Finite Group Databasebeta

← #25079646

Subgroups — #25079646

Order 11008.

592 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#19145340C211yesmaximal, characteristic, complemented
2#19144666C211yesmaximal, characteristic
3#19144383C211yesmaximal, characteristic
4#19134170C211yesmaximal, characteristic, complemented
5#19134142C211yesmaximal, characteristic, complemented
6#19134094C211yesmaximal, characteristic, complemented
7#19134084C211yesmaximal, characteristic, complemented
8#19134053C211yesmaximal, characteristic, complemented
9#19134025C211yesmaximal, characteristic, complemented
10#19133977C211yesmaximal, characteristic, complemented
11#19133965C211yesmaximal, characteristic, complemented
12#19133347C211yesmaximal, characteristic, complemented
13#19133306C211yesmaximal, characteristic, complemented
14#19133296C211yesmaximal, characteristic, complemented
15C43×#2971C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583456C2211yescharacteristic
18#14583297C2211yescharacteristic
19#14583279C2211yescharacteristic
20#14583250C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583240—21no—
23#14583206—21no—
24#14583199—21no—
25#14583194C2211yescharacteristic
26#14583189C2211yescharacteristic
27#14583184C2211yescharacteristic
28#14583184C2211yescharacteristic
29#14583179C2211yescharacteristic
30#14583179C2211yescharacteristic
31#14583157—21no—
32#14583157—21no—
33#14583109C2211yescharacteristic
34#14583104C2211yescharacteristic
35#14583061—21no—
36#14583007—21no—
37#14583007—21no—
38C4×#10621885—21no—
39C4×#10621883—21no—
40#14582952C2211yescharacteristic
41#14582935—21no—
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43#14582895—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582646C2211yescharacteristic
52#14582646C2211yescharacteristic
53#14582646C2211yescharacteristic
54#14582644C2211yescharacteristic
55#14582644C2211yescharacteristic
56C4×#41×C43C2211yescharacteristic
57C8×Q8×C43C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436—21no—
60C43×#436—21no—
61C43×#436C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#432—21no—
64C43×#432C2211yescharacteristic
65C4×M16×C43—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×#41×C43D411yescharacteristic
116C2×M16×C43—21no—
117C2×M16×C43—21no—
118C2×M16×C43D411yescharacteristic
119C2×M16×C43D411yescharacteristic
120C4×Q8×C43D411yescharacteristic
121C4×Q8×C43C2311yescharacteristic
122C4×D4×C43—21no—
123C4×D4×C43—21no—
124C4×D4×C43D411yescharacteristic
125C4×D4×C43C2311yescharacteristic
126#117×C43—21no—
127#117×C43D411yescharacteristic
128C2×C42×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
144#41×C43—22no—
145#41×C43—41no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159M16×C43—22no—
160M16×C43—41no—
161M16×C43—42no—
162M16×C43—42no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43C2×D411yescharacteristic
172C4⋊C4×C43C2×D411yescharacteristic
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43C2×D411yescharacteristic
180C42×C43C2×D411yescharacteristic
181C42×C43#4111yescharacteristic
182C42×C43C2411yescharacteristic
183C22⋊Dic43—41no—
184C22⋊Dic43—41no—
185#10621885—42no—
186#10621883—42no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198Dic43⋊C4—41no—
199C4×Dic43—41no—
200C4×Dic43—41no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—42no—
206Dic172—42no—
207Dic172—42no—
208C23×C43—21no—
209C23×C43#12111yescharacteristic
210Q8×C43—21no—
211Q8×C43#13712yes—
212D4×C43—21no—
213D4×C43—21no—
214D4×C43—42no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43—42no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—81no—
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237Dic86—41no—
238Dic86—41no—
239Dic86—41no—
240Dic86—41no—
241Dic86—41no—
242Dic86—41no—
243Dic86—81no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—21no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43#13512yes—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254#19185—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43C2×#12111yescharacteristic
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—22no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43C2×#13511yescharacteristic
270C4×C43C2×#13711yescharacteristic
271C4×C43#57511yescharacteristic
272C4×C43#57511yescharacteristic
273Dic43—81no—
274Dic43—81no—
275Dic43—81no—
276Dic43—81no—
277#3185—431no—
278#3107—431no—
279#3076—431no—
280#2971D4311yescharacteristic
281#1703—431no—
282#1699—431no—
283#1691—431no—
284#1689—431no—
285#1684—431no—
286#1680—431no—
287#1672—431no—
288#1670—431no—
289#1565—431no—
290#1554—431no—
291#1552—431no—
292C2×C43—41no—
293C2×C43—81no—
294C2×C43#303511yescharacteristic
295C2×C43#305611yescharacteristic
296C2×C43#306911yescharacteristic
297#533—431no—
298#533—431no—
299C4×#41C2×D4311yescharacteristic
300#498—431no—
301#494—431no—
302#487—431no—
303#487—431no—
304#485—861no—
305#479—861no—
306#478—861no—
307#477—431no—
308#476—431no—
309#475—431no—
310#475—431no—
311#474—431no—
312#474—431no—
313#470—861no—
314#470—861no—
315#462—431no—
316#461—431no—
317#452—861no—
