Finite Group Databasebeta

← #25199797

Subgroups — #25199797

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140563C211yesmaximal, characteristic, complemented
2#19137232C211yesmaximal, characteristic
3#19136096C211yesmaximal, characteristic, complemented
4#19135975C211yesmaximal, characteristic, complemented
5#19135912C211yesmaximal, characteristic
6#19135450C211yesmaximal, characteristic
7#19135321C211yesmaximal, characteristic, complemented
8#19135289C211yesmaximal, characteristic
9#19135283C211yesmaximal, characteristic, complemented
10#19135228C211yesmaximal, characteristic, complemented
11#19135176C211yesmaximal, characteristic, complemented
12#19134927C211yesmaximal, characteristic
13#19134858C211yesmaximal, characteristic
14#19134454C211yesmaximal, characteristic, complemented
15C43×#2065C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×#13063257C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×#13063250C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063235C2211yescharacteristic
26C2×C8×Dic43C2211yescharacteristic
27C43⋊#401—21no—
28#14582841—21no—
29#14582838—21no—
30#14582837—21no—
31#14582805C2211yescharacteristic
32#14582804C2211yescharacteristic
33#14582804C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582795C2211yescharacteristic
38#14582795C2211yescharacteristic
39#14582793—21no—
40#14582787—21no—
41#14582760—21no—
42#14582757—21no—
43C4⋊C4×Dic43C2211yescharacteristic
44#14582745C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C23×Dic43—21no—
61C2×#10621883—22no—
62C2×#10621883—22no—
63C2×#10621883—41no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66D4×Dic43—22no—
67D4×Dic43—22no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43C2311yescharacteristic
80C2×C4×Dic43C2311yescharacteristic
81#13063257—22no—
82#13063256—22no—
83C4⋊(C43⋊C8)—22no—
84#13063250—22no—
85#13063250—22no—
86#13063248—41no—
87#13063246—22no—
88#13063235—41no—
89C8×Dic43—41no—
90C43⋊#95—21no—
91C43⋊#95—21no—
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×D4×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C42×C43C2311yescharacteristic
115#106×C43—41no—
116C4⋊C8×C43—22no—
117#102×C43—22no—
118#102×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—24no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
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—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43#4112yes—
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—81no—
169C22⋊Dic43—81no—
170#10621883—44no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—81no—
177C4⋊Dic43#4112yes—
178Dic43⋊C4—81no—
179Dic43⋊C4—81no—
180Dic43⋊C4—81no—
181C4×Dic43—21no—
182C4×Dic43—21no—
183C4×Dic43—21no—
184C4×Dic43—21no—
185C4×Dic43—81no—
186C2×C43⋊C8—21no—
187C2×C43⋊C8—21no—
188C2×C43⋊C8—21no—
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8#4112yes—
192C23×C43—22no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43C22×D411yescharacteristic
200D4×C43—22no—
201D4×C43—22no—
202D4×C43—41no—
203D4×C43—41no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—41no—
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×C43C2×#4111yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C2×C4×C43H(5,𝔽2)11yescharacteristic
224C2×C4×C432−1+411yescharacteristic
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—22no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—41no—
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—84no—
250Dic86—41no—
251Dic86—41no—
252Dic86—41no—
253Dic86—41no—
254C8×C43—22no—
255C8×C43—41no—
256C43⋊C8—22no—
257C43⋊C8—41no—
258#29440—431nomaximal, Sylow
259C22×C43—42no—
260C22×C43—42no—
261C22×C43—42no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43—81no—
266C22×C43#52511yescharacteristic
267C22×C43#53211yescharacteristic
268C22×C43#53711yescharacteristic
269C22×C43#57711yescharacteristic
270C22×C43#57711yescharacteristic
271C22×C43#57711yescharacteristic
272C22×C43#57711yescharacteristic
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43#55111yescharacteristic
279C4×C43#55211yescharacteristic
280C4×C43#55311yescharacteristic
281C4×C43#55611yescharacteristic
282Dic43—41no—
283Dic43—42no—
284Dic43—41no—
285Dic43—41no—
286Dic43—41no—
287Dic43—81no—
288Dic43—81no—
289Dic43—81no—
290#2645—431no—
291#2319—431no—
292#2088—431no—
293#2066—431no—
294#2065D4311yescharacteristic
295#2055—431no—
296#1968—431no—
297#1941—431no—
298#1936—431no—
299#1935—431no—
300#1927—431no—
301#1919—431no—
302#1877—431no—
303#1864—431no—
304#1768—431no—
305C2×C43—82no—
306C2×C43#260111yescharacteristic
307C2×C43#312311yescharacteristic
308C2×C43#312511yescharacteristic
309C2×C43#317311yescharacteristic
310C2×C43#317411yescharacteristic
311C2×C43#326011yescharacteristic
312C2×C43#326311yescharacteristic
