Finite Group Databasebeta

← #25251663

Subgroups — #25251663

Order 11008.

612 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145168C211yesmaximal, characteristic, complemented
2C4×D8×D43C211yesmaximal, characteristic, complemented
3#19136791C211yesmaximal, characteristic, complemented
4#19136777C211yesmaximal, characteristic, complemented
5#19136755C211yesmaximal, characteristic, complemented
6#19136754C211yesmaximal, characteristic, complemented
7#19136653C211yesmaximal, characteristic, complemented
8#19136652C211yesmaximal, characteristic, complemented
9#19136522C211yesmaximal, characteristic, complemented
10#19136508C211yesmaximal, characteristic
11#19136472C211yesmaximal, characteristic, complemented
12#19136469C211yesmaximal, characteristic, complemented
13#19136457C211yesmaximal, characteristic, complemented
14#19136396C211yesmaximal, characteristic, complemented
15C43×#2175C211yesmaximal, characteristic, complemented
16C2×D8×D43C2211yescharacteristic
17#14583436—21no—
18C4×D4×D43—21no—
19C2×#13063268C2211yescharacteristic
20C2×D688C2211yescharacteristic
21C2×#13063266C2211yescharacteristic
22#14583300C2211yescharacteristic, complemented
23#14583284C2211yescharacteristic, complemented
24#14583255—21no—
25#14583137C2211yescharacteristic
26#14583136C2211yescharacteristic
27#14583131—21no—
28C4×#10621884—21no—
29C4×D344C2211yescharacteristic
30C4×D344C2211yescharacteristic, complemented
31D8×Dic43C2211yescharacteristic
32#14582981C2211yescharacteristic
33C4×#10621882—21no—
34#14582979—21no—
35#107×D43C2211yescharacteristic
36#102×D43—21no—
37C4×C8×D43C2211yescharacteristic
38#14582727C2211yescharacteristic, complemented
39#14582726C2211yescharacteristic, complemented
40#14582724C2211yescharacteristic, complemented
41Dic43⋊C16C2211yescharacteristic, complemented
42Dic43⋊C16C2211yescharacteristic, complemented
43#14582703C2211yescharacteristic, complemented
44#14582701C2211yescharacteristic
45#14582701C2211yescharacteristic, complemented
46#14582700C2211yescharacteristic
47#14582699C2211yescharacteristic
48#14582699C2211yescharacteristic, complemented
49(C2×D43)⋊C16C2211yescharacteristic
50(C2×D43)⋊C16C2211yescharacteristic
51#14582675C2211yescharacteristic, complemented
52C2×SD32×C43C2211yescharacteristic
53C4×Q16×C43C2211yescharacteristic, complemented
54C4×D8×C43C2211yescharacteristic
55C43×#366C2211yescharacteristic, complemented
56C43×#358C2211yescharacteristic, complemented
57C43×#357C2211yescharacteristic
58C43×#346C2211yescharacteristic, complemented
59C2×D4×D43—21no—
60C22×C4×D43—41no—
61C2×#10621884—21no—
62C2×D344C2311yescharacteristic
63C2×D344C2311yescharacteristic
64C2×#10621882—21no—
65D8×D43—22no—
66D8×D43—22no—
67C2×C8×D43D411yescharacteristic
68C2×C8×D43C2311yescharacteristic
69#13063320—41no—
70#13063316—21no—
71#13063314—21no—
72#13063310—41no—
73#13063301—21no—
74#13063300—21no—
75C4×D172—21no—
76C4×D172—21no—
77C4×D172—41no—
78D4×Dic43—21no—
79#13063287—21no—
80C4×C22⋊D43—41no—
81(C22⋊D43)⋊C4—41no—
82#13063282—41no—
83C4⋊C4×D43—21no—
84C22⋊C4×D43—41no—
85C42×D43D411yescharacteristic
86#13063268—22no—
87D688—22no—
88#13063266—22no—
89C2×C43⋊C16C2311yescharacteristic
90C2×C43⋊C16C2311yescharacteristic
91#13063259C2311yescharacteristic
92#13063259C2311yescharacteristic
93#13063258—21no—
94#13063256—21no—
95#13063249—21no—
96#13063247—21no—
97#13063247—21no—
98#13063246—21no—
99#13063245—21no—
100#13063245—21no—
101C4×C43⋊C8D411yescharacteristic
102C8×Dic43D411yescharacteristic
103C8×Dic43C2311yescharacteristic
104C2×Q16×C43C2311yescharacteristic
105C2×D8×C43C2311yescharacteristic
106C4×Q8×C43—21no—
107C4×D4×C43—21no—
108SD32×C43—22no—
109C2×C16×C43C2311yescharacteristic
110C2×C16×C43C2311yescharacteristic
111#107×C43C2311yescharacteristic
112#107×C43C2311yescharacteristic
113#103×C43—21no—
114#102×C43—21no—
