Finite Group Databasebeta

← #37545485

Subgroups — #37545485

Order 23168.

464 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042090C211yesmaximal, characteristic, complemented
2#26042086C211yesmaximal, characteristic, complemented
3#26042082C211yesmaximal, characteristic, complemented
4#26041667C211yesmaximal, characteristic, complemented
5#26041547C211yesmaximal, characteristic, complemented
6#26041546C211yesmaximal, characteristic, complemented
7#26041542C211yesmaximal, characteristic, complemented
8#26041540C211yesmaximal, characteristic, complemented
9#26041457C211yesmaximal, characteristic, complemented
10#26041450C211yesmaximal, characteristic, complemented
11#26041447C211yesmaximal, characteristic, complemented
12#26041445C211yesmaximal, characteristic, complemented
13#26041401C211yesmaximal, characteristic, complemented
14#26041399C211yesmaximal, characteristic, complemented
15#576×C181C211yesmaximal, characteristic, complemented
16#19153863C2211yescharacteristic, complemented
17#19153862C2211yescharacteristic, complemented
18#19153848—21no—
19#19153846—21no—
20#19153846C2211yescharacteristic, complemented
21#19153846C2211yescharacteristic, complemented
22#19153842—21no—
23#19153842—21no—
24#19153842C2211yescharacteristic, complemented
25#19153842C2211yescharacteristic, complemented
26#19153841—21no—
27#19153841C2211yescharacteristic
28#19153841C2211yescharacteristic, complemented
29#19153840—21no—
30#19153837—21no—
31#19153836—21no—
32#19153836—21no—
33#19153836C2211yescharacteristic
34C2×#15668438C2211yescharacteristic, complemented
35C2×#15668437—21no—
36C2×#15668437C2211yescharacteristic, complemented
37SD16×D181—21no—
38C2×#15668434—21no—
39C2×#15668434C2211yescharacteristic, complemented
40#19153823C2211yescharacteristic, complemented
41#19153823C2211yescharacteristic, complemented
42#19153822C2211yescharacteristic, complemented
43#19153812C2211yescharacteristic, complemented
44#19153803C2211yescharacteristic, complemented
45#19153752C2211yescharacteristic, complemented
46#19153751C2211yescharacteristic, complemented
47#19153743C2211yescharacteristic, complemented
48#19153743C2211yescharacteristic, complemented
49#19153743C2211yescharacteristic, complemented
50#19153742C2211yescharacteristic, complemented
51#19153734C2211yescharacteristic, complemented
52#19153733C2211yescharacteristic, complemented
53#19153733C2211yescharacteristic, complemented
54#19153732C2211yescharacteristic, complemented
55#19153726C2211yescharacteristic, complemented
56H(5,𝔽2)×C181C2211yescharacteristic
57H(5,𝔽2)×C181C2211yescharacteristic, complemented
58AGL(1,ℤ/8)×C181—21no—
59AGL(1,ℤ/8)×C181—21no—
60AGL(1,ℤ/8)×C181C2211yescharacteristic
61AGL(1,ℤ/8)×C181C2211yescharacteristic, complemented
62#135×C181—21no—
63#135×C181C2211yescharacteristic
64C2×D8×C181—21no—
65C2×D8×C181C2211yescharacteristic, complemented
66#131×C181C2211yescharacteristic, complemented
67#15668450—21no—
68#15668449—21no—
69#15668449—21no—
70#15668449C2311yescharacteristic
71#15668448—21no—
72#15668448—41no—
73C2×Dic362—21no—
74C2×Dic362C2311yescharacteristic
75Q8×D181—21no—
76C2×D724—21no—
77C2×D724C2311yescharacteristic
78C2×C22⋊D181—41no—
79D4×D181—21no—
80D4×D181—41no—
81#15668439—21no—
82#15668439—21no—
83#15668439D411yescharacteristic, complemented
84#15668438—21no—
85#15668438—21no—
86#15668437—21no—
87#15668437—21no—
88#15668437—21no—
89#15668437—21no—
90#15668437—21no—
91#15668437—21no—
92#15668437D411yescharacteristic, complemented
93#15668436—21no—
94#15668436—21no—
95#15668436D411yescharacteristic, complemented
96#15668434—21no—
97#15668434—21no—
98#15668434—21no—
99#15668434—21no—
100#15668434—21no—
101#15668434—21no—
