Finite Group Databasebeta

← #37545513

Subgroups — #37545513

Order 23168.

460 conjugacy classes of subgroups.

The subgroup lattice has 456 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#26042088C211yesmaximal, characteristic, complemented
4#26042085C211yesmaximal, characteristic, complemented
5#26041650C211yesmaximal, characteristic, complemented
6#26041545C211yesmaximal, characteristic, complemented
7#26041543C211yesmaximal, characteristic, complemented
8#26041541C211yesmaximal, characteristic, complemented
9#26041464C211yesmaximal, characteristic, complemented
10#26041460C211yesmaximal, characteristic, complemented
11#26041449C211yesmaximal, characteristic, complemented
12#26041445C211yesmaximal, characteristic, complemented
13#26041395C211yesmaximal, characteristic, complemented
14#26041394C211yesmaximal, characteristic, complemented
15#471×C181C211yesmaximal, characteristic, complemented
16#19153864C2211yescharacteristic
17#19153863C2211yescharacteristic
18#19153862C2211yescharacteristic, complemented
19#19153861C2211yescharacteristic, complemented
20#19153849—21no—
21#19153849C2211yescharacteristic, complemented
22#19153849C2211yescharacteristic, complemented
23#19153848—21no—
24#19153847C2211yescharacteristic, complemented
25#19153845—21no—
26#19153845—21no—
27#19153844—21no—
28#19153844C2211yescharacteristic
29#19153844C2211yescharacteristic
30#19153843—21no—
31#19153843—21no—
32#19153842C2211yescharacteristic
33#19153840—21no—
34#19153839—21no—
35#19153838—21no—
36#19153838C2211yescharacteristic
37#19153837—21no—
38#19153836C2211yescharacteristic
39#19153835—21no—
40C2×#15668438—21no—
41C2×#15668438C2211yescharacteristic, complemented
42C2×#15668437C2211yescharacteristic, complemented
43C2×#15668436C2211yescharacteristic, complemented
44SD16×D181—21no—
45SD16×D181—21no—
46SD16×D181—21no—
47#19153824C2211yescharacteristic, complemented
48#19153824C2211yescharacteristic, complemented
49#19153822C2211yescharacteristic, complemented
50#19153814C2211yescharacteristic, complemented
51#19153812C2211yescharacteristic
52#19153751C2211yescharacteristic, complemented
53#19153743C2211yescharacteristic, complemented
54#19153742C2211yescharacteristic, complemented
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—
88C2×C22⋊D181—41no—
89D4×D181—21no—
90D4×D181—21no—
91D4×D181—21no—
92D4×D181—41no—
93Dic724—21no—
94Dic724—21no—
95Dic724D411yescharacteristic, complemented
96#15668439—21no—
97#15668439D411yescharacteristic, complemented
98#15668438—21no—
99#15668438—21no—
100#15668438—21no—
101#15668438—21no—
102#15668438—21no—
103#15668438—21no—
104#15668438D411yescharacteristic, complemented
105#15668438D411yescharacteristic, complemented
106#15668437—21no—
107#15668437—21no—
108#15668437—21no—
109#15668437D411yescharacteristic, complemented
110#15668436—21no—
111#15668436—21no—
112#15668436—21no—
113#15668436D411yescharacteristic, complemented
114D1448—21no—
115D1448—21no—
116D1448D411yescharacteristic, complemented
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—
127#15668428—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—
168C22⋊D181—82no—
169C2×Dic181—21no—
170C2×Dic181—21no—
171C2×Dic181—41no—
172C2×Dic181—41no—
173C4×D181—21no—
174C4×D181—21no—
175C4×D181—21no—
