Finite Group Databasebeta

← #25080051

Subgroups — #25080051

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#19145932C211yesmaximal, characteristic
2#19145177C211yesmaximal, characteristic, complemented
3#19143571C211yesmaximal, characteristic
4#19134111C211yesmaximal, characteristic, complemented
5#19134106C211yesmaximal, characteristic, complemented
6#19134087C211yesmaximal, characteristic, complemented
7#19134082C211yesmaximal, characteristic, complemented
8#19134027C211yesmaximal, characteristic, complemented
9#19134023C211yesmaximal, characteristic, complemented
10#19134020C211yesmaximal, characteristic, complemented
11#19134016C211yesmaximal, characteristic, complemented
12C2×#14582649C211yesmaximal, characteristic, complemented
13#19133295C211yesmaximal, characteristic, complemented
14#19133293C211yesmaximal, characteristic, complemented
15C43×#3248C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583302C2211yescharacteristic
18#14583278C2211yescharacteristic
19#14583251C2211yescharacteristic
20#14583249C2211yescharacteristic
21#14583203—21no—
22#14583184C2211yescharacteristic
23#14583179C2211yescharacteristic
24#14583138—21no—
25#14583138—21no—
26#14583138—21no—
27#14583126—21no—
28#14583118—21no—
29#14583109C2211yescharacteristic
30#14583104C2211yescharacteristic
31#14583030C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33C4×#10621885—21no—
34C4×#10621885—21no—
35#14582977C2211yescharacteristic
36#14582971—21no—
37D4×C43⋊C8—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582960—21no—
40#14582956C2211yescharacteristic
41C2×C4⋊(C43⋊C8)C2211yescharacteristic
42#14582855—21no—
43C2×C4×C43⋊C8C2211yescharacteristic
44#14582649C2211yescharacteristic
45#14582649C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582644C2211yescharacteristic
55#14582644C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#479—21no—
59C43×#475C2211yescharacteristic
60C43×#474C2211yescharacteristic
61C43×#467—21no—
62C43×#465—21no—
63C43×#464—21no—
64C43×#462C2211yescharacteristic
65C43×#461C2211yescharacteristic
66C2×C4⋊C8×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621883—21no—
71C2×#10621877—21no—
72C22×C43⋊C8—21no—
73C22×C43⋊C8—21no—
74C22×C43⋊C8D411yescharacteristic
75C22×C43⋊C8D411yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063317—21no—
79#13063304—21no—
80#13063304—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83#13063284—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063256—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063249—21no—
96#13063249—21no—
97#13063249—21no—
98#13063248—21no—
99#13063248—21no—
100#13063248—21no—
101#13063248—21no—
102#13063246—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106#13063236—21no—
107#13063236—21no—
108C4×C43⋊C8—21no—
109C4×C43⋊C8D411yescharacteristic
110C4×C43⋊C8D411yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×Q16×C43—21no—
114C2×SD16×C43—21no—
115C22×C8×C43—21no—
116C4⋊Q8×C43C2311yescharacteristic
117C4⋊Q8×C43C2311yescharacteristic
118#126×C43—21no—
119#125×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43D411yescharacteristic
122#123×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43D411yescharacteristic
126#121×C43D411yescharacteristic
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132#117×C43—21no—
133#117×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#107×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
142#103×C43—21no—
143#102×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43#4111yescharacteristic
153C2×Dic86—21no—
154C2×Dic86—21no—
155Q16×C43—81no—
156SD16×C43—81no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—81no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—41no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43C2×D411yescharacteristic
171C4⋊C4×C43C2×D411yescharacteristic
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—41no—
178C42×C43—21no—
179C42×C43—41no—
180C42×C43C2×D411yescharacteristic
181C42×C43C2×D411yescharacteristic
182C42×C43#4111yescharacteristic
183C42×C43C2411yescharacteristic
184C22⋊Dic43—41no—
185#10621885—42no—
186#10621885—42no—
187#10621885—81no—
188#10621883—81no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195C4×Dic43—41no—
196#10621877—42no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—41no—
203C2×C43⋊C8—42no—
204C2×C43⋊C8—81no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C23×C43—21no—
210C23×C43#12111yescharacteristic
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—42no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×Dic43—41no—
239C2×Dic43—41no—
240Dic86—41no—
241Dic86—41no—
242Dic86—41no—
243Dic86—41no—
244C8×C43—41no—
245C8×C43—41no—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8#13512yes—
254#19228—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43#47312yes—
261C22×C43C2×#12111yescharacteristic
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—81no—
270C4×C43—81no—
271C4×C43C2×#13511yescharacteristic
272C4×C43#57511yescharacteristic
273C4×C43#57711yescharacteristic
274C4×C43#57711yescharacteristic
