Finite Group Databasebeta

← #25146406

Subgroups — #25146406

Order 11008.

722 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144981C211yesmaximal, characteristic, complemented
2#19144392C211yesmaximal, characteristic, complemented
3#19143538C211yesmaximal, characteristic, complemented
4#19135960C211yesmaximal, characteristic, complemented
5#19135953C211yesmaximal, characteristic, complemented
6#19135853C211yesmaximal, characteristic, complemented
7#19135848C211yesmaximal, characteristic
8#19135506C211yesmaximal, characteristic
9#19135500C211yesmaximal, characteristic, complemented
10#19135445C211yesmaximal, characteristic, complemented
11#19135371C211yesmaximal, characteristic, complemented
12#19135254C211yesmaximal, characteristic, complemented
13#19135247C211yesmaximal, characteristic, complemented
14C4×#13063242C211yesmaximal, characteristic, complemented
15C2×C43×#463C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583258—21no—
18#14583258—21no—
19#14583253—21no—
20#14583253—21no—
21#14583199—21no—
22#14583199—21no—
23#14583189—21no—
24#14583179—21no—
25#14583028—21no—
26#14583028—21no—
27#14583026—21no—
28#14583023—21no—
29C2×#13063261C2211yescharacteristic
30C2×#13063261C2211yescharacteristic
31#14582939C2211yescharacteristic
32#14582939C2211yescharacteristic
33#14582925C2211yescharacteristic
34#14582925C2211yescharacteristic
35#14582923C2211yescharacteristic
36#14582908C2211yescharacteristic
37#14582908C2211yescharacteristic
38#14582904C2211yescharacteristic
39#14582904C2211yescharacteristic
40#14582904C2211yescharacteristic
41#14582904C2211yescharacteristic
42C2×#13063244C2211yescharacteristic
43C2×#13063244C2211yescharacteristic
44C2×#13063242C2211yescharacteristic
45C2×#13063242C2211yescharacteristic
46C2×#13063242C2211yescharacteristic
47C2×#13063242C2211yescharacteristic
48#14582854C2211yescharacteristic
49#14582854C2211yescharacteristic
50C4×#10621877C2211yescharacteristic
51C4×#10621877C2211yescharacteristic
52#14582668C2211yescharacteristic
53#14582668C2211yescharacteristic
54#14582664C2211yescharacteristic
55#14582664C2211yescharacteristic
56C22×SD16×C43C2211yescharacteristic
57C22×D8×C43C2211yescharacteristic
58C2×#124×C43C2211yescharacteristic
59C2×C4×D4×C43C2211yescharacteristic
60C43×#463—21no—
61C43×#463—21no—
62C43×#463—21no—
63C43×#463—21no—
64C2×C4⋊C8×C43C2211yescharacteristic
65C2×#103×C43C2211yescharacteristic
66C2×#102×C43C2211yescharacteristic
67C2×#10621877C2311yescharacteristic
68C2×#10621877C2311yescharacteristic
69C2×#10621877C2311yescharacteristic
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C2×#10621877C2311yescharacteristic
73#13063325D411yescharacteristic
74#13063325D411yescharacteristic
75#13063317D411yescharacteristic
76#13063317D411yescharacteristic
77#13063304—21no—
78#13063304—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81#13063284C2311yescharacteristic
82#13063284C2311yescharacteristic
83#13063261—41no—
84#13063261—41no—
85#13063258—21no—
86#13063258—21no—
87#13063256—21no—
88#13063256—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91Dic43⋊C8—21no—
92Dic43⋊C8—21no—
93Dic43⋊C8—21no—
94Dic43⋊C8—21no—
95#13063249—21no—
96#13063249—21no—
97#13063249—21no—
98#13063249—21no—
99#13063246—21no—
100#13063246—21no—
101#13063246—21no—
102#13063246—21no—
103#13063246—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063244—22no—
108#13063244—41no—
109#13063242—22no—
110#13063242—22no—
111#13063242—22no—
112#13063242—41no—
113#13063236—21no—
114#13063236—21no—
115#13063235—21no—
116#13063235—21no—
