Finite Group Databasebeta

← #25068624

Subgroups — #25068624

Order 11008.

564 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145178C211yesmaximal, characteristic
2#19143695C211yesmaximal, characteristic
3#19143693C211yesmaximal, characteristic
4#19133502C211yesmaximal, characteristic, complemented
5#19133501C211yesmaximal, characteristic, complemented
6#19133447C211yesmaximal, characteristic, complemented
7#19133446C211yesmaximal, characteristic, complemented
8#19133444C211yesmaximal, characteristic, complemented
9#19133412C211yesmaximal, characteristic, complemented
10#19133411C211yesmaximal, characteristic, complemented
11#19133342C211yesmaximal, characteristic
12#19133014C211yesmaximal, characteristic
13#19133014C211yesmaximal, characteristic
14#19132883C211yesmaximal, characteristic
15C43×#1584C211yesmaximal, characteristic, complemented
16#14583453C2211yescharacteristic
17#14583453C2211yescharacteristic
18#14583303C411yescharacteristic
19#14583277C411yescharacteristic
20#14583248C411yescharacteristic
21#14583248C411yescharacteristic
22#14583141C411yescharacteristic
23#14583139C411yescharacteristic
24#14583139C411yescharacteristic
25#14583137C411yescharacteristic
26#14583030C2211yescharacteristic
27#14583029C2211yescharacteristic
28#14583028—21no—
29#14583027—21no—
30#14583026C2211yescharacteristic
31Q8×C43⋊C8C2211yescharacteristic
32C8×Dic86—21no—
33C8×Dic86C2211yescharacteristic
34#14583023—21no—
35#14583023C2211yescharacteristic
36C4×Dic172C2211yescharacteristic
37C4×#10621885C2211yescharacteristic
38C4×#10621885C2211yescharacteristic
39#14582961—21no—
40#14582959—21no—
41#14582959—21no—
42#14582958—21no—
43#14582951C2211yescharacteristic
44#14582951C2211yescharacteristic
45#14582950C2211yescharacteristic
46C4×#10621872C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic
49#14582649C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582631C2211yescharacteristic
52#14582631C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54Q8⋊(C43⋊C8)C2211yescharacteristic
55#14582629C2211yescharacteristic
56#14582629C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582621C2211yescharacteristic
59#14582621C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C8×Q8×C43C2211yescharacteristic
62C4×Q16×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×Dic172C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621885C2×C411yescharacteristic
70C2×#10621872—21no—
71C2×C8×D43C2×C411yescharacteristic
72C2×C8×D43C2×C411yescharacteristic
73#13063324C2×C411yescharacteristic
74#13063324C2×C411yescharacteristic
75#13063323C2×C411yescharacteristic
76#13063323C2×C411yescharacteristic
77#13063315—21no—
78#13063315—21no—
79#13063305C2×C411yescharacteristic
80#13063305C2×C411yescharacteristic
81#13063303—21no—
82#13063303—21no—
83#13063301C2×C411yescharacteristic
84#13063301C2×C411yescharacteristic
85C4×Dic86—21no—
86C4×Dic86—21no—
87C4×Dic86C2311yescharacteristic
88C4×Dic86C2311yescharacteristic
89#13063282—21no—
90#13063282—21no—
91C42×D43C2311yescharacteristic
92#13063259C2×C411yescharacteristic
93#13063258C2×C411yescharacteristic