313C22×SD16—431no—
314C2×C4×D4—431no—
315C2×#106—431no—
316C2×#106—431no—
317C2×#106C2×D4311yescharacteristic
318C2×C4⋊C8—431no—
319C2×C4⋊C8C2×D4311yescharacteristic
320C2×#103—431no—
321C2×#103—431no—
322C2×#103—431no—
323C2×#102—431no—
324C2×#102C2×D4311yescharacteristic
325C2×#102C2×D4311yescharacteristic
326C2×#97—431no—
327C2×C4×C8—431no—
328#401—861no—
329#400—861no—
330#400—861no—
331#400—861no—
332#391—431no—
333#391—431no—
334#391—431no—
335#390—431no—
336#390C2×D4311yescharacteristic
337#389—431no—
338#389—431no—
339#389—431no—
340#389—431no—
341#389C2×D4311yescharacteristic
342#388—861no—
343#388—861no—
344#381—861no—
345#380—861no—
346C4×C4⋊C4—431no—
347#376—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340C2×D4311yescharacteristic
354#336—431no—
355#336—431no—
356C43#2944011yescharacteristic, complemented, Sylow
357C22×Q8—431no—
358C22×D4C22×D4311yescharacteristic
359C23×C4—861no—
360C2×SD16—862no—
361C2×SD16—862no—
362C2×SD16—1721no—
363C22×C8—431no—
364C22×C8—431no—
365C22×C8C22×D4311yescharacteristic
366C22×C8C22×D4311yescharacteristic
367C4×D4—862no—
368C4×D4—862no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4C22×D4311yescharacteristic
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C42—431no—
386C2×C42—431no—
387C2×C42—861no—
388C2×C42C22×D4311yescharacteristic
389#106—41no—
390#106—862no—
391#106—862no—
392C4⋊C8—22no—
393C4⋊C8—862no—
394#103—862no—
395#103—862no—
396#103—1721no—
397#102—22no—
398#102—41no—
399#102—862no—
400#97—1721no—
401C4×C8—1721no—
402#95—21no—
403#95—431no—
404#95—431no—
405#95—431no—
406#95—431no—
407#95—861no—
408#95—861no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418C24—21no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4#1062190212yes—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—431no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—864no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—3441no—
444C22×C4—3441no—
445C22×C4D4×D4311yescharacteristic
446C22×C4D4×D4311yescharacteristic
447C22×C4C23×D4311yescharacteristic
448SD16—1724no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—432no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8#1062190012yes—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—81no—
468C4⋊C4—432no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—3441no—
475C4⋊C4—3441no—
476C4⋊C4—3441no—
477C4⋊C4—3441no—
478C22⋊C4—81no—
479C22⋊C4—81no—
480C22⋊C4—864no—
481C22⋊C4—3441no—
482C22⋊C4—3441no—
483C42—21no—
484C42—21no—
485C42—861no—
486C42—861no—
487C42—861no—
488C42—861no—
489C42—3441no—
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23C2×D4×D4311yescharacteristic
498Q8—1721no—
499Q8—1721no—
500Q8—1721no—
501Q8—1721no—
502D4—22no—
503D4—22no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—862no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—3444no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4#41×D4311yescharacteristic
547C2×C4#41×D4311yescharacteristic
548C2×C4C2×#1062190011yescharacteristic
549C2×C4C2×#1062190211yescharacteristic
550C2×C4#1306337011yescharacteristic
551C2×C4#1306337211yescharacteristic
552C8—22no—
553C8—41no—
554C8—862no—
555C8—1721no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22#1458341211yescharacteristic
564C22#1458344411yescharacteristic
565C22#1458347811yescharacteristic
566C22#1458370511yescharacteristic
567C22#1458370611yescharacteristic
568C22#1458370911yescharacteristic
569C22#1458370911yescharacteristic
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—3441no—
576C4—3441no—
577C4—3441no—
578C4—1721no—
579C4—1721no—
580C4—1721no—
581C4—1722no—
582C4—1721no—
583C4#1458357611yescharacteristic
584C4#1458359111yescharacteristic
585C4#1458359211yescharacteristic
586C4#1458361611yescharacteristic
587C2—82no—
588C2#1914019311yescharacteristic
589C2#1914484911yescharacteristic
590C2#1914487711yescharacteristic
591C2#1914520711yescharacteristic
592C2#1914521611yescharacteristic
593C2#1914603911yescharacteristic
594C2#1914606211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2065C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2065D43
hypocenterC43#29440
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2065

Complements

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

NH ≅ G/Ntype
1. #19140563C2semidirect
3. #19136096C2semidirect
4. #19135975C2semidirect
7. #19135321C2semidirect
9. #19135283C2semidirect
10. #19135228C2semidirect
11. #19135176C2semidirect
14. #19134454C2semidirect
356. C43#29440semidirect

Maximal subgroups

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

subgroupindex
#191405632
#191372322
#191360962
#191359752
#191359122
#191354502
#191353212
#191352892
#191352832
#191352282
#191351762
#191349272
#191348582
#191344542
C43×#20652
#2944043