Finite Group Databasebeta

← #25081907

Subgroups — #25081907

Order 11008.

610 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145552C211yesmaximal, characteristic
2#19144724C211yesmaximal, characteristic, complemented
3#19144625C211yesmaximal, characteristic
4#19143674C211yesmaximal, characteristic, complemented
5#19134036C211yesmaximal, characteristic, complemented
6#19134028C211yesmaximal, characteristic, complemented
7#19134027C211yesmaximal, characteristic, complemented
8#19133966C211yesmaximal, characteristic, complemented
9#19133965C211yesmaximal, characteristic, complemented
10#19133942C211yesmaximal, characteristic, complemented
11#19133941C211yesmaximal, characteristic, complemented
12#19133374C211yesmaximal, characteristic, complemented
13#19133297C211yesmaximal, characteristic
14#19133258C211yesmaximal, characteristic, complemented
15C43×#1682C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583447C2211yescharacteristic
18C4×Q8×D43C2211yescharacteristic
19#14583279C2211yescharacteristic
20#14583271C2211yescharacteristic
21#14583251C2211yescharacteristic
22#14583228—21no—
23#14583216—21no—
24#14583185C2211yescharacteristic
25#14583185C2211yescharacteristic
26#14583184C2211yescharacteristic
27#14583184C2211yescharacteristic
28#14583120—21no—
29#14583120—21no—
30#14583106C2211yescharacteristic
31#14583096C2211yescharacteristic
32#14583062—21no—
33#14583062—21no—
34#14583053—21no—
35#14583036—21no—
36Q8×C43⋊C8C2211yescharacteristic
37C8×Dic86—21no—
38C8×Dic86C2211yescharacteristic
39#14583023—21no—
40#14583023C2211yescharacteristic
41#14583006—21no—
42#14583003—21no—
43#14582990—21no—
44SD16×Dic43—21no—
45#14582955C2211yescharacteristic
46#14582951—21no—
47#14582951C2211yescharacteristic
48#14582951C2211yescharacteristic
49#14582950—21no—
50#14582950C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582645C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#462C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621900—21no—
68C2×Q8×D43D411yescharacteristic
69C2×Dic172—21no—
70C2×Dic172—21no—
71C2×#10621885—21no—
72C2×#10621883—21no—
73C2×#10621883—21no—
74C2×#10621883—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063316—21no—
78#13063312—21no—
79#13063305—21no—
80#13063301—21no—
81#13063296—21no—
82#13063296—21no—
83Q8×Dic43—21no—
84Q8×Dic43D411yescharacteristic
85C4×Dic86—21no—
86C4×Dic86C2311yescharacteristic
87#13063290—21no—
88#13063290—21no—
89#13063290D411yescharacteristic
90D4×Dic43—21no—
91D4×Dic43—21no—
92#13063283—21no—
93C4⋊C4×D43—21no—
94C4⋊C4×D43D411yescharacteristic
95C42×D43—21no—
96C42×D43C2311yescharacteristic
97#13063257—21no—
98#13063257—21no—
99#13063256—21no—
100#13063256—21no—
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8D411yescharacteristic
108Dic43⋊C8D411yescharacteristic
109#13063250—21no—
110#13063250—21no—
111#13063249—21no—
112#13063249—21no—
113#13063249—21no—
114#13063248—21no—
115#13063248—21no—
116#13063246—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8D411yescharacteristic
121(C2×D43)⋊C8D411yescharacteristic
122#13063235—21no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×Q16×C43—21no—
130C2×SD16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132#127×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43C2×D411yescharacteristic
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×C22⋊D43—41no—
150C22×Dic43—41no—
151Q8×D43—22no—
152Q8×D43—22no—
153#10621900—81no—
154#10621900—81no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43C2×D411yescharacteristic
158C2×C4×D43C2×D411yescharacteristic
159C2×C4×D43#4111yescharacteristic
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86C2×D411yescharacteristic
164Q16×C43—42no—
165SD16×C43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43C2×D411yescharacteristic
