Finite Group Databasebeta

← #37545740

Subgroups — #37545740

Order 23168.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041964C211yesmaximal, characteristic, complemented
2#26041913C211yesmaximal, characteristic
3#26041642C211yesmaximal, characteristic, complemented
4#26041606C211yesmaximal, characteristic, complemented
5#26041582C211yesmaximal, characteristic, complemented
6#26041526C211yesmaximal, characteristic, complemented
7#26041506C211yesmaximal, characteristic, complemented
8#26041478C211yesmaximal, characteristic, complemented
9#26041432C211yesmaximal, characteristic, complemented
10#26041431C211yesmaximal, characteristic, complemented
11#26041378C211yesmaximal, characteristic, complemented
12#26041347C211yesmaximal, characteristic, complemented
13#26041282C211yesmaximal, characteristic, complemented
14C2×#19153736C211yesmaximal, characteristic, complemented
15#480×C181C211yesmaximal, characteristic, complemented
16C22×D724C2211yescharacteristic
17C2×D4×D181—21no—
18C2×D4×D181C2211yescharacteristic
19C2×#15668438C2211yescharacteristic
20C2×#15668438C2211yescharacteristic, complemented
21C2×#15668437C2211yescharacteristic, complemented
22C2×#15668432C2211yescharacteristic, complemented
23C22×#13089678C2211yescharacteristic, complemented
24#19153812C2211yescharacteristic
25#19153811—21no—
26#19153807C2211yescharacteristic, complemented
27#19153806—21no—
28#19153799—21no—
29#19153796C2211yescharacteristic, complemented
30#19153795C2211yescharacteristic, complemented
31#19153791C2211yescharacteristic
32#19153789—21no—
33#19153786—21no—
34#19153784—21no—
35#19153781C2211yescharacteristic, complemented
36#19153778C2211yescharacteristic
37C4×C22⋊D181C2211yescharacteristic
38#19153775—21no—
39#19153774C2211yescharacteristic, complemented
40#19153747C2211yescharacteristic, complemented
41#19153745C2211yescharacteristic, complemented
42#19153739C2211yescharacteristic, complemented
43#19153738C2211yescharacteristic
44#19153738C2211yescharacteristic, complemented
45#19153737C2211yescharacteristic, complemented
46#19153736C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic, complemented
49#19153736C2211yescharacteristic, complemented
50#19153728C2211yescharacteristic, complemented
51#19153726C2211yescharacteristic, complemented
52#121×C181C2211yescharacteristic
53C2×C4⋊C4×C181C2211yescharacteristic, complemented
54#107×C181C2211yescharacteristic, complemented
55#107×C181C2211yescharacteristic, complemented
56#102×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic, complemented
58C22⋊C8×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60C23×D181—21no—
61C2×Dic362C2311yescharacteristic
62C2×D724—22no—
63C2×D724—21no—
64C2×D724—21no—
65C2×D724—41no—
66C2×D724C2311yescharacteristic
67C2×D724C2311yescharacteristic
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C2×C22⋊D181D411yescharacteristic
72D4×D181—22no—
73D4×D181—41no—
74D4×D181—44no—
75C2×C4×D181—21no—
76C2×C4×D181C2311yescharacteristic
77#15668438—22no—
78#15668438—41no—
79#15668437—41no—
80#15668432—41no—
81C2×#13089678—41no—
82C2×#13089678C2311yescharacteristic
83C2×#13089678C2311yescharacteristic
84C4⋊Dic181—21no—
85C4⋊Dic181—21no—
86C4⋊Dic181C2311yescharacteristic
87#15668428—21no—
88#15668428—21no—
89#15668428—21no—
90#15668428D411yescharacteristic
91C22⋊Dic181—21no—
92C22⋊Dic181D411yescharacteristic
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426D411yescharacteristic
98C4×Dic181—21no—
99C4×Dic181—21no—
100C4×Dic181C2311yescharacteristic
101C2×D4×C181—21no—
102C2×D4×C181C2311yescharacteristic
103C22×C4×C181—21no—
104C22×C4×C181C2311yescharacteristic
