Finite Group Databasebeta

← #25251700

Subgroups — #25251700

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#19145227C211yesmaximal, characteristic, complemented
2#19143446C211yesmaximal, characteristic, complemented
3#19136803C211yesmaximal, characteristic, complemented
4#19136741C211yesmaximal, characteristic, complemented
5#19136731C211yesmaximal, characteristic, complemented
6#19136649C211yesmaximal, characteristic, complemented
7#19136649C211yesmaximal, characteristic, complemented
8#19136526C211yesmaximal, characteristic, complemented
9#19136506C211yesmaximal, characteristic
10#19136468C211yesmaximal, characteristic, complemented
11#19136458C211yesmaximal, characteristic, complemented
12#19136446C211yesmaximal, characteristic, complemented
13#19136439C211yesmaximal, characteristic, complemented
14#19136399C211yesmaximal, characteristic, complemented
15C43×#2234C211yesmaximal, characteristic, complemented
16C22×D344C2211yescharacteristic
17#14583516—21no—
18#14583373—21no—
19C2×#13063270C2211yescharacteristic
20C2×#13063270C2211yescharacteristic
21C2×#13063266C2211yescharacteristic
22C2×#13063266C2211yescharacteristic
23#14583303C2211yescharacteristic, complemented
24#14583282C2211yescharacteristic, complemented
25#14583257—21no—
26#14583143—21no—
27#14583140C2211yescharacteristic
28#14583010—21no—
29#14583010—21no—
30#14582996—21no—
31#14582993C2211yescharacteristic, complemented
32D8×Dic43C2211yescharacteristic, complemented
33#14582981C2211yescharacteristic
34#14582981C2211yescharacteristic
35#14582981C2211yescharacteristic
36#14582981C2211yescharacteristic
37#14582903—21no—
38#14582854C2211yescharacteristic
39#14582726C2211yescharacteristic, complemented
40#14582724C2211yescharacteristic, complemented
41Dic43⋊C16C2211yescharacteristic, complemented
42Dic43⋊C16C2211yescharacteristic, complemented
43#14582702C2211yescharacteristic, complemented
44#14582702C2211yescharacteristic, complemented
45#14582701C2211yescharacteristic
46#14582701C2211yescharacteristic
47#14582699C2211yescharacteristic
48#14582699C2211yescharacteristic
49C22⋊(C43⋊C16)C2211yescharacteristic
50#14582674C2211yescharacteristic, complemented
51C16×Dic43C2211yescharacteristic, complemented
52C43×#466C2211yescharacteristic
53C43×#427C2211yescharacteristic
54C43×#367C2211yescharacteristic, complemented
55C43×#366C2211yescharacteristic, complemented
56C43×#357C2211yescharacteristic, complemented
57C43×#357C2211yescharacteristic, complemented
58C43×C22⋊C16C2211yescharacteristic
59C22×D172—21no—
60C2×Dic172C2311yescharacteristic
61C2×#10621883—21no—
62C2×D344—21no—
63C2×D344—22no—
64C2×D344—22no—
65C2×D344C2311yescharacteristic
66C2×D344C2311yescharacteristic
67C2×#10621877D411yescharacteristic
68#13063324—21no—
69#13063318—41no—
70#13063312—21no—
71#13063312—41no—
72#13063306—41no—
73#13063304—21no—
74#13063302—41no—
75#13063290—21no—
76C4×D172—41no—
77C4×D172—41no—
78D4×Dic43—21no—
79#13063287—21no—
80#13063287—21no—
81#13063287—21no—
82#13063287—21no—
83#13063284D411yescharacteristic
84C22⋊C4×D43—41no—
85C22⋊C4×D43—41no—
86#13063270—22no—
87#13063270—22no—
88#13063266—22no—
89#13063266—22no—
90C2×C43⋊C16C2311yescharacteristic
91C2×C43⋊C16C2311yescharacteristic
92#13063259C2311yescharacteristic
93#13063258—21no—
94#13063250—21no—
95#13063248—21no—
96#13063246—21no—
97#13063245—21no—
98#13063245—21no—
99#13063245—21no—
100#13063245—21no—
101#13063235D411yescharacteristic
102#13063235D411yescharacteristic
103C8×Dic43C2311yescharacteristic
104C8×Dic43C2311yescharacteristic
105C2×D8×C43C2311yescharacteristic
106C22×C8×C43C2311yescharacteristic
107#121×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#102×C43—21no—
