Finite Group Databasebeta

← #25253630

Subgroups — #25253630

Order 11008.

610 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146964C211yesmaximal, characteristic, complemented
2D4×D344C211yesmaximal, characteristic
3#19136837C211yesmaximal, characteristic, complemented
4#19136787C211yesmaximal, characteristic, complemented
5#19136776C211yesmaximal, characteristic, complemented
6#19136753C211yesmaximal, characteristic, complemented
7#19136708C211yesmaximal, characteristic, complemented
8#19136691C211yesmaximal, characteristic, complemented
9#19136636C211yesmaximal, characteristic, complemented
10#19136526C211yesmaximal, characteristic, complemented
11#19136526C211yesmaximal, characteristic, complemented
12#19136461C211yesmaximal, characteristic, complemented
13#19136312C211yesmaximal, characteristic, complemented
14C2×#14582701C211yesmaximal, characteristic, complemented
15C43×#2168C211yesmaximal, characteristic, complemented
16C22×D344C2211yescharacteristic
17C22×D344C2211yescharacteristic
18#14583589—21no—
19D4×D172—21no—
20C2×#13063270C2211yescharacteristic
21C2×#13063270C2211yescharacteristic, complemented
22C2×#13063270C2211yescharacteristic, complemented
23#14583301C2211yescharacteristic, complemented
24#14583276C2211yescharacteristic
25#14583241—21no—
26#14583230—21no—
27#14583207—21no—
28#14583140C2211yescharacteristic, complemented
29#14583140C2211yescharacteristic, complemented
30#14583135C2211yescharacteristic
31#14583135C2211yescharacteristic
32#14583095—21no—
33#14583035—21no—
34#14583035—21no—
35C4×Dic172C2211yescharacteristic, complemented
36C4×D344C2211yescharacteristic
37#14582937C2211yescharacteristic, complemented
38C2×#13063259C2211yescharacteristic, complemented
39#14582727C2211yescharacteristic, complemented
40#14582725C2211yescharacteristic, complemented
41#14582725C2211yescharacteristic, complemented
42#14582704C2211yescharacteristic, complemented
43#14582701C2211yescharacteristic
44#14582701C2211yescharacteristic
45#14582701C2211yescharacteristic
46#14582701C2211yescharacteristic, complemented
47#14582701C2211yescharacteristic, complemented
48#14582701C2211yescharacteristic, complemented
49#14582701C2211yescharacteristic, complemented
50#14582701C2211yescharacteristic, complemented
51#14582701C2211yescharacteristic, complemented
52C2×M32×C43C2211yescharacteristic, complemented
53C22×C16×C43C2211yescharacteristic, complemented
54C8×D4×C43C2211yescharacteristic
55C43×C4⋊C16C2211yescharacteristic, complemented
56C43×C22⋊C16C2211yescharacteristic, complemented
57C43×C22⋊C16C2211yescharacteristic, complemented
58C43×#346C2211yescharacteristic, complemented
59C22×D172—21no—
60C22×D172—21no—
61C2×D4×D43—41no—
62C2×Dic172C2311yescharacteristic
63C2×D344—22no—
64C2×D344—22no—
65C2×D344—21no—
66C2×D344—21no—
67C2×D344—21no—
68C2×D344—41no—
69C2×D344—41no—
70C2×D344C2311yescharacteristic
71C2×D344C2311yescharacteristic
72C2×D344C2311yescharacteristic
73#13063322—21no—
74#13063318—41no—
75#13063317—21no—
76#13063315—41no—
77#13063306—41no—
78#13063304—21no—
79#13063304—21no—
80#13063300—41no—
81#13063299—21no—
82#13063299—21no—
83#13063295—41no—
84#13063295—41no—
85C4×Dic86—21no—
86C4×D172—21no—
87#13063284—21no—
88#13063281—41no—
89C2×C4⋊Dic43—21no—
90#13063270—22no—
91#13063270—41no—
92#13063270—41no—
93#13063259—21no—
94#13063259C2311yescharacteristic
95#13063259C2311yescharacteristic
96#13063259C2311yescharacteristic
97#13063259C2311yescharacteristic
98#13063257—21no—
99#13063257—21no—
100#13063250—21no—
101#13063250—21no—
102#13063250—21no—
103#13063247—21no—
104#13063247—21no—
105#13063247—21no—
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C4×D4×C43D411yescharacteristic
109M32×C43—41no—
110C2×C16×C43—41no—
111C2×C16×C43C2311yescharacteristic
112C2×C16×C43C2311yescharacteristic
113C2×C16×C43C2311yescharacteristic
114C2×C16×C43C2311yescharacteristic
115C4⋊C8×C43D411yescharacteristic
116C22⋊C8×C43D411yescharacteristic
117C22⋊C8×C43D411yescharacteristic
118C4×C8×C43C2311yescharacteristic
119C23×D43—41no—
120C23×D43—41no—
121C2×D4×C43D811yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C2×C22⋊D43—41no—
