Finite Group Databasebeta

← #25084205

Subgroups — #25084205

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#19145743C211yesmaximal, characteristic, complemented
2#19145619C211yesmaximal, characteristic
3#19143755C211yesmaximal, characteristic
4#19134147C211yesmaximal, characteristic, complemented
5#19134140C211yesmaximal, characteristic, complemented
6#19134111C211yesmaximal, characteristic, complemented
7#19134106C211yesmaximal, characteristic, complemented
8#19134023C211yesmaximal, characteristic, complemented
9#19134016C211yesmaximal, characteristic, complemented
10#19133987C211yesmaximal, characteristic, complemented
11#19133982C211yesmaximal, characteristic, complemented
12#19133378C211yesmaximal, characteristic, complemented
13#19133295C211yesmaximal, characteristic, complemented
14C2×#14582646C211yesmaximal, characteristic, complemented
15C43×#3248C211yesmaximal, characteristic
16C2×#13063325C2211yescharacteristic
17#14583302C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583294—21no—
20#14583269—21no—
21#14583249C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583232—21no—
24#14583232—21no—
25#14583194—21no—
26#14583194—21no—
27#14583109C2211yescharacteristic
28#14583109C2211yescharacteristic
29#14583104C2211yescharacteristic
30#14583104C2211yescharacteristic
31#14583054—21no—
32#14583037—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#14582646C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582646C2211yescharacteristic
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×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621877—21no—
73C22×C43⋊C8—21no—
74C22×C43⋊C8—21no—
75#13063325—21no—
76#13063325—21no—
77#13063325—21no—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82#13063258—21no—
83#13063258—21no—
84#13063258—21no—
85#13063258—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#13063248—21no—
100#13063248—21no—
101#13063248—21no—
102#13063248—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—81no—
158C2×Dic86—81no—
159Q16×C43—81no—
160SD16×C43—81no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—81no—
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—21no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—41no—
182C42×C43—21no—
183C42×C43—41no—
184C42×C43C2×D411yescharacteristic
185C42×C43C2×D411yescharacteristic
186C42×C43#4111yescharacteristic
187C42×C43C2411yescharacteristic
188#10621885—81no—
189#10621885—81no—
190#10621883—81no—
191#10621883—81no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—41no—
197C4⋊Dic43—41no—
198#10621877—81no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—81no—
204C2×C43⋊C8—81no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C23×C43—21no—
210C23×C43#12111yescharacteristic
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—42no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—82no—
241Dic86—41no—
242Dic86—41no—
243Dic86—41no—
244Dic86—41no—
245Dic86—82no—
246C8×C43—41no—
247C8×C43—41no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256#19590—431nomaximal, Sylow
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43#47312yes—
263C22×C43C2×#12111yescharacteristic
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—81no—
272C4×C43—81no—
273C4×C43#57611yescharacteristic
274C4×C43#57711yescharacteristic
275C4×C43#57711yescharacteristic
276C4×C43#57811yescharacteristic
277Dic43—81no—
278Dic43—81no—
279#3248D4311yescharacteristic
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×#332—431no—
294C2×C43—22no—
295C2×C43—81no—
296C2×C43#304611yescharacteristic
297C2×C43#306211yescharacteristic
298C2×C43C2×#47311yescharacteristic
299#533C2×D4311yescharacteristic
300C2×C4⋊Q8—431no—
301#529C2×D4311yescharacteristic
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—21no—
311#477—861no—
312#477—861no—
313#475C2×D4311yescharacteristic
314#474C2×D4311yescharacteristic
315#467—21no—
316#465—21no—
317#464—21no—
318#462—431no—
319#462—431no—
320#462C2×D4311yescharacteristic
321#461—431no—
322#461—431no—
323#461C2×D4311yescharacteristic
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⋊C8—431no—
