Finite Group Databasebeta

← #25251698

Subgroups — #25251698

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#19143447C211yesmaximal, characteristic, complemented
3#19136804C211yesmaximal, characteristic, complemented
4#19136783C211yesmaximal, characteristic, complemented
5#19136740C211yesmaximal, characteristic, complemented
6#19136730C211yesmaximal, characteristic, complemented
7#19136648C211yesmaximal, characteristic, complemented
8#19136648C211yesmaximal, characteristic, complemented
9#19136524C211yesmaximal, characteristic, complemented
10#19136471C211yesmaximal, characteristic, complemented
11#19136456C211yesmaximal, characteristic, complemented
12#19136450C211yesmaximal, characteristic, complemented
13D16×Dic43C211yesmaximal, characteristic, complemented
14#19136399C211yesmaximal, characteristic, complemented
15C43×#2184C211yesmaximal, characteristic
16#14583516—21no—
17#14583374—21no—
18C2×#13063269C2211yescharacteristic
19C2×#13063269C2211yescharacteristic
20#14583303C2211yescharacteristic, complemented
21#14583282C2211yescharacteristic, complemented
22#14583257—21no—
23#14583143—21no—
24#14583140C2211yescharacteristic
25#14583011—21no—
26#14583011—21no—
27#14582996—21no—
28#14582993C2211yescharacteristic, complemented
29D8×Dic43C2211yescharacteristic
30D8×Dic43C2211yescharacteristic
31D8×Dic43C2211yescharacteristic
32D8×Dic43C2211yescharacteristic
33D8×Dic43C2211yescharacteristic, complemented
34#14582937C2211yescharacteristic
35#14582904—21no—
36#14582854C2211yescharacteristic
37#14582727C2211yescharacteristic, complemented
38#14582726C2211yescharacteristic, complemented
39#14582725C2211yescharacteristic, complemented
40#14582724C2211yescharacteristic, complemented
41Dic43⋊C16C2211yescharacteristic, complemented
42Dic43⋊C16C2211yescharacteristic, complemented
43#14582704C2211yescharacteristic, complemented
44#14582704C2211yescharacteristic, complemented
45#14582700C2211yescharacteristic
46#14582700C2211yescharacteristic
47#14582700C2211yescharacteristic, complemented
48#14582700C2211yescharacteristic, complemented
49C22⋊(C43⋊C16)C2211yescharacteristic
50#14582674C2211yescharacteristic, complemented
51C16×Dic43C2211yescharacteristic, complemented
52C22×D8×C43C2211yescharacteristic
53C2×D16×C43C2211yescharacteristic
54C2×D16×C43C2211yescharacteristic
55C43×#466C2211yescharacteristic
56C43×#357C2211yescharacteristic
57C43×#357C2211yescharacteristic
58C43×C22⋊C16C2211yescharacteristic
59C2×Dic172C2311yescharacteristic
60C2×#10621883—21no—
61C2×#10621877D411yescharacteristic
62#13063324—21no—
63#13063318—41no—
64#13063312—21no—
65#13063312—41no—
66#13063306—41no—
67#13063304—21no—
68#13063302—41no—
69#13063290—21no—
70D4×Dic43—21no—
71D4×Dic43—21no—
72D4×Dic43—21no—
73D4×Dic43—21no—
74D4×Dic43—21no—
75D4×Dic43—41no—
76D4×Dic43—41no—
77#13063284—21no—
78#13063284D411yescharacteristic
79C2×C22⋊Dic43—41no—
80C2×C22⋊Dic43—41no—
81#13063269—22no—
82#13063269—22no—
83C2×C43⋊C16C2311yescharacteristic
84C2×C43⋊C16C2311yescharacteristic
85#13063259C2311yescharacteristic
86#13063259C2311yescharacteristic
87#13063259C2311yescharacteristic
88#13063258—21no—
89#13063257—21no—
90#13063250—21no—
91#13063248—21no—
92#13063246—21no—
93#13063246—21no—
94#13063246—21no—
95#13063246—21no—
96#13063246—21no—
97#13063235D411yescharacteristic
98#13063235D411yescharacteristic
99C8×Dic43C2311yescharacteristic
100C8×Dic43C2311yescharacteristic
101C22×D4×C43—21no—
102C2×D8×C43—22no—
103C2×D8×C43—22no—
104C2×D8×C43—21no—
105C2×D8×C43C2311yescharacteristic
106C2×D8×C43C2311yescharacteristic
107C2×D8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109#121×C43—21no—
110D16×C43—22no—
111D16×C43—22no—
112C2×C16×C43C2311yescharacteristic
113C2×C16×C43C2311yescharacteristic
114#107×C43C2311yescharacteristic
115#102×C43—21no—
116C24×C43—41no—
117C2×D4×C43—24no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—42no—
122C2×D4×C43—41no—
123C2×D4×C43—41no—
124C22×C4×C43C2×D411yescharacteristic
125C22×Dic43—41no—
126C22×Dic43—41no—
127C22×Dic43—41no—
128C22×Dic43—41no—
129C22×Dic43—41no—
130C2×Dic86—21no—
131C2×Dic86—41no—
132D8×C43—24no—
133D8×C43—21no—
134D8×C43—21no—
135D8×C43—21no—
136D8×C43—21no—
137D8×C43#4112yes—
138D8×C43#4112yes—
139C2×C8×C43—21no—
140C2×C8×C43—21no—
141C2×C8×C43C2×D411yescharacteristic
142C2×C8×C43C2411yescharacteristic
143C4⋊C4×C43—21no—
144C22⋊C4×C43—41no—
145C22⋊Dic43—41no—
146C22⋊Dic43—41no—
147C22⋊Dic43—41no—
148C22⋊Dic43—41no—
149C22⋊Dic43—41no—
150C22⋊Dic43—41no—
151C22⋊Dic43—41no—
152C22⋊Dic43—41no—
153C22⋊Dic43—41no—
154C22⋊Dic43D811yescharacteristic
155C22⋊Dic43D811yescharacteristic
156#10621883—42no—
157C4⋊Dic43—21no—
158C4⋊Dic43—21no—
159C4⋊Dic43—21no—
160C4⋊Dic43D811yescharacteristic
161C4⋊Dic43D811yescharacteristic
162Dic43⋊C4—41no—
163Dic43⋊C4—41no—
164Dic43⋊C4—41no—
165C4×Dic43—41no—