105C2×C8×C181C2311yescharacteristic
106C2×C8×C181C2311yescharacteristic
107C4⋊C4×C181—21no—
108C4⋊C4×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C4⋊C4×C181C2311yescharacteristic
111C22⋊C4×C181—21no—
112C22×D181—21no—
113C22×D181—21no—
114C22×D181—42no—
115C22×D181—42no—
116C22×D181—42no—
117C22×D181—42no—
118C22×D181—81no—
119C22×D181—81no—
120C22×D181C2×D411yescharacteristic
121Dic362—21no—
122Dic362—21no—
123D724—21no—
124D724—21no—
125D724—21no—
126D724—42no—
127D724—42no—
128D724#4112yes—
129C22⋊D181—22no—
130C22⋊D181—42no—
131C22⋊D181—42no—
132C22⋊D181—81no—
133C2×Dic181—21no—
134C2×Dic181—21no—
135C2×Dic181C2×D411yescharacteristic
136C2×Dic181C2×D411yescharacteristic
137C2×Dic181C2×D411yescharacteristic
138C4×D181—21no—
139C4×D181—21no—
140C4×D181—42no—
141#13089678—21no—
142#13089678—21no—
143C23×C181—21no—
144C23×C181C2×D411yescharacteristic
145D4×C181—21no—
146D4×C181—21no—
147D4×C181—42no—
148C2×C4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181—21no—
151C2×C4×C181—21no—
152C2×C4×C181—21no—
153C2×C4×C181—42no—
154C2×C4×C181C2×D411yescharacteristic
155C2×C4×C181C2411yescharacteristic
156C8×C181—21no—
157C8×C181—21no—
158C22×C181—21no—
159C22×C181—21no—
160C22×C181—41no—
161C22×C181—41no—
162C22×C181—41no—
163C22×C181AGL(1,ℤ/8)12yes—
164C22×C181C22×D411yescharacteristic
165C2×D181—21no—
166C2×D181—22no—
167C2×D181—21no—
168C2×D181—21no—
169C2×D181—41no—
170C2×D181—41no—
171C2×D181—41no—
172C2×D181—41no—
173C2×D181—41no—
174C2×D181—84no—
175C2×D181—84no—
176C4×C181—21no—
177C4×C181—41no—
178C4×C181—41no—
179C4×C181—41no—
180C4×C181C2×#4111yescharacteristic
181C4×C181H(5,𝔽2)11yescharacteristic
182Dic181—21no—
183Dic181—21no—
184Dic181—21no—
185Dic181—41no—
186Dic181—41no—
187C2×C181—22no—
188C2×C181—81no—
189C2×C181#54611yescharacteristic
190C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C181#57711yescharacteristic
192D181—41no—
193D181—42no—
194D181—81no—
195C181#331011yescharacteristic, complemented, Sylow
196#3310—1811nomaximal, Sylow
197#552—1811no—
198D42—1811no—
199#490—1811no—
200#482—1811no—
201#480D18111yescharacteristic, complemented
202#478—1811no—
203#468—1811no—
204#465—1811no—
205#460—1811no—
206#450—1811no—
207#450—1811no—
208#440—1811no—
209#435—1811no—
210#418—1811no—
211C2×#102—1811no—
212C22×D4—3621no—
213C22×D4—1811no—
214C22×D4—1811no—
215C2×SD16—1811no—
216C2×SD16—1811no—
217C2×SD16—1811no—
218C2×M16—1811no—
219C22×C8—1811no—
220#127—1811no—
221#126—3621no—
222#125—3621no—
223#125—1811no—
224#123—3621no—
225C22⋊Q8—1811no—
226C22⋊Q8—1811no—
227#121—3621no—
228#121—1811no—
229#121C2×D18111yescharacteristic
230#120—3621no—
231#120—3621no—
232C4×Q8—1811no—
233C4×D4—1811no—
234C4×D4—1811no—
235#117—3621no—
236#117—1811no—
237C2×C4⋊C4C2×D18111yescharacteristic, complemented
238#107C2×D18111yescharacteristic, complemented
239#107C2×D18111yescharacteristic, complemented
240#106—1811no—
241C4⋊C8—1811no—
242#103—1811no—
243#102—1811no—
244#102—1811no—
245#102—1811no—
246#102—1811no—
247#102—1811no—
248#102—1811no—
249#102—1811no—
250#102C2×D18111yescharacteristic, complemented
251#102C2×D18111yescharacteristic, complemented
252C22⋊C8—1811no—
253C22⋊C8C2×D18111yescharacteristic, complemented
254#97—1811no—
255C24—3621no—
256C24—3621no—
257C2×Q8—1811no—
258C2×D4—21no—
259C2×D4—3622no—
260C2×D4—3621no—
261C2×D4—3622no—
262C2×D4—3621no—
263C2×D4—3621no—
264C2×D4—3621no—
265C2×D4—3621no—
266C2×D4—1811no—
267C2×D4—1811no—
268C2×D4—1811no—
269C2×D4—7241no—
270C2×D4—7241no—
271C2×D4—7244no—
272C2×D4C22×D18111yescharacteristic
273C22×C4—21no—
274C22×C4—3621no—
275C22×C4—1811no—
276C22×C4C22×D18111yescharacteristic
