Finite Group Databasebeta

← #25067238

Subgroups — #25067238

Order 11008.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145202C211yesmaximal, characteristic
2#19143689C211yesmaximal, characteristic, complemented
3#19133502C211yesmaximal, characteristic, complemented
4#19133497C211yesmaximal, characteristic, complemented
5#19133490C211yesmaximal, characteristic, complemented
6#19133483C211yesmaximal, characteristic, complemented
7#19133412C211yesmaximal, characteristic, complemented
8#19133407C211yesmaximal, characteristic, complemented
9C8×#10621885C211yesmaximal, characteristic, complemented
10C8×#10621883C211yesmaximal, characteristic, complemented
11#19133360C211yesmaximal, characteristic, complemented
12#19133055C211yesmaximal, characteristic
13#19133049C211yesmaximal, characteristic, complemented
14#19132876C211yesmaximal, characteristic, complemented
15C43×#2993C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583309C411yescharacteristic
18#14583294C411yescharacteristic
19#14583269C411yescharacteristic
20#14583258C411yescharacteristic
21#14583155C411yescharacteristic
22#14583155C411yescharacteristic
23#14583143C411yescharacteristic
24#14583143C411yescharacteristic
25#14583029C2211yescharacteristic
26#14583029C2211yescharacteristic
27#14583028—21no—
28#14583028—21no—
29C8×Dic86C2211yescharacteristic
30C8×Dic86C2211yescharacteristic
31C4×#10621885C2211yescharacteristic
32C4×#10621885C2211yescharacteristic
33C4×#10621883C2211yescharacteristic
34C4×#10621883C2211yescharacteristic
35#14582957—21no—
36#14582957—21no—
37#14582956C2211yescharacteristic
38C4×#10621877C2211yescharacteristic
39C2×C4×C43⋊C8C2211yescharacteristic
40#14582651C2211yescharacteristic
41#14582651C2211yescharacteristic
42#14582649C2211yescharacteristic
43#14582649C2211yescharacteristic
44Q8⋊(C43⋊C8)C2211yescharacteristic
45Q8⋊(C43⋊C8)C2211yescharacteristic
46#14582629C2211yescharacteristic
47#14582629C2211yescharacteristic
48#14582629C2211yescharacteristic
49#14582629C2211yescharacteristic
50D4⋊(C43⋊C8)C2211yescharacteristic
51D4⋊(C43⋊C8)C2211yescharacteristic
52#14582621C2211yescharacteristic
53#14582621C2211yescharacteristic
54C8×C43⋊C8C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C43×#529C2211yescharacteristic
57C43×#446C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436—21no—
60C43×#436C2211yescharacteristic
61C43×#435—21no—
62C8×D4×C43C2211yescharacteristic
63C43×#433—21no—
64C43×#431C2211yescharacteristic
65C43×#424—21no—
66C43×#423C2211yescharacteristic
67C2×#10621885C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621883C2×C411yescharacteristic
70C2×#10621883C2×C411yescharacteristic
71C2×#10621877C2×C411yescharacteristic
72C2×#10621877C2×C411yescharacteristic
73C22×C43⋊C8—21no—
74#13063325C2×C411yescharacteristic
75#13063325C2×C411yescharacteristic
76#13063317—21no—
77#13063304—21no—
78#13063304C2×C411yescharacteristic
79#13063304C2×C411yescharacteristic
80C4×Dic86—21no—
81C4×Dic86C2311yescharacteristic
82C4×Dic86C2311yescharacteristic
83#13063284—21no—
84#13063258C2×C411yescharacteristic
85#13063258C2×C411yescharacteristic
86#13063256C2×C411yescharacteristic
87#13063256C2×C411yescharacteristic
88C4⋊(C43⋊C8)C2311yescharacteristic
89C4⋊(C43⋊C8)C2311yescharacteristic
90Dic43⋊C8—21no—
91Dic43⋊C8—21no—
92Dic43⋊C8—21no—
93Dic43⋊C8—21no—
94#13063249C2×C411yescharacteristic
95#13063249C2×C411yescharacteristic
96#13063248C2×C411yescharacteristic
97#13063248C2×C411yescharacteristic
98#13063248C2×C411yescharacteristic
99#13063248C2×C411yescharacteristic
100#13063246C2×C411yescharacteristic
101#13063246C2×C411yescharacteristic
102C22⋊(C43⋊C8)—21no—
103#13063236—21no—
104#13063236C2×C411yescharacteristic
105#13063236C2×C411yescharacteristic
106#13063235—21no—
107#13063235—21no—
108C4×C43⋊C8—21no—
109C4×C43⋊C8C2311yescharacteristic
110C4×C43⋊C8C2311yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C8×Dic43—21no—
114C8×Dic43—21no—
115C2×M16×C43—21no—
116C2×M16×C43—21no—
117C22×C8×C43—21no—
118#126×C43—21no—
119#125×C43C2×C411yescharacteristic
120#124×C43C2×C411yescharacteristic
121#123×C43—21no—
122C22⋊Q8×C43C2×C411yescharacteristic
123#121×C43C2×C411yescharacteristic