125C2×C22⋊D43—41no—
126C22×Dic43—41no—
127D4×D43—84no—
128C2×D172—21no—
129C2×D172—21no—
130C2×D172—21no—
131C2×D172—41no—
132C2×D172—41no—
133C2×D172—41no—
134C2×D172—41no—
135C2×D172—42no—
136C2×D172—42no—
137C2×D172—81no—
138C2×D172—81no—
139C2×C4×D43—41no—
140C2×Dic86—21no—
141C2×C8×C43—21no—
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43C2×D411yescharacteristic
146C2×C8×C43C2×D411yescharacteristic
147C2×C8×C43C2×D411yescharacteristic
148C2×C8×C43C2411yescharacteristic
149C4⋊C4×C43D811yescharacteristic
150C22⋊C4×C43D811yescharacteristic
151C22⋊C4×C43D811yescharacteristic
152C42×C43C2×D411yescharacteristic
153C22⋊Dic43—41no—
154C22⋊Dic43—41no—
155C22⋊Dic43—41no—
156(C2×D43)⋊C4—41no—
157(C2×D43)⋊C4—41no—
158(C2×D43)⋊C4—41no—
159C4⋊Dic43—21no—
160C4⋊Dic43—21no—
161C4⋊Dic43—21no—
162C4⋊Dic43—21no—
163C4⋊Dic43—41no—
164Dic43⋊C4—41no—
165Dic43⋊C4—41no—
166Dic43⋊C4—41no—
167Dic43⋊C4—41no—
168Dic43⋊C4—41no—
169C4×Dic43—41no—
170C4×Dic43—41no—
171Dic172—21no—
172Dic172—21no—
173D344—21no—
174D344—21no—
175D344—21no—
176D344—21no—
177D344—21no—
178D344—42no—
179D344—42no—
180D344—81no—
181D344#4112yes—
182C16×C43—21no—
183C16×C43—21no—
184C16×C43—21no—
185C16×C43—21no—
186C23×C43C2×D811yescharacteristic
187C23×C43C2×D811yescharacteristic
188C22×D43—41no—
189C22×D43—41no—
190C22×D43—41no—
191C22×D43—82no—
192C22×D43—82no—
193C22×D43—82no—
194C22×D43—82no—
195C22×D43—161no—
196C22×D43—161no—
197D4×C43—22no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43C2×D811yescharacteristic
203C2×C4×C43C2×D811yescharacteristic
204C2×C4×C43C2×D811yescharacteristic
205C2×C4×C43C2×D811yescharacteristic
206C2×C4×C43C22×D411yescharacteristic
207C22⋊D43—82no—
208C22⋊D43—82no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—41no—
214C2×Dic43—82no—
215D172—22no—
216D172—41no—
217D172—41no—
218D172—41no—
219D172—41no—
220D172—41no—
221D172—82no—
222D172—82no—
223D172—82no—
224D172—161no—
225C4×D43—82no—
226Dic86—41no—
227Dic86—41no—
228C8×C43—21no—
229C8×C43—21no—
230C8×C43—21no—
231C8×C43C2×#4111yescharacteristic
232C8×C43H(5,𝔽2)11yescharacteristic
233#33877—431nomaximal, Sylow
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—21no—
239C22×C43#50912yes—
240C22×C43C22×D811yescharacteristic
241C2×D43—42no—
242C2×D43—81no—
243C2×D43—81no—
244C2×D43—81no—
245C2×D43—81no—
246C2×D43—81no—
247C2×D43—81no—
248C2×D43—81no—
249C2×D43—81no—
250C2×D43—164no—
251C2×D43—164no—
252C4×C43—21no—
253C4×C43—21no—
254C4×C43—21no—
255C4×C43—21no—
256C4×C43#54611yescharacteristic
257C4×C43#57711yescharacteristic
258Dic43—81no—
259Dic43—81no—
260Dic43—81no—
261Dic43—81no—
262Dic43—81no—
263#3336—431no—
264D4×D8—431no—
265#2244—431no—
266#2234—431no—
267#2232—431no—
268#2228—431no—
269#2220—431no—
270#2217—431no—
271#2207—431no—
272#2187—431no—
273#2187—431no—
274#2175—431no—
275#2168D4311yescharacteristic, complemented
276#2140—431no—
277C2×#357—431no—
278C2×C43—22no—
279C2×C43—41no—
280C2×C43#329411yescharacteristic
281C2×C43C2×#50911yescharacteristic
282C2×C43#341611yescharacteristic
283D43—82no—
284D43—161no—
285D43—161no—
286C22×D8—431no—
287C22×D8—431no—
288#552—861no—
289D42—861no—
290C2×SD32—431no—
291C2×SD32—431no—
292C2×SD32—431no—
293C2×M32C2×D4311yescharacteristic, complemented
294C22×C16C2×D4311yescharacteristic, complemented
295#499—431no—
296#493—431no—
297#485—861no—
298#483—861no—
299#479—861no—
300#467—431no—
301#467—431no—
302#466—431no—
303#466—431no—
304#459—861no—
305#447—861no—
306#447—861no—
307C4×Q16—431no—
308C4×D8—431no—
309C8×D4C2×D4311yescharacteristic
310#427—431no—
311C2×#107—431no—
312#367—431no—
313#366—431no—
314#366—431no—
315C4⋊C16C2×D4311yescharacteristic, complemented
316#358—431no—
317#357—431no—
318#357—431no—
319#357—431no—
320#357—431no—
321#357—431no—
322#357—431no—
323#357—431no—
324#357—431no—
325#357—431no—
326C22⋊C16C2×D4311yescharacteristic, complemented
327C22⋊C16C2×D4311yescharacteristic, complemented
328#346C2×D4311yescharacteristic, complemented
329C43#3387711yescharacteristic, complemented, Sylow
330C22×D4—861no—
331C22×D4—861no—
