Finite Group Databasebeta

← #25066312

Subgroups — #25066312

Order 11008.

660 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143711C211yesmaximal, characteristic, complemented
2#19143705C211yesmaximal, characteristic, complemented
3C4×#13063348C211yesmaximal, characteristic
4#19133467C211yesmaximal, characteristic, complemented
5#19133461C211yesmaximal, characteristic, complemented
6#19133458C211yesmaximal, characteristic, complemented
7#19133438C211yesmaximal, characteristic, complemented
8#19133435C211yesmaximal, characteristic, complemented
9#19133434C211yesmaximal, characteristic, complemented
10#19133429C211yesmaximal, characteristic, complemented
11#334×D43C211yesmaximal, characteristic, complemented
12#19132981C211yesmaximal, characteristic, complemented
13#19132981C211yesmaximal, characteristic, complemented
14#19132886C211yesmaximal, characteristic, complemented
15C43×#1587C211yesmaximal, characteristic, complemented
16C2×#13063348C411yescharacteristic
17C4×#10621902C2211yescharacteristic
18C4×#10621902C2211yescharacteristic
19#14583030C2211yescharacteristic
20Q8×C43⋊C8C2211yescharacteristic
21Q16×Dic43C411yescharacteristic
22C4×#10621884C2211yescharacteristic
23C4×#10621884C2211yescharacteristic
24#14582984C411yescharacteristic
25#14582984C411yescharacteristic
26C4×D344C2211yescharacteristic
27#14582981C411yescharacteristic
28#14582978C2211yescharacteristic
29#14582976C2211yescharacteristic
30#14582972—21no—
31#14582969—21no—
32C8×D172—21no—
33C8×D172C2211yescharacteristic
34#14582964—21no—
35#14582964C2211yescharacteristic
36#14582954—21no—
37#14582950—21no—
38#14582950C2211yescharacteristic
39#14582950C2211yescharacteristic
40#14582936C411yescharacteristic
41#14582921—21no—
42C4⋊C8×D43—21no—
43C4⋊C8×D43C2211yescharacteristic
44C4⋊C8×D43C2211yescharacteristic
45#14582894C411yescharacteristic
46#14582894C411yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582650C2211yescharacteristic
49#14582649C2211yescharacteristic
50#14582649C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582628C2211yescharacteristic
54#14582628C2211yescharacteristic
55#14582626C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582621C2211yescharacteristic
59#14582620C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C8×Q8×C43C2211yescharacteristic
62C4×Q16×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#10621902C2×C411yescharacteristic
68C2×#10621902C2×C411yescharacteristic
69#13063348—24no—
70C2×#10621884C2×C411yescharacteristic
71C2×#10621884C2×C411yescharacteristic
72C2×D344C2×C411yescharacteristic
73C2×#10621872—21no—
74C2×#10621872—21no—
75C2×C8×D43—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79C2×C8×D43C2×C411yescharacteristic
80C2×C8×D43C2×C411yescharacteristic
81Q8×Dic43C2×C411yescharacteristic
82Q8×Dic43C2×C411yescharacteristic
83C4×D172—21no—
84C4×D172—21no—
85C4×D172C2311yescharacteristic
86C4×D172C2311yescharacteristic
87#13063287—21no—
88#13063287—21no—
89#13063287C2×C411yescharacteristic
90#13063287C2×C411yescharacteristic
91#13063283—21no—
92#13063283—21no—
93#13063283C2×C411yescharacteristic
94#13063283C2×C411yescharacteristic
95C42×D43—21no—
96C42×D43—21no—
97C42×D43C2311yescharacteristic
98#13063259C2×C411yescharacteristic