124C4×Q8×C43C2311yescharacteristic
125C4×D4×C43—21no—
126C4×D4×C43C2311yescharacteristic
127#117×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—21no—
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43D411yescharacteristic
133C4⋊C8×C43D411yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43C22×C411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C2×Dic86—21no—
152C2×Dic86C22×C411yescharacteristic
153C2×Dic86C22×C411yescharacteristic
154M16×C43—81no—
155M16×C43—81no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—81no—
159C2×C8×C43C2×D411yescharacteristic
160C2×C8×C43C2×D411yescharacteristic
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43C22×C411yescharacteristic
168C4⋊C4×C43C22×C411yescharacteristic
169C22⋊C4×C43—21no—
170C22⋊C4×C43—21no—
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C42×C43—21no—
175C42×C43C22×C411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43#4111yescharacteristic
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180C22⋊Dic43—21no—
181#10621885—22no—
182#10621885—22no—
183#10621883—22no—
184#10621883—22no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43C22×C411yescharacteristic
189C4⋊Dic43C22×C411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196#10621877—22no—
197#10621877—22no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—42no—
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C22×C411yescharacteristic
207C23×C43—21no—
208C23×C43C4×D411yescharacteristic
209Q8×C43—21no—
210Q8×C43—21no—
211D4×C43—21no—
212D4×C43—21no—
213D4×C43—81no—
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—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43C4×D411yescharacteristic
225C2×C4×C43C4×D411yescharacteristic
226C2×C4×C43C4×D411yescharacteristic
227C2×C4×C43C23×C411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234Dic86—21no—
235Dic86—21no—
236Dic86—21no—
237Dic86—21no—
238Dic86—81no—
239C8×C43—21no—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—41no—
244C8×C43—41no—
245C43⋊C8—22no—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8#13112yes—
252C43⋊C8#13112yes—
253#17969—431nomaximal, Sylow
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43C2×C4×D411yescharacteristic
261C4×C43—21no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43C2×#13111yescharacteristic
269C4×C43C2×#13111yescharacteristic
270C4×C43#57711yescharacteristic
271C4×C43#57811yescharacteristic
272Dic43—41no—
273Dic43—41no—
274Dic43—41no—
275Dic43—41no—
276#3172—431no—
277#2993D4311yescharacteristic
278#2985—431no—
279#1593—431no—
280#1592—431no—
281#1591—431no—
282#1590—431no—
283#1579—431no—
284SD16⋊C8—431no—
285C8×Q16—431no—
286C8×SD16—431no—
287#1569—431no—
288#1494—431no—
289#1493—431no—
290C8×M16—431no—
291C2×C43—41no—
292C2×C43—81no—
293C2×C43#293111yescharacteristic
294C2×C43#294711yescharacteristic
295C2×C43#295611yescharacteristic
296#533—431no—
297#529C2×D4311yescharacteristic
298#501—431no—
299#497—431no—
300#491—431no—
301#489—431no—
302#470—431no—
303#470—431no—
304#468—431no—
305#468—431no—
306#446—431no—
307#446—431no—
308#446—861no—
309#446—861no—
310#446C2×D4311yescharacteristic
311C8×Q8—431no—
312C8×Q8—431no—
313C8×Q8C2×D4311yescharacteristic
314C4×Q16—431no—
315C4×Q16—431no—
316C4×SD16—431no—
317C4×SD16—431no—
318#436—21no—
319#436C2×D4311yescharacteristic
320#435—21no—
321C8×D4C2×D4311yescharacteristic
322#433—21no—
323#433—861no—
324#433—861no—
325#432—431no—
326#431C2×D4311yescharacteristic
327#424—21no—
328#423C2×D4311yescharacteristic
329C4×M16—431no—
330C2×C4×C8—431no—
331#335—431no—
332#335—431no—
333#334—431no—
334#334—431no—
335Q8⋊C8—431no—
336Q8⋊C8—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8—431no—
341D4⋊C8—431no—
342D4⋊C8—431no—
343#322—431no—
344#322—431no—
345C82—431no—
346C82—431no—
347C43#1796911yescharacteristic, complemented, Sylow
348C2×Q16—431no—
349C2×Q16—431no—
350C2×SD16—431no—
351C2×SD16—431no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—431no—
355C2×M16—431no—
356C22×C8—21no—
357C22×C8—861no—
358C4⋊Q8—431no—
359C4⋊Q8—431no—
360#126—21no—
361#125—861no—
362#125C4×D4311yescharacteristic
363#124C4×D4311yescharacteristic
