Finite Group Databasebeta

← #37545869

Subgroups — #37545869

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#26041979C211yesmaximal, characteristic, complemented
2#26041914C211yesmaximal, characteristic, complemented
3#26041643C211yesmaximal, characteristic, complemented
4#26041601C211yesmaximal, characteristic, complemented
5#26041596C211yesmaximal, characteristic, complemented
6#26041580C211yesmaximal, characteristic, complemented
7#26041529C211yesmaximal, characteristic, complemented
8#26041512C211yesmaximal, characteristic, complemented
9#26041411C211yesmaximal, characteristic, complemented
10#26041411C211yesmaximal, characteristic, complemented
11#26041389C211yesmaximal, characteristic, complemented
12#26041349C211yesmaximal, characteristic, complemented
13#26041282C211yesmaximal, characteristic, complemented
14#102×D181C211yesmaximal, characteristic, complemented
15#459×C181C211yesmaximal, characteristic, complemented
16C2×D4×D181—21no—
17C2×D4×D181C2211yescharacteristic
18C2×D4×D181C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20C2×#15668432C2211yescharacteristic, complemented
21C2×C8×D181C2211yescharacteristic, complemented
22#19153809—21no—
23#19153808C2211yescharacteristic, complemented
24#19153799—21no—
25#19153789—21no—
26#19153787—21no—
27#19153787C2211yescharacteristic
28#19153787C2211yescharacteristic
29#19153787C2211yescharacteristic, complemented
30#19153787C2211yescharacteristic, complemented
31#19153784—21no—
32#19153784—21no—
33C4×D724C2211yescharacteristic
34C4×D724C2211yescharacteristic
35C4×C22⋊D181—21no—
36#19153774C2211yescharacteristic, complemented
37C4⋊C4×D181C2211yescharacteristic, complemented
38#19153750C2211yescharacteristic, complemented
39#19153748C2211yescharacteristic, complemented
40#19153747C2211yescharacteristic, complemented
41#19153738C2211yescharacteristic
42#19153738C2211yescharacteristic
43#19153737C2211yescharacteristic, complemented
44#19153737C2211yescharacteristic, complemented
45#19153737C2211yescharacteristic, complemented
46#19153737C2211yescharacteristic, complemented
47#19153737C2211yescharacteristic, complemented
48#19153736C2211yescharacteristic
49#19153728C2211yescharacteristic, complemented
50#19153728C2211yescharacteristic, complemented
51#19153727C2211yescharacteristic, complemented
52C2×D8×C181C2211yescharacteristic, complemented
53C2×D8×C181C2211yescharacteristic, complemented
54#127×C181C2211yescharacteristic
55C4×D4×C181C2211yescharacteristic, complemented
56C4⋊C8×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic, complemented
58#102×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60C23×D181—21no—
61C2×D724D411yescharacteristic
62C2×D724C2311yescharacteristic
63C2×C22⋊D181—21no—
64C2×C22⋊D181—21no—
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69D4×D181—22no—
70D4×D181—22no—
71D4×D181—41no—
72D4×D181—41no—
73D4×D181—44no—
74C2×C4×D181—21no—
75C2×C4×D181—21no—
76C2×C4×D181C2311yescharacteristic
77C2×C4×D181C2311yescharacteristic
78#15668434—22no—
79#15668432—41no—
80C2×#13089678C2311yescharacteristic
81C2×#13089678C2311yescharacteristic
82C8×D181—41no—
83C4⋊Dic181D411yescharacteristic
84C4⋊Dic181C2311yescharacteristic
85C4⋊Dic181C2311yescharacteristic
86C4⋊Dic181C2311yescharacteristic
87#15668428—21no—
88#15668428—21no—
89#15668428—21no—