275Dic43—81no—
276Dic43—81no—
277#3248—431no—
278#3248D4311yescharacteristic
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#1679—431no—
289C2×#334—431no—
290#1552—431no—
291#1552—431no—
292C2×C43—22no—
293C2×C43—81no—
294C2×C43#303511yescharacteristic
295C2×C43#306011yescharacteristic
296C2×C43C2×#47311yescharacteristic
297#533—431no—
298#533C2×D4311yescharacteristic
299#529C2×D4311yescharacteristic
300#500—431no—
301#494—431no—
302#487—431no—
303#487—431no—
304#479—21no—
305#479—861no—
306#475—431no—
307#475C2×D4311yescharacteristic
308#474—431no—
309#474C2×D4311yescharacteristic
310#467—21no—
311#467—861no—
312#467—861no—
313#467—861no—
314#465—21no—
315#465—861no—
316#464—21no—
317#464—861no—
318#462—431no—
319#462C2×D4311yescharacteristic
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—431no—
329C8×D4—861no—
330#433—861no—
331#432—431no—
332C2×C4⋊C8—431no—
333C2×C4⋊C8C2×D4311yescharacteristic
334#405—861no—
335C2×C4×C8—431no—
336#334—431no—
337#334—431no—
338#334—431no—
339#334—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346#332—431no—
347#332—431no—
348C43#1922811yescharacteristic, complemented, Sylow
349C2×Q16—21no—
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—21no—
366#125—21no—
367#125—861no—
368#125C22⋊D4311yescharacteristic
369#124C22⋊D4311yescharacteristic
370#123—21no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—861no—
374C22⋊Q8—861no—
375C22⋊Q8C22⋊D4311yescharacteristic
376#121C22⋊D4311yescharacteristic
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—861no—
380C4×Q8—861no—
381C4×Q8C22×D4311yescharacteristic
382C4×D4—21no—
383C4×D4C22×D4311yescharacteristic
384#117—21no—
385#117—21no—
386#117—861no—
387C2×C42C22×D4311yescharacteristic
388#107—21no—
389#107—861no—
390#107—861no—
391#107—861no—
392#106—21no—
393#106—861no—
394C4⋊C8—21no—
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
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—861no—
417C22⋊C8—861no—
418C22⋊C8—861no—
419#97—861no—
420#97—861no—
421C4×C8—431no—
422C4×C8—431no—
423C4×C8—431no—
424C4×C8—431no—
425C4×C8—861no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×Q8C2×C22⋊D4311yescharacteristic
431C2×D4—21no—
432C2×D4C2×C22⋊D4311yescharacteristic
433C22×C4—21no—
434C22×C4D4×D4311yescharacteristic
435C22×C4#1062190011yescharacteristic
436C22×C4C2×C22⋊D4311yescharacteristic
437Q16—81no—
438Q16—3441no—
439Q16—1722no—
440Q16—1722no—
441SD16—81no—
442SD16—3441no—
443M16—1722no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—81no—
447C2×C8—431no—
448C2×C8—431no—
449C2×C8—431no—
450C2×C8—431no—
451C2×C8—862no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—3441no—
457C2×C8—1721no—
458C2×C8—1722no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—1721no—
474C4⋊C4—1721no—
475C4⋊C4C2×C22⋊D4311yescharacteristic
476C4⋊C4C2×C22⋊D4311yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—41no—
483C22⋊C4—1721no—
484C42—21no—
485C42—41no—
486C42—1721no—
487C42D4×D4311yescharacteristic
488C42#1062190011yescharacteristic
489C42C2×C22⋊D4311yescharacteristic
490C42C23×D4311yescharacteristic
491C23—21no—
492C23#1306329711yescharacteristic
493Q8—21no—
494Q8—21no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—1721no—
500Q8—1721no—
501Q8—1721no—
502Q8—1721no—
503D4—21no—
504D4—21no—
505D4—42no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4#1306329711yescharacteristic
521C2×C4#1306329711yescharacteristic
522C2×C4#1306329711yescharacteristic
523C2×C4C2×D4×D4311yescharacteristic
524C2×C4C22×C22⋊D4311yescharacteristic
525C2×C4C2×#1062190011yescharacteristic
526C8—41no—
527C8—41no—
528C8—432no—
529C8—861no—
530C8—861no—
531C8—861no—
532C8—1721no—
533C8—1721no—
534C8—1721no—
535C8—1721no—
536C22—21no—
537C22—21no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22#1458317212yes—
542C22C2×#1306329711yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—81no—
551C4—81no—
552C4—3441no—
553C4—3441no—
554C4#135×D4311yescharacteristic
555C4#1458369611yescharacteristic
556C4#1458370711yescharacteristic
557C4#1458371011yescharacteristic
558C2—22no—
559C2—81no—
560C2#1914404611yescharacteristic
561C2#1914425411yescharacteristic
562C2C2×#1458317211yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3248C2
socleC22×C43C2×#121
prime radical#121×C43D4
hypercenter#3248D43
hypocenterC43#19228
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3248

Complements

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

NH ≅ G/Ntype
2. #19145177C2semidirect
4. #19134111C2semidirect
5. #19134106C2semidirect
6. #19134087C2semidirect
7. #19134082C2semidirect
8. #19134027C2semidirect
9. #19134023C2semidirect
10. #19134020C2semidirect
11. #19134016C2semidirect
12. C2×#14582649C2semidirect
13. #19133295C2semidirect
14. #19133293C2semidirect
348. C43#19228semidirect

Maximal subgroups

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

subgroupindex
#191459322
#191451772
#191435712
#191341112
#191341062
#191340872
#191340822
#191340272
#191340232
#191340202
#191340162
C2×#145826492
#191332952
#191332932
C43×#32482
#1922843