Finite Group Databasebeta

← #25082093

Subgroups — #25082093

Order 11008.

608 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145747C211yesmaximal, characteristic, complemented
2#19144409C211yesmaximal, characteristic
3#19144386C211yesmaximal, characteristic
4#19143705C211yesmaximal, characteristic
5#19134055C211yesmaximal, characteristic, complemented
6#19134053C211yesmaximal, characteristic, complemented
7#19134049C211yesmaximal, characteristic, complemented
8#19134047C211yesmaximal, characteristic, complemented
9#19133997C211yesmaximal, characteristic, complemented
10#19133993C211yesmaximal, characteristic, complemented
11#19133991C211yesmaximal, characteristic, complemented
12#19133368C211yesmaximal, characteristic, complemented
13#19133282C211yesmaximal, characteristic, complemented
14#333×D43C211yesmaximal, characteristic, complemented
15C43×#1676C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17C4⋊Q8×D43C2211yescharacteristic
18C4×#10621902C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583251C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583236—21no—
23#14583236—21no—
24#14583208—21no—
25#14583202—21no—
26#14583194C2211yescharacteristic
27#14583193—21no—
28#14583193—21no—
29#14583190C2211yescharacteristic
30#14583186C2211yescharacteristic
31#14583186C2211yescharacteristic
32#14583184C2211yescharacteristic
33#14583182—21no—
34#14583180C2211yescharacteristic
35#14583178—21no—
36Q8×C43⋊C8C2211yescharacteristic
37C8×D172—21no—
38C8×D172C2211yescharacteristic
39#14582964—21no—
40#14582964C2211yescharacteristic
41#14582950—21no—
42#14582950C2211yescharacteristic
43#14582940—21no—
44#14582936—21no—
45#14582921C2211yescharacteristic
46C4⋊C8×D43—21no—
47C4⋊C8×D43C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582899—21no—
50#14582894—21no—
51#14582652C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582648C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582646C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#500C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#477C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#333C2211yescharacteristic
67C2×#10621902D411yescharacteristic
68C2×Q8×D43—21no—
69C2×#10621872—21no—
70C2×C8×D43—21no—
71C2×C8×D43—21no—
72C2×C8×D43—21no—
73C2×C8×D43—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063324—21no—
77#13063324—21no—
78#13063323—21no—
79#13063316—21no—
80#13063305—21no—
81#13063301—21no—
82Q8×Dic43—21no—
83Q8×Dic43D411yescharacteristic
84#13063290—21no—
85C4×D172—21no—
86C4×D172C2311yescharacteristic
87#13063287—21no—
88#13063287D411yescharacteristic
89#13063283—21no—
90#13063283—21no—
91#13063283D411yescharacteristic
92C4⋊C4×D43—21no—
93C4⋊C4×D43—21no—
94C42×D43—21no—
95C42×D43C2311yescharacteristic
96#13063259—21no—
97#13063258—21no—
98#13063258—21no—
99#13063258—21no—
100#13063257—21no—
101#13063256—21no—
102#13063256—21no—
103#13063256—21no—
104C4⋊(C43⋊C8)—21no—
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8D411yescharacteristic
112Dic43⋊C8D411yescharacteristic
113#13063250—21no—
114#13063250—21no—
115#13063249—21no—
116#13063249—21no—
117#13063248—21no—
118#13063248—21no—
119#13063247—21no—
120#13063247—21no—
121#13063245—21no—
122#13063245—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8D411yescharacteristic
126(C2×D43)⋊C8D411yescharacteristic
127C4×C43⋊C8—21no—
128C4×C43⋊C8C2311yescharacteristic
129C4⋊Q8×C43C2311yescharacteristic
130C4⋊Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132#107×C43—21no—
133#107×C43—21no—
134#107×C43—21no—
135#107×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147#10621902—22no—
148#10621902Q1614yes—
149Q8×D43—82no—
150C2×D172—21no—
151C2×D172C2×D411yescharacteristic
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—41no—
156C2×C4×D43C2×D411yescharacteristic
157C2×C4×D43C2×D411yescharacteristic
158C2×C4×D43#4111yescharacteristic
