Finite Group Databasebeta

← #25084168

Subgroups — #25084168

Order 11008.

550 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#19145754C211yesmaximal, characteristic, complemented
3#19143755C211yesmaximal, characteristic
4#19134172C211yesmaximal, characteristic, complemented
5#19134151C211yesmaximal, characteristic, complemented
6#19134121C211yesmaximal, characteristic, complemented
7#19134092C211yesmaximal, characteristic, complemented
8#19134055C211yesmaximal, characteristic, complemented
9#19134020C211yesmaximal, characteristic, complemented
10#19133992C211yesmaximal, characteristic, complemented
11#19133975C211yesmaximal, characteristic, complemented
12#19133386C211yesmaximal, characteristic, complemented
13#19133286C211yesmaximal, characteristic, complemented
14#19133252C211yesmaximal, characteristic, complemented
15C43×#3252C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583302C2211yescharacteristic
18#14583298—21no—
19#14583295C2211yescharacteristic
20#14583253—21no—
21#14583251C2211yescharacteristic
22#14583251C2211yescharacteristic
23#14583240—21no—
24#14583240—21no—
25#14583237—21no—
26#14583220—21no—
27#14583203—21no—
28#14583203—21no—
29#14583194C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583184C2211yescharacteristic
32#14583179C2211yescharacteristic
33#14583030C2211yescharacteristic
34Q8×C43⋊C8C2211yescharacteristic
35#14582977C2211yescharacteristic
36#14582971—21no—
37D4×C43⋊C8—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582960—21no—
40#14582952C2211yescharacteristic
41#14582952C2211yescharacteristic
42#14582926—21no—
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
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×#479—21no—
59C43×#477C2211yescharacteristic
60C43×#476C2211yescharacteristic
61C43×#470—21no—
62C43×#468—21no—
63C43×#464—21no—
64C43×#462C2211yescharacteristic
65C43×#461C2211yescharacteristic
66C43×#423C2211yescharacteristic
67C2×#10621877—21no—
68C22×C43⋊C8—21no—
69C22×C43⋊C8—21no—
70#13063325C2311yescharacteristic
71#13063325C2311yescharacteristic
72#13063317—21no—
73#13063304—21no—
74#13063304—21no—
75C4×Dic86—21no—
76C4×Dic86—21no—
77#13063284—21no—
78#13063258—21no—
79#13063258—21no—
80#13063258—21no—
81#13063258—21no—
82#13063256—21no—
83#13063256—21no—
84#13063256—21no—
85#13063256—21no—
86C4⋊(C43⋊C8)—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)D411yescharacteristic
90C4⋊(C43⋊C8)D411yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063249—21no—
96#13063249—21no—
97#13063248—21no—
98#13063248—21no—
99#13063248—21no—
100#13063248—21no—
101#13063246—21no—
102#13063246—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)D411yescharacteristic
107C22⋊(C43⋊C8)D411yescharacteristic
108#13063236—21no—
109C4×C43⋊C8—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×Q16×C43—21no—
114C2×SD16×C43—21no—
115C2×M16×C43—21no—
116C4⋊Q8×C43C2311yescharacteristic
117C4⋊Q8×C43C2311yescharacteristic
118#126×C43—21no—
119#125×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43D411yescharacteristic
122#123×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43D411yescharacteristic
126#121×C43D411yescharacteristic
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132#117×C43—21no—
133#117×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#107×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#103×C43—21no—
143#102×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—
155Q16×C43—81no—
156SD16×C43—81no—
157M16×C43—81no—
158C2×C8×C43—21no—
159C2×C8×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—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—41no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43C2×D411yescharacteristic
171C4⋊C4×C43C2×D411yescharacteristic
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—41no—
178C42×C43—21no—
179C42×C43—41no—
180C42×C43C2×D411yescharacteristic
181C42×C43C2×D411yescharacteristic
