Finite Group Databasebeta

← #25079612

Subgroups — #25079612

Order 11008.

614 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145314C211yesmaximal, characteristic, complemented
2#19144655C211yesmaximal, characteristic
3#19143615C211yesmaximal, characteristic, complemented
4#19134168C211yesmaximal, characteristic, complemented
5#19134130C211yesmaximal, characteristic, complemented
6#19134116C211yesmaximal, characteristic, complemented
7#19134062C211yesmaximal, characteristic, complemented
8#19134051C211yesmaximal, characteristic, complemented
9#19134013C211yesmaximal, characteristic, complemented
10#19133997C211yesmaximal, characteristic, complemented
11#19133945C211yesmaximal, characteristic, complemented
12#19133345C211yesmaximal, characteristic, complemented
13#19133305C211yesmaximal, characteristic, complemented
14#19133288C211yesmaximal, characteristic, complemented
15C43×#3076C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583302C2211yescharacteristic
18#14583273C2211yescharacteristic
19#14583249C2211yescharacteristic
20#14583247C2211yescharacteristic
21#14583223—21no—
22#14583194C2211yescharacteristic
23#14583189C2211yescharacteristic
24#14583147—21no—
25#14583147—21no—
26#14583099C2211yescharacteristic
27#14583094C2211yescharacteristic
28#14583044—21no—
29Q8×C43⋊C8C2211yescharacteristic
30Q8×C43⋊C8C2211yescharacteristic
31#14582997—21no—
32#14582997—21no—
33C4×#10621884—21no—
34C4×#10621882—21no—
35#14582977—21no—
36#14582977—21no—
37#14582977C2211yescharacteristic
38#14582977C2211yescharacteristic
39#14582956—21no—
40#14582956C2211yescharacteristic
41#14582952C2211yescharacteristic
42C4×#10621877—21no—
43C4×#10621877C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C43×#479—21no—
59C43×#478—21no—
60C43×#477C2211yescharacteristic
61C43×#476C2211yescharacteristic
62C43×#475C2211yescharacteristic
63C43×#474C2211yescharacteristic
64C43×#427—21no—
65C2×C4⋊C8×C43C2211yescharacteristic
66C43×#416—21no—
67C2×#10621898—21no—
68C2×#10621884—21no—
69C2×#10621884—21no—
70C2×#10621884—21no—
71C2×#10621882—21no—
72C2×#10621877—21no—
73C2×#10621877—21no—
74C2×#10621877D411yescharacteristic
75C2×#10621877D411yescharacteristic
76#13063325C2311yescharacteristic
77#13063322C2311yescharacteristic
78#13063313—21no—
79#13063299—21no—
80#13063299—21no—
81C4×D172—21no—
82C4×D172—21no—
83#13063258—21no—
84#13063258—21no—
85#13063258—21no—
86#13063256—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)C2311yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93#13063249—21no—
94#13063249—21no—
95#13063249—21no—
96#13063246—21no—
97#13063245—21no—
98#13063245—21no—
99#13063245—21no—
100#13063245—21no—
101C22⋊(C43⋊C8)—21no—
102C22⋊(C43⋊C8)—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105#13063236—21no—
106#13063236D411yescharacteristic
107#13063236D411yescharacteristic
108C4×C43⋊C8—21no—
109C4×C43⋊C8—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×#41×C43D411yescharacteristic
114C22×C8×C43—21no—
115C4⋊Q8×C43C2311yescharacteristic
116C4⋊Q8×C43C2311yescharacteristic
117#125×C43—21no—
118C22⋊Q8×C43—21no—
119C22⋊Q8×C43—21no—
120C4×Q8×C43—21no—
121C4×Q8×C43—21no—
122C4×Q8×C43D411yescharacteristic
123C4×Q8×C43C2311yescharacteristic
124C4×D4×C43—21no—
125C4×D4×C43—21no—
126C4×D4×C43D411yescharacteristic
127C4×D4×C43C2311yescharacteristic
128#117×C43—21no—
129#117×C43—21no—
130#117×C43D411yescharacteristic
131C2×C42×C43—21no—
132C2×C42×C43C2311yescharacteristic
133#107×C43—21no—
134#107×C43—21no—
135#106×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
142#102×C43—21no—
143#102×C43—21no—
144#41×C43—22no—
145#41×C43—41no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43#4111yescharacteristic
157C2×C22⋊D43—41no—
158#10621898—82no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×C4×D43—41no—