102#15668434D411yescharacteristic, complemented
103#15668433—21no—
104#15668433—21no—
105#15668433C2311yescharacteristic
106#15668433C2311yescharacteristic
107#15668433C2311yescharacteristic
108#15668432—21no—
109C2×#13089678—21no—
110C2×#13089678—21no—
111C2×#13089678C2311yescharacteristic
112C8×D181—21no—
113C22⋊Dic181—41no—
114C4×Dic181C2311yescharacteristic
115#41×C181—21no—
116#41×C181—21no—
117#41×C181—21no—
118#41×C181—21no—
119#41×C181C2311yescharacteristic
120#41×C181C2311yescharacteristic
121#41×C181C2311yescharacteristic
122C2×D4×C181—21no—
123C2×D4×C181—21no—
124C2×D4×C181—21no—
125C2×D4×C181—21no—
126C2×D4×C181—41no—
127C2×D4×C181—41no—
128C2×D4×C181C2311yescharacteristic
129C2×D4×C181C2311yescharacteristic
130Q16×C181D411yescharacteristic, complemented
131SD16×C181—21no—
132SD16×C181—21no—
133SD16×C181D411yescharacteristic, complemented
134SD16×C181D411yescharacteristic, complemented
135D8×C181—21no—
136D8×C181—21no—
137D8×C181—21no—
138D8×C181—21no—
139D8×C181D411yescharacteristic, complemented
140M16×C181—21no—
141M16×C181C2311yescharacteristic
142C2×C8×C181—21no—
143C2×C8×C181C2311yescharacteristic
144C22×D181—21no—
145C22×D181—41no—
146Dic362—21no—
147Dic362—21no—
148Dic362—41no—
149Dic362C2×D411yescharacteristic
150D724—21no—
151D724—21no—
152D724—41no—
153D724C2×D411yescharacteristic
154C22⋊D181—21no—
155C22⋊D181—41no—
156C22⋊D181—41no—
157C22⋊D181—82no—
158C2×Dic181—21no—
159C2×Dic181—21no—
160C2×Dic181—41no—
161C4×D181—21no—
162C4×D181—41no—
163C4×D181—41no—
164#13089678—21no—
165#13089678—21no—
166#13089678—21no—
167#13089678C2×D411yescharacteristic
168#13089678C2×D411yescharacteristic
169C23×C181—21no—
170C23×C181—21no—
171C23×C181—41no—
172C23×C181—41no—
173Q8×C181C2×D411yescharacteristic
174Q8×C181C2×D411yescharacteristic
175Q8×C181C2×D411yescharacteristic
176D4×C181—21no—
177D4×C181—21no—
178D4×C181—21no—
179D4×C181—21no—
180D4×C181—21no—
181D4×C181—21no—
182D4×C181—21no—
183D4×C181—41no—
184D4×C181—41no—
185D4×C181—41no—
186D4×C181—41no—
187D4×C181C2×D411yescharacteristic
188D4×C181C2×D411yescharacteristic
189D4×C181C2×D411yescharacteristic
190C2×C4×C181—21no—
191C2×C4×C181—21no—
192C2×C4×C181—21no—
193C2×C4×C181—41no—
194C2×C4×C181—41no—
195C2×C4×C181C2411yescharacteristic
196C8×C181—21no—
197C8×C181C2×D411yescharacteristic
198C8×C181C2×D411yescharacteristic
199C22×C181—21no—
200C22×C181—21no—
201C22×C181—21no—
202C22×C181—41no—
203C22×C181—41no—
204C22×C181—81no—
205C22×C181—81no—
206C22×C181—161no—
207C22×C181—161no—
208C22×C181H(5,𝔽2)11yescharacteristic
209C2×D181—21no—
210C2×D181—41no—
211C2×D181—81no—
212C2×D181—161no—
213C4×C181—21no—
214C4×C181—21no—
215C4×C181—21no—
216C4×C181C22×D411yescharacteristic
217C4×C181C22×D411yescharacteristic
218Dic181—21no—
219Dic181—41no—
220Dic181—41no—
221C2×C181—21no—
222C2×C181—41no—
223C2×C181—41no—
224C2×C181—41no—
225C2×C181—81no—
226C2×C181—81no—
227C2×C181D4211yescharacteristic
228D181—41no—
229D181—81no—
230C181#328811yescharacteristic, complemented, Sylow
231#3288—1811nomaximal, Sylow
232#577—1811no—
233#577—1811no—
234#576—1811no—
235#576D18111yescharacteristic, complemented
236#496—1811no—
237#472—1811no—
238#472—1811no—
239#471—1811no—
240#471—1811no—
241#455—1811no—
242#454—1811no—
243#453—1811no—
244#453—1811no—
245#444—1811no—
246#444—1811no—
2472−1+4—1811no—
248H(5,𝔽2)—1811no—
249H(5,𝔽2)C2×D18111yescharacteristic
250H(5,𝔽2)C2×D18111yescharacteristic, complemented
251#137—3621no—
252#137—3621no—
253#137—1811no—
254#137—1811no—
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—21no—
257AGL(1,ℤ/8)—3621no—
258AGL(1,ℤ/8)—3621no—
259AGL(1,ℤ/8)—3621no—
260AGL(1,ℤ/8)—3621no—
261AGL(1,ℤ/8)—1811no—
262AGL(1,ℤ/8)—1811no—
263AGL(1,ℤ/8)—1811no—
