Finite Group Databasebeta

← #25155543

Subgroups — #25155543

Order 11008.

678 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#19145126C211yesmaximal, characteristic, complemented
2#19144455C211yesmaximal, characteristic
3#19144444C211yesmaximal, characteristic
4#19143195C211yesmaximal, characteristic
5#19136107C211yesmaximal, characteristic, complemented
6#19136102C211yesmaximal, characteristic, complemented
7#19135944C211yesmaximal, characteristic, complemented
8#19135939C211yesmaximal, characteristic, complemented
9#19135380C211yesmaximal, characteristic, complemented
10#19135348C211yesmaximal, characteristic, complemented
11#19134830C211yesmaximal, characteristic
12#19134823C211yesmaximal, characteristic
13#19134763C211yesmaximal, characteristic, complemented
14#19134654C211yesmaximal, characteristic
15C43×#1765C211yesmaximal, characteristic
16#14583527C2211yescharacteristic
17#14583527C2211yescharacteristic
18#14583382C2211yescharacteristic
19#14583382C2211yescharacteristic
20#14583308—21no—
21#14583308—21no—
22#14583301—21no—
23#14583297—21no—
24#14583208—21no—
25#14583204—21no—
26#14583201—21no—
27#14583197—21no—
28#14583192—21no—
29#14583187—21no—
30#14583182—21no—
31#14583177—21no—
32C2×#13063261C2211yescharacteristic
33#14582942C2211yescharacteristic
34#14582942C2211yescharacteristic
35#14582941—21no—
36#14582941—21no—
37#14582941C2211yescharacteristic
38#14582941C2211yescharacteristic
39#14582941C2211yescharacteristic
40#14582941C2211yescharacteristic
41#14582937—21no—
42#14582937C2211yescharacteristic
43C2×#13063259—21no—
44C2×#13063259C2211yescharacteristic
45C2×#13063259C2211yescharacteristic
46C2×#13063257C2211yescharacteristic
47C2×#13063257C2211yescharacteristic
48#14582925C2211yescharacteristic
49#14582925C2211yescharacteristic
50#14582900C2211yescharacteristic
51#14582900C2211yescharacteristic
52#14582769C2211yescharacteristic
53#14582765C2211yescharacteristic
54#14582667C2211yescharacteristic
55#14582667C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582659C2211yescharacteristic
59#14582659C2211yescharacteristic
60C2×#131×C43C2211yescharacteristic
61C2×#104×C43C2211yescharacteristic
62C43×#416C2211yescharacteristic
63C43×#405C2211yescharacteristic
64C2×#97×C43C2211yescharacteristic
65C43×#341C2211yescharacteristic
66C43×#339C2211yescharacteristic
67C2×#10621877C2311yescharacteristic
68C2×#10621877C2311yescharacteristic
69#13063325—21no—
70#13063325—21no—
71#13063324—21no—
72#13063324—21no—
73#13063317—21no—
74#13063317—21no—
75#13063316—21no—
76#13063316—21no—
77#13063302—41no—
78#13063302—41no—
79Q8×Dic43—21no—
80Q8×Dic43—21no—
81D4×Dic43—21no—
82D4×Dic43—21no—
83D4×Dic43—41no—
84D4×Dic43—41no—
85#13063284—21no—
86#13063284—21no—
87#13063284C2311yescharacteristic
88#13063284C2311yescharacteristic
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—41no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96#13063261—22no—
97#13063259—21no—
98#13063259—21no—
99#13063259—21no—
100#13063259—21no—
101#13063259—21no—
102#13063259—21no—
103#13063259—21no—
104#13063259—21no—
105#13063259D411yescharacteristic
106#13063259D411yescharacteristic
107#13063258—21no—
108#13063258—21no—
109#13063257—21no—
110#13063257—21no—
111#13063257—21no—
112#13063257—21no—
113#13063257—21no—
114#13063257—21no—
