Finite Group Databasebeta

← #25102548

Subgroups — #25102548

Order 11008.

1322 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583082C211yesmaximal, characteristic
2C4×#13063355C212yesmaximal, complemented
3#19137311C211yesmaximal, characteristic, complemented
4#19134988C211yesmaximal, characteristic, complemented
5#19134964C212yesmaximal, complemented
6#19134828C212yesmaximal, complemented
7#19134810C211yesmaximal, characteristic, complemented
8#19134554C211yesmaximal, characteristic
9#19134405C212yesmaximal, complemented
10C4×#13063244C211yesmaximal, characteristic, complemented
11C4×2−1+4×C43C211yesmaximal, characteristic
12C2×#13063355C2212yes—
13C2×#13063323C2211yescharacteristic
14C2×C4×Dic86C2211yescharacteristic
15#14583082C418yescomplemented
16#14583004—22no—
17#14582999—22no—
18C4×#10621885—22no—
19C4×#10621883—22no—
20#14582942C2212yes—
21C2×#13063252C2212yes—
22C2×#13063252C2212yes—
23#14582907C2212yes—
24#14582900C2212yes—
25C2×#13063244C2211yescharacteristic
26C2×#13063244C2211yescharacteristic
27C4×#10621877C2212yes—
28#14582806C2211yescharacteristic
29#14582804C2211yescharacteristic
30#14582783—22no—
31#14582780—22no—
32#14582764C2211yescharacteristic
33#14582745C2211yescharacteristic
34#14582668C2212yes—
35#14582658C2212yes—
36#14582658C2212yes—
37C2×2−1+4×C43C2211yescharacteristic
38C43×#520—22no—
39C43×#520—22no—
40C43×#520C2212yes—
41C43×#519—22no—
42C43×#519C2211yescharacteristic
43C4×#41×C43—22no—
44C4×#41×C43—22no—
45C4×#41×C43C2212yes—
46C2×C4×Q8×C43—22no—
47C2×C4×Q8×C43C2211yescharacteristic
48C22×Dic86C2311yescharacteristic
49#13063355—24no—
50#13063355C2×C418yescomplemented
51C2×#10621885—22no—
52C2×#10621883—22no—
53C2×#10621877C2312yes—
54C2×#10621877C2312yes—
55#13063323—22no—
56#13063323C2×C414yescomplemented
57C4×Dic86—22no—
58C4×Dic86—22no—
59C2×C4⋊Dic43C2311yescharacteristic
60C2×Dic43⋊C4—22no—
61C2×Dic43⋊C4—21no—
62C2×C4×Dic43—21no—
63C2×C4×Dic43C2311yescharacteristic
64C2×C4×Dic43C2311yescharacteristic
65#13063258—22no—
66#13063256—22no—
67#13063252—24no—
68#13063252C2×C418yescomplemented
69#13063249—22no—
70#13063248—22no—
71#13063248—22no—
72#13063246—22no—
73#13063244—22no—
74#13063244C2×C414yescomplemented
75#13063236—22no—
76C4×C43⋊C8—22no—
77C43⋊#95—22no—
78C43⋊#95—22no—
79C43⋊#95—21no—
80C43⋊#95—21no—
81C43⋊#95—22no—
822−1+4×C43—24no—
832−1+4×C43—22no—
842−1+4×C43C2×C414yes—
85C2×#41×C43—22no—
86C2×#41×C43—22no—
87C2×#41×C43C2312yes—
88C22×Q8×C43—22no—
89C22×Q8×C43C2311yescharacteristic
90C4×Q8×C43—22no—
91C4×Q8×C43—24no—
92C4×Q8×C43—22no—
93C4×Q8×C43—22no—
94C4×Q8×C43—22no—
95C4×Q8×C43—22no—
96C4×Q8×C43—22no—
97C4×Q8×C43—22no—
98C4×Q8×C43D412yes—
99C4×Q8×C43D412yes—
100C4×D4×C43—22no—
101C4×D4×C43—24no—
102C4×D4×C43—22no—
103C4×D4×C43—22no—
104C4×D4×C43—22no—
105C4×D4×C43—24no—
106C4×D4×C43—22no—
107C4×D4×C43D412yes—
108C4×D4×C43D412yes—
109#117×C43—24no—
