Finite Group Databasebeta

← #25079644

Subgroups — #25079644

Order 11008.

592 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145336C211yesmaximal, characteristic, complemented
2#19144667C211yesmaximal, characteristic
3#19144377C211yesmaximal, characteristic
4#19143612C211yesmaximal, characteristic
5#19134173C211yesmaximal, characteristic, complemented
6#19134141C211yesmaximal, characteristic, complemented
7#19134097C211yesmaximal, characteristic, complemented
8#19134083C211yesmaximal, characteristic, complemented
9#19134056C211yesmaximal, characteristic, complemented
10#19134024C211yesmaximal, characteristic, complemented
11#19133980C211yesmaximal, characteristic, complemented
12#19133964C211yesmaximal, characteristic, complemented
13#19133348C211yesmaximal, characteristic, complemented
14#19133296C211yesmaximal, characteristic, complemented
15C43×#1554C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17C4×#10621898C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583278C2211yescharacteristic
20#14583251C2211yescharacteristic
21#14583249C2211yescharacteristic
22#14583241—21no—
23#14583203—21no—
24#14583196—21no—
25#14583191C2211yescharacteristic
26#14583186C2211yescharacteristic
27#14583185C2211yescharacteristic
28#14583181C2211yescharacteristic
29#14583180C2211yescharacteristic
30#14583176C2211yescharacteristic
31#14583155—21no—
32#14583155—21no—
33#14583110C2211yescharacteristic
34#14583105C2211yescharacteristic
35#14583063—21no—
36#14583023C2211yescharacteristic
37#14583023C2211yescharacteristic
38#14583004—21no—
39#14583004—21no—
40C4×Dic172—21no—
41C4×#10621873—21no—
42#14582976C2211yescharacteristic
43#14582976C2211yescharacteristic
44#14582974—21no—
45#14582974—21no—
46#14582954—21no—
47#14582935—21no—
48C2×C4⋊(C43⋊C8)C2211yescharacteristic
49#14582893—21no—
50C4×#10621877C2211yescharacteristic
51#14582851—21no—
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#533C2211yescharacteristic
61C43×#432C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×#333C2211yescharacteristic
64C43×#333C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621898D411yescharacteristic
68C2×Dic172—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621873—21no—
72C2×#10621877D411yescharacteristic
73C2×#10621877D411yescharacteristic
74C2×#10621872—21no—
75C2×#10621872—21no—
76C22×C43⋊C8—21no—
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063317—21no—
80#13063304—21no—
81#13063304—21no—
82C4×Dic86—21no—
83C4×Dic86—21no—
84C4×Dic86D411yescharacteristic
85C4×Dic86C2311yescharacteristic
86C4×D172D411yescharacteristic
87C4×D172C2311yescharacteristic
88C4×C22⋊D43—21no—
89C4×C22⋊D43—21no—
90#13063284—21no—
91#13063284D411yescharacteristic
92#13063282—21no—
93C42×D43—21no—
94#13063259—21no—
95#13063258—21no—
96#13063258—21no—
97#13063257—21no—
98#13063256—21no—
99#13063256—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#13063250—21no—
110#13063249—21no—
111#13063249—21no—
112#13063248—21no—
113#13063248—21no—
114#13063248—21no—
115#13063248—21no—
116#13063247—21no—
117#13063245—21no—
118#13063245—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063236D411yescharacteristic
122#13063236D411yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C4⋊Q8×C43C2311yescharacteristic
128C4⋊Q8×C43C2311yescharacteristic
129#125×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43—21no—
132C4×Q8×C43—21no—
133C4×Q8×C43—21no—
134#117×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142#97×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#10621898—41no—
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—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—41no—