364#123—21no—
365C22⋊Q8—431no—
366C22⋊Q8—431no—
367C22⋊Q8—861no—
368C22⋊Q8C4×D4311yescharacteristic
369#121C4×D4311yescharacteristic
370C4×Q8—431no—
371C4×Q8—431no—
372C4×Q8—861no—
373C4×Q8C22×D4311yescharacteristic
374C4×D4—21no—
375C4×D4C22×D4311yescharacteristic
376#117—21no—
377#117—861no—
378C2×C42C22×D4311yescharacteristic
379#107—431no—
380#107—431no—
381#106—431no—
382#106—431no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—861no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8C22⋊D4311yescharacteristic
393C4⋊C8C22⋊D4311yescharacteristic
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396#103—431no—
397#103—431no—
398#103—431no—
399#103—431no—
400#103—431no—
401#103—431no—
402#102—431no—
403#102—431no—
404C22⋊C8—21no—
405C22⋊C8—21no—
406C22⋊C8—861no—
407C22⋊C8C22⋊D4311yescharacteristic
408C22⋊C8C22⋊D4311yescharacteristic
409#97—21no—
410#97—431no—
411#97—431no—
412#97—861no—
413#97—861no—
414#97—861no—
415C4×C8—21no—
416C4×C8—431no—
417C4×C8—431no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8C22×D4311yescharacteristic
424C4×C8C22×D4311yescharacteristic
425C2×Q8—431no—
426C2×Q8—431no—
427C2×Q8—861no—
428C2×Q8C2×C4×D4311yescharacteristic
429C2×D4—21no—
430C2×D4C2×C4×D4311yescharacteristic
431C22×C4—21no—
432C22×C4C2×C4×D4311yescharacteristic
433C22×C4#1062189811yescharacteristic
434C22×C4C2×C22⋊D4311yescharacteristic
435Q16—862no—
436Q16—862no—
437SD16—862no—
438SD16—862no—
439M16—81no—
440M16—81no—
441M16—862no—
442M16—862no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—81no—
446C2×C8—431no—
447C2×C8—431no—
448C2×C8—431no—
449C2×C8—431no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—1722no—
455C2×C8C2×C22⋊D4311yescharacteristic
456C2×C8C2×C22⋊D4311yescharacteristic
457C2×C8C2×C22⋊D4311yescharacteristic
458C2×C8C2×C22⋊D4311yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—431no—
464C4⋊C4—431no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4C2×C4×D4311yescharacteristic
473C4⋊C4C2×C4×D4311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—861no—
480C22⋊C4—861no—
481C42—21no—
482C42—861no—
483C42—861no—
484C42C2×C4×D4311yescharacteristic
485C42#1062189811yescharacteristic
486C42C2×C22⋊D4311yescharacteristic
487C42C23×D4311yescharacteristic
488C23—21no—
489C23C4×C22⋊D4311yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—861no—
493Q8—861no—
494Q8—861no—
495Q8—861no—
496Q8—3441no—
497D4—21no—
498D4—21no—
499D4—81no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4C4×C22⋊D4311yescharacteristic
515C2×C4C4×C22⋊D4311yescharacteristic
516C2×C4C4×C22⋊D4311yescharacteristic
517C2×C4C22×C4×D4311yescharacteristic
518C2×C4C22×C22⋊D4311yescharacteristic
519C2×C4C2×#1062189811yescharacteristic
520C8—21no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—432no—
527C8—432no—
528C8—862no—
529C8—861no—
530C8—861no—
531C8—1721no—
532C8—1721no—
533C8—1721no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22C2×C4×C22⋊D4311yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—1721no—
549C4—1721no—
550C4—1721no—
551C4—1721no—
552C4#131×D4311yescharacteristic
553C4#131×D4311yescharacteristic
554C4#1458371011yescharacteristic
555C4#1458371411yescharacteristic
556C2—41no—
557C2—81no—
558C2#1914330511yescharacteristic
559C2#1914343411yescharacteristic
560C2#1914350211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2993C2
socleC22×C43C2×C4×D4
prime radical#121×C43C2×C4
cosocleC42×C43C24
hypercenter#2993D43
hypocenterC43#17969
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #19143689C2semidirect
3. #19133502C2semidirect
4. #19133497C2semidirect
5. #19133490C2semidirect
6. #19133483C2semidirect
7. #19133412C2semidirect
8. #19133407C2semidirect
9. C8×#10621885C2semidirect
10. C8×#10621883C2semidirect
11. #19133360C2semidirect
13. #19133049C2semidirect
14. #19132876C2semidirect
347. C43#17969semidirect

Maximal subgroups

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

subgroupindex
#191452022
#191436892
#191335022
#191334972
#191334902
#191334832
#191334122
#191334072
C8×#106218852
C8×#106218832
#191333602
#191330552
#191330492
#191328762
C43×#29932
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