Finite Group Databasebeta

← #25253564

Subgroups — #25253564

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146940C211yesmaximal, characteristic, complemented
2#19146280C211yesmaximal, characteristic, complemented
3#19136830C211yesmaximal, characteristic, complemented
4#19136792C211yesmaximal, characteristic, complemented
5#19136779C211yesmaximal, characteristic, complemented
6#19136740C211yesmaximal, characteristic, complemented
7#19136697C211yesmaximal, characteristic, complemented
8#19136691C211yesmaximal, characteristic, complemented
9#19136649C211yesmaximal, characteristic, complemented
10#19136519C211yesmaximal, characteristic, complemented
11#19136507C211yesmaximal, characteristic, complemented
12#19136468C211yesmaximal, characteristic, complemented
13#19136420C211yesmaximal, characteristic, complemented
14#19136304C211yesmaximal, characteristic, complemented
15C2×C43×#357C211yesmaximal, characteristic, complemented
16C2×#13063344C2211yescharacteristic
17#14583550—21no—
18#14583543—21no—
19C2×#13063270C2211yescharacteristic, complemented
20C2×#13063266C2211yescharacteristic
21C2×#13063266C2211yescharacteristic
22C2×#13063264C2211yescharacteristic, complemented
23#14583303C2211yescharacteristic, complemented
24#14583282C2211yescharacteristic
25#14583214—21no—
26#14583212—21no—
27#14583178—21no—
28#14583140C2211yescharacteristic
29#14583136C2211yescharacteristic, complemented
30#14583135C2211yescharacteristic
31#14583132C2211yescharacteristic
32#14583112—21no—
33#14583050—21no—
34#14583041—21no—
35D8×Dic43C2211yescharacteristic
36#14582981C2211yescharacteristic, complemented
37C8×C22⋊D43C2211yescharacteristic
38#107×D43C2211yescharacteristic, complemented
39#14582727C2211yescharacteristic, complemented
40#14582726C2211yescharacteristic, complemented
41#14582726C2211yescharacteristic, complemented
42Dic43⋊C16C2211yescharacteristic, complemented
43#14582704C2211yescharacteristic, complemented
44#14582702C2211yescharacteristic, complemented
45#14582702C2211yescharacteristic, complemented
46#14582701C2211yescharacteristic, complemented
47#14582700C2211yescharacteristic
48#14582700C2211yescharacteristic
49C22⋊(C43⋊C16)C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic, complemented
51#14582674C2211yescharacteristic, complemented
52C22×D8×C43C2211yescharacteristic
53C22×C16×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C43×#357C2211yescharacteristic
56C43×#357C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C2×#10621898—41no—
60C2×#10621900—21no—
61#13063344—22no—
62#13063344—41no—
63C2×Dic172C2311yescharacteristic
64C2×#10621883—21no—
65C2×#10621883—21no—
66C2×D344C2311yescharacteristic
67C2×C8×D43C2311yescharacteristic
68#13063324—21no—
69#13063312—21no—
70#13063310—41no—
71#13063308—41no—
72#13063306—41no—
73#13063304—21no—
74#13063303—41no—
75#13063300—21no—
76#13063299—21no—
77#13063297—41no—
78#13063296—21no—
79#13063294—41no—
80D4×Dic43—21no—
81#13063287—21no—
82C4×C22⋊D43D411yescharacteristic
83C4⋊C4×D43—21no—
84C2×C22⋊Dic43—41no—
85#13063270—41no—
86#13063266—22no—
87#13063266—41no—
88#13063264—41no—
89C2×C43⋊C16C2311yescharacteristic
90C2×C43⋊C16C2311yescharacteristic
91#13063259C2311yescharacteristic
92#13063259C2311yescharacteristic
93#13063258—21no—
94#13063258—21no—
