Finite Group Databasebeta

← #25084175

Subgroups — #25084175

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145813C211yesmaximal, characteristic
2#19145736C211yesmaximal, characteristic, complemented
3#19143755C211yesmaximal, characteristic
4#19134175C211yesmaximal, characteristic, complemented
5#19134168C211yesmaximal, characteristic, complemented
6#19134099C211yesmaximal, characteristic, complemented
7#19134092C211yesmaximal, characteristic, complemented
8#19134051C211yesmaximal, characteristic, complemented
9#19134044C211yesmaximal, characteristic, complemented
10#19133975C211yesmaximal, characteristic, complemented
11#19133968C211yesmaximal, characteristic, complemented
12#19133378C211yesmaximal, characteristic, complemented
13#19133295C211yesmaximal, characteristic, complemented
14C2×#14582647C211yesmaximal, characteristic, complemented
15C43×#3248C211yesmaximal, characteristic
16C2×#13063325C2211yescharacteristic
17#14583309—21no—
18#14583295C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583258—21no—
21#14583249C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583227—21no—
24#14583227—21no—
25#14583227—21no—
26#14583210—21no—
27#14583194C2211yescharacteristic
28#14583194C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583184—21no—
32#14583184—21no—
33#14583030C2211yescharacteristic
34Q8×C43⋊C8C2211yescharacteristic
35#14582977C2211yescharacteristic
36#14582971—21no—
37D4×C43⋊C8—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582960—21no—
40#14582956C2211yescharacteristic
41#14582952C2211yescharacteristic
42#14582926—21no—
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582645C2211yescharacteristic
55#14582645C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#479—21no—
59C43×#475C2211yescharacteristic
60C43×#474C2211yescharacteristic
61C43×#467—21no—
62C43×#465—21no—
63C43×#464—21no—
64C43×#462C2211yescharacteristic
65C43×#461C2211yescharacteristic
66C2×C4⋊C8×C43C2211yescharacteristic
67C22×Dic86—21no—
68C2×#10621877—21no—
69C22×C43⋊C8—21no—
70C22×C43⋊C8—21no—
71#13063325—21no—
72#13063325—21no—
73#13063325—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78#13063258—21no—
79#13063258—21no—
80#13063256—21no—
81#13063256—21no—
82#13063256—21no—
83#13063256—21no—
84#13063256—21no—
85#13063256—21no—
86C4⋊(C43⋊C8)—21no—
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)D411yescharacteristic
90C4⋊(C43⋊C8)D411yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063249—21no—
96#13063249—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063246—21no—
102#13063246—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)D411yescharacteristic
107C22⋊(C43⋊C8)D411yescharacteristic
108#13063236—21no—
109#13063236—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×Q16×C43—21no—
114C2×SD16×C43—21no—
115C22×C8×C43—21no—
116C4⋊Q8×C43C2311yescharacteristic
117C4⋊Q8×C43C2311yescharacteristic
118#126×C43—21no—
119#125×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43D411yescharacteristic
122#123×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43D411yescharacteristic
126#121×C43D411yescharacteristic
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132#117×C43—21no—
133#117×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#107×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
142#103×C43—21no—
143#102×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43#4111yescharacteristic
153C22×Dic43—41no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—41no—
157C2×Dic86—82no—
158Q16×C43—81no—
159SD16×C43—81no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—81no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—41no—
181C42×C43—21no—
182C42×C43—41no—
183C42×C43C2×D411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C42×C43#4111yescharacteristic
186C42×C43C2411yescharacteristic
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—41no—
192C4⋊Dic43—41no—
193#10621877—81no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—81no—
199C2×C43⋊C8—81no—
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C23×C43—21no—
205C23×C43#12111yescharacteristic
206Q8×C43—21no—
207Q8×C43—21no—
208Q8×C43—41no—
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—41no—
212D4×C43—21no—
213D4×C43—21no—
214D4×C43—42no—
215C2×C4×C43—22no—
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—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
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—82no—
236Dic86—82no—
237Dic86—81no—
238Dic86—81no—
239C8×C43—41no—
240C8×C43—41no—
241C43⋊C8—21no—
242C43⋊C8—21no—
243C43⋊C8—21no—
244C43⋊C8—21no—
245C43⋊C8—41no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249#19588—431nomaximal, Sylow
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—41no—
253C22×C43—41no—
254C22×C43—41no—
255C22×C43#47112yes—
256C22×C43C2×#12111yescharacteristic
257C4×C43—21no—
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—21no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—81no—
265C4×C43—81no—
266C4×C43#57711yescharacteristic
267C4×C43#57711yescharacteristic
268C4×C43#57811yescharacteristic
269C4×C43#57811yescharacteristic
270Dic43—81no—
271Dic43—81no—
272#3248D4311yescharacteristic
273#3238—431no—
274#3229—431no—
275#2994—431no—
276#1704—431no—
277#1703—431no—
278#1692—431no—
279#1691—431no—
280#1684—431no—
281#1683—431no—
282#1672—431no—
283#1671—431no—
284#1573—431no—
285#1552—431no—
286C2×#333—431no—
