Finite Group Databasebeta

← #25251250

Subgroups — #25251250

Order 11008.

598 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145108C211yesmaximal, characteristic, complemented
2C4×D8×D43C211yesmaximal, characteristic
3#19136753C211yesmaximal, characteristic, complemented
4#19136752C211yesmaximal, characteristic, complemented
5#19136749C211yesmaximal, characteristic, complemented
6#19136741C211yesmaximal, characteristic, complemented
7#19136740C211yesmaximal, characteristic, complemented
8#19136731C211yesmaximal, characteristic, complemented
9#19136730C211yesmaximal, characteristic, complemented
10#19136382C211yesmaximal, characteristic, complemented
11#19136380C211yesmaximal, characteristic, complemented
12#19136349C211yesmaximal, characteristic, complemented
13#19136309C211yesmaximal, characteristic
14#19136309C211yesmaximal, characteristic
15C43×#2228C211yesmaximal, characteristic, complemented
16C2×D8×D43C2211yescharacteristic
17#14583455—21no—
18C4×D4×D43—21no—
19C2×#13063264C2211yescharacteristic
20C2×#13063264C2211yescharacteristic
21#14583303C2211yescharacteristic, complemented
22#14583303C2211yescharacteristic, complemented
23#14583301C2211yescharacteristic, complemented
24#14583298—21no—
25#14583296—21no—
26C4×D344C2211yescharacteristic
27D8×Dic43C2211yescharacteristic
28#14582981C2211yescharacteristic
29C4×#10621882—21no—
30#14582979—21no—
31#14582936C2211yescharacteristic
32#14582936C2211yescharacteristic
33#14582934—21no—
34#107×D43C2211yescharacteristic
35#102×D43—21no—
36C4×C8×D43C2211yescharacteristic
37#14582727C2211yescharacteristic, complemented
38#14582726C2211yescharacteristic, complemented
39#14582726C2211yescharacteristic, complemented
40#14582725C2211yescharacteristic, complemented
41#14582724C2211yescharacteristic, complemented
42#14582724C2211yescharacteristic, complemented
43C4⋊(C43⋊C16)C2211yescharacteristic, complemented
44Dic43⋊C16C2211yescharacteristic, complemented
45Dic43⋊C16C2211yescharacteristic, complemented
46#14582701C2211yescharacteristic
47#14582701C2211yescharacteristic
48#14582700C2211yescharacteristic
49#14582700C2211yescharacteristic
50#14582699C2211yescharacteristic
51#14582699C2211yescharacteristic
52C43×#499C2211yescharacteristic, complemented
53C4×D8×C43C2211yescharacteristic
54C43×#367C2211yescharacteristic, complemented
55C43×#366C2211yescharacteristic, complemented
56C43×C4⋊C16C2211yescharacteristic, complemented
57C43×#357C2211yescharacteristic
58C43×#357C2211yescharacteristic
59C2×D4×D43—21no—
60C22×C4×D43—41no—
61C2×D344C2311yescharacteristic
62C2×#10621882—21no—
63D8×D43—22no—
64D8×D43Q814yescomplemented
65C2×C8×D43D411yescharacteristic
66C2×C8×D43C2311yescharacteristic
67#13063324—21no—
68#13063324—21no—
69#13063317—21no—
70#13063303—41no—
71#13063303—41no—
72#13063290—41no—
73#13063290—41no—
74C4×D172—21no—
75D4×Dic43—21no—
76#13063287—21no—
77C4×C22⋊D43—41no—
78(C22⋊D43)⋊C4—41no—
79#13063283—21no—
80#13063283—21no—
81C4⋊C4×D43—21no—
82C22⋊C4×D43—41no—
83C42×D43D411yescharacteristic
84#13063264—22no—
85#13063264—22no—
