Finite Group Databasebeta

← #25196364

Subgroups — #25196364

Order 11008.

690 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140575C211yesmaximal, characteristic, complemented
2#19137307C211yesmaximal, characteristic
3#19136160C211yesmaximal, characteristic, complemented
4#19136155C211yesmaximal, characteristic, complemented
5#19135834C211yesmaximal, characteristic
6#19135834C211yesmaximal, characteristic
7#19135294C211yesmaximal, characteristic
8#19135286C211yesmaximal, characteristic, complemented
9#19135280C211yesmaximal, characteristic
10#19135272C211yesmaximal, characteristic, complemented
11#19134611C211yesmaximal, characteristic, complemented
12#19134605C211yesmaximal, characteristic
13#19134597C211yesmaximal, characteristic, complemented
14#19134454C211yesmaximal, characteristic, complemented
15C43×#1802C211yesmaximal, characteristic
16C2×#13063312C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×C4⋊(C43⋊C8)C2211yescharacteristic
19C2×#13063250C2211yescharacteristic
20C2×#13063250C2211yescharacteristic
21C2×#13063248C2211yescharacteristic
22C2×#13063248C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063235C2211yescharacteristic
26C2×C8×Dic43C2211yescharacteristic
27#14582838—21no—
28#14582838—21no—
29#14582832—21no—
30#14582832—21no—
31#14582804C2211yescharacteristic
32#14582802C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582795C2211yescharacteristic
37#14582787—21no—
38#14582787—21no—
39#14582772—21no—
40#14582772—21no—
41#14582768C2211yescharacteristic
42#14582765C2211yescharacteristic
43#14582745C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#384C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62#13063312—22no—
63#13063312—22no—
64C4×Dic86—22no—
65C4×Dic86—22no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C4×Dic43—21no—
81C2×C4×Dic43C2311yescharacteristic
82C2×C4×Dic43C2311yescharacteristic
83C4⋊(C43⋊C8)—22no—
84#13063250—41no—
85#13063250—41no—
86#13063248—22no—
87#13063248—22no—
88#13063246—41no—
89#13063246—41no—
90#13063235—41no—
91C8×Dic43—41no—
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⋊#95D411yescharacteristic
101C43⋊#95D411yescharacteristic
102C43⋊#95D411yescharacteristic
103C43⋊#95D411yescharacteristic
104C22×D4×C43C2311yescharacteristic
105C23×C4×C43—21no—
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C4×D4×C43—22no—
109C4×D4×C43—22no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C22⋊C4×C43—21no—
116C2×C42×C43C2311yescharacteristic
117C4⋊C8×C43—22no—
118#102×C43—22no—
119#102×C43—22no—
120C24×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43#4112yes—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—42no—
131C22×C4×C43—81no—
132C22×C4×C43—81no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86#4112yes—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—81no—
163C4⋊C4×C43—81no—
164C22⋊C4×C43—42no—
165C42×C43#4112yes—
166C42×C43#4112yes—
167C22⋊Dic43—24no—
168C22⋊Dic43—24no—
169C22⋊Dic43—81no—
170C22⋊Dic43—81no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—81no—
178C4⋊Dic43—81no—
179Dic43⋊C4—42no—
180Dic43⋊C4—81no—
181Dic43⋊C4—81no—
182Dic43⋊C4—81no—
183Dic43⋊C4—81no—
184C4×Dic43—21no—
185C4×Dic43—21no—
186C4×Dic43—21no—
187C4×Dic43—21no—
188C4×Dic43—42no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C23×C43—22no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43C22×D411yescharacteristic
203D4×C43—22no—
204D4×C43—22no—
205D4×C43—41no—
206D4×C43—41no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—84no—
221C2×C4×C43#12412yes—
222C2×C4×C43#12412yes—
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43H(5,𝔽2)11yescharacteristic
228C2×C4×C432−1+411yescharacteristic
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—22no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253Dic86—22no—
254Dic86—22no—
255Dic86—41no—
256Dic86—41no—
257C8×C43—41no—
258C8×C43—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261#29134—431nomaximal, Sylow
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43#52511yescharacteristic
270C22×C43C2×#12411yescharacteristic
271C22×C43#53711yescharacteristic
272C22×C43#57611yescharacteristic
273C22×C43#57711yescharacteristic
274C22×C43#57711yescharacteristic
275C22×C43#57811yescharacteristic
276C4×C43—22no—
277C4×C43—22no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43#55211yescharacteristic
282C4×C43#55211yescharacteristic
283C4×C43#55311yescharacteristic
284C4×C43#55311yescharacteristic
285Dic43—42no—
286Dic43—41no—
287Dic43—41no—
288Dic43—41no—
289Dic43—41no—
290Dic43—81no—
291Dic43—81no—
292Dic43—81no—
293#2647—431no—
294#2326—431no—
295#2100—431no—
296#2099—431no—
297#2042—431no—
298#2042—431no—
299#1936—431no—
300#1935—431no—
301#1934—431no—
302#1933—431no—
303#1805—431no—
304#1804—431no—
305#1803—431no—
306#1802D4311yescharacteristic
307#1768—431no—