264AGL(1,ℤ/8)—1811no—
265AGL(1,ℤ/8)C2×D18111yescharacteristic
266AGL(1,ℤ/8)C2×D18111yescharacteristic, complemented
267#135—21no—
268#135—3621no—
269#135—3621no—
270#135—3621no—
271#135—1811no—
272#135C2×D18111yescharacteristic
273C2×SD16—3621no—
274C2×SD16—3621no—
275C2×SD16—1811no—
276C2×SD16—1811no—
277C2×D8—21no—
278C2×D8—3621no—
279C2×D8—1811no—
280C2×D8C2×D18111yescharacteristic, complemented
281#131—1811no—
282#131—1811no—
283#131—1811no—
284#131C2×D18111yescharacteristic, complemented
285#127—1811no—
286#124—1811no—
287#108—1811no—
288#108—1811no—
289#104—1811no—
290#104—1811no—
291#104—1811no—
292#104—1811no—
293#101—1811no—
294#100—1811no—
295#100—1811no—
296#100—1811no—
297#97—1811no—
298#41—21no—
299#41—21no—
300#41—21no—
301#41—21no—
302#41—3621no—
303#41—3621no—
304#41—3621no—
305#41—3621no—
306#41—1811no—
307#41—7241no—
308#41C22×D18111yescharacteristic
309#41C22×D18111yescharacteristic
310#41C22×D18111yescharacteristic
311C2×Q8—3621no—
312C2×Q8—3621no—
313C2×Q8—1811no—
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—3621no—
321C2×D4—3621no—
322C2×D4—1811no—
323C2×D4—7241no—
324C2×D4—7241no—
325C2×D4C22×D18111yescharacteristic
326C2×D4C22×D18111yescharacteristic
327Q16—3621no—
328Q16—3621no—
329Q16—1811no—
330Q16C22⋊D18111yescharacteristic, complemented
331SD16—21no—
332SD16—21no—
333SD16—3621no—
334SD16—3621no—
335SD16—3621no—
336SD16—3621no—
337SD16—3621no—
338SD16—3621no—
339SD16—3621no—
340SD16—3621no—
341SD16—3621no—
342SD16—3621no—
343SD16—1811no—
344SD16—1811no—
345SD16C22⋊D18111yescharacteristic, complemented
346SD16C22⋊D18111yescharacteristic, complemented
347D8—21no—
348D8—21no—
349D8—21no—
350D8—21no—
351D8—3621no—
352D8—3621no—
353D8—3621no—
354D8—3621no—
355D8—3621no—
356D8—3621no—
357D8—1811no—
358D8C22⋊D18111yescharacteristic, complemented
359M16—21no—
360M16—3621no—
361M16—3621no—
362M16—3621no—
363M16—1811no—
364M16—1811no—
365M16—1811no—
366M16C22×D18111yescharacteristic
367C2×C8—21no—
368C2×C8—3621no—
369C2×C8—3621no—
370C2×C8—3621no—
371C2×C8—1811no—
372C2×C8C22×D18111yescharacteristic
373C22⋊C4—7241no—
374C42—1811no—
375C23—21no—
376C23—21no—
377C23—41no—
378C23—41no—
379C23—3621no—
380C23—7241no—
381Q8—3621no—
382Q8—3621no—
383Q8—1811no—
384Q8—7241no—
385Q8D4×D18111yescharacteristic
386Q8C2×C22⋊D18111yescharacteristic
387Q8C2×C22⋊D18111yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—21no—
394D4—21no—
395D4—41no—
396D4—41no—
397D4—41no—
398D4—41no—
399D4—3621no—
400D4—3621no—
401D4—3621no—
402D4—14482no—
403D4—1811no—
404D4—7241no—
405D4—7241no—
406D4—7241no—
407D4D4×D18111yescharacteristic
408D4C2×C22⋊D18111yescharacteristic
409D4C2×C22⋊D18111yescharacteristic
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—3621no—
416C2×C4—3621no—
417C2×C4—3621no—
418C2×C4—7241no—
419C2×C4—7241no—
420C2×C4—7241no—
421C2×C4C23×D18111yescharacteristic
422C8—21no—
423C8—3621no—
424C8—3621no—
425C8—3621no—
426C8—1811no—
427C8—1811no—
428C8C2×C22⋊D18111yescharacteristic
429C8C2×C22⋊D18111yescharacteristic
430C22—21no—
431C22—21no—
432C22—21no—
433C22—41no—
434C22—41no—
435C22—81no—
436C22—81no—
437C22—161no—
438C22—161no—
439C22—28961no—
440C22—3621no—
441C22—14481no—
442C22—7241no—
443C22#1915386111yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—3621no—
448C4—7241no—
449C4—7241no—
450C4C2×D4×D18111yescharacteristic
451C4C22×C22⋊D18111yescharacteristic
452C2—21no—
453C2—41no—
454C2—41no—
455C2—41no—
456C2—81no—
457C2—81no—
458C2—14481no—
459C2—7241no—
460C2D4×C22⋊D18111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#576×C181C2
socleC2×C181D42
hypercenter#576D181
hypocenterC181#3288
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C2×C4 ◁ #576

