Finite Group Databasebeta

← #25079043

Subgroups — #25079043

Order 11008.

618 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145177C211yesmaximal, characteristic, complemented
2#19144385C211yesmaximal, characteristic
3#19144377C211yesmaximal, characteristic
4#19143551C211yesmaximal, characteristic
5#19134056C211yesmaximal, characteristic, complemented
6#19134052C211yesmaximal, characteristic, complemented
7#19134049C211yesmaximal, characteristic, complemented
8#19134045C211yesmaximal, characteristic, complemented
9#19133998C211yesmaximal, characteristic, complemented
10#19133993C211yesmaximal, characteristic, complemented
11#19133964C211yesmaximal, characteristic, complemented
12#19133959C211yesmaximal, characteristic, complemented
13C2×#14582651C211yesmaximal, characteristic, complemented
14#19133250C211yesmaximal, characteristic, complemented
15C43×#1542C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17C4×#10621898C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583278C2211yescharacteristic
20#14583251C2211yescharacteristic
21#14583249C2211yescharacteristic
22#14583207—21no—
23#14583203—21no—
24#14583200—21no—
25#14583196—21no—
26#14583195C2211yescharacteristic
27#14583191C2211yescharacteristic
28#14583190C2211yescharacteristic
29#14583186C2211yescharacteristic
30#14583185C2211yescharacteristic
31#14583181C2211yescharacteristic
32#14583180C2211yescharacteristic
33#14583176C2211yescharacteristic
34#14583138—21no—
35#14583138—21no—
36#14583023C2211yescharacteristic
37#14583023C2211yescharacteristic
38C4×#10621885—21no—
39C4×#10621885—21no—
40#14582964C2211yescharacteristic
41#14582964C2211yescharacteristic
42(C22⋊D43)⋊C8—21no—
43(C22⋊D43)⋊C8—21no—
44#14582950—21no—
45#14582937—21no—
46#14582935—21no—
47C2×C4⋊(C43⋊C8)C2211yescharacteristic
48#14582896—21no—
49#14582893—21no—
50C2×C4×C43⋊C8C2211yescharacteristic
51C4×C8×D43—21no—
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582651C2211yescharacteristic
55#14582651C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582646C2211yescharacteristic
59#14582646C2211yescharacteristic
60C43×#533C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#333C2211yescharacteristic
64C43×#333C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621898D411yescharacteristic
68C2×#10621885—21no—
69C2×#10621885—21no—
70C22×C43⋊C8—21no—
71C22×C43⋊C8D411yescharacteristic
72C22×C43⋊C8D411yescharacteristic
73C2×C8×D43—21no—
74C2×C8×D43—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063317—21no—
78#13063304—21no—
79#13063304—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86D411yescharacteristic
83C4×Dic86C2311yescharacteristic
84C4×D172D411yescharacteristic
85C4×D172C2311yescharacteristic
86C4×C22⋊D43—21no—
87C4×C22⋊D43—21no—
88#13063284—21no—
89#13063284D411yescharacteristic
90#13063282—21no—
91C42×D43—21no—
92#13063259—21no—
93#13063259—21no—
94#13063258—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258—21no—
98#13063257—21no—
99#13063257—21no—
100#13063256—21no—
101#13063256—21no—
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107#13063250—21no—
108#13063250—21no—
109#13063249—21no—
110#13063249—21no—
111#13063248—21no—
112#13063248—21no—
113#13063248—21no—
114#13063248—21no—
115#13063247—21no—
116#13063247—21no—
117#13063245—21no—
118#13063245—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121C4×C43⋊C8D411yescharacteristic
122C4×C43⋊C8D411yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C22×C8×C43—21no—
128C4⋊Q8×C43C2311yescharacteristic
129C4⋊Q8×C43C2311yescharacteristic
130#125×C43—21no—
131C22⋊Q8×C43—21no—
132C22⋊Q8×C43—21no—
133C4×Q8×C43—21no—
134C4×Q8×C43—21no—
135#117×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43#4111yescharacteristic
149C2×C22⋊D43—21no—
150#10621898—22no—
151#10621898Q1614yescomplemented
152C2×D172C2×D411yescharacteristic
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86C2×D411yescharacteristic