116C23×D43—41no—
117C2×D4×C43—21no—
118C2×D4×C43—41no—
119C22×C4×C43C2×D411yescharacteristic
120C22×Dic43—41no—
121C2×D172—24no—
122C2×D172—21no—
123C2×D172—21no—
124C2×D172—42no—
125C2×D172—41no—
126C2×C4×D43—41no—
127C2×C4×D43—41no—
128C2×C4×D43—41no—
129C2×C4×D43—41no—
130C2×Dic86—21no—
131C2×Dic86—41no—
132D8×C43—21no—
133D8×C43—21no—
134C2×C8×C43—21no—
135C2×C8×C43—21no—
136C2×C8×C43C2×D411yescharacteristic
137C2×C8×C43C2411yescharacteristic
138C4⋊C4×C43—21no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—21no—
141C22⋊C4×C43—41no—
142C22⋊C4×C43—41no—
143C42×C43—41no—
144C22⋊Dic43—41no—
145C22⋊Dic43—41no—
146C22⋊Dic43—41no—
147C22⋊Dic43—41no—
148C22⋊Dic43D811yescharacteristic
149C22⋊Dic43D811yescharacteristic
150#10621883—42no—
151(C2×D43)⋊C4—41no—
152(C2×D43)⋊C4—41no—
153(C2×D43)⋊C4—41no—
154(C2×D43)⋊C4—41no—
155C4⋊Dic43—21no—
156C4⋊Dic43D811yescharacteristic
157C4⋊Dic43D811yescharacteristic
158Dic43⋊C4—41no—
159Dic43⋊C4—41no—
160Dic43⋊C4—41no—
161C4×Dic43—41no—
162C4×Dic43C2×D411yescharacteristic
163C4×Dic43C2×D411yescharacteristic
164#10621877—41no—
165C2×C43⋊C8C2×D411yescharacteristic
166C2×C43⋊C8C2×D411yescharacteristic
167Dic172—21no—
168Dic172—21no—
169D344—24no—
170D344—21no—
171D344—21no—
172D344#4112yes—
173D344#4112yes—
174C16×C43—21no—
175C16×C43—21no—
176C43⋊C16—21no—
177C43⋊C16—21no—
178C23×C43—41no—
179C23×C43C2×D811yescharacteristic
180C22×D43—41no—
181C22×D43—41no—
182C22×D43—44no—
183C22×D43—161no—
184C22×D43—161no—
185D4×C43—41no—
186D4×C43—41no—
187D4×C43—161no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43C2×D811yescharacteristic
194C2×C4×C43C22×D411yescharacteristic
195C2×Dic43—41no—
196C2×Dic43—41no—
197C2×Dic43—161no—
198C2×Dic43C2×D811yescharacteristic
199C2×Dic43C2×D811yescharacteristic
200C2×Dic43C2×D811yescharacteristic
201C2×Dic43C2×D811yescharacteristic
202D172—22no—
203D172—22no—
204D172—44no—
205D172—41no—
206D172—41no—
207C4×D43—161no—
208C4×D43—161no—
209C4×D43—161no—
210C4×D43—161no—
211Dic86—41no—
212Dic86—41no—
213Dic86—161no—
214C8×C43—21no—
215C8×C43C2×#4111yescharacteristic
216C8×C43C2×#4111yescharacteristic
217C43⋊C8—21no—
218C43⋊C8—21no—
219#33678—431nomaximal, Sylow
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—21no—
223C22×C43—81no—
224C22×C43—81no—
225C22×C43—81no—
226C22×C43C22×D811yescharacteristic
227C2×D43—42no—
228C2×D43—42no—
229C2×D43—81no—
230C2×D43—81no—
231C2×D43—81no—
232C2×D43—81no—
233C2×D43—164no—
234C4×C43—21no—
235C4×C43—81no—
236C4×C43—81no—
237C4×C43—81no—
238C4×C43#52511yescharacteristic
239C4×C43#57511yescharacteristic
240Dic43—21no—
241Dic43—21no—
242Dic43—21no—
243Dic43—21no—
244Dic43—81no—
245Dic43—81no—
246#3175—431no—
247#2948—431no—
248#2237—431no—
249#2234D4311yescharacteristic, complemented
250#2226—431no—
251#2224—431no—
252#2210—431no—
253#2210—431no—
254#2187—431no—
255#2184—431no—
256#2177—431no—
257#2175—431no—
258C4×SD32—431no—
259C4×D16—431no—
260#2164—431no—
261C2×C43—41no—
262C2×C43—161no—
263C2×C43#310011yescharacteristic
264C2×C43#341511yescharacteristic
265C2×C43#341611yescharacteristic
266D43—82no—
267D43—82no—
268C22×D8—431no—
269#542—861no—
270#518—861no—
271C2×SD32—431no—
272C2×SD32—431no—
273C2×D16—431no—
274C2×D16—431no—
275#500—431no—
276#495—431no—
277#489—861no—
278#468—861no—
279#467—431no—
280#466C2×D4311yescharacteristic
281#442—861no—
282#442—861no—
283#440—861no—
284C4×Q16—431no—
285C4×D8—431no—
286C4×D8—431no—
287C4×D8—431no—
288C4×D8—431no—
289C4×D8—431no—
290#427C2×D4311yescharacteristic
291#418—861no—
292#405—431no—
293#367—431no—
294#367C2×D4311yescharacteristic, complemented
295#366—431no—
296#366C2×D4311yescharacteristic, complemented