94#13063258C2×C411yescharacteristic
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8D411yescharacteristic
104Dic43⋊C8D411yescharacteristic
105#13063250C2×C411yescharacteristic
106#13063250C2×C411yescharacteristic
107#13063249C2×C411yescharacteristic
108#13063249C2×C411yescharacteristic
109#13063248C2×C411yescharacteristic
110#13063248C2×C411yescharacteristic
111(C2×D43)⋊C8—21no—
112(C2×D43)⋊C8—21no—
113(C2×D43)⋊C8D411yescharacteristic
114(C2×D43)⋊C8D411yescharacteristic
115#13063236—21no—
116#13063235—21no—
117#13063235—21no—
118#13063235—21no—
119C4×C43⋊C8—21no—
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C8×Dic43—21no—
124C8×Dic43—21no—
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43C2×C411yescharacteristic
128C8×Dic43C2×C411yescharacteristic
129C2×Q16×C43C2×C411yescharacteristic
130C4×Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132#107×C43C2×C411yescharacteristic
133C4⋊C8×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43C2×C411yescharacteristic
138#103×C43C2×C411yescharacteristic
139#97×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×Q8×C43C22×C411yescharacteristic
146C2×C4×D43C22×C411yescharacteristic
147C2×C4×D43C2×D411yescharacteristic
148C2×C4×D43#4111yescharacteristic
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86C22×C411yescharacteristic
152C2×Dic86C22×C411yescharacteristic
153Q16×C43—41no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43C22×C411yescharacteristic
158C2×C8×C43C22×C411yescharacteristic
159C2×C8×C43C2×D411yescharacteristic
160C2×C8×C43C2×D411yescharacteristic
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43C22×C411yescharacteristic
164C4⋊C4×C43C22×C411yescharacteristic
165C42×C43—21no—
166C42×C43—21no—
167C42×C43C2411yescharacteristic
168#10621885—22no—
169#10621885—22no—
170(C2×D43)⋊C4—21no—
171(C2×D43)⋊C4—21no—
172(C2×D43)⋊C4—21no—
173(C2×D43)⋊C4—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43C22×C411yescharacteristic
177C4⋊Dic43C22×C411yescharacteristic
178Dic43⋊C4—21no—
179Dic43⋊C4—21no—
180Dic43⋊C4—21no—
181Dic43⋊C4—21no—
182Dic43⋊C4—21no—
183Dic43⋊C4—21no—
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C4×Dic43C22×C411yescharacteristic
191C4×Dic43C2×D411yescharacteristic
192C4×Dic43#4111yescharacteristic
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8C22×C411yescharacteristic
197C2×C43⋊C8C22×C411yescharacteristic
198C2×C43⋊C8C2×D411yescharacteristic
199C2×C43⋊C8C2×D411yescharacteristic
200Dic172—41no—
201#10621872—42no—
202C8×D43—22no—
203C8×D43—41no—
204C22×D43C4×D411yescharacteristic
205Q8×C43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43C23×C411yescharacteristic
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43C2×#4111yescharacteristic
216C2×Dic43—21no—
217C2×Dic43—21no—
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43C4×D411yescharacteristic
221C2×Dic43C4×D411yescharacteristic
222C2×Dic43C4×D411yescharacteristic
223C4×D43—21no—
224C4×D43—21no—
225C4×D43—21no—
226C4×D43—21no—
227C4×D43—22no—
228Dic86—21no—
229Dic86—21no—
230Dic86—21no—
231Dic86—21no—
232Dic86—42no—
233Dic86—42no—