117C4×C43⋊C8—21no—
118C4×C43⋊C8—21no—
119C8×Dic43—21no—
120C8×Dic43—21no—
121C22×Q8×C43C2311yescharacteristic
122C22×D4×C43C2311yescharacteristic
123C22×D4×C43C2311yescharacteristic
124C23×C4×C43—21no—
125C2×SD16×C43—22no—
126C2×SD16×C43—21no—
127C2×SD16×C43—21no—
128C2×SD16×C43—41no—
129C2×D8×C43—22no—
130C2×D8×C43—21no—
131C2×D8×C43—21no—
132C2×D8×C43—41no—
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135#124×C43—21no—
136#124×C43—21no—
137#124×C43—21no—
138#124×C43—21no—
139C4×D4×C43—21no—
140C4×D4×C43—21no—
141C4×D4×C43—21no—
142C4×D4×C43—21no—
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147C2×C42×C43C2311yescharacteristic
148C4⋊C8×C43D411yescharacteristic
149C4⋊C8×C43D411yescharacteristic
150C4⋊C8×C43D411yescharacteristic
151C4⋊C8×C43D411yescharacteristic
152#103×C43—21no—
153#103×C43—21no—
154#102×C43—21no—
155#102×C43—21no—
156C24×C43—21no—
157C24×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43#4112yes—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—41no—
179C22×C4×C43—41no—
180C22×C4×C43—82no—
181C22×C4×C43#4111yescharacteristic
182C22×C4×C43#4111yescharacteristic
183C22×C4×C43C2411yescharacteristic
184C2×Dic86—21no—
185C2×Dic86—21no—
186SD16×C43—42no—
187SD16×C43—42no—
188D8×C43—42no—
189D8×C43—42no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43C2×D411yescharacteristic
195C2×C8×C43C2×D411yescharacteristic
196C2×C8×C43C2×D411yescharacteristic
197C2×C8×C43C2×D411yescharacteristic
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C22⋊C4×C43—41no—
201C22⋊C4×C43—41no—
202C22⋊C4×C43—41no—
203C22⋊C4×C43—41no—
204C22⋊C4×C43—41no—
205C22⋊C4×C43—41no—
206C42×C43C2×D411yescharacteristic
207C42×C43C2×D411yescharacteristic
208C42×C43C2×D411yescharacteristic
209C42×C43C2×D411yescharacteristic
210C22⋊Dic43—21no—
211C22⋊Dic43—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43C2×D411yescharacteristic
215C4⋊Dic43C2×D411yescharacteristic
216C4⋊Dic43C2×D411yescharacteristic
217C4⋊Dic43C2×D411yescharacteristic
218Dic43⋊C4—21no—
219Dic43⋊C4—21no—
220Dic43⋊C4—21no—
221Dic43⋊C4—21no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224#10621877—21no—
225#10621877—21no—
226#10621877—21no—
227#10621877—21no—
228#10621877—21no—
229#10621877—21no—
230#10621877—21no—
231#10621877—21no—
232#10621877—21no—
233#10621877—21no—
234#10621877—21no—
235#10621877#4112yes—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C23×C43—22no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—81no—
249C23×C43—81no—
250C23×C43—81no—
251C23×C43—81no—
252C23×C43C2×#4111yescharacteristic
253Q8×C43—41no—
254Q8×C43—41no—
255Q8×C43—41no—
256Q8×C43—41no—
257D4×C43—22no—
258D4×C43—22no—
259D4×C43—41no—
260D4×C43—41no—
261D4×C43—41no—
262D4×C43—41no—
263D4×C43—41no—
264D4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—82no—
272C2×C4×C43—82no—
273C2×C4×C43—81no—
274C2×C4×C43#12111yescharacteristic
275C2×C4×C43#12111yescharacteristic
276C2×C4×C43#12111yescharacteristic
277C2×C4×C43#12111yescharacteristic
278C2×C4×C43C22×D411yescharacteristic
279C2×C4×C43C22×D411yescharacteristic
280C2×C4×C43C2×#4111yescharacteristic
281C2×C4×C43C2×#4111yescharacteristic
282C2×C4×C43H(5,𝔽2)11yescharacteristic
283C2×C4×C432−1+411yescharacteristic
284C2×Dic43—21no—
285C2×Dic43—21no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288Dic86—42no—
289Dic86—81no—
290C8×C43—21no—
291C8×C43—21no—
292C8×C43—21no—
293C8×C43—21no—
294C43⋊C8—22no—
295C43⋊C8—41no—
296C43⋊C8—41no—
297C43⋊C8—41no—
298C43⋊C8—41no—
299C43⋊C8—41no—
300#25316—431nomaximal, Sylow
301C22×C43—21no—
302C22×C43—21no—
