Finite Group Databasebeta

← #25084215

Subgroups — #25084215

Order 11008.

580 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145933C211yesmaximal, characteristic
2#19145746C211yesmaximal, characteristic, complemented
3#19145622C211yesmaximal, characteristic
4#19143751C211yesmaximal, characteristic
5#19134152C211yesmaximal, characteristic, complemented
6#19134145C211yesmaximal, characteristic, complemented
7#19134112C211yesmaximal, characteristic, complemented
8#19134107C211yesmaximal, characteristic, complemented
9#19134028C211yesmaximal, characteristic, complemented
10#19134021C211yesmaximal, characteristic, complemented
11#19133988C211yesmaximal, characteristic, complemented
12#19133983C211yesmaximal, characteristic, complemented
13#19133378C211yesmaximal, characteristic, complemented
14#19133293C211yesmaximal, characteristic, complemented
15C2×C43×#332C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583433C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583291—21no—
21#14583267—21no—
22#14583251C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583234—21no—
25#14583234—21no—
26#14583207—21no—
27#14583191—21no—
28#14583191—21no—
29#14583185C2211yescharacteristic
30#14583180C2211yescharacteristic
31#14583140—21no—
32#14583128—21no—
33#14583122—21no—
34#14583110C2211yescharacteristic
35#14583106C2211yescharacteristic
36#14583106C2211yescharacteristic
37#14583105C2211yescharacteristic
38#14583101C2211yescharacteristic
39#14583101C2211yescharacteristic
40#14583055—21no—
41#14583038—21no—
42#14583026C2211yescharacteristic
43#14583023C2211yescharacteristic
44#14582976C2211yescharacteristic
45#14582970—21no—
46#14582964C2211yescharacteristic
47C8×C22⋊D43—21no—
48#14582959—21no—
49#14582956C2211yescharacteristic
50#14582952C2211yescharacteristic
51#14582924—21no—
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C2×C4⋊Q8×C43C2211yescharacteristic
61C2×C4⋊C8×C43C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#332C2211yescharacteristic
64C43×#332C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Dic172—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621873—21no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×#10621872—21no—
74C2×C8×D43—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063319—21no—
78#13063317—21no—
79#13063317D411yescharacteristic
80#13063313D411yescharacteristic
81#13063308—21no—
82#13063304—21no—
83#13063304—21no—
84#13063304D411yescharacteristic
85#13063299D411yescharacteristic
86C4×Dic86—21no—
87C4×Dic86—21no—
88C4×Dic86C2311yescharacteristic
89C4×D172C2311yescharacteristic
90C4×C22⋊D43—21no—
91#13063284—21no—
92#13063282—21no—
93#13063259—21no—
94#13063258—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258—21no—
98#13063257—21no—
99C4⋊(C43⋊C8)D411yescharacteristic
100C4⋊(C43⋊C8)D411yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105#13063250—21no—
106#13063250—21no—
107#13063250—21no—
108#13063249—21no—
109#13063249—21no—
110#13063249—21no—
111#13063249—21no—
112#13063248—21no—
113#13063248—21no—
114#13063248—21no—
115#13063248—21no—
116#13063247—21no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)D411yescharacteristic
119C22⋊(C43⋊C8)D411yescharacteristic
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122#13063236—21no—
123#13063235—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C22×Q8×C43—21no—
128C22×C8×C43—21no—
129C22×C8×C43—21no—
130C4⋊Q8×C43—21no—
131C4⋊Q8×C43—21no—
132C4⋊Q8×C43—21no—
133C4⋊Q8×C43C2311yescharacteristic
134C4⋊Q8×C43C2311yescharacteristic
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43—21no—
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43—21no—
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C4⋊C8×C43C2311yescharacteristic
143C4⋊C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—81no—