163C2×Dic86—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—42no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—41no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—41no—
185C42×C43C2×D411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43#4111yescharacteristic
188C42×C43C2411yescharacteristic
189#10621884—42no—
190#10621884—42no—
191#10621884—42no—
192#10621882—42no—
193(C2×D43)⋊C4—41no—
194(C2×D43)⋊C4—41no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197#10621877—22no—
198#10621877—41no—
199#10621877—42no—
200#10621877—42no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C23×C43—21no—
210C23×C43#12111yescharacteristic
211C22×D43—41no—
212Q8×C43—21no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—81no—
216Q8×C43#13712yes—
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—42no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—42no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—81no—
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43#12111yescharacteristic
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C22⋊D43—82no—
241C2×Dic43—41no—
242D172—41no—
243D172—41no—
244D172—41no—
245D172—41no—
246D172—81no—
247C4×D43—82no—
248Dic86—81no—
249C8×C43—41no—
250C8×C43—41no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8#13512yes—
259#19183—431nomaximal, Sylow
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43C2×#12111yescharacteristic
267C2×D43—81no—
268C2×D43—81no—
269C2×D43—81no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—22no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43C2×#13511yescharacteristic
280C4×C43C2×#13711yescharacteristic
281C4×C43#57511yescharacteristic
282C4×C43#57511yescharacteristic
283Dic43—81no—
284#3182—431no—
285#3106—431no—
286#3076D4311yescharacteristic, complemented
287#2971—431no—
288#1703—431no—
289#1697—431no—
290#1695—431no—
291#1685—431no—
292#1684—431no—
293#1678—431no—
294#1676—431no—
295#1666—431no—
296#1565—431no—
297#1554—431no—
298#1551—431no—
299C2×C43—41no—
300C2×C43—81no—
301C2×C43#303511yescharacteristic
302C2×C43#305611yescharacteristic
303C2×C43#306811yescharacteristic
304D43—161no—
305#533C2×D4311yescharacteristic
306#532—431no—
307C4×#41C2×D4311yescharacteristic
308#500—431no—
309#492—431no—
310#487—431no—
311#486—431no—
312#482—861no—
313#479—21no—
314#478—21no—
315#477—431no—
316#477C2×D4311yescharacteristic
317#476—431no—
318#476C2×D4311yescharacteristic
319#475C2×D4311yescharacteristic
320#474C2×D4311yescharacteristic
321#468—861no—
322#468—861no—
323#460—431no—
324#459—431no—
325#449—861no—
326C8×Q8—431no—
327C8×Q8—431no—
328#440—861no—
329#440—861no—
330C4×SD16—861no—
331C4×D8—861no—
332#436—431no—
333#436—431no—
334#436—861no—
335#436—861no—
336#432—431no—
337#432—861no—
338#431—431no—
339#427—21no—
340C2×C4⋊C8C2×D4311yescharacteristic
341#416—21no—
342C4×M16—431no—
343C4×M16—861no—
344#335—431no—
345#335—431no—
346#334—431no—
347#334—431no—
348#333—431no—
349#333—431no—
350#333—431no—
351#333—431no—
352#332—431no—
353#332—431no—
354#331—431no—
355#331—431no—
356C43#1918311yescharacteristic, complemented, Sylow
357C2×#41—861no—
358C2×#41C22⋊D4311yescharacteristic
359C2×SD16—861no—
360C2×SD16—861no—
361C2×SD16—861no—
362C2×D8—861no—
363C2×M16—431no—
364C2×M16—431no—
365C2×M16—861no—
366C2×M16—861no—
367C22×C8—21no—
368C4⋊Q8—431no—
369C4⋊Q8C22×D4311yescharacteristic
370C4⋊Q8C22×D4311yescharacteristic
371#127—431no—
372#125—21no—
373#124—861no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376#121—861no—
377#121—861no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8C22⋊D4311yescharacteristic
381C4×Q8C22×D4311yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—861no—
385C4×D4—861no—
386C4×D4C22⋊D4311yescharacteristic
387C4×D4C22×D4311yescharacteristic
388#117—21no—
389#117—21no—
390#117C22⋊D4311yescharacteristic
391C2×C42—21no—
