Finite Group Databasebeta

← #25251709

Subgroups — #25251709

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145236C211yesmaximal, characteristic, complemented
2#19143442C211yesmaximal, characteristic, complemented
3#19136801C211yesmaximal, characteristic, complemented
4#19136789C211yesmaximal, characteristic, complemented
5#19136740C211yesmaximal, characteristic, complemented
6#19136731C211yesmaximal, characteristic, complemented
7#19136653C211yesmaximal, characteristic, complemented
8#19136652C211yesmaximal, characteristic, complemented
9#19136522C211yesmaximal, characteristic, complemented
10#19136508C211yesmaximal, characteristic
11#19136472C211yesmaximal, characteristic, complemented
12C4×#13063268C211yesmaximal, characteristic, complemented
13C4×#13063266C211yesmaximal, characteristic, complemented
14#19136403C211yesmaximal, characteristic, complemented
15C43×#2175C211yesmaximal, characteristic, complemented
16C2×D8×D43C2211yescharacteristic
17#14583521—21no—
18#14583371—21no—
19C2×#13063268C2211yescharacteristic
20C2×D688C2211yescharacteristic
21C2×#13063266C2211yescharacteristic
22#14583303C2211yescharacteristic, complemented
23#14583284C2211yescharacteristic, complemented
24#14583260—21no—
25#14583148—21no—
26#14583137C2211yescharacteristic
27#14583136C2211yescharacteristic
28#14583009—21no—
29#14583008—21no—
30#14582997—21no—
31C4×D344C2211yescharacteristic
32C4×D344C2211yescharacteristic, complemented
33D8×Dic43C2211yescharacteristic
34#14582981C2211yescharacteristic
35#14582936C2211yescharacteristic
36#14582902—21no—
37#14582853C2211yescharacteristic
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
51C4×C43⋊C16C2211yescharacteristic, 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—
60C2×#10621884—21no—
61C2×D344C2311yescharacteristic
62C2×D344C2311yescharacteristic
63C2×#10621882—21no—
64D8×D43—22no—
65D8×D43—22no—
66C2×#10621872D411yescharacteristic
67C2×C8×D43C2311yescharacteristic
68#13063324—21no—
69#13063319—41no—
70#13063314—21no—
71#13063313—41no—
72#13063310—41no—
73#13063303—41no—
74#13063301—21no—
75#13063300—21no—
76C4×D172—21no—
77C4×D172—21no—
78D4×Dic43—21no—
79#13063287—21no—
80C4×C22⋊D43—41no—
81(C22⋊D43)⋊C4—41no—
82#13063283—21no—
83#13063282D411yescharacteristic
84C2×(C2×D43)⋊C4—41no—
85C22⋊C4×D43—41no—
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—
101#13063236D411yescharacteristic
102#13063235D411yescharacteristic
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×D43C2×D411yescharacteristic
131C2×Dic86—41no—
132Q16×C43—21no—
133Q16×C43—21no—
134D8×C43—21no—
135D8×C43#4112yes—
136C2×C8×C43C2×D411yescharacteristic
137C2×C8×C43C2411yescharacteristic
138C4⋊C4×C43—21no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—41no—
141C22⋊C4×C43—41no—
142C42×C43—41no—
143C42×C43C2×D411yescharacteristic
144C22⋊Dic43—41no—
145#10621884—42no—
146#10621882—24no—
147(C2×D43)⋊C4—41no—
148(C2×D43)⋊C4—41no—
149(C2×D43)⋊C4—41no—
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)⋊C4D811yescharacteristic
156(C2×D43)⋊C4D811yescharacteristic
157C4⋊Dic43—21no—
158C4⋊Dic43—21no—
159Dic43⋊C4—41no—
160Dic43⋊C4—41no—
161Dic43⋊C4D811yescharacteristic
162Dic43⋊C4D811yescharacteristic
163C4×Dic43—41no—
164C4×Dic43C2×D411yescharacteristic
165C2×C43⋊C8C2×D411yescharacteristic
166C2×C43⋊C8C2×D411yescharacteristic
167D344—21no—
168D344—21no—
169D344—21no—
170D344#4112yes—
171#10621872—41no—
172C8×D43—21no—
173C8×D43—21no—
174C16×C43—21no—
175C16×C43—21no—
176C43⋊C16—21no—
177C43⋊C16—21no—
178C23×C43—41no—
179C22×D43—44no—
180C22×D43—41no—
181C22×D43—41no—
182C22×D43—161no—
183C22×D43—161no—
184C22×D43C2×D811yescharacteristic
