Finite Group Databasebeta

← #37545945

Subgroups — #37545945

Order 23168.

448 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#26042000C211yesmaximal, characteristic, complemented
2D4×C22⋊D181C211yesmaximal, characteristic
3#26041624C211yesmaximal, characteristic, complemented
4#26041604C211yesmaximal, characteristic, complemented
5#26041602C211yesmaximal, characteristic, complemented
6#26041557C211yesmaximal, characteristic, complemented
7#26041527C211yesmaximal, characteristic, complemented
8#26041522C211yesmaximal, characteristic, complemented
9#26041477C211yesmaximal, characteristic, complemented
10#26041428C211yesmaximal, characteristic, complemented
11SD16×Dic181C211yesmaximal, characteristic, complemented
12#26041354C211yesmaximal, characteristic, complemented
13#26041284C211yesmaximal, characteristic, complemented
14#26041282C211yesmaximal, characteristic, complemented
15#450×C181C211yesmaximal, characteristic, complemented
16C22×C22⋊D181—21no—
17C2×D4×D181C2211yescharacteristic
18C2×#15668436C2211yescharacteristic, complemented
19C2×#15668433C2211yescharacteristic, complemented
20C2×#15668432C2211yescharacteristic, complemented
21#19153815C2211yescharacteristic, complemented
22#19153812C2211yescharacteristic
23#19153811—21no—
24#19153809—21no—
25#19153802—21no—
26#19153792C2211yescharacteristic, complemented
27#19153790C2211yescharacteristic
28#19153788—21no—
29#19153787C2211yescharacteristic
30#19153785—21no—
31#19153784—21no—
32Q8×Dic181C2211yescharacteristic, complemented
33#19153781—21no—
34D4×Dic181C2211yescharacteristic
35C4×C22⋊D181C2211yescharacteristic
36#19153775C2211yescharacteristic, complemented
37#19153774C2211yescharacteristic, complemented
38#19153750C2211yescharacteristic, complemented
39#19153749C2211yescharacteristic, complemented
40#19153748C2211yescharacteristic, complemented
41#19153745C2211yescharacteristic, complemented
42#19153740C2211yescharacteristic, complemented
43#19153738C2211yescharacteristic, complemented
44#19153738C2211yescharacteristic, complemented
45#19153737C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153737C2211yescharacteristic, complemented
48#19153737C2211yescharacteristic, complemented
49#19153736C2211yescharacteristic, complemented
50#19153728C2211yescharacteristic, complemented
51C8×Dic181C2211yescharacteristic, complemented
52C22×D4×C181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic
54C2×SD16×C181C2211yescharacteristic, complemented
55C22⋊Q8×C181C2211yescharacteristic, complemented
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic, complemented
58C22⋊C8×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60C2×Dic362—21no—
61C2×D724C2311yescharacteristic
62C2×C22⋊D181—21no—
63C2×C22⋊D181—21no—
64C2×C22⋊D181—21no—
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181—44no—
68C2×C22⋊D181D411yescharacteristic
69D4×D181—22no—
70D4×D181—41no—
71C22×Dic181—21no—
72C2×C4×D181C2311yescharacteristic
73#15668436—41no—
74#15668433—41no—
75#15668432—41no—
76C2×#13089678C2311yescharacteristic
77C2×#13089678C2311yescharacteristic
78C4⋊Dic181—21no—
79C4⋊Dic181C2311yescharacteristic
80C4⋊Dic181C2311yescharacteristic
81C4⋊Dic181C2311yescharacteristic
82#15668428—21no—
83#15668428—21no—
84#15668428D411yescharacteristic
85C22⋊Dic181—21no—
86C22⋊Dic181—21no—
87C22⋊Dic181—21no—
88C22⋊Dic181D411yescharacteristic
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426D411yescharacteristic
93C4×Dic181—21no—
94C4×Dic181—21no—
