Finite Group Databasebeta

← #25079653

Subgroups — #25079653

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#19145339C211yesmaximal, characteristic, complemented
2#19144668C211yesmaximal, characteristic
3#19144384C211yesmaximal, characteristic
4#19143611C211yesmaximal, characteristic
5#19134142C211yesmaximal, characteristic, complemented
6#19134096C211yesmaximal, characteristic, complemented
7#19134082C211yesmaximal, characteristic, complemented
8#19134050C211yesmaximal, characteristic, complemented
9#19134026C211yesmaximal, characteristic, complemented
10#19133980C211yesmaximal, characteristic, complemented
11#19133964C211yesmaximal, characteristic, complemented
12#19133344C211yesmaximal, characteristic, complemented
13#19133304C211yesmaximal, characteristic, complemented
14#19133292C211yesmaximal, characteristic, complemented
15C43×#1703C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18C4×#10621900C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583278C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583242—21no—
23#14583209—21no—
24#14583201—21no—
25#14583191C2211yescharacteristic
26#14583185C2211yescharacteristic
27#14583181C2211yescharacteristic
28#14583179C2211yescharacteristic
29#14583156—21no—
30#14583156—21no—
31#14583110C2211yescharacteristic
32#14583104C2211yescharacteristic
33#14583062—21no—
34C8×Dic86C2211yescharacteristic
35#14583023C2211yescharacteristic
36#14583003—21no—
37#14583003—21no—
38#14582993—21no—
39#14582990—21no—
40#14582977C2211yescharacteristic
41#14582975—21no—
42#14582974—21no—
43#14582955C2211yescharacteristic
44#14582953—21no—
45#14582951C2211yescharacteristic
46#14582934—21no—
47C4⋊C8×D43C2211yescharacteristic
48#14582892—21no—
49M16×Dic43—21no—
50C4×#10621872C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#476C2211yescharacteristic
62C43×#474C2211yescharacteristic
63C43×#436C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621900D411yescharacteristic
68C2×Dic172—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621883—21no—
72C2×#10621877—21no—
73C2×#10621872D411yescharacteristic
74C2×#10621872D411yescharacteristic
75C2×C8×D43—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063316—21no—
79#13063316—21no—
80#13063305—21no—
81#13063305—21no—
82#13063301—21no—
83#13063301—21no—
84Q8×Dic43—21no—
85Q8×Dic43—21no—
86C4×Dic86C2311yescharacteristic
87#13063290—21no—
88#13063290—21no—
89#13063290D411yescharacteristic
90D4×Dic43D411yescharacteristic
91C4×C22⋊D43—21no—
92(C22⋊D43)⋊C4—21no—
93#13063283—21no—
94#13063283—21no—
95#13063283D411yescharacteristic
96#13063281—21no—
97C2×C4×Dic43—21no—
98C42×D43C2311yescharacteristic
99#13063258—21no—
100#13063258—21no—
101#13063257—21no—
102#13063256—21no—
103#13063256—21no—
104#13063256—21no—
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111#13063250—21no—
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063248—21no—
116#13063248—21no—
117#13063248—21no—
118#13063246—21no—
119C22⋊(C43⋊C8)—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122#13063235—21no—
123#13063235D411yescharacteristic
124#13063235D411yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×M16×C43—21no—
130C4⋊Q8×C43C2311yescharacteristic
131C4⋊Q8×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#107×C43—21no—
134#106×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C2×C22⋊D43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151#10621900—22no—
152#10621900—41no—
153C2×C4×D43C2×D411yescharacteristic
154C2×C4×D43C2×D411yescharacteristic
155C2×C4×D43#4111yescharacteristic
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86C2×D411yescharacteristic
159M16×C43—42no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C2×D411yescharacteristic