86C2×C43⋊C16C2311yescharacteristic
87C2×C43⋊C16C2311yescharacteristic
88#13063259C2311yescharacteristic
89#13063259C2311yescharacteristic
90#13063259C2311yescharacteristic
91#13063258—21no—
92#13063258—21no—
93#13063258—21no—
94#13063257—21no—
95#13063256—21no—
96#13063256—21no—
97#13063247—21no—
98#13063246—21no—
99#13063245—21no—
100C4×C43⋊C8D411yescharacteristic
101C8×Dic43D411yescharacteristic
102C8×Dic43C2311yescharacteristic
103C2×D8×C43C2311yescharacteristic
104#125×C43—21no—
105C4×D4×C43—21no—
106C2×C16×C43C2311yescharacteristic
107C2×C16×C43C2311yescharacteristic
108#107×C43C2311yescharacteristic
109#107×C43C2311yescharacteristic
110#107×C43C2311yescharacteristic
111#106×C43—21no—
112#102×C43—21no—
113C4×C8×C43C2311yescharacteristic
114C23×D43—41no—
115C2×D4×C43—21no—
116C22×C4×C43—41no—
117C2×C22⋊D43—41no—
118C22×Dic43—41no—
119D4×D43—24no—
120D4×D43—42no—
121C2×D172—21no—
122C2×C4×D43—41no—
123C2×C4×D43—41no—
124C2×C4×D43—41no—
125C2×C4×D43—84no—
126C2×C4×D43D811yescharacteristic
127C2×C4×D43D811yescharacteristic
128C2×C4×D43C2×D411yescharacteristic
129C2×Dic86—41no—
130C2×Dic86—41no—
131D8×C43—21no—
132D8×C43C2×Q812yes—
133C2×C8×C43C2×D411yescharacteristic
134C2×C8×C43C2411yescharacteristic
135C4⋊C4×C43—21no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—41no—
139C4⋊C4×C43—41no—
140C22⋊C4×C43—41no—
141C42×C43C2×D411yescharacteristic
142C22⋊Dic43—41no—
143#10621882—24no—
144(C2×D43)⋊C4—41no—
145(C2×D43)⋊C4—41no—
146(C2×D43)⋊C4—41no—
147(C2×D43)⋊C4—41no—
148C4⋊Dic43—21no—
149C4⋊Dic43—21no—
150C4⋊Dic43—21no—
151Dic43⋊C4—41no—
152Dic43⋊C4—41no—
153Dic43⋊C4—41no—
154Dic43⋊C4—41no—
155Dic43⋊C4—41no—
156C4×Dic43—41no—
157C4×Dic43—41no—
158C4×Dic43D811yescharacteristic
159C4×Dic43D811yescharacteristic
160C4×Dic43C2×D411yescharacteristic
161C2×C43⋊C8C2×D411yescharacteristic
162C2×C43⋊C8C2×D411yescharacteristic
163D344—21no—
164D344C2×Q812yes—
165C8×D43—22no—
166C8×D43C2×Q812yes—
167C8×D43#4112yes—
168C16×C43—21no—
169C16×C43—21no—
170C43⋊C16—21no—
171C43⋊C16—21no—
172C23×C43—41no—
173C22×D43—41no—
174C22×D43—44no—
175C22×D43—82no—
176C22×D43—82no—
177C22×D43C2×D811yescharacteristic
178D4×C43—22no—
179D4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—82no—
184C2×C4×C43C2×D811yescharacteristic
185C2×C4×C43C2×D811yescharacteristic
186C2×C4×C43C22×D411yescharacteristic
187C22⋊D43—44no—
188C2×Dic43—41no—
189C2×Dic43—41no—
190C2×Dic43—41no—
191C2×Dic43—82no—
192C2×Dic43C2×D811yescharacteristic
193C2×Dic43C2×D811yescharacteristic
194C2×Dic43C2×D811yescharacteristic
195D172—22no—
196D172—41no—
197C4×D43—22no—
198C4×D43—41no—
199C4×D43—82no—
200C4×D43—82no—
201C4×D43—82no—
202C4×D43C22⋊Q812yes—
203C4×D43#13712yes—
204Dic86—82no—
205Dic86—82no—
206C8×C43—21no—
207C8×C43C22×Q811yescharacteristic
208C8×C43C2×#4111yescharacteristic
209C43⋊C8—21no—
210C43⋊C8C22⋊Q812yes—
211#33627—431nomaximal, Sylow
212C22×C43—42no—
213C22×C43—81no—
214C22×C43—81no—
215C22×C43C22×D811yescharacteristic
216C2×D43—21no—
217C2×D43—21no—
218C2×D43—42no—
219C2×D43—88no—
220C2×D43—81no—
221C2×D43—81no—
222C2×D43#47412yes—