175C42×C43—21no—
176C42×C43C2411yescharacteristic
177C22⋊Dic43—41no—
178C22⋊Dic43—41no—
179#10621885—42no—
180#10621883—42no—
181#10621883—81no—
182#10621883—81no—
183(C2×D43)⋊C4—41no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—41no—
190C4⋊Dic43C2×D411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—41no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—41no—
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43C2×D411yescharacteristic
201C4×Dic43#4111yescharacteristic
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207Dic172—81no—
208Dic172—81no—
209C23×C43—41no—
210C22×D43#12111yescharacteristic
211Q8×C43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43#13512yes—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—81no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C22⋊D43—82no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—82no—
232C2×Dic43#12111yescharacteristic
233C2×Dic43#12111yescharacteristic
234C2×Dic43#12111yescharacteristic
235C4×D43—24no—
236C4×D43—21no—
237C4×D43—21no—
238C4×D43—21no—
239C4×D43—21no—
240C4×D43—41no—
241C4×D43—81no—
242Dic86—24no—
243Dic86—21no—
244Dic86—41no—
245Dic86—41no—
246Dic86—41no—
247Dic86—41no—
248Dic86#13512yes—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—41no—
252C8×C43—41no—
253C8×C43—41no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259#19400—431nomaximal, Sylow
260C22×C43—81no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43C2×#12111yescharacteristic
264C2×D43—21no—
265C2×D43—21no—
266C2×D43—21no—
267C4×C43—22no—
268C4×C43—21no—
269C4×C43—41no—
270C4×C43—81no—
271C4×C43C2×#13511yescharacteristic
272C4×C43C2×#13511yescharacteristic
273C4×C43#57711yescharacteristic
274C4×C43#57711yescharacteristic
275Dic43—21no—
276Dic43—21no—
277Dic43—22no—
278Dic43—21no—
279Dic43—41no—
280Dic43—81no—
281Dic43—81no—
282#3210—431no—
283#3113—431no—
284#3103—431no—
285#2982—431no—
286#1682—431no—
287#1682D4311yescharacteristic, complemented
288#1680—431no—
289#1680—431no—
290#1670—431no—
291#1670—431no—
292#1666—431no—
293#1666—431no—
294#1572—431no—
295#1553—431no—
296#1544—431no—
297C2×C43—161no—
298C2×C43#304311yescharacteristic
299C2×C43#305011yescharacteristic
300C2×C43#306911yescharacteristic
301D43—41no—
302#533—431no—
303#532—431no—
304C2×C4×Q8—431no—
305#494—431no—
306#492—431no—
307#487—431no—
308#486C2×D4311yescharacteristic
309#483—861no—
310#481—861no—
311#475—431no—
312#475—431no—
313#475—431no—
314#475—431no—
315#464—861no—
316#464—861no—
317#462—431no—
318#462C2×D4311yescharacteristic
319#460—431no—
320#460C2×D4311yescharacteristic
321#452—861no—
322#452—861no—
323#451—861no—
324#448—861no—
325C8×Q8—431no—
326C8×Q8—431no—
327C8×Q8—431no—
328C8×Q8—861no—
329C8×Q8—861no—
330C8×Q8C2×D4311yescharacteristic
331#441—861no—
332#441—861no—
333C4×SD16—861no—
334C4×SD16—861no—
335#432—431no—
336#431—431no—
337#431—431no—
338#431—431no—
339#431—861no—
340#431—861no—
341#335—431no—
342#335C2×D4311yescharacteristic
343#334—431no—
344#334—431no—
345#332—431no—
346#332—431no—
347#332—431no—
348#332—431no—
349#332—431no—
350#332C2×D4311yescharacteristic
351#331—431no—
352#331C2×D4311yescharacteristic
353C43#1940011yescharacteristic, complemented, Sylow
354C2×#41—861no—
355C22×Q8—431no—
356C2×Q16—21no—
357C2×Q16—861no—
358C2×Q16—861no—
359C2×Q16—861no—
360C2×SD16—21no—
361C2×SD16—861no—
362C2×SD16—861no—
363C2×SD16—861no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8C22×D4311yescharacteristic
367#127C22×D4311yescharacteristic
368#125—861no—
369#124—861no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372#121—861no—
373#121—861no—
374C4×Q8—431no—
375C4×Q8—431no—
376C4×Q8—431no—
377C4×Q8—861no—
378C4×Q8—861no—
379C4×Q8—861no—
380C4×Q8—861no—
381C4×Q8C22×D4311yescharacteristic