95Dic43⋊C8D411yescharacteristic
96#13063250—21no—
97#13063247—21no—
98#13063246—21no—
99#13063246—21no—
100#13063245—21no—
101#13063245—21no—
102C22⋊(C43⋊C8)D411yescharacteristic
103(C2×D43)⋊C8D411yescharacteristic
104C8×Dic43C2311yescharacteristic
105C22×D4×C43—21no—
106C2×D8×C43—22no—
107C2×D8×C43—21no—
108C2×D8×C43—41no—
109C2×D8×C43C2311yescharacteristic
110C2×D8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112C2×C4⋊C4×C43—21no—
113C2×C16×C43—41no—
114C2×C16×C43C2311yescharacteristic
115C2×C16×C43C2311yescharacteristic
116#107×C43—21no—
117#107×C43C2311yescharacteristic
118#107×C43C2311yescharacteristic
119C24×C43—41no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—41no—
123C2×D4×C43—42no—
124C2×D4×C43—81no—
125C22×C4×C43—41no—
126C22×C4×C43C2×D411yescharacteristic
127C2×C22⋊D43—41no—
128C2×C22⋊D43—41no—
129C2×C22⋊D43—41no—
130C2×C22⋊D43D811yescharacteristic
131C22×Dic43—41no—
132C22×Dic43—41no—
133#10621900—42no—
134#10621900—81no—
135#10621898—84no—
136C2×D172—21no—
137C2×D172—41no—
138C2×C4×D43—41no—
139C2×C4×D43—41no—
140C2×C4×D43C2×D411yescharacteristic
141C2×Dic86—21no—
142C2×Dic86—41no—
143D8×C43—21no—
144D8×C43—21no—
145D8×C43—21no—
146D8×C43—42no—
147D8×C43#4112yescomplemented
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43C2×D411yescharacteristic
151C2×C8×C43C2411yescharacteristic
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—41no—
155C22⋊Dic43—41no—
156C22⋊Dic43—41no—
157C22⋊Dic43—41no—
158C22⋊Dic43—41no—
159C22⋊Dic43—41no—
160C22⋊Dic43D811yescharacteristic
161#10621883—42no—
162#10621883—81no—
163(C2×D43)⋊C4—41no—
164(C2×D43)⋊C4—41no—
165(C2×D43)⋊C4—41no—
166(C2×D43)⋊C4D811yescharacteristic
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169Dic43⋊C4—41no—
170Dic43⋊C4—41no—
171Dic43⋊C4—41no—
172Dic43⋊C4D811yescharacteristic
173C4×Dic43C2×D411yescharacteristic
174C2×C43⋊C8C2×D411yescharacteristic
175C2×C43⋊C8C2×D411yescharacteristic
176Dic172—21no—
177Dic172—21no—
178D344—21no—
179D344—21no—
180C8×D43—21no—
181C8×D43—21no—
182C16×C43—21no—
183C16×C43—21no—
184C43⋊C16—21no—
185C43⋊C16—21no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—82no—
189C23×C43—82no—
190C23×C43—161no—
191C23×C43C2×D811yescharacteristic
192C22×D43—41no—
193C22×D43C2×D811yescharacteristic
194D4×C43—22no—
195D4×C43—41no—
196D4×C43—41no—
197D4×C43—41no—
198D4×C43—82no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—82no—
204C2×C4×C43C2×D811yescharacteristic
205C2×C4×C43C22×D411yescharacteristic
206C22⋊D43—22no—
207C22⋊D43—82no—
208C22⋊D43—82no—
209C22⋊D43—161no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—82no—
214C2×Dic43—161no—
215C2×Dic43C2×D811yescharacteristic
216C2×Dic43C2×D811yescharacteristic
217C2×Dic43C2×D811yescharacteristic
218D172—41no—
219D172—41no—
220D172—82no—
221C4×D43—21no—
222C4×D43—21no—
223C4×D43—82no—
224C4×D43—82no—
225Dic86—41no—
226Dic86—41no—
227Dic86—82no—
228C8×C43—21no—
229C8×C43C2×#4111yescharacteristic
230C8×C43H(5,𝔽2)11yescharacteristic
231C43⋊C8—21no—
232C43⋊C8—21no—
233#33873—431nomaximal, Sylow
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—42no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43—81no—
240C22×C43—81no—
241C22×C43—81no—
242C22×C43—164no—
243C22×C43#50912yes—
244C22×C43C22×D811yescharacteristic
245C2×D43—21no—
246C2×D43—21no—
247C2×D43—21no—