176C4×D181—41no—
177C4×D181—41no—
178C4×D181—41no—
179C4×D181—41no—
180#13089678—21no—
181#13089678C2×D411yescharacteristic
182#13089678C2×D411yescharacteristic
183C23×C181—21no—
184Q8×C181—21no—
185Q8×C181—21no—
186Q8×C181C2×D411yescharacteristic
187D4×C181—21no—
188D4×C181—21no—
189D4×C181—21no—
190D4×C181C2×D411yescharacteristic
191C2×C4×C181—21no—
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—81no—
202C22×C181H(5,𝔽2)11yescharacteristic
203C2×D181—21no—
204C2×D181—21no—
205C2×D181—21no—
206C2×D181—41no—
207C2×D181—81no—
208C2×D181—161no—
209C2×D181—161no—
210C4×C181—21no—
211C4×C181—41no—
212C4×C181C22×D411yescharacteristic
213C4×C181C22×D411yescharacteristic
214Dic181—22no—
215Dic181—21no—
216Dic181—21no—
217Dic181—21no—
218Dic181—41no—
219C2×C181—21no—
220C2×C181—41no—
221C2×C181—81no—
222C2×C181D4211yescharacteristic
223D181—41no—
224D181—41no—
225D181—41no—
226D181—81no—
227C181#329111yescharacteristic, complemented, Sylow
228#3291—1811nomaximal, Sylow
229#577—1811no—
230#577—1811no—
231#577—1811no—
232#577—1811no—
233#492—1811no—
234#471—1811no—
235#471—1811no—
236#471—1811no—
237#471D18111yescharacteristic, complemented
238#456—1811no—
239#456—1811no—
240#453—1811no—
241#453—1811no—
242#443—1811no—
243#443—1811no—
2442−1+4—1811no—
2452−1+4—1811no—
246H(5,𝔽2)—1811no—
247H(5,𝔽2)—1811no—
248#137—3621no—
249#137—3621no—
250#137—3621no—
251#137—3621no—
252#137—1811no—
253#137—1811no—
254#137—1811no—
255#137C2×D18111yescharacteristic, complemented
256AGL(1,ℤ/8)—3621no—
257AGL(1,ℤ/8)—3621no—
258AGL(1,ℤ/8)—3621no—
259AGL(1,ℤ/8)—3621no—
260AGL(1,ℤ/8)—1811no—
261AGL(1,ℤ/8)—1811no—
262AGL(1,ℤ/8)—1811no—
263AGL(1,ℤ/8)C2×D18111yescharacteristic
264#135—3621no—
265#135—3621no—
266#135—3621no—
267#135—3621no—
268#135—1811no—
269#135—1811no—
270C2×SD16—3621no—
271C2×SD16—3621no—
272C2×SD16—3621no—
273C2×SD16—3621no—
274C2×SD16—1811no—
275C2×SD16—1811no—
276C2×SD16—1811no—
277C2×SD16C2×D18111yescharacteristic, complemented
278#131—1811no—
279#131—1811no—
280#131—1811no—
281#131C2×D18111yescharacteristic, complemented
282C4⋊Q8—1811no—
283#127—1811no—
284#108—1811no—
285#108C2×D18111yescharacteristic, complemented
286#104—1811no—
287#104—1811no—
288#104—1811no—
289#104—1811no—
290#101—1811no—
291#101C2×D18111yescharacteristic, complemented
292#100—1811no—
293#100C2×D18111yescharacteristic, complemented
294C4×C8—1811no—
295#41—3621no—
296#41—3621no—
297#41—3621no—
298#41—3621no—
299#41—3621no—
300#41—3621no—
301#41—3621no—
302#41—3621no—
303#41—1811no—
304#41—1811no—
305#41—1811no—
306#41—7241no—
307#41—7241no—
308#41C22×D18111yescharacteristic
309C2×Q8—3621no—
310C2×Q8—3621no—
311C2×Q8—3621no—
312C2×Q8—3621no—
313C2×Q8—1811no—
314C2×Q8C22×D18111yescharacteristic
315C2×D4—3621no—
316C2×D4—3621no—
317C2×D4—3621no—
318C2×D4—3621no—
319C2×D4—1811no—
320C2×D4—7241no—
321C2×D4—7241no—
322C2×D4—7241no—
323C2×D4C22×D18111yescharacteristic
324Q16—21no—
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—3621no—
343SD16—3621no—
344SD16—3621no—
345SD16—3621no—
346SD16—1811no—
347SD16—1811no—
348SD16—1811no—
349SD16—1811no—
350D8—21no—
351D8—3621no—
352D8—3621no—
353D8—3621no—
354D8—1811no—
355D8—1811no—
356M16—21no—
357M16—3621no—
358M16—3621no—
359M16—3621no—
360M16—1811no—
361M16C22×D18111yescharacteristic
