Finite Group Databasebeta

← #25080535

Subgroups — #25080535

Order 11008.

608 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#19145104C211yesmaximal, characteristic, complemented
2#19144759C211yesmaximal, characteristic
3#19144754C211yesmaximal, characteristic
4C8×#10621900C211yesmaximal, characteristic
5#19133998C211yesmaximal, characteristic, complemented
6#19133992C211yesmaximal, characteristic, complemented
7#19133988C211yesmaximal, characteristic, complemented
8#19133982C211yesmaximal, characteristic, complemented
9#19133978C211yesmaximal, characteristic, complemented
10#19133974C211yesmaximal, characteristic, complemented
11#19133970C211yesmaximal, characteristic, complemented
12#19133355C211yesmaximal, characteristic, complemented
13#19133304C211yesmaximal, characteristic, complemented
14#19133302C211yesmaximal, characteristic, complemented
15C43×#1671C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18C4×#10621900C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583302C2211yescharacteristic
21#14583299—21no—
22#14583299—21no—
23#14583297C2211yescharacteristic
24#14583243—21no—
25#14583239—21no—
26#14583195C2211yescharacteristic
27#14583191C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583110C2211yescharacteristic
30#14583106C2211yescharacteristic
31#14583104C2211yescharacteristic
32#14583062—21no—
33#14583058—21no—
34C8×Dic86C2211yescharacteristic
35#14583023C2211yescharacteristic
36#14583005—21no—
37#14583003—21no—
38#14583000—21no—
39#14582996—21no—
40D4×C43⋊C8C2211yescharacteristic
41C8×C22⋊D43—21no—
42(C22⋊D43)⋊C8—21no—
43#14582955C2211yescharacteristic
44#14582955C2211yescharacteristic
45#14582951C2211yescharacteristic
46#14582949—21no—
47#14582934—21no—
48#14582934—21no—
49C2×C8×Dic43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582650C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#498C2211yescharacteristic
61C43×#476C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621900D411yescharacteristic
68C2×Dic172—21no—
69C2×#10621885—21no—
70C2×#10621883—21no—
71C22×C43⋊C8—21no—
72C2×C8×D43D411yescharacteristic
73C2×C8×D43D411yescharacteristic
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063316—21no—
77#13063316—21no—
78#13063305—21no—
79#13063305—21no—
80#13063301—21no—
81#13063301—21no—
82Q8×Dic43—21no—
83Q8×Dic43—21no—
84C4×Dic86C2311yescharacteristic
85#13063290—21no—
86#13063290—21no—
87#13063290D411yescharacteristic
88D4×Dic43D411yescharacteristic
89C4×C22⋊D43—21no—
90(C22⋊D43)⋊C4—21no—
91#13063283—21no—
92#13063283—21no—
93#13063283D411yescharacteristic
94#13063281—21no—
95C2×C4×Dic43—21no—
96C42×D43C2311yescharacteristic
97#13063259—21no—
98#13063258—21no—
99#13063258—21no—
100#13063258—21no—
101#13063258—21no—
102#13063258—21no—
103#13063257—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—
111#13063250—21no—
112#13063250—21no—
113#13063249—21no—
114#13063248—21no—
115#13063248—21no—
116#13063246—21no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063235—21no—
122#13063235—21no—
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C8×Dic43—21no—
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#106×C43—21no—
135#106×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
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—
149C22×Dic43—21no—
150C22×Dic43—21no—
151#10621900—22no—
152#10621900—22no—
153C2×C4×D43C2×D411yescharacteristic
154C2×C4×D43C2×D411yescharacteristic
155C2×C4×D43#4111yescharacteristic
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86C2×D411yescharacteristic
159SD16×C43—42no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—42no—
