Finite Group Databasebeta

← #25079880

Subgroups — #25079880

Order 11008.

594 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#19145738C211yesmaximal, characteristic
2#19145542C211yesmaximal, characteristic
3#487×D43C211yesmaximal, characteristic
4#19143526C211yesmaximal, characteristic
5#19134150C211yesmaximal, characteristic, complemented
6#19134149C211yesmaximal, characteristic, complemented
7#19134146C211yesmaximal, characteristic, complemented
8#19134028C211yesmaximal, characteristic, complemented
9#19134027C211yesmaximal, characteristic, complemented
10#19134024C211yesmaximal, characteristic, complemented
11#19134023C211yesmaximal, characteristic, complemented
12#19133342C211yesmaximal, characteristic
13#19133278C211yesmaximal, characteristic
14#19133265C211yesmaximal, characteristic
15C43×#1700C211yesmaximal, characteristic, complemented
16#14583453C2211yescharacteristic
17C4⋊Q8×D43C2211yescharacteristic
18C4⋊Q8×D43C2211yescharacteristic
19#14583296—21no—
20#14583277—21no—
21#14583251C2211yescharacteristic
22#14583250C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583248—21no—
25#14583248—21no—
26#14583248—21no—
27#14583248—21no—
28#14583231—21no—
29#14583228—21no—
30#14583185C2211yescharacteristic
31#14583184C2211yescharacteristic
32#14583181C2211yescharacteristic
33#14583110C2211yescharacteristic
34#14583109C2211yescharacteristic
35#14583106C2211yescharacteristic
36#14583056—21no—
37#14583053—21no—
38#14583029C2211yescharacteristic
39#14583027—21no—
40Q8×C43⋊C8C2211yescharacteristic
41#14583023—21no—
42#14583023C2211yescharacteristic
43#14582951C2211yescharacteristic
44#14582951C2211yescharacteristic
45#14582924—21no—
46#14582921C2211yescharacteristic
47#103×D43—21no—
48#103×D43—21no—
49#14582856—21no—
50C4×C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582645C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#475C2211yescharacteristic
62C43×#462C2211yescharacteristic
63C43×#446C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×Q8×D43—21no—
69C2×Dic172—21no—
70C2×#10621885—21no—
71C2×#10621885—21no—
72C2×#10621872—21no—
73C2×C8×D43D411yescharacteristic
74C2×C8×D43D411yescharacteristic
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063324—21no—
78#13063324—21no—
79#13063324—21no—
80#13063324—21no—
81#13063324D411yescharacteristic
82#13063323—21no—
83#13063323—21no—
84#13063323D411yescharacteristic
85#13063315—21no—
86#13063305D411yescharacteristic
87#13063303—21no—
88#13063301D411yescharacteristic
89C4×Dic86—21no—
90C4×Dic86C2311yescharacteristic
91#13063282—21no—
92C4⋊C4×D43—21no—
93C4⋊C4×D43—21no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43—21no—
96C42×D43C2311yescharacteristic
97#13063257—21no—
98#13063256—21no—
99#13063256—21no—
100C4⋊(C43⋊C8)—21no—
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107#13063250—21no—
108#13063250—21no—
109#13063250—21no—
110#13063250—21no—
111#13063249—21no—
112#13063249—21no—
113#13063249—21no—
114#13063249—21no—
115#13063248—21no—
116#13063248—21no—
117#13063248—21no—
118#13063248—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063235—21no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C2×Q16×C43—21no—
130C4⋊Q8×C43C2311yescharacteristic
131C4⋊Q8×C43C2311yescharacteristic
132C4×Q8×C43C2311yescharacteristic
133#106×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#103×C43—21no—
142#97×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147Q8×D43—42no—
148Q8×D43—42no—
149Q8×D43—81no—
150Q8×D43—81no—
151C2×C4×D43—41no—
152C2×C4×D43—41no—
153C2×C4×D43C2×D411yescharacteristic
154C2×C4×D43C2×D411yescharacteristic
