Finite Group Databasebeta

← #25080029

Subgroups — #25080029

Order 11008.

562 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145770C211yesmaximal, characteristic
2#19145177C211yesmaximal, characteristic, complemented
3#19143571C211yesmaximal, characteristic
4#19134121C211yesmaximal, characteristic, complemented
5#19134116C211yesmaximal, characteristic, complemented
6#19134087C211yesmaximal, characteristic, complemented
7#19134082C211yesmaximal, characteristic, complemented
8#19134055C211yesmaximal, characteristic, complemented
9#19134051C211yesmaximal, characteristic, complemented
10#19134048C211yesmaximal, characteristic, complemented
11#19134044C211yesmaximal, characteristic, complemented
12#19133341C211yesmaximal, characteristic, complemented
13#19133305C211yesmaximal, characteristic, complemented
14#19133303C211yesmaximal, characteristic, complemented
15C43×#3233C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583302C2211yescharacteristic
18#14583298—21no—
19#14583278C2211yescharacteristic
20#14583253—21no—
21#14583251C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583237—21no—
24#14583220—21no—
25#14583194C2211yescharacteristic
26#14583189C2211yescharacteristic
27#14583184C2211yescharacteristic
28#14583179C2211yescharacteristic
29#14583138—21no—
30#14583138—21no—
31#14583030C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33C4×#10621885—21no—
34C4×#10621885—21no—
35#14582977C2211yescharacteristic
36#14582971—21no—
37D4×C43⋊C8—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582960—21no—
40#14582956C2211yescharacteristic
41#14582952C2211yescharacteristic
42#14582855—21no—
43C2×C4×C43⋊C8C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582644C2211yescharacteristic
55#14582644C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#499—21no—
59C43×#488—21no—
60C43×#485—21no—
61C43×#482—21no—
62C43×#477C2211yescharacteristic
63C43×#476C2211yescharacteristic
64C43×#475C2211yescharacteristic
65C43×#474C2211yescharacteristic
66C43×#431C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621877—21no—
70C22×C43⋊C8—21no—
71C22×C43⋊C8D411yescharacteristic
72C22×C43⋊C8D411yescharacteristic
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063317—21no—
76#13063304—21no—
77#13063304—21no—
78C4×Dic86—21no—
79C4×Dic86—21no—
80#13063284—21no—
81#13063258—21no—
82#13063258—21no—
83#13063258—21no—
84#13063258—21no—
85#13063256—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#13063249—21no—
97#13063248—21no—
98#13063248—21no—
99#13063246—21no—
100#13063246—21no—
101C22⋊(C43⋊C8)—21no—
102C22⋊(C43⋊C8)—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105#13063236—21no—
106#13063236—21no—
107C4×C43⋊C8—21no—
108C4×C43⋊C8—21no—
109C4×C43⋊C8D411yescharacteristic
110C4×C43⋊C8D411yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C4⋊Q8×C43C2311yescharacteristic
114C4⋊Q8×C43C2311yescharacteristic
115#126×C43—21no—
116#125×C43—21no—
117#125×C43D411yescharacteristic
118#124×C43D411yescharacteristic
119#123×C43—21no—
120C22⋊Q8×C43—21no—
121C22⋊Q8×C43—21no—
122C22⋊Q8×C43D411yescharacteristic
123#121×C43D411yescharacteristic
124C4×Q8×C43—21no—
125C4×Q8×C43—21no—
126C4×Q8×C43C2311yescharacteristic
127C4×D4×C43—21no—
128C4×D4×C43C2311yescharacteristic
129#117×C43—21no—
130#117×C43—21no—
131C2×C42×C43C2311yescharacteristic
132#107×C43—21no—
133#107×C43—21no—
134#106×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43#4111yescharacteristic
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—41no—
166C4⋊C4×C43—41no—
167C4⋊C4×C43C2×D411yescharacteristic
168C4⋊C4×C43C2×D411yescharacteristic
169C22⋊C4×C43—21no—
