Finite Group Databasebeta

← #25155539

Subgroups — #25155539

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#19144453C211yesmaximal, characteristic
2#19144442C211yesmaximal, characteristic
3#19143192C211yesmaximal, characteristic
4#19136108C211yesmaximal, characteristic, complemented
5#19136103C211yesmaximal, characteristic, complemented
6#19135942C211yesmaximal, characteristic, complemented
7#19135937C211yesmaximal, characteristic, complemented
8#19135380C211yesmaximal, characteristic, complemented
9#19135349C211yesmaximal, characteristic, complemented
10#19134825C211yesmaximal, characteristic
11#19134818C211yesmaximal, characteristic
12#19134760C211yesmaximal, characteristic, complemented
13#19134655C211yesmaximal, characteristic
14#19134441C211yesmaximal, characteristic
15C43×#3163C211yesmaximal, characteristic, complemented
16C2×#13063331C2211yescharacteristic
17#14583379C2211yescharacteristic
18#14583379C2211yescharacteristic
19#14583203—21no—
20#14583203—21no—
21#14583196—21no—
22#14583196—21no—
23#14583191—21no—
24#14583186—21no—
25#14583181—21no—
26#14583176—21no—
27C2×#13063261C2211yescharacteristic
28#14582942C2211yescharacteristic
29#14582942C2211yescharacteristic
30#14582942C2211yescharacteristic
31#14582942C2211yescharacteristic
32#14582938—21no—
33#14582938—21no—
34#14582936—21no—
35C2×#13063259C2211yescharacteristic
36C2×#13063258C2211yescharacteristic
37#107×D43—21no—
38C2×#13063256C2211yescharacteristic
39#14582926C2211yescharacteristic
40#14582926C2211yescharacteristic
41C2×#13063251C2211yescharacteristic
42#14582898C2211yescharacteristic
43#14582898C2211yescharacteristic
44#14582893C2211yescharacteristic
45C2×#13063235C2211yescharacteristic
46#14582768C2211yescharacteristic
47#14582764C2211yescharacteristic
48#14582668C2211yescharacteristic
49#14582668C2211yescharacteristic
50#14582667C2211yescharacteristic
51#14582667C2211yescharacteristic
52#14582663C2211yescharacteristic
53#14582658C2211yescharacteristic
54#14582658C2211yescharacteristic
55#14582658C2211yescharacteristic
56C43×#544C2211yescharacteristic
57C43×#544C2211yescharacteristic
58C43×#501—21no—
59C43×#501—21no—
60C43×#499—21no—
61C43×#498—21no—
62C43×#428C2211yescharacteristic
63C43×#428C2211yescharacteristic
64C43×#427C2211yescharacteristic
65C2×#106×C43C2211yescharacteristic
66C43×#405C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063331—22no—
69#13063331Q814yescomplemented
70C2×#10621877C2311yescharacteristic
71C2×#10621877C2311yescharacteristic
72C2×#10621877C2311yescharacteristic
73C2×#10621872—21no—
74C22×C43⋊C8C2311yescharacteristic
75C2×C8×D43—21no—
76C4×Dic86—21no—
77C4×Dic86—21no—
78C4×D172—21no—
79C4×D172—21no—
80(C22⋊D43)⋊C4—41no—
81(C22⋊D43)⋊C4—41no—
82#13063283—21no—
83#13063283—21no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—41no—
87C4⋊C4×D43—21no—
88C4⋊C4×D43—21no—
89C2×C4×Dic43C2311yescharacteristic
90#13063261—22no—
91#13063259—21no—
92#13063259—21no—
93#13063258—21no—
94#13063258—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258—21no—
98#13063258—21no—
99#13063256—21no—
100#13063256—21no—
101#13063256—21no—
102#13063256—21no—
