Finite Group Databasebeta

← #25068648

Subgroups — #25068648

Order 11008.

598 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145159C211yesmaximal, characteristic
2#19143755C211yesmaximal, characteristic, complemented
3#19143751C211yesmaximal, characteristic, complemented
4#19133506C211yesmaximal, characteristic, complemented
5#19133501C211yesmaximal, characteristic, complemented
6#19133441C211yesmaximal, characteristic, complemented
7#19133435C211yesmaximal, characteristic, complemented
8#19133434C211yesmaximal, characteristic, complemented
9#19133428C211yesmaximal, characteristic, complemented
10#19133416C211yesmaximal, characteristic, complemented
11#19133411C211yesmaximal, characteristic, complemented
12C2×#14582649C211yesmaximal, characteristic, complemented
13#19133009C211yesmaximal, characteristic, complemented
14#19132882C211yesmaximal, characteristic, complemented
15C43×#1483C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583298C411yescharacteristic
18#14583281C411yescharacteristic
19#14583256C411yescharacteristic
20#14583253C411yescharacteristic
21#14583138C411yescharacteristic
22#14583133C411yescharacteristic
23#14583130C411yescharacteristic
24#14583126C411yescharacteristic
25#14583030C2211yescharacteristic
26#14583026C2211yescharacteristic
27Q8×C43⋊C8C2211yescharacteristic
28#14583023C2211yescharacteristic
29C4×#10621885C2211yescharacteristic
30C4×#10621884C2211yescharacteristic
31C4×#10621883C2211yescharacteristic
32C4×#10621882C2211yescharacteristic
33#14582977C2211yescharacteristic
34#14582976C2211yescharacteristic
35#14582971—21no—
36#14582970—21no—
37D4×C43⋊C8—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582964C2211yescharacteristic
40C8×C22⋊D43—21no—
41#14582960—21no—
42#14582959—21no—
43#14582952C2211yescharacteristic
44#14582926—21no—
45#14582924—21no—
46C2×C4⋊(C43⋊C8)C2211yescharacteristic
47C2×C4×C43⋊C8C2211yescharacteristic
48#14582649C2211yescharacteristic
49#14582649C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582649C2211yescharacteristic
52#14582631C2211yescharacteristic
53#14582631C2211yescharacteristic
54#14582628C2211yescharacteristic
55#14582628C2211yescharacteristic
56#14582621C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582621C2211yescharacteristic
59#14582621C2211yescharacteristic
60C43×#529C2211yescharacteristic
61C2×C4⋊C8×C43C2211yescharacteristic
62C4×M16×C43C2211yescharacteristic
63C43×Q8⋊C8C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic
67C2×#10621885C2×C411yescharacteristic
68C2×#10621883C2×C411yescharacteristic
69C2×#10621884C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621877—21no—
72C2×#10621872—21no—
73C22×C43⋊C8—21no—
74C22×C43⋊C8—21no—
75C22×C43⋊C8C2×C411yescharacteristic
76C22×C43⋊C8C2×C411yescharacteristic
77C2×C8×D43—21no—
78#13063319—21no—
79#13063317C2×C411yescharacteristic
80#13063313C2×C411yescharacteristic
81#13063308—21no—
82#13063304C2×C411yescharacteristic
83#13063299C2×C411yescharacteristic
84C4×Dic86C2311yescharacteristic
85C4×D172C2311yescharacteristic
86C4×C22⋊D43—21no—
87#13063282—21no—
88#13063258C2×C411yescharacteristic
89#13063258C2×C411yescharacteristic
90#13063256C2×C411yescharacteristic
91#13063256C2×C411yescharacteristic
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)D411yescharacteristic
96C4⋊(C43⋊C8)D411yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101#13063249C2×C411yescharacteristic
102#13063249C2×C411yescharacteristic
103#13063248C2×C411yescharacteristic
104#13063248C2×C411yescharacteristic
105#13063246C2×C411yescharacteristic
106#13063246C2×C411yescharacteristic
107#13063245C2×C411yescharacteristic
108#13063245C2×C411yescharacteristic
109C22⋊(C43⋊C8)—21no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)D411yescharacteristic
112C22⋊(C43⋊C8)D411yescharacteristic
113(C2×D43)⋊C8—21no—
114(C2×D43)⋊C8—21no—
115#13063236—21no—
116#13063235—21no—
117C4×C43⋊C8—21no—
118C4×C43⋊C8C2×C411yescharacteristic
119C4×C43⋊C8C2×C411yescharacteristic
120C4×C43⋊C8C2311yescharacteristic
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C2×M16×C43—21no—
126C22×C8×C43—21no—
127#126×C43—21no—
128#125×C43C2×C411yescharacteristic
129#124×C43C2×C411yescharacteristic
130#123×C43—21no—
131C22⋊Q8×C43C2×C411yescharacteristic