170C22⋊C4×C43—21no—
171C42×C43C2411yescharacteristic
172C22⋊Dic43—21no—
173#10621885—42no—
174#10621885—42no—
175#10621883—42no—
176(C2×D43)⋊C4—21no—
177(C2×D43)⋊C4—41no—
178(C2×D43)⋊C4—41no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—41no—
184C4⋊Dic43—41no—
185C4⋊Dic43C2×D411yescharacteristic
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—41no—
189Dic43⋊C4—41no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—41no—
194C4×Dic43—41no—
195C4×Dic43C2×D411yescharacteristic
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43#4111yescharacteristic
198#10621877—42no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204Dic172—42no—
205#10621872—22no—
206#10621872—41no—
207C8×D43—42no—
208C23×C43—21no—
209C22×D43#12111yescharacteristic
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—81no—
213D4×C43—21no—
214D4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C2×C4×C43C2×#4111yescharacteristic
223C22⋊D43—42no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—42no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—81no—
230C2×Dic43#12111yescharacteristic
231C2×Dic43#12111yescharacteristic
232C2×Dic43#12111yescharacteristic
233C4×D43—21no—
234C4×D43—21no—
235C4×D43—21no—
236C4×D43—21no—
237C4×D43—41no—
238Dic86—21no—
239Dic86—41no—
240Dic86—41no—
241Dic86—41no—
242Dic86—41no—
243Dic86#13712yes—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C43⋊C8—21no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8#13512yes—
254#19185—431nomaximal, Sylow
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43C2×#12111yescharacteristic
259C2×D43—21no—
260C2×D43—21no—
261C2×D43—21no—
262C4×C43—21no—
263C4×C43—41no—
264C4×C43—81no—
265C4×C43—81no—
266C4×C43C2×#13511yescharacteristic
267C4×C43C2×#13711yescharacteristic
268C4×C43#57511yescharacteristic
269C4×C43#57511yescharacteristic
270Dic43—21no—
271Dic43—22no—
272Dic43—21no—
273Dic43—21no—
274Dic43—41no—
275Dic43—81no—
276Dic43—81no—
277#3185—431no—
278#3107—431no—
279#3076—431no—
280#2971—431no—
281#1703D4311yescharacteristic, complemented
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#1554—431no—
291#1552—431no—
292C2×C43—81no—
293C2×C43#303511yescharacteristic
294C2×C43#305611yescharacteristic
295C2×C43#306911yescharacteristic
296D43—41no—
297#533—431no—
298#533—431no—
299C4×#41—431no—
300#498—431no—
301#494—431no—
302#487—431no—
303#487C2×D4311yescharacteristic
304#485—861no—
305#479—861no—
306#478—861no—
307#477—431no—
308#476C2×D4311yescharacteristic
309#475—431no—
310#475—431no—
311#474—431no—
312#474C2×D4311yescharacteristic
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—861no—
326#436—861no—
327#436C2×D4311yescharacteristic
328#432—431no—
329#432—861no—
330#431—431no—
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#334C2×D4311yescharacteristic
340#333—431no—
341#333C2×D4311yescharacteristic
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346#332—431no—
347#332C2×D4311yescharacteristic
348C43#1918511yescharacteristic, complemented, Sylow
349C2×#41—431no—
350C2×Q16—861no—
351C2×Q16—861no—
352C2×Q16—861no—
353C2×SD16—861no—
354C2×M16—21no—
355C2×M16—431no—
356C2×M16—431no—
357C2×M16—861no—
358C22×C8—861no—
359C4⋊Q8—431no—
360C4⋊Q8—431no—
361C4⋊Q8C22×D4311yescharacteristic
362C4⋊Q8C22×D4311yescharacteristic
363#125—861no—
364#125—861no—
365C22⋊Q8—861no—
366C22⋊Q8—861no—
367C22⋊Q8—861no—
368C22⋊Q8—861no—
369C4×Q8—431no—
370C4×Q8—431no—
371C4×Q8—861no—
372C4×Q8—861no—
373C4×Q8—861no—
374C4×Q8—861no—
375C4×D4—431no—
376C4×D4—861no—
377C4×D4—861no—
378C4×D4C22×D4311yescharacteristic
379#117—431no—
380#117—861no—
381#117—861no—
382#117—861no—
383C2×C42—431no—
384C2×C42—861no—
385#107—21no—