277SD16—3622no—
278SD16—7241no—
279SD16—7241no—
280M16—7241no—
281C2×C8—1811no—
282C2×C8—1811no—
283C2×C8—7241no—
284C2×C8C22×D18111yescharacteristic
285C2×C8C22×D18111yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—3621no—
288C4⋊C4—3621no—
289C4⋊C4—3621no—
290C4⋊C4—3621no—
291C4⋊C4—3621no—
292C4⋊C4—1811no—
293C4⋊C4—1811no—
294C4⋊C4C22×D18111yescharacteristic
295C4⋊C4C22×D18111yescharacteristic
296C4⋊C4C22×D18111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—3621no—
299C22⋊C4—3621no—
300C22⋊C4—3621no—
301C22⋊C4—3621no—
302C22⋊C4—3621no—
303C22⋊C4—1811no—
304C22⋊C4—1811no—
305C42—3621no—
306C42—3621no—
307C42—1811no—
308C23—21no—
309C23—3621no—
310C23—3621no—
311C23—14481no—
312C23—14481no—
313C23—1811no—
314C23—7242no—
315C23—7242no—
316C23—7242no—
317C23—7242no—
318C23D4×D18111yescharacteristic
319Q8—3621no—
320Q8—3621no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—3622no—
325D4—3621no—
326D4—3621no—
327D4—3621no—
328D4—14481no—
329D4—1812no—
330D4—7242no—
331D4—7242no—
332D4—7242no—
333D4—7242no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—3621no—
341C2×C4—3621no—
342C2×C4—3621no—
343C2×C4—3621no—
344C2×C4—1811no—
345C2×C4—1811no—
346C2×C4—1811no—
347C2×C4—7242no—
348C2×C4D4×D18111yescharacteristic
349C2×C4C23×D18111yescharacteristic
350C8—21no—
351C8—21no—
352C8—3621no—
353C8—3621no—
354C22—21no—
355C22—21no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—3621no—
360C22—3622no—
361C22—3621no—
362C22—3621no—
363C22—14484no—
364C22—14484no—
365C22—7241no—
366C22—7241no—
367C22—7241no—
368C22—7241no—
369C22—7241no—
370C22#1915384012yes—
371C22C2×D4×D18111yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—3621no—
377C4—3621no—
378C4—3621no—
379C4—7241no—
380C4—7241no—
381C4#41×D18111yescharacteristic
382C4#1915386211yescharacteristic
383C2—22no—
384C2—81no—
385C2—14481no—
386C2—7241no—
387C2—7242no—
388C2#2604192111yescharacteristic
389C2C2×#1915384011yescharacteristic
390C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#480×C181C2
socleC22×C181C22×D4
prime radical#26041913C2
hypercenter#480D181
hypocenterC181#3310
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #26041964C2semidirect
3. #26041642C2semidirect
4. #26041606C2semidirect
5. #26041582C2semidirect
6. #26041526C2semidirect
7. #26041506C2semidirect
8. #26041478C2semidirect
9. #26041432C2semidirect
10. #26041431C2semidirect
11. #26041378C2semidirect
12. #26041347C2semidirect
13. #26041282C2semidirect
14. C2×#19153736C2semidirect
15. #480×C181C2semidirect
20. C2×#15668438C22semidirect
21. C2×#15668437C22semidirect
22. C2×#15668432C22semidirect
23. C22×#13089678C22semidirect
26. #19153807C22semidirect
29. #19153796C22semidirect
30. #19153795C22semidirect
35. #19153781C22semidirect
39. #19153774C22semidirect
40. #19153747C22semidirect
41. #19153745C22semidirect
42. #19153739C22semidirect
44. #19153738C22semidirect
45. #19153737C22semidirect
48. #19153736C22semidirect
49. #19153736C22semidirect
50. #19153728C22semidirect
51. #19153726C22semidirect
53. C2×C4⋊C4×C181C22semidirect
54. #107×C181C22semidirect
55. #107×C181C22semidirect
56. #102×C181C22semidirect
57. #102×C181C22semidirect
58. C22⋊C8×C181C22semidirect
195. C181#3310semidirect
201. #480D181semidirect
237. C2×C4⋊C4C2×D181semidirect
238. #107C2×D181semidirect
239. #107C2×D181semidirect
250. #102C2×D181semidirect
251. #102C2×D181semidirect
253. C22⋊C8C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419642
#260419132
#260416422
#260416062
#260415822
#260415262
#260415062
#260414782
#260414322
#260414312
#260413782
#260413472
#260412822
C2×#191537362
#480×C1812
#3310181