Finite Group Databasebeta

← #25067539

Subgroups — #25067539

Order 11008.

616 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144619C211yesmaximal, characteristic
2#19143614C211yesmaximal, characteristic, complemented
3#19143598C211yesmaximal, characteristic, complemented
4#19133482C211yesmaximal, characteristic, complemented
5#19133481C211yesmaximal, characteristic, complemented
6#19133446C211yesmaximal, characteristic, complemented
7#19133438C211yesmaximal, characteristic, complemented
8#19133438C211yesmaximal, characteristic, complemented
9#19133423C211yesmaximal, characteristic, complemented
10#19133392C211yesmaximal, characteristic, complemented
11#19133374C211yesmaximal, characteristic, complemented
12#19133054C211yesmaximal, characteristic, complemented
13#19132976C211yesmaximal, characteristic, complemented
14C8×#10621872C211yesmaximal, characteristic, complemented
15C8×Q16×C43C211yesmaximal, characteristic, complemented
16#14583436C2211yescharacteristic
17C4×#10621902C2211yescharacteristic
18#14583239C411yescharacteristic
19#14583226C411yescharacteristic
20#14583208C411yescharacteristic
21#14583202C411yescharacteristic
22#14583123C411yescharacteristic
23#14583117C411yescharacteristic
24#14583060C411yescharacteristic
25#14583047C411yescharacteristic
26#14583030C2211yescharacteristic
27Q8×C43⋊C8C2211yescharacteristic
28C4×#10621884C2211yescharacteristic
29C4×#10621884C2211yescharacteristic
30C4×D344C2211yescharacteristic
31#14582978—21no—
32#14582978—21no—
33#14582978C2211yescharacteristic
34#14582978C2211yescharacteristic
35#14582976—21no—
36#14582976C2211yescharacteristic
37#14582969—21no—
38#14582964C2211yescharacteristic
39#14582959—21no—
40#14582955—21no—
41#14582955C2211yescharacteristic
42#14582951C2211yescharacteristic
43#14582950C2211yescharacteristic
44#14582853—21no—
45C4×#10621872—21no—
46C4×#10621872C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic
49#14582649C2211yescharacteristic
50#14582649C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582628C2211yescharacteristic
54#14582628C2211yescharacteristic
55#14582626C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C8×Q8×C43C2211yescharacteristic
61C8×Q8×C43C2211yescharacteristic
62C4×Q16×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C2×#10621902C2×C411yescharacteristic
68C2×#10621884C2×C411yescharacteristic
69C2×#10621884C2×C411yescharacteristic
70C2×D344C2×C411yescharacteristic
71C2×#10621872—21no—
72C2×#10621872—21no—
73C2×#10621872—21no—
74C2×#10621872D411yescharacteristic
75C2×#10621872D411yescharacteristic
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78#13063320—21no—
79#13063316C2×C411yescharacteristic
80#13063314C2×C411yescharacteristic
81#13063310—21no—
82#13063301C2×C411yescharacteristic
83#13063300C2×C411yescharacteristic
84Q8×Dic43C2×C411yescharacteristic
85C4×D172—21no—
86C4×D172—21no—
87C4×D172C2311yescharacteristic
88C4×D172C2311yescharacteristic
89#13063287—21no—
90#13063287C2×C411yescharacteristic
91#13063283—21no—
92#13063283C2×C411yescharacteristic
93#13063282—21no—
94C42×D43—21no—
95C42×D43C2311yescharacteristic
96#13063259C2×C411yescharacteristic
97#13063256C2×C411yescharacteristic
98#13063256C2×C411yescharacteristic
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)—21no—
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8C2×C411yescharacteristic
104Dic43⋊C8C2×C411yescharacteristic
105#13063249C2×C411yescharacteristic
106#13063249C2×C411yescharacteristic
107#13063247C2×C411yescharacteristic
108#13063247C2×C411yescharacteristic
109#13063245C2×C411yescharacteristic
110#13063245C2×C411yescharacteristic
111(C2×D43)⋊C8—21no—
112(C2×D43)⋊C8—21no—
113(C2×D43)⋊C8—21no—
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8C2×C411yescharacteristic
118(C2×D43)⋊C8C2×C411yescharacteristic
119#13063236—21no—
120#13063235—21no—
121#13063235D411yescharacteristic
122#13063235D411yescharacteristic
123C4×C43⋊C8—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×Q16×C43C2×C411yescharacteristic
130C4×Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132#107×C43C2×C411yescharacteristic
133C4⋊C8×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43C2×C411yescharacteristic
138#103×C43C2×C411yescharacteristic
139C4×C8×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×Q8×C43C22×C411yescharacteristic
