Finite Group Databasebeta

← #37545855

Subgroups — #37545855

Order 23168.

462 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#26041976C211yesmaximal, characteristic, complemented
2D4×C22⋊D181C211yesmaximal, characteristic, complemented
3#26041642C211yesmaximal, characteristic, complemented
4#26041604C211yesmaximal, characteristic, complemented
5#26041596C211yesmaximal, characteristic, complemented
6#26041577C211yesmaximal, characteristic, complemented
7#26041530C211yesmaximal, characteristic, complemented
8#26041512C211yesmaximal, characteristic, complemented
9#26041472C211yesmaximal, characteristic, complemented
10#26041411C211yesmaximal, characteristic, complemented
11#26041391C211yesmaximal, characteristic, complemented
12#26041353C211yesmaximal, characteristic, complemented
13#26041284C211yesmaximal, characteristic, complemented
14#102×D181C211yesmaximal, characteristic, complemented
15#447×C181C211yesmaximal, characteristic, complemented
16C22×C22⋊D181—21no—
17C2×D4×D181C2211yescharacteristic
18C2×#15668434C2211yescharacteristic, complemented
19C2×#15668433C2211yescharacteristic, complemented
20C2×C8×D181C2211yescharacteristic, complemented
21#19153812C2211yescharacteristic
22#19153809—21no—
23#19153807C2211yescharacteristic, complemented
24#19153797—21no—
25#19153790C2211yescharacteristic
26#19153788—21no—
27#19153787—21no—
28#19153787C2211yescharacteristic
29#19153787C2211yescharacteristic, complemented
30#19153785—21no—
31#19153784—21no—
32D4×Dic181C2211yescharacteristic
33D4×Dic181C2211yescharacteristic, complemented
34C4×C22⋊D181C2211yescharacteristic
35#19153776—21no—
36#19153775C2211yescharacteristic, complemented
37C4⋊C4×D181C2211yescharacteristic, complemented
38#19153750C2211yescharacteristic, complemented
39#19153748C2211yescharacteristic, complemented
40#19153747C2211yescharacteristic, complemented
41#19153745C2211yescharacteristic, complemented
42#19153738C2211yescharacteristic, complemented
43#19153738C2211yescharacteristic, complemented
44#19153737C2211yescharacteristic
45#19153737C2211yescharacteristic
46#19153737C2211yescharacteristic, complemented
47#19153737C2211yescharacteristic, complemented
48#19153737C2211yescharacteristic, complemented
49#19153736C2211yescharacteristic, complemented
50#19153728C2211yescharacteristic, complemented
51#19153726C2211yescharacteristic, complemented
52C22×D4×C181C2211yescharacteristic
53C2×D8×C181C2211yescharacteristic
54C2×D8×C181C2211yescharacteristic, complemented
55#121×C181C2211yescharacteristic, complemented
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic, complemented
58C22⋊C8×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60C2×D724C2311yescharacteristic
61C2×C22⋊D181—21no—
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—
72C22×Dic181—21no—
73C2×C4×D181—21no—
74C2×C4×D181C2311yescharacteristic
75#15668434—41no—
76#15668433—41no—
77C2×#13089678C2311yescharacteristic
78C2×#13089678C2311yescharacteristic
79C8×D181—41no—
80C4⋊Dic181—21no—
81C4⋊Dic181C2311yescharacteristic
82C4⋊Dic181C2311yescharacteristic
83C4⋊Dic181C2311yescharacteristic
84#15668428—21no—
85#15668428—21no—
86#15668428D411yescharacteristic
87C22⋊Dic181—21no—
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92C22⋊Dic181D411yescharacteristic
93#15668426—21no—
94#15668426D411yescharacteristic
95C4×Dic181—21no—
96C4×Dic181C2311yescharacteristic
97C24×C181—21no—
98C2×D4×C181—22no—
99C2×D4×C181—21no—
100C2×D4×C181—21no—
101C2×D4×C181—41no—