234C8×C43—21no—
235C8×C43—21no—
236C8×C43—21no—
237C8×C43—21no—
238C8×C43—41no—
239C8×C43—41no—
240C8×C43—41no—
241C43⋊C8—21no—
242C43⋊C8—21no—
243C43⋊C8—21no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246C43⋊C8—41no—
247C43⋊C8#13112yes—
248#18090—431nomaximal, Sylow
249C22×C43C2×C4×D411yescharacteristic
250C2×D43—21no—
251C2×D43—21no—
252C2×D43—21no—
253C4×C43—21no—
254C4×C43—41no—
255C4×C43—41no—
256C4×C43—41no—
257C4×C43—41no—
258C4×C43C2×#13111yescharacteristic
259C4×C43#56811yescharacteristic
260C4×C43#57811yescharacteristic
261C4×C43#57811yescharacteristic
262Dic43—21no—
263Dic43—21no—
264Dic43—41no—
265Dic43—41no—
266Dic43—41no—
267Dic43—41no—
268Dic43#44412yes—
269#3170—431no—
270#2986—431no—
271#2986—431no—
272#1593—431no—
273#1593—431no—
274#1584—431no—
275#1584—431no—
276#1584—431no—
277#1584D4311yescharacteristic, complemented
278#1579—431no—
279#1579—431no—
280#1564—431no—
281#1485—431no—
282#1485—431no—
283#1451—431no—
284C2×C43#293511yescharacteristic
285C2×C43#295011yescharacteristic
286C2×C43C2×#44411yescharacteristic
287D43—41no—
288#533—431no—
289#533—431no—
290#500—431no—
291#494—431no—
292#487—431no—
293#487—431no—
294#467—431no—
295#467—431no—
296#467—431no—
297#467—431no—
298#446—431no—
299#446—431no—
300#446—431no—
301#446—861no—
302#446—861no—
303#446C2×D4311yescharacteristic
304C8×Q8—431no—
305C8×Q8—431no—
306C8×Q8—431no—
307C8×Q8—861no—
308C8×Q8—861no—
309C8×Q8C2×D4311yescharacteristic
310C4×Q16—431no—
311C4×Q16—431no—
312C4×Q16—431no—
313C4×Q16C2×D4311yescharacteristic
314#433—861no—
315#433—861no—
316#433—861no—
317#433—861no—
318#431—431no—
319#431—431no—
320#431—431no—
321C4×M16—431no—
322C2×C4×C8—431no—
323#335—431no—
324#335C2×D4311yescharacteristic
325#334—431no—
326#334—431no—
327Q8⋊C8—431no—
328Q8⋊C8—431no—
329Q8⋊C8—431no—
330Q8⋊C8—431no—
331Q8⋊C8—431no—
332Q8⋊C8—431no—
333Q8⋊C8C2×D4311yescharacteristic
334Q8⋊C8C2×D4311yescharacteristic
335#322—431no—
336#322—431no—
337#322—431no—
338#322C2×D4311yescharacteristic
339C43#1809011yescharacteristic, complemented, Sylow
340C2×Q16—431no—
341C2×Q16—431no—
342C2×Q16—431no—
343C2×Q16C4×D4311yescharacteristic
344C2×M16—861no—
345C22×C8—431no—
346C22×C8—431no—
347C4⋊Q8—431no—
348C4⋊Q8—431no—
349C4⋊Q8—431no—
350C4⋊Q8—431no—
351#125—861no—
352#125—861no—
353C22⋊Q8—431no—
354C22⋊Q8—431no—
355C22⋊Q8—431no—
356C22⋊Q8—431no—
357C22⋊Q8—861no—
358C22⋊Q8—861no—
359C4×Q8—431no—
360C4×Q8—431no—
361C4×Q8—861no—
362C4×Q8—861no—
363C4×Q8C22×D4311yescharacteristic
364C4×Q8C22×D4311yescharacteristic
365#117—861no—
366#117—861no—
367C2×C42—431no—
368#107—431no—
369#107—431no—
370#107—431no—
371#107C4×D4311yescharacteristic
372C4⋊C8—21no—
373C4⋊C8—21no—
374C4⋊C8—431no—
375C4⋊C8—431no—
376C4⋊C8—431no—
377C4⋊C8—431no—
378C4⋊C8—861no—
379C4⋊C8—861no—
380C4⋊C8—861no—
381C4⋊C8—861no—
382C4⋊C8—861no—
383C4⋊C8—861no—
384C4⋊C8C22×D4311yescharacteristic
385C4⋊C8C22×D4311yescharacteristic
386#103—431no—
387#103—431no—
388#103—431no—
389#103—431no—
390#103—431no—
391#103—431no—
392#103C4×D4311yescharacteristic
393#103C4×D4311yescharacteristic
394C22⋊C8—431no—
395C22⋊C8—431no—
