Finite Group Databasebeta

← #37545501

Subgroups — #37545501

Order 23168.

454 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042094C211yesmaximal, characteristic, complemented
2#26042086C211yesmaximal, characteristic, complemented
3#26042082C211yesmaximal, characteristic, complemented
4#26041660C211yesmaximal, characteristic, complemented
5#26041552C211yesmaximal, characteristic, complemented
6#26041547C211yesmaximal, characteristic, complemented
7#26041542C211yesmaximal, characteristic, complemented
8#26041539C211yesmaximal, characteristic, complemented
9#26041457C211yesmaximal, characteristic, complemented
10#26041455C211yesmaximal, characteristic, complemented
11#26041452C211yesmaximal, characteristic, complemented
12#26041450C211yesmaximal, characteristic, complemented
13#26041396C211yesmaximal, characteristic, complemented
14#26041394C211yesmaximal, characteristic, complemented
15#577×C181C211yesmaximal, characteristic, complemented
16#19153863C2211yescharacteristic, complemented
17#19153862C2211yescharacteristic
18#19153848—21no—
19#19153847—21no—
20#19153847C2211yescharacteristic, complemented
21#19153846—21no—
22#19153846C2211yescharacteristic
23#19153846C2211yescharacteristic, complemented
24#19153842—21no—
25#19153842C2211yescharacteristic
26#19153841—21no—
27#19153841C2211yescharacteristic
28#19153841C2211yescharacteristic, complemented
29#19153840—21no—
30#19153837—21no—
31#19153836—21no—
32#19153836—21no—
33#19153836C2211yescharacteristic
34C2×#15668439—21no—
35C2×#15668439C2211yescharacteristic, complemented
36C2×#15668438C2211yescharacteristic, complemented
37SD16×D181—21no—
38C2×#15668434—21no—
39C2×#15668434C2211yescharacteristic
40#19153823C2211yescharacteristic
41#19153823C2211yescharacteristic, complemented
42#19153822C2211yescharacteristic, complemented
43#19153805C2211yescharacteristic, complemented
44#19153803C2211yescharacteristic, complemented
45#19153752C2211yescharacteristic, complemented
46#19153751C2211yescharacteristic, complemented
47#19153743C2211yescharacteristic
48#19153743C2211yescharacteristic, complemented
49#19153743C2211yescharacteristic, complemented
50#19153742C2211yescharacteristic, complemented
51#19153735C2211yescharacteristic, complemented
52#19153734C2211yescharacteristic, complemented
53#19153733C2211yescharacteristic, complemented
54#19153732C2211yescharacteristic, complemented
55C8×Dic181C2211yescharacteristic, complemented
562−1+4×C181C2211yescharacteristic, complemented
57H(5,𝔽2)×C181C2211yescharacteristic
58#137×C181—21no—
59#137×C181C2211yescharacteristic
60AGL(1,ℤ/8)×C181—21no—
61AGL(1,ℤ/8)×C181C2211yescharacteristic, complemented
62#135×C181—21no—
63#135×C181C2211yescharacteristic
64C2×SD16×C181—21no—
65C2×SD16×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
78D4×D181—21no—
79D4×D181—41no—
80#15668439—21no—
81#15668439—21no—
82#15668439—21no—
83#15668439—21no—
84#15668439—21no—
85#15668439D411yescharacteristic
86#15668438—21no—
87#15668438—21no—
88#15668437—21no—
89#15668437—21no—
90#15668437—21no—
91#15668437D411yescharacteristic
92#15668436—21no—
93#15668436—21no—
94#15668436—21no—
95#15668436D411yescharacteristic
96#15668434—21no—
97#15668434—21no—
98#15668434—21no—
99#15668434—21no—
100#15668434—21no—
101#15668434D411yescharacteristic
102#15668433—21no—
103#15668433—21no—
104#15668433C2311yescharacteristic
105#15668433C2311yescharacteristic
106#15668433C2311yescharacteristic
107#15668432—21no—
108C2×#13089678—21no—
109C2×#13089678—21no—
110C2×#13089678C2311yescharacteristic
111C8×D181—21no—
112C22⋊Dic181—41no—
113#15668426—41no—
114C4×Dic181C2311yescharacteristic
115#41×C181—21no—
116#41×C181—21no—
117#41×C181—21no—
118#41×C181—21no—
119#41×C181—41no—
120#41×C181C2311yescharacteristic