308C2×C43—82no—
309C2×C43#256211yescharacteristic
310C2×C43#311911yescharacteristic
311C2×C43#312011yescharacteristic
312C2×C43#313611yescharacteristic
313C2×C43#313711yescharacteristic
314C2×C43#326211yescharacteristic
315C2×C43#326311yescharacteristic
316C2×#124—431no—
317C2×C4×Q8—431no—
318C2×C4×D4C2×D4311yescharacteristic
319C2×C4⋊C8—431no—
320C2×C4⋊C8C2×D4311yescharacteristic
321C2×#103—431no—
322C2×#103—431no—
323C2×#103—431no—
324C2×#103—431no—
325C2×#102—431no—
326C2×#102—431no—
327C2×#102C2×D4311yescharacteristic
328C2×#102C2×D4311yescharacteristic
329C2×#97—431no—
330C2×C4×C8—431no—
331#400—861no—
332#400—861no—
333#398—861no—
334#398—861no—
335#391—431no—
336#390—431no—
337#389—431no—
338#389—431no—
339#389—431no—
340#389—431no—
341#388—861no—
342#388—861no—
343#385—861no—
344#385—861no—
345#384—431no—
346#384C2×D4311yescharacteristic
347#382—431no—
348#376—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340C2×D4311yescharacteristic
356#340C2×D4311yescharacteristic
357#336—431no—
358#336—431no—
359C43#2913411yescharacteristic, complemented, Sylow
360C22×Q8—431no—
361C22×D4C22×D4311yescharacteristic
362C23×C4—21no—
363C22×C8—431no—
364C22×C8—431no—
365C22×C8C22×D4311yescharacteristic
366C22×C8C22×D4311yescharacteristic
367#124—862no—
368#124—862no—
369C4×Q8—862no—
370C4×Q8—862no—
371C4×D4—22no—
372C4×D4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C42—431no—
394C2×C42—431no—
395C2×C42—861no—
396C2×C42C22×D4311yescharacteristic
397C4⋊C8—22no—
398C4⋊C8—862no—
399#103—862no—
400#103—862no—
401#103—1721no—
402#103—1721no—
403#102—22no—
404#102—22no—
405#102—1721no—
406#102—1721no—
407#97—1721no—
408C4×C8—1721no—
409#95—431no—
410#95—431no—
411#95—431no—
412#95—431no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421C24—21no—
422C2×Q8—432no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4#1062190012yes—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—42no—
438C22×C4—81no—
439C22×C4—81no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—861no—
445C22×C4—861no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4D4×D4311yescharacteristic
449C22×C4D4×D4311yescharacteristic
450C22×C4C23×D4311yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—81no—
470C4⋊C4—81no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—3441no—
478C4⋊C4—3441no—
479C4⋊C4—3441no—
480C4⋊C4—3441no—
481C4⋊C4—3441no—
482C4⋊C4—3441no—
483C4⋊C4—1722no—
484C22⋊C4—42no—
485C22⋊C4—864no—
486C22⋊C4—864no—
487C22⋊C4—3441no—
488C22⋊C4—3441no—
489C42—861no—
490C42—861no—
491C42—861no—
492C42—861no—
493C42—1722no—
494C42#1062189812yes—
495C42#1062190012yes—
496C23—22no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23C2×D4×D4311yescharacteristic
504Q8—862no—
505Q8—862no—
506Q8—1721no—
507Q8—1721no—
508D4—22no—
509D4—22no—
510D4—41no—
511D4—41no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—84no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—862no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4#1306331112yes—
551C2×C4#1306331112yes—
552C2×C4#41×D4311yescharacteristic
553C2×C4C2×#1062190011yescharacteristic
554C2×C4C2×#1062190011yescharacteristic
555C2×C4C2×#1062189811yescharacteristic
556C2×C4#1306337111yescharacteristic
557C2×C4#1306337311yescharacteristic
558C8—41no—
559C8—41no—
560C8—1721no—
561C8—1721no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22#1458340911yescharacteristic
570C22C2×#1306331111yescharacteristic
571C22#1458347911yescharacteristic
572C22#1458370011yescharacteristic
573C22#1458370511yescharacteristic
574C22#1458370911yescharacteristic
575C22#1458371511yescharacteristic
576C4—22no—
577C4—22no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—3441no—
582C4—3441no—
583C4—3441no—
584C4—1721no—
585C4—1721no—
586C4—1721no—
587C4—1721no—
588C4—1722no—
589C4#1458358311yescharacteristic
590C4#1458358411yescharacteristic
591C4#1458359311yescharacteristic
592C4#1458360111yescharacteristic
593C2—82no—
594C2#1913975811yescharacteristic
595C2#1914479111yescharacteristic
596C2#1914480611yescharacteristic
597C2#1914494711yescharacteristic
598C2#1914496311yescharacteristic
599C2#1914605511yescharacteristic
600C2#1914606711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1802C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1802D43
hypocenterC43#29134
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
1. #19140575C2semidirect
3. #19136160C2semidirect
4. #19136155C2semidirect
8. #19135286C2semidirect
10. #19135272C2semidirect
11. #19134611C2semidirect
13. #19134597C2semidirect
14. #19134454C2semidirect
359. C43#29134semidirect

Maximal subgroups

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

subgroupindex
#191405752
#191373072
#191361602
#191361552
#191358342
#191352942
#191352862
#191352802
#191352722
#191346112
#191346052
#191345972
#191344542
C43×#18022
#2913443