110#117×C43—24no—
111#117×C43—22no—
112#117×C43—22no—
113#117×C43—22no—
114#117×C43C2312yes—
115C2×C4⋊C4×C43—24no—
116C2×C4⋊C4×C43—22no—
117C2×C4⋊C4×C43D412yes—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C42×C43—24no—
120C2×C42×C43—22no—
121C2×C42×C43D412yes—
122C2×C42×C43C2311yescharacteristic
123#41×C43—28no—
124#41×C43—28no—
125#41×C43—28no—
126#41×C43—28no—
127#41×C43—22no—
128#41×C43—22no—
129#41×C43C22×C414yes—
130#41×C43#4114yes—
131C2×Q8×C43—22no—
132C2×Q8×C43—28no—
133C2×Q8×C43—28no—
134C2×Q8×C43—22no—
135C2×Q8×C43—22no—
136C2×Q8×C43C22×C412yes—
137C2×Q8×C43C2×D412yes—
138C2×Q8×C43#4112yes—
139C2×D4×C43—22no—
140C2×D4×C43—22no—
141C2×D4×C43C2×D412yes—
142C22×C4×C43—24no—
143C22×C4×C43—22no—
144C22×C4×C43—24no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43C2×D412yes—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C2×Dic86—22no—
157C2×Dic86—22no—
158C2×Dic86—21no—
159C2×Dic86C22×C412yes—
160C4⋊C4×C43—24no—
161C4⋊C4×C43—22no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—24no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43C2×D412yes—
168C4⋊C4×C43C2×D412yes—
169C22⋊C4×C43—24no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—22no—
173C42×C43—24no—
174C42×C43—24no—
175C42×C43—22no—
176C42×C43—22no—
177C42×C43—22no—
178C42×C43—22no—
179C42×C43—22no—
180C42×C43C2×D412yes—
181C42×C43C2×D412yes—
182#10621885—28no—
183#10621883—28no—
184C4⋊Dic43—22no—
185Dic43⋊C4—28no—
186Dic43⋊C4—41no—
187Dic43⋊C4—41no—
188C4×Dic43—21no—
189C4×Dic43—22no—
190C4×Dic43—42no—
191C4×Dic43C22×C412yes—
192#10621877—22no—
193#10621877—22no—
194#10621877—22no—
195#10621877C22×C414yes—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—22no—
198C23×C43—22no—
199C23×C43C22×D411yescharacteristic
200Q8×C43—28no—
201Q8×C43—24no—
202Q8×C43—22no—
203Q8×C43—24no—
204Q8×C43C4×D414yes—
205D4×C43—28no—
206D4×C43—24no—
207D4×C43—24no—
208D4×C43—22no—
209D4×C43C4×D414yes—
210C2×C4×C43—216no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—24no—
215C2×C4×C43—24no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—44no—
222C2×C4×C43—42no—
223C2×C4×C43—82no—
224C2×C4×C43—84no—
225C2×C4×C43C4×D414yes—
226C2×C4×C43#12012yes—
227C2×C4×C43#12011yescharacteristic
228C2×C4×C43#12011yescharacteristic
229C2×C4×C43C23×C411yescharacteristic
230C2×C4×C43C22×D412yes—
231C2×C4×C43C2×#4112yes—
232C2×C4×C43C2×#4111yescharacteristic
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—42no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244Dic86—24no—
245Dic86—42no—
246C43⋊C8—24no—
247C43⋊C8—42no—
248#21476—431nomaximal, Sylow
249C22×C43—21no—
250C22×C43—21no—
251C22×C43—24no—
252C22×C43—42no—
253C22×C43—42no—
254C22×C43C2×C4×D411yescharacteristic
255C22×C43C2×#12011yescharacteristic
256C22×C43#52511yescharacteristic
257C4×C43—21no—
258C4×C43—21no—
259C4×C43—22no—
260C4×C43—24no—
261C4×C43—24no—
262C4×C43—42no—
263C4×C43—42no—
