Finite Group Databasebeta

← #25080048

Subgroups — #25080048

Order 11008.

584 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#19145934C211yesmaximal, characteristic
2#19145928C211yesmaximal, characteristic
3#19145180C211yesmaximal, characteristic, complemented
4#19143567C211yesmaximal, characteristic
5#19134112C211yesmaximal, characteristic, complemented
6#19134106C211yesmaximal, characteristic, complemented
7#19134088C211yesmaximal, characteristic, complemented
8#19134082C211yesmaximal, characteristic, complemented
9#19134026C211yesmaximal, characteristic, complemented
10#19134022C211yesmaximal, characteristic, complemented
11#19134018C211yesmaximal, characteristic, complemented
12#334×D43C211yesmaximal, characteristic, complemented
13#19133294C211yesmaximal, characteristic, complemented
14#19133292C211yesmaximal, characteristic, complemented
15C43×#1679C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18#14583431C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583278C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583205—21no—
23#14583204—21no—
24#14583185C2211yescharacteristic
25#14583181C2211yescharacteristic
26#14583179C2211yescharacteristic
27#14583141—21no—
28#14583139—21no—
29#14583139—21no—
30#14583139—21no—
31#14583127—21no—
32#14583125—21no—
33#14583120—21no—
34#14583119—21no—
35#14583110C2211yescharacteristic
36#14583106C2211yescharacteristic
37#14583104C2211yescharacteristic
38#14583026C2211yescharacteristic
39C8×Dic86C2211yescharacteristic
40#14582991—21no—
41#14582991—21no—
42#14582977C2211yescharacteristic
43#14582973—21no—
44C8×C22⋊D43—21no—
45#14582957—21no—
46#14582955C2211yescharacteristic
47C4⋊C8×D43C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582854—21no—
50C4×C8×D43C2211yescharacteristic
51#14582650C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582645C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#474C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Dic172—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621883—21no—
72C2×#10621877—21no—
73C2×C8×D43—21no—
74C2×C8×D43—21no—
75C2×C8×D43D411yescharacteristic
76C2×C8×D43D411yescharacteristic
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063318—21no—
80#13063316—21no—
81#13063316—21no—
82#13063316D411yescharacteristic
83#13063312D411yescharacteristic
84#13063307—21no—
85#13063305—21no—
86#13063305—21no—
87#13063305D411yescharacteristic
88#13063301—21no—
89#13063301—21no—
90#13063296D411yescharacteristic
91Q8×Dic43—21no—
92Q8×Dic43—21no—
93C4×Dic86C2311yescharacteristic
94#13063290—21no—
95#13063290—21no—
96C4×C22⋊D43—21no—
97#13063284—21no—
98#13063283—21no—
99#13063283—21no—
100C42×D43C2311yescharacteristic
101#13063258—21no—
102#13063258—21no—
103#13063258—21no—
104#13063257—21no—
105#13063256—21no—
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113#13063250—21no—
114#13063250—21no—
115#13063250—21no—
116#13063250—21no—
117#13063249—21no—
118#13063248—21no—
119#13063248—21no—
120#13063246—21no—
121C22⋊(C43⋊C8)—21no—
122(C2×D43)⋊C8—21no—
123#13063235—21no—
124#13063235—21no—
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C2×SD16×C43—21no—
130C22×C8×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132C4⋊Q8×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#107×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×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—
149C2×C4×D43C2×D411yescharacteristic
150C2×C4×D43C2×D411yescharacteristic
151C2×C4×D43#4111yescharacteristic
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86C2×D411yescharacteristic