168C4⋊C4×C43—41no—
169C22⋊C4×C43—41no—
170C42×C43—41no—
171C42×C43C2×D411yescharacteristic
172C42×C43C2×D411yescharacteristic
173C42×C43#4111yescharacteristic
174C42×C43C2411yescharacteristic
175C22⋊Dic43—21no—
176C22⋊Dic43—41no—
177#10621885—42no—
178#10621885—42no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43C2×D411yescharacteristic
186C4⋊Dic43C2×D411yescharacteristic
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—41no—
195#10621877—22no—
196#10621877—41no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—42no—
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204Dic172—42no—
205#10621873—42no—
206#10621872—42no—
207#10621872—42no—
208C23×C43#12111yescharacteristic
209C22×D43—21no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—81no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C22⋊D43—42no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232D172—21no—
233D172—21no—
234C4×D43—42no—
235C4×D43—41no—
236C4×D43—41no—
237C4×D43—81no—
238Dic86—21no—
239Dic86—41no—
240Dic86—41no—
241Dic86—41no—
242Dic86—41no—
243Dic86#13712yes—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43—41no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8#13512yes—
254#19185—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43C2×#12111yescharacteristic
259C2×D43—41no—
260C2×D43—41no—
261C2×D43—41no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—81no—
267C4×C43—81no—
268C4×C43C2×#13511yescharacteristic
269C4×C43C2×#13711yescharacteristic
270C4×C43#57511yescharacteristic
271C4×C43#57511yescharacteristic
272Dic43—22no—
273Dic43—41no—
274Dic43—41no—
275Dic43—81no—
276Dic43—81no—
277#3185—431no—
278#3107—431no—
279#3076—431no—
280#2971—431no—
281#1703—431no—
282#1699—431no—
283#1691—431no—
284#1689—431no—
285#1684—431no—
286#1680—431no—
287#1672—431no—
288#1670—431no—
289#1565—431no—
290#1554D4311yescharacteristic, complemented
291#1552—431no—
292C2×C43—41no—
293C2×C43#303511yescharacteristic
294C2×C43#305611yescharacteristic
295C2×C43#306911yescharacteristic
296D43—81no—
297#533—431no—
298#533C2×D4311yescharacteristic
299C4×#41—431no—
300#498—431no—
301#494—431no—
302#487—431no—
303#487—431no—
304#485—861no—
305#479—861no—
306#478—861no—
307#477—431no—
308#476—431no—
309#475—431no—
310#475—431no—
311#474—431no—
312#474—431no—
313#470—861no—
314#470—861no—
315#462—431no—
316#461—431no—
317#452—861no—
318C8×Q8—431no—
319C8×Q8—431no—
320#441—861no—
321#441—861no—
322C4×Q16—861no—
323C4×SD16—861no—
324#436—431no—
325#436—431no—
326#436—861no—
327#436—861no—
328#432—861no—
329#432C2×D4311yescharacteristic
330#431C2×D4311yescharacteristic
331#427—861no—
332C2×C4⋊C8—431no—
333#416—861no—
334C4×M16—431no—
335C4×M16—861no—
336#335—431no—
337#335—431no—
338#334—431no—
339#334—431no—
340#333C2×D4311yescharacteristic
341#333C2×D4311yescharacteristic
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346#332C2×D4311yescharacteristic
347#332C2×D4311yescharacteristic
348C43#1918511yescharacteristic, complemented, Sylow
349C2×#41—431no—
350C2×Q16—861no—
351C2×Q16—861no—
352C2×Q16—861no—
353C2×SD16—861no—
354C2×M16—431no—
355C2×M16—431no—
356C2×M16—861no—
357C2×M16—861no—
358C22×C8—861no—
359C4⋊Q8—431no—
360C4⋊Q8—431no—
361C4⋊Q8C22×D4311yescharacteristic
362C4⋊Q8C22×D4311yescharacteristic
363#125—21no—
364#125—861no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—861no—
368C22⋊Q8—861no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—431no—
372C4×Q8—431no—
373C4×Q8—861no—
374C4×Q8—861no—
375C4×D4—431no—
376C4×D4—431no—
377C4×D4—861no—
378C4×D4—861no—
379#117—21no—
