Finite Group Databasebeta

← #25169725

Subgroups — #25169725

Order 11008.

672 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138996C211yesmaximal, characteristic
2#19137621C211yesmaximal, characteristic
3#19136017C211yesmaximal, characteristic, complemented
4#19135971C211yesmaximal, characteristic, complemented
5#19135800C211yesmaximal, characteristic
6#19135794C211yesmaximal, characteristic
7#19135360C211yesmaximal, characteristic, complemented
8#19135208C211yesmaximal, characteristic
9#19135190C211yesmaximal, characteristic, complemented
10#19135177C211yesmaximal, characteristic, complemented
11#19134848C211yesmaximal, characteristic, complemented
12#19134793C211yesmaximal, characteristic
13#19134689C211yesmaximal, characteristic
14#19134426C211yesmaximal, characteristic, complemented
15C43×#1943C211yesmaximal, characteristic, complemented
16C2×#13063305C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18C2×#13063283C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063250C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C43⋊#401—21no—
29#14582826—21no—
30#14582804C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582789—21no—
33#14582789—21no—
34#14582788—21no—
35#14582785—21no—
36#14582782—21no—
37#14582764C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582756C2211yescharacteristic
40C4⋊C4×Dic43—21no—
41C4⋊C4×Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C4×(C2×D43)⋊C4C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#97×C43C2211yescharacteristic
55C43×#389C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×C4×D43C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063305—22no—
64#13063305—22no—
65C4×Dic86—22no—
66C4×Dic86—41no—
67#13063283—22no—
68#13063283—41no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4D411yescharacteristic
80C2×(C2×D43)⋊C4D411yescharacteristic
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43C2311yescharacteristic
86#13063258—22no—
87#13063256—22no—
88Dic43⋊C8—22no—
89#13063250—22no—
90#13063250—22no—
91#13063248—22no—
92#13063248—41no—
93(C2×D43)⋊C8—22no—
94(C2×D43)⋊C8—41no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C42×C43C2311yescharacteristic
115#107×C43—22no—
116#106×C43—41no—
117#97×C43—41no—
118#95×C43—21no—
119#95×C43—21no—
120C23×D43C2×D411yescharacteristic
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2411yescharacteristic
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×C4×D43—21no—
138C2×C4×D43—21no—
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×Dic86—21no—
142C2×Dic86—21no—
143C2×Dic86—21no—
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86#4112yes—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43#4112yes—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—42no—
161C4⋊C4×C43—42no—
162C4⋊C4×C43#4112yes—
163C42×C43—21no—
164C42×C43—21no—
165(C2×D43)⋊C4—24no—
166(C2×D43)⋊C4—41no—
167(C2×D43)⋊C4—41no—
168(C2×D43)⋊C4—42no—
169(C2×D43)⋊C4—42no—
170(C2×D43)⋊C4—81no—
171C4⋊Dic43—24no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—81no—
178C4⋊Dic43#4112yes—
179Dic43⋊C4—42no—
180C4×Dic43—21no—
181C4×Dic43—21no—
182C4×Dic43—42no—
183C4×Dic43—42no—
184C4×Dic43—42no—
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—21no—
192C23×C43C22×D411yescharacteristic
193C22×D43—21no—
194C22×D43—21no—
195C22×D43—21no—
196C22×D43—21no—
197C22×D43—21no—
198C22×D43—21no—
199C22×D43—21no—
200C2×C4×C43—22no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
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×C43C2×#4111yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43H(5,𝔽2)11yescharacteristic
223C2×C4×C432−1+411yescharacteristic
224C2×Dic43—21no—
225C2×Dic43—22no—
226C2×Dic43—22no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C4×D43—41no—
246C4×D43—41no—
247C4×D43—41no—
248C4×D43—41no—
249Dic86—22no—
250Dic86—22no—
251Dic86—41no—
252Dic86—41no—
253C8×C43—22no—
254C8×C43—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#27061—431nomaximal, Sylow
258C22×C43#52511yescharacteristic
259C22×C43#54611yescharacteristic
260C22×C43#54711yescharacteristic
261C22×C43#57511yescharacteristic
262C22×C43#57511yescharacteristic
263C22×C43#57711yescharacteristic
264C22×C43#57811yescharacteristic
265C2×D43—41no—
266C2×D43—41no—
267C2×D43—41no—
268C2×D43—41no—
269C2×D43—41no—
270C2×D43—41no—
271C2×D43—41no—
272C4×C43—42no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43#52911yescharacteristic
279C4×C43#53911yescharacteristic
280C4×C43#55311yescharacteristic
281C4×C43#55611yescharacteristic
282Dic43—41no—
283Dic43—41no—
284Dic43—42no—
285Dic43—41no—
286Dic43—42no—
287Dic43—81no—
288Dic43—81no—
289#2494—431no—
290#2362—431no—
291#2074—431no—
292#2066—431no—
293#2036—431no—
294#2035—431no—
295#1949—431no—
296#1943D4311yescharacteristic, complemented
297#1924—431no—
298#1921—431no—
299#1920—431no—
300#1863—431no—
301#1854—431no—
302#1825—431no—
303#1763—431no—
304C2×C43#246611yescharacteristic
305C2×C43#311111yescharacteristic
306C2×C43#312111yescharacteristic
307C2×C43#330711yescharacteristic
308C2×C43#332711yescharacteristic