303C22×C43—42no—
304C22×C43—82no—
305C22×C43—82no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43—161no—
312C22×C43—161no—
313C22×C43C2×#12111yescharacteristic
314C22×C43#52911yescharacteristic
315C22×C43#54211yescharacteristic
316C4×C43—21no—
317C4×C43—21no—
318C4×C43—21no—
319C4×C43—21no—
320C4×C43—81no—
321C4×C43—81no—
322C4×C43#54611yescharacteristic
323C4×C43#54811yescharacteristic
324C4×C43#54811yescharacteristic
325C4×C43#55011yescharacteristic
326Dic43—41no—
327Dic43—41no—
328Dic43—41no—
329Dic43—41no—
330#3140—431no—
331#3077—431no—
332C2×#463D4311yescharacteristic
333#2962—431no—
334#2064—431no—
335#2063—431no—
336#2046—431no—
337#2045—431no—
338#1978—431no—
339#1977—431no—
340#1967—431no—
341#1950—431no—
342#1931—431no—
343#1930—431no—
344C4×#100—431no—
345C2×C43—21no—
346C2×C43—21no—
347C2×C43—82no—
348C2×C43—161no—
349C2×C43#242611yescharacteristic
350C2×C43#306711yescharacteristic
351C2×C43#306811yescharacteristic
352C22×SD16C2×D4311yescharacteristic
353C22×D8C2×D4311yescharacteristic
354#533—431no—
355C2×#124C2×D4311yescharacteristic
356C2×C4×D4C2×D4311yescharacteristic
357#489—861no—
358#489—861no—
359#488—861no—
360#488—861no—
361#478—861no—
362#478—861no—
363#476—861no—
364#474—861no—
365#463—21no—
366#463—21no—
367#463—21no—
368#463—21no—
369#446—861no—
370#446—861no—
371#446—861no—
372C8×Q8—861no—
373C2×#108—431no—
374C2×#108—431no—
375#428—431no—
376#428—431no—
377#424—431no—
378#424—431no—
379#423—431no—
380C2×C4⋊C8C2×D4311yescharacteristic
381#419—431no—
382#419—431no—
383#418—431no—
384#418—431no—
385#418—431no—
386#418—431no—
387C2×#103C2×D4311yescharacteristic
388C2×#102C2×D4311yescharacteristic
389C2×#101—431no—
390C2×#101—431no—
391C2×#100—431no—
392C2×#100—431no—
393C2×#100—431no—
394C2×#100—431no—
395#405—431no—
396#405—431no—
397C4×M16—431no—
398C4×M16—431no—
399#343—431no—
400#343—431no—
401#341—431no—
402#341—431no—
403C43#2531611yescharacteristic, complemented, Sylow
404C22×Q8C22×D4311yescharacteristic
405C22×D4C22×D4311yescharacteristic
406C22×D4C22×D4311yescharacteristic
407C23×C4—21no—
408C2×SD16—22no—
409C2×SD16—21no—
410C2×SD16—21no—
411C2×SD16—41no—
412C2×D8—22no—
413C2×D8—21no—
414C2×D8—21no—
415C2×D8—41no—
416C2×M16—431no—
417C2×M16—431no—
418C2×M16—431no—
419C2×M16—431no—
420C2×M16—431no—
421C2×M16—431no—
422C22×C8C22×D4311yescharacteristic
423C22×C8C22×D4311yescharacteristic
424C4⋊Q8—431no—
425C4⋊Q8—431no—
426#125—431no—
427#125—431no—
428#124—21no—
429#124—21no—
430#124—21no—
431#124—21no—
432C22⋊Q8—861no—
433C22⋊Q8—861no—
434C4×Q8—861no—
435C4×Q8—861no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440#117—431no—
441#117—431no—
442C2×C4⋊C4C22×D4311yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C42C22×D4311yescharacteristic
447#108—1721no—
448#108—1721no—
449#107—861no—
450#107—861no—
451#106—861no—
452#106—861no—
453C4⋊C8—861no—
454C4⋊C8—861no—
455C4⋊C8—861no—
456C4⋊C8—861no—
457C4⋊C8—861no—
458C4⋊C8—861no—
459C4⋊C8C22⋊D4311yescharacteristic
460C4⋊C8C22⋊D4311yescharacteristic
461C4⋊C8C22⋊D4311yescharacteristic
462C4⋊C8C22⋊D4311yescharacteristic
463#103—21no—
464#103—21no—
465#103—861no—
466#103—861no—
467#103—861no—
468#103—861no—
469#102—21no—
470#102—21no—
471#102—861no—
472#102—861no—
473#102—861no—
474#102—861no—
475#102—861no—
476#102—861no—
477#102—861no—
478#102—861no—
479#101—862no—
480#101—1721no—
481#100—862no—
482#100—862no—
483#100—862no—
484#100—1721no—
485#97—861no—
486#97—861no—
487#97—861no—
488#97—861no—
489C4×C8—861no—
490C4×C8—861no—
491C4×C8—861no—
492C4×C8—861no—
493C24—21no—