182C42×C43#4111yescharacteristic
183C42×C43C2411yescharacteristic
184C22⋊Dic43—41no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
191C4×Dic43—41no—
192#10621877—81no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—81no—
198C2×C43⋊C8—81no—
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—21no—
242C43⋊C8—41no—
243C43⋊C8—41no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246#19587—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×C43#57711yescharacteristic
264C4×C43#57711yescharacteristic
265C4×C43#57811yescharacteristic
266C4×C43#57811yescharacteristic
267Dic43—81no—
268Dic43—81no—
269#3252D4311yescharacteristic
270#3233—431no—
271#3231—431no—
272#2994—431no—
273#1703—431no—
274#1700—431no—
275#1696—431no—
276#1691—431no—
277#1684—431no—
278#1679—431no—
279#1675—431no—
280#1672—431no—
281#1574—431no—
282#1550—431no—
283#1542—431no—
284C2×C43—41no—
285C2×C43—81no—
286C2×C43#304611yescharacteristic
287C2×C43#306311yescharacteristic
288C2×C43#306711yescharacteristic
289#533—431no—
290#533C2×D4311yescharacteristic
291#529C2×D4311yescharacteristic
292#500—431no—
293#499—861no—
294#498—431no—
295#488—861no—
296#487—431no—
297#487—431no—
298#485—861no—
299#485—861no—
300#485—861no—
301#482—861no—
302#479—21no—
303#479—861no—
304#479—861no—
305#477—431no—
306#477C2×D4311yescharacteristic
307#476—431no—
308#476C2×D4311yescharacteristic
309#475—431no—
310#474—431no—
311#470—21no—
312#468—21no—
313#464—21no—
314#462C2×D4311yescharacteristic
315#461C2×D4311yescharacteristic
316#446—431no—
317C8×Q8—431no—
318#436—431no—
319#435—861no—
320C8×D4—431no—
321C8×D4—861no—
322#433—861no—
323#431—431no—
324#431—431no—
325#424—861no—
326#423C2×D4311yescharacteristic
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#1958711yescharacteristic, complemented, Sylow
341C2×Q16—21no—
342C2×SD16—21no—
343C2×M16—21no—
344C2×M16—861no—
345C22×C8—861no—
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—861no—
376#107—861no—
377#107—861no—
378#107—861no—
379#106—21no—
380#106—861no—
381#106—861no—
382#106—861no—
383#106—861no—
384C4⋊C8—21no—
385C4⋊C8—431no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—861no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#102—21no—
406#102—861no—
407#102—861no—
408C22⋊C8—431no—
409C22⋊C8—431no—
410C22⋊C8—861no—
411C22⋊C8—861no—
412C22⋊C8—861no—
413#97—861no—
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—81no—
430SD16—81no—
431M16—81no—
432M16—3441no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—431no—
436C2×C8—431no—
437C2×C8—431no—
438C2×C8—431no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8—861no—
442C2×C8—861no—
443C2×C8—3441no—
444C2×C8—3441no—
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—861no—
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#1458370811yescharacteristic
539C4#1458371011yescharacteristic
540C4#1458371411yescharacteristic
541C4#1458371511yescharacteristic
542C2—41no—
543C2—81no—
544C2#1914414911yescharacteristic
545C2#1914428811yescharacteristic
546C2#1914431211yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3252C2
socleC22×C43C2×#121
prime radical#121×C43D4
hypercenter#3252D43
hypocenterC43#19587
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3252

Complements

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

NH ≅ G/Ntype
2. #19145754C2semidirect
4. #19134172C2semidirect
5. #19134151C2semidirect
6. #19134121C2semidirect
7. #19134092C2semidirect
8. #19134055C2semidirect
9. #19134020C2semidirect
10. #19133992C2semidirect
11. #19133975C2semidirect
12. #19133386C2semidirect
13. #19133286C2semidirect
14. #19133252C2semidirect
340. C43#19587semidirect

Maximal subgroups

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

subgroupindex
#191457702
#191457542
#191437552
#191341722
#191341512
#191341212
#191340922
#191340552
#191340202
#191339922
#191339752
#191333862
#191332862
#191332522
C43×#32522
#1958743