Finite Group Databasebeta

← #25081716

Subgroups — #25081716

Order 11008.

572 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#19145969C211yesmaximal, characteristic
2#19145827C211yesmaximal, characteristic
3#19144976C211yesmaximal, characteristic, complemented
4#19143599C211yesmaximal, characteristic
5#19134178C211yesmaximal, characteristic, complemented
6#19134171C211yesmaximal, characteristic, complemented
7#19134150C211yesmaximal, characteristic, complemented
8#19134143C211yesmaximal, characteristic, complemented
9#19134054C211yesmaximal, characteristic, complemented
10#19134047C211yesmaximal, characteristic, complemented
11#19134026C211yesmaximal, characteristic, complemented
12#19134019C211yesmaximal, characteristic, complemented
13#19133306C211yesmaximal, characteristic, complemented
14#19133281C211yesmaximal, characteristic, complemented
15C43×#1569C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18#14583433C2211yescharacteristic
19#14583308—21no—
20#14583268—21no—
21#14583268—21no—
22#14583259—21no—
23#14583250C2211yescharacteristic
24#14583250C2211yescharacteristic
25#14583250C2211yescharacteristic
26#14583250C2211yescharacteristic
27#14583235—21no—
28#14583218—21no—
29#14583207—21no—
30#14583195C2211yescharacteristic
31#14583190C2211yescharacteristic
32#14583185C2211yescharacteristic
33#14583185C2211yescharacteristic
34#14583180C2211yescharacteristic
35#14583180C2211yescharacteristic
36#14583157—21no—
37#14583145—21no—
38#14583122—21no—
39#14583110C2211yescharacteristic
40#14583105C2211yescharacteristic
41#14583029C2211yescharacteristic
42C8×Dic86C2211yescharacteristic
43#14582978C2211yescharacteristic
44#14582975—21no—
45#14582968—21no—
46C8×D172C2211yescharacteristic
47#14582961—21no—
48#14582952C2211yescharacteristic
49#14582909—21no—
50#14582909—21no—
51#14582856—21no—
52#14582647C2211yescharacteristic
53#14582647C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582644C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#432C2211yescharacteristic
61C43×#423C2211yescharacteristic
62C4×M16×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C22×Dic86—21no—
68C2×Dic172—21no—
69C2×#10621873—21no—
70C2×#10621872—21no—
71C2×C8×D43—21no—
72#13063325—21no—
73#13063325—21no—
74#13063325—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063325C2311yescharacteristic
79#13063319—21no—
80#13063317—21no—
81#13063317D411yescharacteristic
82#13063313D411yescharacteristic
83#13063308—21no—
84#13063304—21no—
85#13063304—21no—
86#13063304D411yescharacteristic
87#13063299D411yescharacteristic
88C4×Dic86—21no—
89C4×Dic86—21no—
90C4×Dic86C2311yescharacteristic
91C4×D172C2311yescharacteristic
92C4×C22⋊D43—21no—
93#13063284—21no—
94#13063282—21no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—21no—
97#13063259—21no—
98#13063259—21no—
99#13063259—21no—
100#13063257—21no—
101#13063257—21no—
102#13063257—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107#13063250—21no—
108#13063250—21no—
109#13063250—21no—
110#13063250—21no—
111#13063250—21no—
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063250—21no—
116#13063250—21no—
117#13063250—21no—
118#13063250—21no—
119#13063250—21no—
120#13063247—21no—
121#13063247—21no—
122#13063247—21no—
123C22⋊(C43⋊C8)—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126#13063235—21no—
127C4×C43⋊C8—21no—
128C8×Dic43—21no—
129C2×M16×C43—21no—
130C2×M16×C43D411yescharacteristic
131C2×M16×C43D411yescharacteristic
132C2×C42×C43C2311yescharacteristic
133C4⋊C8×C43—21no—
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C22⋊C8×C43—21no—
139#97×C43—21no—
140#97×C43D411yescharacteristic
141#97×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C2×C22⋊D43—21no—
148C22×Dic43—41no—