166C4×Dic43—41no—
167C4×Dic43C2×D411yescharacteristic
168C4×Dic43C2×D411yescharacteristic
169#10621877—41no—
170C2×C43⋊C8C2×D411yescharacteristic
171C2×C43⋊C8C2×D411yescharacteristic
172Dic172—21no—
173Dic172—21no—
174C16×C43—21no—
175C16×C43—21no—
176C43⋊C16—21no—
177C43⋊C16—21no—
178C23×C43—44no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43—41no—
182C23×C43—161no—
183C23×C43—161no—
184C23×C43C2×D811yescharacteristic
185D4×C43—22no—
186D4×C43—22no—
187D4×C43—44no—
188D4×C43—41no—
189D4×C43—41no—
190D4×C43—41no—
191D4×C43—41no—
192D4×C43—161no—
193C2×C4×C43—21no—
194C2×C4×C43—21no—
195C2×C4×C43—41no—
196C2×C4×C43C2×D811yescharacteristic
197C2×C4×C43C22×D411yescharacteristic
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—41no—
201C2×Dic43—41no—
202C2×Dic43—161no—
203C2×Dic43—161no—
204C2×Dic43—161no—
205C2×Dic43—161no—
206C2×Dic43—161no—
207C2×Dic43C2×D811yescharacteristic
208C2×Dic43C2×D811yescharacteristic
209C2×Dic43C2×D811yescharacteristic
210C2×Dic43C2×D811yescharacteristic
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—42no—
224C22×C43—42no—
225C22×C43—81no—
226C22×C43—81no—
227C22×C43—81no—
228C22×C43—81no—
229C22×C43—81no—
230C22×C43—81no—
231C22×C43—81no—
232C22×C43—164no—
233C22×C43C22×D811yescharacteristic
234C4×C43—21no—
235C4×C43—81no—
236C4×C43#52511yescharacteristic
237C4×C43#57511yescharacteristic
238Dic43—21no—
239Dic43—21no—
240Dic43—21no—
241Dic43—21no—
242Dic43—81no—
243Dic43—81no—
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#2184D4311yescharacteristic
256#2177—431no—
257#2175—431no—
258C4×SD32—431no—
259C4×D16—431no—
260#2164—431no—
261C2×C43—41no—
262C2×C43—82no—
263C2×C43—82no—
264C2×C43—161no—
265C2×C43#310011yescharacteristic
266C2×C43#341511yescharacteristic
267C2×C43#341611yescharacteristic
268C22×D8C2×D4311yescharacteristic
269#542—861no—
270#518—861no—
271C2×SD32—431no—
272C2×SD32—431no—
273C2×D16C2×D4311yescharacteristic
274C2×D16C2×D4311yescharacteristic
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#427—431no—
291#418—861no—
292#405—431no—
293#367—431no—
294#367—431no—
295#366—431no—
296#366—431no—
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
306#357C2×D4311yescharacteristic
307C22⋊C16—431no—
308C22⋊C16C2×D4311yescharacteristic
309#346—431no—
310C4×C16—431no—
311C43#3367811yescharacteristic, complemented, Sylow
312C22×D4—21no—
313C2×Q16—431no—
314C2×SD16—861no—
315C2×D8—22no—
316C2×D8—22no—
317C2×D8—21no—
318C2×D8C22×D4311yescharacteristic
319C2×D8C22×D4311yescharacteristic
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—431no—
340#117—861no—
341C2×C22⋊C4—1721no—
342C2×C22⋊C4—1721no—
343SD32—862no—
344SD32—862no—
345D16—22no—
346D16—22no—
347C2×C16—431no—
348C2×C16—431no—
349C2×C16C22×D4311yescharacteristic
350C2×C16C22×D4311yescharacteristic
351#107—431no—
352#107—431no—
353#107—431no—
354#107—861no—
355#107C22×D4311yescharacteristic
356#106—861no—
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—41no—
370C2×Q8—861no—
371C2×Q8—1721no—
372C2×D4—24no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—42no—
377C2×D4—41no—
378C2×D4—41no—
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—24no—
389D8—21no—
390D8—21no—
391D8—21no—
392D8—21no—
393D8#1062190012yes—
394D8#1062190012yes—
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—431no—
404C4⋊C4—431no—
405C4⋊C4—861no—
406C4⋊C4—861no—
407C4⋊C4—861no—
408C4⋊C4—1721no—
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—431no—
424C42—431no—
425C42—1721no—
426C42—1721no—
427C16—21no—
428C16—21no—
429C16—861no—
430C16—861no—
431C23—44no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—161no—
436C23—161no—
437C23D8×D4311yescharacteristic
438Q8—1721no—
439Q8—1721no—
440Q8—6881no—
441D4—22no—
442D4—22no—
443D4—44no—
444D4—41no—
445D4—41no—
446D4—41no—
447D4—41no—
448D4—161no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—431no—
453C2×C4—431no—
454C2×C4—431no—
455C2×C4—431no—
456C2×C4—1721no—
457C2×C4—1721no—
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—
470C8C2×#1062190011yescharacteristic
471C8C2×#1062190011yescharacteristic
472C22—21no—
473C22—21no—
474C22—21no—
475C22—42no—
476C22—42no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22—164no—
485C22C2×D8×D4311yescharacteristic
486C4—21no—
487C4—81no—
488C4—861no—
489C4—861no—
490C4—861no—
491C4—861no—
492C4—3441no—
493C4—3441no—
494C4—3441no—
495C4—3441no—
496C4#1458340511yescharacteristic
497C4#1458369511yescharacteristic
498C2—41no—
499C2—82no—
500C2—82no—
501C2—161no—
502C2#1914459011yescharacteristic
503C2#1914773211yescharacteristic
504C2#1914774111yescharacteristic
subgroupG/H
centerC22C2×D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
Fitting, prime radicalC43×#2184C2
socleC22×C43C22×D8
hypercenter#2184D43
hypocenterC43#33678
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2184

