Finite Group Databasebeta

← #25253253

Subgroups — #25253253

Order 11008.

718 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583330C211yesmaximal, characteristic, complemented
2C22×#13063266C211yesmaximal, characteristic, complemented
3#19146280C211yesmaximal, characteristic, complemented
4#19146277C211yesmaximal, characteristic, complemented
5#19136855C211yesmaximal, characteristic, complemented
6#19136684C211yesmaximal, characteristic, complemented
7#19136680C211yesmaximal, characteristic, complemented
8#19136652C211yesmaximal, characteristic, complemented
9#19136649C211yesmaximal, characteristic, complemented
10#19136526C211yesmaximal, characteristic, complemented
11#19136519C211yesmaximal, characteristic, complemented
12#19136517C211yesmaximal, characteristic, complemented
13#19136439C211yesmaximal, characteristic, complemented
14(C22⋊D43)⋊C16C211yesmaximal, characteristic, complemented
15C43×#2187C211yesmaximal, characteristic, complemented
16C2×#13063348C2211yescharacteristic, complemented
17C2×#13063344C2211yescharacteristic, complemented
18C22×D344C2211yescharacteristic
19#14583543—21no—
20#14583540—21no—
21#14583330—24no—
22C2×#13063271C2211yescharacteristic, complemented
23C2×#13063270C2211yescharacteristic, complemented
24C2×#13063270C2211yescharacteristic, complemented
25C2×#13063266—24no—
26C2×#13063266C2211yescharacteristic
27C2×#13063266C2211yescharacteristic
28C2×#13063266C2211yescharacteristic
29C2×#13063266C2211yescharacteristic
30C22×C43⋊C16C2211yescharacteristic
31C2×C16×D43C2211yescharacteristic, complemented
32#14583284C2211yescharacteristic, complemented
33#14583282C2211yescharacteristic, complemented
34#14583140C2211yescharacteristic
35#14583136C2211yescharacteristic, complemented
36#14583132C2211yescharacteristic, complemented
37#14583117—21no—
38#14583112—21no—
39#14583050—21no—
40#14583049—21no—
41#14583047—21no—
42#14583041—21no—
43D8×Dic43C2211yescharacteristic, complemented
44#14582981C2211yescharacteristic, complemented
45C8×C22⋊D43C2211yescharacteristic
46#14582724C2211yescharacteristic, complemented
47Dic43⋊C16C2211yescharacteristic, complemented
48#14582703C2211yescharacteristic, complemented
49#14582702C2211yescharacteristic, complemented
50#14582701C2211yescharacteristic, complemented
51#14582701C2211yescharacteristic, complemented
52(C2×D43)⋊C16C2211yescharacteristic, complemented
53C16×Dic43C2211yescharacteristic, complemented
54C22×D8×C43C2211yescharacteristic
55C2×SD32×C43C2211yescharacteristic, complemented
56C2×SD32×C43C2211yescharacteristic, complemented
57C43×#467C2211yescharacteristic
58C43×#357C2211yescharacteristic, complemented
59C43×#357C2211yescharacteristic, complemented
60C43×C22⋊C16C2211yescharacteristic
61C2×#10621902—21no—
62C2×#10621900—21no—
63C22×D172—21no—
64#13063348—22no—
65#13063348—41no—
66#13063344—22no—
67#13063344—41no—
68C2×Dic172C2311yescharacteristic
69C2×#10621883—21no—
70C2×#10621883—21no—
71C2×#10621884—21no—
72C2×#10621884—21no—
73C2×D344—22no—
74C2×D344—21no—
75C2×D344—41no—
76C2×D344C2311yescharacteristic
77C2×D344C2311yescharacteristic
78C2×C8×D43C2311yescharacteristic
79#13063314—21no—
80#13063312—21no—
81#13063310—41no—
82#13063306—41no—
83#13063304—21no—
84#13063300—21no—
85#13063300—41no—
86#13063297—41no—
87#13063296—21no—
88#13063295—41no—
89#13063294—41no—