382C4×D4—861no—
383C4×D4—861no—
384#117—861no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—861no—
387C2×C42—431no—
388C2×C42—861no—
389#106—861no—
390#106—861no—
391#106—861no—
392#106—861no—
393C4⋊C8—21no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8C22×D4311yescharacteristic
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405#103—21no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—861no—
417C22⋊C8—431no—
418C22⋊C8—431no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422#97—861no—
423C4×C8—21no—
424C4×C8—431no—
425C4×C8—861no—
426C4×C8—861no—
427C4×C8—861no—
428C4×C8—861no—
429C4×C8—861no—
430C4×C8C22×D4311yescharacteristic
431#41—3441no—
432#41—3441no—
433C2×Q8—21no—
434C2×Q8—431no—
435C2×Q8—861no—
436C2×Q8—862no—
437C2×Q8—862no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8D4×D4311yescharacteristic
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—1721no—
445C22×C4—431no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—861no—
449C22×C4—861no—
450C22×C4—1721no—
451Q16—42no—
452Q16—3441no—
453Q16—3441no—
454Q16—1722no—
455SD16—42no—
456SD16—3441no—
457SD16—3441no—
458SD16—1722no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8D4×D4311yescharacteristic
468C2×C8D4×D4311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—431no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—1721no—
482C4⋊C4—1721no—
483C4⋊C4D4×D4311yescharacteristic
484C22⋊C4—1721no—
485C22⋊C4—1721no—
486C22⋊C4—1721no—
487C42—21no—
488C42—431no—
489C42—431no—
490C42—431no—
491C42—861no—
492C42—861no—
493C42—861no—
494C42—1721no—
495C42C23×D4311yescharacteristic
496C23—41no—
497C23—431no—
498Q8—21no—
499Q8—41no—
500Q8—41no—
501Q8—432no—
502Q8—864no—
503Q8—861no—
504Q8—1721no—
505Q8—1721no—
506Q8—1721no—
507Q8—1721no—
508Q8#1306334412yes—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—81no—
514D4—3442no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—431no—
519C2×C4—431no—
520C2×C4—431no—
521C2×C4—864no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—3441no—
529C2×C4—3442no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4C2×D4×D4311yescharacteristic
534C2×C4C2×D4×D4311yescharacteristic
535C2×C4#41×D4311yescharacteristic
536C8—21no—
537C8—21no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—861no—
542C8—861no—
543C8—1721no—
544C8—1721no—
545C8—1721no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22—861no—
550C22—861no—
551C22—861no—
552C22#121×D4311yescharacteristic
553C4—21no—
554C4—22no—
555C4—41no—
556C4—81no—
557C4—861no—
558C4—861no—
559C4—861no—
560C4—862no—
561C4—3441no—
562C4—3441no—
563C4—1721no—
564C4#135×D4311yescharacteristic
565C4C2×#1306334411yescharacteristic
566C4#1458370611yescharacteristic
567C4#1458370811yescharacteristic
568C2—161no—
569C2—1721no—
570C2#1914411411yescharacteristic
571C2#1914417411yescharacteristic
572C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1682C2
socleC22×C43C2×#121
prime radical#14583447C22
hypercenter#1682D43
hypocenterC43#19400
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1682

Complements

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

NH ≅ G/Ntype
2. #19144724C2semidirect
4. #19143674C2semidirect
5. #19134036C2semidirect
6. #19134028C2semidirect
7. #19134027C2semidirect
8. #19133966C2semidirect
9. #19133965C2semidirect
10. #19133942C2semidirect
11. #19133941C2semidirect
12. #19133374C2semidirect
14. #19133258C2semidirect
15. C43×#1682C2semidirect
287. #1682D43semidirect
353. C43#19400semidirect

Maximal subgroups

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

subgroupindex
#191455522
#191447242
#191446252
#191436742
#191340362
#191340282
#191340272
#191339662
#191339652
#191339422
#191339412
#191333742
#191332972
#191332582
C43×#16822
#1940043