102C2×D4×C181C2311yescharacteristic
103C2×D4×C181C2311yescharacteristic
104C2×D4×C181C2311yescharacteristic
105C22×C4×C181C2311yescharacteristic
106D8×C181—22no—
107D8×C181—41no—
108C2×C8×C181C2311yescharacteristic
109C2×C8×C181C2311yescharacteristic
110C4⋊C4×C181C2311yescharacteristic
111C22⋊C4×C181—21no—
112C22×D181—21no—
113C22×D181—42no—
114C22×D181—42no—
115C22×D181—81no—
116C22×D181C2×D411yescharacteristic
117D724—21no—
118D724—21no—
119C22⋊D181—22no—
120C22⋊D181—42no—
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×Dic181—81no—
131C2×Dic181C2×D411yescharacteristic
132C2×Dic181C2×D411yescharacteristic
133C2×Dic181C2×D411yescharacteristic
134C4×D181—21no—
135C4×D181—21no—
136C4×D181—81no—
137#13089678—21no—
138#13089678—21no—
139C23×C181—21no—
140C23×C181—21no—
141C23×C181—21no—
142C23×C181—42no—
143C23×C181—42no—
144C23×C181—81no—
145C23×C181C2×D411yescharacteristic
146D4×C181—21no—
147D4×C181—21no—
148D4×C181—21no—
149D4×C181—21no—
150D4×C181—21no—
151D4×C181—42no—
152D4×C181—81no—
153D4×C181#4112yes—
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—22no—
163C22×C181—21no—
164C22×C181—21no—
165C22×C181—41no—
166C22×C181—41no—
167C22×C181—41no—
168C22×C181—41no—
169C22×C181—41no—
170C22×C181—41no—
171C22×C181—41no—
172C22×C181—41no—
173C22×C181—84no—
174C22×C181C22×D411yescharacteristic
175C2×D181—21no—
176C2×D181—21no—
177C2×D181—41no—
178C2×D181—41no—
179C2×D181—41no—
180C2×D181—84no—
181C2×D181AGL(1,ℤ/8)12yes—
182C4×C181—21no—
183C4×C181—41no—
184C4×C181C2×#4111yescharacteristic
185C4×C181H(5,𝔽2)11yescharacteristic
186Dic181—21no—
187Dic181—21no—
188Dic181—21no—
189Dic181—41no—
190Dic181—41no—
191Dic181—41no—
192C2×C181—42no—
193C2×C181—41no—
194C2×C181—81no—
195C2×C181—81no—
196C2×C181#54611yescharacteristic
197C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
198C2×C181#57611yescharacteristic
199D181—22no—
200D181—81no—
201C181#331811yescharacteristic, complemented, Sylow
202#3318—1811nomaximal, Sylow
203#553—1811no—
204D42—1811no—
205#490—1811no—
206#482—1811no—
207#481—1811no—
208#478—1811no—
209#469—1811no—
210#466—1811no—
211#459—1811no—
212#447—1811no—
213#447D18111yescharacteristic, complemented
214#442—1811no—
215#435—1811no—
216#418—1811no—
217C2×#102—1811no—
218C22×D4—3621no—
219C22×D4—1811no—
220C22×D4C2×D18111yescharacteristic
221C2×D8—1811no—
222C2×D8C2×D18111yescharacteristic
223C2×D8C2×D18111yescharacteristic, complemented
224C2×M16—1811no—
225C22×C8—1811no—
226#127—1811no—
227#126—3621no—
228#125—1811no—
229#123—3621no—
230#121—3621no—
231#121—3621no—
232#121—1811no—
233#121—1811no—
234#121—1811no—
235#121C2×D18111yescharacteristic, complemented
236#120—3621no—
237#120—3621no—
238C4×D4—3621no—
239C4×D4—1811no—
240C4×D4—1811no—
241C4×D4—1811no—
242#117—1811no—
243C2×C4⋊C4—1811no—
244#107—1811no—
245#106—1811no—
246#106—1811no—
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
257#102C2×D18111yescharacteristic, complemented
258C22⋊C8—1811no—
259C22⋊C8C2×D18111yescharacteristic, complemented
260#97—1811no—
261C24—21no—
262C24—3621no—
263C2×D4—22no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—3622no—
268C2×D4—3621no—
269C2×D4—3621no—
270C2×D4—3621no—
271C2×D4—3621no—
272C2×D4—3621no—
273C2×D4—3621no—
274C2×D4—1811no—
275C2×D4—1811no—
276C2×D4—7241no—
277C2×D4—7244no—
278C2×D4C22×D18111yescharacteristic
279C2×D4C22×D18111yescharacteristic
280C2×D4C22×D18111yescharacteristic
281C22×C4—3621no—
282C22×C4—3621no—
283C22×C4—3621no—
284C22×C4—1811no—
285C22×C4C22×D18111yescharacteristic