185Q8×C43—41no—
186Q8×C43—41no—
187D4×C43—22no—
188D4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—161no—
193C2×C4×C43C2×D811yescharacteristic
194C2×C4×C43C2×D811yescharacteristic
195C2×C4×C43C22×D411yescharacteristic
196C22⋊D43—44no—
197C2×Dic43—41no—
198C2×Dic43—41no—
199C2×Dic43—161no—
200C2×Dic43C2×D811yescharacteristic
201C2×Dic43C2×D811yescharacteristic
202C2×Dic43C2×D811yescharacteristic
203D172—22no—
204D172—41no—
205D172—41no—
206D172—41no—
207D172—161no—
208C4×D43—21no—
209C4×D43—21no—
210C4×D43—161no—
211C4×D43—161no—
212C4×D43—161no—
213Dic86—161no—
214C8×C43—21no—
215C8×C43C2×#4111yescharacteristic
216C8×C43C2×#4111yescharacteristic
217C43⋊C8—21no—
218C43⋊C8—21no—
219#33678—431nomaximal, Sylow
220C22×C43—42no—
221C22×C43—81no—
222C22×C43—81no—
223C22×C43C22×D811yescharacteristic
224C2×D43—21no—
225C2×D43—21no—
226C2×D43—21no—
227C2×D43—42no—
228C2×D43—81no—
229C2×D43—81no—
230C2×D43—81no—
231C2×D43—81no—
232C2×D43—81no—
233C2×D43—164no—
234C4×C43—21no—
235C4×C43—21no—
236C4×C43—81no—
237C4×C43—81no—
238C4×C43—81no—
239C4×C43#52511yescharacteristic
240C4×C43#57511yescharacteristic
241Dic43—21no—
242Dic43—21no—
243Dic43—21no—
244Dic43—81no—
245Dic43—81no—
246#3175—431no—
247#2948—431no—
248#2237—431no—
249#2234—431no—
250#2226—431no—
251#2224—431no—
252#2210—431no—
253#2210—431no—
254#2187—431no—
255#2184—431no—
256#2177—431no—
257#2175D4311yescharacteristic, complemented
258C4×SD32—431no—
259C4×D16—431no—
260#2164—431no—
261C2×C43—82no—
262C2×C43#310011yescharacteristic
263C2×C43#341511yescharacteristic
264C2×C43#341611yescharacteristic
265D43—41no—
266D43—82no—
267D43—161no—
268C22×D8—431no—
269#542—861no—
270#518—861no—
271C2×SD32—431no—
272C2×SD32C2×D4311yescharacteristic
273C2×D16—431no—
274C2×D16—431no—
275#500—431no—
276#495—431no—
277#489—861no—
278#468—861no—
279#467—431no—
280#466—431no—
281#442—861no—
282#442—861no—
283#440—861no—
284C4×Q16C2×D4311yescharacteristic, complemented
285C4×D8—431no—
286C4×D8—431no—
287C4×D8—431no—
288C4×D8—431no—
289C4×D8C2×D4311yescharacteristic
290#427—431no—
291#418—861no—
292#405—431no—
293#367—431no—
294#367—431no—
295#366—431no—
296#366C2×D4311yescharacteristic, complemented
297C4⋊C16—431no—
298C4⋊C16—431no—
299#358—431no—
300#358C2×D4311yescharacteristic, complemented
301#357—431no—
302#357—431no—
303#357—431no—
304#357—431no—
305#357—431no—
306#357C2×D4311yescharacteristic
307C22⋊C16—431no—
308C22⋊C16—431no—
309#346C2×D4311yescharacteristic, complemented
310C4×C16—431no—
311C43#3367811yescharacteristic, complemented, Sylow
312C22×D4—861no—
313C2×Q16C22×D4311yescharacteristic
314C2×SD16—861no—
315C2×D8—431no—
316C2×D8—431no—
317C2×D8—861no—
318C2×D8—862no—
319C2×D8—862no—
320C2×D8C22×D4311yescharacteristic
321C2×M16—431no—
322C22×C8—431no—
323C4⋊Q8—861no—
324#126—1721no—
325#124—861no—
326#124—1721no—
327#123—1721no—
328C22⋊Q8—861no—
329C22⋊Q8—1721no—
330#121—861no—
331C4×Q8—21no—
332C4×D4—21no—
333C4×D4—861no—
334C4×D4—861no—
335C4×D4—861no—
336C4×D4—861no—
337C4×D4—1721no—
338C4×D4—1721no—
339#117—431no—
340#117—861no—
341C2×C22⋊C4—1721no—
342C2×C22⋊C4—1721no—
343SD32—22no—
344SD32—862no—
345D16—862no—
346D16—862no—
347C2×C16—431no—
348C2×C16—431no—
349C2×C16C22×D4311yescharacteristic
350C2×C16C22×D4311yescharacteristic
351#107—431no—
352#107—431no—
353#107—861no—
354#107C22×D4311yescharacteristic
355#107C22×D4311yescharacteristic
356#106—861no—
357#103—21no—
358#103—861no—
359#102—21no—
360#102—861no—
361#102—861no—
362#102—861no—
363#102—861no—
364#102—861no—
365#97—431no—
366#97—431no—
367C4×C8—431no—
368C4×C8C22×D4311yescharacteristic
369C24—1721no—
370C2×Q8—21no—
371C2×Q8—1721no—
372C2×D4—21no—