494C24—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—861no—
502C2×Q8—861no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4#1062190012yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—82no—
520C22×C4#1062190011yescharacteristic
521C22×C4#1062190011yescharacteristic
522C22×C4C23×D4311yescharacteristic
523SD16—42no—
524SD16—42no—
525D8—42no—
526D8—42no—
527M16—432no—
528M16—861no—
529M16—861no—
530M16—861no—
531M16—861no—
532M16—861no—
533M16—861no—
534M16—861no—
535M16—861no—
536M16—861no—
537M16—861no—
538M16—861no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8C2×C22⋊D4311yescharacteristic
550C2×C8C2×C22⋊D4311yescharacteristic
551C2×C8C2×C22⋊D4311yescharacteristic
552C2×C8C2×C22⋊D4311yescharacteristic
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—431no—
556C4⋊C4—431no—
557C4⋊C4—431no—
558C4⋊C4—431no—
559C4⋊C4—861no—
560C4⋊C4—861no—
561C4⋊C4—861no—
562C4⋊C4—861no—
563C4⋊C4—861no—
564C4⋊C4—861no—
565C22⋊C4—41no—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4—861no—
572C22⋊C4—861no—
573C42—861no—
574C42—861no—
575C42D4×D4311yescharacteristic
576C42D4×D4311yescharacteristic
577C42C2×C22⋊D4311yescharacteristic
578C42C2×C22⋊D4311yescharacteristic
579C23—22no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—81no—
586C23—81no—
587C23—81no—
588C23—81no—
589C23C2×#1062190011yescharacteristic
590Q8—41no—
591Q8—41no—
592Q8—41no—
593Q8—41no—
594Q8—3441no—
595Q8—1722no—
596D4—22no—
597D4—22no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—82no—
611C2×C4—82no—
612C2×C4—81no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4#1306329611yescharacteristic
618C2×C4#1306329611yescharacteristic
619C2×C4#1306329611yescharacteristic
620C2×C4#1306329611yescharacteristic
621C2×C4C2×D4×D4311yescharacteristic
622C2×C4C22×C22⋊D4311yescharacteristic
623C2×C4#41×D4311yescharacteristic
624C2×C4C2×#1062190011yescharacteristic
625C2×C4#1306337011yescharacteristic
626C2×C4#1306337211yescharacteristic
627C8—21no—
628C8—21no—
629C8—21no—
630C8—21no—
631C8—862no—
632C8—1721no—
633C8—1721no—
634C8—1721no—
635C8—1721no—
636C8—1721no—
637C22—21no—
638C22—21no—
639C22—42no—
640C22—82no—
641C22—82no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—161no—
648C22—161no—
649C22C2×#1306329611yescharacteristic
650C22#1458343011yescharacteristic
651C22#1458351611yescharacteristic
652C4—21no—
653C4—21no—
654C4—21no—
655C4—21no—
656C4—81no—
657C4—81no—
658C4—1721no—
659C4—1721no—
660C4—1721no—
661C4—1721no—
662C4#1458354311yescharacteristic
663C4#1458355511yescharacteristic
664C4#1458355611yescharacteristic
665C4#1458356711yescharacteristic
666C2—21no—
667C2—21no—
668C2—82no—
669C2—161no—
670C2#1913815711yescharacteristic
671C2#1914431111yescharacteristic
672C2#1914431911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#463C2
socleC22×C43C2×#121
prime radicalC22×D8×C43C22
hypercenterC2×#463D43
hypocenterC43#25316
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. #19144981C2semidirect
2. #19144392C2semidirect
3. #19143538C2semidirect
4. #19135960C2semidirect
5. #19135953C2semidirect
6. #19135853C2semidirect
9. #19135500C2semidirect
10. #19135445C2semidirect
11. #19135371C2semidirect
12. #19135254C2semidirect
13. #19135247C2semidirect
14. C4×#13063242C2semidirect
403. C43#25316semidirect

Maximal subgroups

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

subgroupindex
#191449812
#191443922
#191435382
#191359602
#191359532
#191358532
#191358482
#191355062
#191355002
#191354452
#191353712
#191352542
#191352472
C4×#130632422
C2×C43×#4632
#2531643