Finite Group Databasebeta

← #25080332

Subgroups — #25080332

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145932C211yesmaximal, characteristic
2#19145770C211yesmaximal, characteristic
3#19145340C211yesmaximal, characteristic, complemented
4#19134177C211yesmaximal, characteristic, complemented
5#19134149C211yesmaximal, characteristic, complemented
6#19134094C211yesmaximal, characteristic, complemented
7#19134084C211yesmaximal, characteristic, complemented
8#19134046C211yesmaximal, characteristic, complemented
9#19134018C211yesmaximal, characteristic, complemented
10#19133977C211yesmaximal, characteristic, complemented
11#19133965C211yesmaximal, characteristic, complemented
12#19133347C211yesmaximal, characteristic, complemented
13#19133259C211yesmaximal, characteristic, complemented
14#19133250C211yesmaximal, characteristic, complemented
15C43×#2969C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583456C2211yescharacteristic
18#14583298—21no—
19#14583297C2211yescharacteristic
20#14583279C2211yescharacteristic
21#14583253—21no—
22#14583250C2211yescharacteristic
23#14583250C2211yescharacteristic
24#14583237—21no—
25#14583220—21no—
26#14583203—21no—
27#14583194C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583184C2211yescharacteristic
30#14583184C2211yescharacteristic
31#14583179C2211yescharacteristic
32#14583179C2211yescharacteristic
33#14583157—21no—
34#14583157—21no—
35#14583138—21no—
36#14583126—21no—
37#14583118—21no—
38#14583109C2211yescharacteristic
39#14583104C2211yescharacteristic
40#14583007—21no—
41#14583007—21no—
42#14582952C2211yescharacteristic
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582646C2211yescharacteristic
52#14582646C2211yescharacteristic
53#14582646C2211yescharacteristic
54#14582644C2211yescharacteristic
55#14582644C2211yescharacteristic
56C43×#529C2211yescharacteristic
57C43×#446C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436—21no—
60C43×#436C2211yescharacteristic
61C43×#435—21no—
62C8×D4×C43C2211yescharacteristic
63C43×#433—21no—
64C43×#431C2211yescharacteristic
65C43×#405—21no—
66C4×M16×C43C2211yescharacteristic
67C2×Dic172—21no—
68C2×Dic172—21no—
69C2×#10621885—21no—
70C2×#10621883—21no—
71C22×C43⋊C8—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063317—21no—
77#13063317—21no—
78#13063304—21no—
79#13063304—21no—
80#13063304—21no—
81#13063304—21no—
82C4×Dic86—21no—
83C4×Dic86—21no—
84C4×Dic86—21no—
85C4×Dic86—21no—
86#13063284—21no—
87#13063284—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—21no—
91#13063257—21no—
92#13063257—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063250—21no—
102#13063250—21no—
103#13063250—21no—
104#13063250—21no—
105#13063249—21no—
106#13063249—21no—
107#13063249—21no—
108#13063248—21no—
109#13063248—21no—
110#13063246—21no—
111#13063246—21no—
112#13063246—21no—
113C22⋊(C43⋊C8)—21no—
114C4×C43⋊C8—21no—
115C2×M16×C43—21no—
116C2×M16×C43D411yescharacteristic
117C2×M16×C43D411yescharacteristic
118C22×C8×C43—21no—
119#126×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43D411yescharacteristic
122#123×C43—21no—
123C22⋊Q8×C43D411yescharacteristic
124#121×C43D411yescharacteristic
125C4×Q8×C43C2311yescharacteristic
126C4×D4×C43—21no—
127C4×D4×C43C2311yescharacteristic
128#117×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137#97×C43—21no—
138#97×C43D411yescharacteristic
139#97×C43D411yescharacteristic
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C2×D411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155M16×C43—22no—
156M16×C43—41no—
