Finite Group Databasebeta

← #25199789

Subgroups — #25199789

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#19140561C211yesmaximal, characteristic, complemented
2#19137232C211yesmaximal, characteristic
3#19136093C211yesmaximal, characteristic, complemented
4#19135976C211yesmaximal, characteristic, complemented
5#19135969C211yesmaximal, characteristic
6#19135451C211yesmaximal, characteristic
7#19135322C211yesmaximal, characteristic, complemented
8#19135294C211yesmaximal, characteristic
9#19135282C211yesmaximal, characteristic, complemented
10#19135232C211yesmaximal, characteristic, complemented
11#19135172C211yesmaximal, characteristic, complemented
12#19134931C211yesmaximal, characteristic
13#19134854C211yesmaximal, characteristic
14#19134454C211yesmaximal, characteristic, complemented
15C43×#2055C211yesmaximal, characteristic
16C2×D4×Dic43C2211yescharacteristic
17C2×#13063257C2211yescharacteristic
18C2×#13063256C2211yescharacteristic
19C2×#13063256C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063235C2211yescharacteristic
26C2×C8×Dic43C2211yescharacteristic
27C43⋊#401—21no—
28#14582841—21no—
29#14582840—21no—
30#14582839—21no—
31#14582806C2211yescharacteristic
32#14582806C2211yescharacteristic
33#14582802C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582797C2211yescharacteristic
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#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×SD16×C43C2211yescharacteristic
53C2×C4⋊C8×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#390C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C23×Dic43—21no—
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62D4×Dic43—22no—
63D4×Dic43—22no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43C2311yescharacteristic
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×C22⋊Dic43—21no—
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—21no—
76C2×C4×Dic43—21no—
77C2×C4×Dic43C2311yescharacteristic
78C2×C4×Dic43C2311yescharacteristic
79#13063257—22no—
80#13063256—22no—
81#13063256—41no—
82C4⋊(C43⋊C8)—22no—
83#13063249—22no—
84#13063249—22no—
85#13063246—22no—
86#13063246—41no—
87#13063235—41no—
88C8×Dic43—41no—
89C43⋊#95—21no—
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⋊#95D411yescharacteristic
100C43⋊#95D411yescharacteristic
101C43⋊#95D411yescharacteristic
102C43⋊#95D411yescharacteristic
103C22×Q8×C43C2311yescharacteristic
104C22×D4×C43C2311yescharacteristic
105C2×SD16×C43—22no—
106C2×SD16×C43—22no—
107C2×SD16×C43—41no—
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C42×C43C2311yescharacteristic
115C4⋊C8×C43—22no—
116#103×C43—41no—
117#102×C43—22no—
118#95×C43—21no—
119#95×C43—21no—
120C24×C43—21no—
121C2×Q8×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43#4112yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—24no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—81no—
145C22×Dic43—81no—
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150SD16×C43—44no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43#4112yes—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C22⋊C4×C43—81no—
162C22⋊C4×C43—81no—
163C42×C43—21no—
164C42×C43—21no—
165C22⋊Dic43—24no—
166C22⋊Dic43—81no—
167C22⋊Dic43—81no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—81no—
176C4⋊Dic43#4112yes—
177Dic43⋊C4—81no—
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
200Q8×C43—41no—
201Q8×C43—41no—
202Q8×C43—41no—
203Q8×C43—41no—
204D4×C43—22no—
205D4×C43—22no—
206D4×C43—41no—
207D4×C43—41no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
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×C43—41no—
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—
253C2×Dic43—84no—
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#2065—431no—
295#2055D4311yescharacteristic
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×SD16C2×D4311yescharacteristic
314C2×C4×D4—431no—
315C2×#106—431no—
316C2×#106—431no—
317C2×#106—431no—
318C2×C4⋊C8—431no—
319C2×C4⋊C8C2×D4311yescharacteristic
320C2×#103—431no—
321C2×#103—431no—
322C2×#103C2×D4311yescharacteristic
323C2×#102—431no—
324C2×#102—431no—
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#391C2×D4311yescharacteristic
335#390—431no—
336#390C2×D4311yescharacteristic
337#389—431no—
338#389—431no—
339#389—431no—
340#389—431no—
341#389—431no—
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×Q8C22×D4311yescharacteristic
358C22×D4C22×D4311yescharacteristic
359C23×C4—861no—
360C2×SD16—22no—
361C2×SD16—22no—
362C2×SD16—41no—
363C22×C8—431no—
364C22×C8—431no—
365C22×C8C22×D4311yescharacteristic
366C22×C8C22×D4311yescharacteristic
367C4×D4—862no—
368C4×D4—862no—
369C2×C4⋊C4—431no—
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⋊C4—861no—
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—862no—
390#106—862no—
391#106—1721no—
392C4⋊C8—22no—
393C4⋊C8—862no—
394#103—41no—
395#103—862no—
396#103—862no—
397#102—22no—
398#102—862no—
399#102—1721no—
400#97—1721no—
401C4×C8—1721no—
402#95—21no—
403#95—21no—
404#95—431no—
405#95—431no—
406#95—431no—
407#95—431no—
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—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4#1062190012yes—
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—44no—
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—432no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—3441no—
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—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
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×#1062190011yescharacteristic
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#1458340911yescharacteristic
564C22#1458344411yescharacteristic
565C22#1458347811yescharacteristic
566C22#1458370511yescharacteristic
567C22#1458370611yescharacteristic
568C22#1458370811yescharacteristic
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#1458358011yescharacteristic
584C4#1458358611yescharacteristic
585C4#1458359411yescharacteristic
586C4#1458361811yescharacteristic
587C2—82no—
588C2#1914018511yescharacteristic
589C2#1914484511yescharacteristic
590C2#1914486911yescharacteristic
591C2#1914520511yescharacteristic
592C2#1914521811yescharacteristic
593C2#1914603911yescharacteristic
594C2#1914606311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2055C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
hypercenter#2055D43
hypocenterC43#29440
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
1. #19140561C2semidirect
3. #19136093C2semidirect
4. #19135976C2semidirect
7. #19135322C2semidirect
9. #19135282C2semidirect
10. #19135232C2semidirect
11. #19135172C2semidirect
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
#191405612
#191372322
#191360932
#191359762
#191359692
#191354512
#191353222
#191352942
#191352822
#191352322
#191351722
#191349312
#191348542
#191344542
C43×#20552
#2944043