103#13063256—21no—
104#13063256—21no—
105C4⋊(C43⋊C8)—21no—
106C4⋊(C43⋊C8)—21no—
107C4⋊(C43⋊C8)—21no—
108C4⋊(C43⋊C8)—21no—
109#13063251Q814yescomplemented
110#13063248—21no—
111#13063248—21no—
112#13063248D411yescharacteristic
113#13063248D411yescharacteristic
114#13063245—21no—
115#13063245—21no—
116#13063245D411yescharacteristic
117#13063245D411yescharacteristic
118#13063235—22no—
119C43⋊#95—41no—
120C2×M16×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C4⋊Q8×C43—21no—
123C4⋊Q8×C43—21no—
124C4⋊Q8×C43—21no—
125C4⋊Q8×C43—21no—
126#125×C43—21no—
127#125×C43—21no—
128#125×C43—21no—
129#125×C43—21no—
130C22⋊Q8×C43—41no—
131C22⋊Q8×C43—41no—
132#117×C43C2311yescharacteristic
133#117×C43C2311yescharacteristic
134#117×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137#107×C43—21no—
138#107×C43—21no—
139#107×C43D411yescharacteristic
140#107×C43D411yescharacteristic
141#106×C43—21no—
142#106×C43—21no—
143#106×C43—21no—
144#106×C43—21no—
145#106×C43D411yescharacteristic
146#106×C43D411yescharacteristic
147#97×C43—21no—
148C4×C8×C43—21no—
149C2×Q8×C43—41no—
150C2×Q8×C43—41no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43C2411yescharacteristic
154C2×C22⋊D43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158#10621898—21no—
159#10621898—21no—
160#10621898C2×Q812yes—
161#10621898C2×Q812yes—
162C2×D172C2×D411yescharacteristic
163C2×C4×D43—21no—
164C2×C4×D43—41no—
165C2×C4×D43—41no—
166C2×Dic86C2×D411yescharacteristic
167M16×C43—21no—
168M16×C43C2×Q812yes—
169C2×C8×C43—21no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×Q812yes—
173C2×C8×C43#4112yes—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—41no—
179C4⋊C4×C43—41no—
180C4⋊C4×C43—41no—
181C4⋊C4×C43—41no—
182C4⋊C4×C43—41no—
183C4⋊C4×C43—41no—
184C4⋊C4×C43C2×D411yescharacteristic
185C4⋊C4×C43C2×D411yescharacteristic
186C4⋊C4×C43C2×D411yescharacteristic
187C4⋊C4×C43C2×D411yescharacteristic
188C4⋊C4×C43C2×D411yescharacteristic
189C4⋊C4×C43C2×D411yescharacteristic
190C22⋊C4×C43—21no—
191C22⋊C4×C43—21no—
192C22⋊C4×C43—21no—
193C42×C43—21no—
194C42×C43—21no—
195C42×C43—21no—
196(C2×D43)⋊C4—41no—
197(C2×D43)⋊C4—41no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202Dic43⋊C4—41no—
203Dic43⋊C4—41no—
204Dic43⋊C4—82no—
205C4×Dic43—21no—
206C4×Dic43—41no—
207C4×Dic43—41no—
208C4×Dic43C2×Q812yes—
209#10621877—21no—
210#10621877—21no—
211#10621877—21no—
212#10621877—21no—
213#10621877—21no—
214#10621877C2×Q812yes—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8C2×D411yescharacteristic
221C2×C43⋊C8C2×D411yescharacteristic
222#10621872—24no—
223C8×D43—24no—
224C23×C43H(5,𝔽2)11yescharacteristic
225C22×D43—21no—
226Q8×C43—161no—
227Q8×C43—161no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—81no—
237C2×C4×C43—81no—
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×Q811yescharacteristic
241C2×C4×C43C22×Q811yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C432−1+411yescharacteristic
244C22⋊D43—22no—
245C22⋊D43—22no—
246C2×Dic43—21no—
247C2×Dic43—22no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—81no—
253C2×Dic43—81no—
254D172—21no—
255D172C4⋊Q812yes—
256C4×D43—22no—