95C4×Dic181—21no—
96C4×Dic181C2311yescharacteristic
97C24×C181—21no—
98C2×Q8×C181C2311yescharacteristic
99C2×D4×C181—22no—
100C2×D4×C181—21no—
101C2×D4×C181—41no—
102C2×D4×C181C2311yescharacteristic
103C2×D4×C181C2311yescharacteristic
104C22×C4×C181C2311yescharacteristic
105SD16×C181—22no—
106SD16×C181—41no—
107C2×C8×C181C2311yescharacteristic
108C2×C8×C181C2311yescharacteristic
109C4⋊C4×C181—21no—
110C4⋊C4×C181C2311yescharacteristic
111C22⋊C4×C181—21no—
112C22×D181—21no—
113C22×D181—42no—
114C22×D181—42no—
115C22×D181—81no—
116C22×D181C2×D411yescharacteristic
117Dic362—42no—
118D724—21no—
119D724—21no—
120C22⋊D181—22no—
121C22⋊D181—42no—
122C22⋊D181—42no—
123C22⋊D181—42no—
124C22⋊D181—42no—
125C22⋊D181—81no—
126C2×Dic181—21no—
127C2×Dic181—21no—
128C2×Dic181—21no—
129C2×Dic181—42no—
130C2×Dic181C2×D411yescharacteristic
131C2×Dic181C2×D411yescharacteristic
132C2×Dic181C2×D411yescharacteristic
133C4×D181—21no—
134C4×D181—21no—
135#13089678—21no—
136#13089678—21no—
137C23×C181—21no—
138C23×C181—21no—
139C23×C181—42no—
140C23×C181—42no—
141C23×C181—81no—
142C23×C181C2×D411yescharacteristic
143Q8×C181—21no—
144Q8×C181—21no—
145D4×C181—21no—
146D4×C181—21no—
147D4×C181—21no—
148D4×C181—42no—
149D4×C181#4112yes—
150C2×C4×C181—21no—
151C2×C4×C181—21no—
152C2×C4×C181—21no—
153C2×C4×C181—21no—
154C2×C4×C181C2×D411yescharacteristic
155C2×C4×C181C2411yescharacteristic
156C8×C181—21no—
157C8×C181—21no—
158C22×C181—21no—
159C22×C181—22no—
160C22×C181—21no—
161C22×C181—21no—
162C22×C181—41no—
163C22×C181—41no—
164C22×C181—41no—
165C22×C181—41no—
166C22×C181—41no—
167C22×C181—84no—
168C22×C181C22×D411yescharacteristic
169C2×D181—21no—
170C2×D181—21no—
171C2×D181—21no—
172C2×D181—41no—
173C2×D181—41no—
174C2×D181—41no—
175C2×D181—84no—
176C4×C181—21no—
177C4×C181—41no—
178C4×C181—41no—
179C4×C181C2×#4111yescharacteristic
180C4×C181H(5,𝔽2)11yescharacteristic
181Dic181—21no—
182Dic181—21no—
183Dic181—41no—
184Dic181—41no—
185Dic181—41no—
186Dic181AGL(1,ℤ/8)12yes—
187C2×C181—42no—
188C2×C181—41no—
189C2×C181—81no—
190C2×C181#54611yescharacteristic
191C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C181#57711yescharacteristic
193D181—41no—
194D181—81no—
195C181#332411yescharacteristic, complemented, Sylow
196#3324—1811nomaximal, Sylow
197#556—1811no—
198D42—1811no—
199#486—1811no—
200#482—1811no—
201#482—1811no—
202#474—1811no—
203#468—1811no—
204#468—1811no—
205#460—1811no—
206#450—1811no—
207#450D18111yescharacteristic, complemented
208C4×SD16—1811no—
209#436—1811no—
210#418—1811no—
211#418—1811no—
212C22×D4—3621no—
213C22×D4—1811no—
214C22×D4C2×D18111yescharacteristic
215C2×SD16—1811no—
216C2×SD16C2×D18111yescharacteristic
217C2×SD16C2×D18111yescharacteristic, complemented
218C2×M16—1811no—
219C2×M16—1811no—
220C4⋊Q8—1811no—
221#127—1811no—
222#126—3621no—
223#126—3621no—
224#124—3621no—
225C22⋊Q8—1811no—
226C22⋊Q8C2×D18111yescharacteristic, complemented
227#121—3621no—
228#121—1811no—
229#121—1811no—
230#120—3621no—
231#120—3621no—
232C4×Q8—3621no—
233C4×Q8—1811no—
234C4×D4—1811no—
235C4×D4—1811no—
236#117—1811no—
237#117—1811no—
238#107—1811no—
239#107—1811no—
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
251#102C2×D18111yescharacteristic, complemented
252C22⋊C8—1811no—
253C22⋊C8C2×D18111yescharacteristic, complemented
254C4×C8—1811no—
255C24—21no—
256C24—3621no—
257C2×Q8—3621no—
258C2×Q8C22×D18111yescharacteristic
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—3622no—
263C2×D4—3621no—