373C2×D4—864no—
374C2×D4—861no—
375C2×D4—861no—
376C2×D4—1721no—
377C2×D4—1721no—
378C2×D4—1722no—
379C22×C4—41no—
380C22×C4—431no—
381C22×C4—1721no—
382C22×C4—1721no—
383C22×C4—1721no—
384C22×C4—1721no—
385Q16—21no—
386Q16—21no—
387SD16—1722no—
388D8—21no—
389D8—432no—
390D8—864no—
391D8—861no—
392D8—861no—
393D8—861no—
394D8#1062189812yes—
395M16—1721no—
396C2×C8—431no—
397C2×C8—431no—
398C2×C8—861no—
399C2×C8—861no—
400C2×C8D4×D4311yescharacteristic
401C2×C8C23×D4311yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—431no—
406C4⋊C4—431no—
407C4⋊C4—861no—
408C4⋊C4—861no—
409C4⋊C4—1721no—
410C4⋊C4—1721no—
411C22⋊C4—41no—
412C22⋊C4—431no—
413C22⋊C4—431no—
414C22⋊C4—1721no—
415C22⋊C4—1721no—
416C22⋊C4—1721no—
417C22⋊C4—1721no—
418C22⋊C4—1721no—
419C22⋊C4—1721no—
420C22⋊C4—1721no—
421C22⋊C4—1721no—
422C22⋊C4—1721no—
423C42—41no—
424C42—431no—
425C42—1721no—
426C42D4×D4311yescharacteristic
427C16—21no—
428C16—21no—
429C16—861no—
430C16—861no—
431C23—41no—
432C23—431no—
433C23—1724no—
434C23—1721no—
435C23—1721no—
436C23—6881no—
437C23—6881no—
438Q8—41no—
439Q8—41no—
440Q8—6881no—
441D4—22no—
442D4—41no—
443D4—862no—
444D4—1724no—
445D4—1721no—
446D4—1721no—
447D4—1721no—
448D4—6881no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—161no—
453C2×C4—431no—
454C2×C4—431no—
455C2×C4—431no—
456C2×C4—861no—
457C2×C4—861no—
458C2×C4—1721no—
459C2×C4—1721no—
460C2×C4—6881no—
461C2×C4—6881no—
462C2×C4—6881no—
463C2×C4—6881no—
464C2×C4D8×D4311yescharacteristic
465C2×C4D8×D4311yescharacteristic
466C2×C4C2×D4×D4311yescharacteristic
467C8—21no—
468C8—861no—
469C8—861no—
470C8#41×D4311yescharacteristic
471C8C2×#1062189811yescharacteristic
472C22—42no—
473C22—81no—
474C22—81no—
475C22—861no—
476C22—861no—
477C22—861no—
478C22—3441no—
479C22—3441no—
480C22—3441no—
481C22—3441no—
482C22—3441no—
483C22—1722no—
484C22—6884no—
485C22C2×D8×D4311yescharacteristic
486C4—21no—
487C4—21no—
488C4—81no—
489C4—81no—
490C4—81no—
491C4—861no—
492C4—861no—
493C4—861no—
494C4—3441no—
495C4—3441no—
496C4#1458340811yescharacteristic
497C4#1458369611yescharacteristic
498C2—82no—
499C2—3442no—
500C2—1721no—
501C2—6881no—
502C2#1914459311yescharacteristic
503C2#1914773511yescharacteristic
504C2#1914774011yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2175C2
socleC22×C43C22×D8
prime radical#19136508C2
hypercenter#2175D43
hypocenterC43#33678
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. #19145236C2semidirect
2. #19143442C2semidirect
3. #19136801C2semidirect
4. #19136789C2semidirect
5. #19136740C2semidirect
6. #19136731C2semidirect
7. #19136653C2semidirect
8. #19136652C2semidirect
9. #19136522C2semidirect
11. #19136472C2semidirect
12. C4×#13063268C2semidirect
13. C4×#13063266C2semidirect
14. #19136403C2semidirect
15. C43×#2175C2semidirect
22. #14583303C22semidirect
23. #14583284C22semidirect
32. C4×D344C22semidirect
38. #14582727C22semidirect
39. #14582726C22semidirect
40. #14582724C22semidirect
41. Dic43⋊C16C22semidirect
42. Dic43⋊C16C22semidirect
43. #14582703C22semidirect
45. #14582701C22semidirect
48. #14582699C22semidirect
51. C4×C43⋊C16C22semidirect
53. C4×Q16×C43C22semidirect
55. C43×#366C22semidirect
56. C43×#358C22semidirect
58. C43×#346C22semidirect
257. #2175D43semidirect
284. C4×Q16C2×D43semidirect
296. #366C2×D43semidirect
300. #358C2×D43semidirect
309. #346C2×D43semidirect
311. C43#33678semidirect

Maximal subgroups

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

subgroupindex
#191452362
#191434422
#191368012
#191367892
#191367402
#191367312
#191366532
#191366522
#191365222
#191365082
#191364722
C4×#130632682
C4×#130632662
#191364032
C43×#21752
#3367843