Finite Group Databasebeta

← #25087869

Subgroups — #25087869

Order 11008.

778 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146408C211yesmaximal, characteristic, complemented
2#19146402C211yesmaximal, characteristic, complemented
3#19146196C211yesmaximal, characteristic, complemented
4#19134185C211yesmaximal, characteristic, complemented
5#19134060C211yesmaximal, characteristic, complemented
6#19134057C211yesmaximal, characteristic, complemented
7#19134034C211yesmaximal, characteristic, complemented
8#19134030C211yesmaximal, characteristic, complemented
9#19133830C211yesmaximal, characteristic, complemented
10#19133828C211yesmaximal, characteristic, complemented
11#19133649C211yesmaximal, characteristic, complemented
12#19133648C211yesmaximal, characteristic, complemented
13#19133478C211yesmaximal, characteristic, complemented
14D8×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3272C211yesmaximal, characteristic, complemented
16C2×#13063349—21no—
17#14583553C2211yescharacteristic
18D4×D172C2211yescharacteristic, complemented
19#14583302C2211yescharacteristic, complemented
20#14583275C2211yescharacteristic
21#14583272C2211yescharacteristic, complemented
22#14583247C2211yescharacteristic, complemented
23#14583245C2211yescharacteristic, complemented
24#14583212—21no—
25#14583210—21no—
26#14583179C2211yescharacteristic, complemented
27#14583176C2211yescharacteristic, complemented
28#14583146—21no—
29#14583133—21no—
30#14583133—21no—
31#14583104C2211yescharacteristic, complemented
32#14583094C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583091C2211yescharacteristic
35#14583051—21no—
36#14583045—21no—
37#14583033—21no—
38#14583032—21no—
39C4×#10621882C2211yescharacteristic
40#14582978C2211yescharacteristic, complemented
41D4×C43⋊C8C2211yescharacteristic, complemented
42D4×C43⋊C8C2211yescharacteristic, complemented
43C2×#13063246—21no—
44C2×#13063245—21no—
45#14582652C2211yescharacteristic, complemented
46#14582651C2211yescharacteristic, complemented
47#14582646C2211yescharacteristic, complemented
48#14582645C2211yescharacteristic, complemented
49#14582643C2211yescharacteristic, complemented
50#14582642C2211yescharacteristic, complemented
51D4⋊(C43⋊C8)C2211yescharacteristic, complemented
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
58D42×C43C2211yescharacteristic, complemented
59C43×#492C2211yescharacteristic, complemented
60C43×#468—21no—
61C43×#461C2211yescharacteristic, complemented
62C43×#459C2211yescharacteristic
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—41no—
78C2×#10621882D411yescharacteristic
79C2×#10621872—21no—
80C22×C43⋊C8—21no—
81C22×C43⋊C8—21no—
82#13063325C2311yescharacteristic
83#13063322C2311yescharacteristic
84#13063309—41no—
85#13063305—21no—
86#13063300—21no—
87#13063299—21no—
88#13063299—21no—
89#13063295—41no—
90C4×D172C2311yescharacteristic
91C2×C4⋊Dic43—21no—
92#13063258—21no—
93#13063258—21no—
94#13063258—41no—
95#13063258D411yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063248—21no—
100#13063246—21no—
