Finite Group Databasebeta

← #25080446

Subgroups — #25080446

Order 11008.

602 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#19145180C211yesmaximal, characteristic
2#19144401C211yesmaximal, characteristic
3#19144395C211yesmaximal, characteristic
4C8×Q8×D43C211yesmaximal, characteristic
5#19134054C211yesmaximal, characteristic, complemented
6#19134053C211yesmaximal, characteristic, complemented
7#19134050C211yesmaximal, characteristic, complemented
8#19133998C211yesmaximal, characteristic, complemented
9#19133997C211yesmaximal, characteristic, complemented
10#19133964C211yesmaximal, characteristic, complemented
11#19133963C211yesmaximal, characteristic, complemented
12#19133352C211yesmaximal, characteristic
13#19133284C211yesmaximal, characteristic
14#19133282C211yesmaximal, characteristic
15C43×#1684C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18C4×Q8×D43C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583278C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583209—21no—
23#14583208—21no—
24#14583205—21no—
25#14583204—21no—
26#14583195C2211yescharacteristic
27#14583194C2211yescharacteristic
28#14583191C2211yescharacteristic
29#14583185C2211yescharacteristic
30#14583184C2211yescharacteristic
31#14583181C2211yescharacteristic
32#14583139—21no—
33#14583139—21no—
34Q8×C43⋊C8C2211yescharacteristic
35C8×Dic86—21no—
36C8×Dic86C2211yescharacteristic
37#14583023—21no—
38#14583023C2211yescharacteristic
39#14582991—21no—
40#14582991—21no—
41#14582940—21no—
42#14582938—21no—
43#14582921C2211yescharacteristic
44#14582921C2211yescharacteristic
45C4⋊C8×D43—21no—
46C4⋊C8×D43C2211yescharacteristic
47#14582906—21no—
48#14582906—21no—
49C4×C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#475C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Q8×D43D411yescharacteristic
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621872—21no—
71C2×#10621872—21no—
72C2×C8×D43—21no—
73C2×C8×D43D411yescharacteristic
74C2×C8×D43D411yescharacteristic
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063316—21no—
78#13063316—21no—
79#13063305—21no—
80#13063305—21no—
81#13063301—21no—
82#13063301—21no—
83Q8×Dic43—21no—
84Q8×Dic43—21no—
85Q8×Dic43D411yescharacteristic
86C4×Dic86—21no—
87C4×Dic86C2311yescharacteristic
88#13063290—21no—
89#13063290—21no—
90#13063290—21no—
91#13063290D411yescharacteristic
92#13063283—21no—
93#13063283—21no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43D411yescharacteristic
96C42×D43—21no—
97C42×D43C2311yescharacteristic
98#13063259—21no—
99#13063258—21no—
100#13063258—21no—
101#13063258—21no—
102#13063258—21no—
103#13063257—21no—
104#13063256—21no—
105#13063256—21no—
106C4⋊(C43⋊C8)—21no—
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109C4⋊(C43⋊C8)C2311yescharacteristic
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115#13063250—21no—
116#13063250—21no—
117#13063250—21no—
118#13063250—21no—
119#13063249—21no—
120#13063249—21no—
121#13063248—21no—
122#13063248—21no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C4⋊Q8×C43C2311yescharacteristic
130C4⋊Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132#107×C43—21no—
133#106×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#103×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147Q8×D43—22no—
148Q8×D43Q1614yescomplemented
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43C2×D411yescharacteristic
152C2×C4×D43C2×D411yescharacteristic
153C2×C4×D43#4111yescharacteristic
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86C2×D411yescharacteristic
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
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×C43—21no—