264C4×C43—42no—
265C4×C43C2×C4×D412yes—
266C4×C43#52512yes—
267Dic43—42no—
268Dic43—42no—
269Dic43—81no—
270Dic43—81no—
271C4×2−1+4D4311yescharacteristic
272C2×#456—431no—
273C4×#137—432no—
274#2327—431no—
275#1886—431no—
276#1882—432no—
277#1860—432no—
278#1857—431no—
279#1793—431no—
280#1759—432no—
281C4×#101—431no—
282C2×C43—21no—
283C2×C43—21no—
284C2×C43—44no—
285C2×C43C4×#12011yescharacteristic
286C2×C43#302011yescharacteristic
287C2×C43#302211yescharacteristic
288C2×2−1+4C2×D4311yescharacteristic
289C2×#137—432no—
290C2×C4⋊Q8—431no—
291#520—22no—
292#520—22no—
293#520C2×D4312yes—
294#519—22no—
295#519C2×D4311yescharacteristic
296C4×#41—22no—
297C4×#41—22no—
298C4×#41C2×D4312yes—
299C2×C4×Q8—22no—
300C2×C4×Q8—431no—
301C2×C4×Q8C2×D4311yescharacteristic
302#456—438no—
303#441—862no—
304#440—862no—
305C4×Q16—862no—
306C4×SD16—862no—
307#428—432no—
308C2×#104—432no—
309C2×#104—432no—
310#419—432no—
311#417—432no—
312C2×#101—431no—
313C2×#101—431no—
314C4×M16—432no—
315#391—431no—
316#391—431no—
317#387—862no—
318#387—862no—
319#382—431no—
320#376—431no—
321#343—432no—
322#339—432no—
323#339—432no—
324C43#2147611yescharacteristic, complemented, Sylow
3252−1+4—24no—
3262−1+4—22no—
3272−1+4C4×D4314yes—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41C22×D4312yes—
331C22×Q8—22no—
332C22×Q8—431no—
333C22×Q8C22×D4311yescharacteristic
334#137—438no—
335#137—864no—
336C2×Q16—862no—
337C2×SD16—862no—
338C2×M16—432no—
339C2×M16—432no—
340C4⋊Q8—434no—
341C4⋊Q8—862no—
342C4×Q8—22no—
343C4×Q8—24no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8—862no—
351C4×Q8—862no—
352C4×Q8C22⋊D4312yes—
353C4×Q8C22⋊D4312yes—
354C4×D4—22no—
355C4×D4—24no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—24no—
360C4×D4—22no—
361C4×D4C22⋊D4312yes—
362C4×D4C22⋊D4312yes—
363#117—24no—
364#117—24no—
365#117—22no—
366#117—22no—
367#117—22no—
368#117C22×D4312yes—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—862no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4C22⋊D4312yes—
375C2×C4⋊C4C22×D4311yescharacteristic
376C2×C42—24no—
377C2×C42—22no—
378C2×C42—431no—
379C2×C42—431no—
380C2×C42—861no—
381C2×C42C22⋊D4312yes—
382C2×C42C22×D4311yescharacteristic
383#107—862no—
384#106—862no—
385#104—438no—
386#104—864no—
387#103—862no—
388#103—862no—
389#103—862no—
390#102—862no—
391#101—434no—
392#101—862no—
393#97—862no—
394C4×C8—862no—
395#95—861no—
396#95—861no—
397#95—862no—
398#95—862no—
399#95—862no—
400#41—28no—
401#41—28no—
402#41—28no—
403#41—28no—
404#41—22no—
405#41—22no—
406#41C2×C4×D4314yes—
407#41#1062189814yes—
408C2×Q8—22no—
409C2×Q8—28no—
410C2×Q8—28no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—432no—
414C2×Q8—861no—
415C2×Q8—862no—
416C2×Q8—862no—
417C2×Q8C2×C4×D4312yes—
418C2×Q8#1062189812yes—
419C2×Q8C2×C22⋊D4312yes—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4C2×C22⋊D4312yes—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4C2×C22⋊D4312yes—