115C4×C8×C43C2311yescharacteristic
116C23×D43—41no—
117C2×Q8×C43—21no—
118C2×D4×C43—21no—
119C22×C4×C43—41no—
120C2×C22⋊D43—41no—
121C22×Dic43—41no—
122D4×D43—24no—
123D4×D43—42no—
124C2×D172—21no—
125C2×D172—21no—
126C2×D172—41no—
127C2×C4×D43—41no—
128C2×C4×D43—41no—
129C2×C4×D43—41no—
130C2×C4×D43—41no—
131C2×C4×D43—84no—
132C2×C4×D43D811yescharacteristic
133C2×C4×D43D811yescharacteristic
134C2×C4×D43C2×D411yescharacteristic
135Q16×C43—21no—
136Q16×C43—21no—
137D8×C43—21no—
138D8×C43#4112yes—
139C2×C8×C43C2×D411yescharacteristic
140C2×C8×C43C2411yescharacteristic
141C4⋊C4×C43—21no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—41no—
144C22⋊C4×C43—41no—
145C42×C43—41no—
146C42×C43C2×D411yescharacteristic
147C22⋊Dic43—41no—
148#10621884—42no—
149#10621882—24no—
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—
156(C2×D43)⋊C4—41no—
157C4⋊Dic43—21no—
158C4⋊Dic43—21no—
159C4⋊Dic43—41no—
160Dic43⋊C4—41no—
161Dic43⋊C4—41no—
162Dic43⋊C4—41no—
163C4×Dic43D811yescharacteristic
164C4×Dic43D811yescharacteristic
165C4×Dic43C2×D411yescharacteristic
166C2×C43⋊C8C2×D411yescharacteristic
167C2×C43⋊C8C2×D411yescharacteristic
168D344—21no—
169D344—21no—
170D344—21no—
171D344#4112yes—
172C8×D43—21no—
173C8×D43—21no—
174C8×D43—41no—
175C16×C43—21no—
176C16×C43—21no—
177C43⋊C16—21no—
178C43⋊C16—21no—
179C23×C43—41no—
180C22×D43—44no—
181C22×D43—41no—
182C22×D43—41no—
183C22×D43—82no—
184C22×D43—82no—
185C22×D43C2×D811yescharacteristic
186Q8×C43—41no—
187Q8×C43—41no—
188D4×C43—22no—
189D4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—82no—
194C2×C4×C43C2×D811yescharacteristic
195C2×C4×C43C2×D811yescharacteristic
196C2×C4×C43C22×D411yescharacteristic
197C22⋊D43—44no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—82no—
201C2×Dic43C2×D811yescharacteristic
202C2×Dic43C2×D811yescharacteristic
203C2×Dic43C2×D811yescharacteristic
204D172—22no—
205D172—41no—
206D172—41no—
207D172—41no—
208D172—82no—
209C4×D43—22no—
210C4×D43—21no—
211C4×D43—21no—
212C4×D43—41no—
213C4×D43—82no—
214C4×D43—82no—
215C4×D43—82no—
216C4×D43—82no—
217C8×C43—21no—
218C8×C43C2×#4111yescharacteristic
219C8×C43C2×#4111yescharacteristic
220C43⋊C8—21no—
221C43⋊C8—21no—
222#33674—431nomaximal, Sylow
223C22×C43—42no—
224C22×C43—81no—
225C22×C43—81no—
226C22×C43C22×D811yescharacteristic
227C2×D43—21no—
228C2×D43—21no—
229C2×D43—42no—
230C2×D43—88no—
231C2×D43—81no—
232C2×D43—81no—
233C2×D43—81no—
234C2×D43—81no—
235C2×D43—81no—
236C2×D43#50912yes—
237C4×C43—21no—
238C4×C43—21no—
239C4×C43—81no—
240C4×C43—81no—
241C4×C43—81no—
242C4×C43#52511yescharacteristic
243C4×C43#57511yescharacteristic
244Dic43—21no—
245Dic43—21no—
246Dic43—21no—
247Dic43—81no—
248Dic43—81no—
249#3168—431no—
250C2×C4×D8—431no—
251#2235—431no—
252#2232—431no—
253#2228—431no—
254#2228—431no—
255#2210—431no—
256#2210—431no—
257#2187—431no—
258#2184—431no—
259#2177—431no—
260#2177—431no—
261#2175—431no—
262#2175D4311yescharacteristic, complemented
263#2163—431no—
264C2×C43—82no—
265C2×C43#310011yescharacteristic
266C2×C43C2×#50911yescharacteristic
267C2×C43#341411yescharacteristic
268D43—22no—
269D43—82no—
270D43—161no—
271C22×D8—431no—
272#529—861no—
273C2×C4×D4—861no—
274C2×SD32—431no—
275C2×SD32C2×D4311yescharacteristic
276C2×D16—431no—
277C2×D16—431no—
278#499—431no—
279#495—431no—
280#488—861no—
281#467—431no—
282#466—431no—
283#465—861no—
284C4×Q16C2×D4311yescharacteristic, complemented
285C4×SD16—861no—
286C4×D8—431no—
287C4×D8—431no—
288C4×D8—431no—
289C4×D8—431no—
290C4×D8—861no—
291C4×D8—861no—
292C4×D8C2×D4311yescharacteristic
293C2×#107—431no—
294C2×#102—861no—
295C2×C4×C8—431no—
296#367—431no—
297#367—431no—
298#366—431no—
299#366C2×D4311yescharacteristic, complemented
300C4⋊C16—431no—
301C4⋊C16—431no—
302#358—431no—
303#358C2×D4311yescharacteristic, complemented
304#357—431no—
305#357—431no—
306#357—431no—
