Finite Group Databasebeta

← #37545958

Subgroups — #37545958

Order 23168.

460 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041993C211yesmaximal, characteristic, complemented
2#26041913C211yesmaximal, characteristic, complemented
3#26041624C211yesmaximal, characteristic, complemented
4#26041605C211yesmaximal, characteristic, complemented
5#26041600C211yesmaximal, characteristic, complemented
6#26041568C211yesmaximal, characteristic, complemented
7#26041531C211yesmaximal, characteristic, complemented
8#26041472C211yesmaximal, characteristic, complemented
9#26041412C211yesmaximal, characteristic, complemented
10#26041411C211yesmaximal, characteristic, complemented
11#26041359C211yesmaximal, characteristic, complemented
12#26041355C211yesmaximal, characteristic, complemented
13#26041285C211yesmaximal, characteristic, complemented
14#26041282C211yesmaximal, characteristic, complemented
15#469×C181C211yesmaximal, characteristic, complemented
16C22×D724C2211yescharacteristic
17C2×D4×D181—21no—
18C2×D4×D181C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20C2×#15668434C2211yescharacteristic, complemented
21C2×#15668432C2211yescharacteristic, complemented
22#19153815C2211yescharacteristic, complemented
23#19153812C2211yescharacteristic
24#19153803—21no—
25#19153802—21no—
26#19153791C2211yescharacteristic
27#19153789—21no—
28#19153788—21no—
29#19153787C2211yescharacteristic, complemented
30#19153786—21no—
31#19153784—21no—
32D4×Dic181C2211yescharacteristic, complemented
33#19153778C2211yescharacteristic
34C4×C22⋊D181C2211yescharacteristic
35#19153775C2211yescharacteristic, complemented
36#19153774C2211yescharacteristic, complemented
37#19153772—21no—
38#19153749C2211yescharacteristic, complemented
39#19153747C2211yescharacteristic, complemented
40#19153745C2211yescharacteristic, complemented
41#19153738C2211yescharacteristic
42#19153738C2211yescharacteristic
43#19153738C2211yescharacteristic, complemented
44#19153738C2211yescharacteristic, complemented
45#19153737C2211yescharacteristic, complemented
46#19153737C2211yescharacteristic, complemented
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic, complemented
49C22⋊#13089678C2211yescharacteristic, complemented
50#19153728C2211yescharacteristic, complemented
51C8×Dic181C2211yescharacteristic, complemented
52C2×D8×C181C2211yescharacteristic, complemented
53C2×M16×C181C2211yescharacteristic, complemented
54#121×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic, complemented
56#106×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic, complemented
58#102×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60C23×D181—21no—
61C2×Dic362—21no—
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⋊D181—21no—
72C2×C22⋊D181D411yescharacteristic
73D4×D181—22no—
74D4×D181—41no—
75D4×D181—44no—
76C22×Dic181—21no—
77C2×C4×D181—21no—
78C2×C4×D181C2311yescharacteristic
79#15668434—22no—
80#15668434—41no—
81#15668432—41no—
82C2×#13089678C2311yescharacteristic
83C2×#13089678C2311yescharacteristic
84C4⋊Dic181C2311yescharacteristic
85C4⋊Dic181C2311yescharacteristic
86#15668428—21no—
87#15668428D411yescharacteristic
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181—21no—
91C22⋊Dic181D411yescharacteristic
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426D411yescharacteristic
96C4×Dic181—21no—
97C4×Dic181—21no—
98C4×Dic181C2311yescharacteristic
99C2×D4×C181—21no—
100C2×D4×C181—21no—
101C2×D4×C181C2311yescharacteristic
102C2×D4×C181C2311yescharacteristic
103C22×C4×C181C2311yescharacteristic
104D8×C181—41no—
105M16×C181—41no—