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43C2×D411yescharacteristic
171C22⋊C4×C43—21no—
172C42×C43C2411yescharacteristic
173C22⋊Dic43—21no—
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
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—42no—
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204Dic172—42no—
205C8×D43—22no—
206C8×D43—22no—
207C23×C43—21no—
208C22×D43#12111yescharacteristic
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—81no—
212D4×C43—21no—
213D4×C43#13512yes—
214C2×C4×C43—21no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C22⋊D43—24no—
223C2×Dic43—24no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—42no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43#12111yescharacteristic
230C2×Dic43#12111yescharacteristic
231C2×Dic43#12111yescharacteristic
232C4×D43—21no—
233C4×D43—21no—
234C4×D43—21no—
235C4×D43—21no—
236C4×D43—41no—
237Dic86—21no—
238Dic86—41no—
239Dic86—41no—
240Dic86—81no—
241Dic86#13512yes—
242C8×C43—21no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43#13712yes—
247C43⋊C8—21no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8#13712yes—
252#19273—431nomaximal, Sylow
253C22×C43—22no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43C2×#12111yescharacteristic
257C2×D43—21no—
258C2×D43—21no—
259C2×D43—21no—
260C4×C43—21no—
261C4×C43—41no—
262C4×C43—81no—
263C4×C43—81no—
264C4×C43C2×#13511yescharacteristic
265C4×C43C2×#13511yescharacteristic
266C4×C43C2×#13711yescharacteristic
267C4×C43C2×#13711yescharacteristic
268Dic43—21no—
269Dic43—22no—
270Dic43—21no—
271Dic43—21no—
272Dic43—41no—
273Dic43—81no—
274Dic43—81no—
275#3160—431no—
276#3116—431no—
277#3116—431no—
278C8×#41—431no—
279#1676—431no—
280#1675—431no—
281#1674—431no—
282#1673—431no—
283#1672—431no—
284#1672—431no—
285#1671—431no—
286#1671D4311yescharacteristic, complemented
287#1568—431no—
288#1554—431no—
289#1554—431no—
290C2×C43—42no—
291C2×C43#303911yescharacteristic
292C2×C43#305011yescharacteristic
293C2×C43#306711yescharacteristic
294D43—41no—
295#533—431no—
296#533—431no—
297C4×#41—431no—
298#500—431no—
299#500—431no—
300#499—861no—
301#499—861no—
302#498—431no—
303#498C2×D4311yescharacteristic
304#485—861no—
305#485—861no—
306#477—431no—
307#477—431no—
308#476—431no—
309#476C2×D4311yescharacteristic
310#462—431no—
311#462—431no—
312#461—431no—
313#461C2×D4311yescharacteristic
314#452—861no—
315#452—861no—
316C8×Q8—431no—
317C8×Q8—431no—
318#441—861no—
319#441—861no—
320#440—861no—
321#440—861no—
322C8×D4—431no—
323C8×D4—861no—
324C8×D4—861no—
325C8×D4C2×D4311yescharacteristic
326#432—431no—
327#432—431no—
328#431—431no—
329#431—861no—
330#427—861no—
331#427—861no—
332C2×C4×C8—431no—
333C2×C4×C8—861no—
334#335—431no—
335#335—431no—
336#334—431no—
337#334C2×D4311yescharacteristic
338#333—431no—
339#333—431no—
340#333—431no—
341#333C2×D4311yescharacteristic
342#332—431no—
343#332—431no—
344#332—431no—
345#332C2×D4311yescharacteristic
346C43#1927311yescharacteristic, complemented, Sylow
347C2×#41—431no—
348C2×Q16—861no—
349C2×Q16—861no—
350C2×SD16—21no—
351C2×SD16—861no—
352C22×C8—21no—
353C22×C8—431no—
354C22×C8—431no—
355C22×C8—861no—
356C4⋊Q8—431no—
357C4⋊Q8—431no—
358C4⋊Q8C22×D4311yescharacteristic
359C4⋊Q8C22×D4311yescharacteristic
360#125—861no—
361#125—861no—
362C22⋊Q8—861no—
363C22⋊Q8—861no—
364C22⋊Q8—861no—
365C22⋊Q8—861no—
366C4×Q8—431no—
367C4×Q8—431no—
368C4×Q8—861no—
369C4×Q8—861no—
370C4×Q8—861no—
371C4×Q8—861no—
372C4×D4—431no—
373C4×D4—861no—
374C4×D4—861no—
375C4×D4C22×D4311yescharacteristic
376#117—431no—
377#117—861no—
378#117—861no—
379#117—861no—
380C2×C42—431no—
381C2×C42—861no—