309C2×C43#334911yescharacteristic
310C2×C43#335011yescharacteristic
311D43—81no—
312C2×C22⋊Q8—431no—
313C2×C4×Q8—431no—
314C2×#117—431no—
315C2×#107—431no—
316C2×#107C2×D4311yescharacteristic
317C2×#106—431no—
318C2×#106C2×D4311yescharacteristic
319C2×C4⋊C8—431no—
320C2×#103—431no—
321C2×#103—431no—
322C2×#103—431no—
323C2×#103—431no—
324C2×C22⋊C8—431no—
325C2×C22⋊C8—431no—
326C2×#97C2×D4311yescharacteristic
327#401—861no—
328#397—861no—
329#391—431no—
330#389—431no—
331#389C2×D4311yescharacteristic
332#389C2×D4311yescharacteristic
333#388—861no—
334#388—861no—
335#388—861no—
336#387—861no—
337#387—861no—
338#382—431no—
339#380—431no—
340#380—431no—
341C4×C4⋊C4—431no—
342C4×C4⋊C4—431no—
343C4×C4⋊C4—861no—
344C4×C22⋊C4—431no—
345#340—431no—
346#340—431no—
347#340—431no—
348#340—431no—
349#340—431no—
350#340—431no—
351#340C2×D4311yescharacteristic
352#340C2×D4311yescharacteristic
353#336—431no—
354#336—431no—
355C43#2706111yescharacteristic, complemented, Sylow
356C22×Q8—431no—
357C23×C4—431no—
358C22×C8—431no—
359C22×C8—431no—
360C22×C8C22×D4311yescharacteristic
361C22×C8C22×D4311yescharacteristic
362C22⋊Q8—862no—
363C22⋊Q8—862no—
364C4×Q8—862no—
365C4×Q8—1721no—
366#117—862no—
367#117—1721no—
368C2×C4⋊C4—21no—
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⋊C4C22×D4311yescharacteristic
377C2×C4⋊C4C22×D4311yescharacteristic
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C22⋊C4—431no—
381C2×C22⋊C4—431no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C42—431no—
387C2×C42—861no—
388C2×C42—861no—
389C2×C42—861no—
390C2×C42—861no—
391C2×C42C22×D4311yescharacteristic
392#107—22no—
393#107—862no—
394#106—41no—
395#106—862no—
396C4⋊C8—862no—
397#103—862no—
398#103—862no—
399#103—862no—
400#103—1721no—
401C22⋊C8—862no—
402C22⋊C8—1721no—
403#97—41no—
404#95—21no—
405#95—21no—
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—
417C24—431no—
418C2×Q8—432no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×Q8—861no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—431no—
429C22×C4—431no—
430C22×C4—431no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4D4×D4311yescharacteristic
442C22×C4D4×D4311yescharacteristic
443C22×C4C23×D4311yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8#1062190212yes—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—42no—
464C4⋊C4—42no—
465C4⋊C4—432no—
466C4⋊C4—864no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—3441no—
473C4⋊C4—1722no—
474C4⋊C4#1062189812yes—
475C22⋊C4—864no—
476C22⋊C4—3441no—
477C22⋊C4—1721no—
478C22⋊C4—1721no—
479C22⋊C4—1722no—
480C22⋊C4—1722no—
481C42—21no—
482C42—21no—
483C42—861no—
484C42—861no—
485C42—3441no—
486C42—1722no—
487C42—1722no—
488C42—1722no—
489C23—861no—
490C23—861no—
491C23—861no—
492C23—861no—
493C23—861no—
494C23—861no—
495C23—861no—
496C23C2×D4×D4311yescharacteristic
497Q8—862no—
498Q8—862no—
499Q8—1721no—
500Q8—1721no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—862no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—862no—
529C2×C4—861no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
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#41×D4311yescharacteristic
545C2×C4#41×D4311yescharacteristic
546C2×C4C2×#1062189811yescharacteristic
547C2×C4C2×#1062190211yescharacteristic
548C2×C4#1306337011yescharacteristic
549C2×C4#1306337311yescharacteristic
550C8—22no—
551C8—41no—
552C8—1721no—
553C8—1721no—
554C22—1721no—
555C22—1721no—
556C22—1721no—
557C22—1721no—
558C22—1721no—
559C22—1721no—
560C22—1721no—
561C22#1458340811yescharacteristic
562C22#1458353811yescharacteristic
563C22#1458355211yescharacteristic
564C22#1458369511yescharacteristic
565C22#1458369511yescharacteristic
566C22#1458370811yescharacteristic
567C22#1458371511yescharacteristic
568C4—41no—
569C4—41no—
570C4—42no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—3441no—
575C4—3441no—
576C4—1722no—
577C4—1721no—
578C4—1722no—
579C4—1721no—
580C4—1721no—
581C4#1458343411yescharacteristic
582C4#1458349511yescharacteristic
583C4#1458359711yescharacteristic
584C4#1458362111yescharacteristic
585C2—3441no—
586C2#1913863711yescharacteristic
587C2#1914470011yescharacteristic
588C2#1914482811yescharacteristic
589C2#1914656611yescharacteristic
590C2#1914686911yescharacteristic
591C2#1914712411yescharacteristic
592C2#1914713911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1943C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1943D43
hypocenterC43#27061
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1943

Complements

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

NH ≅ G/Ntype
3. #19136017C2semidirect
4. #19135971C2semidirect
7. #19135360C2semidirect
9. #19135190C2semidirect
10. #19135177C2semidirect
11. #19134848C2semidirect
14. #19134426C2semidirect
15. C43×#1943C2semidirect
296. #1943D43semidirect
355. C43#27061semidirect

Maximal subgroups

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

subgroupindex
#191389962
#191376212
#191360172
#191359712
#191358002
#191357942
#191353602
#191352082
#191351902
#191351772
#191348482
#191347932
#191346892
#191344262
C43×#19432
#2706143