Complements

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

NH ≅ G/Ntype
1. #19145227C2semidirect
2. #19143447C2semidirect
3. #19136804C2semidirect
4. #19136783C2semidirect
5. #19136740C2semidirect
6. #19136730C2semidirect
7. #19136648C2semidirect
8. #19136648C2semidirect
9. #19136524C2semidirect
10. #19136471C2semidirect
11. #19136456C2semidirect
12. #19136450C2semidirect
13. D16×Dic43C2semidirect
14. #19136399C2semidirect
20. #14583303C22semidirect
21. #14583282C22semidirect
28. #14582993C22semidirect
33. D8×Dic43C22semidirect
37. #14582727C22semidirect
38. #14582726C22semidirect
39. #14582725C22semidirect
40. #14582724C22semidirect
41. Dic43⋊C16C22semidirect
42. Dic43⋊C16C22semidirect
43. #14582704C22semidirect
44. #14582704C22semidirect
47. #14582700C22semidirect
48. #14582700C22semidirect
50. #14582674C22semidirect
51. C16×Dic43C22semidirect
311. C43#33678semidirect

Maximal subgroups

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

subgroupindex
#191452272
#191434472
#191368042
#191367832
#191367402
#191367302
#191366482
#191365242
#191364712
#191364562
#191364502
D16×Dic432
#191363992
C43×#21842
#3367843