382#107—861no—
383#107—861no—
384#107—861no—
385#107—861no—
386#107—861no—
387#107—861no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106—861no—
392#106—861no—
393#106—861no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—861no—
398C4⋊C8—861no—
399C4⋊C8C22×D4311yescharacteristic
400C4⋊C8C22×D4311yescharacteristic
401C4⋊C8C22×D4311yescharacteristic
402#103—21no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#102—21no—
409#102—861no—
410C22⋊C8—21no—
411C22⋊C8—861no—
412C22⋊C8—861no—
413C22⋊C8—861no—
414C22⋊C8—861no—
415#97—861no—
416#97—861no—
417C4×C8—431no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8C22×D4311yescharacteristic
424#41—862no—
425#41—862no—
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—
437C22×C4—861no—
438C22×C4—861no—
439Q16—1722no—
440Q16—1722no—
441SD16—42no—
442SD16—1722no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—42no—
447C2×C8—431no—
448C2×C8—431no—
449C2×C8—862no—
450C2×C8—862no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—1722no—
455C2×C8D4×D4311yescharacteristic
456C2×C8D4×D4311yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—431no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—1721no—
469C4⋊C4—1721no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C4⋊C4D4×D4311yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—861no—
475C22⋊C4—861no—
476C22⋊C4—1721no—
477C22⋊C4—1721no—
478C42—431no—
479C42—431no—
480C42—431no—
481C42—861no—
482C42—861no—
483C42—861no—
484C42—1721no—
485C42—1721no—
486C42C23×D4311yescharacteristic
487C23—21no—
488C23—431no—
489Q8—41no—
490Q8—41no—
491Q8—81no—
492Q8—432no—
493Q8—861no—
494Q8—3441no—
495Q8—1721no—
496Q8—1721no—
497D4—21no—
498D4—864no—
499D4#1306334612yes—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—431no—
506C2×C4—431no—
507C2×C4—431no—
508C2×C4—864no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—1721no—
516C2×C4—1722no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4C2×D4×D4311yescharacteristic
520C2×C4C2×D4×D4311yescharacteristic
521C2×C4#41×D4311yescharacteristic
522C8—21no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—432no—
527C8—861no—
528C8—1721no—
529C8—1721no—
530C8—1721no—
531C8#1306335412yes—
532C22—22no—
533C22—41no—
534C22—41no—
535C22—861no—
536C22—861no—
537C22—861no—
538C22#121×D4311yescharacteristic
539C4—21no—
540C4—41no—
541C4—81no—
542C4—81no—
543C4—861no—
544C4—861no—
545C4—861no—
546C4—862no—
547C4—3441no—
548C4—3441no—
549C4—1721no—
550C4#135×D4311yescharacteristic
551C4C2×#1306334611yescharacteristic
552C4#137×D4311yescharacteristic
553C4C2×#1306335411yescharacteristic
554C2—42no—
555C2—1721no—
556C2#1914407711yescharacteristic
557C2#1914417111yescharacteristic
558C2#1914431011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1671C2
socleC22×C43C2×#121
prime radicalC2×#10621900D4
hypercenter#1671D43
hypocenterC43#19273
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1671

Complements

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

NH ≅ G/Ntype
1. #19145104C2semidirect
5. #19133998C2semidirect
6. #19133992C2semidirect
7. #19133988C2semidirect
8. #19133982C2semidirect
9. #19133978C2semidirect
10. #19133974C2semidirect
11. #19133970C2semidirect
12. #19133355C2semidirect
13. #19133304C2semidirect
14. #19133302C2semidirect
15. C43×#1671C2semidirect
286. #1671D43semidirect
346. C43#19273semidirect

Maximal subgroups

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

subgroupindex
#191451042
#191447592
#191447542
C8×#106219002
#191339982
#191339922
#191339882
#191339822
#191339782
#191339742
#191339702
#191333552
#191333042
#191333022
C43×#16712
#1927343