Finite Group Databasebeta

← #37545484

Subgroups — #37545484

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#26042091C211yesmaximal, characteristic, complemented
2#26042089C211yesmaximal, characteristic, complemented
3#26042083C211yesmaximal, characteristic, complemented
4#26042080C211yesmaximal, characteristic, complemented
5#26041667C211yesmaximal, characteristic, complemented
6#26041548C211yesmaximal, characteristic, complemented
7#26041543C211yesmaximal, characteristic, complemented
8#26041541C211yesmaximal, characteristic, complemented
9#26041459C211yesmaximal, characteristic, complemented
10#26041450C211yesmaximal, characteristic, complemented
11#26041449C211yesmaximal, characteristic, complemented
12#26041445C211yesmaximal, characteristic, complemented
13#26041400C211yesmaximal, characteristic, complemented
14#26041399C211yesmaximal, characteristic, complemented
15#472×C181C211yesmaximal, characteristic, complemented
16#19153863C2211yescharacteristic, complemented
17#19153862C2211yescharacteristic, complemented
18#19153861C2211yescharacteristic
19#19153861C2211yescharacteristic, complemented
20#19153849—21no—
21#19153849C2211yescharacteristic, complemented
22#19153849C2211yescharacteristic, complemented
23#19153845—21no—
24#19153844—21no—
25#19153844C2211yescharacteristic
26#19153844C2211yescharacteristic, complemented
27#19153843—21no—
28#19153842C2211yescharacteristic
29#19153842C2211yescharacteristic, complemented
30#19153840—21no—
31#19153840—21no—
32#19153840—21no—
33#19153840—21no—
34#19153838—21no—
35#19153838C2211yescharacteristic
36#19153837—21no—
37#19153836C2211yescharacteristic
38#19153835—21no—
39#19153835—21no—
40C2×#15668438—21no—
41C2×#15668438C2211yescharacteristic, complemented
42C2×#15668437C2211yescharacteristic, complemented
43SD16×D181—21no—
44C2×#15668434C2211yescharacteristic, complemented
45D8×D181—21no—
46D8×D181—21no—
47#19153824C2211yescharacteristic, complemented
48#19153824C2211yescharacteristic, complemented
49#19153822C2211yescharacteristic, complemented
50#19153812C2211yescharacteristic, complemented
51#19153803C2211yescharacteristic, complemented
52#19153751C2211yescharacteristic, complemented
53#19153743C2211yescharacteristic, complemented
54#19153742C2211yescharacteristic, complemented
55#19153742C2211yescharacteristic, complemented
56#19153742C2211yescharacteristic, complemented
57#19153734C2211yescharacteristic, complemented
58#19153732C2211yescharacteristic, complemented
59#19153726C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C181C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C181C2211yescharacteristic, complemented
62C2×D8×C181C2211yescharacteristic, complemented
63#131×C181C2211yescharacteristic, complemented
64#108×C181C2211yescharacteristic, complemented
65#100×C181C2211yescharacteristic, complemented
66#100×C181C2211yescharacteristic, complemented
67#15668450—21no—
68#15668449—21no—
69#15668449—21no—
70#15668449C2311yescharacteristic
71#15668449C2311yescharacteristic
72#15668449C2311yescharacteristic
