Finite Group Databasebeta

← #37545504

Subgroups — #37545504

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#26042095C211yesmaximal, characteristic, complemented
2#26042091C211yesmaximal, characteristic, complemented
3#26042085C211yesmaximal, characteristic, complemented
4#26042083C211yesmaximal, characteristic, complemented
5#26041660C211yesmaximal, characteristic, complemented
6#26041553C211yesmaximal, characteristic, complemented
7#26041548C211yesmaximal, characteristic, complemented
8#26041543C211yesmaximal, characteristic, complemented
9#26041459C211yesmaximal, characteristic, complemented
10#26041455C211yesmaximal, characteristic, complemented
11#26041454C211yesmaximal, characteristic, complemented
12#26041450C211yesmaximal, characteristic, complemented
13#26041395C211yesmaximal, characteristic, complemented
14#26041394C211yesmaximal, characteristic, complemented
15#471×C181C211yesmaximal, characteristic, complemented
16#19153864C2211yescharacteristic, complemented
17#19153863C2211yescharacteristic, complemented
18#19153862C2211yescharacteristic
19#19153861C2211yescharacteristic
20#19153849—21no—
21#19153849C2211yescharacteristic
22#19153849C2211yescharacteristic, complemented
23#19153848—21no—
24#19153847C2211yescharacteristic
25#19153845—21no—
26#19153845—21no—
27#19153844—21no—
28#19153844C2211yescharacteristic
29#19153844C2211yescharacteristic, complemented
30#19153843—21no—
31#19153843—21no—
32#19153842C2211yescharacteristic, complemented
33#19153840—21no—
34#19153838—21no—
35#19153838C2211yescharacteristic
36#19153837—21no—
37#19153837—21no—
38#19153837—21no—
39#19153836C2211yescharacteristic
40C2×#15668439C2211yescharacteristic, complemented
41Q16×D181—21no—
42C2×#15668438—21no—
43C2×#15668438C2211yescharacteristic, complemented
44SD16×D181—21no—
45C2×#15668434C2211yescharacteristic
46D8×D181—21no—
47#19153824C2211yescharacteristic
48#19153824C2211yescharacteristic, complemented
49#19153822C2211yescharacteristic, complemented
50#19153805C2211yescharacteristic, complemented
51#19153803C2211yescharacteristic, complemented
52#19153751C2211yescharacteristic, complemented
53#19153743C2211yescharacteristic, complemented
54#19153742C2211yescharacteristic
55#19153742C2211yescharacteristic, complemented
56#19153742C2211yescharacteristic, complemented
57#19153734C2211yescharacteristic, complemented
58#19153732C2211yescharacteristic, complemented
59C8×Dic181C2211yescharacteristic, complemented
60#137×C181C2211yescharacteristic, complemented
61AGL(1,ℤ/8)×C181C2211yescharacteristic
62C2×SD16×C181C2211yescharacteristic, complemented
63#131×C181C2211yescharacteristic, complemented
64#108×C181C2211yescharacteristic, complemented
65#101×C181C2211yescharacteristic, complemented
66#100×C181C2211yescharacteristic, complemented
67#15668450—21no—
68#15668450—21no—
69#15668450—21no—
70#15668449—21no—
71#15668449—21no—
72#15668449—41no—
73#15668449C2311yescharacteristic
74#15668449C2311yescharacteristic
75#15668449C2311yescharacteristic
76#15668448—21no—
77#15668448—21no—
78#15668448—21no—
79#15668448—41no—
80C2×Dic362—21no—
81C2×Dic362C2311yescharacteristic
82Q8×D181—21no—
83Q8×D181—21no—
84Q8×D181—21no—
85C2×D724—21no—
86C2×D724C2311yescharacteristic
87C2×C22⋊D181—41no—
88D4×D181—21no—
89D4×D181—21no—
90D4×D181—21no—
91D4×D181—41no—
92Dic724—21no—
93Dic724—21no—
94Dic724D411yescharacteristic
95#15668439—21no—
96#15668439—21no—
97#15668439—21no—
98#15668439D411yescharacteristic
99#15668438—21no—
100#15668438—21no—
101#15668438—21no—
102#15668438—21no—
103#15668438—21no—
104#15668438—21no—
105#15668438D411yescharacteristic
106#15668438D411yescharacteristic
107#15668437—21no—
108#15668437D411yescharacteristic
109#15668436—21no—
110#15668436D411yescharacteristic
