Finite Group Databasebeta

← #25302684

Subgroups — #25302684

Order 11008.

2130 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19142976C213yesmaximal, complemented
2#19142975C211yesmaximal, characteristic, complemented
3#19142961C213yesmaximal, complemented
4#19142960C211yesmaximal, characteristic, complemented
5#19142913C213yesmaximal, complemented
6#19142911C211yesmaximal, characteristic, complemented
7#19142909C213yesmaximal, complemented
8#19142907C211yesmaximal, characteristic, complemented
9C4×#13063320C213yesmaximal, complemented
10C4×#13063319C211yesmaximal, characteristic, complemented
11C4×#13063318C213yesmaximal, complemented
12#19137081C213yesmaximal
13#19137075C213yesmaximal, complemented
14C43×D43C211yesmaximal, characteristic, complemented
15C4×#126×C43C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063320C2213yes—
18C2×#13063319C2211yescharacteristic
19C2×#13063318C2213yes—
20C2×#13063282C2213yes—
21C2×C42×D43C2213yes—
22C2×C42×D43C2213yes—
23C2×C42×D43C2211yescharacteristic
24#14582803C2213yes—
25#14582803C2213yes—
26#14582799C2213yes—
27#14582799C2213yes—
28#14582796C2213yes—
29#14582796C2213yes—
30#14582794C2213yes—
31#14582794C2213yes—
32#14582793C2213yes—
33#14582792C2213yes—
34#14582791C2213yes—
35#14582790C2213yes—
36#14582789C2213yes—
37#14582788C2213yes—
38#14582787C2213yes—
39#14582786C2213yes—
40#14582785C2213yes—
41#14582784C2213yes—
42#14582783C2213yes—
43#14582782C2213yes—
44#14582781C2213yes—
45#14582780C2213yes—
46#14582777C2213yes—
47#14582777C2213yes—
48#14582775C2213yes—
49#14582775C2213yes—
50#14582773C2213yes—
51#14582773C2213yes—
52#14582770C2213yes—
53#14582770C2213yes—
54#14582767C2211yescharacteristic
55#14582766C2213yes—
56#14582766C2213yes—
57C4×Dic43⋊C4C2213yes—
58C4×Dic43⋊C4C2213yes—
59C4×C4⋊Dic43C2213yes—
60C4×(C2×D43)⋊C4C2213yes—
61C4×(C2×D43)⋊C4C2213yes—
62C4×C22⋊Dic43C2213yes—
63C42×Dic43C2211yescharacteristic
64C42×Dic43C2213yes—
65C42×Dic43C2213yes—
66C2×#126×C43C2211yescharacteristic
67C43×#388C2213yes—
68C43×#387C2213yes—
69C43×#383C2211yescharacteristic
70C4×C4⋊C4×C43C2213yes—
71C4×C22⋊C4×C43C2213yes—
72C43×C43C2211yescharacteristic
73C2×#10621898—212no—
74C22×Dic86C2311yescharacteristic
75C22×D172C2311yescharacteristic
76C22×C22⋊D43C2311yescharacteristic
77C22×C22⋊D43C2311yescharacteristic
78C22×C4×D43C2313yes—
79C22×C4×D43C2313yes—
80C22×C4×D43C2311yescharacteristic
81C22×C4×D43C2311yescharacteristic
82#13063320—212no—
83#13063319—24no—
84#13063318—212no—
85#13063282—212no—
86C2×C4⋊Dic43C2313yes—