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—81no—
226C4×C43—81no—
227C4×C43—81no—
228C4×C43C2×C22⋊Q811yescharacteristic
229C4×C43C2×#13711yescharacteristic
230Dic43—21no—
231Dic43—81no—
232Dic43—81no—
233Dic43—81no—
234Dic43#47412yes—
235Dic43#50912yes—
236#3160—431no—
237C2×C4×D8—431no—
238#2228—431no—
239#2228—431no—
240#2228—431no—
241#2228D4311yescharacteristic, complemented
242#2226—431no—
243#2226—431no—
244#2224—431no—
245#2224—431no—
246#2159—431no—
247#2159—431no—
248#2150—431no—
249#2140—431no—
250#2140—431no—
251C2×C43—82no—
252C2×C43C2×#47411yescharacteristic
253C2×C43C2×#50911yescharacteristic
254C2×C43#341411yescharacteristic
255D43—22no—
256D43—82no—
257C22×D8—431no—
258#533—861no—
259C2×C4×D4—861no—
260C2×M32—431no—
261C2×M32—431no—
262#500—431no—
263#500—431no—
264#499—431no—
265#499—861no—
266#499C2×D4311yescharacteristic, complemented
267#498—861no—
268C4×D8—431no—
269C4×D8—431no—
270C4×D8—431no—
271C4×D8—861no—
272C4×D8—861no—
273C4×D8C2×D4311yescharacteristic
274#427—431no—
275#427—431no—
276#427—861no—
277C2×#107—431no—
278C2×#102—861no—
279C2×C4×C8—431no—
280#367—431no—
281#367—431no—
282#367—431no—
283#367C2×D4311yescharacteristic, complemented
284#366—431no—
285#366—431no—
286#366—431no—
287#366C2×D4311yescharacteristic, complemented
288C4⋊C16—431no—
289C4⋊C16—431no—
290C4⋊C16—431no—
291C4⋊C16C2×D4311yescharacteristic, complemented
292#357—431no—
293#357—431no—
294#357—431no—
295#357—431no—
296#357—431no—
297#357—431no—
298#357C2×D4311yescharacteristic
299#357C2×D4311yescharacteristic
300C43#3362711yescharacteristic, complemented, Sylow
301C22×D4—861no—
302C23×C4—1721no—
303C2×D8—434no—
304C2×D8—431no—
305C2×D8—862no—
306C2×D8—861no—
307C2×D8C22×D4311yescharacteristic
308C22×C8—431no—
309C22×C8—431no—
310C4⋊Q8—861no—
311C4⋊Q8—861no—
312#125—21no—
313#125—861no—
314C22⋊Q8—1721no—
315C22⋊Q8—1721no—
316C4×Q8—1721no—
317C4×Q8—1721no—
318C4×D4—21no—
319C4×D4—861no—
320C4×D4—861no—
321C4×D4—861no—
322C4×D4—1721no—
323C4×D4—1721no—
324#117—861no—
325#117—861no—
326C2×C4⋊C4—861no—
327C2×C22⋊C4—1721no—
328C2×C42—431no—
329M32—862no—
330M32—862no—
331C2×C16—431no—
332C2×C16—431no—
333C2×C16C22×D4311yescharacteristic
334C2×C16C22×D4311yescharacteristic
335#107—431no—
336#107—431no—
337#107—431no—
338#107—861no—
339#107—861no—
340#107—861no—
341#107C22×D4311yescharacteristic
342#107C22×D4311yescharacteristic
343#107C22×D4311yescharacteristic
344#106—21no—
345#106—861no—
346#106—861no—
347#106—861no—
348#102—21no—
349#102—861no—
350#102—861no—
351#102—861no—
352C4×C8—431no—
353C4×C8—431no—
354C4×C8—431no—
355C4×C8C22×D4311yescharacteristic
356C24—1721no—
357C2×Q8—1721no—
358C2×Q8—1721no—
359C2×D4—21no—
360C2×D4—864no—
361C2×D4—861no—
362C2×D4—1722no—
363C2×D4—1721no—
364C22×C4—41no—
365C22×C4—431no—
366C22×C4—431no—
367C22×C4—431no—
368C22×C4—3444no—
369C22×C4—1721no—
370C22×C4—1721no—
371C22×C4—1721no—
372C22×C4—1721no—
373D8—21no—
374D8—432no—
375D8—864no—
376D8—861no—
377D8Q8×D4312yes—
378C2×C8—431no—
379C2×C8—432no—
380C2×C8—432no—
381C2×C8—431no—
382C2×C8—862no—