286D8—22no—
287D8—41no—
288D8—7241no—
289M16—7241no—
290C2×C8—1811no—
291C2×C8—1811no—
292C2×C8—7241no—
293C2×C8C22×D18111yescharacteristic
294C2×C8C22×D18111yescharacteristic
295C4⋊C4—3621no—
296C4⋊C4—3621no—
297C4⋊C4—3621no—
298C4⋊C4—1811no—
299C4⋊C4—1811no—
300C4⋊C4—1811no—
301C4⋊C4—1811no—
302C4⋊C4C22×D18111yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—3621no—
305C22⋊C4—3621no—
306C22⋊C4—3621no—
307C22⋊C4—3621no—
308C22⋊C4—3621no—
309C22⋊C4—3621no—
310C22⋊C4—1811no—
311C22⋊C4—1811no—
312C42—3621no—
313C42—1811no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—42no—
318C23—42no—
319C23—81no—
320C23—3621no—
321C23—14481no—
322C23—1811no—
323C23—7242no—
324C23—7242no—
325C23D4×D18111yescharacteristic
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—42no—
332D4—81no—
333D4—3622no—
334D4—3621no—
335D4—3621no—
336D4—14481no—
337D4—7242no—
338D4—7242no—
339D4—7242no—
340D4—7242no—
341D4—7242no—
342D4#1566844812yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—3621no—
347C2×C4—3621no—
348C2×C4—3621no—
349C2×C4—3621no—
350C2×C4—3621no—
351C2×C4—14481no—
352C2×C4—14481no—
353C2×C4—1811no—
354C2×C4—1811no—
355C2×C4—1811no—
356C2×C4—7242no—
357C2×C4D4×D18111yescharacteristic
358C2×C4C23×D18111yescharacteristic
359C8—21no—
360C8—21no—
361C8—3621no—
362C8—3621no—
363C22—21no—
364C22—22no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—84no—
376C22—3621no—
377C22—3621no—
378C22—14484no—
379C22—1812no—
380C22—7241no—
381C22—7241no—
382C22—7241no—
383C22C2×D4×D18111yescharacteristic
384C4—21no—
385C4—41no—
386C4—3621no—
387C4—3621no—
388C4—3621no—
389C4—7241no—
390C4—7241no—
391C4—7241no—
392C4C2×#1566844811yescharacteristic
393C4#1915386111yescharacteristic
394C2—41no—
395C2—42no—
396C2—81no—
397C2—81no—
398C2—3622no—
399C2—14481no—
400C2#2604191611yescharacteristic
401C2AGL(1,ℤ/8)×D18111yescharacteristic
402C2#2604208011yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#447×C181C2
socleC22×C181C22×D4
hypercenter#447D181
hypocenterC181#3318
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #26041976C2semidirect
2. D4×C22⋊D181C2semidirect
3. #26041642C2semidirect
4. #26041604C2semidirect
5. #26041596C2semidirect
6. #26041577C2semidirect
7. #26041530C2semidirect
8. #26041512C2semidirect
9. #26041472C2semidirect
10. #26041411C2semidirect
11. #26041391C2semidirect
12. #26041353C2semidirect
13. #26041284C2semidirect
14. #102×D181C2semidirect
15. #447×C181C2semidirect
18. C2×#15668434C22semidirect
19. C2×#15668433C22semidirect
20. C2×C8×D181C22semidirect
23. #19153807C22semidirect
29. #19153787C22semidirect
33. D4×Dic181C22semidirect
36. #19153775C22semidirect
37. C4⋊C4×D181C22semidirect
38. #19153750C22semidirect
39. #19153748C22semidirect
40. #19153747C22semidirect
41. #19153745C22semidirect
42. #19153738C22semidirect
43. #19153738C22semidirect
46. #19153737C22semidirect
47. #19153737C22semidirect
48. #19153737C22semidirect
49. #19153736C22semidirect
50. #19153728C22semidirect
51. #19153726C22semidirect
54. C2×D8×C181C22semidirect
55. #121×C181C22semidirect
57. #102×C181C22semidirect
58. C22⋊C8×C181C22semidirect
201. C181#3318semidirect
213. #447D181semidirect
223. C2×D8C2×D181semidirect
235. #121C2×D181semidirect
257. #102C2×D181semidirect
259. C22⋊C8C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419762
D4×C22⋊D1812
#260416422
#260416042
#260415962
#260415772
#260415302
#260415122
#260414722
#260414112
#260413912
#260413532
#260412842
#102×D1812
#447×C1812
#3318181