248C2×D43—81no—
249C2×D43—81no—
250C2×D43—81no—
251C4×C43—21no—
252C4×C43—81no—
253C4×C43—81no—
254C4×C43#54611yescharacteristic
255C4×C43#57711yescharacteristic
256Dic43—21no—
257Dic43—21no—
258Dic43—21no—
259Dic43—81no—
260Dic43—81no—
261Dic43—81no—
262#3334—431no—
263#3280—431no—
264#2243—431no—
265#2235—431no—
266#2233—431no—
267#2226—431no—
268#2218—431no—
269#2217—431no—
270#2210—431no—
271#2186—431no—
272#2184—431no—
273#2177—431no—
274#2168—431no—
275#2139—431no—
276C2×#357D4311yescharacteristic, complemented
277C2×C43—22no—
278C2×C43—82no—
279C2×C43—161no—
280C2×C43#329411yescharacteristic
281C2×C43C2×#50911yescharacteristic
282C2×C43#341611yescharacteristic
283D43—41no—
284D43—161no—
285C2×#135—431no—
286C22×D8C2×D4311yescharacteristic
287#547—861no—
288#546—861no—
289C2×SD32—431no—
290C2×D16—431no—
291C2×D16—431no—
292C2×M32—431no—
293C22×C16C2×D4311yescharacteristic
294#500—431no—
295#495—431no—
296#480—861no—
297#480—861no—
298#474—861no—
299#467—431no—
300#466—431no—
301#466—431no—
302#466—431no—
303#463—861no—
304#450—861no—
305#449—861no—
306C4×D8—431no—
307C4×D8—431no—
308C8×D4—431no—
309C2×#107—431no—
310C2×#107C2×D4311yescharacteristic
311#367—431no—
312#367—431no—
313#367—431no—
314C4⋊C16—431no—
315#358—431no—
316#358—431no—
317#358—431no—
318#357—431no—
319#357—431no—
320#357—431no—
321#357C2×D4311yescharacteristic
322#357C2×D4311yescharacteristic
323#357C2×D4311yescharacteristic
324#357C2×D4311yescharacteristic
325C22⋊C16—431no—
326C22⋊C16—431no—
327#346—431no—
328C43#3387311yescharacteristic, complemented, Sylow
329C2×#41—861no—
330C2×#41—1721no—
331C22×D4—21no—
332#135—862no—
333#135—1721no—
334C2×Q16—431no—
335C2×SD16—861no—
336C2×SD16—861no—
337C2×D8—22no—
338C2×D8—21no—
339C2×D8—41no—
340C2×D8—431no—
341C2×D8C22×D4311yescharacteristic
342C2×D8C22×D4311yescharacteristic
343C22×C8—431no—
344C22×C8C22×D4311yescharacteristic
345C4⋊Q8—861no—
346#124—861no—
347#123—1721no—
348#123—1721no—
349#123—1721no—
350C22⋊Q8—861no—
351C22⋊Q8—1721no—
352#121—861no—
353#121—861no—
354#121—861no—
355#121—1721no—
356#120—1721no—
357C4×D4—431no—
358C4×D4—861no—
359C4×D4—861no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—861no—
362C2×C22⋊C4—1721no—
363SD32—1721no—
364D16—862no—
365D16—1721no—
366M32—1721no—
367C2×C16—41no—
368C2×C16—431no—
369C2×C16—431no—
370C2×C16C22×D4311yescharacteristic
371C2×C16C22×D4311yescharacteristic
372#107—21no—
373#107—431no—
374#107—431no—
375#107—861no—
376#107—861no—
377#107C22×D4311yescharacteristic
378#107C22×D4311yescharacteristic
379C4⋊C8—431no—
380#103—861no—
381#102—861no—
382#102—861no—
383#102—861no—
384#102—861no—
385#102—861no—
386C22⋊C8—431no—
387C22⋊C8—431no—
388C4×C8—431no—
389C24—41no—
390#41—3444no—
391#41—3441no—
392#41—1722no—
393C2×Q8—861no—
394C2×Q8—1721no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—42no—
398C2×D4—41no—
399C2×D4—81no—
400C2×D4—431no—
401C2×D4—861no—
402C2×D4—1721no—
403C2×D4—1721no—
404C2×D4—1721no—
405C2×D4—1721no—
406C22×C4—41no—
407C22×C4—431no—
408C22×C4—1721no—
409C22×C4—1721no—
410C22×C4—1721no—
411C22×C4—1721no—
412C22×C4D4×D4311yescharacteristic
413Q16—861no—
414Q16—861no—
415SD16—3441no—
416SD16—1722no—
417D8—21no—
418D8—21no—
419D8—21no—
420D8—42no—
421D8—861no—
422D8—861no—
423D8#1062189812yescomplemented