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92C22⋊Dic181—21no—
93C22⋊Dic181—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426D411yescharacteristic
97#15668426D411yescharacteristic
98C4×Dic181—21no—
99C2×D4×C181—21no—
100C2×D4×C181—21no—
101C2×D4×C181C2311yescharacteristic
102C2×D4×C181C2311yescharacteristic
103C2×D4×C181C2311yescharacteristic
104C22×C4×C181—21no—
105D8×C181—41no—
106D8×C181—41no—
107C2×C8×C181C2311yescharacteristic
108C2×C8×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C22⋊C4×C181—21no—
111C42×C181C2311yescharacteristic
112C22×D181—21no—
113C22×D181—42no—
114C22×D181—42no—
115C22×D181—42no—
116C22×D181—42no—
117C22×D181—81no—
118C22×D181—81no—
119C22×D181C2×D411yescharacteristic
120C22×D181C2×D411yescharacteristic
121D724—22no—
122D724—21no—
123D724#4112yes—
124C22⋊D181—42no—
125C22⋊D181—42no—
126C22⋊D181—42no—
127C22⋊D181—42no—
128C22⋊D181—42no—
129C22⋊D181—81no—
130C2×Dic181—21no—
131C2×Dic181—21no—
132C2×Dic181—21no—
133C2×Dic181C2×D411yescharacteristic
134C2×Dic181C2×D411yescharacteristic
135C4×D181—21no—
136C4×D181—21no—
137C4×D181—21no—
138C4×D181—21no—
139C4×D181—42no—
140C4×D181—81no—
141#13089678—21no—
142#13089678—21no—
143C23×C181—21no—
144C23×C181—21no—
145C23×C181—21no—
146D4×C181—21no—
147D4×C181—21no—
148D4×C181—21no—
149D4×C181—21no—
150D4×C181—21no—
151D4×C181—21no—
152D4×C181—42no—
153D4×C181—81no—
154C2×C4×C181—21no—
155C2×C4×C181—81no—
156C2×C4×C181C2×D411yescharacteristic
157C2×C4×C181C2×D411yescharacteristic
158C2×C4×C181C2411yescharacteristic
159C8×C181—21no—
160C8×C181—21no—
161C22×C181—41no—
162C22×C181—41no—
163C22×C181—41no—
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—21no—
173C2×D181—21no—
174C2×D181—22no—
175C2×D181—21no—
176C2×D181—21no—
177C2×D181—41no—
178C2×D181—41no—
179C2×D181—84no—
180C2×D181—84no—
181C2×D181AGL(1,ℤ/8)12yes—
182C4×C181—21no—
183C4×C181—21no—
184C4×C181—41no—
185C4×C181C2×#4111yescharacteristic
186C4×C181H(5,𝔽2)11yescharacteristic
187Dic181—21no—
188Dic181—21no—
189Dic181—41no—
190Dic181—41no—
191Dic181—41no—
192C2×C181—81no—
193C2×C181—81no—
194C2×C181—81no—
195C2×C181#54611yescharacteristic
196C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C181#57611yescharacteristic
198D181—22no—
199D181—41no—
200D181—42no—
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#459D18111yescharacteristic, complemented
212#447—1811no—
213#447—1811no—
214#442—1811no—
215#435—1811no—
216#418—1811no—
217C2×#102—1811no—
218C22×D4—3621no—
219C22×D4—1811no—
220C22×D4—1811no—
221C2×D8—1811no—
222C2×D8C2×D18111yescharacteristic, complemented
223C2×D8C2×D18111yescharacteristic, complemented
224C2×M16—1811no—
225C22×C8—1811no—
226#127C2×D18111yescharacteristic
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#121—1811no—
236#120—3621no—
237#120—3621no—
238C4×D4—3621no—
239C4×D4—1811no—
240C4×D4—1811no—
241C4×D4C2×D18111yescharacteristic, complemented
242#117—1811no—
243C2×C4⋊C4—1811no—
244#107—1811no—
245#106—1811no—
246#106—1811no—
247C4⋊C8C2×D18111yescharacteristic, complemented
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—
260#97—1811no—
261C24—3621no—
262C24—3621no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—3622no—
266C2×D4—3622no—
267C2×D4—3621no—
268C2×D4—3621no—
269C2×D4—3621no—
270C2×D4—3621no—
271C2×D4—3621no—
272C2×D4—3621no—
273C2×D4—1811no—