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—41no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43C2×D411yescharacteristic
173C42×C43—21no—
174C42×C43C2411yescharacteristic
175(C2×D43)⋊C4—21no—
176(C2×D43)⋊C4—21no—
177(C2×D43)⋊C4—21no—
178(C2×D43)⋊C4—41no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—41no—
185C4⋊Dic43C2×D411yescharacteristic
186Dic43⋊C4—41no—
187Dic43⋊C4—41no—
188Dic43⋊C4—41no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—41no—
192C4×Dic43C2×D411yescharacteristic
193C4×Dic43C2×D411yescharacteristic
194C4×Dic43#4111yescharacteristic
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C2×D411yescharacteristic
199C2×C43⋊C8C2×D411yescharacteristic
200#10621872—42no—
201C8×D43—42no—
202C8×D43—81no—
203C8×D43—81no—
204C8×D43—81no—
205C22×D43—21no—
206C22×D43#12111yescharacteristic
207Q8×C43—21no—
208Q8×C43—81no—
209Q8×C43—81no—
210Q8×C43C2×Q1612yes—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C2×#4111yescharacteristic
218C2×Dic43—21no—
219C2×Dic43—41no—
220C2×Dic43—41no—
221C2×Dic43#12111yescharacteristic
222C2×Dic43#12111yescharacteristic
223C2×Dic43#12111yescharacteristic
224D172—24no—
225D172—21no—
226D172C2×Q1612yes—
227C4×D43—21no—
228C4×D43—21no—
229C4×D43—24no—
230C4×D43—41no—
231C4×D43—41no—
232C4×D43—41no—
233C4×D43—81no—
234C4×D43—82no—
235C4×D43C2×Q1612yes—
236C4×D43#13512yes—
237Dic86—41no—
238Dic86—41no—
239Dic86—82no—
240Dic86—81no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43—41no—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251#19417—431nomaximal, Sylow
252C22×C43C2×#12111yescharacteristic
253C2×D43—21no—
254C2×D43—21no—
255C2×D43—22no—
256C2×D43—41no—
257C2×D43—41no—
258C2×D43#46712yes—
259C4×C43—22no—
260C4×C43—21no—
261C4×C43—41no—
262C4×C43—81no—
263C4×C43—81no—
264C4×C43C22×Q1611yescharacteristic
265C4×C43C2×#13511yescharacteristic
266C4×C43#57711yescharacteristic
267C4×C43#57811yescharacteristic
268Dic43—21no—
269Dic43—21no—
270Dic43—41no—
271Dic43—81no—
272Dic43—81no—
273Dic43#46712yes—
274#3230—431no—
275#3079—431no—
276#3076—431no—
277#2988—431no—
278#1684—431no—
279#1684—431no—
280#1683—431no—
281#1683—431no—
282#1676—431no—
283#1676D4311yescharacteristic, complemented
284#1675—431no—
285#1675—431no—
286#1571—431no—
287#1550—431no—
288C2×#333—431no—
289C2×C43#304611yescharacteristic
290C2×C43C2×#46711yescharacteristic
291C2×C43#306811yescharacteristic
292D43—22no—
293D43—42no—
294#533—431no—
295C2×C4⋊Q8—431no—
296C4×#41—431no—
297#500—431no—
298#500C2×D4311yescharacteristic
299#487—431no—
300#487—431no—
301#484—861no—
302#484—861no—
303#479—861no—
304#478—861no—
305#477—431no—
306#477—861no—
307#477—861no—
308#477C2×D4311yescharacteristic
309#477C2×D4311yescharacteristic
310#476—431no—
311#476—431no—
312#476—431no—
313#475—431no—
314#475—861no—
315#474—431no—
316#474—861no—
317C8×Q8—431no—
318C8×Q8C2×D4311yescharacteristic
319C8×D4—431no—
320C8×D4—431no—
321C8×D4—861no—
322C8×D4—861no—
323#431—431no—
324#431—861no—
325#428—861no—
326#427—861no—
327#423—431no—
328C2×C4⋊C8—431no—
329C2×C4⋊C8—431no—
330C2×C4⋊C8—861no—
331#417—861no—
332#416—861no—
333#335—431no—
334#335—431no—
335#335—431no—
336#335C2×D4311yescharacteristic
337#333—431no—
338#333—431no—
339#333—431no—
340#333—431no—
341#333C2×D4311yescharacteristic
342#333C2×D4311yescharacteristic
343#332—431no—
344#332—431no—
345C43#1941711yescharacteristic, complemented, Sylow
346C2×#41—431no—
347C22×Q8—861no—
348C2×M16—861no—
349C22×C8—861no—
350C22×C8—861no—
351C22×C8—861no—
352C22×C8—861no—
353C4⋊Q8—431no—
354C4⋊Q8—431no—
355C4⋊Q8—861no—
356C4⋊Q8—861no—
357C4⋊Q8—861no—
358C4⋊Q8C22×D4311yescharacteristic
359C4⋊Q8C22×D4311yescharacteristic
360#125—861no—
361C22⋊Q8—861no—
362C22⋊Q8—861no—
363C4×Q8—431no—
364C4×Q8—861no—
365C4×Q8—861no—
366C4×Q8C22×D4311yescharacteristic
367C4×D4—431no—
368C4×D4—431no—
369C4×D4—861no—
370C4×D4—861no—
371#117—431no—
372#117—861no—