106C2×C8×C181C2311yescharacteristic
107C2×C8×C181C2311yescharacteristic
108C4⋊C4×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C22⋊C4×C181—21no—
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—81no—
122D724—21no—
123D724—21no—
124D724—21no—
125D724—42no—
126D724—42no—
127D724#4112yes—
128C22⋊D181—22no—
129C22⋊D181—42no—
130C22⋊D181—42no—
131C22⋊D181—81no—
132C22⋊D181—81no—
133C2×Dic181—21no—
134C2×Dic181—21no—
135C2×Dic181—42no—
136C2×Dic181C2×D411yescharacteristic
137C2×Dic181C2×D411yescharacteristic
138C2×Dic181C2×D411yescharacteristic
139C4×D181—21no—
140C4×D181—21no—
141C4×D181—42no—
142#13089678—21no—
143#13089678—21no—
144C23×C181—21no—
145C23×C181—21no—
146C23×C181C2×D411yescharacteristic
147D4×C181—21no—
148D4×C181—21no—
149D4×C181—21no—
150D4×C181—21no—
151D4×C181—42no—
152D4×C181—81no—
153C2×C4×C181—21no—
154C2×C4×C181—21no—
155C2×C4×C181—21no—
156C2×C4×C181—21no—
157C2×C4×C181C2×D411yescharacteristic
158C2×C4×C181C2411yescharacteristic
159C8×C181—21no—
160C8×C181—21no—
161C22×C181—21no—
162C22×C181—21no—
163C22×C181—21no—
164C22×C181—41no—
165C22×C181—41no—
166C22×C181—41no—
167C22×C181—41no—
168C22×C181—41no—
169C22×C181—41no—
170C22×C181C22×D411yescharacteristic
171C2×D181—21no—
172C2×D181—22no—
173C2×D181—21no—
174C2×D181—21no—
175C2×D181—41no—
176C2×D181—41no—
177C2×D181—41no—
178C2×D181—41no—
179C2×D181—41no—
180C2×D181—84no—
181C2×D181—84no—
182C4×C181—21no—
183C4×C181—41no—
184C4×C181—41no—
185C4×C181C2×#4111yescharacteristic
186C4×C181H(5,𝔽2)11yescharacteristic
187Dic181—21no—
188Dic181—21no—
189Dic181—41no—
190Dic181—41no—
191Dic181AGL(1,ℤ/8)12yes—
192C2×C181—41no—
193C2×C181—81no—
194C2×C181—81no—
195C2×C181#54611yescharacteristic
196C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C181#57611yescharacteristic
198D181—41no—
199D181—42no—
200D181—81no—
201C181#332511yescharacteristic, complemented, Sylow
202#3325—1811nomaximal, Sylow
203#555—1811no—
204D42—1811no—
205#486—1811no—
206#482—1811no—
207#482—1811no—
208#476—1811no—
209#469—1811no—
210#469D18111yescharacteristic, complemented
211#459—1811no—
212#447—1811no—
213#447—1811no—
214C4×D8—1811no—
215#436—1811no—
216#418—1811no—
217#418—1811no—
218C22×D4—3621no—
219C22×D4—1811no—
220C22×D4—1811no—
221C2×D8—1811no—
222C2×D8—1811no—
223C2×D8C2×D18111yescharacteristic, complemented
224C2×M16—1811no—
225C2×M16C2×D18111yescharacteristic, complemented
226C4⋊Q8—1811no—
227#127—1811no—
228#124—3621no—
229#124—3621no—
230#121—3621no—
231#121—3621no—
232#121—1811no—
233#121—1811no—
234#121C2×D18111yescharacteristic
235#121C2×D18111yescharacteristic, complemented
236#120—3621no—
237#120—3621no—
238C4×D4—1811no—
239C4×D4—1811no—
240C4×D4—1811no—
241#117—3621no—
242#117—1811no—
243#117—1811no—
244#107—1811no—
245#106—1811no—
246#106C2×D18111yescharacteristic, complemented
247C4⋊C8—1811no—
248#102—1811no—
249#102—1811no—
250#102—1811no—
251#102—1811no—
252#102—1811no—
253#102—1811no—
254#102—1811no—
255#102—1811no—
256#102C2×D18111yescharacteristic, complemented
257#102C2×D18111yescharacteristic, complemented
258C22⋊C8—1811no—
259C22⋊C8—1811no—
260C4×C8—1811no—
261C24—3621no—
262C24—3621no—
263C2×Q8—3621no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—3622no—
267C2×D4—3621no—
268C2×D4—3622no—
269C2×D4—3621no—
270C2×D4—3621no—
271C2×D4—3621no—
272C2×D4—3621no—
273C2×D4—3621no—
274C2×D4—1811no—
275C2×D4—1811no—
276C2×D4—1811no—
277C2×D4—7241no—
278C2×D4—7241no—
279C2×D4—7244no—
280C2×D4C22×D18111yescharacteristic
281C2×D4C22×D18111yescharacteristic
282C22×C4—3621no—
283C22×C4—3621no—
