Finite Group Databasebeta

← #25099825

Subgroups — #25099825

Order 11008.

772 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#19143391C211yesmaximal, characteristic
2#19143238C211yesmaximal, characteristic, complemented
3#131×Dic43C211yesmaximal, characteristic, complemented
4#19135244C211yesmaximal, characteristic, complemented
5#19135242C211yesmaximal, characteristic, complemented
6#19135197C211yesmaximal, characteristic, complemented
7#19135191C211yesmaximal, characteristic, complemented
8#19134922C211yesmaximal, characteristic
9#19134920C211yesmaximal, characteristic
10#19134872C211yesmaximal, characteristic, complemented
11#19134503C211yesmaximal, characteristic, complemented
12#19134407C211yesmaximal, characteristic, complemented
13#19134404C211yesmaximal, characteristic, complemented
14#19134345C211yesmaximal, characteristic, complemented
15C43×#1866C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C2×#13063332C2211yescharacteristic
18#41×Dic43C2211yescharacteristic
19#14583367C2211yescharacteristic
20#14583008C411yescharacteristic, complemented
21#14583008C411yescharacteristic, complemented
22#14583003C411yescharacteristic, complemented
23#14583003C411yescharacteristic, complemented
24#14583002C411yescharacteristic, complemented
25#14583002C411yescharacteristic, complemented
26#14582996C411yescharacteristic, complemented
27#14582996C411yescharacteristic, complemented
28#14582959—21no—
29#14582959—21no—
30#14582951—21no—
31#14582951—21no—
32C2×#13063261C2211yescharacteristic
33#14582935C2211yescharacteristic
34#14582926C2211yescharacteristic
35C2×#13063253C2211yescharacteristic
36C2×#13063252C2211yescharacteristic
37C2×#13063251C2211yescharacteristic
38#14582896C2211yescharacteristic
39#14582867C2211yescharacteristic
40#14582865C2211yescharacteristic
41#14582857—21no—
42#14582857C2211yescharacteristic
43#14582854—21no—
44#14582854C2211yescharacteristic
45M16×Dic43—21no—
46M16×Dic43C2211yescharacteristic
47M16×Dic43C2211yescharacteristic
48C2×#13063235C2211yescharacteristic
49C2×C8×Dic43—21no—
50C2×C8×Dic43C2211yescharacteristic
51#14582745C2211yescharacteristic
52#14582663C2211yescharacteristic
53#14582663C2211yescharacteristic
54#14582660C2211yescharacteristic
55#14582659C2211yescharacteristic
56#14582658C2211yescharacteristic
57#14582654C2211yescharacteristic
58#14582653C2211yescharacteristic
59#14582653C2211yescharacteristic
60C2×#131×C43C2211yescharacteristic
61C2×#108×C43C2211yescharacteristic
62C43×#424C2211yescharacteristic
63C2×#104×C43C2211yescharacteristic
64C43×#416C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#336C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063345—22no—
69#13063345—22no—
70C2×#10621885C2×C411yescharacteristic
71C2×#10621883C2×C411yescharacteristic
72C2×#10621884C2×C411yescharacteristic
73C2×#10621882C2×C411yescharacteristic
74#13063332—22no—
75#13063332—22no—
76C2×#10621877—21no—
77C2×#10621877C2311yescharacteristic
78C2×#10621877C2311yescharacteristic
79C22×C43⋊C8—21no—
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82Q8×Dic43C2×C411yescharacteristic
83Q8×Dic43C2×C411yescharacteristic