168C4⋊C4×C43C2×D411yescharacteristic
169C42×C43—21no—
170C42×C43C2411yescharacteristic
171#10621885—42no—
172#10621885—42no—
173(C2×D43)⋊C4—41no—
174(C2×D43)⋊C4—41no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—41no—
181C4⋊Dic43—41no—
182C4⋊Dic43C2×D411yescharacteristic
183Dic43⋊C4—21no—
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—41no—
187Dic43⋊C4—41no—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—41no—
192C4×Dic43—41no—
193C4×Dic43C2×D411yescharacteristic
194C4×Dic43C2×D411yescharacteristic
195C4×Dic43#4111yescharacteristic
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8C2×D411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201#10621872—42no—
202#10621872—42no—
203C8×D43—22no—
204C8×D43—41no—
205C8×D43—42no—
206C22×D43#12111yescharacteristic
207Q8×C43—21no—
208Q8×C43—41no—
209Q8×C43—41no—
210Q8×C43—81no—
211Q8×C43C2×Q1612yes—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43#12111yescharacteristic
224C2×Dic43#12111yescharacteristic
225C2×Dic43#12111yescharacteristic
226C4×D43—24no—
227C4×D43—21no—
228C4×D43—21no—
229C4×D43—41no—
230C4×D43—42no—
231C4×D43C2×Q1612yes—
232C4×D43#13512yes—
233Dic86—21no—
234Dic86—24no—
235Dic86—41no—
236Dic86—41no—
237Dic86—81no—
238Dic86C2×Q1612yes—
239C8×C43—21no—
240C8×C43—21no—
241C8×C43—41no—
242C8×C43—41no—
243C8×C43—41no—
244C43⋊C8—21no—
245C43⋊C8—41no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8#13712yes—
249#19262—431nomaximal, Sylow
250C22×C43C2×#12111yescharacteristic
251C2×D43—21no—
252C2×D43—21no—
253C2×D43#46712yes—
254C4×C43—22no—
255C4×C43—21no—
256C4×C43—41no—
257C4×C43—81no—
258C4×C43—81no—
259C4×C43C22×Q1611yescharacteristic
260C4×C43C2×#13511yescharacteristic
261C4×C43C2×#13711yescharacteristic
262C4×C43#57511yescharacteristic
263Dic43—21no—
264Dic43—22no—
265Dic43—21no—
266Dic43—41no—
267Dic43—81no—
268Dic43—81no—
269Dic43#46712yes—
270#3170—431no—
271#3078—431no—
272#3078—431no—
273C2×C8×Q8—431no—
274#1684—431no—
275#1684—431no—
276#1684—431no—
277#1684D4311yescharacteristic, complemented
278#1676—431no—
279#1676—431no—
280#1670—431no—
281#1670—431no—
282#1567—431no—
283#1550—431no—
284#1550—431no—
285C2×C43#303711yescharacteristic
286C2×C43C2×#46711yescharacteristic
287C2×C43#306711yescharacteristic
288D43—22no—
289#533—431no—
290#533—431no—
291C2×C4×Q8—431no—
292#500—431no—
293#494—431no—
294#487—431no—
295#487C2×D4311yescharacteristic
296#479—861no—
297#479—861no—
298#479—861no—
299#479—861no—
300#477—431no—
301#477—431no—
302#477—431no—
303#477C2×D4311yescharacteristic
304#475—431no—
305#475—431no—
306#475—431no—
307#475C2×D4311yescharacteristic
308#467—861no—
309#467—861no—
310C8×Q8—431no—
311C8×Q8—431no—
312C8×Q8—431no—
313C8×Q8—861no—
314C8×Q8—861no—
315C8×Q8C2×D4311yescharacteristic
316C4×Q16—861no—
317C4×Q16—861no—
318#428—861no—
319#428—861no—
320#423—431no—
321#423—431no—
322C2×C4⋊C8—431no—
323C2×C4⋊C8—861no—
324#419—861no—
325#419—861no—
326C2×C4×C8—431no—
327C2×C4×C8—861no—
328#335—431no—
329#335—431no—
330#335—431no—
331#335C2×D4311yescharacteristic
332#333—431no—
333#333—431no—
334#333—431no—
335#333C2×D4311yescharacteristic
336#332—431no—
337#332—431no—
338#332—431no—
339#332C2×D4311yescharacteristic
340C43#1926211yescharacteristic, complemented, Sylow
341C22×Q8—431no—
342C2×Q16—861no—
343C2×Q16—861no—
344C2×M16—861no—
345C2×M16—861no—
346C22×C8—431no—
347C22×C8—431no—
348C22×C8—861no—
349C4⋊Q8—431no—
350C4⋊Q8—431no—
351C4⋊Q8C22×D4311yescharacteristic
352C4⋊Q8C22×D4311yescharacteristic
353#125—861no—
354#125—861no—
355C22⋊Q8—861no—
356C22⋊Q8—861no—
357C22⋊Q8—861no—
358C22⋊Q8—861no—
359C4×Q8—431no—