386#107—861no—
387#107—861no—
388#106—21no—
389#106—861no—
390#106—861no—
391#106—861no—
392#106—861no—
393C4⋊C8—431no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—861no—
397C4⋊C8—861no—
398C4⋊C8—861no—
399C4⋊C8C22×D4311yescharacteristic
400C4⋊C8C22×D4311yescharacteristic
401C4⋊C8C22×D4311yescharacteristic
402#103—21no—
403#103—21no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#102—21no—
412#102—21no—
413#102—861no—
414C22⋊C8—21no—
415C22⋊C8—861no—
416C22⋊C8—861no—
417C22⋊C8—861no—
418#97—431no—
419#97—431no—
420#97—861no—
421C4×C8—431no—
422C4×C8—861no—
423C4×C8—861no—
424C4×C8—861no—
425C4×C8C22×D4311yescharacteristic
426#41—862no—
427#41—1721no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—431no—
431C2×Q8—861no—
432C2×Q8—861no—
433C2×D4—861no—
434C2×D4D4×D4311yescharacteristic
435C22×C4—21no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—861no—
440C22×C4—861no—
441Q16—1722no—
442Q16—1722no—
443Q16—1722no—
444SD16—1722no—
445M16—42no—
446M16—862no—
447M16—1721no—
448M16—1722no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—431no—
453C2×C8—431no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—1722no—
458C2×C8D4×D4311yescharacteristic
459C2×C8D4×D4311yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
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—
473C4⋊C4—1721no—
474C4⋊C4—1721no—
475C4⋊C4D4×D4311yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—861no—
478C22⋊C4—861no—
479C22⋊C4—1721no—
480C22⋊C4—1721no—
481C42—431no—
482C42—431no—
483C42—431no—
484C42—861no—
485C42—861no—
486C42—861no—
487C42—1721no—
488C42—1721no—
489C42C23×D4311yescharacteristic
490C23—21no—
491C23—431no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—432no—
496Q8—861no—
497Q8—1721no—
498Q8—1721no—
499Q8—1721no—
500Q8—1721no—
501D4—21no—
502D4—21no—
503D4—1722no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—431no—
510C2×C4—431no—
511C2×C4—431no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—3441no—
519C2×C4—1721no—
520C2×C4—1722no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4C2×D4×D4311yescharacteristic
524C2×C4C2×D4×D4311yescharacteristic
525C2×C4#41×D4311yescharacteristic
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—432no—
532C8—861no—
533C8—1721no—
534C8—1721no—
535C8—1721no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—861no—
540C22—861no—
541C22—861no—
542C22#121×D4311yescharacteristic
543C4—21no—
544C4—41no—
545C4—81no—
546C4—81no—
547C4—861no—
548C4—862no—
549C4—861no—
550C4—861no—
551C4—3441no—
552C4—3441no—
553C4—1721no—
554C4#135×D4311yescharacteristic
555C4#137×D4311yescharacteristic
556C4#1458369511yescharacteristic
557C4#1458369811yescharacteristic
558C2—81no—
559C2—1721no—
560C2#1914404711yescharacteristic
561C2#1914422411yescharacteristic
562C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1703C2
socleC22×C43C2×#121
prime radicalC2×#10621900D4
hypercenter#1703D43
hypocenterC43#19185
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1703

Complements

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

NH ≅ G/Ntype
1. #19145339C2semidirect
5. #19134142C2semidirect
6. #19134096C2semidirect
7. #19134082C2semidirect
8. #19134050C2semidirect
9. #19134026C2semidirect
10. #19133980C2semidirect
11. #19133964C2semidirect
12. #19133344C2semidirect
13. #19133304C2semidirect
14. #19133292C2semidirect
15. C43×#1703C2semidirect
281. #1703D43semidirect
348. C43#19185semidirect

Maximal subgroups

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

subgroupindex
#191453392
#191446682
#191443842
#191436112
#191341422
#191340962
#191340822
#191340502
#191340262
#191339802
#191339642
#191333442
#191333042
#191332922
C43×#17032
#1918543