132#121×C43C2×C411yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134C4×D4×C43—21no—
135C4×D4×C43C2311yescharacteristic
136#117×C43—21no—
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43C22×C411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C2×C22⋊D43—21no—
152C2×D172C22×C411yescharacteristic
153C2×C4×D43—21no—
154C2×Dic86C22×C411yescharacteristic
155M16×C43—42no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—81no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43C22×C411yescharacteristic
166C4⋊C4×C43C22×C411yescharacteristic
167C22⋊C4×C43—21no—
168C22⋊C4×C43—21no—
169C22⋊C4×C43—21no—
170C22⋊C4×C43—21no—
171C22⋊C4×C43—21no—
172C42×C43—21no—
173C42×C43C22×C411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43#4111yescharacteristic
176C42×C43C2411yescharacteristic
177C22⋊Dic43—21no—
178#10621885—22no—
179#10621884—41no—
180#10621883—41no—
181#10621882—22no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186C4⋊Dic43C22×C411yescharacteristic
187C4⋊Dic43C22×C411yescharacteristic
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192C4×Dic43—21no—
193#10621877—81no—
194C2×C43⋊C8—22no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—41no—
198C2×C43⋊C8—81no—
199C2×C43⋊C8—81no—
200C2×C43⋊C8C22×C411yescharacteristic
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208#10621872—81no—
209C8×D43—81no—
210C23×C43—21no—
211C23×C43C4×D411yescharacteristic
212C22×D43—21no—
213Q8×C43—21no—
214Q8×C43—21no—
215D4×C43—21no—
216D4×C43—21no—
217D4×C43—42no—
218C2×C4×C43—22no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43C4×D411yescharacteristic
229C2×C4×C43C4×D411yescharacteristic
230C2×C4×C43C4×D411yescharacteristic
231C2×C4×C43C23×C411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C22⋊D43—42no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238D172—21no—
239D172—21no—
240C4×D43—41no—
241C4×D43—41no—
242Dic86—21no—
243Dic86—21no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43—41no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8#13112yes—
258#18093—431nomaximal, Sylow
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43#44412yes—
265C22×C43C2×C4×D411yescharacteristic
266C2×D43—41no—
267C2×D43—41no—
268C2×D43—41no—
269C4×C43—21no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43C2×#13111yescharacteristic
277C4×C43#56811yescharacteristic
278C4×C43#57711yescharacteristic
279C4×C43#57711yescharacteristic
280Dic43—41no—
281Dic43—41no—
282Dic43—41no—
283#3168—431no—
284#2994—431no—
285#2994—431no—
286#1594—431no—
287#1593—431no—
288#1583—431no—
289#1583—431no—
290#1582—431no—
291#1582—431no—
292#1580—431no—
293#1579—431no—
294C2×#334—431no—
295#1483—431no—
296#1483D4311yescharacteristic, complemented
297#1451—431no—
298C2×C43—22no—
299C2×C43—81no—
300C2×C43#293511yescharacteristic
301C2×C43#295211yescharacteristic
302C2×C43C2×#44411yescharacteristic
303D43—81no—
304#529—431no—
305#529C2×D4311yescharacteristic
306#499—431no—
307#495—431no—
308#488—431no—
309#488—431no—
310#467—431no—
311#466—431no—
312#465—431no—
313#465—431no—
314#446—431no—
315#446—431no—
316C8×Q8—431no—
317C8×Q8—431no—
318C4×Q16—431no—
319C4×SD16—431no—
320C4×SD16—431no—
321C4×D8—431no—
322#436—431no—
323#436—431no—
324#435—861no—
325#435—861no—
326C8×D4—431no—
327C8×D4—431no—
328C8×D4—861no—
329C8×D4—861no—
330#433—861no—
331#433—861no—
332#431—431no—
333#424—861no—
334#424—861no—
335C2×C4⋊C8—431no—
336C2×C4⋊C8C2×D4311yescharacteristic
337C4×M16C2×D4311yescharacteristic
338C2×C4×C8—431no—
339#334—431no—
340#334—431no—
341#334—431no—
342#334—431no—
343Q8⋊C8—431no—
344Q8⋊C8—431no—
345Q8⋊C8C2×D4311yescharacteristic
346Q8⋊C8C2×D4311yescharacteristic
347D4⋊C8—431no—
348D4⋊C8—431no—
349D4⋊C8C2×D4311yescharacteristic
350D4⋊C8C2×D4311yescharacteristic
351#322—431no—
352#322—431no—
353#322—431no—
354#322—431no—
355C43#1809311yescharacteristic, complemented, Sylow
356C2×Q16—431no—
357C2×SD16—431no—
358C2×SD16—431no—
359C2×D8—431no—
360C2×M16—21no—
361C2×M16—861no—
362C2×M16—861no—
363C22×C8—21no—
364C22×C8—431no—
365C22×C8—431no—
366C22×C8—861no—
367C22×C8—861no—
368C22×C8—861no—
369#126—21no—
370#126—861no—
371#125—431no—
372#125C4×D4311yescharacteristic
373#124—431no—
374#124C4×D4311yescharacteristic
375#123—21no—