111D1448—21no—
112D1448—21no—
113D1448D411yescharacteristic
114#15668434—21no—
115#15668434—21no—
116#15668434—21no—
117#15668434D411yescharacteristic
118#15668433C2311yescharacteristic
119#15668432—21no—
120#15668432—21no—
121#15668432—21no—
122C2×#13089678C2311yescharacteristic
123C8×D181—21no—
124C8×D181—21no—
125C8×D181—21no—
126C22⋊Dic181—41no—
127#15668426—41no—
128C4×Dic181C2311yescharacteristic
129#41×C181C2311yescharacteristic
130C2×Q8×C181C2311yescharacteristic
131C2×D4×C181C2311yescharacteristic
132Q16×C181—21no—
133SD16×C181—21no—
134SD16×C181—21no—
135SD16×C181—21no—
136SD16×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—
147Dic362—21no—
148Dic362—21no—
149Dic362—41no—
150Dic362—41no—
151Dic362C2×D411yescharacteristic
152Dic362C2×D411yescharacteristic
153Dic362C2×D411yescharacteristic
154D724—21no—
155D724—21no—
156D724—41no—
157D724—41no—
158D724C2×D411yescharacteristic
159D724C2×D411yescharacteristic
160D724C2×D411yescharacteristic
161C22⋊D181—21no—
162C22⋊D181—21no—
163C22⋊D181—21no—
164C22⋊D181—41no—
165C22⋊D181—41no—
166C22⋊D181—41no—
167C22⋊D181—41no—
168C2×Dic181—21no—
169C2×Dic181—21no—
170C2×Dic181—41no—
171C2×Dic181—41no—
172C4×D181—21no—
173C4×D181—21no—
174C4×D181—21no—
175C4×D181—41no—
176C4×D181—41no—
177C4×D181—41no—
178C4×D181—41no—
179#13089678—21no—
180#13089678C2×D411yescharacteristic
181#13089678C2×D411yescharacteristic
182C23×C181—21no—
183Q8×C181—21no—
184Q8×C181—21no—
185Q8×C181C2×D411yescharacteristic
186D4×C181—21no—
187D4×C181—21no—
188D4×C181—21no—
189D4×C181C2×D411yescharacteristic
190C2×C4×C181—21no—
191C2×C4×C181—21no—
192C2×C4×C181C2411yescharacteristic
193C8×C181—21no—
194C8×C181—21no—
195C8×C181—21no—
196C8×C181C2×D411yescharacteristic
197C8×C181C2×D411yescharacteristic
198C22×C181—21no—
199C22×C181—41no—
200C22×C181—81no—
201C22×C181H(5,𝔽2)11yescharacteristic
202C2×D181—21no—
203C2×D181—21no—
204C2×D181—21no—
205C2×D181—41no—
206C2×D181—81no—
207C2×D181—161no—
208C2×D181—161no—
209C4×C181—21no—
210C4×C181—41no—
211C4×C181C22×D411yescharacteristic
212C4×C181C22×D411yescharacteristic
213Dic181—21no—
214Dic181—21no—
215Dic181—21no—
216Dic181—41no—
217Dic181—41no—
218C2×C181—21no—
219C2×C181—41no—
220C2×C181—81no—
221C2×C181D4211yescharacteristic
222D181—41no—
223D181—41no—
224D181—41no—
225D181—81no—
226C181#329011yescharacteristic, complemented, Sylow
227#3290—1811nomaximal, Sylow
228#578—1811no—
229#577—1811no—
230#577—1811no—
231#576—1811no—
232#495—1811no—
233#473—1811no—
234#472—1811no—
235#471—1811no—
236#471D18111yescharacteristic, complemented
237#455—1811no—
238#455—1811no—
239#454—1811no—
240#454—1811no—
241#443—1811no—
242#443—1811no—
2432−1+4—1811no—
2442−1+4—1811no—
245H(5,𝔽2)—1811no—
246H(5,𝔽2)—1811no—
247#137—3621no—
248#137—3621no—
249#137—3621no—
250#137—3621no—
251#137—1811no—
252#137—1811no—
253#137—1811no—
254#137C2×D18111yescharacteristic, complemented
255AGL(1,ℤ/8)—3621no—
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
263#135—3621no—
264#135—3621no—
265#135—3621no—
266#135—3621no—
267#135—1811no—
268#135—1811no—
269C2×Q16—3621no—
270C2×Q16—1811no—
271C2×SD16—3621no—
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#108C2×D18111yescharacteristic, complemented
285#104—1811no—
286#104—1811no—
287#104—1811no—
288#104—1811no—
289#101—1811no—
290#101C2×D18111yescharacteristic, complemented
291#100—1811no—
292#100C2×D18111yescharacteristic, complemented
293C4×C8—1811no—
294#41—3621no—
295#41—3621no—
296#41—3621no—
297#41—3621no—
298#41—3621no—
299#41—3621no—
300#41—3621no—
301#41—3621no—
302#41—1811no—
303#41—1811no—
304#41—1811no—
305#41—7241no—
306#41—7241no—
307#41C22×D18111yescharacteristic
308C2×Q8—3621no—
309C2×Q8—3621no—
310C2×Q8—3621no—