332C22×D4—1721no—
333C2×Q16—431no—
334C2×D8—431no—
335C2×D8—431no—
336C2×D8—431no—
337C2×D8—862no—
338C2×D8—862no—
339C2×D8—861no—
340C2×D8—861no—
341C2×D8—861no—
342C2×D8—1721no—
343C2×D8—1721no—
344C22×C8C22×D4311yescharacteristic
345C22×C8C22×D4311yescharacteristic
346#127—861no—
347#126—1721no—
348#125—861no—
349#125—1721no—
350#123—1721no—
351C22⋊Q8—861no—
352C22⋊Q8—861no—
353#121—861no—
354#121—861no—
355#121—1721no—
356#120—1721no—
357#120—1721no—
358C4×Q8—861no—
359C4×D4—861no—
360C4×D4D17211yescharacteristic
361#117—861no—
362#117—1721no—
363C2×C4⋊C4—861no—
364SD32—862no—
365SD32—1721no—
366SD32—1721no—
367M32—41no—
368C2×C16—41no—
369C2×C16C22×D4311yescharacteristic
370C2×C16C22×D4311yescharacteristic
371C2×C16C22×D4311yescharacteristic
372C2×C16C22×D4311yescharacteristic
373#107—431no—
374#107—431no—
375#107—431no—
376#107—431no—
377#107—861no—
378#106—861no—
379#106—861no—
380C4⋊C8D17211yescharacteristic
381#103—861no—
382#103—861no—
383#103—861no—
384#102—861no—
385#102—861no—
386#102—861no—
387C22⋊C8D17211yescharacteristic
388C22⋊C8D17211yescharacteristic
389C4×C8C22×D4311yescharacteristic
390C24—1721no—
391C24—1721no—
392C2×Q8—861no—
393C2×D4—861no—
394C2×D4—861no—
395C2×D4—861no—
396C2×D4—3441no—
397C2×D4—3441no—
398C2×D4—3444no—
399C2×D4—1722no—
400C2×D4—1722no—
401C2×D4—1721no—
402C2×D4—1721no—
403C2×D4—1721no—
404C2×D4—1721no—
405C2×D4—1721no—
406C2×D4—1721no—
407C2×D4D34411yescharacteristic
408C22×C4—1721no—
409C22×C4—1721no—
410C22×C4C2×D17211yescharacteristic
411C22×C4C2×D17211yescharacteristic
412Q16—861no—
413Q16—861no—
414D8—432no—
415D8—861no—
416D8—861no—
417D8—861no—
418D8—861no—
419D8—861no—
420D8—3441no—
421D8—1722no—
422D8—1722no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8C2×D17211yescharacteristic
428C2×C8C2×D17211yescharacteristic
429C2×C8C2×D17211yescharacteristic
430C2×C8C23×D4311yescharacteristic
431C4⋊C4—861no—
432C4⋊C4—861no—
433C4⋊C4—861no—
434C4⋊C4—861no—
435C4⋊C4—1721no—
436C4⋊C4—1721no—
437C4⋊C4—1721no—
438C4⋊C4—1721no—
439C4⋊C4—1721no—
440C4⋊C4—1721no—
441C4⋊C4D34411yescharacteristic
442C22⋊C4—1721no—
443C22⋊C4—1721no—
444C22⋊C4—1721no—
445C22⋊C4—1721no—
446C22⋊C4—1721no—
447C22⋊C4—1721no—
448C22⋊C4D34411yescharacteristic
449C22⋊C4D34411yescharacteristic
450C42—1721no—
451C42—1721no—
452C42C2×D17211yescharacteristic
453C16—21no—
454C16—21no—
455C16—21no—
456C16—21no—
457C23—3442no—
458C23—3442no—
459C23—3442no—
460C23—3442no—
461C23—1721no—
462C23—1721no—
463C23—1721no—
464C23—6881no—
465C23—6881no—
466C23C2×D34411yescharacteristic
467C23C2×D34411yescharacteristic
468Q8—1721no—
469Q8—1721no—
470D4—22no—
471D4—862no—
472D4—3442no—
473D4—3442no—
474D4—3442no—
475D4—3442no—
476D4—3442no—
477D4—1721no—
478D4—1721no—
479D4—1721no—
480D4—1721no—
481D4—1721no—
482D4—6881no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—3442no—
488C2×C4—3442no—
489C2×C4—1721no—
490C2×C4—1721no—
491C2×C4—1721no—
492C2×C4—1721no—
493C2×C4—1721no—
494C2×C4C2×D34411yescharacteristic
495C2×C4C2×D34411yescharacteristic
496C2×C4C2×D34411yescharacteristic
497C2×C4C2×D34411yescharacteristic
498C2×C4C22×D17211yescharacteristic
499C8—21no—
500C8—21no—
501C8—21no—
502C8#41×D4311yescharacteristic
503C8#1306337011yescharacteristic
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—3441no—
510C22—3441no—
511C22—3441no—
512C22—3441no—
513C22—3441no—
514C22—3441no—
515C22—3441no—
516C22—3441no—
517C22—1722no—
518C22—6884no—
519C22—6884no—
520C22#1458333712yes—
521C22C22×D34411yescharacteristic
522C4—21no—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—3441no—
527C4—3441no—
528C4—3441no—
529C4—3441no—
530C4—3441no—
531C4#1458354411yescharacteristic
532C4#1458371111yescharacteristic
533C2—22no—
534C2—41no—
535C2—3442no—
536C2—6881no—
537C2—6881no—
538C2#1914640911yescharacteristic
539C2C2×#1458333711yescharacteristic
540C2#1914774311yescharacteristic
subgroupG/H
centerC22C22×D344
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2168C2
socleC22×C43C22×D8
prime radicalD4×D344C2
hypercenter#2168D43
hypocenterC43#33877
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2168