157M16×C43—42no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—42no—
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C2×D411yescharacteristic
170C4⋊C4×C43C2×D411yescharacteristic
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C42×C43—21no—
177C42×C43C2×D411yescharacteristic
178C42×C43C2×D411yescharacteristic
179C42×C43#4111yescharacteristic
180C42×C43C2411yescharacteristic
181C22⋊Dic43—41no—
182C22⋊Dic43—41no—
183#10621885—81no—
184#10621883—81no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197C4×Dic43—41no—
198C4×Dic43—41no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—81no—
204Dic172—42no—
205Dic172—42no—
206C23×C43—21no—
207C23×C43#12111yescharacteristic
208Q8×C43—21no—
209Q8×C43—21no—
210D4×C43—21no—
211D4×C43—21no—
212D4×C43—81no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233Dic86—41no—
234Dic86—41no—
235Dic86—41no—
236Dic86—41no—
237Dic86—41no—
238Dic86—41no—
239Dic86—81no—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43#13512yes—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250#19251—431nomaximal, Sylow
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43C2×#12111yescharacteristic
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43C2×#13511yescharacteristic
266C4×C43#57511yescharacteristic
267C4×C43#57711yescharacteristic
268C4×C43#57811yescharacteristic
269Dic43—81no—
270Dic43—81no—
271Dic43—81no—
272Dic43—81no—
273#3248—431no—
274#3233—431no—
275#3185—431no—
276#2969D4311yescharacteristic
277#1704—431no—
278#1700—431no—
279#1691—431no—
280#1689—431no—
281#1683—431no—
282#1679—431no—
283#1672—431no—
284#1670—431no—
285#1565—431no—
286#1544—431no—
287#1542—431no—
288C2×C43—41no—
289C2×C43—81no—
290C2×C43#303511yescharacteristic
291C2×C43#306311yescharacteristic
292C2×C43#306911yescharacteristic
293#533—431no—
294#533—431no—
295#529C2×D4311yescharacteristic
296#499—861no—
297#498—431no—
298#494—431no—
299#488—861no—
300#487—431no—
301#487—431no—
302#485—861no—
303#482—861no—
304#479—861no—
305#477—431no—
306#476—431no—
307#475—431no—
308#475—431no—
309#474—431no—
310#474—431no—
311#470—861no—
312#470—861no—
313#467—861no—
314#465—861no—
315#464—861no—
316#462—431no—
317#461—431no—
318#446C2×D4311yescharacteristic
319C8×Q8C2×D4311yescharacteristic
320#441—861no—
321#441—861no—
322#436—21no—
323#436C2×D4311yescharacteristic
324#435—21no—
325C8×D4C2×D4311yescharacteristic
326#433—21no—
327#431—431no—
328#431C2×D4311yescharacteristic
329C2×C4⋊C8—431no—
330#405—21no—
331C4×M16C2×D4311yescharacteristic
332#335—431no—
333#335—431no—
334#334—431no—
335#334—431no—
336#333—431no—
337#333—431no—
338#332—431no—
339#332—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344C43#1925111yescharacteristic, complemented, Sylow
345C2×Q16—861no—
346C2×Q16—861no—
347C2×Q16—861no—
348C2×SD16—861no—
349C2×M16—21no—
350C2×M16C22⋊D4311yescharacteristic
351C2×M16C22⋊D4311yescharacteristic
352C22×C8—21no—
353C22×C8—861no—
354C4⋊Q8—431no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8—431no—
358#126—21no—
359#125—861no—
360#125—861no—
361#125D17211yescharacteristic
362#124D17211yescharacteristic
363#123—21no—
364C22⋊Q8—861no—
365C22⋊Q8—861no—
366C22⋊Q8—861no—
367C22⋊Q8—861no—
368C22⋊Q8D17211yescharacteristic
369#121D17211yescharacteristic
370C4×Q8—861no—
371C4×Q8—861no—
372C4×Q8—861no—
373C4×Q8—861no—
374C4×Q8C22×D4311yescharacteristic
375C4×D4—21no—
376C4×D4C22×D4311yescharacteristic
377#117—21no—
378#117—861no—
379#117—861no—
380C2×C42C22×D4311yescharacteristic
381#107—861no—
382#107—861no—
383#107—861no—
384#106—861no—
385#106—861no—