383C2×C8D4×D4311yescharacteristic
384C2×C8C23×D4311yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—861no—
391C4⋊C4—861no—
392C4⋊C4—861no—
393C4⋊C4—1721no—
394C4⋊C4—1721no—
395C4⋊C4—1721no—
396C4⋊C4—1721no—
397C4⋊C4—1721no—
398C22⋊C4—41no—
399C22⋊C4—1721no—
400C22⋊C4—1721no—
401C22⋊C4—1721no—
402C22⋊C4—1721no—
403C22⋊C4—1721no—
404C42—431no—
405C42—431no—
406C42—431no—
407C42—1721no—
408C42—1721no—
409C42D4×D4311yescharacteristic
410C16—21no—
411C16—21no—
412C16—861no—
413C16—861no—
414C23—41no—
415C23—431no—
416C23—3442no—
417C23—3442no—
418C23—1724no—
419C23—1721no—
420Q8—3442no—
421Q8—3442no—
422D4—22no—
423D4—41no—
424D4—862no—
425D4—1724no—
426D4—1721no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—82no—
431C2×C4—431no—
432C2×C4—431no—
433C2×C4—432no—
434C2×C4—432no—
435C2×C4—431no—
436C2×C4—862no—
437C2×C4—3442no—
438C2×C4—3442no—
439C2×C4—3442no—
440C2×C4—3442no—
441C2×C4—1721no—
442C2×C4—1721no—
443C2×C4—1721no—
444C2×C4—1721no—
445C2×C4D8×D4311yescharacteristic
446C2×C4D8×D4311yescharacteristic
447C2×C4C2×D4×D4311yescharacteristic
448C8—21no—
449C8—432no—
450C8—861no—
451C8C2×Q8×D4311yescharacteristic
452C8#41×D4311yescharacteristic
453C22—42no—
454C22—81no—
455C22—81no—
456C22—432no—
457C22—861no—
458C22—861no—
459C22—3448no—
460C22—3441no—
461C22—3441no—
462C22—1722no—
463C22C2×D8×D4311yescharacteristic
464C4—21no—
465C4—21no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—432no—
470C4—432no—
471C4—861no—
472C4—3441no—
473C4—3441no—
474C4—3441no—
475C4C22⋊Q8×D4311yescharacteristic
476C4#137×D4311yescharacteristic
477C2—82no—
478C2—862no—
479C2—3442no—
480C2#474×D4311yescharacteristic
481C2#509×D4311yescharacteristic
482C2#1914772811yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2228C2
socleC22×C43C22×D8
prime radicalC2×D8×D43C22
hypercenter#2228D43
hypocenterC43#33627
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #19145108C2semidirect
3. #19136753C2semidirect
4. #19136752C2semidirect
5. #19136749C2semidirect
6. #19136741C2semidirect
7. #19136740C2semidirect
8. #19136731C2semidirect
9. #19136730C2semidirect
10. #19136382C2semidirect
11. #19136380C2semidirect
12. #19136349C2semidirect
15. C43×#2228C2semidirect
21. #14583303C22semidirect
22. #14583303C22semidirect
23. #14583301C22semidirect
37. #14582727C22semidirect
38. #14582726C22semidirect
39. #14582726C22semidirect
40. #14582725C22semidirect
41. #14582724C22semidirect
42. #14582724C22semidirect
43. C4⋊(C43⋊C16)C22semidirect
44. Dic43⋊C16C22semidirect
45. Dic43⋊C16C22semidirect
52. C43×#499C22semidirect
54. C43×#367C22semidirect
55. C43×#366C22semidirect
56. C43×C4⋊C16C22semidirect
64. D8×D43Q8semidirect
241. #2228D43semidirect
266. #499C2×D43semidirect
283. #367C2×D43semidirect
287. #366C2×D43semidirect
291. C4⋊C16C2×D43semidirect
300. C43#33627semidirect

Maximal subgroups

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

subgroupindex
#191451082
C4×D8×D432
#191367532
#191367522
#191367492
#191367412
#191367402
#191367312
#191367302
#191363822
#191363802
#191363492
#191363092
C43×#22282
#3362743