318C8×Q8C2×D4311yescharacteristic
319C8×Q8C2×D4311yescharacteristic
320#441—861no—
321#441—861no—
322C4×Q16—861no—
323C4×SD16—861no—
324#436—21no—
325#436—21no—
326#436C2×D4311yescharacteristic
327#436C2×D4311yescharacteristic
328#432—21no—
329#432C2×D4311yescharacteristic
330#431—431no—
331#427—861no—
332C2×C4⋊C8—431no—
333#416—861no—
334C4×M16—21no—
335C4×M16C2×D4311yescharacteristic
336#335—431no—
337#335—431no—
338#334—431no—
339#334—431no—
340#333—431no—
341#333—431no—
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346#332—431no—
347#332—431no—
348C43#1918511yescharacteristic, complemented, Sylow
349C2×#41D17211yescharacteristic
350C2×Q16—861no—
351C2×Q16—861no—
352C2×Q16—861no—
353C2×SD16—861no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16C22⋊D4311yescharacteristic
357C2×M16C22⋊D4311yescharacteristic
358C22×C8—861no—
359C4⋊Q8—431no—
360C4⋊Q8—431no—
361C4⋊Q8—431no—
362C4⋊Q8—431no—
363#125—861no—
364#125—861no—
365C22⋊Q8—861no—
366C22⋊Q8—861no—
367C22⋊Q8—861no—
368C22⋊Q8—861no—
369C4×Q8—861no—
370C4×Q8—861no—
371C4×Q8—861no—
372C4×Q8—861no—
373C4×Q8D17211yescharacteristic
374C4×Q8C22×D4311yescharacteristic
375C4×D4—21no—
376C4×D4—21no—
377C4×D4D17211yescharacteristic
378C4×D4C22×D4311yescharacteristic
379#117—21no—
380#117—861no—
381#117—861no—
382#117D17211yescharacteristic
383C2×C42—21no—
384C2×C42C22×D4311yescharacteristic
385#107—861no—
386#107—861no—
387#107—861no—
388#106—861no—
389#106—861no—
390#106—861no—
391#106—861no—
392#106—861no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—861no—
400C4⋊C8C22×D4311yescharacteristic
401C4⋊C8C22×D4311yescharacteristic
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#102—861no—
412#102—861no—
413#102—861no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—861no—
418#97—21no—
419#97C22⋊D4311yescharacteristic
420#97C22⋊D4311yescharacteristic
421C4×C8—21no—
422C4×C8—21no—
423C4×C8—861no—
424C4×C8C22×D4311yescharacteristic
425C4×C8C22×D4311yescharacteristic
426#41—22no—
427#41—41no—
428C2×Q8—861no—
429C2×Q8—861no—
430C2×Q8—861no—
431C2×Q8—861no—
432C2×Q8C2×D17211yescharacteristic
433C2×D4—21no—
434C2×D4C2×D17211yescharacteristic
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4C2×D17211yescharacteristic
439C22×C4#1062189811yescharacteristic
440C22×C4C2×C22⋊D4311yescharacteristic
441Q16—1722no—
442Q16—1722no—
443Q16—1722no—
444SD16—1722no—
445M16—22no—
446M16—41no—
447M16—42no—
448M16—42no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—1722no—
456C2×C8C2×C22⋊D4311yescharacteristic
457C2×C8C2×C22⋊D4311yescharacteristic
458C2×C8C2×C22⋊D4311yescharacteristic
459C2×C8C2×C22⋊D4311yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
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—
474C4⋊C4C2×D17211yescharacteristic
475C4⋊C4C2×D17211yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—1721no—
480C22⋊C4—1721no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—1721no—
485C42—1721no—
486C42C2×D17211yescharacteristic
487C42#1062189811yescharacteristic
488C42C2×C22⋊D4311yescharacteristic
489C42C23×D4311yescharacteristic
490C23—21no—
491C23#1306329911yescharacteristic
492Q8—21no—
493Q8—3441no—
494Q8—1721no—
495Q8—1721no—
496Q8—1721no—
497Q8—1721no—
498Q8—1721no—
499Q8—1721no—
500Q8#1306335812yes—
501D4—21no—
502D4—21no—
503D4—42no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—81no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4#1306329911yescharacteristic
521C2×C4#1306329911yescharacteristic
522C2×C4#1306329911yescharacteristic
523C2×C4C22×C22⋊D4311yescharacteristic
524C2×C4C22×D17211yescharacteristic
525C2×C4C2×#1062189811yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—1721no—
532C8—1721no—
533C8—1721no—
534C8—1721no—
535C8#1306334512yes—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22C2×#1306329911yescharacteristic
543C4—21no—
544C4—22no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—41no—
549C4—41no—
550C4—3441no—
551C4—3441no—
552C4—3441no—
553C4—3441no—
554C4C2×#1306334511yescharacteristic
555C4C2×#1306335811yescharacteristic
556C4#1458369711yescharacteristic
557C4#1458369911yescharacteristic
558C2—41no—
559C2—81no—
560C2#1914405011yescharacteristic
561C2#1914422511yescharacteristic
562C2#1914433211yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2971C2
socleC22×C43C2×#121
prime radicalC2×#41×C43D4
hypercenter#2971D43
hypocenterC43#19185
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2971

Complements

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

NH ≅ G/Ntype
1. #19145340C2semidirect
4. #19134170C2semidirect
5. #19134142C2semidirect
6. #19134094C2semidirect
7. #19134084C2semidirect
8. #19134053C2semidirect
9. #19134025C2semidirect
10. #19133977C2semidirect
11. #19133965C2semidirect
12. #19133347C2semidirect
13. #19133306C2semidirect
14. #19133296C2semidirect
348. C43#19185semidirect

Maximal subgroups

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

subgroupindex
#191453402
#191446662
#191443832
#191341702
#191341422
#191340942
#191340842
#191340532
#191340252
#191339772
#191339652
#191333472
#191333062
#191332962
C43×#29712
#1918543