115#13063257—21no—
116#13063257—21no—
117#13063257D411yescharacteristic
118#13063257D411yescharacteristic
119#13063256—21no—
120#13063256—21no—
121Dic43⋊C8—21no—
122Dic43⋊C8—21no—
123Dic43⋊C8—21no—
124Dic43⋊C8—21no—
125#13063249—21no—
126#13063249—21no—
127#13063246—21no—
128#13063246—21no—
129C43⋊#95—41no—
130C2×#41×C43C2311yescharacteristic
131#131×C43—22no—
132#131×C43Q814yescomplemented
133C2×M16×C43—21no—
134C2×M16×C43C2311yescharacteristic
135C2×M16×C43C2311yescharacteristic
136C22×C8×C43—21no—
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139#117×C43C2311yescharacteristic
140C2×C42×C43C2311yescharacteristic
141#104×C43Q814yescomplemented
142#103×C43D411yescharacteristic
143#103×C43D411yescharacteristic
144#102×C43D411yescharacteristic
145#102×C43D411yescharacteristic
146#97×C43—21no—
147#97×C43—22no—
148C4×C8×C43—21no—
149#41×C43—21no—
150#41×C43—21no—
151#41×C43C2×Q812yes—
152#41×C43C2×Q812yes—
153C2×Q8×C43C2×D411yescharacteristic
154C2×D4×C43—21no—
155C2×D4×C43C2×D411yescharacteristic
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43C2411yescharacteristic
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—41no—
164C22×Dic43—41no—
165C2×Dic86—41no—
166C2×Dic86—41no—
167M16×C43—21no—
168M16×C43—21no—
169M16×C43—24no—
170M16×C43C2×Q812yes—
171M16×C43C2×Q812yes—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—24no—
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C2×C8×C43C2×Q812yes—
182C2×C8×C43#4112yes—
183C4⋊C4×C43C2×D411yescharacteristic
184C4⋊C4×C43C2×D411yescharacteristic
185C22⋊C4×C43—21no—
186C42×C43—21no—
187C42×C43—21no—
188C42×C43C2×Q812yes—
189C22⋊Dic43—21no—
190C22⋊Dic43—21no—
191C22⋊Dic43—41no—
192C22⋊Dic43—41no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—41no—
202C4⋊Dic43—41no—
203C4⋊Dic43—41no—
204C4⋊Dic43—41no—
205C4⋊Dic43—82no—
206C4⋊Dic43C2×D411yescharacteristic
207C4⋊Dic43C2×D411yescharacteristic
208C4⋊Dic43C2×D411yescharacteristic
209C4⋊Dic43C2×D411yescharacteristic
210Dic43⋊C4—41no—
211Dic43⋊C4—41no—
212Dic43⋊C4—41no—
213Dic43⋊C4—41no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—41no—
217C4×Dic43—41no—
218#10621877—21no—
219#10621877—21no—
220#10621877—21no—
221#10621877—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C23×C43—21no—
225C23×C43H(5,𝔽2)11yescharacteristic
226Q8×C43—21no—
227Q8×C43C4⋊Q812yes—
228D4×C43—22no—
229D4×C43—22no—
230D4×C43—21no—
231D4×C43C4⋊Q812yes—
232C2×C4×C43—21no—
233C2×C4×C43—22no—
234C2×C4×C43—22no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×Q811yescharacteristic
243C2×C4×C43C22×Q811yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C432−1+411yescharacteristic
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—81no—
255C2×Dic43—81no—
256C2×Dic43—81no—
257C2×Dic43—81no—
258C2×Dic43—161no—
259C2×Dic43—161no—
260Dic86—161no—
261Dic86—161no—
262C8×C43—22no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—22no—
266C8×C43C22⋊Q812yes—
267C8×C43C22⋊Q812yes—
268C43⋊C8—41no—
269C43⋊C8—41no—
270#26085—431nomaximal, Sylow
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—22no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43#54411yescharacteristic
277C22×C43D4211yescharacteristic
278C22×C43#55411yescharacteristic
279C4×C43—22no—
280C4×C43—42no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43C2×C22⋊Q811yescharacteristic