148C2×Q8×C43—81no—
149C22×C4×C43—41no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43#4111yescharacteristic
153C2×C22⋊D43—21no—
154C2×D172C2×D411yescharacteristic
155C2×C4×D43—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86C2×D411yescharacteristic
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—81no—
164C2×C8×C43—81no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43—41no—
171C42×C43C2×D411yescharacteristic
172C42×C43C2×D411yescharacteristic
173C42×C43#4111yescharacteristic
174C42×C43C2411yescharacteristic
175C22⋊Dic43—21no—
176C22⋊Dic43—41no—
177#10621885—81no—
178#10621885—81no—
179#10621884—81no—
180#10621884—81no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43C2×D411yescharacteristic
190C4⋊Dic43C2×D411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—41no—
196Dic43⋊C4—41no—
197C4×Dic43—21no—
198C4×Dic43—41no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205Dic172—81no—
206#10621873—81no—
207#10621872—81no—
208C8×D43—81no—
209C23×C43#12111yescharacteristic
210C22×D43—21no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—82no—
216C2×C4×C43—22no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—82no—
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C22⋊D43—42no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236D172—21no—
237D172—21no—
238C4×D43—41no—
239C4×D43—41no—
240Dic86—21no—
241Dic86—21no—
242Dic86—41no—
243Dic86—41no—
244Dic86—41no—
245Dic86—41no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43—41no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256#19590—431nomaximal, Sylow
257C22×C43—21no—
258C22×C43—21no—
259C22×C43#47312yes—
260C22×C43C2×#12111yescharacteristic
261C2×D43—41no—
262C2×D43—41no—
263C2×D43—41no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—81no—
269C4×C43—81no—
270C4×C43#57611yescharacteristic
271C4×C43#57711yescharacteristic
272C4×C43#57711yescharacteristic
273C4×C43#57811yescharacteristic
274Dic43—41no—
275Dic43—41no—
276Dic43—41no—
277Dic43—81no—
278Dic43—81no—
279#3248—431no—
280#3230—431no—
281#3218—431no—
282#2994—431no—
283#1700—431no—
284#1699—431no—
285#1694—431no—
286#1693—431no—
287#1680—431no—
288#1679—431no—
289#1674—431no—
290#1673—431no—
291#1573—431no—
292#1552—431no—
293C2×#332D4311yescharacteristic, complemented
294C2×C43—22no—
295C2×C43#304611yescharacteristic
296C2×C43#306211yescharacteristic
297C2×C43C2×#47311yescharacteristic
298D43—81no—
299#533—431no—
300C2×C4⋊Q8C2×D4311yescharacteristic
301#529—431no—
302#500—431no—
303#500—431no—
304#497—861no—
305#491—861no—
306#487—431no—
307#487—431no—
308#484—861no—
309#484—861no—
310#479—861no—
311#477—861no—
312#477—861no—
313#475—431no—
314#474—431no—
315#467—861no—
316#465—861no—
317#464—861no—
318#462—431no—
319#462—431no—
320#462—431no—
321#461—431no—
322#461—431no—
323#461—431no—
324#451—861no—
325#448—861no—
326#446—431no—
327C8×Q8—431no—
328#436—431no—
329#435—861no—
330C8×D4—431no—
331C8×D4—861no—
332#433—861no—
333#432—431no—
334#431—431no—
335#424—861no—
336C2×C4⋊C8C2×D4311yescharacteristic
337C2×C4⋊C8C2×D4311yescharacteristic
338#335—431no—
339#335—431no—
340#334—431no—
341#334—431no—
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346#332C2×D4311yescharacteristic
347#332C2×D4311yescharacteristic
348#332C2×D4311yescharacteristic
349#332C2×D4311yescharacteristic
350C43#1959011yescharacteristic, complemented, Sylow
351C22×Q8—21no—
352C2×Q16—861no—
353C2×Q16—861no—
354C2×Q16—861no—
355C2×SD16—861no—
356C2×SD16—861no—
357C2×SD16—861no—
358C2×M16—861no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—861no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—431no—
366C4⋊Q8—431no—
367C4⋊Q8C22×D4311yescharacteristic
368C4⋊Q8C22×D4311yescharacteristic
369#126—861no—
370#125—431no—
371#125—861no—
