Finite Group Databasebeta

← #25200747

Subgroups — #25200747

Order 11008.

724 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140561C211yesmaximal, characteristic, complemented
2#19137308C211yesmaximal, characteristic
3#19136073C211yesmaximal, characteristic, complemented
4#19136003C211yesmaximal, characteristic, complemented
5#19135831C211yesmaximal, characteristic
6#19135467C211yesmaximal, characteristic, complemented
7#19135451C211yesmaximal, characteristic
8#19135289C211yesmaximal, characteristic
9#19135268C211yesmaximal, characteristic, complemented
10#19134938C211yesmaximal, characteristic, complemented
11#19134931C211yesmaximal, characteristic
12#19134865C211yesmaximal, characteristic, complemented
13#19134858C211yesmaximal, characteristic
14#19134345C211yesmaximal, characteristic, complemented
15C43×#2015C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×#13063257C2211yescharacteristic
19C2×#13063257C2211yescharacteristic
20C2×#13063249C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063235C2211yescharacteristic
27C2×C8×Dic43C2211yescharacteristic
28C43⋊#401—21no—
29#14582841—21no—
30#14582840—21no—
31#14582839—21no—
32#14582806C2211yescharacteristic
33#14582806C2211yescharacteristic
34#14582806C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582798C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582792—21no—
40#14582792—21no—
41#14582774—21no—
42#14582774—21no—
43#14582769C2211yescharacteristic
44#14582745C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×Q16×C43C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C2×#124×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C23×Dic43—21no—
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62Q8×Dic43—41no—
63Q8×Dic43—41no—
64D4×Dic43—41no—
65D4×Dic43—41no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C4×Dic43—21no—
80C2×C4×Dic43C2311yescharacteristic
81C2×C4×Dic43C2311yescharacteristic
82#13063257—41no—
83#13063257—41no—
84#13063249—22no—
85#13063249—41no—
86#13063249—41no—
87#13063249—41no—
88#13063246—22no—
89#13063246—41no—
90#13063235—22no—
91C8×Dic43—22no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95D411yescharacteristic
102C43⋊#95D411yescharacteristic
103C43⋊#95D411yescharacteristic
104C43⋊#95D411yescharacteristic
105C22×Q8×C43C2311yescharacteristic
106C22×Q8×C43C2311yescharacteristic
107C22×D4×C43C2311yescharacteristic
108C2×Q16×C43—22no—
109C2×Q16×C43—22no—
110C2×Q16×C43—41no—
111C2×SD16×C43—22no—
112C2×SD16×C43—22no—
113C2×SD16×C43—41no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116#124×C43—22no—
117#124×C43—22no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C42×C43C2311yescharacteristic
122#103×C43—22no—
123#102×C43—22no—
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—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43#4112yes—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43#4112yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—42no—
156C22×Dic43—81no—
157C22×Dic43—81no—
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162Q16×C43—44no—
163SD16×C43—44no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43#4112yes—
169C2×C8×C43#4112yes—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C22⋊C4×C43—24no—
173C22⋊C4×C43—24no—
174C42×C43—21no—
175C42×C43—21no—
176C22⋊Dic43—42no—
177C22⋊Dic43—81no—
178C22⋊Dic43—81no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—42no—
188C4⋊Dic43—81no—
189C4⋊Dic43—81no—
190C4⋊Dic43—81no—
191Dic43⋊C4—81no—
192Dic43⋊C4—81no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—42no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C23×C43—22no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43C22×D411yescharacteristic
212Q8×C43—22no—
213Q8×C43—22no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220D4×C43—22no—
221D4×C43—22no—
222D4×C43—41no—
223D4×C43—41no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—22no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43H(5,𝔽2)11yescharacteristic
244C2×C4×C43H(5,𝔽2)11yescharacteristic
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
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—
268C2×Dic43—41no—
269C2×Dic43—84no—
270C8×C43—22no—
271C8×C43—22no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274#29506—431nomaximal, Sylow
275C22×C43—42no—
276C22×C43—42no—
277C22×C43—42no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43#52511yescharacteristic
283C22×C43#53211yescharacteristic
284C22×C43#53511yescharacteristic
285C22×C43#57711yescharacteristic
286C22×C43#57711yescharacteristic
287C22×C43#57711yescharacteristic
288C22×C43#57811yescharacteristic
289C4×C43—42no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43#55111yescharacteristic
295C4×C43#55111yescharacteristic
296C4×C43#55311yescharacteristic
297C4×C43#55311yescharacteristic
298Dic43—41no—
299Dic43—41no—
300Dic43—41no—
301Dic43—41no—
302Dic43—81no—
303Dic43—81no—
304Dic43—81no—
305Dic43—81no—
306#2645—431no—
307#2326—431no—
308#2084—431no—
309#2072—431no—
310#2042—431no—
311#2015D4311yescharacteristic
312#1971—431no—
313#1968—431no—
314#1936—431no—
315#1933—431no—
316#1878—431no—
317#1877—431no—