287C2×C43—22no—
288C2×C43—81no—
289C2×C43#304611yescharacteristic
290C2×C43#306311yescharacteristic
291C2×C43C2×#47111yescharacteristic
292#533C2×D4311yescharacteristic
293C2×C4⋊Q8—431no—
294#529C2×D4311yescharacteristic
295#501—861no—
296#498—431no—
297#498—431no—
298#489—861no—
299#487—431no—
300#487—431no—
301#483—861no—
302#483—861no—
303#483—861no—
304#480—861no—
305#479—21no—
306#477—431no—
307#477—431no—
308#476—431no—
309#476—431no—
310#475—861no—
311#475—861no—
312#475C2×D4311yescharacteristic
313#474C2×D4311yescharacteristic
314#467—21no—
315#465—21no—
316#464—21no—
317#462C2×D4311yescharacteristic
318#461C2×D4311yescharacteristic
319#446—431no—
320C8×Q8—431no—
321#436—431no—
322#435—861no—
323C8×D4—431no—
324C8×D4—861no—
325#433—861no—
326#432—431no—
327#431—431no—
328#424—861no—
329C2×C4⋊C8—431no—
330C2×C4⋊C8C2×D4311yescharacteristic
331#335—431no—
332#335—431no—
333#334—431no—
334#334—431no—
335#333—431no—
336#333—431no—
337#333—431no—
338#333—431no—
339#332—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343C43#1958811yescharacteristic, complemented, Sylow
344C22×Q8—861no—
345C2×Q16—21no—
346C2×SD16—21no—
347C2×M16—861no—
348C22×C8—21no—
349C22×C8—861no—
350C22×C8—861no—
351C4⋊Q8—431no—
352C4⋊Q8—431no—
353C4⋊Q8—861no—
354C4⋊Q8—861no—
355C4⋊Q8—861no—
356C4⋊Q8C22×D4311yescharacteristic
357C4⋊Q8C22×D4311yescharacteristic
358#126—21no—
359#125—21no—
360#125C22⋊D4311yescharacteristic
361#124C22⋊D4311yescharacteristic
362#123—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8C22⋊D4311yescharacteristic
366#121C22⋊D4311yescharacteristic
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8C22×D4311yescharacteristic
370C4×D4—21no—
371C4×D4C22×D4311yescharacteristic
372#117—21no—
373#117—21no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C42C22×D4311yescharacteristic
377#107—21no—
378#107—861no—
379#107—861no—
380#106—21no—
381#106—861no—
382#106—861no—
383#106—861no—
384#106—861no—
385#106—861no—
386#106—861no—
387C4⋊C8—21no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—431no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396C4⋊C8—861no—
397C4⋊C8C22×D4311yescharacteristic
398C4⋊C8C22×D4311yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#102—21no—
409#102—861no—
410#102—861no—
411C22⋊C8—431no—
412C22⋊C8—431no—
413C22⋊C8—861no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416#97—861no—
417#97—861no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—861no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—861no—
424C2×Q8—861no—
425C2×Q8—3442no—
426C2×Q8—1721no—
427C2×Q8C2×C22⋊D4311yescharacteristic
428C2×D4—21no—
429C2×D4C2×C22⋊D4311yescharacteristic
430C22×C4—21no—
431C22×C4—1721no—
432C22×C4D4×D4311yescharacteristic
433C22×C4#1062190011yescharacteristic
434C22×C4C2×C22⋊D4311yescharacteristic
435Q16—81no—
436SD16—81no—
437M16—3441no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—81no—
441C2×C8—431no—
442C2×C8—431no—
443C2×C8—431no—
444C2×C8—431no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—3441no—
450C2×C8—3441no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—1721no—
466C4⋊C4—1721no—
467C4⋊C4C2×C22⋊D4311yescharacteristic
468C4⋊C4C2×C22⋊D4311yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—41no—
475C42—21no—
476C42—41no—
477C42D4×D4311yescharacteristic
478C42#1062190011yescharacteristic
479C42C2×C22⋊D4311yescharacteristic
480C42C23×D4311yescharacteristic
481C23—21no—
482C23#1306329711yescharacteristic
483Q8—21no—
484Q8—21no—
485Q8—41no—
486Q8—41no—
487Q8—41no—
488Q8—41no—
489Q8—3441no—
490Q8—3441no—
491Q8—3442no—
492D4—21no—
493D4—21no—
494D4—42no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—3442no—
508C2×C4—1721no—
509C2×C4—1721no—
510C2×C4#1306329711yescharacteristic
511C2×C4#1306329711yescharacteristic
512C2×C4#1306329711yescharacteristic
513C2×C4C2×D4×D4311yescharacteristic
514C2×C4C22×C22⋊D4311yescharacteristic
515C2×C4C2×#1062190011yescharacteristic
516C8—41no—
517C8—41no—
518C8—861no—
519C8—861no—
520C8—861no—
521C8—861no—
522C8—1721no—
523C8—1721no—
524C8—1721no—
525C8—1721no—
526C22—21no—
527C22—21no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22#1458316412yes—
532C22C2×#1306329711yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—81no—
541C4—81no—
542C4—3441no—
543C4—3441no—
544C4#1458370611yescharacteristic
545C4#1458371011yescharacteristic
546C4#1458371311yescharacteristic
547C4#1458371411yescharacteristic
548C2—22no—
549C2—81no—
550C2#1914414311yescharacteristic
551C2#1914428811yescharacteristic
552C2C2×#1458316411yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3248C2
socleC22×C43C2×#121
prime radical#121×C43D4
hypercenter#3248D43
hypocenterC43#19588
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3248

Complements

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

NH ≅ G/Ntype
2. #19145736C2semidirect
4. #19134175C2semidirect
5. #19134168C2semidirect
6. #19134099C2semidirect
7. #19134092C2semidirect
8. #19134051C2semidirect
9. #19134044C2semidirect
10. #19133975C2semidirect
11. #19133968C2semidirect
12. #19133378C2semidirect
13. #19133295C2semidirect
14. C2×#14582647C2semidirect
343. C43#19588semidirect

Maximal subgroups

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

subgroupindex
#191458132
#191457362
#191437552
#191341752
#191341682
#191340992
#191340922
#191340512
#191340442
#191339752
#191339682
#191333782
#191332952
C2×#145826472
C43×#32482
#1958843