101#13063246—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246D411yescharacteristic
105#13063245—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245—21no—
110#13063245D411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113(C2×D43)⋊C8—21no—
114C4×C43⋊C8C2311yescharacteristic
115C4×C43⋊C8C2311yescharacteristic
116C2×#41×C43—21no—
117C22×D4×C43—21no—
118C22×D4×C43—21no—
119AGL(1,ℤ/8)×C43—44no—
120C2×SD16×C43—21no—
121C2×SD16×C43—21no—
122C2×SD16×C43—21no—
123C2×D8×C43—21no—
124C2×D8×C43D411yescharacteristic
125C2×M16×C43—21no—
126C4⋊Q8×C43C2311yescharacteristic
127#127×C43C2311yescharacteristic
128#123×C43—41no—
129C22⋊Q8×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132#121×C43—21no—
133#120×C43—41no—
134C4×D4×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136C4×D4×C43C2311yescharacteristic
137C2×C4⋊C4×C43—21no—
138#107×C43D411yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#102×C43—21no—
142#102×C43D411yescharacteristic
143#102×C43D411yescharacteristic
144C22⋊C8×C43—21no—
145C4×C8×C43C2311yescharacteristic
146C24×C43—41no—
147C23×D43—41no—
148#41×C43—42no—
149#41×C43—81no—
150C2×Q8×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—41no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—42no—
158C2×D4×C43—42no—
159C2×D4×C43—81no—
160C2×D4×C43—81no—
161C2×D4×C43C2×D411yescharacteristic
162C2×D4×C43C2×D411yescharacteristic
163C2×D4×C43C2×D411yescharacteristic
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—41no—
168C2×C22⋊D43—41no—
169C2×C22⋊D43—41no—
170C22×Dic43—41no—
171#10621900—42no—
172#10621900—81no—
173D4×D43—42no—
174D4×D43—81no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—41no—
179C2×D172—42no—
180C2×D172—81no—
181C2×D172C2×D411yescharacteristic
182C2×C4×D43—21no—
183C2×Dic86—21no—
184SD16×C43—42no—
185SD16×C43—42no—
186SD16×C43—81no—
187D8×C43—42no—
188D8×C43D814yescomplemented
189M16×C43—42no—
190C2×C8×C43—21no—
191C2×C8×C43C2×D411yescharacteristic
192C2×C8×C43C2×D411yescharacteristic
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—41no—
196C4⋊C4×C43C2×D411yescharacteristic
197C4⋊C4×C43C2×D411yescharacteristic
198C4⋊C4×C43C2×D411yescharacteristic
199C22⋊C4×C43—21no—
200C22⋊C4×C43—21no—
201C22⋊C4×C43—21no—
202C22⋊C4×C43—41no—
203C22⋊C4×C43—41no—
204C42×C43C2411yescharacteristic
205#10621883—42no—
206#10621882—41no—
207#10621882—42no—
208#10621882—82no—
209#10621882—81no—
210#10621882—81no—
211(C2×D43)⋊C4—21no—
212(C2×D43)⋊C4—41no—
213(C2×D43)⋊C4—41no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—41no—
217C4⋊Dic43C2×D411yescharacteristic
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—81no—
223C2×C43⋊C8—81no—
224C2×C43⋊C8C2×D411yescharacteristic
225C2×C43⋊C8C2×D411yescharacteristic
226#10621873—42no—
227#10621873—81no—
228#10621872—42no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43—41no—
233C23×C43—82no—
234C23×C43—82no—
235C23×C43—161no—
236C22×D43—21no—
237C22×D43—41no—
238C22×D43—82no—
239C22×D43—82no—
240C22×D43—161no—
241Q8×C43—41no—
242Q8×C43—41no—
243D4×C43—21no—
244D4×C43—21no—
245D4×C43—21no—
246D4×C43—21no—