99#13063256C2×C411yescharacteristic
100#13063256C2×C411yescharacteristic
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8D411yescharacteristic
109Dic43⋊C8D411yescharacteristic
110#13063249C2×C411yescharacteristic
111#13063249C2×C411yescharacteristic
112#13063247C2×C411yescharacteristic
113#13063247C2×C411yescharacteristic
114#13063245C2×C411yescharacteristic
115#13063245C2×C411yescharacteristic
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8D411yescharacteristic
122(C2×D43)⋊C8D411yescharacteristic
123#13063236—21no—
124C4×C43⋊C8—21no—
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43C2×C411yescharacteristic
129C8×Dic43C2×C411yescharacteristic
130C2×Q16×C43C2×C411yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132C4×Q8×C43C2311yescharacteristic
133#107×C43C2×C411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43C2×C411yescharacteristic
139#103×C43C2×C411yescharacteristic
140#97×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43C22×C411yescharacteristic
146C2×Q8×C43C22×C411yescharacteristic
147#10621902—22no—
148#10621902—22no—
149#10621902—22no—
150#10621902M1614yescomplemented
151C2×D172—21no—
152C2×D172—21no—
153C2×D172C22×C411yescharacteristic
154C2×D172C22×C411yescharacteristic
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43C22×C411yescharacteristic
162C2×C4×D43C2×D411yescharacteristic
163C2×C4×D43#4111yescharacteristic
164Q16×C43—22no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43C22×C411yescharacteristic
169C2×C8×C43C22×C411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43C22×C411yescharacteristic
175C4⋊C4×C43C22×C411yescharacteristic
176C42×C43—21no—
177C42×C43—21no—
178C42×C43C2411yescharacteristic
179#10621884—22no—
180#10621884—22no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43C22×C411yescharacteristic
190C4⋊Dic43C22×C411yescharacteristic
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43C22×C411yescharacteristic
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43#4111yescharacteristic
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205D344—22no—
206#10621872—81no—
207#10621872—81no—
208C8×D43—22no—
209C8×D43—22no—
210C8×D43—81no—
211C8×D43—81no—
212C8×D43—81no—
213C8×D43—81no—
214C22×D43—21no—
215C22×D43—21no—
216C22×D43C4×D411yescharacteristic
217Q8×C43—21no—
218Q8×C43—21no—
219Q8×C43—21no—
220Q8×C43C2×M1612yes—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43C23×C411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43C4×D411yescharacteristic
231C2×Dic43C4×D411yescharacteristic
232C2×Dic43C4×D411yescharacteristic
233D172—24no—
234D172—21no—
235D172—21no—
236D172—21no—
237D172—42no—
238D172C2×M1612yes—
239C4×D43—21no—
240C4×D43—21no—
241C4×D43—24no—
242C4×D43—41no—
243C4×D43—41no—
244C4×D43—41no—
245C4×D43—41no—
246C4×D43—41no—
247C4×D43—42no—
248C4×D43—81no—
249C4×D43—81no—
250C4×D43C2×M1612yes—
251C4×D43#13112yes—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43—41no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266#17882—431nomaximal, Sylow
267C22×C43C2×C4×D411yescharacteristic
268C2×D43—21no—
269C2×D43—21no—
270C2×D43—22no—
271C2×D43—41no—
272C2×D43—41no—
273C2×D43—41no—
274C2×D43—41no—
275C2×D43—41no—
276C2×D43#43512yes—
277C4×C43—22no—