90D4×Dic43—21no—
91#13063287—21no—
92C4×C22⋊D43D411yescharacteristic
93C2×C22⋊Dic43—41no—
94C22⋊C4×D43—41no—
95#13063271—22no—
96#13063270—22no—
97#13063270—41no—
98#13063266—22no—
99#13063266—22no—
100#13063266—22no—
101#13063266D414yescomplemented
102C2×C43⋊C16—22no—
103C2×C43⋊C16C2311yescharacteristic
104C2×C43⋊C16C2311yescharacteristic
105C16×D43—22no—
106#13063259C2311yescharacteristic
107Dic43⋊C8D411yescharacteristic
108#13063250—21no—
109#13063246—21no—
110#13063246—21no—
111#13063245—21no—
112#13063245—21no—
113C22⋊(C43⋊C8)D411yescharacteristic
114(C2×D43)⋊C8D411yescharacteristic
115C8×Dic43C2311yescharacteristic
116C22×D4×C43—21no—
117C2×Q16×C43C2311yescharacteristic
118C2×D8×C43—22no—
119C2×D8×C43—21no—
120C2×D8×C43—41no—
121C2×D8×C43C2311yescharacteristic
122C2×D8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C22⋊Q8×C43—21no—
125SD32×C43—22no—
126SD32×C43—41no—
127C2×C16×C43C2311yescharacteristic
128C2×C16×C43C2311yescharacteristic
129#107×C43C2311yescharacteristic
130#103×C43—21no—
131C24×C43—41no—
132C23×D43—41no—
133C2×Q8×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—41no—
137C2×D4×C43—42no—
138C2×D4×C43—81no—
139C22×C4×C43C2×D411yescharacteristic
140C2×C22⋊D43—41no—
141C2×C22⋊D43—41no—
142C2×C22⋊D43D811yescharacteristic
143C22×Dic43—41no—
144C22×Dic43—41no—
145#10621902—42no—
146#10621902—81no—
147#10621900—42no—
148#10621900—81no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—41no—
152C2×D172—41no—
153C2×D172—41no—
154C2×D172—42no—
155C2×D172—81no—
156C2×C4×D43—41no—
157C2×C4×D43—41no—
158C2×C4×D43C2×D411yescharacteristic
159C2×Dic86—21no—
160Q16×C43—21no—
161Q16×C43—21no—
162D8×C43—21no—
163D8×C43—21no—
164D8×C43—21no—
165D8×C43—42no—
166D8×C43C2×D412yes—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2411yescharacteristic
171C4⋊C4×C43—21no—
172C4⋊C4×C43—41no—
173C22⋊C4×C43—41no—
174C22⋊Dic43—41no—
175C22⋊Dic43—41no—
176C22⋊Dic43—41no—
177C22⋊Dic43—41no—
178C22⋊Dic43—41no—
179C22⋊Dic43D811yescharacteristic
180#10621884—42no—
181#10621884—81no—
182#10621883—42no—
183#10621883—81no—
184(C2×D43)⋊C4—41no—
185(C2×D43)⋊C4—41no—
186(C2×D43)⋊C4—41no—
187(C2×D43)⋊C4—41no—
188(C2×D43)⋊C4D811yescharacteristic
189C4⋊Dic43—21no—
190Dic43⋊C4—41no—
191Dic43⋊C4D811yescharacteristic
192C4×Dic43C2×D411yescharacteristic
193C2×C43⋊C8C2×D411yescharacteristic
194C2×C43⋊C8C2×D411yescharacteristic
195Dic172—21no—
196Dic172—21no—
197D344—21no—
198D344—21no—
199D344—21no—
200D344—42no—
201D344C2×D412yes—
202C8×D43—21no—
203C8×D43—21no—
204C16×C43—21no—
205C16×C43—21no—
206C43⋊C16—21no—
207C43⋊C16C2×D412yes—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—82no—
211C23×C43—82no—
212C23×C43—161no—
213C23×C43C2×D811yescharacteristic
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—82no—
217C22×D43—82no—
218C22×D43—161no—
219C22×D43C2×D811yescharacteristic
220Q8×C43—41no—
221Q8×C43—41no—
222D4×C43—22no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226D4×C43—82no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43C2×D811yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C22⋊D43—22no—
234C22⋊D43—82no—
235C22⋊D43—161no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—82no—
239C2×Dic43—161no—
240C2×Dic43C2×D811yescharacteristic
241C2×Dic43C2×D811yescharacteristic
242C2×Dic43C2×D811yescharacteristic