121#41×C181C2311yescharacteristic
122#41×C181C2311yescharacteristic
123C2×Q8×C181—21no—
124C2×Q8×C181—21no—
125C2×Q8×C181C2311yescharacteristic
126C2×D4×C181—21no—
127C2×D4×C181—21no—
128C2×D4×C181—41no—
129C2×D4×C181C2311yescharacteristic
130Q16×C181—21no—
131Q16×C181D411yescharacteristic
132SD16×C181—21no—
133SD16×C181—21no—
134SD16×C181—21no—
135SD16×C181—21no—
136SD16×C181D411yescharacteristic
137SD16×C181D411yescharacteristic
138D8×C181—21no—
139D8×C181D411yescharacteristic
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—
157C2×Dic181—21no—
158C2×Dic181—21no—
159C2×Dic181—41no—
160C4×D181—21no—
161C4×D181—41no—
162C4×D181—41no—
163#13089678—21no—
164#13089678—21no—
165#13089678—21no—
166#13089678C2×D411yescharacteristic
167#13089678C2×D411yescharacteristic
168C23×C181—21no—
169C23×C181—41no—
170Q8×C181—21no—
171Q8×C181—21no—
172Q8×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—41no—
182D4×C181—41no—
183D4×C181—41no—
184D4×C181C2×D411yescharacteristic
185D4×C181C2×D411yescharacteristic
186D4×C181C2×D411yescharacteristic
187C2×C4×C181—21no—
188C2×C4×C181—21no—
189C2×C4×C181—21no—
190C2×C4×C181—21no—
191C2×C4×C181—41no—
192C2×C4×C181—41no—
193C2×C4×C181—41no—
194C2×C4×C181C2411yescharacteristic
195C8×C181—21no—
196C8×C181C2×D411yescharacteristic
197C8×C181C2×D411yescharacteristic
198C22×C181—21no—
199C22×C181—21no—
200C22×C181—21no—
201C22×C181—41no—
202C22×C181—81no—
203C22×C181—161no—
204C22×C181H(5,𝔽2)11yescharacteristic
205C2×D181—21no—
206C2×D181—41no—
207C2×D181—81no—
208C2×D181—161no—
209C4×C181—21no—
210C4×C181—21no—
211C4×C181—21no—
212C4×C181—41no—
213C4×C181C22×D411yescharacteristic
214C4×C181C22×D411yescharacteristic
215Dic181—21no—
216Dic181—41no—
217Dic181—41no—
218C2×C181—21no—
219C2×C181—41no—
220C2×C181—41no—
221C2×C181—41no—
222C2×C181—81no—
223C2×C181D4211yescharacteristic
224D181—41no—
225D181—81no—
226C181#329011yescharacteristic, complemented, Sylow
227#3290—1811nomaximal, Sylow
228#578—1811no—
229#577—1811no—
230#577D18111yescharacteristic, complemented
231#576—1811no—
232#495—1811no—
233#473—1811no—
234#472—1811no—
235#471—1811no—
236#471—1811no—
237#455—1811no—
238#455—1811no—
239#454—1811no—
240#454—1811no—
241#443—1811no—
242#443—1811no—
2432−1+4—1811no—
2442−1+4C2×D18111yescharacteristic, complemented
245H(5,𝔽2)—1811no—
246H(5,𝔽2)C2×D18111yescharacteristic
247#137—21no—
248#137—3621no—
249#137—3621no—
250#137—3621no—
251#137—1811no—
252#137—1811no—
253#137—1811no—
254#137C2×D18111yescharacteristic
255AGL(1,ℤ/8)—21no—
256AGL(1,ℤ/8)—3621no—
257AGL(1,ℤ/8)—3621no—
258AGL(1,ℤ/8)—3621no—
259AGL(1,ℤ/8)—1811no—
260AGL(1,ℤ/8)—1811no—
261AGL(1,ℤ/8)—1811no—
262AGL(1,ℤ/8)C2×D18111yescharacteristic, complemented
263#135—21no—
264#135—3621no—
265#135—3621no—
266#135—3621no—
267#135—1811no—
268#135C2×D18111yescharacteristic
269C2×Q16—3621no—
270C2×Q16—1811no—
271C2×SD16—21no—
272C2×SD16—3621no—
273C2×SD16—1811no—
274C2×SD16C2×D18111yescharacteristic, complemented
275C2×D8—3621no—
276C2×D8—1811no—
277#131—1811no—
278#131—1811no—
279#131—1811no—
280#131C2×D18111yescharacteristic, complemented
281#124—1811no—
282#124—1811no—
283#108—1811no—
284#108—1811no—
285#104—1811no—
286#104—1811no—
287#104—1811no—
288#104—1811no—
289#101—1811no—
290#101—1811no—
291#100—1811no—
292#100—1811no—
293C4×C8—1811no—
294#41—21no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—41no—
299#41—3621no—
300#41—3621no—
301#41—3621no—
302#41—3621no—
303#41—1811no—
304#41—7241no—
305#41C22×D18111yescharacteristic
306#41C22×D18111yescharacteristic
307#41C22×D18111yescharacteristic
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—3621no—
311C2×Q8—3621no—
312C2×Q8—1811no—
313C2×Q8C22×D18111yescharacteristic
314C2×D4—21no—
315C2×D4—21no—
316C2×D4—41no—
317C2×D4—3621no—