278C4×C43—21no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43C22×M1611yescharacteristic
283C4×C43C2×#13111yescharacteristic
284C4×C43#57711yescharacteristic
285C4×C43#57711yescharacteristic
286Dic43—21no—
287Dic43—21no—
288Dic43—41no—
289Dic43—41no—
290Dic43#43512yes—
291#2989—431no—
292#2988—431no—
293C4×#135—431no—
294#1587—431no—
295#1587D4311yescharacteristic, complemented
296#1586—431no—
297#1586—431no—
298#1583—431no—
299#1583—431no—
300#1582—431no—
301#1582—431no—
302C2×#334—431no—
303#1477—431no—
304#1477—431no—
305#1452—431no—
306C2×C43C2×#43511yescharacteristic
307C2×C43#295211yescharacteristic
308C2×C43#295711yescharacteristic
309D43—22no—
310D43—42no—
311D43—81no—
312C2×#135—431no—
313C4×#41—431no—
314C4×#41—431no—
315#446—431no—
316#446C2×D4311yescharacteristic
317C8×Q8—431no—
318C8×Q8C2×D4311yescharacteristic
319C4×Q16—431no—
320C4×Q16C2×D4311yescharacteristic
321C4×SD16—431no—
322C4×SD16—431no—
323C4×SD16—431no—
324C4×SD16—431no—
325C4×D8—431no—
326C4×D8—431no—
327#436—431no—
328#436—431no—
329#435—861no—
330#435—861no—
331C8×D4—431no—
332C8×D4—431no—
333C8×D4—861no—
334C8×D4—861no—
335#432—861no—
336#431—431no—
337#431—431no—
338#431—861no—
339#427—431no—
340#423—861no—
341C2×C4⋊C8—431no—
342C2×C4⋊C8—431no—
343C2×C4⋊C8—861no—
344#416—431no—
345#416—431no—
346C2×C4×C8—431no—
347#334—431no—
348#334—431no—
349#334—431no—
350#334C2×D4311yescharacteristic
351Q8⋊C8—431no—
352Q8⋊C8—431no—
353Q8⋊C8C2×D4311yescharacteristic
354Q8⋊C8C2×D4311yescharacteristic
355D4⋊C8—431no—
356D4⋊C8—431no—
357D4⋊C8—431no—
358D4⋊C8—431no—
359#322—431no—
360#322—431no—
361#322—431no—
362#322C2×D4311yescharacteristic
363C43#1788211yescharacteristic, complemented, Sylow
364C2×#41—431no—
365C2×#41—431no—
366#135—864no—
367C2×Q16C4×D4311yescharacteristic
368C2×SD16—431no—
369C2×SD16—431no—
370C2×D8—431no—
371C2×M16—861no—
372C2×M16—861no—
373C22×C8—431no—
374C22×C8—431no—
375C22×C8—861no—
376C22×C8—861no—
377C22×C8—861no—
378C22×C8—861no—
379C4×Q8—431no—
380C4×Q8—431no—
381C4×Q8C22×D4311yescharacteristic
382C4×Q8C22×D4311yescharacteristic
383C4×D4—431no—
384C4×D4—431no—
385C4×D4—431no—
386C4×D4—431no—
387C4×D4—861no—
388C4×D4—861no—
389C4×D4—861no—
390C4×D4—861no—
391#117—431no—
392#117—431no—
393#117—861no—
394#117—861no—
395C2×C42—431no—
396C2×C42—861no—
397C2×C42—861no—
398#107—431no—
399#107C4×D4311yescharacteristic
400#106—431no—
401#106—431no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8—861no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412C4⋊C8—861no—
413C4⋊C8C22×D4311yescharacteristic
414C4⋊C8C22×D4311yescharacteristic
415#103—431no—
416#103—431no—
417#103C4×D4311yescharacteristic
418#103C4×D4311yescharacteristic
419#102—431no—
420#102—431no—
421#102—431no—
422#102—431no—
423C22⋊C8—431no—
424C22⋊C8—431no—
425C22⋊C8—861no—
426C22⋊C8—861no—
427C22⋊C8—861no—
428C22⋊C8—861no—
429C22⋊C8—861no—
430#97—21no—
431#97—861no—
432C4×C8—21no—
433C4×C8—431no—
434C4×C8—431no—
435C4×C8—431no—
436C4×C8—431no—
437C4×C8—431no—
438C4×C8—861no—
439C4×C8C22×D4311yescharacteristic
440C4×C8C22×D4311yescharacteristic
441C4×C8C22×D4311yescharacteristic
442#41—434no—
443#41—862no—
444#41—862no—
445#41—862no—
446C2×Q8C2×C4×D4311yescharacteristic
447C2×Q8C2×C4×D4311yescharacteristic
448C2×D4—431no—