87C2×C4⋊Dic43C2313yes—
88C2×Dic43⋊C4C2313yes—
89C2×Dic43⋊C4C2313yes—
90C2×Dic43⋊C4C2313yes—
91C2×Dic43⋊C4C2313yes—
92C2×Dic43⋊C4C2313yes—
93C2×Dic43⋊C4C2313yes—
94C2×C22⋊Dic43C2313yes—
95C2×C22⋊Dic43C2313yes—
96C2×(C2×D43)⋊C4C2313yes—
97C2×(C2×D43)⋊C4C2313yes—
98C2×(C2×D43)⋊C4C2313yes—
99C2×(C2×D43)⋊C4C2313yes—
100C2×(C2×D43)⋊C4C2313yes—
101C2×(C2×D43)⋊C4C2313yes—
102C2×C4×Dic43C2313yes—
103C2×C4×Dic43C2313yes—
104C2×C4×Dic43C2313yes—
105C2×C4×Dic43C2313yes—
106C2×C4×Dic43C2313yes—
107C2×C4×Dic43C2313yes—
108C2×C4×Dic43C2313yes—
109C2×C4×Dic43C2313yes—
110C42×D43—212no—
111C42×D43—24no—
112C42×D43—212no—
113C43⋊#95C2313yes—
114C43⋊#95C2313yes—
115C43⋊#95C2313yes—
116C43⋊#95C2313yes—
117C43⋊#95C2313yes—
118C43⋊#95C2313yes—
119C43⋊#95C2313yes—
120C43⋊#95C2313yes—
121C43⋊#95C2313yes—
122C43⋊#95C2313yes—
123C43⋊#95C2313yes—
124C43⋊#95C2313yes—
125C23×C4×C43C2311yescharacteristic
126#126×C43—24no—
127C2×C4⋊C4×C43C2313yes—
128C2×C4⋊C4×C43C2313yes—
129C2×C22⋊C4×C43C2313yes—
130C2×C22⋊C4×C43C2313yes—
131C2×C42×C43C2313yes—
132C2×C42×C43C2313yes—
133C2×C42×C43C2313yes—
134C2×C42×C43C2311yescharacteristic
135#95×C43C2313yes—
136#95×C43C2313yes—
137#95×C43C2313yes—
138#95×C43C2313yes—
139C24×C43C2411yescharacteristic
140C23×D43C2411yescharacteristic
141C23×D43C2411yescharacteristic
142C22×C4×C43—26no—
143C22×C4×C43C2411yescharacteristic
144C22×C4×C43C2413yes—
145C22×C4×C43C2413yes—
146C22×C4×C43C2413yes—
147C22×C4×C43C2413yes—
148C22×C4×C43C2411yescharacteristic
149C2×C22⋊D43—26no—
150C2×C22⋊D43—26no—
151C22×Dic43C2411yescharacteristic
152C22×Dic43C2413yes—
153C22×Dic43C2413yes—
154C22×Dic43C2413yes—
155C22×Dic43C2413yes—
156C22×Dic43C2411yescharacteristic
157#10621898—416no—
158C2×D172—26no—
159C2×C4×D43—26no—
160C2×C4×D43—26no—
161C2×C4×D43—26no—
162C2×C4×D43—26no—
163C2×C4×D43—26no—
164C2×C4×D43—26no—
165C2×C4×D43—26no—
166C2×C4×D43#41112yes—
167C2×Dic86—26no—
168C4⋊C4×C43—26no—
169C4⋊C4×C43—26no—
170C22⋊C4×C43—26no—
171C22⋊C4×C43—26no—
172C42×C43—26no—
173C42×C43—26no—
174C42×C43—26no—
175C42×C43#4114yescomplemented
176C22⋊Dic43—26no—
177C22⋊Dic43—26no—
178(C2×D43)⋊C4—26no—
179(C2×D43)⋊C4—26no—
180(C2×D43)⋊C4—26no—
181(C2×D43)⋊C4—26no—
182(C2×D43)⋊C4—26no—
183(C2×D43)⋊C4—26no—
184C4⋊Dic43—26no—
185C4⋊Dic43—26no—
186Dic43⋊C4—26no—
187Dic43⋊C4—26no—
188Dic43⋊C4—26no—
189Dic43⋊C4—26no—
190Dic43⋊C4—26no—
191Dic43⋊C4—26no—
192C4×Dic43—26no—
193C4×Dic43—26no—
194C4×Dic43—26no—
195C4×Dic43—26no—
196C4×Dic43—26no—
197C4×Dic43—26no—
198C4×Dic43—26no—
