Finite Group Databasebeta

← #25251401

Subgroups — #25251401

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144178C211yesmaximal, characteristic
2#427×D43C211yesmaximal, characteristic, complemented
3#19136800C211yesmaximal, characteristic, complemented
4#19136796C211yesmaximal, characteristic, complemented
5#19136791C211yesmaximal, characteristic, complemented
6#19136787C211yesmaximal, characteristic, complemented
7#19136786C211yesmaximal, characteristic, complemented
8#19136782C211yesmaximal, characteristic, complemented
9#19136777C211yesmaximal, characteristic, complemented
10#19136378C211yesmaximal, characteristic, complemented
11#19136376C211yesmaximal, characteristic, complemented
12#19136301C211yesmaximal, characteristic, complemented
13#19136301C211yesmaximal, characteristic, complemented
14C22⋊C16×D43C211yesmaximal, characteristic, complemented
15C43×#2237C211yesmaximal, characteristic, complemented
16C2×#13063348C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18#14583412—21no—
19#117×D43—21no—
20C2×C16×D43C2211yescharacteristic
21C2×C16×D43C2211yescharacteristic
22#14583137C2211yescharacteristic
23#14583136C2211yescharacteristic
24#14583135C2211yescharacteristic
25#14583131—21no—
26#14583130—21no—
27#14582937C2211yescharacteristic
28#14582936C2211yescharacteristic
29#14582936C2211yescharacteristic
30#14582936C2211yescharacteristic
31#14582935—21no—
32#14582934—21no—
33#107×D43C2211yescharacteristic
34#107×D43C2211yescharacteristic
35#106×D43—21no—
36#14582894—21no—
37#14582727C2211yescharacteristic, complemented
38#14582726C2211yescharacteristic, complemented
39#14582726C2211yescharacteristic, complemented
40#14582725C2211yescharacteristic, complemented
41#14582724C2211yescharacteristic, complemented
42#14582724C2211yescharacteristic, complemented
43#14582703C2211yescharacteristic, complemented
44#14582703C2211yescharacteristic, complemented
45#14582701C2211yescharacteristic, complemented
46#14582701C2211yescharacteristic, complemented
47#14582699C2211yescharacteristic, complemented
48#14582699C2211yescharacteristic, complemented
49C22⋊(C43⋊C16)C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic
51(C2×D43)⋊C16C2211yescharacteristic
52C43×#467C2211yescharacteristic
53C43×#427C2211yescharacteristic
54C43×#367C2211yescharacteristic, complemented
55C43×#366C2211yescharacteristic, complemented
56C43×#358C2211yescharacteristic, complemented
57C43×#358C2211yescharacteristic, complemented
58C43×C22⋊C16C2211yescharacteristic
59C2×#10621902—21no—
60C22×C4×D43D411yescharacteristic
61#13063348—22no—
62#13063348—22no—
63C2×#10621884—21no—
64C2×D344C2311yescharacteristic
65C22×C43⋊C8D411yescharacteristic
66C2×C8×D43—22no—
67C2×C8×D43—22no—
68C2×C8×D43D411yescharacteristic
69C2×C8×D43D411yescharacteristic
70C2×C8×D43C2311yescharacteristic
71C2×C8×D43C2311yescharacteristic
72#13063310—41no—
73#13063301—21no—
74#13063300—21no—
75#13063299—21no—
76#13063295—41no—
77#13063287—41no—
78(C22⋊D43)⋊C4—41no—
79#13063284—21no—
80#13063283—21no—
81#13063283—21no—
82#13063283—21no—
83#13063282—41no—
84#13063281—41no—
85C4⋊C4×D43—21no—
86C4⋊C4×D43—21no—
87C22⋊C4×D43—41no—
88C42×D43—41no—
89C2×C43⋊C16C2311yescharacteristic
90C2×C43⋊C16C2311yescharacteristic
91C16×D43—22no—
92C16×D43—22no—
93#13063259C2311yescharacteristic
94#13063259C2311yescharacteristic
95#13063259C2311yescharacteristic
96#13063258—21no—
97#13063258—21no—
98#13063257—21no—
99#13063256—21no—
100#13063256—21no—
101#13063256—21no—
102#13063249—21no—
103#13063247—21no—
104#13063245—21no—
105C2×Q16×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107C22⋊Q8×C43—21no—
108#117×C43—21no—
109C2×C16×C43C2311yescharacteristic
110C2×C16×C43C2311yescharacteristic
111#107×C43C2311yescharacteristic
112#107×C43C2311yescharacteristic
113#107×C43C2311yescharacteristic
114#106×C43—21no—
115#103×C43—21no—