360C4×Q8—431no—
361C4×Q8—431no—
362C4×Q8—861no—
363C4×Q8—861no—
364C4×Q8—861no—
365C4×Q8—861no—
366C4×Q8—861no—
367C4×Q8—861no—
368C4×Q8C22×D4311yescharacteristic
369#117—861no—
370#117—861no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—861no—
373C2×C42—431no—
374C2×C42—861no—
375#107—21no—
376#107—861no—
377#107—861no—
378#107—861no—
379#107—861no—
380#107—861no—
381#106—21no—
382#106—861no—
383#106—861no—
384#106—861no—
385C4⋊C8—21no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8C22×D4311yescharacteristic
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410C4×C8—21no—
411C4×C8—431no—
412C4×C8—431no—
413C4×C8—431no—
414C4×C8—861no—
415C4×C8—861no—
416C4×C8—861no—
417C4×C8C22×D4311yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—434no—
421C2×Q8—431no—
422C2×Q8—861no—
423C2×Q8—862no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8D4×D4311yescharacteristic
427C22×C4—431no—
428C22×C4—431no—
429C22×C4—431no—
430C22×C4—861no—
431C22×C4—861no—
432Q16—1722no—
433Q16—1722no—
434M16—1722no—
435M16—1722no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—431no—
440C2×C8—431no—
441C2×C8—862no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—1721no—
446C2×C8—1722no—
447C2×C8D4×D4311yescharacteristic
448C2×C8D4×D4311yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—431no—
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⋊C4—1721no—
464C4⋊C4—1721no—
465C4⋊C4—1721no—
466C4⋊C4—1721no—
467C4⋊C4D4×D4311yescharacteristic
468C22⋊C4—1721no—
469C22⋊C4—1721no—
470C42—21no—
471C42—431no—
472C42—431no—
473C42—431no—
474C42—861no—
475C42—861no—
476C42—861no—
477C42—1721no—
478C42—1721no—
479C42C23×D4311yescharacteristic
480C23—431no—
481Q8—21no—
482Q8—41no—
483Q8—41no—
484Q8—81no—
485Q8—432no—
486Q8—864no—
487Q8—861no—
488Q8—3441no—
489Q8—1721no—
490Q8—1721no—
491Q8Q16×D4312yes—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—431no—
497C2×C4—432no—
498C2×C4—432no—
499C2×C4—431no—
500C2×C4—431no—
501C2×C4—864no—
502C2×C4—861no—
503C2×C4—861no—
504C2×C4—861no—
505C2×C4—861no—
506C2×C4—1721no—
507C2×C4—1722no—
508C2×C4—1721no—
509C2×C4—1721no—
510C2×C4C2×D4×D4311yescharacteristic
511C2×C4C2×D4×D4311yescharacteristic
512C2×C4#41×D4311yescharacteristic
513C8—21no—
514C8—21no—
515C8—41no—
516C8—41no—
517C8—41no—
518C8—432no—
519C8—861no—
520C8—1721no—
521C8—1721no—
522C8—1721no—
523C22—432no—
524C22—861no—
525C22—861no—
526C22#121×D4311yescharacteristic
527C4—21no—
528C4—22no—
529C4—41no—
530C4—81no—
531C4—81no—
532C4—432no—
533C4—861no—
534C4—861no—
535C4—862no—
536C4—3441no—
537C4—3441no—
538C4—1721no—
539C4C2×Q16×D4311yescharacteristic
540C4#135×D4311yescharacteristic
541C4#137×D4311yescharacteristic
542C4#1458369611yescharacteristic
543C2—862no—
544C2#1914406511yescharacteristic
545C2#467×D4311yescharacteristic
546C2#1914431011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1684C2
socleC22×C43C2×#121
prime radicalC22×D43#121
hypercenter#1684D43
hypocenterC43#19262
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1684

Complements

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

NH ≅ G/Ntype
5. #19134054C2semidirect
6. #19134053C2semidirect
7. #19134050C2semidirect
8. #19133998C2semidirect
9. #19133997C2semidirect
10. #19133964C2semidirect
11. #19133963C2semidirect
15. C43×#1684C2semidirect
148. Q8×D43Q16semidirect
277. #1684D43semidirect
340. C43#19262semidirect

Maximal subgroups

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

subgroupindex
#191451802
#191444012
#191443952
C8×Q8×D432
#191340542
#191340532
#191340502
#191339982
#191339972
#191339642
#191339632
#191333522
#191332842
#191332822
C43×#16842
#1926243