155C2×C4×D43#4111yescharacteristic
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—41no—
160C2×Dic86—41no—
161C2×Dic86C2×D411yescharacteristic
162Q16×C43—81no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43C2×D411yescharacteristic
174C42×C43—21no—
175C42×C43C2411yescharacteristic
176#10621885—81no—
177#10621885—81no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43C2×D411yescharacteristic
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195C4×Dic43—21no—
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43#4111yescharacteristic
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204Dic172—81no—
205#10621872—42no—
206C8×D43—22no—
207C8×D43—22no—
208C22×D43#12111yescharacteristic
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—41no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43#12111yescharacteristic
227C2×Dic43#12111yescharacteristic
228C2×Dic43#12111yescharacteristic
229C4×D43—21no—
230C4×D43—21no—
231C4×D43—22no—
232C4×D43—82no—
233C4×D43—82no—
234C4×D43#13512yes—
235C4×D43#13712yes—
236Dic86—21no—
237Dic86—21no—
238Dic86—42no—
239Dic86—41no—
240Dic86—41no—
241Dic86—41no—
242Dic86—41no—
243Dic86—82no—
244Dic86—82no—
245C8×C43—21no—
246C8×C43—21no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43—41no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255#19213—431nomaximal, Sylow
256C22×C43C2×#12111yescharacteristic
257C2×D43—21no—
258C2×D43—21no—
259C2×D43#46412yes—
260C4×C43—21no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—81no—
264C4×C43—81no—
265C4×C43C2×#13511yescharacteristic
266C4×C43C2×#13711yescharacteristic
267C4×C43#57711yescharacteristic
268C4×C43#57711yescharacteristic
269Dic43—21no—
270Dic43—41no—
271Dic43—41no—
272Dic43—81no—
273Dic43—81no—
274Dic43#46412yes—
275Dic43#47312yes—
276#3229—431no—
277#3209—431no—
278C2×#487—431no—
279#2960—431no—
280#1700—431no—
281#1700—431no—
282#1700—431no—
283#1700D4311yescharacteristic, complemented
284#1680—431no—
285#1680—431no—
286#1680—431no—
287#1680—431no—
288#1564—431no—
289#1549—431no—
290#1546—431no—
291C2×C43C2×#46411yescharacteristic
292C2×C43#305711yescharacteristic
293C2×C43C2×#47311yescharacteristic
294D43—22no—
295#533—431no—
296C2×C4⋊Q8—431no—
297C2×C4⋊Q8—431no—
298#498—861no—
299#494—861no—
300#487—431no—
301#487—431no—
302#487—431no—
303#487—861no—
304#487—861no—
305#487—861no—
306#487—861no—
307#487C2×D4311yescharacteristic
308#483—861no—
309#483—861no—
310#475—431no—
311#475—431no—
312#475—431no—
313#475C2×D4311yescharacteristic
314#462—431no—
315#462—431no—
316#462—431no—
317#462C2×D4311yescharacteristic
318#451—861no—
319#451—861no—
320#446—431no—
321#446—861no—
322#446C2×D4311yescharacteristic
323C8×Q8—431no—
324C8×Q8—431no—
325C8×Q8—861no—
326#431—431no—
327#431—431no—
328#424—861no—
329#423—431no—
330C2×#103—861no—
331C2×#103—861no—
332#405—861no—
333C2×C4×C8—431no—
334#335—431no—
335#335C2×D4311yescharacteristic
336#334—431no—
337#334—431no—
338#332—431no—
339#332—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344#332C2×D4311yescharacteristic
345#332C2×D4311yescharacteristic
346C43#1921311yescharacteristic, complemented, Sylow
347C22×Q8—861no—
348C22×Q8—861no—
349C2×Q16—21no—
350C2×Q16—861no—
351C2×Q16—861no—
352C2×Q16—861no—
353C2×M16—861no—
354C22×C8—431no—
355C22×C8—431no—
356C4⋊Q8—431no—
357C4⋊Q8—431no—
358C4⋊Q8—431no—
359C4⋊Q8—431no—
360C4⋊Q8—861no—
361C4⋊Q8—861no—
362C4⋊Q8—861no—
363C4⋊Q8—861no—
364C4⋊Q8—861no—
365C4⋊Q8—861no—
366C4⋊Q8C22×D4311yescharacteristic
367C4⋊Q8C22×D4311yescharacteristic
368#125—861no—
369C22⋊Q8—431no—
370C22⋊Q8—431no—