84#13063290C2×C411yescharacteristic
85#13063290C2×C411yescharacteristic
86D4×Dic43—21no—
87D4×Dic43—21no—
88D4×Dic43C2×C411yescharacteristic
89D4×Dic43C2×C411yescharacteristic
90#13063287C2×C411yescharacteristic
91#13063287C2×C411yescharacteristic
92(C22⋊D43)⋊C4—21no—
93(C22⋊D43)⋊C4—21no—
94#13063284—21no—
95#13063284C2311yescharacteristic
96#13063282—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100C42×D43—21no—
101#13063261—22no—
102#13063258C2×C411yescharacteristic
103#13063258C2×C411yescharacteristic
104#13063256C2×C411yescharacteristic
105#13063256C2×C411yescharacteristic
106C4⋊(C43⋊C8)—21no—
107C4⋊(C43⋊C8)—21no—
108#13063253—22no—
109#13063252—22no—
110#13063251—22no—
111#13063250C2×C411yescharacteristic
112#13063250C2×C411yescharacteristic
113#13063247C2×C411yescharacteristic
114#13063247C2×C411yescharacteristic
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119#13063235—21no—
120#13063235—21no—
121#13063235—21no—
122#13063235—21no—
123#13063235C2×C411yescharacteristic
124#13063235C2×C411yescharacteristic
125#13063235C2×C411yescharacteristic
126#13063235C2×C411yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C8×Dic43—21no—
130C8×Dic43—21no—
131C8×Dic43D411yescharacteristic
132C8×Dic43D411yescharacteristic
133C8×Dic43D411yescharacteristic
134C8×Dic43D411yescharacteristic
135C43⋊#95—21no—
136C43⋊#95—21no—
137C2×#41×C43C2311yescharacteristic
138#131×C43—22no—
139#131×C43—22no—
140C2×M16×C43—21no—
141C2×M16×C43C2311yescharacteristic
142C2×M16×C43C2311yescharacteristic
143C22×C8×C43—21no—
144C22×C8×C43C2311yescharacteristic
145C22×C8×C43C2311yescharacteristic
146#117×C43C2311yescharacteristic
147C2×C42×C43C2311yescharacteristic
148#108×C43—22no—
149C4⋊C8×C43—21no—
150C4⋊C8×C43—21no—
151#104×C43—22no—
152#103×C43C2×C411yescharacteristic
153#103×C43C2×C411yescharacteristic
154#102×C43C2×C411yescharacteristic
155#102×C43C2×C411yescharacteristic
156#41×C43—21no—
157#41×C43—21no—
158#41×C43#4112yes—
159#41×C43#4112yes—
160C2×Q8×C43C22×C411yescharacteristic
161C2×D4×C43—21no—
162C2×D4×C43C22×C411yescharacteristic
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43C2411yescharacteristic
166C2×C22⋊D43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43#4111yescharacteristic
171C22×Dic43#4111yescharacteristic
172#10621898—21no—
173#10621898—21no—
174#10621898—21no—
175#10621898—21no—
176C2×D172C22×C411yescharacteristic
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×Dic86C22×C411yescharacteristic
181M16×C43—24no—
182M16×C43—21no—
183M16×C43—21no—
184M16×C43—21no—
185M16×C43#4112yes—
186C2×C8×C43—24no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43C22×C411yescharacteristic
194C2×C8×C43C22×C411yescharacteristic
195C2×C8×C43C2×D411yescharacteristic
196C2×C8×C43C2×D411yescharacteristic
197C4⋊C4×C43C22×C411yescharacteristic
198C4⋊C4×C43C22×C411yescharacteristic
199C22⋊C4×C43—21no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43—21no—
203C22⋊Dic43—21no—
204C22⋊Dic43—21no—
205C22⋊Dic43—21no—
206#10621885—22no—
207#10621884—22no—
208#10621883—22no—
209#10621882—22no—
210(C2×D43)⋊C4—21no—