247D4×C43—41no—
248D4×C43—41no—
249D4×C43—41no—
250D4×C43—41no—
251D4×C43—81no—
252D4×C43—82no—
253D4×C43—82no—
254D4×C43—82no—
255D4×C43C2×D812yes—
256D4×C43C2×D812yes—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—82no—
268C2×C4×C43C22×D411yescharacteristic
269C2×C4×C43C22×D411yescharacteristic
270C2×C4×C43H(5,𝔽2)11yescharacteristic
271C22⋊D43—82no—
272C22⋊D43—82no—
273C2×Dic43—21no—
274C2×Dic43—41no—
275C2×Dic43—82no—
276D172—21no—
277D172—21no—
278D172—41no—
279D172—41no—
280D172—41no—
281D172—41no—
282D172—81no—
283D172—82no—
284C4×D43—41no—
285C4×D43—41no—
286Dic86—41no—
287Dic86—41no—
288C8×C43—21no—
289C8×C43—41no—
290C8×C43C2×D812yes—
291C43⋊C8—22no—
292C43⋊C8—21no—
293C43⋊C8—21no—
294C43⋊C8—41no—
295C43⋊C8—41no—
296C43⋊C8—41no—
297#19884—431nomaximal, Sylow
298C22×C43—22no—
299C22×C43—22no—
300C22×C43—41no—
301C22×C43—41no—
302C22×C43—41no—
303C22×C43—41no—
304C22×C43—41no—
305C22×C43—41no—
306C22×C43—41no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—164no—
311C22×C43D4211yescharacteristic
312C2×D43—41no—
313C2×D43—41no—
314C2×D43—41no—
315C2×D43—81no—
316C2×D43—81no—
317C2×D43—81no—
318C2×D43—164no—
319C4×C43—21no—
320C4×C43—41no—
321C4×C43—41no—
322C4×C43—41no—
323C4×C43—81no—
324C4×C43C22×D811yescharacteristic
325C4×C43#57511yescharacteristic
326C4×C43#57611yescharacteristic
327C4×C43#57611yescharacteristic
328Dic43—41no—
329Dic43—81no—
330#3294—431no—
331#3294—431no—
332#3272—431no—
333#3272D4311yescharacteristic, complemented
334#1706—431no—
335#1685—431no—
336#1685—431no—
337#1681—431no—
338#1681—431no—
339#1647—431no—
340#1647—431no—
341#1619—431no—
342#1619—431no—
343#1589—431no—
344C8×D8—431no—
345C2×C43—42no—
346C2×C43—42no—
347C2×C43—81no—
348C2×C43—161no—
349C2×C43#327311yescharacteristic
350C2×C43D4×D811yescharacteristic
351C2×C43#329111yescharacteristic
352D43—81no—
353D43—161no—
354C2×AGL(1,ℤ/8)—21no—
355C2×AGL(1,ℤ/8)—861no—
356#547—431no—
357#547C2×D4311yescharacteristic
358D42—431no—
359D42C2×D4311yescharacteristic, complemented
360#500—431no—
361#493—431no—
362#492—431no—
363#492C2×D4311yescharacteristic, complemented
364#486—431no—
365#486—431no—
366#480—861no—
367#480—861no—
368#474—431no—
369#474—431no—
370#468—21no—
371#468—861no—
372#466—861no—
373#466—861no—
374#461—431no—
375#461C2×D4311yescharacteristic, complemented
376#459—431no—
377#459—431no—
378#459—431no—
379#459C2×D4311yescharacteristic
380#450—21no—
381#450—861no—
382#449—21no—
383#449—861no—
384#447—861no—
385#447—861no—
386C4×D8—431no—
387C4×D8C2×D4311yescharacteristic
388#436—431no—
389#436C2×D4311yescharacteristic, complemented
390C8×D4—431no—
391C8×D4—431no—
392C2×#102—861no—
393C2×#102—861no—
394#335—431no—
395#335—431no—
396#332—431no—
397#332—431no—
398#331—431no—
399#331—431no—
400D4⋊C8—431no—
401D4⋊C8—431no—
402D4⋊C8—431no—
403D4⋊C8—431no—
404C82—431no—
405C43#1988411yescharacteristic, complemented, Sylow
406C2×#41—21no—
407C2×#41—861no—
408C22×D4—21no—
409C22×D4—21no—
410C22×D4—861no—
411C22×D4—861no—
412AGL(1,ℤ/8)—44no—
413AGL(1,ℤ/8)—1724no—
414C2×SD16—21no—
415C2×SD16—21no—
