Finite Group Databasebeta

← #25196373

Subgroups — #25196373

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#19140572C211yesmaximal, characteristic, complemented
2#19137305C211yesmaximal, characteristic
3#19136161C211yesmaximal, characteristic, complemented
4#19136155C211yesmaximal, characteristic, complemented
5#19135835C211yesmaximal, characteristic
6#19135834C211yesmaximal, characteristic
7#19135285C211yesmaximal, characteristic, complemented
8#19135281C211yesmaximal, characteristic
9#19135270C211yesmaximal, characteristic, complemented
10#19134609C211yesmaximal, characteristic, complemented
11#19134603C211yesmaximal, characteristic
12#19134599C211yesmaximal, characteristic, complemented
13#19134593C211yesmaximal, characteristic
14#19134455C211yesmaximal, characteristic, complemented
15C43×#1936C211yesmaximal, characteristic
16C2×#13063312C2211yescharacteristic
17C2×#13063290C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×Dic43⋊C8C2211yescharacteristic
20C2×Dic43⋊C8C2211yescharacteristic
21C2×#13063250C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×C4×C43⋊C8C2211yescharacteristic
28#14582840—21no—
29#14582837—21no—
30#14582833—21no—
31#14582829—21no—
32#14582805C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582793—21no—
37#14582793—21no—
38#14582771—21no—
39#14582771—21no—
40#14582768C2211yescharacteristic
41#14582768C2211yescharacteristic
42#14582764C2211yescharacteristic
43#14582745C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#102×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#97×C43C2211yescharacteristic
55C43×#390C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063312—22no—
64#13063312—22no—
65#13063290—22no—
66#13063290—22no—
67D4×Dic43—22no—
68D4×Dic43—22no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43C2311yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86Dic43⋊C8—22no—
87Dic43⋊C8—22no—
88#13063250—22no—
89#13063250—41no—
90#13063248—22no—
91#13063248—41no—
92#13063246—22no—
93#13063246—41no—
94C4×C43⋊C8—41no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95D411yescharacteristic
103C43⋊#95D411yescharacteristic
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C22×D4×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C42×C43C2311yescharacteristic
116#102×C43—22no—
117#102×C43—41no—
118#97×C43—41no—
119#95×C43—21no—
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×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—42no—
138C22×Dic43—81no—
139C22×Dic43—81no—
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—
163C22⋊C4×C43—81no—
164C22⋊C4×C43—81no—
165C42×C43—21no—
166C42×C43—21no—
167C22⋊Dic43—24no—
168C22⋊Dic43—24no—
169C22⋊Dic43—42no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—81no—
177Dic43⋊C4—42no—
178Dic43⋊C4—81no—
179Dic43⋊C4—81no—
180Dic43⋊C4—81no—
181Dic43⋊C4—81no—
182Dic43⋊C4—81no—
183Dic43⋊C4—81no—
184C4×Dic43—21no—
185C4×Dic43—21no—
186C4×Dic43—42no—
187C4×Dic43#4112yes—
188C4×Dic43#4112yes—
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—21no—
212C2×C4×C43—21no—
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—41no—
221C2×C4×C43—41no—
222C2×C4×C43C2×#4111yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43H(5,𝔽2)11yescharacteristic
227C2×C4×C432−1+411yescharacteristic
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—22no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
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—84no—
251C2×Dic43#12412yes—
252C2×Dic43#12412yes—
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—41no—
277C4×C43—41no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43—81no—
281C4×C43#55211yescharacteristic
282C4×C43#55211yescharacteristic
283C4×C43#55311yescharacteristic
284C4×C43#55311yescharacteristic
285Dic43—22no—
286Dic43—22no—
287Dic43—42no—
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#1936D4311yescharacteristic
300#1935—431no—
301#1934—431no—
302#1933—431no—
303#1805—431no—
304#1804—431no—
305#1803—431no—
306#1802—431no—
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×D4—431no—
319C2×C4⋊C8—431no—
320C2×C4⋊C8—431no—
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×#97C2×D4311yescharacteristic
330C2×C4×C8—431no—
331#400—861no—
332#400—861no—
333#398—861no—
334#398—861no—
335#391—431no—
336#390C2×D4311yescharacteristic
337#389—431no—
338#389—431no—
339#389—431no—
340#389C2×D4311yescharacteristic
341#388—861no—
342#388—861no—
343#385—861no—
344#385—861no—
345#384—431no—
346#384—431no—
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—861no—
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—862no—
372C4×D4—862no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—861no—
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—21no—
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—862no—
398C4⋊C8—862no—
399#103—862no—
400#103—862no—
401#103—1721no—
402#103—1721no—
403#102—22no—
404#102—41no—
405#102—862no—
406#102—1721no—
407#97—41no—
408C4×C8—1721no—
409#95—21no—
410#95—431no—
411#95—431no—
412#95—431no—
413#95—431no—
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#1062189812yes—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—431no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—861no—
445C22×C4—3441no—
446C22×C4—3441no—
447C22×C4—1722no—
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—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—3441no—
477C4⋊C4—3441no—
478C4⋊C4—3441no—
479C4⋊C4—3441no—
480C4⋊C4—3441no—
481C4⋊C4—3441no—
482C4⋊C4—3441no—
483C4⋊C4—1722no—
484C22⋊C4—81no—
485C22⋊C4—81no—
486C22⋊C4—864no—
487C22⋊C4—864no—
488C22⋊C4—1722no—
489C42—21no—
490C42—21no—
491C42—432no—
492C42—432no—
493C42—861no—
494C42—861no—
495C42—1722no—
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—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—432no—
528C2×C4—432no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—862no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—3444no—
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—1721no—
551C2×C4—1721no—
552C2×C4#41×D4311yescharacteristic
553C2×C4#41×D4311yescharacteristic
554C2×C4#41×D4311yescharacteristic
555C2×C4C2×#1062189811yescharacteristic
556C2×C4#1306337011yescharacteristic
557C2×C4#1306337211yescharacteristic
558C8—41no—
559C8—41no—
560C8—1721no—
561C8—1721no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22#1458340811yescharacteristic
570C22#124×D4311yescharacteristic
571C22#1458347611yescharacteristic
572C22#1458370311yescharacteristic
573C22#1458370911yescharacteristic
574C22#1458370911yescharacteristic
575C22#1458371511yescharacteristic
576C4—41no—
577C4—41no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—862no—
582C4—862no—
583C4—3441no—
584C4—3441no—
585C4—3441no—
586C4—1721no—
587C4—1721no—
588C4—1722no—
589C4#1458358211yescharacteristic
590C4#1458358511yescharacteristic
591C4#1458359411yescharacteristic
592C4#1458359811yescharacteristic
593C2—82no—
594C2#1913975911yescharacteristic
595C2#1914479811yescharacteristic
596C2#1914481311yescharacteristic
597C2#1914495011yescharacteristic
598C2#1914495711yescharacteristic
599C2#1914605211yescharacteristic
600C2#1914606511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1936C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#1936D43
hypocenterC43#29134
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
1. #19140572C2semidirect
3. #19136161C2semidirect
4. #19136155C2semidirect
7. #19135285C2semidirect
9. #19135270C2semidirect
10. #19134609C2semidirect
12. #19134599C2semidirect
14. #19134455C2semidirect
359. C43#29134semidirect

Maximal subgroups

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

subgroupindex
#191405722
#191373052
#191361612
#191361552
#191358352
#191358342
#191352852
#191352812
#191352702
#191346092
#191346032
#191345992
#191345932
#191344552
C43×#19362
#2913443