73#15668448—21no—
74#15668448—21no—
75#15668448—21no—
76#15668448—21no—
77#15668448—21no—
78#15668448—41no—
79C2×Dic362—21no—
80C2×Dic362C2311yescharacteristic
81Q8×D181—21no—
82C2×D724—21no—
83C2×D724C2311yescharacteristic
84C2×C22⋊D181—41no—
85C2×C22⋊D181—41no—
86C2×C22⋊D181—41no—
87D4×D181—21no—
88D4×D181—21no—
89D4×D181—21no—
90D4×D181—21no—
91D4×D181—21no—
92D4×D181—41no—
93Dic724—21no—
94Dic724—21no—
95Dic724D411yescharacteristic, complemented
96#15668439D411yescharacteristic, complemented
97#15668438—21no—
98#15668438—21no—
99#15668438—21no—
100#15668438—21no—
101#15668438—21no—
102#15668438—21no—
103#15668438D411yescharacteristic, complemented
104#15668438D411yescharacteristic, complemented
105#15668437—21no—
106#15668437—21no—
107#15668437—21no—
108#15668437—21no—
109#15668437D411yescharacteristic, complemented
110#15668436D411yescharacteristic, complemented
111D1448—21no—
112D1448—21no—
113D1448D411yescharacteristic, complemented
114#15668434—21no—
115#15668434—21no—
116#15668434—21no—
117#15668434—21no—
118#15668434D411yescharacteristic, complemented
119#15668433C2311yescharacteristic
120#15668432—21no—
121#15668432—21no—
122#15668432—21no—
123C2×#13089678C2311yescharacteristic
124C8×D181—21no—
125C8×D181—21no—
126C8×D181—21no—
127C22⋊Dic181—41no—
128C4×Dic181C2311yescharacteristic
129#41×C181C2311yescharacteristic
130C2×D4×C181C2311yescharacteristic
131C2×D4×C181C2311yescharacteristic
132SD16×C181—21no—
133SD16×C181—21no—
134D8×C181—21no—
135D8×C181—21no—
136D8×C181—21no—
137D8×C181—21no—
138M16×C181—21no—
139M16×C181C2311yescharacteristic
140M16×C181C2311yescharacteristic
141M16×C181C2311yescharacteristic
142C2×C8×C181—21no—
143C2×C8×C181C2311yescharacteristic
144C22×D181—21no—
145C22×D181—41no—
146C22×D181—41no—
147C22×D181—41no—
148Dic362—21no—
149Dic362—21no—
150Dic362—41no—
151Dic362C2×D411yescharacteristic
152Dic362C2×D411yescharacteristic
153Dic362C2×D411yescharacteristic
154D724—21no—
155D724—21no—
156D724—41no—
157D724C2×D411yescharacteristic
158D724C2×D411yescharacteristic
159D724C2×D411yescharacteristic
160C22⋊D181—21no—
161C22⋊D181—21no—
162C22⋊D181—21no—
163C22⋊D181—41no—
164C22⋊D181—41no—
165C22⋊D181—41no—
166C22⋊D181—41no—
167C22⋊D181—41no—
168C22⋊D181—41no—
169C22⋊D181—82no—
170C2×Dic181—21no—
171C2×Dic181—21no—
172C2×Dic181—41no—
173C2×Dic181—41no—
174C2×Dic181—41no—
175C4×D181—21no—
176C4×D181—21no—
177C4×D181—21no—
178C4×D181—41no—
179C4×D181—41no—
180#13089678—21no—
181#13089678C2×D411yescharacteristic
182#13089678C2×D411yescharacteristic
183C23×C181—21no—
184C23×C181—21no—
185Q8×C181C2×D411yescharacteristic
186D4×C181—21no—
187D4×C181—21no—
188D4×C181—21no—
189D4×C181—21no—
190D4×C181—21no—
191D4×C181C2×D411yescharacteristic
192C2×C4×C181—21no—
193C2×C4×C181C2411yescharacteristic
194C8×C181—21no—
195C8×C181—21no—
196C8×C181—21no—
197C8×C181C2×D411yescharacteristic
198C8×C181C2×D411yescharacteristic
199C22×C181—21no—
200C22×C181—41no—
201C22×C181—41no—
202C22×C181—81no—
203C22×C181—81no—
204C22×C181H(5,𝔽2)11yescharacteristic