416C2×SD16—21no—
417C2×SD16—861no—
418C2×SD16—861no—
419C2×SD16—861no—
420C2×D8—21no—
421C2×D8—431no—
422C2×D8—861no—
423C2×D8—861no—
424C2×D8—861no—
425C2×D8—1721no—
426C2×D8C22⋊D4311yescharacteristic
427C2×M16—21no—
428C2×M16—861no—
429C22×C8—861no—
430C22×C8—861no—
431C4⋊Q8—431no—
432C4⋊Q8C22×D4311yescharacteristic
433#127—431no—
434#127C22×D4311yescharacteristic
435#123—41no—
436#123—1721no—
437C22⋊Q8—21no—
438C22⋊Q8—861no—
439#121—21no—
440#121—21no—
441#121—21no—
442#121—861no—
443#121—861no—
444#121—861no—
445#120—41no—
446#120—1721no—
447C4×D4—431no—
448C4×D4C22×D4311yescharacteristic
449C4×D4C22×D4311yescharacteristic
450C4×D4C22×D4311yescharacteristic
451C2×C4⋊C4—21no—
452C2×C4⋊C4—861no—
453#107—431no—
454#107—861no—
455#107—861no—
456#107—1721no—
457#107C22⋊D4311yescharacteristic
458C4⋊C8—431no—
459C4⋊C8—431no—
460C4⋊C8—431no—
461C4⋊C8C22×D4311yescharacteristic
462#103—21no—
463#103—861no—
464#102—21no—
465#102—431no—
466#102—431no—
467#102—861no—
468#102—861no—
469#102—861no—
470#102—861no—
471#102—861no—
472#102—861no—
473#102—861no—
474#102—861no—
475#102—861no—
476#102C22⋊D4311yescharacteristic
477#102C22⋊D4311yescharacteristic
478C22⋊C8—21no—
479C22⋊C8—861no—
480C22⋊C8—861no—
481C22⋊C8—861no—
482C4×C8—431no—
483C4×C8—431no—
484C4×C8C22×D4311yescharacteristic
485C24—41no—
486C24—1721no—
487#41—42no—
488#41—81no—
489#41—3441no—
490#41—1722no—
491C2×Q8—21no—
492C2×Q8—861no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—41no—
497C2×D4—41no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—41no—
501C2×D4—81no—
502C2×D4—81no—
503C2×D4—431no—
504C2×D4—861no—
505C2×D4—861no—
506C2×D4—861no—
507C2×D4—3441no—
508C2×D4—3441no—
509C2×D4—1721no—
510C2×D4—1722no—
511C2×D4—1721no—
512C2×D4—1721no—
513C2×D4—1722no—
514C2×D4D4×D4311yescharacteristic
515C2×D4C2×C22⋊D4311yescharacteristic
516C2×D4C2×C22⋊D4311yescharacteristic
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—41no—
521C22×C4—861no—
522C22×C4—1721no—
523SD16—42no—
524SD16—42no—
525SD16—81no—
526SD16—3441no—
527SD16—1722no—
528SD16—1722no—
529D8—42no—
530D8—3442no—
531D8—3441no—
532D8—3441no—
533D8—1721no—
534D8—1722no—
535D8#1062188214yescomplemented
536M16—42no—
537M16—1722no—
538C2×C8—21no—
539C2×C8—431no—
540C2×C8—431no—
541C2×C8—861no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8—3441no—
546C2×C8—3441no—
547C2×C8C2×C22⋊D4311yescharacteristic
548C2×C8C2×C22⋊D4311yescharacteristic
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—41no—
552C4⋊C4—431no—
553C4⋊C4—861no—
554C4⋊C4—861no—
555C4⋊C4—1721no—
556C4⋊C4D4×D4311yescharacteristic
557C4⋊C4C2×C22⋊D4311yescharacteristic
558C4⋊C4C2×C22⋊D4311yescharacteristic
559C22⋊C4—21no—
560C22⋊C4—21no—
561C22⋊C4—21no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—861no—
565C22⋊C4—1721no—
566C22⋊C4—1721no—
567C42C23×D4311yescharacteristic
568C23—21no—
569C23—21no—
570C23—21no—
571C23—41no—
572C23—82no—
573C23—82no—
574C23—161no—
575C23—861no—
576C23—3442no—
577C23—3442no—
578C23—1721no—
579C23—6881no—
580Q8—41no—
581Q8—41no—
582Q8—1721no—
583Q8—1721no—