284C4×C43C2×C4⋊Q811yescharacteristic
285C4×C43#54711yescharacteristic
286C4×C43D4×Q811yescharacteristic
287Dic43—41no—
288Dic43—41no—
289Dic43—41no—
290Dic43—41no—
291Dic43—81no—
292Dic43—81no—
293Dic43—81no—
294Dic43—81no—
295#3163—431no—
296#3084—431no—
297#3083—431no—
298#2913—431no—
299#2090—431no—
300#2089—431no—
301#2061—431no—
302#2060—431no—
303#1952—431no—
304#1946—431no—
305#1860—431no—
306#1859—431no—
307#1847—431no—
308#1815—431no—
309#1765D4311yescharacteristic
310C2×C43—21no—
311C2×C43—21no—
312C2×C43—42no—
313C2×C43#244011yescharacteristic
314C2×C43#328811yescharacteristic
315C2×C43#328911yescharacteristic
316C2×#131C2×D4311yescharacteristic
317#544—431no—
318#544—431no—
319#520—431no—
320#520—431no—
321#501—861no—
322#501—861no—
323#499—861no—
324#498—861no—
325#479—861no—
326#479—861no—
327#478—861no—
328#478—861no—
329#477—861no—
330#476—861no—
331#475—861no—
332#474—861no—
333C2×#108—431no—
334#428—431no—
335#428—431no—
336#428—431no—
337#428—431no—
338#428—431no—
339#428—431no—
340#428—861no—
341#428—861no—
342#427—431no—
343#427—861no—
344C2×#107—431no—
345C2×#107—431no—
346C2×#107—861no—
347C2×#106—431no—
348C2×#106—431no—
349#424—431no—
350#424—431no—
351C2×#104C2×D4311yescharacteristic
352#417—431no—
353#417—431no—
354#416C2×D4311yescharacteristic
355#405C2×D4311yescharacteristic
356C2×#97C2×D4311yescharacteristic
357#384—431no—
358#382—431no—
359#343—431no—
360#343—431no—
361#343—431no—
362#343—431no—
363#341C2×D4311yescharacteristic
364#339—431no—
365#339—431no—
366#339C2×D4311yescharacteristic
367C43#2608511yescharacteristic, complemented, Sylow
368C2×#41C22×D4311yescharacteristic
369#131—22no—
370#131Dic8614yescomplemented
371C2×M16—21no—
372C2×M16—431no—
373C2×M16—431no—
374C2×M16C22×D4311yescharacteristic
375C2×M16C22×D4311yescharacteristic
376C22×C8—21no—
377C22×C8C22×D4311yescharacteristic
378C22×C8C22×D4311yescharacteristic
379C4⋊Q8—861no—
380C4⋊Q8—861no—
381C4⋊Q8—861no—
382C4⋊Q8—861no—
383#125—861no—
384#125—861no—
385#125—861no—
386#125—861no—
387C22⋊Q8—1721no—
388C22⋊Q8—1721no—
389C4×Q8—861no—
390C4×Q8—861no—
391C4×D4—861no—
392C4×D4—861no—
393C4×D4—1721no—
394C4×D4—1721no—
395#117—431no—
396#117—431no—
397#117—861no—
398#117—861no—
399#117C22×D4311yescharacteristic
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—431no—
403C2×C4⋊C4—431no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—861no—
406C2×C4⋊C4—1721no—
407C2×C42C22×D4311yescharacteristic
408#108—862no—
409#107—431no—
410#107—431no—
411#107—861no—
412#107—861no—
413#107—861no—
414#107—861no—
415#107—861no—
416#107—861no—
417#107—861no—
418#107—861no—
419#107—861no—
420#107—861no—
421#106—431no—
422#106—431no—
423#106—861no—
424#106—861no—
425#106—861no—
426#106—861no—
427#106—861no—
428#106—861no—
429#106—861no—
430#106—861no—
431#106—861no—
432#106—861no—
433C4⋊C8—861no—
434C4⋊C8—861no—
435C4⋊C8—861no—
436C4⋊C8—861no—
437#104Dic8614yescomplemented
438#103—861no—
439#103—861no—
440#103D17211yescharacteristic
441#103D17211yescharacteristic
442#102—861no—
443#102—861no—
444#102D17211yescharacteristic
445#102D17211yescharacteristic
446#97—21no—
447#97—22no—
448C4×C8—21no—
449#95—1721no—
450#41—21no—
451#41—21no—
452#41C2×Dic8612yes—
453#41C2×Dic8612yes—
454C2×Q8—1721no—
455C2×Q8—1721no—