211(C2×D43)⋊C4—21no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43C22×C411yescharacteristic
215C4⋊Dic43C22×C411yescharacteristic
216Dic43⋊C4—21no—
217Dic43⋊C4—21no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43C22×C411yescharacteristic
226C4×Dic43C22×C411yescharacteristic
227C4×Dic43C2×D411yescharacteristic
228C4×Dic43C2×D411yescharacteristic
229#10621877—24no—
230#10621877—21no—
231#10621877—21no—
232#10621877—21no—
233#10621877#4112yes—
234C2×C43⋊C8—24no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8C22×C411yescharacteristic
242C2×C43⋊C8C22×C411yescharacteristic
243C2×C43⋊C8C2×D411yescharacteristic
244C2×C43⋊C8C2×D411yescharacteristic
245C23×C43—21no—
246C23×C43C2×#4111yescharacteristic
247C22×D43—21no—
248Q8×C43—21no—
249Q8×C43#11712yes—
250D4×C43—22no—
251D4×C43—22no—
252D4×C43—21no—
253D4×C43#11712yes—
254C2×C4×C43—21no—
255C2×C4×C43—22no—
256C2×C4×C43—22no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43C23×C411yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C22⋊D43—41no—
269C22⋊D43—41no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—42no—
276C2×Dic43—42no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43C4×D411yescharacteristic
281C2×Dic43C4×D411yescharacteristic
282C2×Dic43C4×D411yescharacteristic
283C2×Dic43C4×D411yescharacteristic
284D172—21no—
285D172—21no—
286C4×D43—42no—
287C4×D43—42no—
288C4×D43—41no—
289C4×D43—41no—
290Dic86—21no—
291Dic86—21no—
292C8×C43—21no—
293C8×C43—21no—
294C8×C43—21no—
295C8×C43—22no—
296C8×C43—21no—
297C8×C43—41no—
298C43⋊C8—21no—
299C43⋊C8—21no—
300C43⋊C8—21no—
301C43⋊C8—22no—
302C43⋊C8—21no—
303C43⋊C8—41no—
304#21138—431nomaximal, Sylow
305C22×C43—21no—
306C22×C43—21no—
307C22×C43—22no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43C2×C4×D411yescharacteristic
311C22×C43#52911yescharacteristic
312C22×C43#52911yescharacteristic
313C2×D43—41no—
314C2×D43—41no—
315C2×D43—41no—
316C4×C43—22no—
317C4×C43—41no—
318C4×C43—41no—
319C4×C43—81no—
320C4×C43C2×#11711yescharacteristic
321C4×C43C4×#4111yescharacteristic
322C4×C43#52511yescharacteristic
323C4×C43#52511yescharacteristic
324Dic43—21no—
325Dic43—21no—
326Dic43—21no—
327Dic43—21no—
328Dic43—41no—
329Dic43—41no—
330Dic43—41no—
331Dic43—81no—
332#2943—431no—
333#2922—431no—
334C4×#131—431no—
335#1929—431no—
336#1929—431no—
337#1922—431no—
338#1922—431no—
339#1876—431no—
340#1876—431no—
341#1866—431no—
342#1866D4311yescharacteristic, complemented
343#1778—431no—
344#1759—431no—
345#1759—431no—
346#1746—431no—
347C2×C43—21no—
348C2×C43—21no—
349C2×C43—42no—
350C2×C43#229011yescharacteristic
351C2×C43#295511yescharacteristic
352C2×C43#295511yescharacteristic
353D43—81no—
354C2×#135—431no—
355C2×#131—431no—
356C2×#131C2×D4311yescharacteristic
357C4×#41—431no—
358C4×#41—431no—
359#442—431no—
360#442—431no—
361#441—431no—
362#441—431no—
363#440—431no—
364#440—431no—
365#440—431no—
366#440—431no—
367#433—861no—
368#433—861no—
369#431—861no—
370#431—861no—
371C2×#108—431no—
372C2×#108C2×D4311yescharacteristic
373#427—431no—
374#424—431no—
375#424C2×D4311yescharacteristic
376C2×#104—431no—
377C2×#104—431no—
378C2×#104—431no—
379C2×#104C2×D4311yescharacteristic
380#416—431no—