116C23×D43D811yescharacteristic
117C2×Q8×C43—21no—
118C22×C4×C43C2×D411yescharacteristic
119C2×C22⋊D43—41no—
120C22×Dic43D811yescharacteristic
121#10621902—42no—
122#10621902—42no—
123C2×D172—21no—
124C2×D172—41no—
125C2×D172—41no—
126C2×C4×D43—22no—
127C2×C4×D43—22no—
128C2×C4×D43—41no—
129C2×C4×D43—41no—
130C2×C4×D43—41no—
131C2×C4×D43D811yescharacteristic
132C2×C4×D43D811yescharacteristic
133C2×C4×D43C2×D411yescharacteristic
134C2×C4×D43C2×D411yescharacteristic
135Q16×C43—21no—
136Q16×C43—21no—
137C2×C8×C43—21no—
138C2×C8×C43—21no—
139C2×C8×C43C2×D411yescharacteristic
140C2×C8×C43C2411yescharacteristic
141C4⋊C4×C43—21no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—41no—
145C22⋊C4×C43—41no—
146C22⋊C4×C43—41no—
147C42×C43—41no—
148C22⋊Dic43—41no—
149#10621884—42no—
150(C2×D43)⋊C4—41no—
151(C2×D43)⋊C4—41no—
152(C2×D43)⋊C4—41no—
153(C2×D43)⋊C4—41no—
154(C2×D43)⋊C4—41no—
155(C2×D43)⋊C4—41no—
156C4⋊Dic43—21no—
157C4⋊Dic43—21no—
158C4⋊Dic43—21no—
159Dic43⋊C4—41no—
160Dic43⋊C4—41no—
161Dic43⋊C4—41no—
162C4×Dic43—41no—
163C4×Dic43—41no—
164C4×Dic43—41no—
165C4×Dic43—41no—
166C2×C43⋊C8—22no—
167C2×C43⋊C8C2×D411yescharacteristic
168C2×C43⋊C8C2×D411yescharacteristic
169D344—21no—
170D344—21no—
171C8×D43—22no—
172C8×D43—21no—
173C8×D43—21no—
174C8×D43—22no—
175C8×D43#4112yes—
176C8×D43#4112yes—
177C16×C43—21no—
178C16×C43—21no—
179C43⋊C16—21no—
180C43⋊C16—21no—
181C23×C43C2×D811yescharacteristic
182C22×D43—22no—
183C22×D43—22no—
184C22×D43—41no—
185C22×D43—41no—
186C22×D43C2×D811yescharacteristic
187C22×D43C2×D811yescharacteristic
188Q8×C43—41no—
189Q8×C43—41no—
190C2×C4×C43—21no—
191C2×C4×C43—21no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43C2×D811yescharacteristic
197C2×C4×C43C22×D411yescharacteristic
198C22⋊D43—82no—
199C2×Dic43—22no—
200C2×Dic43—41no—
201C2×Dic43—41no—
202C2×Dic43—41no—
203C2×Dic43C2×D811yescharacteristic
204C2×Dic43C2×D811yescharacteristic
205D172—41no—
206D172—41no—
207D172—82no—
208D172—82no—
209C4×D43—22no—
210C4×D43—21no—
211C4×D43—21no—
212C4×D43—22no—
213C4×D43—82no—
214C4×D43—82no—
215C4×D43—82no—
216C4×D43#12312yes—
217C4×D43#13712yes—
218C8×C43—21no—
219C8×C43C2×#4111yescharacteristic
220C8×C43C2×#4111yescharacteristic
221C43⋊C8—21no—
222C43⋊C8#12312yes—
223#33645—431nomaximal, Sylow
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—21no—
227C22×C43C22×D811yescharacteristic
228C2×D43—21no—
229C2×D43—21no—
230C2×D43—21no—
231C2×D43—21no—
232C2×D43—44no—
233C2×D43—81no—
234C2×D43—81no—
235C2×D43—81no—
236C2×D43#48012yes—
237C2×D43#50812yes—
238C4×C43—21no—
239C4×C43—81no—
240C4×C43—81no—
241C4×C43—81no—
242C4×C43—81no—
243C4×C43C2×#12311yescharacteristic
244C4×C43C2×#13711yescharacteristic
245Dic43—21no—
246Dic43—81no—
247Dic43—81no—
248Dic43—81no—
249Dic43#48012yes—
250#3050—431no—
251C2×#427—431no—
252#2237—431no—
253#2237D4311yescharacteristic, complemented
254#2236—431no—
255#2235—431no—
256#2234—431no—
257#2234—431no—
258#2233—431no—
259#2232—431no—
260#2158—431no—
261#2158—431no—
262#2138—431no—
263#2138—431no—
264C2×C22⋊C16—431no—
265C2×C43—41no—
266C2×C43C2×#48011yescharacteristic
267C2×C43C2×#50811yescharacteristic
268C2×C43#341411yescharacteristic
269D43—22no—
270D43—22no—
271D43—161no—
272C2×#135—431no—
273C23×C8—431no—
274#525—861no—
275C2×#117—861no—
276C22×C16—431no—
277C22×C16—431no—
278#467—431no—
279#467C2×D4311yescharacteristic
280#466—431no—
281#466—431no—
282#465—861no—
283#465—861no—
284#427—431no—
285#427—431no—
286#427—431no—
287#427—431no—
288#427—861no—
289#427—861no—
290#427C2×D4311yescharacteristic
291C2×#107—431no—
292C2×#107—431no—
293C2×#106—861no—
294#416—861no—
295#367—431no—
296#367—431no—
297#367—431no—
298#367C2×D4311yescharacteristic, complemented
299#366—431no—
300#366—431no—
301#366—431no—
302#366C2×D4311yescharacteristic, complemented
303#358—431no—
304#358—431no—
305#358C2×D4311yescharacteristic, complemented