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—42no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—41no—
169C4⋊C4×C43—41no—
170C22⋊C4×C43—41no—
171C42×C43—41no—
172C42×C43C2×D411yescharacteristic
173C42×C43C2×D411yescharacteristic
174C42×C43#4111yescharacteristic
175C42×C43C2411yescharacteristic
176C22⋊Dic43—21no—
177C22⋊Dic43—41no—
178#10621885—42no—
179#10621885—42no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43C2×D411yescharacteristic
187C4⋊Dic43C2×D411yescharacteristic
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—41no—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—41no—
200C2×C43⋊C8—42no—
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C8×D43—42no—
206C8×D43—42no—
207C23×C43#12111yescharacteristic
208C22×D43—21no—
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—81no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43#12111yescharacteristic
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43C2×Q1612yes—
221C2×C4×C43#13512yes—
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C22⋊D43—24no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231D172—21no—
232D172C2×Q1612yes—
233C4×D43—24no—
234C4×D43—42no—
235C4×D43—41no—
236C4×D43—41no—
237Dic86—21no—
238Dic86—41no—
239Dic86—41no—
240Dic86—81no—
241Dic86C2×Q1612yes—
242C8×C43—41no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43—41no—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8#13512yes—
252#19126—431nomaximal, Sylow
253C22×C43—21no—
254C22×C43—21no—
255C22×C43#46712yes—
256C22×C43C2×#12111yescharacteristic
257C2×D43—22no—
258C2×D43—41no—
259C2×D43—41no—
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—21no—
263C4×C43—81no—
264C4×C43—81no—
265C4×C43#46712yes—
266C4×C43C22×Q1611yescharacteristic
267C4×C43C2×#13511yescharacteristic
268C4×C43C2×#13511yescharacteristic
269C4×C43#57511yescharacteristic
270Dic43—22no—
271Dic43—41no—
272Dic43—41no—
273Dic43—81no—
274Dic43—81no—
275#3170—431no—
276#3076—431no—
277#3076—431no—
278C8×#41—431no—
279#1684—431no—
280#1684—431no—
281#1683—431no—
282#1683—431no—
283#1676—431no—
284#1675—431no—
285#1670—431no—
286#1669—431no—
287C2×#335—431no—
288#1542—431no—
289#1542D4311yescharacteristic, complemented
290C2×C43—22no—
291C2×C43#303511yescharacteristic
292C2×C43C2×#46711yescharacteristic
293C2×C43#306711yescharacteristic
294D43—42no—
295#533—431no—
296#533C2×D4311yescharacteristic
297C4×#41—431no—
298#500—431no—
299#494—431no—
300#487—431no—
301#487—431no—
302#479—861no—
303#479—861no—
304#478—861no—
305#478—861no—
306#477—431no—
307#477—431no—
308#476—431no—
309#476—431no—
310#475—431no—
311#475—431no—
312#474—431no—
313#474—431no—
314#467—861no—
315#467—861no—
316C8×Q8—431no—
317C8×Q8—431no—
318C4×Q16—861no—
319C4×Q16—861no—
320C8×D4—431no—
321C8×D4—431no—
322C8×D4—861no—
323C8×D4—861no—
324#431—861no—
325#431C2×D4311yescharacteristic
326#427—861no—
327#427—861no—
328C2×C4⋊C8—431no—
329C2×C4⋊C8C2×D4311yescharacteristic
330#416—861no—
331#416—861no—
332C2×C4×C8—431no—
333C2×C4×C8—861no—
334#335—431no—
335#335—431no—
336#335—431no—
337#335—431no—
338#333—431no—
339#333—431no—
340#333C2×D4311yescharacteristic
341#333C2×D4311yescharacteristic
342#332—431no—
343#332—431no—
344#332C2×D4311yescharacteristic
345#332C2×D4311yescharacteristic
346C43#1912611yescharacteristic, complemented, Sylow
347C2×#41—431no—
348C2×Q16—861no—
349C2×Q16—861no—
350C22×C8—21no—
351C22×C8—431no—
352C22×C8—431no—
353C22×C8—861no—
354C22×C8—861no—
355C22×C8—861no—
356C4⋊Q8—431no—
357C4⋊Q8—431no—
358C4⋊Q8C22×D4311yescharacteristic
359C4⋊Q8C22×D4311yescharacteristic
360#125—21no—
361#125—861no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—861no—
365C22⋊Q8—861no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—431no—
369C4×Q8—431no—
370C4×Q8—861no—
371C4×Q8—861no—
372C4×D4—431no—
373C4×D4—431no—
374C4×D4—861no—
375C4×D4—861no—
376#117—21no—
377#117—431no—
378#117—861no—
379#117—861no—