381#416C2×D4311yescharacteristic
382#408—431no—
383#408—431no—
384#405—431no—
385#405—431no—
386#405—861no—
387#405—861no—
388C4×M16—431no—
389C4×M16—431no—
390C4×M16—861no—
391C2×#97—431no—
392C2×C4×C8—431no—
393C2×C4×C8—861no—
394#376—431no—
395#341—431no—
396#341—431no—
397#339—431no—
398#339—431no—
399#339—431no—
400#339C2×D4311yescharacteristic
401#336—431no—
402#336—431no—
403#336—431no—
404#336C2×D4311yescharacteristic
405C43#2113811yescharacteristic, complemented, Sylow
406C2×#41—431no—
407C2×#41C22×D4311yescharacteristic
408#135—862no—
409#135—862no—
410C2×Q16—431no—
411C2×SD16—431no—
412C2×SD16—431no—
413C2×D8—431no—
414#131—22no—
415#131—22no—
416#131—862no—
417#131—862no—
418C2×M16—21no—
419C2×M16—431no—
420C2×M16—431no—
421C2×M16—861no—
422C2×M16C22×D4311yescharacteristic
423C2×M16C22×D4311yescharacteristic
424C22×C8—21no—
425C22×C8—431no—
426C22×C8—431no—
427C22×C8—861no—
428C22×C8C22×D4311yescharacteristic
429C22×C8C22×D4311yescharacteristic
430C4×Q8—431no—
431C4×Q8—431no—
432C4×Q8—431no—
433C4×Q8—431no—
434C4×D4—431no—
435C4×D4—431no—
436C4×D4—431no—
437C4×D4—431no—
438C4×D4—861no—
439C4×D4—861no—
440C4×D4—861no—
441C4×D4—861no—
442#117—431no—
443#117—861no—
444#117—861no—
445#117C22×D4311yescharacteristic
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—861no—
449C2×C42—861no—
450C2×C42C22×D4311yescharacteristic
451#108—22no—
452#108—862no—
453#107—431no—
454#107—431no—
455#106—431no—
456#106—431no—
457C4⋊C8—21no—
458C4⋊C8—21no—
459C4⋊C8—861no—
460C4⋊C8—861no—
461#104—22no—
462#104—862no—
463#104—862no—
464#104—862no—
465#103—431no—
466#103—431no—
467#103C4×D4311yescharacteristic
468#103C4×D4311yescharacteristic
469#102—431no—
470#102—431no—
471#102C4×D4311yescharacteristic
472#102C4×D4311yescharacteristic
473C22⋊C8—861no—
474C22⋊C8—861no—
475C22⋊C8—861no—
476C22⋊C8—861no—
477#97—431no—
478#97—431no—
479#97—431no—
480#97—431no—
481#97—861no—
482#97—861no—
483#97—861no—
484#97—861no—
485C4×C8—431no—
486C4×C8—431no—
487C4×C8—431no—
488C4×C8—431no—
489C4×C8—861no—
490C4×C8—861no—
491C4×C8—861no—
492C4×C8—861no—
493#95—861no—
494#95—861no—
495#41—21no—
496#41—21no—
497#41—861no—
498#41—861no—
499#41—861no—
500#41—861no—
501#41#1062190012yes—
502#41#1062190212yes—
503C2×Q8—431no—
504C2×Q8C2×C4×D4311yescharacteristic
505C2×D4—21no—
506C2×D4—431no—
507C2×D4—861no—
508C2×D4C2×C4×D4311yescharacteristic
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—431no—
512C22×C4—431no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—861no—
519C22×C4C23×D4311yescharacteristic
520Q16—862no—
521SD16—862no—
522SD16—862no—
523D8—862no—
524M16—24no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—432no—
529M16—864no—
530M16—861no—
531M16—861no—
532M16—861no—
533M16#1062190012yes—
534C2×C8—24no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—431no—
542C2×C8—431no—
543C2×C8—431no—
544C2×C8—431no—
545C2×C8—864no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8—861no—
552C2×C8C2×C4×D4311yescharacteristic
553C2×C8C2×C4×D4311yescharacteristic
554C2×C8D4×D4311yescharacteristic
555C2×C8D4×D4311yescharacteristic
556C4⋊C4—431no—
557C4⋊C4—431no—