306#358C2×D4311yescharacteristic, complemented
307#357—431no—
308#357—431no—
309#357—431no—
310#357—431no—
311C22⋊C16—431no—
312C22⋊C16—431no—
313C22⋊C16—431no—
314C22⋊C16C2×D4311yescharacteristic
315C43#3364511yescharacteristic, complemented, Sylow
316C2×#41—861no—
317C23×C4—431no—
318#135—862no—
319#135—862no—
320C2×Q16C22×D4311yescharacteristic
321C2×SD16—861no—
322C2×D8—431no—
323C22×C8—431no—
324C22×C8—431no—
325C22×C8—431no—
326C22×C8—431no—
327C22×C8—431no—
328C22×C8—862no—
329C22×C8—862no—
330C22×C8C22×D4311yescharacteristic
331#123—1721no—
332C22⋊Q8—21no—
333C22⋊Q8—861no—
334#121—861no—
335#121—861no—
336#120—1721no—
337C4×D4—1721no—
338C4×D4—1721no—
339#117—21no—
340#117—861no—
341#117—861no—
342#117—861no—
343#117—861no—
344#117—1721no—
345#117—1721no—
346C2×C4⋊C4—861no—
347C2×C4⋊C4—861no—
348C2×C22⋊C4—1721no—
349C2×C42—1721no—
350C2×C16—431no—
351C2×C16—431no—
352C2×C16—862no—
353C2×C16—862no—
354C2×C16C22×D4311yescharacteristic
355C2×C16C22×D4311yescharacteristic
356#107—431no—
357#107—431no—
358#107—431no—
359#107—861no—
360#107—861no—
361#107C22×D4311yescharacteristic
362#107C22×D4311yescharacteristic
363#107C22×D4311yescharacteristic
364#106—21no—
365#106—861no—
366#106—861no—
367#106—861no—
368#106—861no—
369#103—21no—
370#103—861no—
371#102—861no—
372#102—861no—
373C24—431no—
374#41—1722no—
375#41—1722no—
376C2×Q8—21no—
377C2×D4—861no—
378C2×D4—1721no—
379C2×D4—1721no—
380C2×D4—1721no—
381C22×C4—431no—
382C22×C4—431no—
383C22×C4—431no—
384C22×C4—431no—
385C22×C4—431no—
386C22×C4—862no—
387C22×C4—862no—
388C22×C4—1721no—
389C22×C4—1721no—
390C22×C4—1721no—
391C22×C4D4×D4311yescharacteristic
392Q16—21no—
393Q16—21no—
394SD16—1722no—
395D8—861no—
396D8—861no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—431no—
400C2×C8—432no—
401C2×C8—432no—
402C2×C8—431no—
403C2×C8—862no—
404C2×C8—862no—
405C2×C8—862no—
406C2×C8—861no—
407C2×C8—861no—
408C2×C8D4×D4311yescharacteristic
409C2×C8C23×D4311yescharacteristic
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—41no—
414C4⋊C4—861no—
415C4⋊C4—861no—
416C4⋊C4—861no—
417C4⋊C4—1721no—
418C4⋊C4—1721no—
419C4⋊C4—1721no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—1721no—
423C22⋊C4—1721no—
424C22⋊C4—1721no—
425C22⋊C4—1721no—
426C22⋊C4—1721no—
427C22⋊C4—1721no—
428C22⋊C4—1721no—
429C42—41no—
430C42—1721no—
431C42—1721no—
432C42—1721no—
433C42—1721no—
434C16—21no—
435C16—21no—
436C16—861no—
437C16—861no—
438C23—431no—
439C23—431no—
440C23—862no—
441C23—862no—
442C23—1721no—
443C23—1721no—
444C23D8×D4311yescharacteristic
445Q8—41no—
446Q8—41no—
447D4—3442no—
448D4—3442no—
449D4—3442no—
450D4—1721no—
451D4—1721no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—431no—
459C2×C4—432no—
460C2×C4—432no—
461C2×C4—431no—
462C2×C4—862no—
463C2×C4—862no—
464C2×C4—862no—
465C2×C4—861no—
466C2×C4—861no—
467C2×C4—3442no—
468C2×C4—3442no—
469C2×C4—3442no—
470C2×C4—1721no—
471C2×C4—1721no—
472C2×C4—1721no—
473C2×C4D8×D4311yescharacteristic
474C2×C4C2×D4×D4311yescharacteristic
475C8—21no—
476C8—432no—
477C8—861no—
478C8#41×D4311yescharacteristic
479C8#41×D4311yescharacteristic
480C22—21no—
481C22—21no—
482C22—21no—
483C22—432no—
484C22—432no—
485C22—861no—
486C22—861no—
487C22—861no—
488C22—861no—
489C22—3441no—
490C22—3441no—
491C22—3441no—
492C22—1724no—
493C22C2×D8×D4311yescharacteristic
494C4—21no—
495C4—81no—
496C4—81no—
497C4—81no—
498C4—81no—
499C4—432no—
500C4—861no—
501C4—3441no—
502C4—3441no—
503C4—3441no—
504C4#123×D4311yescharacteristic
505C4#137×D4311yescharacteristic
506C2—41no—
507C2—862no—
508C2—862no—
509C2—6881no—
510C2#480×D4311yescharacteristic
511C2#508×D4311yescharacteristic
512C2#1914773011yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2237C2
socleC22×C43C22×D8
prime radical#19144178C2
hypercenter#2237D43
hypocenterC43#33645
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2237