386#106—861no—
387#106—861no—
388#106—861no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—431no—
394C4⋊C8—431no—
395C4⋊C8—861no—
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
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#102—861no—
408#102—861no—
409#102—861no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—861no—
414#97—21no—
415#97C22⋊D4311yescharacteristic
416#97C22⋊D4311yescharacteristic
417C4×C8—21no—
418C4×C8—21no—
419C4×C8—861no—
420C4×C8C22×D4311yescharacteristic
421C4×C8C22×D4311yescharacteristic
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8C2×D17211yescharacteristic
427C2×D4—21no—
428C2×D4C2×D17211yescharacteristic
429C22×C4—21no—
430C22×C4C2×D17211yescharacteristic
431C22×C4#1062189811yescharacteristic
432C22×C4C2×C22⋊D4311yescharacteristic
433Q16—3441no—
434Q16—1722no—
435Q16—1722no—
436SD16—3441no—
437M16—22no—
438M16—41no—
439M16—42no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—42no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—3441no—
448C2×C8C2×C22⋊D4311yescharacteristic
449C2×C8C2×C22⋊D4311yescharacteristic
450C2×C8C2×C22⋊D4311yescharacteristic
451C2×C8C2×C22⋊D4311yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—1721no—
465C4⋊C4—1721no—
466C4⋊C4—1721no—
467C4⋊C4—1721no—
468C4⋊C4C2×D17211yescharacteristic
469C4⋊C4C2×D17211yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—1721no—
476C22⋊C4—1721no—
477C42—21no—
478C42—1721no—
479C42—1721no—
480C42C2×D17211yescharacteristic
481C42#1062189811yescharacteristic
482C42C2×C22⋊D4311yescharacteristic
483C42C23×D4311yescharacteristic
484C23—21no—
485C23#1306329911yescharacteristic
486Q8—21no—
487Q8—21no—
488Q8—3441no—
489Q8—1721no—
490Q8—1721no—
491Q8—1721no—
492Q8—1721no—
493Q8—1721no—
494Q8—1721no—
495D4—21no—
496D4—21no—
497D4—81no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—1721no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4#1306329911yescharacteristic
513C2×C4#1306329911yescharacteristic
514C2×C4#1306329911yescharacteristic
515C2×C4C22×C22⋊D4311yescharacteristic
516C2×C4C22×D17211yescharacteristic
517C2×C4C2×#1062189811yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—41no—
522C8—41no—
523C8—1721no—
524C8—1721no—
525C8—1721no—
526C8—1721no—
527C8#1306334512yes—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22C2×#1306329911yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—3441no—
543C4—3441no—
544C4—3441no—
545C4—3441no—
546C4C2×#1306334511yescharacteristic
547C4#1458369711yescharacteristic
548C4#1458371111yescharacteristic
549C4#1458371611yescharacteristic
550C2—41no—
551C2—81no—
552C2#1914405011yescharacteristic
553C2#1914428611yescharacteristic
554C2#1914433211yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2969C2
socleC22×C43C2×#121
prime radical#121×C43D4
hypercenter#2969D43
hypocenterC43#19251
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2969

Complements

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

NH ≅ G/Ntype
3. #19145340C2semidirect
4. #19134177C2semidirect
5. #19134149C2semidirect
6. #19134094C2semidirect
7. #19134084C2semidirect
8. #19134046C2semidirect
9. #19134018C2semidirect
10. #19133977C2semidirect
11. #19133965C2semidirect
12. #19133347C2semidirect
13. #19133259C2semidirect
14. #19133250C2semidirect
344. C43#19251semidirect

Maximal subgroups

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

subgroupindex
#191459322
#191457702
#191453402
#191341772
#191341492
#191340942
#191340842
#191340462
#191340182
#191339772
#191339652
#191333472
#191332592
#191332502
C43×#29692
#1925143