376#123—861no—
377C22⋊Q8—431no—
378C22⋊Q8C4×D4311yescharacteristic
379#121—431no—
380#121C4×D4311yescharacteristic
381C4×Q8—431no—
382C4×Q8C22×D4311yescharacteristic
383C4×D4—21no—
384C4×D4—431no—
385C4×D4—861no—
386C4×D4C22×D4311yescharacteristic
387#117—21no—
388#117—861no—
389C2×C42C22×D4311yescharacteristic
390#107—431no—
391#107—431no—
392#106—431no—
393#106—431no—
394C4⋊C8—21no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406#103—431no—
407#103—431no—
408#103—431no—
409#103—431no—
410#102—431no—
411#102—431no—
412#102—431no—
413#102—431no—
414C22⋊C8—431no—
415C22⋊C8—431no—
416C22⋊C8—861no—
417C22⋊C8—861no—
418C22⋊C8—861no—
419C22⋊C8—861no—
420#97—21no—
421#97—861no—
422#97—861no—
423C4×C8—431no—
424C4×C8—431no—
425C4×C8—431no—
426C4×C8—431no—
427C4×C8—431no—
428C4×C8—431no—
429C4×C8—861no—
430C4×C8—861no—
431C4×C8C22×D4311yescharacteristic
432C4×C8C22×D4311yescharacteristic
433C2×Q8—431no—
434C2×Q8C2×C4×D4311yescharacteristic
435C2×D4—21no—
436C2×D4—431no—
437C2×D4—861no—
438C2×D4C2×C4×D4311yescharacteristic
439C22×C4—21no—
440C22×C4—861no—
441C22×C4C2×C4×D4311yescharacteristic
442C22×C4D4×D4311yescharacteristic
443C22×C4#1062190011yescharacteristic
444Q16—862no—
445SD16—1721no—
446SD16—1721no—
447D8—862no—
448M16—42no—
449M16—3441no—
450M16—3441no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—81no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—431no—
459C2×C8—431no—
460C2×C8—431no—
461C2×C8—431no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—862no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—3441no—
468C2×C8—3441no—
469C2×C8—3441no—
470C2×C8—1721no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—431no—
476C4⋊C4—431no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4C2×C4×D4311yescharacteristic
482C4⋊C4C2×C4×D4311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—861no—
489C22⋊C4—861no—
490C22⋊C4—861no—
491C22⋊C4—861no—
492C22⋊C4—861no—
493C42—21no—
494C42—861no—
495C42C2×C4×D4311yescharacteristic
496C42D4×D4311yescharacteristic
497C42#1062190011yescharacteristic
498C42C23×D4311yescharacteristic
499C23—21no—
500C23—861no—
501C23(C22⋊D43)⋊C411yescharacteristic
502Q8—21no—
503Q8—21no—
504Q8—861no—
505Q8—861no—
506D4—21no—
507D4—21no—
508D4—42no—
509D4—861no—
510D4—861no—
511D4—1722no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4(C22⋊D43)⋊C411yescharacteristic
528C2×C4(C22⋊D43)⋊C411yescharacteristic
529C2×C4(C22⋊D43)⋊C411yescharacteristic
530C2×C4C22×C4×D4311yescharacteristic
531C2×C4C2×D4×D4311yescharacteristic
532C2×C4C2×#1062190011yescharacteristic
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—432no—
538C8—861no—
539C8—861no—
540C8—861no—
541C8—861no—
542C8—861no—
543C8—861no—
544C8—861no—
545C8—1721no—
546C8—1721no—
547C22—21no—
548C22—21no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—1721no—
553C22—1721no—
554C22—1721no—
555C22#1458301812yes—
556C22C2×(C22⋊D43)⋊C411yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—1721no—
565C4—1721no—
566C4—1721no—
567C4#131×D4311yescharacteristic
568C4#1458366411yescharacteristic
569C4#1458370811yescharacteristic
570C4#1458370911yescharacteristic
571C2—22no—
572C2—81no—
573C2—3441no—
574C2#1914333511yescharacteristic
575C2#1914347411yescharacteristic
576C2C2×#1458301811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1483C2
socleC22×C43C2×C4×D4
prime radical#14583133C4
cosocleC42×C43C24
hypercenter#1483D43
hypocenterC43#18093
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1483

Complements

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

NH ≅ G/Ntype
2. #19143755C2semidirect
3. #19143751C2semidirect
4. #19133506C2semidirect
5. #19133501C2semidirect
6. #19133441C2semidirect
7. #19133435C2semidirect
8. #19133434C2semidirect
9. #19133428C2semidirect
10. #19133416C2semidirect
11. #19133411C2semidirect
12. C2×#14582649C2semidirect
13. #19133009C2semidirect
14. #19132882C2semidirect
15. C43×#1483C2semidirect
296. #1483D43semidirect
355. C43#18093semidirect

Maximal subgroups

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

subgroupindex
#191451592
#191437552
#191437512
#191335062
#191335012
#191334412
#191334352
#191334342
#191334282
#191334162
#191334112
C2×#145826492
#191330092
#191328822
C43×#14832
#1809343