Complements

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

NH ≅ G/Ntype
1. #26042090C2semidirect
2. #26042086C2semidirect
3. #26042082C2semidirect
4. #26041667C2semidirect
5. #26041547C2semidirect
6. #26041546C2semidirect
7. #26041542C2semidirect
8. #26041540C2semidirect
9. #26041457C2semidirect
10. #26041450C2semidirect
11. #26041447C2semidirect
12. #26041445C2semidirect
13. #26041401C2semidirect
14. #26041399C2semidirect
15. #576×C181C2semidirect
16. #19153863C22semidirect
17. #19153862C22semidirect
20. #19153846C22semidirect
21. #19153846C22semidirect
24. #19153842C22semidirect
25. #19153842C22semidirect
28. #19153841C22semidirect
34. C2×#15668438C22semidirect
36. C2×#15668437C22semidirect
39. C2×#15668434C22semidirect
40. #19153823C22semidirect
41. #19153823C22semidirect
42. #19153822C22semidirect
43. #19153812C22semidirect
44. #19153803C22semidirect
45. #19153752C22semidirect
46. #19153751C22semidirect
47. #19153743C22semidirect
48. #19153743C22semidirect
49. #19153743C22semidirect
50. #19153742C22semidirect
51. #19153734C22semidirect
52. #19153733C22semidirect
53. #19153733C22semidirect
54. #19153732C22semidirect
55. #19153726C22semidirect
57. H(5,𝔽2)×C181C22semidirect
61. AGL(1,ℤ/8)×C181C22semidirect
65. C2×D8×C181C22semidirect
66. #131×C181C22semidirect
83. #15668439D4semidirect
92. #15668437D4semidirect
95. #15668436D4semidirect
102. #15668434D4semidirect
130. Q16×C181D4semidirect
133. SD16×C181D4semidirect
134. SD16×C181D4semidirect
139. D8×C181D4semidirect
230. C181#3288semidirect
235. #576D181semidirect
250. H(5,𝔽2)C2×D181semidirect
266. AGL(1,ℤ/8)C2×D181semidirect
280. C2×D8C2×D181semidirect
284. #131C2×D181semidirect
330. Q16C22⋊D181semidirect
345. SD16C22⋊D181semidirect
346. SD16C22⋊D181semidirect
358. D8C22⋊D181semidirect

Maximal subgroups

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

subgroupindex
#260420902
#260420862
#260420822
#260416672
#260415472
#260415462
#260415422
#260415402
#260414572
#260414502
#260414472
#260414452
#260414012
#260413992
#576×C1812
#3288181