318C2×D4—3621no—
319C2×D4—1811no—
320C2×D4—7241no—
321C2×D4C22×D18111yescharacteristic
322Q16—21no—
323Q16—3621no—
324Q16—3621no—
325Q16—3621no—
326Q16—3621no—
327Q16—3621no—
328Q16—1811no—
329Q16C22⋊D18111yescharacteristic
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—3621no—
335SD16—3621no—
336SD16—3621no—
337SD16—3621no—
338SD16—3621no—
339SD16—3621no—
340SD16—3621no—
341SD16—3621no—
342SD16—1811no—
343SD16—1811no—
344SD16C22⋊D18111yescharacteristic
345SD16C22⋊D18111yescharacteristic
346D8—21no—
347D8—3621no—
348D8—3621no—
349D8—3621no—
350D8—3621no—
351D8—3621no—
352D8—1811no—
353D8C22⋊D18111yescharacteristic
354M16—21no—
355M16—3621no—
356M16—3621no—
357M16—3621no—
358M16—1811no—
359M16—1811no—
360M16—1811no—
361M16C22×D18111yescharacteristic
362C2×C8—21no—
363C2×C8—3621no—
364C2×C8—3621no—
365C2×C8—3621no—
366C2×C8—1811no—
367C2×C8C22×D18111yescharacteristic
368C22⋊C4—7241no—
369C22⋊C4—7241no—
370C42—1811no—
371C23—21no—
372C23—41no—
373C23—3621no—
374C23—7241no—
375Q8—21no—
376Q8—21no—
377Q8—41no—
378Q8—3621no—
379Q8—3621no—
380Q8—1811no—
381Q8—7241no—
382Q8D4×D18111yescharacteristic
383Q8C2×C22⋊D18111yescharacteristic
384Q8C2×C22⋊D18111yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—3621no—
394D4—3621no—
395D4—3621no—
396D4—1811no—
397D4—7241no—
398D4—7241no—
399D4—7241no—
400D4D4×D18111yescharacteristic
401D4C2×C22⋊D18111yescharacteristic
402D4C2×C22⋊D18111yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—3621no—
411C2×C4—3621no—
412C2×C4—3621no—
413C2×C4—7241no—
414C2×C4—7241no—
415C2×C4—7241no—
416C2×C4C23×D18111yescharacteristic
417C8—21no—
418C8—3621no—
419C8—3621no—
420C8—3621no—
421C8—1811no—
422C8—1811no—
423C8C2×C22⋊D18111yescharacteristic
424C8C2×C22⋊D18111yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—81no—
430C22—161no—
431C22—28961no—
432C22—3621no—
433C22—14481no—
434C22—7241no—
435C22#1915386111yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—3621no—
441C4—7241no—
442C4—7241no—
443C4C2×D4×D18111yescharacteristic
444C4C22×C22⋊D18111yescharacteristic
445C2—21no—
446C2—41no—
447C2—41no—
448C2—41no—
449C2—81no—
450C2—14481no—
451C2—7241no—
452C2D4×C22⋊D18111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#577×C181C2
socleC2×C181D42
hypercenter#577D181
hypocenterC181#3290
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #26042094C2semidirect
2. #26042086C2semidirect
3. #26042082C2semidirect
4. #26041660C2semidirect
5. #26041552C2semidirect
6. #26041547C2semidirect
7. #26041542C2semidirect
8. #26041539C2semidirect
9. #26041457C2semidirect
10. #26041455C2semidirect
11. #26041452C2semidirect
12. #26041450C2semidirect
13. #26041396C2semidirect
14. #26041394C2semidirect
15. #577×C181C2semidirect
16. #19153863C22semidirect
20. #19153847C22semidirect
23. #19153846C22semidirect
28. #19153841C22semidirect
35. C2×#15668439C22semidirect
36. C2×#15668438C22semidirect
41. #19153823C22semidirect
42. #19153822C22semidirect
43. #19153805C22semidirect
44. #19153803C22semidirect
45. #19153752C22semidirect
46. #19153751C22semidirect
48. #19153743C22semidirect
49. #19153743C22semidirect
50. #19153742C22semidirect
51. #19153735C22semidirect
52. #19153734C22semidirect
53. #19153733C22semidirect
54. #19153732C22semidirect
55. C8×Dic181C22semidirect
56. 2−1+4×C181C22semidirect
61. AGL(1,ℤ/8)×C181C22semidirect
65. C2×SD16×C181C22semidirect
66. #131×C181C22semidirect
226. C181#3290semidirect
230. #577D181semidirect
244. 2−1+4C2×D181semidirect
262. AGL(1,ℤ/8)C2×D181semidirect
274. C2×SD16C2×D181semidirect
280. #131C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260420942
#260420862
#260420822
#260416602
#260415522
#260415472
#260415422
#260415392
#260414572
#260414552
#260414522
#260414502
#260413962
#260413942
#577×C1812
#3290181