380C2×C42—861no—
381C2×C42C22×D4311yescharacteristic
382#107—861no—
383#107—861no—
384#107—861no—
385#107—861no—
386#107—861no—
387#107—861no—
388#106—861no—
389#106—861no—
390#106—861no—
391#106—861no—
392C4⋊C8—21no—
393C4⋊C8—431no—
394C4⋊C8—431no—
395C4⋊C8—861no—
396C4⋊C8—861no—
397C4⋊C8—861no—
398C4⋊C8C22×D4311yescharacteristic
399C4⋊C8C22×D4311yescharacteristic
400C4⋊C8C22×D4311yescharacteristic
401C4⋊C8C22×D4311yescharacteristic
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#102—861no—
411#102—861no—
412#102—861no—
413#102—861no—
414C22⋊C8—21no—
415C22⋊C8—861no—
416C22⋊C8—861no—
417C4×C8—21no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8—431no—
422C4×C8—861no—
423C4×C8—861no—
424#41—434no—
425#41—862no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—431no—
429C2×Q8—861no—
430C2×Q8—861no—
431C2×D4—431no—
432C2×D4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4#1062189811yescharacteristic
437C22×C4D4×D4311yescharacteristic
438C22×C4D4×D4311yescharacteristic
439Q16—1722no—
440Q16—1722no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—42no—
446C2×C8—431no—
447C2×C8—431no—
448C2×C8—431no—
449C2×C8—431no—
450C2×C8—862no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—1722no—
454C2×C8—1722no—
455C2×C8—1721no—
456C2×C8—1722no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—41no—
462C4⋊C4—41no—
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—1721no—
472C4⋊C4—1721no—
473C22⋊C4—41no—
474C22⋊C4—861no—
475C22⋊C4—861no—
476C22⋊C4—861no—
477C22⋊C4—1721no—
478C42—41no—
479C42—861no—
480C42—861no—
481C42—861no—
482C42—1721no—
483C42#1062189811yescharacteristic
484C42D4×D4311yescharacteristic
485C42D4×D4311yescharacteristic
486C42C23×D4311yescharacteristic
487C23—861no—
488C23#1306329811yescharacteristic
489Q8—41no—
490Q8—41no—
491Q8—81no—
492Q8—432no—
493Q8—861no—
494Q8—3441no—
495Q8—1721no—
496Q8—1721no—
497D4—432no—
498D4—864no—
499D4—861no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—861no—
506C2×C4—864no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—1722no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4#1306329811yescharacteristic
515C2×C4#1306329811yescharacteristic
516C2×C4#1306329811yescharacteristic
517C2×C4Q16×D4312yes—
518C2×C4#1306334612yes—
519C2×C4C2×D4×D4311yescharacteristic
520C2×C4C2×D4×D4311yescharacteristic
521C2×C4C2×#1062189811yescharacteristic
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—432no—
527C8—861no—
528C8—861no—
529C8—861no—
530C8—1721no—
531C8—1721no—
532C22—21no—
533C22—21no—
534C22—862no—
535C22—1721no—
536C22—1721no—
537C22#1458313912yes—
538C22C2×#1306329811yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—81no—
543C4—81no—
544C4—862no—
545C4—3441no—
546C4—3441no—
547C4—1721no—
548C4—1721no—
549C4#1458313912yes—
550C4C2×Q16×D4311yescharacteristic
551C4#135×D4311yescharacteristic
552C4C2×#1306334611yescharacteristic
553C4#1458369611yescharacteristic
554C2—22no—
555C2—1722no—
556C2#1914404811yescharacteristic
557C2C2×#1458313911yescharacteristic
558C2#1914431411yescharacteristic
subgroupG/H
centerC2×C4#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1542C2
socleC22×C43C2×#121
prime radicalC2×#10621898D4
hypercenter#1542D43
hypocenterC43#19126
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
1. #19145177C2semidirect
5. #19134056C2semidirect
6. #19134052C2semidirect
7. #19134049C2semidirect
8. #19134045C2semidirect
9. #19133998C2semidirect
10. #19133993C2semidirect
11. #19133964C2semidirect
12. #19133959C2semidirect
13. C2×#14582651C2semidirect
14. #19133250C2semidirect
15. C43×#1542C2semidirect
151. #10621898Q16semidirect
289. #1542D43semidirect
346. C43#19126semidirect

Maximal subgroups

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

subgroupindex
#191451772
#191443852
#191443772
#191435512
#191340562
#191340522
#191340492
#191340452
#191339982
#191339932
#191339642
#191339592
C2×#145826512
#191332502
C43×#15422
#1912643