392C2×C42C22×D4311yescharacteristic
393#107—21no—
394#107—21no—
395#107—861no—
396#107—861no—
397#107—861no—
398#106—21no—
399#106—21no—
400#106—861no—
401C4⋊C8—21no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—861no—
407C4⋊C8—861no—
408C4⋊C8C22×D4311yescharacteristic
409C4⋊C8C22×D4311yescharacteristic
410#103—21no—
411#103—21no—
412#103—861no—
413#103—861no—
414#103—861no—
415#102—21no—
416#102—21no—
417#102—861no—
418#102—861no—
419#102—861no—
420#102—861no—
421#102—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—431no—
427#97—431no—
428#97—861no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—861no—
432C4×C8—861no—
433C4×C8—861no—
434#41—22no—
435#41—41no—
436#41—3442no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—861no—
440C2×Q8C2×C22⋊D4311yescharacteristic
441C2×D4—21no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C2×D4—1721no—
446C2×D4C2×C22⋊D4311yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—1721no—
451C22×C4D4×D4311yescharacteristic
452C22×C4#1062190011yescharacteristic
453C22×C4C2×C22⋊D4311yescharacteristic
454SD16—1722no—
455SD16—1722no—
456SD16—1722no—
457D8—1722no—
458M16—862no—
459M16—1722no—
460M16—1721no—
461M16—1722no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—42no—
465C2×C8—431no—
466C2×C8—431no—
467C2×C8—431no—
468C2×C8—431no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—861no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4C2×C22⋊D4311yescharacteristic
484C4⋊C4C2×C22⋊D4311yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—1721no—
490C22⋊C4—1721no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—41no—
495C42D4×D4311yescharacteristic
496C42#1062190011yescharacteristic
497C42C2×C22⋊D4311yescharacteristic
498C42C23×D4311yescharacteristic
499C23—21no—
500C23—1721no—
501C23#1306329711yescharacteristic
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—81no—
506Q8—3441no—
507Q8#1306335612yes—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—3441no—
512D4—3442no—
513D4—1721no—
514D4—1721no—
515D4—1721no—
516D4—1721no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—81no—
531C2×C4—3442no—
532C2×C4—1721no—
533C2×C4#1306329711yescharacteristic
534C2×C4#1306329711yescharacteristic
535C2×C4#1306329711yescharacteristic
536C2×C4C2×D4×D4311yescharacteristic
537C2×C4C22×C22⋊D4311yescharacteristic
538C2×C4C2×#1062190011yescharacteristic
539C8—41no—
540C8—41no—
541C8—432no—
542C8—861no—
543C8—861no—
544C8—861no—
545C8—1721no—
546C8—1721no—
547C8—1721no—
548C8—1721no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—3441no—
556C22—3441no—
557C22—3441no—
558C22C2×#1306329711yescharacteristic
559C4—21no—
560C4—22no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—3441no—
569C4#135×D4311yescharacteristic
570C4C2×#1306335611yescharacteristic
571C4#1458369611yescharacteristic
572C4#1458369711yescharacteristic
573C2—41no—
574C2—81no—
575C2—6881no—
576C2#1914404611yescharacteristic
577C2#1914422111yescharacteristic
578C2#1914432511yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3076C2
socleC22×C43C2×#121
prime radical#19144655C2
hypercenter#3076D43
hypocenterC43#19183
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #19145314C2semidirect
3. #19143615C2semidirect
4. #19134168C2semidirect
5. #19134130C2semidirect
6. #19134116C2semidirect
7. #19134062C2semidirect
8. #19134051C2semidirect
9. #19134013C2semidirect
10. #19133997C2semidirect
11. #19133945C2semidirect
12. #19133345C2semidirect
13. #19133305C2semidirect
14. #19133288C2semidirect
15. C43×#3076C2semidirect
286. #3076D43semidirect
356. C43#19183semidirect

Maximal subgroups

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

subgroupindex
#191453142
#191446552
#191436152
#191341682
#191341302
#191341162
#191340622
#191340512
#191340132
#191339972
#191339452
#191333452
#191333052
#191332882
C43×#30762
#1918343