318#1865—431no—
319#1864—431no—
320#1746—431no—
321C2×C43—82no—
322C2×C43#260311yescharacteristic
323C2×C43#312011yescharacteristic
324C2×C43#312511yescharacteristic
325C2×C43#317311yescharacteristic
326C2×C43#317811yescharacteristic
327C2×C43#322211yescharacteristic
328C2×C43#322511yescharacteristic
329C22×Q16C2×D4311yescharacteristic
330C22×SD16C2×D4311yescharacteristic
331C2×#124C2×D4311yescharacteristic
332C2×C4×Q8—431no—
333C2×C4×D4—431no—
334C2×#106—431no—
335C2×#106—431no—
336C2×#103—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#103—431no—
340C2×#103C2×D4311yescharacteristic
341C2×#102—431no—
342C2×#102—431no—
343C2×#102C2×D4311yescharacteristic
344C2×#97—431no—
345C2×C4×C8—431no—
346#401—861no—
347#400—861no—
348#400—861no—
349#400—861no—
350#391—431no—
351#391—431no—
352#391—431no—
353#391C2×D4311yescharacteristic
354#390—431no—
355#389—431no—
356#389—431no—
357#389—431no—
358#388—861no—
359#388—861no—
360#385—861no—
361#385—861no—
362#384—431no—
363#376—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#336—431no—
369#336—431no—
370#336—431no—
371#336C2×D4311yescharacteristic
372C43#2950611yescharacteristic, complemented, Sylow
373C22×Q8C22×D4311yescharacteristic
374C22×Q8C22×D4311yescharacteristic
375C22×D4C22×D4311yescharacteristic
376C23×C4—861no—
377C2×Q16—22no—
378C2×Q16—22no—
379C2×Q16—41no—
380C2×SD16—22no—
381C2×SD16—22no—
382C2×SD16—41no—
383C22×C8—431no—
384C22×C8—431no—
385C22×C8C22×D4311yescharacteristic
386C22×C8C22×D4311yescharacteristic
387#124—22no—
388#124—22no—
389C4×Q8—1721no—
390C4×Q8—1721no—
391C4×D4—1721no—
392C4×D4—1721no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C42—431no—
410C2×C42—431no—
411C2×C42—861no—
412C2×C42C22×D4311yescharacteristic
413#106—1721no—
414#106—1721no—
415#103—22no—
416#103—862no—
417#103—1721no—
418#103—1721no—
419#103—1721no—
420#102—22no—
421#102—862no—
422#102—1721no—
423#97—862no—
424C4×C8—862no—
425#95—21no—
426#95—21no—
427#95—431no—
428#95—431no—
429#95—431no—
430#95—431no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440C24—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8#1062190012yes—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4#1062190012yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—3441no—
471C22×C4—3441no—
472C22×C4—1722no—
473C22×C4D4×D4311yescharacteristic
474C22×C4D4×D4311yescharacteristic
475C22×C4C23×D4311yescharacteristic
476Q16—44no—
477SD16—44no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8#1062190012yes—
489C2×C8#1062190012yes—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—3441no—
501C4⋊C4—3441no—
502C4⋊C4—3441no—
503C4⋊C4—3441no—
504C4⋊C4—3441no—
505C4⋊C4—1722no—
506C22⋊C4—24no—
507C22⋊C4—24no—
508C22⋊C4—3441no—
509C22⋊C4—3441no—
510C22⋊C4—1722no—
511C42—21no—
512C42—21no—
513C42—861no—
514C42—861no—
515C42—861no—
516C42—861no—
517C42—1722no—
518C23—22no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23C2×D4×D4311yescharacteristic
526Q8—22no—
527Q8—22no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533Q8—41no—
534D4—22no—
535D4—22no—
536D4—41no—
537D4—41no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—3444no—
566C2×C4—1721no—
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×C4C2×#1062190011yescharacteristic
579C2×C4C2×#1062190011yescharacteristic
580C2×C4C2×#1062190011yescharacteristic
581C2×C4C2×#1062190011yescharacteristic
582C2×C4#1306337011yescharacteristic
583C2×C4#1306337111yescharacteristic
584C8—22no—
585C8—22no—
586C8—1721no—
587C8—1721no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—81no—
592C22—81no—
593C22—81no—
594C22—81no—
595C22#1458340511yescharacteristic
596C22#1458344711yescharacteristic
597C22#1458346511yescharacteristic
598C22#1458370611yescharacteristic
599C22#1458370611yescharacteristic
600C22#1458370811yescharacteristic
601C22#1458371511yescharacteristic
602C4—41no—
603C4—42no—
604C4—41no—
605C4—81no—
606C4—81no—
607C4—3441no—
608C4—3441no—
609C4—3441no—
610C4—3441no—
611C4—1721no—
612C4—1721no—
613C4—1721no—
614C4—1721no—
615C4#1458358011yescharacteristic
616C4#1458358011yescharacteristic
617C4#1458360111yescharacteristic
618C4#1458360111yescharacteristic
619C2—82no—
620C2#1914021511yescharacteristic
621C2#1914480211yescharacteristic
622C2#1914486511yescharacteristic
623C2#1914520911yescharacteristic
624C2#1914526011yescharacteristic
625C2#1914566411yescharacteristic
626C2#1914570911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2015C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2015D43
hypocenterC43#29506
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2015

Complements

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

NH ≅ G/Ntype
1. #19140561C2semidirect
3. #19136073C2semidirect
4. #19136003C2semidirect
6. #19135467C2semidirect
9. #19135268C2semidirect
10. #19134938C2semidirect
12. #19134865C2semidirect
14. #19134345C2semidirect
372. C43#29506semidirect

Maximal subgroups

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

subgroupindex
#191405612
#191373082
#191360732
#191360032
#191358312
#191354672
#191354512
#191352892
#191352682
#191349382
#191349312
#191348652
#191348582
#191343452
C43×#20152
#2950643