Complements

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

NH ≅ G/Ntype
2. #427×D43C2semidirect
3. #19136800C2semidirect
4. #19136796C2semidirect
5. #19136791C2semidirect
6. #19136787C2semidirect
7. #19136786C2semidirect
8. #19136782C2semidirect
9. #19136777C2semidirect
10. #19136378C2semidirect
11. #19136376C2semidirect
12. #19136301C2semidirect
13. #19136301C2semidirect
14. C22⋊C16×D43C2semidirect
15. C43×#2237C2semidirect
37. #14582727C22semidirect
38. #14582726C22semidirect
39. #14582726C22semidirect
40. #14582725C22semidirect
41. #14582724C22semidirect
42. #14582724C22semidirect
43. #14582703C22semidirect
44. #14582703C22semidirect
45. #14582701C22semidirect
46. #14582701C22semidirect
47. #14582699C22semidirect
48. #14582699C22semidirect
54. C43×#367C22semidirect
55. C43×#366C22semidirect
56. C43×#358C22semidirect
57. C43×#358C22semidirect
253. #2237D43semidirect
298. #367C2×D43semidirect
302. #366C2×D43semidirect
305. #358C2×D43semidirect
306. #358C2×D43semidirect
315. C43#33645semidirect

Maximal subgroups

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

subgroupindex
#191441782
#427×D432
#191368002
#191367962
#191367912
#191367872
#191367862
#191367822
#191367772
#191363782
#191363762
#191363012
C22⋊C16×D432
C43×#22372
#3364543