205C2×D181—21no—
206C2×D181—21no—
207C2×D181—21no—
208C2×D181—41no—
209C2×D181—81no—
210C2×D181—161no—
211C2×D181—161no—
212C2×D181—161no—
213C4×C181—21no—
214C4×C181C22×D411yescharacteristic
215C4×C181C22×D411yescharacteristic
216Dic181—21no—
217Dic181—21no—
218Dic181—21no—
219Dic181—41no—
220Dic181—41no—
221C2×C181—21no—
222C2×C181—41no—
223C2×C181—81no—
224C2×C181—81no—
225C2×C181D4211yescharacteristic
226D181—41no—
227D181—41no—
228D181—41no—
229D181—81no—
230C181#328811yescharacteristic, complemented, Sylow
231#3288—1811nomaximal, Sylow
232#577—1811no—
233#577—1811no—
234#576—1811no—
235#576—1811no—
236#496—1811no—
237#472—1811no—
238#472D18111yescharacteristic, complemented
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)—1811no—
250H(5,𝔽2)—1811no—
251#137—3621no—
252#137—3621no—
253#137—1811no—
254#137—1811no—
255AGL(1,ℤ/8)—3621no—
256AGL(1,ℤ/8)—3621no—
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, complemented
266AGL(1,ℤ/8)C2×D18111yescharacteristic, complemented
267#135—3621no—
268#135—3621no—
269#135—3621no—
270#135—3621no—
271#135—1811no—
272#135—1811no—
273C2×SD16—3621no—
274C2×SD16—3621no—
275C2×SD16—1811no—
276C2×SD16—1811no—
277C2×D8—3621no—
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#108C2×D18111yescharacteristic, complemented
289#104—1811no—
290#104—1811no—
291#104—1811no—
292#104—1811no—
293#101—1811no—
294#100—1811no—
295#100C2×D18111yescharacteristic, complemented
296#100C2×D18111yescharacteristic, complemented
297#97—1811no—
298#41—3621no—
299#41—3621no—
300#41—3621no—
301#41—3621no—
302#41—3621no—
303#41—3621no—
304#41—3621no—
305#41—3621no—
306#41—1811no—
307#41—1811no—
308#41—1811no—
309#41—7241no—
310#41C22×D18111yescharacteristic
311C2×Q8—3621no—
312C2×Q8—3621no—
313C2×Q8—1811no—
314C2×D4—3621no—
315C2×D4—3621no—
316C2×D4—3621no—
317C2×D4—3621no—
318C2×D4—3621no—
319C2×D4—3621no—
320C2×D4—1811no—
321C2×D4—7241no—
322C2×D4—7241no—
323C2×D4—7241no—
324C2×D4—7241no—
325C2×D4C22×D18111yescharacteristic
326C2×D4C22×D18111yescharacteristic
327Q16—3621no—
328Q16—3621no—
329Q16—1811no—
330Q16—1811no—
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—
345SD16—1811no—
346SD16—1811no—
347D8—21no—
348D8—21no—
349D8—21no—
350D8—21no—
351D8—3621no—
352D8—3621no—
353D8—3621no—
354D8—3621no—
355D8—3621no—
356D8—3621no—
357D8—1811no—
358D8—1811no—
359M16—21no—
360M16—3621no—
361M16—3621no—
362M16—3621no—
363M16—1811no—
364M16C22×D18111yescharacteristic
365M16C22×D18111yescharacteristic
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—3621no—
378C23—7241no—
379C23—7241no—
380C23—7241no—
381Q8—3621no—
382Q8—3621no—
383Q8—1811no—
384Q8—1811no—
385Q8—1811no—
386Q8—7241no—
387Q8D4×D18111yescharacteristic
388D4—21no—
389D4—21no—
390D4—21no—
391D4—21no—
392D4—21no—
393D4—3621no—
394D4—3621no—
395D4—3621no—
396D4—3621no—
397D4—3621no—
398D4—14482no—
399D4—1811no—
400D4—1811no—
401D4—1811no—
402D4—7241no—
403D4—7241no—
404D4—7241no—
405D4—7241no—
406D4—7241no—
407D4—7241no—
408D4—7241no—
409D4D4×D18111yescharacteristic
410C2×C4—21no—