307#357—431no—
308#357—431no—
309#357C2×D4311yescharacteristic
310C22⋊C16—431no—
311C22⋊C16—431no—
312#346—431no—
313#346C2×D4311yescharacteristic, complemented
314C43#3367411yescharacteristic, complemented, Sylow
315C22×D4—861no—
316C23×C4—1721no—
317C2×Q16C22×D4311yescharacteristic
318C2×SD16—861no—
319C2×D8—431no—
320C2×D8—431no—
321C2×D8—861no—
322C2×D8—862no—
323C2×D8—862no—
324C2×D8C22×D4311yescharacteristic
325C22×C8—431no—
326C22×C8—431no—
327#126—1721no—
328#125—861no—
329#124—861no—
330#123—1721no—
331C22⋊Q8—861no—
332#121—861no—
333C4×Q8—21no—
334C4×D4—21no—
335C4×D4—861no—
336C4×D4—861no—
337C4×D4—861no—
338C4×D4—861no—
339C4×D4—1721no—
340C4×D4—1721no—
341C4×D4—1721no—
342#117—1721no—
343C2×C4⋊C4—861no—
344C2×C22⋊C4—1721no—
345C2×C42—431no—
346SD32—22no—
347SD32—862no—
348D16—862no—
349D16—862no—
350C2×C16—431no—
351C2×C16—431no—
352C2×C16C22×D4311yescharacteristic
353C2×C16C22×D4311yescharacteristic
354#107—431no—
355#107—431no—
356#107—861no—
357#107C22×D4311yescharacteristic
358#107C22×D4311yescharacteristic
359#106—861no—
360#103—21no—
361#103—861no—
362#102—21no—
363#102—861no—
364#102—861no—
365#102—861no—
366#102—861no—
367#102—861no—
368C4×C8—431no—
369C4×C8—431no—
370C4×C8—431no—
371C4×C8C22×D4311yescharacteristic
372C24—1721no—
373C2×Q8—21no—
374C2×D4—21no—
375C2×D4—864no—
376C2×D4—861no—
377C2×D4—861no—
378C2×D4—1721no—
379C2×D4—1721no—
380C2×D4—1722no—
381C22×C4—41no—
382C22×C4—431no—
383C22×C4—431no—
384C22×C4—431no—
385C22×C4—3444no—
386C22×C4—1721no—
387C22×C4—1721no—
388C22×C4—1721no—
389C22×C4—1721no—
390C22×C4—1721no—
391Q16—21no—
392Q16—21no—
393SD16—1722no—
394D8—21no—
395D8—432no—
396D8—864no—
397D8—861no—
398D8—861no—
399D8—861no—
400D8#1062189812yes—
401C2×C8—431no—
402C2×C8—431no—
403C2×C8—861no—
404C2×C8—861no—
405C2×C8—1721no—
406C2×C8D4×D4311yescharacteristic
407C2×C8C23×D4311yescharacteristic
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—41no—
411C4⋊C4—861no—
412C4⋊C4—861no—
413C4⋊C4—1721no—
414C4⋊C4—1721no—
415C4⋊C4—1721no—
416C4⋊C4—1721no—
417C22⋊C4—41no—
418C22⋊C4—1721no—
419C22⋊C4—1721no—
420C22⋊C4—1721no—
421C22⋊C4—1721no—
422C22⋊C4—1721no—
423C22⋊C4—1721no—
424C22⋊C4—1721no—
425C22⋊C4—1721no—
426C42—41no—
427C42—431no—
428C42—431no—
429C42—431no—
430C42D4×D4311yescharacteristic
431C16—21no—
432C16—21no—
433C16—861no—
434C16—861no—
435C23—41no—
436C23—431no—
437C23—3442no—
438C23—3442no—
439C23—1724no—
440C23—1721no—
441C23—1721no—
442Q8—41no—
443Q8—41no—
444D4—22no—
445D4—41no—
446D4—862no—
447D4—3442no—
448D4—1724no—
449D4—1721no—
450D4—1721no—
451D4—1721no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—82no—
456C2×C4—431no—
457C2×C4—431no—
458C2×C4—431no—
459C2×C4—862no—
460C2×C4—861no—
461C2×C4—861no—
462C2×C4—3442no—
463C2×C4—3442no—
464C2×C4—3442no—
465C2×C4—3442no—
466C2×C4—3442no—
467C2×C4—1721no—
468C2×C4—1721no—
469C2×C4—1721no—
470C2×C4D8×D4311yescharacteristic
471C2×C4D8×D4311yescharacteristic
472C2×C4C2×D4×D4311yescharacteristic
473C8—21no—
474C8—861no—
475C8—861no—
476C8#41×D4311yescharacteristic
477C8C2×#1062189811yescharacteristic
478C22—42no—
479C22—81no—
480C22—81no—
481C22—432no—
482C22—861no—
483C22—861no—
484C22—3448no—
485C22—3441no—
486C22—3441no—
487C22—3441no—
488C22—3441no—
489C22—3441no—
490C22—1722no—
491C22C2×D8×D4311yescharacteristic
492C4—21no—
493C4—21no—
494C4—81no—
495C4—81no—
496C4—81no—
497C4—861no—
498C4—861no—
499C4—861no—
500C4—3441no—
501C4—3441no—
502C4#1458340811yescharacteristic
503C4#1458369611yescharacteristic
504C2—82no—
505C2—862no—
506C2—3442no—
507C2—6881no—
508C2#1914459311yescharacteristic
509C2#509×D4311yescharacteristic
510C2#1914773011yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2175C2
socleC22×C43C22×D8
prime radical#19136508C2
hypercenter#2175D43
hypocenterC43#33674
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2175