Complements

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

NH ≅ G/Ntype
1. #19146964C2semidirect
3. #19136837C2semidirect
4. #19136787C2semidirect
5. #19136776C2semidirect
6. #19136753C2semidirect
7. #19136708C2semidirect
8. #19136691C2semidirect
9. #19136636C2semidirect
10. #19136526C2semidirect
11. #19136526C2semidirect
12. #19136461C2semidirect
13. #19136312C2semidirect
14. C2×#14582701C2semidirect
15. C43×#2168C2semidirect
21. C2×#13063270C22semidirect
22. C2×#13063270C22semidirect
23. #14583301C22semidirect
28. #14583140C22semidirect
29. #14583140C22semidirect
35. C4×Dic172C22semidirect
37. #14582937C22semidirect
38. C2×#13063259C22semidirect
39. #14582727C22semidirect
40. #14582725C22semidirect
41. #14582725C22semidirect
42. #14582704C22semidirect
46. #14582701C22semidirect
47. #14582701C22semidirect
48. #14582701C22semidirect
49. #14582701C22semidirect
50. #14582701C22semidirect
51. #14582701C22semidirect
52. C2×M32×C43C22semidirect
53. C22×C16×C43C22semidirect
55. C43×C4⋊C16C22semidirect
56. C43×C22⋊C16C22semidirect
57. C43×C22⋊C16C22semidirect
58. C43×#346C22semidirect
275. #2168D43semidirect
293. C2×M32C2×D43semidirect
294. C22×C16C2×D43semidirect
315. C4⋊C16C2×D43semidirect
326. C22⋊C16C2×D43semidirect
327. C22⋊C16C2×D43semidirect
328. #346C2×D43semidirect
329. C43#33877semidirect

Maximal subgroups

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

subgroupindex
#191469642
D4×D3442
#191368372
#191367872
#191367762
#191367532
#191367082
#191366912
#191366362
#191365262
#191364612
#191363122
C2×#145827012
C43×#21682
#3387743