155SD16×C43—81no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—42no—
160C2×C8×C43C2×D411yescharacteristic
161C2×C8×C43C2×D411yescharacteristic
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43C2×D411yescharacteristic
167C22⋊C4×C43—21no—
168C42×C43C2411yescharacteristic
169C22⋊Dic43—21no—
170C22⋊Dic43—21no—
171C22⋊Dic43—21no—
172#10621885—42no—
173#10621885—42no—
174#10621885—81no—
175#10621883—81no—
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—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—41no—
186C4⋊Dic43—41no—
187C4⋊Dic43C2×D411yescharacteristic
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
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—81no—
205C8×D43—22no—
206C8×D43—41no—
207C8×D43—81no—
208C8×D43—81no—
209C23×C43—21no—
210C22×D43#12111yescharacteristic
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—41no—
215D4×C43—21no—
216D4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C22⋊D43—42no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43#12111yescharacteristic
231C2×Dic43#12111yescharacteristic
232C2×Dic43#12111yescharacteristic
233C4×D43—22no—
234C4×D43—21no—
235C4×D43—21no—
236C4×D43—21no—
237C4×D43—21no—
238Dic86—21no—
239Dic86—21no—
240Dic86—41no—
241Dic86—41no—
242Dic86—41no—
243Dic86—41no—
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#19228—431nomaximal, Sylow
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43C2×#12111yescharacteristic
259C2×D43—21no—
260C2×D43—21no—
261C2×D43#47312yes—
262C4×C43—21no—
263C4×C43—41no—
264C4×C43—81no—
265C4×C43—81no—
266C4×C43C2×#13511yescharacteristic
267C4×C43#57511yescharacteristic
268C4×C43#57711yescharacteristic
269C4×C43#57711yescharacteristic
270Dic43—21no—
271Dic43—21no—
272Dic43—21no—
273Dic43—41no—
274Dic43—41no—
275Dic43—81no—
276Dic43—81no—
277#3248—431no—
278#3248—431no—
279#3170—431no—
280#2966—431no—
281#1694—431no—
282#1693—431no—
283#1690—431no—
284#1689—431no—
285#1680—431no—
286#1680—431no—
287#1679—431no—
288#1679D4311yescharacteristic, complemented
289C2×#334—431no—
290#1552—431no—
291#1552—431no—
292C2×C43—81no—
293C2×C43#303511yescharacteristic
294C2×C43#306011yescharacteristic
295C2×C43C2×#47311yescharacteristic
296D43—22no—
297#533—431no—
298#533—431no—
299#529—431no—
300#500—431no—
301#494—431no—
302#487—431no—
303#487C2×D4311yescharacteristic
304#479—861no—
305#479—861no—
306#475—431no—
307#475—431no—
308#474—431no—
309#474C2×D4311yescharacteristic
310#467—861no—
311#467—861no—
312#467—861no—
313#467—861no—
314#465—861no—
315#465—861no—
316#464—861no—
317#464—861no—
318#462—431no—
319#462—431no—
320#461—431no—
321#461C2×D4311yescharacteristic
322#446—431no—
323C8×Q8—431no—
324C4×Q16—861no—
325C4×Q16—861no—
326#436—431no—
327#435—861no—
328C8×D4—861no—
329C8×D4C2×D4311yescharacteristic
330#433—861no—
331#432—431no—
332C2×C4⋊C8—431no—
333C2×C4⋊C8—431no—
334#405—861no—
335C2×C4×C8—431no—
336#334—431no—
337#334—431no—
338#334—431no—
339#334C2×D4311yescharacteristic
340#332—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346#332C2×D4311yescharacteristic
347#332C2×D4311yescharacteristic
348C43#1922811yescharacteristic, complemented, Sylow
349C2×Q16—861no—
350C2×Q16—861no—
351C2×Q16—861no—
352C2×Q16—861no—
353C2×SD16—21no—
354C2×SD16—861no—
355C2×M16—861no—
356C22×C8—21no—
357C22×C8—431no—
358C22×C8—431no—
359C22×C8—861no—
360C22×C8—861no—
361C4⋊Q8—431no—
362C4⋊Q8—431no—
363C4⋊Q8C22×D4311yescharacteristic
364C4⋊Q8C22×D4311yescharacteristic
365#126—861no—
366#125—431no—
367#125—861no—
368#125—861no—
369#124—431no—
370#123—861no—
371C22⋊Q8—431no—
372C22⋊Q8—861no—
373C22⋊Q8—861no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376#121—431no—