170C22⋊C4×C43—21no—
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—41no—
175C42×C43—21no—
176C42×C43—41no—
177C42×C43C2×D411yescharacteristic
178C42×C43C2×D411yescharacteristic
179C42×C43#4111yescharacteristic
180C42×C43C2411yescharacteristic
181C22⋊Dic43—41no—
182#10621885—42no—
183#10621885—42no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188Dic43⋊C4—41no—
189Dic43⋊C4—41no—
190C4×Dic43—41no—
191#10621877—42no—
192C2×C43⋊C8—22no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—41no—
198C2×C43⋊C8—42no—
199C2×C43⋊C8C2×D411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C23×C43—21no—
204C23×C43#12111yescharacteristic
205Q8×C43—21no—
206Q8×C43—21no—
207Q8×C43—41no—
208Q8×C43—41no—
209Q8×C43—81no—
210D4×C43—21no—
211D4×C43—21no—
212D4×C43—42no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×Dic43—41no—
232C2×Dic43—41no—
233Dic86—41no—
234Dic86—41no—
235Dic86—81no—
236C8×C43—41no—
237C8×C43—41no—
238C43⋊C8—21no—
239C43⋊C8—21no—
240C43⋊C8—21no—
241C43⋊C8—41no—
242C43⋊C8—41no—
243C43⋊C8—41no—
244C43⋊C8—41no—
245C43⋊C8#13512yes—
246#19226—431nomaximal, Sylow
247C22×C43—21no—
248C22×C43—21no—
249C22×C43—21no—
250C22×C43—41no—
251C22×C43—41no—
252C22×C43—41no—
253C22×C43C2×#12111yescharacteristic
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—21no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—81no—
262C4×C43—81no—
263C4×C43C2×#13511yescharacteristic
264C4×C43#57511yescharacteristic
265C4×C43#57811yescharacteristic
266C4×C43#57811yescharacteristic
267Dic43—81no—
268Dic43—81no—
269#3233—431no—
270#3233D4311yescharacteristic
271#3170—431no—
272#2966—431no—
273#1696—431no—
274#1695—431no—
275#1690—431no—
276#1689—431no—
277#1684—431no—
278#1684—431no—
279#1683—431no—
280#1683—431no—
281#1564—431no—
282#1554—431no—
283#1554—431no—
284C2×C43—41no—
285C2×C43—81no—
286C2×C43#303511yescharacteristic
287C2×C43#305911yescharacteristic
288C2×C43#306711yescharacteristic
289#533—431no—
290#533C2×D4311yescharacteristic
291#529C2×D4311yescharacteristic
292#500—431no—
293#499—21no—
294#499—861no—
295#494—431no—
296#488—21no—
297#488—861no—
298#487—431no—
299#487—431no—
300#485—21no—
301#485—861no—
302#482—21no—
303#482—861no—
304#477—431no—
305#477C2×D4311yescharacteristic
306#476—431no—
307#476C2×D4311yescharacteristic
308#475—431no—
309#475C2×D4311yescharacteristic
310#474—431no—
311#474C2×D4311yescharacteristic
312#467—861no—
313#467—861no—
314#446—431no—
315C8×Q8—431no—
316C4×Q16—861no—
317C4×Q16—861no—
318#436—431no—
319#435—861no—
320C8×D4—431no—
321C8×D4—861no—
322#433—861no—
323#432—431no—
324#431—431no—
325#431C2×D4311yescharacteristic
326#405—861no—
327C2×C4×C8—431no—
328#335—431no—
329#335—431no—
330#334—431no—
331#334—431no—
332#333—431no—
333#333—431no—
334#333—431no—
335#333—431no—
336#332—431no—
337#332—431no—
338#332—431no—
339#332—431no—
340C43#1922611yescharacteristic, complemented, Sylow
341C2×Q16—861no—
342C2×Q16—861no—
343C2×M16—861no—
344C22×C8—431no—
345C22×C8—431no—
346C22×C8—861no—
347C4⋊Q8—431no—
348C4⋊Q8—431no—
349C4⋊Q8C22×D4311yescharacteristic
350C4⋊Q8C22×D4311yescharacteristic
351#126—21no—
352#125—21no—
353#125—861no—
354#125C22⋊D4311yescharacteristic
355#124C22⋊D4311yescharacteristic
356#123—21no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—861no—
360C22⋊Q8—861no—
361C22⋊Q8C22⋊D4311yescharacteristic
362#121C22⋊D4311yescharacteristic
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—861no—
366C4×Q8—861no—
367C4×Q8C22×D4311yescharacteristic
368C4×D4—21no—
369C4×D4C22×D4311yescharacteristic
370#117—21no—
371#117—21no—
372#117—861no—
373C2×C42C22×D4311yescharacteristic
374#107—21no—