Complements

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

NH ≅ G/Ntype
1. #19145168C2semidirect
2. C4×D8×D43C2semidirect
3. #19136791C2semidirect
4. #19136777C2semidirect
5. #19136755C2semidirect
6. #19136754C2semidirect
7. #19136653C2semidirect
8. #19136652C2semidirect
9. #19136522C2semidirect
11. #19136472C2semidirect
12. #19136469C2semidirect
13. #19136457C2semidirect
14. #19136396C2semidirect
15. C43×#2175C2semidirect
22. #14583300C22semidirect
23. #14583284C22semidirect
30. C4×D344C22semidirect
38. #14582727C22semidirect
39. #14582726C22semidirect
40. #14582724C22semidirect
41. Dic43⋊C16C22semidirect
42. Dic43⋊C16C22semidirect
43. #14582703C22semidirect
45. #14582701C22semidirect
48. #14582699C22semidirect
51. #14582675C22semidirect
53. C4×Q16×C43C22semidirect
55. C43×#366C22semidirect
56. C43×#358C22semidirect
58. C43×#346C22semidirect
262. #2175D43semidirect
284. C4×Q16C2×D43semidirect
299. #366C2×D43semidirect
303. #358C2×D43semidirect
313. #346C2×D43semidirect
314. C43#33674semidirect

Maximal subgroups

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

subgroupindex
#191451682
C4×D8×D432
#191367912
#191367772
#191367552
#191367542
#191366532
#191366522
#191365222
#191365082
#191364722
#191364692
#191364572
#191363962
C43×#21752
#3367443