297C4⋊C16—431no—
298C4⋊C16—431no—
299#358—431no—
300#358—431no—
301#357—431no—
302#357—431no—
303#357—431no—
304#357—431no—
305#357C2×D4311yescharacteristic, complemented
306#357C2×D4311yescharacteristic, complemented
307C22⋊C16—431no—
308C22⋊C16C2×D4311yescharacteristic
309#346—431no—
310C4×C16—431no—
311C43#3367811yescharacteristic, complemented, Sylow
312C22×D4—861no—
313C2×Q16—431no—
314C2×SD16—861no—
315C2×D8—431no—
316C2×D8—431no—
317C2×D8—862no—
318C2×D8—862no—
319C2×D8—861no—
320C2×D8C22×D4311yescharacteristic
321C2×M16—431no—
322C22×C8C22×D4311yescharacteristic
323C4⋊Q8—861no—
324#126—1721no—
325#124—861no—
326#124—1721no—
327#123—1721no—
328C22⋊Q8—861no—
329C22⋊Q8—1721no—
330#121—21no—
331C4×Q8—861no—
332C4×D4—861no—
333C4×D4—861no—
334C4×D4—861no—
335C4×D4—861no—
336C4×D4—861no—
337C4×D4—1721no—
338C4×D4—1721no—
339#117—21no—
340#117—431no—
341C2×C22⋊C4—1721no—
342C2×C22⋊C4—1721no—
343SD32—862no—
344SD32—862no—
345D16—862no—
346D16—862no—
347C2×C16—431no—
348C2×C16—431no—
349C2×C16C22×D4311yescharacteristic
350C2×C16C22×D4311yescharacteristic
351#107—431no—
352#107—861no—
353#107C22×D4311yescharacteristic
354#107C22×D4311yescharacteristic
355#107C22×D4311yescharacteristic
356#106—21no—
357#103—861no—
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×C8—431no—
369C24—1721no—
370C2×Q8—861no—
371C2×Q8—1721no—
372C2×D4—21no—
373C2×D4—41no—
374C2×D4—864no—
375C2×D4—861no—
376C2×D4—861no—
377C2×D4—1722no—
378C2×D4—1721no—
379C22×C4—1721no—
380C22×C4—1721no—
381C22×C4—1721no—
382C22×C4—1721no—
383C22×C4—1721no—
384C22×C4D4×D4311yescharacteristic
385Q16—861no—
386Q16—861no—
387SD16—1722no—
388D8—21no—
389D8—21no—
390D8—432no—
391D8—432no—
392D8—864no—
393D8—861no—
394D8—861no—
395M16—1721no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—431no—
399C2×C8—431no—
400C2×C8D4×D4311yescharacteristic
401C2×C8C23×D4311yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—431no—
406C4⋊C4—431no—
407C4⋊C4—861no—
408C4⋊C4—1721no—
409C4⋊C4—1721no—
410C4⋊C4—1721no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—431no—
414C22⋊C4—431no—
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—431no—
426C42—1721no—
427C16—21no—
428C16—21no—
429C16—861no—
430C16—861no—
431C23—41no—
432C23—1724no—
433C23—1721no—
434C23—1721no—
435C23—6881no—
436C23—6881no—
437C23D8×D4311yescharacteristic
438Q8—1721no—
439Q8—1721no—
440Q8—6881no—
441D4—41no—
442D4—41no—
443D4—161no—
444D4—862no—
445D4—862no—
446D4—1724no—
447D4—1721no—
448D4—1721no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—431no—
455C2×C4—431no—
456C2×C4—431no—
457C2×C4—431no—
458C2×C4—1721no—
459C2×C4—1721no—
460C2×C4—6881no—
461C2×C4—6881no—
462C2×C4—6881no—
463C2×C4—6881no—
464C2×C4—6881no—
465C2×C4D8×D4311yescharacteristic
466C2×C4C2×D4×D4311yescharacteristic
467C8—21no—
468C8—861no—
469C8—861no—
470C8#41×D4311yescharacteristic
471C8#41×D4311yescharacteristic
472C22—21no—
473C22—21no—
474C22—21no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—3441no—
479C22—3441no—
480C22—3441no—
481C22—3441no—
482C22—1722no—
483C22—1722no—
484C22—6884no—
485C22C2×D8×D4311yescharacteristic
486C4—21no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—861no—
491C4—861no—
492C4—861no—
493C4—861no—
494C4—3441no—
495C4—3441no—
496C4#1458340711yescharacteristic
497C4#1458369811yescharacteristic
498C2—41no—
499C2—161no—
500C2—3442no—
501C2—3442no—
502C2#1914459211yescharacteristic
503C2#1914773511yescharacteristic
504C2#1914773811yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2234C2
socleC22×C43C22×D8
prime radical#19136506C2
hypercenter#2234D43
hypocenterC43#33678
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2234