199C4×Dic43#41112yescomplemented
200C23×C43—23no—
201C23×C43—21no—
202C23×C43—23no—
203C23×C43C2511yescharacteristic
204C22×D43—23no—
205C22×D43—21no—
206C22×D43—23no—
207C22×D43—21no—
208C22×D43—23no—
209C22×D43C2×#4116yes—
210C2×C4×C43—23no—
211C2×C4×C43—23no—
212C2×C4×C43—23no—
213C2×C4×C43—23no—
214C2×C4×C43—23no—
215C2×C4×C43—23no—
216C2×C4×C43—23no—
217C2×C4×C43—23no—
218C2×C4×C43—23no—
219C2×C4×C43—23no—
220C2×C4×C43—23no—
221C2×C4×C43—44no—
222C2×C4×C43C2×#4116yes—
223C2×C4×C43C2×#4116yes—
224C2×C4×C43C2×#4116yes—
225C22⋊D43—44no—
226C22⋊D43—44no—
227C2×Dic43—23no—
228C2×Dic43—23no—
229C2×Dic43—23no—
230C2×Dic43—23no—
231C2×Dic43—23no—
232C2×Dic43—23no—
233C2×Dic43—23no—
234C2×Dic43—23no—
235C2×Dic43—23no—
236C2×Dic43—23no—
237C2×Dic43—23no—
238C2×Dic43C2×#4116yes—
239C2×Dic43C2×#4116yes—
240C2×Dic43C2×#4116yes—
241D172—44no—
242C4×D43—224no—
243C4×D43—224no—
244C4×D43—44no—
245C4×D43#126116yescomplemented
246Dic86—44no—
247#36641—431nomaximal, Sylow
248C22×C43—41no—
249C22×C43—43no—
250C22×C43—43no—
251C22×C43C22×#4113yes—
252C22×C43C22×#4113yes—
253C22×C43C22×#4111yescharacteristic
254C2×D43—26no—
255C2×D43—26no—
256C2×D43—41no—
257C2×D43—43no—
258C2×D43—43no—
259C2×D43C2×#12614yes—
260C4×C43—26no—
261C4×C43—26no—
262C4×C43—41no—
263C4×C43—43no—
264C4×C43—43no—
265C4×C43C2×#12614yes—
266Dic43—26no—
267Dic43—26no—
268Dic43—41no—
269Dic43—43no—
270Dic43—43no—
271Dic43C2×#12614yes—
272#2863—433no—
273#2863—431no—
274#2860—433no—
275#2860—431no—
276#2852—433no—
277#2852—433no—
278#2852—431no—
279#2852—431no—
280C4×#126—433no—
281C4×#126—433no—
282C4×#126—431no—
283C4×#126D4311yescharacteristic, complemented
284#2297—433no—
285#2296—433no—
286C2×C43—431no—
287C2×C43—81no—
288C2×C43C22×#12611yescharacteristic
289C2×C43#344413yes—
290C2×C43#344413yes—
291D43—24no—
292D43—81no—
293C22×#41—431no—
294C2×#126—433no—
295C2×#126—433no—
296C2×#126—431no—
297C2×#126C2×D4311yescharacteristic
298C2×#117—433no—
299C22×C42—433no—
300C22×C42—431no—
301C22×C42—433no—
302#391—433no—
303#391—433no—
304#390—433no—
305#390—433no—
306#389—433no—
307#389—433no—
308#389—433no—
309#389—433no—
310#388—433no—
311#388—433no—
312#388—433no—
313#388—433no—
314#388—433no—
315#388—433no—
316#388—433no—
317#388C2×D4313yes—
318#387—433no—
319#387—433no—
320#387—433no—
321#387—433no—
322#387—433no—
323#387—433no—
324#387—433no—
325#387C2×D4313yes—
326#386—433no—
327#386—433no—
328#386—433no—
329#386—433no—
330#385—433no—
331#385—433no—
332#385—433no—
333#385—433no—
334#383—431no—
335#383—433no—