146#10621902—22no—
147#10621902—41no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172C22×C411yescharacteristic
151C2×D172C22×C411yescharacteristic
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43C22×C411yescharacteristic
157C2×C4×D43C2×D411yescharacteristic
158C2×C4×D43#4111yescharacteristic
159Q16×C43—22no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C22×C411yescharacteristic
164C2×C8×C43C22×C411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C22×C411yescharacteristic
170C4⋊C4×C43C22×C411yescharacteristic
171C42×C43—21no—
172C42×C43—21no—
173C42×C43C2411yescharacteristic
174#10621884—22no—
175#10621884—41no—
176(C2×D43)⋊C4—21no—
177(C2×D43)⋊C4—21no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43C22×C411yescharacteristic
187C4⋊Dic43C22×C411yescharacteristic
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43C22×C411yescharacteristic
193C4×Dic43C2×D411yescharacteristic
194C4×Dic43#4111yescharacteristic
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C22×C411yescharacteristic
199C2×C43⋊C8C22×C411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202D344—41no—
203#10621872—22no—
204#10621872—22no—
205#10621872—42no—
206#10621872—42no—
207#10621872—42no—
208C8×D43—42no—
209C8×D43—42no—
210C22×D43—21no—
211C22×D43—21no—
212C22×D43C4×D411yescharacteristic
213Q8×C43—21no—
214Q8×C43—21no—
215Q8×C43—21no—
216Q8×C43#13112yes—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43C23×C411yescharacteristic
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43C4×D411yescharacteristic
227C2×Dic43C4×D411yescharacteristic
228C2×Dic43C4×D411yescharacteristic
229D172—21no—
230D172—21no—
231D172—21no—
232D172—21no—
233D172—42no—
234D172—81no—
235C4×D43—21no—
236C4×D43—21no—
237C4×D43—21no—
238C4×D43—21no—
239C4×D43—41no—
240C4×D43—42no—
241C4×D43—41no—
242C4×D43—41no—
243C4×D43—41no—
244C4×D43—41no—
245C4×D43—81no—
246C8×C43—22no—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—41no—
251C8×C43—41no—
252C8×C43#13512yes—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8#13512yes—
260#17999—431nomaximal, Sylow
261C22×C43C2×C4×D411yescharacteristic
262C2×D43—21no—
263C2×D43—21no—
264C2×D43—21no—
265C2×D43—41no—
266C2×D43—41no—
267C2×D43—41no—
268C2×D43—41no—
269C2×D43—41no—
270C2×D43—41no—
271C4×C43—22no—
272C4×C43—21no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—41no—
276C4×C43C2×#13111yescharacteristic
277C4×C43#56811yescharacteristic
278C4×C43C2×#13511yescharacteristic
279C4×C43C2×#13511yescharacteristic
280Dic43—21no—
281Dic43—21no—
282Dic43—21no—
283Dic43—41no—
284Dic43—41no—
285#3102—431no—
286#2971—431no—
287#2969—431no—
288#1590—431no—
289#1589—431no—
290#1584—431no—
291#1583—431no—
292#1583—431no—
293#1581—431no—
294C8×Q16D4311yescharacteristic, complemented
295C8×SD16—431no—
296#1572—431no—
297#1494—431no—
298#1476—431no—
299C8×M16—431no—
300C2×C43#293311yescharacteristic
301C2×C43C4×#13511yescharacteristic
302C2×C43#295611yescharacteristic
303D43—41no—
304D43—81no—
305D43—81no—
306#529—431no—
307C4×#41—431no—
308#485—431no—
309#482—431no—
310#479—431no—
311#478—431no—
312#464—431no—
313#463—431no—
314#452—431no—
315#449—431no—
316#446—431no—
317C8×Q8—431no—
318C8×Q8C2×D4311yescharacteristic
319C8×Q8C2×D4311yescharacteristic
320C4×Q16C2×D4311yescharacteristic
321C4×SD16—431no—
322C4×SD16—431no—
323C4×D8—431no—
324#436—431no—
325#436—431no—
326#436—431no—
327#436—861no—
328#436—861no—
329#436—861no—
330#435—861no—
331C8×D4—431no—
332#433—861no—
333#432—431no—
334#432—861no—
335#431—431no—
336#431—431no—
337#405—861no—
338C4×M16—431no—
339C4×M16—861no—
340C2×C4×C8—431no—
341#335—431no—
342#335C2×D4311yescharacteristic
343#334—431no—
344#334—431no—
345Q8⋊C8—431no—
346Q8⋊C8—431no—
347Q8⋊C8C2×D4311yescharacteristic
348Q8⋊C8C2×D4311yescharacteristic
349D4⋊C8—431no—
350D4⋊C8—431no—
351D4⋊C8—431no—
352D4⋊C8—431no—
353#322—431no—
354#322—431no—
355C82—431no—
356C82C2×D4311yescharacteristic
357C43#1799911yescharacteristic, complemented, Sylow
358C2×#41—431no—
359C2×Q16C4×D4311yescharacteristic
360C2×SD16—431no—
361C2×SD16—431no—
362C2×D8—431no—
363C2×M16—431no—
364C2×M16—431no—
365C2×M16—861no—
366C2×M16—861no—
367C2×M16—861no—
368C22×C8—861no—
369C22×C8—861no—
370#126—861no—
371#125—431no—
372#124—431no—
373#123—861no—
374C22⋊Q8—431no—
375#121—431no—
376C4×Q8—431no—