377C4×Q8—431no—
378C4×Q8—861no—
379C4×Q8—861no—
380C4×Q8—861no—
381C4×Q8—861no—
382C4×D4—861no—
383C4×D4C22×D4311yescharacteristic
384#117—861no—
385#117—861no—
386#117—861no—
387C2×C42—431no—
388#107—21no—
389#107—861no—
390#107—861no—
391#107—861no—
392#106—861no—
393#106—861no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—861no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8C22×D4311yescharacteristic
402C4⋊C8C22×D4311yescharacteristic
403C4⋊C8C22×D4311yescharacteristic
404#103—21no—
405#103—21no—
406#103—21no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#102—21no—
415#102—861no—
416C22⋊C8—21no—
417C22⋊C8—861no—
418C22⋊C8—861no—
419#97—861no—
420#97—861no—
421C4×C8—431no—
422C4×C8—431no—
423C4×C8—431no—
424C4×C8—861no—
425C4×C8C22×D4311yescharacteristic
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—431no—
429C2×Q8—861no—
430C2×Q8—861no—
431C2×D4—861no—
432C2×D4D4×D4311yescharacteristic
433C22×C4—21no—
434C22×C4—431no—
435C22×C4—431no—
436C22×C4—431no—
437Q16—3441no—
438Q16—3441no—
439Q16—1722no—
440Q16—1722no—
441SD16—81no—
442SD16—3441no—
443M16—1722no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—42no—
448C2×C8—431no—
449C2×C8—431no—
450C2×C8—862no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—3441no—
455C2×C8—3441no—
456C2×C8—1721no—
457C2×C8D4×D4311yescharacteristic
458C2×C8D4×D4311yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—431no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—1721no—
473C4⋊C4—1721no—
474C4⋊C4—1721no—
475C4⋊C4—1721no—
476C4⋊C4D4×D4311yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—861no—
479C22⋊C4—861no—
480C22⋊C4—861no—
481C22⋊C4—861no—
482C22⋊C4—1721no—
483C22⋊C4—1721no—
484C42—431no—
485C42—431no—
486C42—431no—
487C42—861no—
488C42—1721no—
489C42—1721no—
490C42C23×D4311yescharacteristic
491C23—21no—
492C23—431no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—861no—
498Q8—861no—
499Q8—1721no—
500Q8—1721no—
501Q8—1721no—
502Q8—1721no—
503D4—21no—
504D4—21no—
505D4—1722no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—431no—
512C2×C4—431no—
513C2×C4—431no—
514C2×C4—862no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
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—432no—
540C22—861no—
541C22—861no—
542C22#121×D4311yescharacteristic
543C4—21no—
544C4—41no—
545C4—81no—
546C4—81no—
547C4—861no—
548C4—861no—
549C4—861no—
550C4—3441no—
551C4—3441no—
552C4—1721no—
553C4—1721no—
554C4#135×D4311yescharacteristic
555C4#1458369511yescharacteristic
556C4#1458370511yescharacteristic
557C4#1458370611yescharacteristic
558C2—81no—
559C2—862no—
560C2#1914404711yescharacteristic
561C2#1914425211yescharacteristic
562C2#473×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1679C2
socleC22×C43C2×#121
prime radical#13063296D4
hypercenter#1679D43
hypocenterC43#19228
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1679

Complements

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

NH ≅ G/Ntype
3. #19145180C2semidirect
5. #19134112C2semidirect
6. #19134106C2semidirect
7. #19134088C2semidirect
8. #19134082C2semidirect
9. #19134026C2semidirect
10. #19134022C2semidirect
11. #19134018C2semidirect
12. #334×D43C2semidirect
13. #19133294C2semidirect
14. #19133292C2semidirect
15. C43×#1679C2semidirect
288. #1679D43semidirect
348. C43#19228semidirect

Maximal subgroups

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

subgroupindex
#191459342
#191459282
#191451802
#191435672
#191341122
#191341062
#191340882
#191340822
#191340262
#191340222
#191340182
#334×D432
#191332942
#191332922
C43×#16792
#1922843