274C2×D4—1811no—
275C2×D4—7241no—
276C2×D4—7241no—
277C2×D4—7244no—
278C2×D4C22×D18111yescharacteristic
279C2×D4C22×D18111yescharacteristic
280C2×D4C22×D18111yescharacteristic
281C22×C4—21no—
282C22×C4—3621no—
283C22×C4—3621no—
284C22×C4—1811no—
285C22×C4—1811no—
286D8—41no—
287D8—41no—
288D8—3622no—
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—
313C42C22×D18111yescharacteristic
314C23—21no—
315C23—21no—
316C23—21no—
317C23—3621no—
318C23—14481no—
319C23—14481no—
320C23—1811no—
321C23—1811no—
322C23—7242no—
323C23—7242no—
324C23—7242no—
325C23—7242no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—81no—
334D4—3622no—
335D4—3621no—
336D4—14481no—
337D4—1812no—
338D4—7242no—
339D4—7242no—
340D4—7242no—
341D4—7242no—
342D4—7242no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—3621no—
346C2×C4—3621no—
347C2×C4—3621no—
348C2×C4—3621no—
349C2×C4—3621no—
350C2×C4—3621no—
351C2×C4—3621no—
352C2×C4—14481no—
353C2×C4—1811no—
354C2×C4—1811no—
355C2×C4—7242no—
356C2×C4D4×D18111yescharacteristic
357C2×C4D4×D18111yescharacteristic
358C2×C4C23×D18111yescharacteristic
359C8—21no—
360C8—21no—
361C8—3621no—
362C8—3621no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—3621no—
373C22—3621no—
374C22—3621no—
375C22—3622no—
376C22—3621no—
377C22—3621no—
378C22—14484no—
379C22—14484no—
380C22—1812no—
381C22—7241no—
382C22—7241no—
383C22C2×D4×D18111yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—3621no—
388C4—3621no—
389C4—7241no—
390C4—7241no—
391C4—7241no—
392C4#41×D18111yescharacteristic
393C4#1915386111yescharacteristic
394C2—81no—
395C2—81no—
396C2—81no—
397C2—3622no—
398C2—7241no—
399C2—7242no—
400C2#2604192611yescharacteristic
401C2AGL(1,ℤ/8)×D18111yescharacteristic
402C2#2604208011yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#459×C181C2
socleC22×C181C22×D4
hypercenter#459D181
hypocenterC181#3318
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #26041979C2semidirect
2. #26041914C2semidirect
3. #26041643C2semidirect
4. #26041601C2semidirect
5. #26041596C2semidirect
6. #26041580C2semidirect
7. #26041529C2semidirect
8. #26041512C2semidirect
9. #26041411C2semidirect
10. #26041411C2semidirect
11. #26041389C2semidirect
12. #26041349C2semidirect
13. #26041282C2semidirect
14. #102×D181C2semidirect
15. #459×C181C2semidirect
20. C2×#15668432C22semidirect
21. C2×C8×D181C22semidirect
23. #19153808C22semidirect
29. #19153787C22semidirect
30. #19153787C22semidirect
36. #19153774C22semidirect
37. C4⋊C4×D181C22semidirect
38. #19153750C22semidirect
39. #19153748C22semidirect
40. #19153747C22semidirect
43. #19153737C22semidirect
44. #19153737C22semidirect
45. #19153737C22semidirect
46. #19153737C22semidirect
47. #19153737C22semidirect
49. #19153728C22semidirect
50. #19153728C22semidirect
51. #19153727C22semidirect
52. C2×D8×C181C22semidirect
53. C2×D8×C181C22semidirect
55. C4×D4×C181C22semidirect
56. C4⋊C8×C181C22semidirect
57. #102×C181C22semidirect
58. #102×C181C22semidirect
201. C181#3318semidirect
211. #459D181semidirect
222. C2×D8C2×D181semidirect
223. C2×D8C2×D181semidirect
241. C4×D4C2×D181semidirect
247. C4⋊C8C2×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
#260419792
#260419142
#260416432
#260416012
#260415962
#260415802
#260415292
#260415122
#260414112
#260413892
#260413492
#260412822
#102×D1812
#459×C1812
#3318181