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—431no—
427C2×C8—431no—
428C2×C8—861no—
429C2×C8—861no—
430C2×C8D4×D4311yescharacteristic
431C2×C8C23×D4311yescharacteristic
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—41no—
435C4⋊C4—431no—
436C4⋊C4—861no—
437C4⋊C4—861no—
438C4⋊C4—1721no—
439C4⋊C4—1721no—
440C4⋊C4—1721no—
441C22⋊C4—431no—
442C22⋊C4—431no—
443C22⋊C4—1721no—
444C22⋊C4—1721no—
445C22⋊C4—1721no—
446C22⋊C4—1721no—
447C22⋊C4—1721no—
448C22⋊C4—1721no—
449C22⋊C4—1721no—
450C22⋊C4—1721no—
451C42—431no—
452C16—21no—
453C16—21no—
454C16—861no—
455C16—861no—
456C23—41no—
457C23—41no—
458C23—82no—
459C23—82no—
460C23—161no—
461C23—431no—
462C23—1721no—
463C23D8×D4311yescharacteristic
464Q8—3442no—
465Q8—1721no—
466Q8—1721no—
467D4—22no—
468D4—41no—
469D4—41no—
470D4—41no—
471D4—82no—
472D4—862no—
473D4—3442no—
474D4—3442no—
475D4—3442no—
476D4—1721no—
477D4—1721no—
478D4—6881no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—82no—
484C2×C4—431no—
485C2×C4—431no—
486C2×C4—431no—
487C2×C4—861no—
488C2×C4—861no—
489C2×C4—3442no—
490C2×C4—3442no—
491C2×C4—3442no—
492C2×C4—1721no—
493C2×C4—1721no—
494C2×C4—1721no—
495C2×C4—6881no—
496C2×C4D8×D4311yescharacteristic
497C2×C4C2×D4×D4311yescharacteristic
498C8—21no—
499C8—861no—
500C8—861no—
501C8C2×#1062189811yescharacteristic
502C8#1306337011yescharacteristic
503C22—21no—
504C22—21no—
505C22—42no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—164no—
512C22—861no—
513C22—861no—
514C22—861no—
515C22—3441no—
516C22—3441no—
517C22—3441no—
518C22#1458333312yes—
519C22C2×D8×D4311yescharacteristic
520C4—21no—
521C4—81no—
522C4—81no—
523C4—861no—
524C4—861no—
525C4—861no—
526C4—3441no—
527C4—3441no—
528C4—3441no—
529C4#1458353911yescharacteristic
530C4#1458370511yescharacteristic
531C2—22no—
532C2—82no—
533C2—161no—
534C2—1721no—
535C2—6881no—
536C2#1914640411yescharacteristic
537C2C2×#1458333311yescharacteristic
538C2#1914773711yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#357C2
socleC22×C43C22×D8
hypercenterC2×#357D43
hypocenterC43#33873
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
1. #19146940C2semidirect
2. #19146280C2semidirect
3. #19136830C2semidirect
4. #19136792C2semidirect
5. #19136779C2semidirect
6. #19136740C2semidirect
7. #19136697C2semidirect
8. #19136691C2semidirect
9. #19136649C2semidirect
10. #19136519C2semidirect
11. #19136507C2semidirect
12. #19136468C2semidirect
13. #19136420C2semidirect
14. #19136304C2semidirect
15. C2×C43×#357C2semidirect
19. C2×#13063270C22semidirect
22. C2×#13063264C22semidirect
23. #14583303C22semidirect
29. #14583136C22semidirect
36. #14582981C22semidirect
38. #107×D43C22semidirect
39. #14582727C22semidirect
40. #14582726C22semidirect
41. #14582726C22semidirect
42. Dic43⋊C16C22semidirect
43. #14582704C22semidirect
44. #14582702C22semidirect
45. #14582702C22semidirect
46. #14582701C22semidirect
50. (C2×D43)⋊C16C22semidirect
51. #14582674C22semidirect
147. D8×C43#41semidirect
276. C2×#357D43semidirect
328. C43#33873semidirect
423. D8#10621898semidirect

Maximal subgroups

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

subgroupindex
#191469402
#191462802
#191368302
#191367922
#191367792
#191367402
#191366972
#191366912
#191366492
#191365192
#191365072
#191364682
#191364202
#191363042
C2×C43×#3572
#3387343