449C2×D4—431no—
450C2×D4—861no—
451C2×D4—861no—
452C22×C4—431no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461Q16—22no—
462SD16—862no—
463SD16—862no—
464D8—862no—
465M16—3441no—
466M16—3441no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—431no—
471C2×C8—431no—
472C2×C8—431no—
473C2×C8—431no—
474C2×C8—862no—
475C2×C8—862no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—3441no—
480C2×C8—3441no—
481C2×C8—3441no—
482C2×C8—3441no—
483C2×C8C2×C4×D4311yescharacteristic
484C2×C8C2×C4×D4311yescharacteristic
485C2×C8D4×D4311yescharacteristic
486C2×C8D4×D4311yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—431no—
490C4⋊C4—431no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4C2×C4×D4311yescharacteristic
494C4⋊C4C2×C4×D4311yescharacteristic
495C22⋊C4—861no—
496C22⋊C4—861no—
497C22⋊C4—861no—
498C22⋊C4—861no—
499C22⋊C4—861no—
500C22⋊C4—861no—
501C42—21no—
502C42—21no—
503C42—431no—
504C42—431no—
505C42—431no—
506C42—861no—
507C42—861no—
508C42—861no—
509C42—861no—
510C42C23×D4311yescharacteristic
511C23—431no—
512C23—861no—
513C23—861no—
514Q8—21no—
515Q8—21no—
516Q8—21no—
517Q8M16×D4312yes—
518D4—432no—
519D4—864no—
520D4—861no—
521D4—861no—
522D4—861no—
523D4—1722no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—431no—
529C2×C4—432no—
530C2×C4—432no—
531C2×C4—431no—
532C2×C4—431no—
533C2×C4—864no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—3441no—
539C2×C4—3441no—
540C2×C4—1721no—
541C2×C4—1722no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4C22×C4×D4311yescharacteristic
547C2×C4C2×D4×D4311yescharacteristic
548C2×C4#41×D4311yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—861no—
557C8—861no—
558C8—861no—
559C8—861no—
560C8—1721no—
561C8—1721no—
562C8—1721no—
563C22—432no—
564C22—861no—
565C22—861no—
566C22—862no—
567C22—1721no—
568C22—1721no—
569C22—1721no—
570C22—1721no—
571C22—1721no—
572C22C4×D4×D4311yescharacteristic
573C4—21no—
574C4—22no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—432no—
579C4—861no—
580C4—861no—
581C4—1721no—
582C4—1721no—
583C4C2×M16×D4311yescharacteristic
584C4#131×D4311yescharacteristic
585C4#1458370811yescharacteristic
586C4#1458370811yescharacteristic
587C2—862no—
588C2—3441no—
589C2—1722no—
590C2#435×D4311yescharacteristic
591C2#1914347511yescharacteristic
592C2#1914350711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1587C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063348C4
cosocleC42×C43C24
hypercenter#1587D43
hypocenterC43#17882
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
1. #19143711C2semidirect
2. #19143705C2semidirect
4. #19133467C2semidirect
5. #19133461C2semidirect
6. #19133458C2semidirect
7. #19133438C2semidirect
8. #19133435C2semidirect
9. #19133434C2semidirect
10. #19133429C2semidirect
11. #334×D43C2semidirect
12. #19132981C2semidirect
13. #19132981C2semidirect
14. #19132886C2semidirect
15. C43×#1587C2semidirect
150. #10621902M16semidirect
295. #1587D43semidirect
363. C43#17882semidirect

Maximal subgroups

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

subgroupindex
#191437112
#191437052
C4×#130633482
#191334672
#191334612
#191334582
#191334382
#191334352
#191334342
#191334292
#334×D432
#191329812
#191328862
C43×#15872
#1788243