436C2×D43semidirect
407. C43#19883semidirect
539. D8#10621882semidirect
611. D4C2×#10621882semidirect
639. C8C2×#10621882semidirect

Maximal subgroups

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

subgroupindex
#191469382
D4×#106218822
#191461962
#191341852
#191340602
#191340572
#191339822
#191339482
#191337742
#191337722
#191336842
#191336822
#191334782
D8×C43⋊C82
C43×#32722
#1988343