243D172—22no—
244D172—41no—
245D172—41no—
246D172—41no—
247D172—82no—
248D172—82no—
249D172—161no—
250C4×D43—21no—
251C4×D43—21no—
252C4×D43—82no—
253C4×D43—161no—
254Dic86—41no—
255Dic86—41no—
256C8×C43—21no—
257C8×C43C22×D411yescharacteristic
258C8×C43H(5,𝔽2)11yescharacteristic
259C43⋊C8—21no—
260C43⋊C8—21no—
261#33846—431nomaximal, Sylow
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—42no—
265C22×C43—81no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43—164no—
271C22×C43#50812yescomplemented
272C22×C43C22×D811yescharacteristic
273C2×D43—21no—
274C2×D43—21no—
275C2×D43—21no—
276C2×D43—42no—
277C2×D43—81no—
278C2×D43—81no—
279C2×D43—81no—
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—164no—
283C4×C43—21no—
284C4×C43—81no—
285C4×C43—81no—
286C4×C43D4211yescharacteristic
287C4×C43#57611yescharacteristic
288Dic43—21no—
289Dic43—21no—
290Dic43—21no—
291Dic43—81no—
292Dic43—81no—
293C2×#508—431no—
294C22×D16—431no—
295#3280—431no—
296#3280—431no—
297#2249—431no—
298#2216—431no—
299#2215—431no—
300#2210—431no—
301#2210—431no—
302#2187—431no—
303#2187D4311yescharacteristic, complemented
304#2186—431no—
305#2186—431no—
306C4×D16—431no—
307D4×C16—431no—
308C2×C43—22no—
309C2×C43—82no—
310C2×C43—161no—
311C2×C43D4×D811yescharacteristic
312C2×C43C2×#50811yescharacteristic
313C2×C43#341511yescharacteristic
314D43—41no—
315D43—82no—
316D43—161no—
317C2×#135—431no—
318C2×#135—431no—
319C22×D8—431no—
320C22×D8C2×D4311yescharacteristic
321#546—861no—
322#546—861no—
323#508—864no—
324C2×Q32—431no—
325C2×SD32—431no—
326C2×SD32—431no—
327C2×SD32C2×D4311yescharacteristic, complemented
328C2×SD32C2×D4311yescharacteristic, complemented
329C2×D16—431no—
330C2×D16—431no—
331C2×D16—431no—
332C2×D16—431no—
333C2×D16—864no—
334C22×C16—431no—
335C22×C16—431no—
336#495—431no—
337#495—431no—
338#467—431no—
339#467C2×D4311yescharacteristic
340#466—431no—
341#466—431no—
342#463—861no—
343#463—861no—
344#450—861no—
345#450—861no—
346#449—861no—
347#449—861no—
348C4×D8—431no—
349C4×D8—431no—
350C8×D4—431no—
351#366—431no—
352C4⋊C16—431no—
353#358—431no—
354#358—431no—
355#357—431no—
356#357—431no—
357#357C2×D4311yescharacteristic, complemented
358#357C2×D4311yescharacteristic, complemented
359C22⋊C16—431no—
360C22⋊C16C2×D4311yescharacteristic
361C4×C16—431no—
362C43#3384611yescharacteristic, complemented, Sylow
363C2×#41—861no—
364C2×#41—861no—
365C22×D4—21no—
366C22×D4—861no—
367#135—862no—
368#135—862no—
369#135—1721no—
370#135—1721no—
371C2×Q16—431no—
372C2×Q16C22×D4311yescharacteristic
373C2×SD16—861no—
374C2×SD16—861no—
375C2×SD16—861no—
376C2×SD16—861no—
377C2×D8—22no—
378C2×D8—21no—
379C2×D8—41no—
380C2×D8—431no—
381C2×D8—431no—
382C2×D8—862no—
383C2×D8—861no—
384C2×D8—1721no—
385C2×D8C22×D4311yescharacteristic
386C2×D8C22×D4311yescharacteristic
387C22×C8—431no—
388C22×C8C22×D4311yescharacteristic
389#124—861no—
390#124—861no—
391#123—1721no—
392#123—1721no—
393C22⋊Q8—21no—
394C22⋊Q8—861no—
395#121—861no—
396#121—861no—
397#121—1721no—
398#121—1721no—
399#120—1721no—
400#120—1721no—
401C4×D4—431no—
402C4×D4—861no—
403C4×D4—861no—
404C2×C22⋊C4—1721no—
405C2×C22⋊C4—1721no—
406Q32—862no—
407SD32—22no—
408SD32—41no—
409SD32—862no—
410SD32—1721no—
411D16—434no—
412D16—862no—
413D16—862no—
414D16—862no—
415C2×C16—431no—
416C2×C16—431no—
417C2×C16—862no—