396C22⋊C8—861no—
397C22⋊C8—861no—
398#97—21no—
399#97—861no—
400#97—861no—
401#97—861no—
402#97—861no—
403C4×C8—21no—
404C4×C8—431no—
405C4×C8—431no—
406C4×C8—431no—
407C4×C8—431no—
408C4×C8—431no—
409C4×C8—861no—
410C4×C8—861no—
411C4×C8—861no—
412C4×C8—861no—
413C4×C8—861no—
414C4×C8C22×D4311yescharacteristic
415C4×C8C22×D4311yescharacteristic
416C4×C8C22×D4311yescharacteristic
417C2×Q8—431no—
418C2×Q8—431no—
419C2×Q8—861no—
420C2×Q8—861no—
421C2×Q8C2×C4×D4311yescharacteristic
422C2×Q8C2×C4×D4311yescharacteristic
423C22×C4—431no—
424C22×C4—431no—
425C22×C4—431no—
426Q16—41no—
427Q16—862no—
428Q16—862no—
429Q16—1721no—
430M16—1722no—
431C2×C8—21no—
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—1721no—
443C2×C8C2×C4×D4311yescharacteristic
444C2×C8C2×C4×D4311yescharacteristic
445C2×C8D4×D4311yescharacteristic
446C2×C8D4×D4311yescharacteristic
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—431no—
450C4⋊C4—431no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4C2×C4×D4311yescharacteristic
464C4⋊C4C2×C4×D4311yescharacteristic
465C22⋊C4—861no—
466C22⋊C4—861no—
467C22⋊C4—861no—
468C22⋊C4—861no—
469C42—21no—
470C42—21no—
471C42—431no—
472C42—431no—
473C42—431no—
474C42—861no—
475C42—861no—
476C42C23×D4311yescharacteristic
477C23—431no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—861no—
483Q8—861no—
484Q8—861no—
485Q8—861no—
486Q8—1722no—
487Q8—1722no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—431no—
493C2×C4—431no—
494C2×C4—431no—
495C2×C4—862no—
496C2×C4—861no—
497C2×C4—861no—
498C2×C4—861no—
499C2×C4—861no—
500C2×C4—861no—
501C2×C4—861no—
502C2×C4—861no—
503C2×C4—861no—
504C2×C4C22×C4×D4311yescharacteristic
505C2×C4C2×D4×D4311yescharacteristic
506C2×C4#41×D4311yescharacteristic
507C8—21no—
508C8—21no—
509C8—21no—
510C8—21no—
511C8—41no—
512C8—41no—
513C8—41no—
514C8—432no—
515C8—861no—
516C8—861no—
517C8—861no—
518C8—1721no—
519C8—1721no—
520C8—1721no—
521C22—861no—
522C22—861no—
523C22—861no—
524C22C4×D4×D4311yescharacteristic
525C4—21no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—432no—
531C4—861no—
532C4—861no—
533C4—1721no—
534C4—1721no—
535C4—1721no—
536C4—1721no—
537C4#131×D4311yescharacteristic
538C4#1458366511yescharacteristic
539C4#1458371211yescharacteristic
540C4#1458371311yescharacteristic
541C2—1721no—
542C2#1914333611yescharacteristic
543C2#1914345811yescharacteristic
544C2#444×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1584C2
socleC22×C43C2×C4×D4
prime radicalC22×D43C4×D4
cosocleC42×C43C24
hypercenter#1584D43
hypocenterC43#18090
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #19133502C2semidirect
5. #19133501C2semidirect
6. #19133447C2semidirect
7. #19133446C2semidirect
8. #19133444C2semidirect
9. #19133412C2semidirect
10. #19133411C2semidirect
15. C43×#1584C2semidirect
277. #1584D43semidirect
339. C43#18090semidirect

Maximal subgroups

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

subgroupindex
#191451782
#191436952
#191436932
#191335022
#191335012
#191334472
#191334462
#191334442
#191334122
#191334112
#191333422
#191330142
#191328832
C43×#15842
#1809043