380#117—431no—
381#117—861no—
382#117—861no—
383C2×C42—861no—
384C2×C42C22×D4311yescharacteristic
385#107—861no—
386#107—861no—
387#107—861no—
388#106—861no—
389#106—861no—
390#106—861no—
391#106—861no—
392#106—861no—
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#103—861no—
411#102—861no—
412#102—861no—
413#102—861no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—861no—
417C22⋊C8—861no—
418#97—21no—
419#97—431no—
420#97—431no—
421C4×C8—21no—
422C4×C8—431no—
423C4×C8—431no—
424C4×C8—861no—
425C4×C8—861no—
426#41—862no—
427#41—1721no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—431no—
431C2×Q8—861no—
432C2×Q8—861no—
433C2×D4—431no—
434C2×D4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4#1062189811yescharacteristic
439C22×C4D4×D4311yescharacteristic
440C22×C4D4×D4311yescharacteristic
441Q16—1722no—
442Q16—1722no—
443Q16—1722no—
444SD16—1722no—
445M16—862no—
446M16—1722no—
447M16—1722no—
448M16—1721no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—431no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—1722no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—431no—
467C4⋊C4—431no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—1721no—
475C4⋊C4—1721no—
476C22⋊C4—41no—
477C22⋊C4—861no—
478C22⋊C4—861no—
479C22⋊C4—861no—
480C22⋊C4—1721no—
481C42—41no—
482C42—861no—
483C42—861no—
484C42—861no—
485C42—1721no—
486C42#1062189811yescharacteristic
487C42D4×D4311yescharacteristic
488C42D4×D4311yescharacteristic
489C42C23×D4311yescharacteristic
490C23—861no—
491C23#1306329811yescharacteristic
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—432no—
496Q8—861no—
497Q8—1721no—
498Q8—1721no—
499Q8—1721no—
500Q8—1721no—
501D4—861no—
502D4—861no—
503D4—1722no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—3441no—
515C2×C4—1722no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4#1306329811yescharacteristic
521C2×C4#1306329811yescharacteristic
522C2×C4#1306329811yescharacteristic
523C2×C4C2×D4×D4311yescharacteristic
524C2×C4C2×D4×D4311yescharacteristic
525C2×C4C2×#1062189811yescharacteristic
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—432no—
531C8—861no—
532C8—861no—
533C8—861no—
534C8—1721no—
535C8—1721no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—1721no—
540C22—1721no—
541C22—1721no—
542C22C2×#1306329811yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—81no—
548C4—81no—
549C4—862no—
550C4—3441no—
551C4—3441no—
552C4—1721no—
553C4—1721no—
554C4#135×D4311yescharacteristic
555C4#137×D4311yescharacteristic
556C4#1458369611yescharacteristic
557C4#1458369811yescharacteristic
558C2—41no—
559C2—3441no—
560C2#1914404811yescharacteristic
561C2#1914422311yescharacteristic
562C2#1914433511yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1554C2
socleC22×C43C2×#121
prime radicalC2×#10621898D4
hypercenter#1554D43
hypocenterC43#19185
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1554

Complements

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

NH ≅ G/Ntype
1. #19145336C2semidirect
5. #19134173C2semidirect
6. #19134141C2semidirect
7. #19134097C2semidirect
8. #19134083C2semidirect
9. #19134056C2semidirect
10. #19134024C2semidirect
11. #19133980C2semidirect
12. #19133964C2semidirect
13. #19133348C2semidirect
14. #19133296C2semidirect
15. C43×#1554C2semidirect
290. #1554D43semidirect
348. C43#19185semidirect

Maximal subgroups

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

subgroupindex
#191453362
#191446672
#191443772
#191436122
#191341732
#191341412
#191340972
#191340832
#191340562
#191340242
#191339802
#191339642
#191333482
#191332962
C43×#15542
#1918543