311C2×Q8—3621no—
312C2×Q8—1811no—
313C2×Q8C22×D18111yescharacteristic
314C2×D4—3621no—
315C2×D4—3621no—
316C2×D4—3621no—
317C2×D4—3621no—
318C2×D4—1811no—
319C2×D4—7241no—
320C2×D4—7241no—
321C2×D4C22×D18111yescharacteristic
322Q16—21no—
323Q16—3621no—
324Q16—3621no—
325Q16—3621no—
326Q16—3621no—
327Q16—3621no—
328Q16—1811no—
329Q16—1811no—
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—
344SD16—1811no—
345SD16—1811no—
346D8—21no—
347D8—3621no—
348D8—3621no—
349D8—3621no—
350D8—3621no—
351D8—3621no—
352D8—1811no—
353D8—1811no—
354M16—21no—
355M16—3621no—
356M16—3621no—
357M16—3621no—
358M16—1811no—
359M16C22×D18111yescharacteristic
360M16C22×D18111yescharacteristic
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—3621no—
373C23—7241no—
374C23—7241no—
375Q8—21no—
376Q8—21no—
377Q8—3621no—
378Q8—3621no—
379Q8—1811no—
380Q8—1811no—
381Q8—1811no—
382Q8—7241no—
383Q8—7241no—
384Q8D4×D18111yescharacteristic
385D4—21no—
386D4—21no—
387D4—21no—
388D4—3621no—
389D4—3621no—
390D4—3621no—
391D4—3621no—
392D4—3621no—
393D4—1811no—
394D4—1811no—
395D4—1811no—
396D4—7241no—
397D4—7241no—
398D4—7241no—
399D4—7241no—
400D4—7241no—
401D4—7241no—
402D4D4×D18111yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—3621no—
406C2×C4—3621no—
407C2×C4—3621no—
408C2×C4—3621no—
409C2×C4—3621no—
410C2×C4—7241no—
411C2×C4—7241no—
412C2×C4—7241no—
413C2×C4—7241no—
414C2×C4—7241no—
415C2×C4—7241no—
416C2×C4C23×D18111yescharacteristic
417C8—21no—
418C8—21no—
419C8—21no—
420C8—3621no—
421C8—1811no—
422C8—1811no—
423C8D4×D18111yescharacteristic
424C8D4×D18111yescharacteristic
425C22—21no—
426C22—41no—
427C22—81no—
428C22—28961no—
429C22—28961no—
430C22—3621no—
431C22—3621no—
432C22—3621no—
433C22—14481no—
434C22—7241no—
435C22#1915386211yescharacteristic
436C4—21no—
437C4—41no—
438C4—3621no—
439C4—3621no—
440C4—3621no—
441C4—7241no—
442C4—7241no—
443C4C2×D4×D18111yescharacteristic
444C4C2×D4×D18111yescharacteristic
445C2—21no—
446C2—41no—
447C2—81no—
448C2—14481no—
449C2—7241no—
450C2—7241no—
451C2—7241no—
452C2#2604191311yescharacteristic
subgroupG/H
centerC2#26041913
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#471×C181C2
socleC2×C181D42
hypercenter#471D181
hypocenterC181#3290
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #26042095C2semidirect
2. #26042091C2semidirect
3. #26042085C2semidirect
4. #26042083C2semidirect
5. #26041660C2semidirect
6. #26041553C2semidirect
7. #26041548C2semidirect
8. #26041543C2semidirect
9. #26041459C2semidirect
10. #26041455C2semidirect
11. #26041454C2semidirect
12. #26041450C2semidirect
13. #26041395C2semidirect
14. #26041394C2semidirect
15. #471×C181C2semidirect
16. #19153864C22semidirect
17. #19153863C22semidirect
22. #19153849C22semidirect
29. #19153844C22semidirect
32. #19153842C22semidirect
40. C2×#15668439C22semidirect
43. C2×#15668438C22semidirect
48. #19153824C22semidirect
49. #19153822C22semidirect
50. #19153805C22semidirect
51. #19153803C22semidirect
52. #19153751C22semidirect
53. #19153743C22semidirect
55. #19153742C22semidirect
56. #19153742C22semidirect
57. #19153734C22semidirect
58. #19153732C22semidirect
59. C8×Dic181C22semidirect
60. #137×C181C22semidirect
62. C2×SD16×C181C22semidirect
63. #131×C181C22semidirect
64. #108×C181C22semidirect
65. #101×C181C22semidirect
66. #100×C181C22semidirect
226. C181#3290semidirect
236. #471D181semidirect
254. #137C2×D181semidirect
274. C2×SD16C2×D181semidirect
280. #131C2×D181semidirect
284. #108C2×D181semidirect
290. #101C2×D181semidirect
292. #100C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260420952
#260420912
#260420852
#260420832
#260416602
#260415532
#260415482
#260415432
#260414592
#260414552
#260414542
#260414502
#260413952
#260413942
#471×C1812
#3290181