372#124—431no—
373#123—861no—
374C22⋊Q8—431no—
375C22⋊Q8—861no—
376C22⋊Q8—861no—
377#121—431no—
378C4×Q8—431no—
379C4×Q8—861no—
380C4×Q8—861no—
381C4×D4—431no—
382C4×D4—861no—
383#117—861no—
384#117—861no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C42C22×D4311yescharacteristic
388#107—861no—
389#107—861no—
390#107—861no—
391#107—861no—
392#107—861no—
393#106—861no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8C22×D4311yescharacteristic
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#102—861no—
418C22⋊C8—431no—
419C22⋊C8—431no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423#97—861no—
424#97—861no—
425C4×C8—431no—
426C4×C8—431no—
427C4×C8—861no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—41no—
431C2×Q8—81no—
432C2×Q8—81no—
433C2×Q8—431no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×D4—431no—
437C2×D4—861no—
438C22×C4—41no—
439C22×C4—861no—
440C22×C4#1062189811yescharacteristic
441C22×C4D4×D4311yescharacteristic
442C22×C4D4×D4311yescharacteristic
443Q16—3441no—
444Q16—3441no—
445Q16—3441no—
446SD16—3441no—
447SD16—3441no—
448SD16—3441no—
449M16—3441no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—81no—
455C2×C8—81no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—431no—
459C2×C8—431no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—3441no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—431no—
470C4⋊C4—431no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—1721no—
480C4⋊C4—1721no—
481C22⋊C4—861no—
482C22⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—861no—
485C22⋊C4—861no—
486C22⋊C4—1721no—
487C42—861no—
488C42—1721no—
489C42#1062189811yescharacteristic
490C42D4×D4311yescharacteristic
491C42D4×D4311yescharacteristic
492C42C23×D4311yescharacteristic
493C23—861no—
494C23#1306329811yescharacteristic
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—82no—
500Q8—861no—
501Q8—861no—
502Q8—1721no—
503Q8—1721no—
504Q8—1721no—
505Q8—1721no—
506D4—861no—
507D4—861no—
508D4—1722no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—82no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4#1306329811yescharacteristic
525C2×C4#1306329811yescharacteristic
526C2×C4#1306329811yescharacteristic
527C2×C4C2×D4×D4311yescharacteristic
528C2×C4C2×D4×D4311yescharacteristic
529C2×C4C2×#1062189811yescharacteristic
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—861no—
535C8—861no—
536C8—861no—
537C8—861no—
538C8—1721no—
539C8—1721no—
540C22—21no—
541C22—21no—
542C22—1721no—
543C22—1721no—
544C22—1721no—
545C22#1458317312yes—
546C22C2×#1306329811yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—81no—
552C4—81no—
553C4—3441no—
554C4—3441no—
555C4—1721no—
556C4—1721no—
557C4—1721no—
558C4#1458370011yescharacteristic
559C4#1458370511yescharacteristic
560C4#1458370511yescharacteristic
561C4#1458371211yescharacteristic
562C2—22no—
563C2—3441no—
564C2#1914415011yescharacteristic
565C2#1914427311yescharacteristic
566C2C2×#1458317311yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#332C2
socleC22×C43C2×#121
prime radical#13063299D4
hypercenterC2×#332D43
hypocenterC43#19590
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #19145746C2semidirect
5. #19134152C2semidirect
6. #19134145C2semidirect
7. #19134112C2semidirect
8. #19134107C2semidirect
9. #19134028C2semidirect
10. #19134021C2semidirect
11. #19133988C2semidirect
12. #19133983C2semidirect
13. #19133378C2semidirect
14. #19133293C2semidirect
15. C2×C43×#332C2semidirect
293. C2×#332D43semidirect
350. C43#19590semidirect

Maximal subgroups

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

subgroupindex
#191459332
#191457462
#191456222
#191437512
#191341522
#191341452
#191341122
#191341072
#191340282
#191340212
#191339882
#191339832
#191333782
#191332932
C2×C43×#3322
#1959043