373#117—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C42—431no—
377C2×C42—861no—
378#107—21no—
379#107—21no—
380#107—21no—
381#107—21no—
382#107—861no—
383#107—861no—
384#107—861no—
385#107—861no—
386#106—861no—
387#106—861no—
388#106—861no—
389#106—861no—
390C4⋊C8—21no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—431no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—861no—
397C4⋊C8—861no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8C22×D4311yescharacteristic
401C4⋊C8C22×D4311yescharacteristic
402C4⋊C8C22×D4311yescharacteristic
403#103—21no—
404#103—21no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#102—861no—
412#102—861no—
413#102—861no—
414#102—861no—
415C22⋊C8—431no—
416C22⋊C8—431no—
417C22⋊C8—861no—
418C22⋊C8—861no—
419C4×C8—21no—
420C4×C8—431no—
421C4×C8—861no—
422C4×C8C22×D4311yescharacteristic
423#41—434no—
424#41—862no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8—3442no—
430C2×Q8—1721no—
431C2×Q8D4×D4311yescharacteristic
432C2×D4—431no—
433C2×D4—861no—
434C22×C4—431no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—1721no—
441M16—1722no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—431no—
446C2×C8—431no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—3441no—
451C2×C8—3441no—
452C2×C8—3441no—
453C2×C8—1722no—
454C2×C8D4×D4311yescharacteristic
455C2×C8D4×D4311yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—431no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—1721no—
468C4⋊C4—1721no—
469C4⋊C4—1721no—
470C4⋊C4—1721no—
471C4⋊C4D4×D4311yescharacteristic
472C22⋊C4—861no—
473C22⋊C4—861no—
474C22⋊C4—861no—
475C22⋊C4—1721no—
476C42—21no—
477C42—431no—
478C42—431no—
479C42—431no—
480C42—861no—
481C42—861no—
482C42—1721no—
483C42C23×D4311yescharacteristic
484C23—431no—
485C23—861no—
486Q8—21no—
487Q8—81no—
488Q8—81no—
489Q8—3441no—
490Q8—3442no—
491Q8—1721no—
492Q8—1721no—
493Q8Q16×D4312yes—
494D4—432no—
495D4—864no—
496D4—861no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—431no—
502C2×C4—432no—
503C2×C4—432no—
504C2×C4—431no—
505C2×C4—431no—
506C2×C4—864no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—3441no—
511C2×C4—3442no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4—1721no—
517C2×C4C2×D4×D4311yescharacteristic
518C2×C4C2×D4×D4311yescharacteristic
519C2×C4#41×D4311yescharacteristic
520C8—21no—
521C8—21no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—861no—
526C8—861no—
527C8—1721no—
528C8—1721no—
529C8—1721no—
530C22—432no—
531C22—861no—
532C22—861no—
533C22—862no—
534C22—1721no—
535C22—1721no—
536C22#121×D4311yescharacteristic
537C4—21no—
538C4—22no—
539C4—41no—
540C4—81no—
541C4—81no—
542C4—432no—
543C4—861no—
544C4—861no—
545C4—3441no—
546C4—3441no—
547C4—1721no—
548C4C2×Q16×D4311yescharacteristic
549C4#135×D4311yescharacteristic
550C4#1458370811yescharacteristic
551C4#1458371211yescharacteristic
552C2—862no—
553C2—1722no—
554C2#1914414211yescharacteristic
555C2#467×D4311yescharacteristic
556C2#1914432111yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1676C2
socleC22×C43C2×#121
prime radicalC2×#10621902D4
hypercenter#1676D43
hypocenterC43#19417
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1676

Complements

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

NH ≅ G/Ntype
1. #19145747C2semidirect
5. #19134055C2semidirect
6. #19134053C2semidirect
7. #19134049C2semidirect
8. #19134047C2semidirect
9. #19133997C2semidirect
10. #19133993C2semidirect
11. #19133991C2semidirect
12. #19133368C2semidirect
13. #19133282C2semidirect
14. #333×D43C2semidirect
15. C43×#1676C2semidirect
283. #1676D43semidirect
345. C43#19417semidirect

Maximal subgroups

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

subgroupindex
#191457472
#191444092
#191443862
#191437052
#191340552
#191340532
#191340492
#191340472
#191339972
#191339932
#191339912
#191333682
#191332822
#333×D432
C43×#16762
#1941743