Finite Group Databasebeta

← #25200614

Subgroups — #25200614

Order 11008.

760 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142977C211yesmaximal, characteristic, complemented
2#19136077C211yesmaximal, characteristic, complemented
3#19136014C211yesmaximal, characteristic, complemented
4#19135831C211yesmaximal, characteristic
5#19135689C211yesmaximal, characteristic
6#19135455C211yesmaximal, characteristic, complemented
7#19135448C211yesmaximal, characteristic
8#19135281C211yesmaximal, characteristic
9#19135274C211yesmaximal, characteristic, complemented
10#19134936C211yesmaximal, characteristic, complemented
11#19134929C211yesmaximal, characteristic
12#19134863C211yesmaximal, characteristic, complemented
13#19134842C211yesmaximal, characteristic
14#19134341C211yesmaximal, characteristic, complemented
15C4×#124×C43C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063258C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×#13063249C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×C4×C43⋊C8C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30#14582805C2211yescharacteristic
31#14582805C2211yescharacteristic
32#14582805C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582783—21no—
37#14582783—21no—
38#14582783—21no—
39#14582767—21no—
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582654C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×#124×C43C2211yescharacteristic
49C2×C4×Q8×C43C2211yescharacteristic
50C2×C4×D4×C43C2211yescharacteristic
51C43×#391C2211yescharacteristic
52C43×#390C2211yescharacteristic
53C43×#388—21no—
54C43×#388—21no—
55C43×#382C2211yescharacteristic
56C4×C22⋊C4×C43—21no—
57C4×C22⋊C4×C43—21no—
58C43×C43C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C2×#10621885—22no—
61C2×#10621885—22no—
62C2×#10621885—41no—
63C2×#10621883—22no—
64C2×#10621883—22no—
65C2×#10621883—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76#13063258—41no—
77#13063256—41no—
78#13063249—22no—
79#13063249—22no—
80#13063249—41no—
81#13063248—41no—
82#13063248—41no—
83#13063246—22no—
84#13063246—22no—
85#13063246—41no—
86C4×C43⋊C8—22no—
87C4×C43⋊C8—22no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C22×Q8×C43C2311yescharacteristic
98C22×D4×C43C2311yescharacteristic
99C23×C4×C43—21no—
100#124×C43—22no—
101#124×C43—22no—
102C4×Q8×C43—41no—
103C4×Q8×C43—41no—
104C4×D4×C43—41no—
105C4×D4×C43—41no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C42×C43—21no—
115C2×C42×C43D411yescharacteristic
116C2×C42×C43D411yescharacteristic
117C2×C42×C43D411yescharacteristic
118C2×C42×C43D411yescharacteristic
119C2×C42×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C24×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43#4112yes—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43#4112yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—42no—
143C22×C4×C43—42no—
144C22×C4×C43—42no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—42no—
167C22⋊C4×C43—24no—
168C22⋊C4×C43—24no—
169C22⋊C4×C43—42no—
170C22⋊C4×C43—42no—
171C22⋊C4×C43—42no—
172C42×C43—22no—
173C42×C43—22no—
174C42×C43—22no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—41no—
182C42×C43—42no—
183#10621885—44no—
184#10621883—44no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8#4112yes—
205C2×C43⋊C8#4112yes—
206C23×C43—22no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43C22×D411yescharacteristic
214Q8×C43—22no—
215Q8×C43—22no—
216Q8×C43—41no—
217Q8×C43—41no—
218D4×C43—22no—
219D4×C43—22no—
220D4×C43—41no—
221D4×C43—41no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—84no—
247C2×C4×C43#13512yes—
248C2×C4×C43#13512yes—
249C2×C4×C43#13712yes—
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43H(5,𝔽2)11yescharacteristic
255C2×C4×C43H(5,𝔽2)11yescharacteristic
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268Dic86—41no—
269Dic86—41no—
270Dic86—41no—
271Dic86—41no—
272C43⋊C8—22no—
273C43⋊C8—22no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276#29496—431nomaximal, Sylow
277C22×C43—42no—
278C22×C43—42no—
279C22×C43—42no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43#52511yescharacteristic
285C22×C43#53211yescharacteristic
286C22×C43#53511yescharacteristic
287C22×C43C2×#13511yescharacteristic
288C22×C43C2×#13511yescharacteristic
289C22×C43C2×#13711yescharacteristic
290C22×C43#57511yescharacteristic
291C4×C43—22no—
292C4×C43—22no—
293C4×C43—22no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43—42no—
297C4×C43—41no—
298C4×C43—81no—
299C4×C43—81no—
300C4×C43#55111yescharacteristic
301C4×C43#55111yescharacteristic
302C4×C43#55311yescharacteristic
303C4×C43#55311yescharacteristic
304Dic43—81no—
305Dic43—81no—
306Dic43—81no—
307Dic43—81no—
308#2863—431no—
309C4×#124D4311yescharacteristic
310#2085—431no—
311#2074—431no—
312#2042—431no—
313#2015—431no—
314#1969—431no—
315#1968—431no—
316#1934—431no—
317#1933—431no—
318#1878—431no—
319#1877—431no—
320#1865—431no—
321#1862—431no—
322#1744—431no—
323C2×C43—82no—
324C2×C43#260311yescharacteristic
325C2×C43#310211yescharacteristic
326C2×C43#310711yescharacteristic
327C2×C43#316811yescharacteristic
328C2×C43#318111yescharacteristic