Complements

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

NH ≅ G/Ntype
1. #19145227C2semidirect
2. #19143446C2semidirect
3. #19136803C2semidirect
4. #19136741C2semidirect
5. #19136731C2semidirect
6. #19136649C2semidirect
7. #19136649C2semidirect
8. #19136526C2semidirect
10. #19136468C2semidirect
11. #19136458C2semidirect
12. #19136446C2semidirect
13. #19136439C2semidirect
14. #19136399C2semidirect
15. C43×#2234C2semidirect
23. #14583303C22semidirect
24. #14583282C22semidirect
31. #14582993C22semidirect
32. D8×Dic43C22semidirect
39. #14582726C22semidirect
40. #14582724C22semidirect
41. Dic43⋊C16C22semidirect
42. Dic43⋊C16C22semidirect
43. #14582702C22semidirect
44. #14582702C22semidirect
50. #14582674C22semidirect
51. C16×Dic43C22semidirect
54. C43×#367C22semidirect
55. C43×#366C22semidirect
56. C43×#357C22semidirect
57. C43×#357C22semidirect
249. #2234D43semidirect
294. #367C2×D43semidirect
296. #366C2×D43semidirect
305. #357C2×D43semidirect
306. #357C2×D43semidirect
311. C43#33678semidirect

Maximal subgroups

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

subgroupindex
#191452272
#191434462
#191368032
#191367412
#191367312
#191366492
#191365262
#191365062
#191364682
#191364582
#191364462
#191364392
#191363992
C43×#22342
#3367843