433C22×C4C2×C22⋊D4312yes—
434C22×C4C2×C22⋊D4311yescharacteristic
435C22×C4C2×C22⋊D4311yescharacteristic
436C22×C4C23×D4311yescharacteristic
437Q16—868no—
438SD16—868no—
439M16—434no—
440M16—862no—
441M16—862no—
442M16—862no—
443C2×C8—862no—
444C2×C8—862no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—24no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—868no—
453C4⋊C4—862no—
454C4⋊C4—1721no—
455C4⋊C4—1721no—
456C4⋊C4C2×C22⋊D4312yes—
457C4⋊C4C2×C22⋊D4312yes—
458C22⋊C4—24no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C42—24no—
463C42—24no—
464C42—22no—
465C42—22no—
466C42—22no—
467C42—22no—
468C42—22no—
469C42—432no—
470C42—861no—
471C42—862no—
472C42—1722no—
473C42C2×C22⋊D4312yes—
474C42C2×C22⋊D4312yes—
475C23—22no—
476C23C22×C22⋊D4311yescharacteristic
477Q8—28no—
478Q8—24no—
479Q8—24no—
480Q8—22no—
481Q8—864no—
482Q8—1722no—
483Q8C4×C22⋊D4314yes—
484D4—28no—
485D4—24no—
486D4—24no—
487D4—22no—
488D4C4×C22⋊D4314yes—
489C2×C4—216no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—44no—
501C2×C4—42no—
502C2×C4—82no—
503C2×C4—84no—
504C2×C4—862no—
505C2×C4—862no—
506C2×C4—1721no—
507C2×C4—1721no—
508C2×C4—1722no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4C4×C22⋊D4314yes—
516C2×C4#1306329411yescharacteristic
517C2×C4#1306329411yescharacteristic
518C2×C4#1306329412yes—
519C2×C4C22×C4×D4311yescharacteristic
520C2×C4C22×C22⋊D4312yes—
521C2×C4C2×#1062189812yes—
522C2×C4C2×#1062189811yescharacteristic
523C8—864no—
524C8—1722no—
525C22—21no—
526C22—21no—
527C22—24no—
528C22—42no—
529C22—42no—
530C22C2×C4×C22⋊D4311yescharacteristic
531C22C2×#1306329411yescharacteristic
532C22#1458341011yescharacteristic
533C4—21no—
534C4—21no—
535C4—22no—
536C4—24no—
537C4—24no—
538C4—42no—
539C4—42no—
540C4—42no—
541C4—3441no—
542C4—3441no—
543C4—1722no—
544C4—1722no—
545C4C2×C4×C22⋊D4312yes—
546C4#1458341012yes—
547C2—21no—
548C2—21no—
549C2—44no—
550C2C4×#1306329411yescharacteristic
551C2#1914395911yescharacteristic
552C2#1914397411yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×2−1+4×C43C2
socleC22×C43C2×#120
prime radicalC2×2−1+4×C43C22
cosocleC22×C4×C43C24
hypercenterC4×2−1+4D43
hypocenterC43#21476
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
2. C4×#13063355C2semidirect
3. #19137311C2semidirect
4. #19134988C2semidirect
5. #19134964C2semidirect
6. #19134828C2semidirect
7. #19134810C2semidirect
9. #19134405C2semidirect
10. C4×#13063244C2semidirect
15. #14583082C4semidirect
50. #13063355C2×C4semidirect
56. #13063323C2×C4semidirect
68. #13063252C2×C4semidirect
74. #13063244C2×C4semidirect
324. C43#21476semidirect

Maximal subgroups

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

subgroupindex
C2×#145830822
C4×#130633552
#191373112
#191349882
#191349642
#191348282
#191348102
#191345542
#191344052
C4×#130632442
C4×2−1+4×C432
#2147643