329C2×C43#321011yescharacteristic
330C2×C43#321111yescharacteristic
331C22×Q16—431no—
332C22×SD16—431no—
333C2×#124C2×D4311yescharacteristic
334C2×C4×Q8C2×D4311yescharacteristic
335C2×C4×D4C2×D4311yescharacteristic
336C2×#107—431no—
337C2×#106—431no—
338C2×#103—431no—
339C2×#103—431no—
340C2×#103—431no—
341C2×#103—431no—
342C2×#103—431no—
343C2×#102—431no—
344C2×#102—431no—
345C2×#102—431no—
346C2×C4×C8—431no—
347C2×C4×C8—431no—
348#391—431no—
349#391—431no—
350#391—431no—
351#391C2×D4311yescharacteristic
352#390C2×D4311yescharacteristic
353#389—431no—
354#389—431no—
355#389—431no—
356#388—21no—
357#388—21no—
358#387—861no—
359#387—861no—
360#387—861no—
361#383—861no—
362#382C2×D4311yescharacteristic
363C4×C22⋊C4—21no—
364C4×C22⋊C4—21no—
365C43C2×D4311yescharacteristic
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#336—431no—
371#336—431no—
372#336—431no—
373#336—431no—
374C43#2949611yescharacteristic, complemented, Sylow
375C22×Q8—431no—
376C22×Q8C22×D4311yescharacteristic
377C22×D4C22×D4311yescharacteristic
378C23×C4—21no—
379C2×Q16—862no—
380C2×Q16—862no—
381C2×Q16—1721no—
382C2×SD16—862no—
383C2×SD16—862no—
384C2×SD16—1721no—
385C22×C8—431no—
386C22×C8—431no—
387C22×C8—431no—
388C22×C8—431no—
389#124—22no—
390#124—22no—
391C4×Q8—41no—
392C4×Q8—41no—
393C4×D4—41no—
394C4×D4—41no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C42—21no—
410C2×C42C22⋊D4311yescharacteristic
411C2×C42C22⋊D4311yescharacteristic
412C2×C42C22⋊D4311yescharacteristic
413C2×C42C22⋊D4311yescharacteristic
414C2×C42C22×D4311yescharacteristic
415C2×C42C22×D4311yescharacteristic
416C2×C42C22×D4311yescharacteristic
417#107—1721no—
418#106—1721no—
419#103—862no—
420#103—862no—
421#103—1721no—
422#103—1721no—
423#103—1721no—
424#102—862no—
425#102—862no—
426#102—1721no—
427C4×C8—862no—
428C4×C8—862no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442C24—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8—861no—
452C2×Q8—861no—
453C2×Q8—861no—
454C2×Q8#1062189812yes—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4#1062189812yes—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4C2×C22⋊D4311yescharacteristic
472C22×C4C2×C22⋊D4311yescharacteristic
473C22×C4C2×C22⋊D4311yescharacteristic
474C22×C4C2×C22⋊D4311yescharacteristic
475C22×C4C2×C22⋊D4311yescharacteristic
476C22×C4C2×C22⋊D4311yescharacteristic
477C22×C4C23×D4311yescharacteristic
478Q16—1724no—
479SD16—1724no—
480C2×C8—432no—
481C2×C8—432no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—42no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—1722no—
504C4⋊C4—1722no—
505C4⋊C4—1722no—
506C22⋊C4—24no—
507C22⋊C4—24no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C42—22no—
512C42—22no—
513C42—22no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—41no—
521C42—42no—
522C23—22no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23C22×C22⋊D4311yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—41no—
533Q8—41no—
534Q8—1721no—
535Q8—1721no—
536Q8—1721no—
537Q8—1721no—
538D4—22no—
539D4—22no—
540D4—41no—
541D4—41no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—84no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4#1306334512yes—
580C2×C4#1306334512yes—
581C2×C4#1306335512yes—
582C2×C4#41×D4311yescharacteristic
583C2×C4#41×D4311yescharacteristic
584C2×C4C2×#1062189811yescharacteristic
585C2×C4C2×#1062189811yescharacteristic
586C2×C4#1306337011yescharacteristic
587C2×C4#1306337011yescharacteristic
588C8—862no—
589C8—862no—
590C8—1721no—
591C8—1721no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22#1458341011yescharacteristic
600C22#1458344511yescharacteristic
601C22#1458346611yescharacteristic
602C22C2×#1306334511yescharacteristic
603C22C2×#1306334511yescharacteristic
604C22C2×#1306335511yescharacteristic
605C22#1458369711yescharacteristic
606C4—22no—
607C4—22no—
608C4—22no—
609C4—41no—
610C4—42no—
611C4—41no—
612C4—41no—
613C4—81no—
614C4—81no—
615C4—3441no—
616C4—3441no—
617C4—3441no—
618C4—3441no—
619C4#1458357811yescharacteristic
620C4#1458357811yescharacteristic
621C4#1458359811yescharacteristic
622C4#1458359811yescharacteristic
623C2—82no—
624C2#1914021611yescharacteristic
625C2#1914461311yescharacteristic
626C2#1914466611yescharacteristic
627C2#1914515911yescharacteristic
628C2#1914530511yescharacteristic
629C2#1914555111yescharacteristic
630C2#1914556011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC4×#124×C43C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenterC4×#124D43
hypocenterC43#29496
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C43 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
1. #19142977C2semidirect
2. #19136077C2semidirect
3. #19136014C2semidirect
6. #19135455C2semidirect
9. #19135274C2semidirect
10. #19134936C2semidirect
12. #19134863C2semidirect
14. #19134341C2semidirect
374. C43#29496semidirect

Maximal subgroups

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

subgroupindex
#191429772
#191360772
#191360142
#191358312
#191356892
#191354552
#191354482
#191352812
#191352742
#191349362
#191349292
#191348632
#191348422
#191343412
C4×#124×C432
#2949643