418C2×C16—862no—
419C2×C16C22×D4311yescharacteristic
420C2×C16C22×D4311yescharacteristic
421#107—431no—
422#107C22×D4311yescharacteristic
423C4⋊C8—431no—
424#103—21no—
425#103—861no—
426#102—861no—
427#102—861no—
428#102—861no—
429#102—861no—
430C22⋊C8—431no—
431C22⋊C8—431no—
432C4×C8—431no—
433C24—41no—
434C24—1721no—
435#41—3441no—
436#41—3441no—
437#41—1722no—
438#41—1722no—
439C2×Q8—21no—
440C2×Q8—861no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—42no—
444C2×D4—41no—
445C2×D4—81no—
446C2×D4—431no—
447C2×D4—861no—
448C2×D4—861no—
449C2×D4—3441no—
450C2×D4—1722no—
451C2×D4—1721no—
452C2×D4—1721no—
453C2×D4—1721no—
454C2×D4—1721no—
455C2×D4—1721no—
456C22×C4—431no—
457C22×C4—1721no—
458C22×C4—1721no—
459C22×C4—1721no—
460C22×C4—1721no—
461C22×C4D4×D4311yescharacteristic
462Q16—21no—
463Q16—21no—
464Q16—861no—
465Q16—861no—
466SD16—3441no—
467SD16—3441no—
468SD16—1722no—
469SD16—1722no—
470D8—21no—
471D8—21no—
472D8—21no—
473D8—42no—
474D8—432no—
475D8—861no—
476D8—861no—
477D8—861no—
478D8—1722no—
479D8D4×D4312yes—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—431no—
483C2×C8—431no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8D4×D4311yescharacteristic
487C2×C8C23×D4311yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—431no—
491C4⋊C4—861no—
492C4⋊C4—1721no—
493C22⋊C4—41no—
494C22⋊C4—431no—
495C22⋊C4—431no—
496C22⋊C4—1721no—
497C22⋊C4—1721no—
498C22⋊C4—1721no—
499C22⋊C4—1721no—
500C22⋊C4—1721no—
501C22⋊C4—1721no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C22⋊C4—1721no—
505C42—431no—
506C16—21no—
507C16—21no—
508C16—432no—
509C16—861no—
510C23—41no—
511C23—41no—
512C23—82no—
513C23—82no—
514C23—161no—
515C23—431no—
516C23—3442no—
517C23—3442no—
518C23—1721no—
519C23—1721no—
520C23—6881no—
521C23D8×D4311yescharacteristic
522Q8—41no—
523Q8—41no—
524Q8—1721no—
525Q8—1721no—
526D4—22no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—82no—
531D4—862no—
532D4—862no—
533D4—3442no—
534D4—3442no—
535D4—3442no—
536D4—1721no—
537D4—1721no—
538D4—1721no—
539D4—6881no—
540D4—6881no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—431no—
546C2×C4—431no—
547C2×C4—431no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—3442no—
551C2×C4—3442no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—6881no—
555C2×C4—6881no—
556C2×C4D8×D4311yescharacteristic
557C2×C4C2×D4×D4311yescharacteristic
558C8—21no—
559C8—861no—
560C8—861no—
561C8C2×D4×D4311yescharacteristic
562C8#1306337011yescharacteristic
563C22—21no—
564C22—21no—
565C22—42no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—164no—
572C22—861no—
573C22—861no—
574C22—861no—
575C22—3441no—
576C22—3441no—
577C22—3441no—
578C22—3441no—
579C22—3441no—
580C22—1722no—
581C22—6884no—
582C22#1458333012yescomplemented
583C22C2×D8×D4311yescharacteristic
584C4—21no—
585C4—81no—
586C4—81no—
587C4—861no—
588C4—861no—
589C4—861no—
590C4—3441no—
591C4—3441no—
592C4#1458353111yescharacteristic
593C4#1458370311yescharacteristic
594C2—22no—
595C2—82no—
596C2—161no—
597C2—3442no—
598C2—1721no—
599C2—6881no—
600C2#1914626511yescharacteristic
601C2C2×#1458333011yescharacteristic
602C2#1914773511yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2187C2
socleC22×C43C22×D8
hypercenter#2187D43
hypocenterC43#33846
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2187