336#383—433no—
337#383C2×D4311yescharacteristic
338C4×C4⋊C4—433no—
339C4×C4⋊C4—433no—
340C4×C4⋊C4—433no—
341C4×C4⋊C4C2×D4313yes—
342C4×C22⋊C4—433no—
343C4×C22⋊C4—433no—
344C4×C22⋊C4—433no—
345C4×C22⋊C4C2×D4313yes—
346C43—433no—
347C43—433no—
348C43—431no—
349C43C2×D4311yescharacteristic
350C43#3664111yescharacteristic, complemented, Sylow
351C2×#41—8612no—
352C22×Q8—431no—
353C22×D4—431no—
354C22×D4—431no—
355C22×D4—431no—
356C23×C4—431no—
357C23×C4—433no—
358C23×C4—433no—
359C23×C4—431no—
360C23×C4C22×D4311yescharacteristic
361#126—24no—
362#126—8612no—
363#126—8612no—
364#126—864no—
365#117—8612no—
366C2×C4⋊C4—433no—
367C2×C4⋊C4—433no—
368C2×C4⋊C4—433no—
369C2×C4⋊C4—433no—
370C2×C4⋊C4—433no—
371C2×C4⋊C4—433no—
372C2×C4⋊C4—433no—
373C2×C4⋊C4—433no—
374C2×C4⋊C4C22×D4313yes—
375C2×C4⋊C4C22×D4313yes—
376C2×C22⋊C4—433no—
377C2×C22⋊C4—433no—
378C2×C22⋊C4—433no—
379C2×C22⋊C4—433no—
380C2×C22⋊C4—433no—
381C2×C22⋊C4—433no—
382C2×C22⋊C4—433no—
383C2×C22⋊C4—433no—
384C2×C22⋊C4C22×D4313yes—
385C2×C22⋊C4C22×D4313yes—
386C2×C42—433no—
387C2×C42—433no—
388C2×C42—433no—
389C2×C42—433no—
390C2×C42—433no—
391C2×C42—433no—
392C2×C42—433no—
393C2×C42—433no—
394C2×C42—8612no—
395C2×C42—8612no—
396C2×C42—864no—
397C2×C42C22×D4313yes—
398C2×C42C22×D4313yes—
399C2×C42C22×D4313yes—
400C2×C42C22×D4311yescharacteristic
401#95—433no—
402#95—433no—
403#95—433no—
404#95—433no—
405#95—433no—
406#95—433no—
407#95—433no—
408#95—433no—
409#95—433no—
410#95—433no—
411#95—433no—
412#95—433no—
413#95C22×D4313yes—
414#95C22×D4313yes—
415#95C22×D4313yes—
416#95C22×D4313yes—
417C24—431no—
418C24—431no—
419C24C23×D4311yescharacteristic
420#41—17216no—
421C2×Q8—866no—
422C2×D4—866no—
423C2×D4—866no—
424C2×D4—866no—
425C22×C4—26no—
426C22×C4—431no—
427C22×C4—4312no—
428C22×C4—433no—
429C22×C4—433no—
430C22×C4—431no—
431C22×C4—433no—
432C22×C4—433no—
433C22×C4—866no—
434C22×C4—866no—
435C22×C4—866no—
436C22×C4—866no—
437C22×C4—866no—
438C22×C4—866no—
439C22×C4—866no—
440C22×C4C23×D4311yescharacteristic
441C22×C4C23×D4313yes—
442C22×C4C23×D4313yes—
443C22×C4C23×D4313yes—
444C22×C4C23×D4313yes—
445C22×C4C23×D4311yescharacteristic
446C4⋊C4—26no—
447C4⋊C4—26no—
448C4⋊C4—866no—
449C4⋊C4—866no—
450C4⋊C4—866no—
451C4⋊C4—866no—
452C4⋊C4—866no—
453C4⋊C4—866no—
454C4⋊C4—866no—
455C4⋊C4—866no—
456C22⋊C4—26no—
457C22⋊C4—26no—
458C22⋊C4—866no—
459C22⋊C4—866no—
460C22⋊C4—866no—
461C22⋊C4—866no—
462C22⋊C4—866no—
463C22⋊C4—866no—
464C22⋊C4—866no—
465C22⋊C4—866no—
466C42—26no—
467C42—26no—
468C42—26no—
469C42—4312no—