584D4—21no—
585D4—21no—
586D4—21no—
587D4—21no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—81no—
593D4—82no—
594D4—82no—
595D4—82no—
596D4—861no—
597D4—861no—
598D4—3441no—
599D4—3442no—
600D4—3442no—
601D4—3442no—
602D4—1721no—
603D4—1721no—
604D4—1721no—
605D4—1721no—
606D4C2×#1062188212yes—
607D4C2×#1062188212yes—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—82no—
619C2×C4—861no—
620C2×C4—3442no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4C2×D4×D4311yescharacteristic
625C2×C4C22×C22⋊D4311yescharacteristic
626C2×C4#1306337011yescharacteristic
627C8—21no—
628C8—41no—
629C8—862no—
630C8—861no—
631C8—861no—
632C8—1721no—
633C8—1721no—
634C8—1721no—
635C8C2×#1062188212yes—
636C22—22no—
637C22—22no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—164no—
649C22—3441no—
650C22—3441no—
651C22—3441no—
652C22—1721no—
653C22—1721no—
654C22—1721no—
655C22—6884no—
656C22D4×C22⋊D4311yescharacteristic
657C4—21no—
658C4—41no—
659C4—41no—
660C4—41no—
661C4—81no—
662C4—3441no—
663C4—1721no—
664C4C22×#1062188211yescharacteristic
665C4#1458369511yescharacteristic
666C4#1458370211yescharacteristic
667C4#1458370311yescharacteristic
668C2—42no—
669C2—42no—
670C2—81no—
671C2—161no—
672C2—3441no—
673C2—6881no—
674C2#1914620011yescharacteristic
675C2D4×#1062188211yescharacteristic
676C2#1914638611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3272C2
socleC22×C43D42
hypercenter#3272D43
hypocenterC43#19884
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. #19146408C2semidirect
2. #19146402C2semidirect
3. #19146196C2semidirect
4. #19134185C2semidirect
5. #19134060C2semidirect
6. #19134057C2semidirect
7. #19134034C2semidirect
8. #19134030C2semidirect
9. #19133830C2semidirect
10. #19133828C2semidirect
11. #19133649C2semidirect
12. #19133648C2semidirect
13. #19133478C2semidirect
14. D8×C43⋊C8C2semidirect
15. C43×#3272C2semidirect
18. D4×D172C22semidirect
19. #14583302C22semidirect
21. #14583272C22semidirect
22. #14583247C22semidirect
23. #14583245C22semidirect
26. #14583179C22semidirect
27. #14583176C22semidirect
31. #14583104C22semidirect
40. #14582978C22semidirect
41. D4×C43⋊C8C22semidirect
42. D4×C43⋊C8C22semidirect
45. #14582652C22semidirect
46. #14582651C22semidirect
47. #14582646C22semidirect
48. #14582645C22semidirect
49. #14582643C22semidirect
50. #14582642C22semidirect
51. D4⋊(C43⋊C8)C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. D4⋊(C43⋊C8)C22semidirect
54. #14582626C22semidirect
55. C8×C43⋊C8C22semidirect
58. D42×C43C22semidirect
59. C43×#492C22semidirect
61. C43×#461C22semidirect
66. C43×#436C22semidirect
188. D8×C43D8semidirect
333. #3272D43semidirect
359. D42C2×D43semidirect
363. #492C2×D43semidirect
375. #461C2×D43semidirect
389. #436C2×D43semidirect
405. C43#19884semidirect
535. D8#10621882semidirect

Maximal subgroups

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

subgroupindex
#191464082
#191464022
#191461962
#191341852
#191340602
#191340572
#191340342
#191340302
#191338302
#191338282
#191336492
#191336482
#191334782
D8×C43⋊C82
C43×#32722
#1988443