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#332—431no—
347#332—431no—
348#332—431no—
349#332—431no—
350C43#1959011yescharacteristic, complemented, Sylow
351C22×Q8—861no—
352C2×Q16—21no—
353C2×Q16—861no—
354C2×Q16—861no—
355C2×SD16—21no—
356C2×SD16—861no—
357C2×SD16—861no—
358C2×M16—861no—
359C22×C8—21no—
360C22×C8—861no—
361C22×C8—861no—
362C4⋊Q8—431no—
363C4⋊Q8—431no—
364C4⋊Q8—861no—
365C4⋊Q8—861no—
366C4⋊Q8—861no—
367C4⋊Q8C22×D4311yescharacteristic
368C4⋊Q8C22×D4311yescharacteristic
369#126—21no—
370#125—21no—
371#125C22⋊D4311yescharacteristic
372#124C22⋊D4311yescharacteristic
373#123—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8C22⋊D4311yescharacteristic
377#121C22⋊D4311yescharacteristic
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8C22×D4311yescharacteristic
381C4×D4—21no—
382C4×D4C22×D4311yescharacteristic
383#117—21no—
384#117—21no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C42C22×D4311yescharacteristic
388#107—21no—
389#107—861no—
390#107—861no—
391#107—861no—
392#107—861no—
393#106—21no—
394C4⋊C8—21no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406#103—21no—
407#103—21no—
408#103—21no—
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—21no—
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—861no—
431C2×Q8—861no—
432C2×Q8—3441no—
433C2×Q8—3441no—
434C2×Q8—1721no—
435C2×Q8C2×C22⋊D4311yescharacteristic
436C2×D4—21no—
437C2×D4C2×C22⋊D4311yescharacteristic
438C22×C4—21no—
439C22×C4—1721no—
440C22×C4D4×D4311yescharacteristic
441C22×C4#1062190011yescharacteristic
442C22×C4C2×C22⋊D4311yescharacteristic
443Q16—81no—
444Q16—3441no—
445Q16—3441no—
446SD16—81no—
447SD16—3441no—
448SD16—3441no—
449M16—3441no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—81no—
453C2×C8—431no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—3441no—
462C2×C8—3441no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—1721no—
478C4⋊C4—1721no—
479C4⋊C4C2×C22⋊D4311yescharacteristic
480C4⋊C4C2×C22⋊D4311yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—41no—
487C42—21no—
488C42—41no—
489C42D4×D4311yescharacteristic
490C42#1062190011yescharacteristic
491C42C2×C22⋊D4311yescharacteristic
492C42C23×D4311yescharacteristic
493C23—21no—
494C23#1306329711yescharacteristic
495Q8—21no—
496Q8—21no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—3442no—
502Q8—1721no—
503Q8—1721no—
504Q8—1721no—
505Q8—1721no—
506D4—21no—
507D4—21no—
508D4—42no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—3442no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4#1306329711yescharacteristic
525C2×C4#1306329711yescharacteristic
526C2×C4#1306329711yescharacteristic
527C2×C4C2×D4×D4311yescharacteristic
528C2×C4C22×C22⋊D4311yescharacteristic
529C2×C4C2×#1062190011yescharacteristic
530C8—41no—
531C8—41no—
532C8—861no—
533C8—861no—
534C8—861no—
535C8—861no—
536C8—1721no—
537C8—1721no—
538C8—1721no—
539C8—1721no—
540C22—21no—
541C22—21no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22#1458317212yes—
546C22C2×#1306329711yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—81no—
555C4—81no—
556C4—3441no—
557C4—3441no—
558C4#1458370211yescharacteristic
559C4#1458370611yescharacteristic
560C4#1458370711yescharacteristic
561C4#1458371311yescharacteristic
562C2—22no—
563C2—81no—
564C2#1914414311yescharacteristic
565C2#1914427711yescharacteristic
566C2C2×#1458317211yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3248C2
socleC22×C43C2×#121
prime radical#121×C43D4
hypercenter#3248D43
hypocenterC43#19590
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
1. #19145743C2semidirect
4. #19134147C2semidirect
5. #19134140C2semidirect
6. #19134111C2semidirect
7. #19134106C2semidirect
8. #19134023C2semidirect
9. #19134016C2semidirect
10. #19133987C2semidirect
11. #19133982C2semidirect
12. #19133378C2semidirect
13. #19133295C2semidirect
14. C2×#14582646C2semidirect
350. C43#19590semidirect

Maximal subgroups

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

subgroupindex
#191457432
#191456192
#191437552
#191341472
#191341402
#191341112
#191341062
#191340232
#191340162
#191339872
#191339822
#191333782
#191332952
C2×#145826462
C43×#32482
#1959043