377C4×Q8C22×D4311yescharacteristic
378C4×Q8C22×D4311yescharacteristic
379C4×D4—431no—
380C4×D4—431no—
381C4×D4—431no—
382C4×D4—861no—
383C4×D4—861no—
384C4×D4—861no—
385#117—431no—
386#117—861no—
387#117—861no—
388C2×C42—431no—
389C2×C42—861no—
390#107—431no—
391#107C4×D4311yescharacteristic
392#106—431no—
393#106—431no—
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
404#103—431no—
405#103—431no—
406#103C4×D4311yescharacteristic
407#103C4×D4311yescharacteristic
408#102—431no—
409#102—431no—
410#102—431no—
411#102—431no—
412C22⋊C8—431no—
413C22⋊C8—431no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416C22⋊C8—861no—
417C22⋊C8—861no—
418C22⋊C8—861no—
419C22⋊C8—861no—
420#97—431no—
421#97—431no—
422#97—861no—
423#97—861no—
424C4×C8—21no—
425C4×C8—21no—
426C4×C8—431no—
427C4×C8—431no—
428C4×C8—431no—
429C4×C8—861no—
430C4×C8—861no—
431C4×C8—861no—
432C4×C8C22×D4311yescharacteristic
433C4×C8C22×D4311yescharacteristic
434C4×C8C22×D4311yescharacteristic
435#41—862no—
436#41—1721no—
437C2×Q8C2×C4×D4311yescharacteristic
438C2×Q8C2×C4×D4311yescharacteristic
439C2×D4—431no—
440C2×D4—431no—
441C2×D4—861no—
442C2×D4—861no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450Q16—22no—
451SD16—862no—
452SD16—1721no—
453D8—1721no—
454M16—862no—
455M16—862no—
456M16—1722no—
457M16—1722no—
458M16—1722no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—431no—
465C2×C8—431no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—1722no—
470C2×C8—1722no—
471C2×C8C2×C4×D4311yescharacteristic
472C2×C8C2×C4×D4311yescharacteristic
473C2×C8D4×D4311yescharacteristic
474C2×C8D4×D4311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—431no—
478C4⋊C4—431no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4C2×C4×D4311yescharacteristic
484C4⋊C4C2×C4×D4311yescharacteristic
485C22⋊C4—861no—
486C22⋊C4—861no—
487C22⋊C4—861no—
488C22⋊C4—861no—
489C22⋊C4—861no—
490C22⋊C4—861no—
491C22⋊C4—861no—
492C22⋊C4—861no—
493C42—21no—
494C42—21no—
495C42—431no—
496C42—431no—
497C42—431no—
498C42—861no—
499C42—861no—
500C42C23×D4311yescharacteristic
501C23—431no—
502C23—861no—
503C23—861no—
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8#1306333112yes—
508D4—861no—
509D4—861no—
510D4—861no—
511D4—861no—
512D4—3441no—
513D4—1722no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—431no—
519C2×C4—431no—
520C2×C4—431no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—3441no—
528C2×C4—1721no—
529C2×C4—1722no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4C22×C4×D4311yescharacteristic
535C2×C4C2×D4×D4311yescharacteristic
536C2×C4#41×D4311yescharacteristic
537C8—22no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—432no—
544C8—861no—
545C8—861no—
546C8—861no—
547C8—1721no—
548C8—1721no—
549C8—1721no—
550C8#1306334812yes—
551C22—861no—
552C22—861no—
553C22—861no—
554C22—1721no—
555C22—1721no—
556C22—1721no—
557C22—1721no—
558C22—1721no—
559C22—1721no—
560C22C4×D4×D4311yescharacteristic
561C4—21no—
562C4—22no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—861no—
567C4—861no—
568C4—861no—
569C4—1721no—
570C4—1721no—
571C4C2×#1306333111yescharacteristic
572C4#1458366411yescharacteristic
573C4#135×D4311yescharacteristic
574C4C2×#1306334811yescharacteristic
575C2—3441no—
576C2—3441no—
577C2—1721no—
578C2#1914331511yescharacteristic
579C2C4×#1306334811yescharacteristic
580C2#1914350011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC8×Q16×C43C2
socleC22×C43C2×C4×D4
prime radical#14583047C4
cosocleC42×C43C24
hypercenterC8×Q16D43
hypocenterC43#17999
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×Q16

Complements

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

NH ≅ G/Ntype
2. #19143614C2semidirect
3. #19143598C2semidirect
4. #19133482C2semidirect
5. #19133481C2semidirect
6. #19133446C2semidirect
7. #19133438C2semidirect
8. #19133438C2semidirect
9. #19133423C2semidirect
10. #19133392C2semidirect
11. #19133374C2semidirect
12. #19133054C2semidirect
13. #19132976C2semidirect
14. C8×#10621872C2semidirect
15. C8×Q16×C43C2semidirect
294. C8×Q16D43semidirect
357. C43#17999semidirect

Maximal subgroups

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

subgroupindex
#191446192
#191436142
#191435982
#191334822
#191334812
#191334462
#191334382
#191334232
#191333922
#191333742
#191330542
#191329762
C8×#106218722
C8×Q16×C432
#1799943