371C22⋊Q8—861no—
372C4×Q8—431no—
373C4×Q8—861no—
374C4×Q8C22×D4311yescharacteristic
375#117—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C42—431no—
381#106—21no—
382#106—861no—
383#106—861no—
384#106—861no—
385C4⋊C8—21no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8C22×D4311yescharacteristic
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—861no—
401#103—861no—
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#103—861no—
412C22⋊C8—861no—
413C22⋊C8—861no—
414#97—21no—
415#97—861no—
416C4×C8—431no—
417C4×C8—431no—
418C4×C8—431no—
419C4×C8—861no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8C22×D4311yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—431no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×Q8—3441no—
431C2×Q8—3441no—
432C2×Q8—1721no—
433C2×Q8—1721no—
434C2×Q8—1722no—
435C2×Q8—1722no—
436C2×Q8D4×D4311yescharacteristic
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—1721no—
441C22×C4—1721no—
442Q16—81no—
443Q16—3441no—
444Q16—3441no—
445Q16—3441no—
446M16—1722no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—431no—
451C2×C8—431no—
452C2×C8—862no—
453C2×C8—862no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8D4×D4311yescharacteristic
458C2×C8D4×D4311yescharacteristic
459C4⋊C4—21no—
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—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—1721no—
476C4⋊C4—1721no—
477C4⋊C4—1721no—
478C4⋊C4—1721no—
479C4⋊C4D4×D4311yescharacteristic
480C22⋊C4—861no—
481C22⋊C4—861no—
482C42—21no—
483C42—431no—
484C42—431no—
485C42—431no—
486C42—861no—
487C42C23×D4311yescharacteristic
488C23—431no—
489Q8—21no—
490Q8—21no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—861no—
496Q8—861no—
497Q8—3442no—
498Q8—3442no—
499Q8—1722no—
500Q8—1721no—
501Q8—1721no—
502Q8—1721no—
503Q8—1721no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—431no—
509C2×C4—431no—
510C2×C4—432no—
511C2×C4—432no—
512C2×C4—431no—
513C2×C4—862no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—3442no—
519C2×C4—3442no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4C2×D4×D4311yescharacteristic
523C2×C4C2×D4×D4311yescharacteristic
524C2×C4#41×D4311yescharacteristic
525C8—21no—
526C8—21no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—861no—
531C8—861no—
532C8—1721no—
533C8—1721no—
534C8—1721no—
535C22—432no—
536C22—861no—
537C22—861no—
538C22#121×D4311yescharacteristic
539C4—21no—
540C4—41no—
541C4—41no—
542C4—81no—
543C4—81no—
544C4—432no—
545C4—432no—
546C4—861no—
547C4—3441no—
548C4—3441no—
549C4—1721no—
550C4—1721no—
551C4#135×D4311yescharacteristic
552C4#137×D4311yescharacteristic
553C4#1458370811yescharacteristic
554C4#1458370911yescharacteristic
555C2—862no—
556C2#464×D4311yescharacteristic
557C2#1914423211yescharacteristic
558C2#473×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1700C2
socleC22×C43C2×#121
prime radicalC22×D43#121
hypercenter#1700D43
hypocenterC43#19213
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1700

Complements

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

NH ≅ G/Ntype
5. #19134150C2semidirect
6. #19134149C2semidirect
7. #19134146C2semidirect
8. #19134028C2semidirect
9. #19134027C2semidirect
10. #19134024C2semidirect
11. #19134023C2semidirect
15. C43×#1700C2semidirect
283. #1700D43semidirect
346. C43#19213semidirect

Maximal subgroups

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

subgroupindex
#191457382
#191455422
#487×D432
#191435262
#191341502
#191341492
#191341462
#191340282
#191340272
#191340242
#191340232
#191333422
#191332782
#191332652
C43×#17002
#1921343