257C4×D43—22no—
258C4×D43—161no—
259C4×D43—161no—
260Dic86—21no—
261Dic86C4⋊Q812yes—
262C8×C43—22no—
263C8×C43C22⋊Q812yes—
264C8×C43C22⋊Q812yes—
265C43⋊C8—22no—
266C43⋊C8—21no—
267C43⋊C8—21no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270#26085—431nomaximal, Sylow
271C22×C43—21no—
272C22×C43—21no—
273C22×C43#54411yescharacteristic
274C22×C43D4211yescharacteristic
275C22×C43#55411yescharacteristic
276C2×D43—22no—
277C2×D43—41no—
278C2×D43—41no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—81no—
286C4×C43—81no—
287C4×C43C2×C22⋊Q811yescharacteristic
288C4×C43C2×C4⋊Q811yescharacteristic
289C4×C43#54711yescharacteristic
290C4×C43D4×Q811yescharacteristic
291Dic43—22no—
292Dic43—42no—
293Dic43—81no—
294Dic43—81no—
295#3163D4311yescharacteristic, complemented
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#1765—431no—
310C2×C43—21no—
311C2×C43—21no—
312C2×C43#244011yescharacteristic
313C2×C43#328811yescharacteristic
314C2×C43#328911yescharacteristic
315D43—42no—
316C2×#131—431no—
317#544C2×D4311yescharacteristic
318#544C2×D4311yescharacteristic
319#520—431no—
320#520—431no—
321#501—21no—
322#501—21no—
323#499—21no—
324#498—21no—
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—861no—
339#428—861no—
340#428C2×D4311yescharacteristic
341#428C2×D4311yescharacteristic
342#427—861no—
343#427C2×D4311yescharacteristic
344C2×#107—431no—
345C2×#107—431no—
346C2×#107—861no—
347C2×#106—431no—
348C2×#106C2×D4311yescharacteristic
349#424—431no—
350#424—431no—
351C2×#104—431no—
352#417—431no—
353#417—431no—
354#416—431no—
355#405C2×D4311yescharacteristic
356C2×#97—431no—
357#384—431no—
358#382—431no—
359#343—431no—
360#343—431no—
361#343—431no—
362#343—431no—
363#341—431no—
364#339—431no—
365#339—431no—
366#339—431no—
367C43#2608511yescharacteristic, complemented, Sylow
368C2×#41—431no—
369#131—434no—
370#131—862no—
371C2×M16—431no—
372C2×M16—431no—
373C2×M16—431no—
374C2×M16—861no—
375C2×M16C22×D4311yescharacteristic
376C22×C8—431no—
377C22×C8—861no—
378C22×C8C22×D4311yescharacteristic
379C4⋊Q8—21no—
380C4⋊Q8—21no—
381C4⋊Q8—21no—
382C4⋊Q8—21no—
383#125—21no—
384#125—21no—
385#125—21no—
386#125—21no—
387C22⋊Q8—41no—
388C22⋊Q8—41no—
389C4×Q8—861no—
390C4×Q8—861no—
391C4×D4—861no—
392C4×D4—861no—
393C4×D4—1721no—
394C4×D4—1721no—
395#117—861no—
396#117—861no—
397#117C22×D4311yescharacteristic
398#117C22×D4311yescharacteristic
399#117C22×D4311yescharacteristic
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—1721no—
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C42—431no—
408#108—862no—
409#107—21no—
410#107—21no—
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#107C22⋊D4311yescharacteristic
420#107C22⋊D4311yescharacteristic
421#106—21no—
422#106—21no—
423#106—21no—
424#106—21no—
425#106—861no—
426#106—861no—
427#106—861no—
428#106—861no—
429#106—861no—
430#106—861no—
431#106C22⋊D4311yescharacteristic
432#106C22⋊D4311yescharacteristic
433C4⋊C8—861no—
434C4⋊C8—861no—
435C4⋊C8—861no—
436C4⋊C8—861no—
437#104—434no—
438#103—431no—
439#103—431no—
440#103—861no—
441#103—861no—
442#102—431no—
443#102—431no—
444#102—861no—
445#102—861no—