558C4⋊C4—861no—
559C4⋊C4—861no—
560C4⋊C4—861no—
561C4⋊C4—861no—
562C4⋊C4C2×C4×D4311yescharacteristic
563C4⋊C4C2×C4×D4311yescharacteristic
564C22⋊C4—21no—
565C22⋊C4—861no—
566C22⋊C4—861no—
567C22⋊C4—861no—
568C22⋊C4—861no—
569C22⋊C4—861no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—431no—
574C42—431no—
575C42—431no—
576C42—431no—
577C42—861no—
578C42—861no—
579C42—861no—
580C42—861no—
581C42—861no—
582C42—861no—
583C42—861no—
584C23—21no—
585C23—861no—
586C23#41×D4311yescharacteristic
587Q8—21no—
588Q8—861no—
589Q8—861no—
590Q8#1306328312yes—
591D4—22no—
592D4—22no—
593D4—21no—
594D4—861no—
595D4—861no—
596D4—1721no—
597D4—1721no—
598D4#1306328312yes—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—431no—
608C2×C4—431no—
609C2×C4—431no—
610C2×C4—431no—
611C2×C4—861no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—1722no—
615C2×C4—1722no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4—1722no—
619C2×C4—1722no—
620C2×C4—1721no—
621C2×C4—1721no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4C22×C4×D4311yescharacteristic
626C2×C4C2×D4×D4311yescharacteristic
627C2×C4#41×D4311yescharacteristic
628C2×C4C2×#1062190011yescharacteristic
629C2×C4C2×#1062190011yescharacteristic
630C2×C4C2×#1062190211yescharacteristic
631C8—21no—
632C8—21no—
633C8—21no—
634C8—22no—
635C8—21no—
636C8—41no—
637C8—861no—
638C8—861no—
639C8—861no—
640C8—861no—
641C8—862no—
642C8—1721no—
643C22—21no—
644C22—21no—
645C22—22no—
646C22—41no—
647C22—41no—
648C22—1721no—
649C22—1721no—
650C22—1721no—
651C22C4×D4×D4311yescharacteristic
652C22#1458342611yescharacteristic
653C22#1458343511yescharacteristic
654C4—22no—
655C4—41no—
656C4—41no—
657C4—81no—
658C4—861no—
659C4—861no—
660C4—861no—
661C4—861no—
662C4—3441no—
663C4—1721no—
664C4—1721no—
665C4—1721no—
666C4C2×#1306328311yescharacteristic
667C4C4×#1062190011yescharacteristic
668C4#1458340511yescharacteristic
669C4#1458341211yescharacteristic
670C2—21no—
671C2—21no—
672C2—42no—
673C2—3441no—
674C2#1913703111yescharacteristic
675C2#1914349311yescharacteristic
676C2#1914349511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1866C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063345C22
cosocleC22×C4×C43C24
hypercenter#1866D43
hypocenterC43#21138
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
2. #19143238C2semidirect
3. #131×Dic43C2semidirect
4. #19135244C2semidirect
5. #19135242C2semidirect
6. #19135197C2semidirect
7. #19135191C2semidirect
10. #19134872C2semidirect
11. #19134503C2semidirect
12. #19134407C2semidirect
13. #19134404C2semidirect
14. #19134345C2semidirect
15. C43×#1866C2semidirect
20. #14583008C4semidirect
21. #14583008C4semidirect
22. #14583003C4semidirect
23. #14583003C4semidirect
24. #14583002C4semidirect
25. #14583002C4semidirect
26. #14582996C4semidirect
27. #14582996C4semidirect
342. #1866D43semidirect
405. C43#21138semidirect

Maximal subgroups

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

subgroupindex
#191433912
#191432382
#131×Dic432
#191352442
#191352422
#191351972
#191351912
#191349222
#191349202
#191348722
#191345032
#191344072
#191344042
#191343452
C43×#18662
#2113843