470C42—866no—
471C42—866no—
472C42—866no—
473C42—866no—
474C42—866no—
475C42—866no—
476C42—866no—
477C42#1062189814yescomplemented
478C23—23no—
479C23—23no—
480C23—21no—
481C23—436no—
482C23—863no—
483C23—861no—
484C23—863no—
485C23—863no—
486C23—861no—
487C23C24×D4311yescharacteristic
488Q8—1724no—
489D4—1724no—
490D4—1724no—
491D4—1724no—
492C2×C4—23no—
493C2×C4—23no—
494C2×C4—23no—
495C2×C4—23no—
496C2×C4—23no—
497C2×C4—23no—
498C2×C4—23no—
499C2×C4—23no—
500C2×C4—23no—
501C2×C4—23no—
502C2×C4—23no—
503C2×C4—44no—
504C2×C4—436no—
505C2×C4—4316no—
506C2×C4—436no—
507C2×C4—436no—
508C2×C4—8624no—
509C2×C4—8624no—
510C2×C4—863no—
511C2×C4—863no—
512C2×C4—863no—
513C2×C4—863no—
514C2×C4—863no—
515C2×C4—863no—
516C2×C4—863no—
517C2×C4—863no—
518C2×C4—863no—
519C2×C4—863no—
520C2×C4—863no—
521C2×C4—1724no—
522C2×C4#41×D4316yes—
523C2×C4#41×D4316yes—
524C2×C4C2×#1062189816yes—
525C22—41no—
526C22—43no—
527C22—43no—
528C22—434no—
529C22—866no—
530C22—866no—
531C22—1721no—
532C22—1723no—
533C22—1723no—
534C22C2×#41×D4313yes—
535C22C2×#41×D4313yes—
536C22C22×#1062189811yescharacteristic
537C4—26no—
538C4—26no—
539C4—41no—
540C4—43no—
541C4—43no—
542C4—434no—
543C4—866no—
544C4—866no—
545C4—1721no—
546C4—1723no—
547C4—1723no—
548C4#126×D4314yes—
549C2—81no—
550C2—864no—
551C2—3441no—
552C2C2×#126×D4311yescharacteristic
553C2#1914788813yes—
554C2#1914788913yes—
subgroupG/H
centerC22×C4C23×D43
commutator, socle, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC4×#126×C43C2
prime radicalC22×#10621898C22
hypercenterC4×#126D43
hypocenterC43#36641
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C4×#126

Complements

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

NH ≅ G/Ntype
1. #19142976C2semidirect
2. #19142975C2semidirect
3. #19142961C2semidirect
4. #19142960C2semidirect
5. #19142913C2semidirect
6. #19142911C2semidirect
7. #19142909C2semidirect
8. #19142907C2semidirect
9. C4×#13063320C2semidirect
10. C4×#13063319C2semidirect
11. C4×#13063318C2semidirect
13. #19137075C2semidirect
14. C43×D43C2semidirect
15. C4×#126×C43C2semidirect
175. C42×C43#41semidirect
199. C4×Dic43#41semidirect
245. C4×D43#126semidirect
283. C4×#126D43semidirect
350. C43#36641semidirect
477. C42#10621898semidirect

Maximal subgroups

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

subgroupindex
#191429762
#191429752
#191429612
#191429602
#191429132
#191429112
#191429092
#191429072
C4×#130633202
C4×#130633192
C4×#130633182
#191370812
#191370752
C43×D432
C4×#126×C432
#3664143