446#97—21no—
447#97—862no—
448C4×C8—21no—
449#95—1721no—
450#41—432no—
451#41—432no—
452#41—861no—
453#41—861no—
454C2×Q8—41no—
455C2×Q8—41no—
456C2×Q8—431no—
457C2×D4—431no—
458C2×D4—861no—
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—432no—
470M16—861no—
471M16—864no—
472M16—861no—
473M16—861no—
474M16—861no—
475M16—861no—
476M16Q8×D4312yes—
477C2×C8—21no—
478C2×C8—431no—
479C2×C8—431no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—864no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8Q8×D4312yes—
487C2×C8#1062190212yes—
488C2×C8C2×C22⋊D4311yescharacteristic
489C2×C8C2×C22⋊D4311yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—3442no—
505C4⋊C4—1721no—
506C4⋊C4—1721no—
507C4⋊C4D4×D4311yescharacteristic
508C4⋊C4D4×D4311yescharacteristic
509C4⋊C4C2×C22⋊D4311yescharacteristic
510C4⋊C4C2×C22⋊D4311yescharacteristic
511C4⋊C4C2×C22⋊D4311yescharacteristic
512C4⋊C4C2×C22⋊D4311yescharacteristic
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—1721no—
517C22⋊C4—1721no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—432no—
522C42—861no—
523C42—1721no—
524C42—1721no—
525C23—861no—
526C23#1306337011yescharacteristic
527Q8—161no—
528Q8—161no—
529Q8—432no—
530Q8—861no—
531D4—432no—
532D4—862no—
533D4—862no—
534D4—861no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—861no—
546C2×C4—862no—
547C2×C4—862no—
548C2×C4—862no—
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×C22⋊D4311yescharacteristic
559C2×C4C2×Q8×D4311yescharacteristic
560C2×C4C2×Q8×D4311yescharacteristic
561C2×C4C2×#1062190211yescharacteristic
562C2×C4#1306337311yescharacteristic
563C8—22no—
564C8—861no—
565C8—861no—
566C8—862no—
567C8—1721no—
568C8—1721no—
569C8#1306330112yes—
570C8#1306330112yes—
571C22—21no—
572C22—21no—
573C22—862no—
574C22—1721no—
575C22—1721no—
576C22#1458352611yescharacteristic
577C22D4×C22⋊D4311yescharacteristic
578C22#1458361011yescharacteristic
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4—862no—
588C4—3441no—
589C4—3441no—
590C4—1722no—
591C4C2×#1306330111yescharacteristic
592C4C4⋊Q8×D4311yescharacteristic
593C4#1458355211yescharacteristic
594C4Q8×C22⋊D4311yescharacteristic
595C2—21no—
596C2—21no—
597C2—1722no—
598C2#1913829311yescharacteristic
599C2#1914635711yescharacteristic
600C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3163C2
socleC22×C43D42
prime radicalC2×#10621898C23
hypercenter#3163D43
hypocenterC43#26085
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #3163

Complements

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

NH ≅ G/Ntype
4. #19136108C2semidirect
5. #19136103C2semidirect
6. #19135942C2semidirect
7. #19135937C2semidirect
8. #19135380C2semidirect
9. #19135349C2semidirect
12. #19134760C2semidirect
15. C43×#3163C2semidirect
69. #13063331Q8semidirect
109. #13063251Q8semidirect
295. #3163D43semidirect
367. C43#26085semidirect

Maximal subgroups

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

subgroupindex
#191444532
#191444422
#191431922
#191361082
#191361032
#191359422
#191359372
#191353802
#191353492
#191348252
#191348182
#191347602
#191346552
#191344412
C43×#31632
#2608543