411C2×C4—3621no—
412C2×C4—3621no—
413C2×C4—3621no—
414C2×C4—3621no—
415C2×C4—3621no—
416C2×C4—7241no—
417C2×C4—7241no—
418C2×C4—7241no—
419C2×C4—7241no—
420C2×C4—7241no—
421C2×C4C23×D18111yescharacteristic
422C8—21no—
423C8—21no—
424C8—21no—
425C8—3621no—
426C8—1811no—
427C8—1811no—
428C8D4×D18111yescharacteristic
429C8D4×D18111yescharacteristic
430C22—21no—
431C22—41no—
432C22—41no—
433C22—81no—
434C22—81no—
435C22—28961no—
436C22—28961no—
437C22—28961no—
438C22—3621no—
439C22—3621no—
440C22—3621no—
441C22—14481no—
442C22—7241no—
443C22#1915386211yescharacteristic
444C4—21no—
445C4—3621no—
446C4—3621no—
447C4—3621no—
448C4—7241no—
449C4—7241no—
450C4C2×D4×D18111yescharacteristic
451C4C2×D4×D18111yescharacteristic
452C2—21no—
453C2—41no—
454C2—81no—
455C2—81no—
456C2—14481no—
457C2—7241no—
458C2—7241no—
459C2—7241no—
460C2#2604191311yescharacteristic
subgroupG/H
centerC2#26041913
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#472×C181C2
socleC2×C181D42
hypercenter#472D181
hypocenterC181#3288
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

Complements

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

NH ≅ G/Ntype
1. #26042091C2semidirect
2. #26042089C2semidirect
3. #26042083C2semidirect
4. #26042080C2semidirect
5. #26041667C2semidirect
6. #26041548C2semidirect
7. #26041543C2semidirect
8. #26041541C2semidirect
9. #26041459C2semidirect
10. #26041450C2semidirect
11. #26041449C2semidirect
12. #26041445C2semidirect
13. #26041400C2semidirect
14. #26041399C2semidirect
15. #472×C181C2semidirect
16. #19153863C22semidirect
17. #19153862C22semidirect
19. #19153861C22semidirect
21. #19153849C22semidirect
22. #19153849C22semidirect
26. #19153844C22semidirect
29. #19153842C22semidirect
41. C2×#15668438C22semidirect
42. C2×#15668437C22semidirect
44. C2×#15668434C22semidirect
47. #19153824C22semidirect
48. #19153824C22semidirect
49. #19153822C22semidirect
50. #19153812C22semidirect
51. #19153803C22semidirect
52. #19153751C22semidirect
53. #19153743C22semidirect
54. #19153742C22semidirect
55. #19153742C22semidirect
56. #19153742C22semidirect
57. #19153734C22semidirect
58. #19153732C22semidirect
59. #19153726C22semidirect
60. AGL(1,ℤ/8)×C181C22semidirect
61. AGL(1,ℤ/8)×C181C22semidirect
62. C2×D8×C181C22semidirect
63. #131×C181C22semidirect
64. #108×C181C22semidirect
65. #100×C181C22semidirect
66. #100×C181C22semidirect
95. Dic724D4semidirect
96. #15668439D4semidirect
103. #15668438D4semidirect
104. #15668438D4semidirect
109. #15668437D4semidirect
110. #15668436D4semidirect
113. D1448D4semidirect
118. #15668434D4semidirect
230. C181#3288semidirect
238. #472D181semidirect
265. AGL(1,ℤ/8)C2×D181semidirect
266. AGL(1,ℤ/8)C2×D181semidirect
280. C2×D8C2×D181semidirect
284. #131C2×D181semidirect
288. #108C2×D181semidirect
295. #100C2×D181semidirect
296. #100C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260420912
#260420892
#260420832
#260420802
#260416672
#260415482
#260415432
#260415412
#260414592
#260414502
#260414492
#260414452
#260414002
#260413992
#472×C1812
#3288181