264C2×D4—3621no—
265C2×D4—3621no—
266C2×D4—3621no—
267C2×D4—3621no—
268C2×D4—1811no—
269C2×D4—1811no—
270C2×D4—7241no—
271C2×D4—7244no—
272C2×D4C22×D18111yescharacteristic
273C2×D4C22×D18111yescharacteristic
274C22×C4—3621no—
275C22×C4—1811no—
276C22×C4C22×D18111yescharacteristic
277SD16—22no—
278SD16—41no—
279SD16—7241no—
280M16—7241no—
281M16—7241no—
282C2×C8—1811no—
283C2×C8—1811no—
284C2×C8C22×D18111yescharacteristic
285C2×C8C22×D18111yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—3621no—
288C4⋊C4—3621no—
289C4⋊C4—3621no—
290C4⋊C4—1811no—
291C4⋊C4—1811no—
292C4⋊C4—1811no—
293C4⋊C4—1811no—
294C4⋊C4C22×D18111yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—3621no—
297C22⋊C4—3621no—
298C22⋊C4—3621no—
299C22⋊C4—3621no—
300C22⋊C4—3621no—
301C22⋊C4—3621no—
302C22⋊C4—1811no—
303C22⋊C4—1811no—
304C42—3621no—
305C42—3621no—
306C42—3621no—
307C42—1811no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—3621no—
314C23—14481no—
315C23—1811no—
316C23—7242no—
317C23—7242no—
318C23D4×D18111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—7242no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—3622no—
327D4—3621no—
328D4—3621no—
329D4—14481no—
330D4—7242no—
331D4—7242no—
332D4—7242no—
333D4—7242no—
334D4#1566844812yes—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—3621no—
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—22no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—84no—
364C22—3621no—
365C22—3621no—
366C22—3621no—
367C22—14484no—
368C22—7241no—
369C22—7241no—
370C22—7241no—
371C22C2×D4×D18111yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—3621no—
376C4—3621no—
377C4—1812no—
378C4—7241no—
379C4—7241no—
380C4—7241no—
381C4C2×#1566844811yescharacteristic
382C4#1915386111yescharacteristic
383C2—41no—
384C2—42no—
385C2—81no—
386C2—14481no—
387C2—7241no—
388C2#2604191611yescharacteristic
389C2AGL(1,ℤ/8)×D18111yescharacteristic
390C2#2604208511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#450×C181C2
socleC22×C181C22×D4
prime radicalD4×C22⋊D181C2
hypercenter#450D181
hypocenterC181#3324
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #26042000C2semidirect
3. #26041624C2semidirect
4. #26041604C2semidirect
5. #26041602C2semidirect
6. #26041557C2semidirect
7. #26041527C2semidirect
8. #26041522C2semidirect
9. #26041477C2semidirect
10. #26041428C2semidirect
11. SD16×Dic181C2semidirect
12. #26041354C2semidirect
13. #26041284C2semidirect
14. #26041282C2semidirect
15. #450×C181C2semidirect
18. C2×#15668436C22semidirect
19. C2×#15668433C22semidirect
20. C2×#15668432C22semidirect
21. #19153815C22semidirect
26. #19153792C22semidirect
32. Q8×Dic181C22semidirect
36. #19153775C22semidirect
37. #19153774C22semidirect
38. #19153750C22semidirect
39. #19153749C22semidirect
40. #19153748C22semidirect
41. #19153745C22semidirect
42. #19153740C22semidirect
43. #19153738C22semidirect
44. #19153738C22semidirect
47. #19153737C22semidirect
48. #19153737C22semidirect
49. #19153736C22semidirect
50. #19153728C22semidirect
51. C8×Dic181C22semidirect
54. C2×SD16×C181C22semidirect
55. C22⋊Q8×C181C22semidirect
57. #102×C181C22semidirect
58. C22⋊C8×C181C22semidirect
195. C181#3324semidirect
207. #450D181semidirect
217. C2×SD16C2×D181semidirect
226. C22⋊Q8C2×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
#260420002
D4×C22⋊D1812
#260416242
#260416042
#260416022
#260415572
#260415272
#260415222
#260414772
#260414282
SD16×Dic1812
#260413542
#260412842
#260412822
#450×C1812
#3324181