284C22×C4—1811no—
285C22×C4C22×D18111yescharacteristic
286D8—41no—
287D8—3622no—
288D8—7241no—
289M16—41no—
290M16—7241no—
291C2×C8—1811no—
292C2×C8—1811no—
293C2×C8C22×D18111yescharacteristic
294C2×C8C22×D18111yescharacteristic
295C4⋊C4—3621no—
296C4⋊C4—1811no—
297C4⋊C4—1811no—
298C4⋊C4—1811no—
299C4⋊C4C22×D18111yescharacteristic
300C4⋊C4C22×D18111yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—3621no—
304C22⋊C4—3621no—
305C22⋊C4—3621no—
306C22⋊C4—3621no—
307C22⋊C4—3621no—
308C22⋊C4—3621no—
309C22⋊C4—1811no—
310C22⋊C4—1811no—
311C42—3621no—
312C42—3621no—
313C42—1811no—
314C23—21no—
315C23—21no—
316C23—3621no—
317C23—3621no—
318C23—14481no—
319C23—14481no—
320C23—1811no—
321C23—7242no—
322C23—7242no—
323C23—7242no—
324C23—7242no—
325C23D4×D18111yescharacteristic
326Q8—14481no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—42no—
332D4—81no—
333D4—3622no—
334D4—3621no—
335D4—3621no—
336D4—3621no—
337D4—14481no—
338D4—14481no—
339D4—1812no—
340D4—7242no—
341D4—7242no—
342D4—7242no—
343D4—7242no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—3621no—
349C2×C4—3621no—
350C2×C4—3621no—
351C2×C4—3621no—
352C2×C4—1811no—
353C2×C4—1811no—
354C2×C4—1811no—
355C2×C4—7242no—
356C2×C4—7242no—
357C2×C4D4×D18111yescharacteristic
358C2×C4C23×D18111yescharacteristic
359C8—21no—
360C8—21no—
361C8—3621no—
362C8—3621no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—3621no—
373C22—3622no—
374C22—3621no—
375C22—3621no—
376C22—14484no—
377C22—14484no—
378C22—7241no—
379C22—7241no—
380C22—7241no—
381C22—7241no—
382C22—7241no—
383C22C2×D4×D18111yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—3621no—
388C4—3621no—
389C4—1812no—
390C4—7241no—
391C4—7241no—
392C4#41×D18111yescharacteristic
393C4#1915386111yescharacteristic
394C2—41no—
395C2—81no—
396C2—81no—
397C2—14481no—
398C2—7241no—
399C2—7242no—
400C2#2604191811yescharacteristic
401C2AGL(1,ℤ/8)×D18111yescharacteristic
402C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#469×C181C2
socleC22×C181C22×D4
hypercenter#469D181
hypocenterC181#3325
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #26041993C2semidirect
2. #26041913C2semidirect
3. #26041624C2semidirect
4. #26041605C2semidirect
5. #26041600C2semidirect
6. #26041568C2semidirect
7. #26041531C2semidirect
8. #26041472C2semidirect
9. #26041412C2semidirect
10. #26041411C2semidirect
11. #26041359C2semidirect
12. #26041355C2semidirect
13. #26041285C2semidirect
14. #26041282C2semidirect
15. #469×C181C2semidirect
20. C2×#15668434C22semidirect
21. C2×#15668432C22semidirect
22. #19153815C22semidirect
29. #19153787C22semidirect
32. D4×Dic181C22semidirect
35. #19153775C22semidirect
36. #19153774C22semidirect
38. #19153749C22semidirect
39. #19153747C22semidirect
40. #19153745C22semidirect
43. #19153738C22semidirect
44. #19153738C22semidirect
45. #19153737C22semidirect
46. #19153737C22semidirect
48. #19153736C22semidirect
49. C22⋊#13089678C22semidirect
50. #19153728C22semidirect
51. C8×Dic181C22semidirect
52. C2×D8×C181C22semidirect
53. C2×M16×C181C22semidirect
55. #121×C181C22semidirect
56. #106×C181C22semidirect
57. #102×C181C22semidirect
58. #102×C181C22semidirect
201. C181#3325semidirect
210. #469D181semidirect
223. C2×D8C2×D181semidirect
225. C2×M16C2×D181semidirect
235. #121C2×D181semidirect
246. #106C2×D181semidirect
256. #102C2×D181semidirect
257. #102C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419932
#260419132
#260416242
#260416052
#260416002
#260415682
#260415312
#260414722
#260414122
#260414112
#260413592
#260413552
#260412852
#260412822
#469×C1812
#3325181