Complements

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

NH ≅ G/Ntype
1. C2×#14583330C2semidirect
2. C22×#13063266C2semidirect
3. #19146280C2semidirect
4. #19146277C2semidirect
5. #19136855C2semidirect
6. #19136684C2semidirect
7. #19136680C2semidirect
8. #19136652C2semidirect
9. #19136649C2semidirect
10. #19136526C2semidirect
11. #19136519C2semidirect
12. #19136517C2semidirect
13. #19136439C2semidirect
14. (C22⋊D43)⋊C16C2semidirect
15. C43×#2187C2semidirect
16. C2×#13063348C22semidirect
17. C2×#13063344C22semidirect
22. C2×#13063271C22semidirect
23. C2×#13063270C22semidirect
24. C2×#13063270C22semidirect
31. C2×C16×D43C22semidirect
32. #14583284C22semidirect
33. #14583282C22semidirect
35. #14583136C22semidirect
36. #14583132C22semidirect
43. D8×Dic43C22semidirect
44. #14582981C22semidirect
46. #14582724C22semidirect
47. Dic43⋊C16C22semidirect
48. #14582703C22semidirect
49. #14582702C22semidirect
50. #14582701C22semidirect
51. #14582701C22semidirect
52. (C2×D43)⋊C16C22semidirect
53. C16×Dic43C22semidirect
55. C2×SD32×C43C22semidirect
56. C2×SD32×C43C22semidirect
58. C43×#357C22semidirect
59. C43×#357C22semidirect
101. #13063266D4semidirect
271. C22×C43#508semidirect
303. #2187D43semidirect
327. C2×SD32C2×D43semidirect
328. C2×SD32C2×D43semidirect
357. #357C2×D43semidirect
358. #357C2×D43semidirect
362. C43#33846semidirect
582. C22#14583330semidirect

Maximal subgroups

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

subgroupindex
C2×#145833302
C22×#130632662
#191462802
#191462772
#191368552
#191366842
#191366802
#191366522
#191366492
#191365262
#191365192
#191365172
#191364392
(C22⋊D43)⋊C162
C43×#21872
#3384643