149C2×D172C2×D411yescharacteristic
150C2×C4×D43—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—42no—
156C2×Dic86—42no—
157C2×Dic86—41no—
158C2×Dic86C2×D411yescharacteristic
159M16×C43—41no—
160M16×C43—41no—
161M16×C43—81no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C42×C43C2×D411yescharacteristic
171C42×C43C2×D411yescharacteristic
172C42×C43#4111yescharacteristic
173C42×C43C2411yescharacteristic
174C22⋊Dic43—21no—
175C22⋊Dic43—41no—
176(C2×D43)⋊C4—21no—
177(C2×D43)⋊C4—21no—
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⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—41no—
189C4⋊Dic43—41no—
190C4⋊Dic43C2×D411yescharacteristic
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198C4×Dic43—21no—
199C4×Dic43—41no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202Dic172—81no—
203#10621873—81no—
204#10621872—42no—
205C8×D43—42no—
206C23×C43#12111yescharacteristic
207C22×D43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—41no—
213C2×C4×C43#12111yescharacteristic
214C2×C4×C43#12111yescharacteristic
215C2×C4×C43#12111yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C22⋊D43—81no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—82no—
228D172—21no—
229D172—21no—
230C4×D43—41no—
231C4×D43—41no—
232Dic86—21no—
233Dic86—21no—
234Dic86—41no—
235Dic86—41no—
236Dic86—41no—
237Dic86—41no—
238Dic86—41no—
239Dic86—41no—
240Dic86—82no—
241Dic86—81no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252#19381—431nomaximal, Sylow
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43C2×#12111yescharacteristic
257C2×D43—41no—
258C2×D43—41no—
259C2×D43—41no—
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43#57511yescharacteristic
265C4×C43#57511yescharacteristic
266C4×C43#57711yescharacteristic
267C4×C43#57811yescharacteristic
268Dic43—41no—
269Dic43—41no—
270Dic43—41no—
271Dic43—81no—
272Dic43—81no—
273Dic43—81no—
274Dic43—81no—
275#3252—431no—
276#3239—431no—
277#3139—431no—
278#2969—431no—
279#1704—431no—
280#1703—431no—
281#1700—431no—
282#1699—431no—
283#1684—431no—
284#1683—431no—
285#1680—431no—
286#1679—431no—
287#1569D4311yescharacteristic, complemented
288#1554—431no—
289#1549—431no—
290C2×C43—41no—
291C2×C43#304011yescharacteristic
292C2×C43#306311yescharacteristic
293C2×C43#306911yescharacteristic
294D43—81no—
295#533—431no—
296C2×C4⋊Q8—431no—
297#529—431no—
298#501—861no—
299#491—861no—
300#491—861no—
301#489—861no—
302#487—431no—
303#487—431no—
304#487—431no—
305#487—431no—
306#484—861no—
307#481—861no—
308#479—861no—
309#477—431no—
310#476—431no—
311#475—431no—
312#475—431no—
313#474—431no—
314#474—431no—
315#470—861no—
316#468—861no—
317#464—861no—
318#462—431no—
319#461—431no—
320#446—431no—
321C8×Q8—431no—
322#436—431no—
323#436—861no—
324#435—861no—
325C8×D4—431no—
326#433—861no—
327#432C2×D4311yescharacteristic
328#431—431no—
329#423C2×D4311yescharacteristic
330#419—861no—
331#419—861no—
332#405—861no—
333C4×M16C2×D4311yescharacteristic
334#335C2×D4311yescharacteristic
335#335C2×D4311yescharacteristic
336#334C2×D4311yescharacteristic
337#334C2×D4311yescharacteristic
338#333—431no—
339#333—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346C43#1938111yescharacteristic, complemented, Sylow
347C22×Q8—861no—
348C2×Q16—861no—
349C2×SD16—861no—
350C2×M16—21no—
351C2×M16—861no—
352C2×M16D17211yescharacteristic
353C2×M16D17211yescharacteristic
354C22×C8—861no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8—431no—
358C4⋊Q8—431no—
359C4⋊Q8—861no—
360C4⋊Q8—861no—
361C4⋊Q8—861no—
362#126—861no—
363#125—431no—
364#125—861no—
365#124—431no—
366#123—861no—
367C22⋊Q8—431no—
368C22⋊Q8—861no—
369C22⋊Q8—861no—
370#121—431no—
371C4×Q8—431no—
372C4×Q8—861no—
373C4×Q8—861no—
374C4×D4—431no—