456C2×Q8C2×D17211yescharacteristic
457C2×D4—21no—
458C2×D4C2×D17211yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—1721no—
466C22×C4—1721no—
467C22×C4C23×D4311yescharacteristic
468M16—21no—
469M16—21no—
470M16—24no—
471M16—861no—
472M16—861no—
473M16—861no—
474M16—861no—
475M16C2×Dic8612yes—
476M16C2×Dic8612yes—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—24no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8C2×Dic8612yes—
485C2×C8C2×D17211yescharacteristic
486C2×C8C2×D17211yescharacteristic
487C2×C8D4×D4311yescharacteristic
488C2×C8D4×D4311yescharacteristic
489C2×C8#1062190012yes—
490C4⋊C4—431no—
491C4⋊C4—431no—
492C4⋊C4—431no—
493C4⋊C4—431no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—3442no—
503C4⋊C4—1721no—
504C4⋊C4—1721no—
505C4⋊C4—1721no—
506C4⋊C4—1721no—
507C4⋊C4—1721no—
508C4⋊C4—1721no—
509C4⋊C4—1721no—
510C4⋊C4—1721no—
511C4⋊C4C2×D17211yescharacteristic
512C4⋊C4C2×D17211yescharacteristic
513C22⋊C4—21no—
514C22⋊C4—861no—
515C22⋊C4—861no—
516C22⋊C4—1721no—
517C22⋊C4—1721no—
518C42—21no—
519C42—21no—
520C42—861no—
521C42—861no—
522C42—1721no—
523C42—1721no—
524C42C2×Dic8612yes—
525C23—21no—
526C23#1306337111yescharacteristic
527Q8—21no—
528Q8—6881no—
529Q8—6881no—
530Q8#1306332512yes—
531D4—22no—
532D4—22no—
533D4—21no—
534D4#1306332512yes—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—3441no—
548C2×C4—3441no—
549C2×C4—3441no—
550C2×C4—3441no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—6881no—
556C2×C4—6881no—
557C2×C4C2×D4×D4311yescharacteristic
558C2×C4C22×D17211yescharacteristic
559C2×C4C22×Dic8611yescharacteristic
560C2×C4C22×Dic8611yescharacteristic
561C2×C4C2×#1062190011yescharacteristic
562C2×C4#1306337211yescharacteristic
563C8—21no—
564C8—21no—
565C8—22no—
566C8—22no—
567C8—1721no—
568C8—1721no—
569C8#1306330212yes—
570C8#1306330212yes—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22#1458352711yescharacteristic
577C22D4×D17211yescharacteristic
578C22#1458360611yescharacteristic
579C4—22no—
580C4—42no—
581C4—41no—
582C4—41no—
583C4—3441no—
584C4—3441no—
585C4—3441no—
586C4—3441no—
587C4—1721no—
588C4—1721no—
589C4—1721no—
590C4—1721no—
591C4C2×#1306330211yescharacteristic
592C4C2×#1306332511yescharacteristic
593C4#1458355311yescharacteristic
594C4D4×Dic8611yescharacteristic
595C2—21no—
596C2—21no—
597C2—42no—
598C2#1913829711yescharacteristic
599C2#1914636211yescharacteristic
600C2#1914637111yescharacteristic
subgroupG/H
centerC22D4×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1765C2
socleC22×C43D42
prime radicalC2×#41×C43C23
hypercenter#1765D43
hypocenterC43#26085
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1765

Complements

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

NH ≅ G/Ntype
1. #19145126C2semidirect
5. #19136107C2semidirect
6. #19136102C2semidirect
7. #19135944C2semidirect
8. #19135939C2semidirect
9. #19135380C2semidirect
10. #19135348C2semidirect
13. #19134763C2semidirect
132. #131×C43Q8semidirect
141. #104×C43Q8semidirect
367. C43#26085semidirect
370. #131Dic86semidirect
437. #104Dic86semidirect

Maximal subgroups

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

subgroupindex
#191451262
#191444552
#191444442
#191431952
#191361072
#191361022
#191359442
#191359392
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