375#107—21no—
376#107—861no—
377#107—861no—
378#107—861no—
379#107—861no—
380#106—21no—
381#106—21no—
382#106—861no—
383#106—861no—
384C4⋊C8—431no—
385C4⋊C8—431no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—861no—
389C4⋊C8—861no—
390C4⋊C8C22×D4311yescharacteristic
391C4⋊C8C22×D4311yescharacteristic
392#103—21no—
393#103—21no—
394#103—861no—
395#103—861no—
396#103—861no—
397#103—861no—
398#103—861no—
399#103—861no—
400#102—21no—
401#102—21no—
402#102—861no—
403#102—861no—
404C22⋊C8—21no—
405C22⋊C8—861no—
406C22⋊C8—861no—
407C22⋊C8—861no—
408C22⋊C8—861no—
409#97—861no—
410#97—861no—
411C4×C8—21no—
412C4×C8—431no—
413C4×C8—431no—
414C4×C8—431no—
415C4×C8—431no—
416C4×C8—861no—
417C4×C8—861no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—861no—
421C2×Q8—861no—
422C2×Q8C2×C22⋊D4311yescharacteristic
423C2×D4—21no—
424C2×D4C2×C22⋊D4311yescharacteristic
425C22×C4—21no—
426C22×C4D4×D4311yescharacteristic
427C22×C4#1062190011yescharacteristic
428C22×C4C2×C22⋊D4311yescharacteristic
429Q16—1722no—
430Q16—1722no—
431M16—1722no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—431no—
435C2×C8—431no—
436C2×C8—431no—
437C2×C8—431no—
438C2×C8—862no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8—861no—
442C2×C8—861no—
443C2×C8—1721no—
444C2×C8—1722no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—1721no—
460C4⋊C4—1721no—
461C4⋊C4C2×C22⋊D4311yescharacteristic
462C4⋊C4C2×C22⋊D4311yescharacteristic
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—41no—
469C22⋊C4—1721no—
470C42—21no—
471C42—41no—
472C42—1721no—
473C42D4×D4311yescharacteristic
474C42#1062190011yescharacteristic
475C42C2×C22⋊D4311yescharacteristic
476C42C23×D4311yescharacteristic
477C23—21no—
478C23#1306329711yescharacteristic
479Q8—21no—
480Q8—21no—
481Q8—41no—
482Q8—41no—
483Q8—81no—
484Q8—3441no—
485Q8—1721no—
486Q8—1721no—
487D4—21no—
488D4—21no—
489D4—42no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—1721no—
503C2×C4—1721no—
504C2×C4#1306329711yescharacteristic
505C2×C4#1306329711yescharacteristic
506C2×C4#1306329711yescharacteristic
507C2×C4C2×D4×D4311yescharacteristic
508C2×C4C22×C22⋊D4311yescharacteristic
509C2×C4C2×#1062190011yescharacteristic
510C8—41no—
511C8—41no—
512C8—432no—
513C8—861no—
514C8—861no—
515C8—861no—
516C8—1721no—
517C8—1721no—
518C8—1721no—
519C8—1721no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22C2×#1306329711yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—81no—
535C4—81no—
536C4—3441no—
537C4—3441no—
538C4#135×D4311yescharacteristic
539C4#1458369611yescharacteristic
540C4#1458371411yescharacteristic
541C4#1458371411yescharacteristic
542C2—41no—
543C2—81no—
544C2#1914404611yescharacteristic
545C2#1914424711yescharacteristic
546C2#1914431211yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3233C2
socleC22×C43C2×#121
prime radical#121×C43D4
hypercenter#3233D43
hypocenterC43#19226
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3233

Complements

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

NH ≅ G/Ntype
2. #19145177C2semidirect
4. #19134121C2semidirect
5. #19134116C2semidirect
6. #19134087C2semidirect
7. #19134082C2semidirect
8. #19134055C2semidirect
9. #19134051C2semidirect
10. #19134048C2semidirect
11. #19134044C2semidirect
12. #19133341C2semidirect
13. #19133305C2semidirect
14. #19133303C2semidirect
340. C43#19226semidirect

Maximal subgroups

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

subgroupindex
#191457702
#191451772
#191435712
#191341212
#191341162
#191340872
#191340822
#191340552
#191340512
#191340482
#191340442
#191333412
#191333052
#191333032
C43×#32332
#1922643