375C4×D4—861no—
376#117—861no—
377#117—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C42C22×D4311yescharacteristic
381#107—861no—
382#107—861no—
383#107—861no—
384#106—861no—
385#106—861no—
386#106—861no—
387C4⋊C8—21no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8C22×D4311yescharacteristic
393C4⋊C8C22×D4311yescharacteristic
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396#103—861no—
397#103—861no—
398#103—861no—
399#103—861no—
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#102—861no—
410#102—861no—
411#102—861no—
412C22⋊C8—21no—
413C22⋊C8—861no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416#97—21no—
417#97—861no—
418#97D17211yescharacteristic
419#97D17211yescharacteristic
420C4×C8—861no—
421C4×C8—861no—
422C4×C8C22×D4311yescharacteristic
423C4×C8C22×D4311yescharacteristic
424C2×Q8—431no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8—1722no—
430C2×Q8—1722no—
431C2×Q8—1721no—
432C2×D4—431no—
433C2×D4—861no—
434C22×C4—861no—
435C22×C4—1721no—
436C22×C4C2×D17211yescharacteristic
437C22×C4D4×D4311yescharacteristic
438C22×C4#1062190211yescharacteristic
439Q16—3441no—
440SD16—3441no—
441M16—41no—
442M16—41no—
443M16—81no—
444M16—1722no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—1722no—
452C2×C8C2×D17211yescharacteristic
453C2×C8C2×D17211yescharacteristic
454C2×C8C2×D17211yescharacteristic
455C2×C8C2×D17211yescharacteristic
456C4⋊C4—431no—
457C4⋊C4—431no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C4⋊C4—1721no—
473C4⋊C4—1721no—
474C22⋊C4—861no—
475C22⋊C4—861no—
476C22⋊C4—861no—
477C22⋊C4—861no—
478C22⋊C4—861no—
479C22⋊C4—1721no—
480C42—861no—
481C42—1721no—
482C42C2×D17211yescharacteristic
483C42D4×D4311yescharacteristic
484C42#1062190211yescharacteristic
485C42C23×D4311yescharacteristic
486C23—861no—
487C23#1306330011yescharacteristic
488Q8—861no—
489Q8—861no—
490Q8—3441no—
491Q8—3442no—
492Q8—1721no—
493Q8—1721no—
494Q8—1721no—
495Q8—1721no—
496Q8—1721no—
497Q8—1721no—
498D4—861no—
499D4—861no—
500D4—3441no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—3442no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4#1306330011yescharacteristic
517C2×C4#1306330011yescharacteristic
518C2×C4#1306330011yescharacteristic
519C2×C4C2×D4×D4311yescharacteristic
520C2×C4C22×D17211yescharacteristic
521C2×C4C2×#1062190211yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—1721no—
531C8—1721no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—1721no—
536C22—1721no—
537C22—1721no—
538C22C2×#1306330011yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—3441no—
544C4—3441no—
545C4—3441no—
546C4—3441no—
547C4—1721no—
548C4—1721no—
549C4—1721no—
550C4#1458369911yescharacteristic
551C4#1458369911yescharacteristic
552C4#1458370911yescharacteristic
553C4#1458371511yescharacteristic
554C2—41no—
555C2—3441no—
556C2#1914409011yescharacteristic
557C2#1914428711yescharacteristic
558C2#1914433311yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1569C2
socleC22×C43C2×#121
prime radical#13063299D4
hypercenter#1569D43
hypocenterC43#19381
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
3. #19144976C2semidirect
5. #19134178C2semidirect
6. #19134171C2semidirect
7. #19134150C2semidirect
8. #19134143C2semidirect
9. #19134054C2semidirect
10. #19134047C2semidirect
11. #19134026C2semidirect
12. #19134019C2semidirect
13. #19133306C2semidirect
14. #19133281C2semidirect
15. C43×#1569C2semidirect
287. #1569D43semidirect
346. C43#19381semidirect

Maximal subgroups

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

subgroupindex
#191459692
#191458272
#191449762
#191435992
#191341782
#191341712
#191341502
#191341432
#191340542
#191340472
#191340262
#191340192
#191333062
#191332812
C43×#15692
#1938143