362M16C22×D18111yescharacteristic
363M16C22×D18111yescharacteristic
364C2×C8—21no—
365C2×C8—3621no—
366C2×C8—3621no—
367C2×C8—3621no—
368C2×C8—1811no—
369C2×C8C22×D18111yescharacteristic
370C4⋊C4—7241no—
371C42—1811no—
372C23—21no—
373C23—3621no—
374C23—7241no—
375C23—7241no—
376Q8—21no—
377Q8—21no—
378Q8—3621no—
379Q8—3621no—
380Q8—1811no—
381Q8—1811no—
382Q8—1811no—
383Q8—7241no—
384Q8—7241no—
385Q8D4×D18111yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—3621no—
390D4—3621no—
391D4—3621no—
392D4—3621no—
393D4—3621no—
394D4—14482no—
395D4—1811no—
396D4—1811no—
397D4—1811no—
398D4—7241no—
399D4—7241no—
400D4—7241no—
401D4—7241no—
402D4—7241no—
403D4—7241no—
404D4D4×D18111yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—3621no—
408C2×C4—3621no—
409C2×C4—3621no—
410C2×C4—3621no—
411C2×C4—3621no—
412C2×C4—7241no—
413C2×C4—7241no—
414C2×C4—7241no—
415C2×C4—7241no—
416C2×C4—7241no—
417C2×C4—7241no—
418C2×C4C23×D18111yescharacteristic
419C8—21no—
420C8—21no—
421C8—21no—
422C8—3621no—
423C8—1811no—
424C8—1811no—
425C8D4×D18111yescharacteristic
426C8D4×D18111yescharacteristic
427C22—21no—
428C22—41no—
429C22—81no—
430C22—28961no—
431C22—28961no—
432C22—3621no—
433C22—3621no—
434C22—3621no—
435C22—14481no—
436C22—7241no—
437C22#1915386211yescharacteristic
438C4—21no—
439C4—41no—
440C4—3622no—
441C4—3621no—
442C4—3621no—
443C4—3621no—
444C4—7241no—
445C4C2×D4×D18111yescharacteristic
446C4C2×D4×D18111yescharacteristic
447C2—21no—
448C2—41no—
449C2—81no—
450C2—14481no—
451C2—7241no—
452C2—7241no—
453C2—7241no—
454C2#2604191311yescharacteristic
subgroupG/H
centerC2#26041913
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#471×C181C2
socleC2×C181D42
hypercenter#471D181
hypocenterC181#3291
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. #26042091C2semidirect
2. #26042089C2semidirect
3. #26042088C2semidirect
4. #26042085C2semidirect
5. #26041650C2semidirect
6. #26041545C2semidirect
7. #26041543C2semidirect
8. #26041541C2semidirect
9. #26041464C2semidirect
10. #26041460C2semidirect
11. #26041449C2semidirect
12. #26041445C2semidirect
13. #26041395C2semidirect
14. #26041394C2semidirect
15. #471×C181C2semidirect
18. #19153862C22semidirect
19. #19153861C22semidirect
21. #19153849C22semidirect
22. #19153849C22semidirect
24. #19153847C22semidirect
41. C2×#15668438C22semidirect
42. C2×#15668437C22semidirect
43. C2×#15668436C22semidirect
47. #19153824C22semidirect
48. #19153824C22semidirect
49. #19153822C22semidirect
50. #19153814C22semidirect
52. #19153751C22semidirect
53. #19153743C22semidirect
54. #19153742C22semidirect
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
95. Dic724D4semidirect
97. #15668439D4semidirect
104. #15668438D4semidirect
105. #15668438D4semidirect
109. #15668437D4semidirect
113. #15668436D4semidirect
116. D1448D4semidirect
118. #15668434D4semidirect
227. C181#3291semidirect
237. #471D181semidirect
255. #137C2×D181semidirect
277. C2×SD16C2×D181semidirect
281. #131C2×D181semidirect
285. #108C2×D181semidirect
291. #101C2×D181semidirect
293. #100C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260420912
#260420892
#260420882
#260420852
#260416502
#260415452
#260415432
#260415412
#260414642
#260414602
#260414492
#260414452
#260413952
#260413942
#471×C1812
#3291181