Finite Group Databasebeta

← #37545859

Subgroups — #37545859

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#26041982C211yesmaximal, characteristic, complemented
2D4×D724C211yesmaximal, characteristic, complemented
3#26041645C211yesmaximal, characteristic, complemented
4#26041606C211yesmaximal, characteristic, complemented
5#26041599C211yesmaximal, characteristic, complemented
6#26041533C211yesmaximal, characteristic, complemented
7#26041516C211yesmaximal, characteristic, complemented
8#26041475C211yesmaximal, characteristic, complemented
9#26041414C211yesmaximal, characteristic, complemented
10#26041414C211yesmaximal, characteristic, complemented
11#26041389C211yesmaximal, characteristic, complemented
12#26041349C211yesmaximal, characteristic, complemented
13#26041282C211yesmaximal, characteristic, complemented
14#102×D181C211yesmaximal, characteristic, complemented
15#478×C181C211yesmaximal, characteristic, complemented
16C22×D724—21no—
17C2×D4×D181C2211yescharacteristic
18C2×D4×D181C2211yescharacteristic
19C2×D1448C2211yescharacteristic, complemented
20C2×D1448C2211yescharacteristic, complemented
21C2×#15668434C2211yescharacteristic
22C2×#15668432C2211yescharacteristic, complemented
23C2×C8×D181C2211yescharacteristic, complemented
24#19153813C2211yescharacteristic
25#19153811—21no—
26#19153801—21no—
27#19153791—21no—
28#19153791C2211yescharacteristic
29#19153791C2211yescharacteristic
30#19153791C2211yescharacteristic, complemented
31#19153791C2211yescharacteristic, complemented
32#19153790—21no—
33#19153786—21no—
34#19153786—21no—
35C4×D724C2211yescharacteristic
36C4×D724C2211yescharacteristic, complemented
37#19153778—21no—
38#19153774C2211yescharacteristic, complemented
39C4⋊C4×D181C2211yescharacteristic, complemented
40#19153747C2211yescharacteristic, complemented
41#19153738C2211yescharacteristic, complemented
42#19153738C2211yescharacteristic, complemented
43#19153737C2211yescharacteristic
44#19153736C2211yescharacteristic, complemented
45#19153736C2211yescharacteristic, complemented
46#19153736C2211yescharacteristic, complemented
47#19153736C2211yescharacteristic, complemented
48#19153736C2211yescharacteristic, complemented
49#19153728C2211yescharacteristic, complemented
50#19153728C2211yescharacteristic, complemented
51#19153727C2211yescharacteristic, complemented
52#125×C181C2211yescharacteristic, complemented
53C4×D4×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic, complemented
55#106×C181C2211yescharacteristic, complemented
56C4⋊C8×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C23×D181—21no—
60C23×D181—21no—
61C2×D724—21no—
62C2×D724—21no—
63C2×D724—21no—
64C2×D724—21no—
65C2×D724—21no—
66C2×D724—21no—
67C2×D724—44no—
68C2×D724D411yescharacteristic
69C2×D724C2311yescharacteristic
70C2×D724C2311yescharacteristic
71C2×D724C2311yescharacteristic
72C2×C22⋊D181—21no—
73C2×C22⋊D181—21no—
74D4×D181—22no—
75D4×D181—22no—
76D4×D181—41no—
77D4×D181—41no—
78C2×C4×D181—21no—
79C2×C4×D181—21no—
80C2×C4×D181C2311yescharacteristic
81C2×C4×D181C2311yescharacteristic
82D1448—41no—
83D1448—41no—
84#15668434—22no—
85#15668432—41no—
86C2×#13089678C2311yescharacteristic
87C2×#13089678C2311yescharacteristic
88C8×D181—41no—
89C4⋊Dic181D411yescharacteristic
90C4⋊Dic181C2311yescharacteristic
91#15668428—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426—21no—
98#15668426D411yescharacteristic
99#15668426D411yescharacteristic
100C4×Dic181—21no—
101C2×D4×C181C2311yescharacteristic
102C22×C4×C181—21no—
103C2×C8×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C4⋊C4×C181—21no—
106C4⋊C4×C181—21no—
107C4⋊C4×C181C2311yescharacteristic
108C4⋊C4×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C22⋊C4×C181—21no—
111C42×C181C2311yescharacteristic
112C22×D181—21no—
113C22×D181—21no—
114C22×D181—21no—
115C22×D181—42no—
116C22×D181—42no—
117C22×D181—42no—
118C22×D181—42no—
119C22×D181—81no—
120C22×D181—81no—
121C22×D181C2×D411yescharacteristic
122C22×D181C2×D411yescharacteristic
123D724—22no—
124D724—21no—
125D724—21no—
126D724—21no—
127D724—21no—
128D724—21no—
129D724—21no—
130D724—42no—
131D724—42no—
132D724—42no—
133D724—42no—
134D724—81no—
135D724—81no—
136C22⋊D181—42no—
137C22⋊D181—42no—
138C2×Dic181—21no—
139C2×Dic181C2×D411yescharacteristic
140C2×Dic181C2×D411yescharacteristic
141C4×D181—21no—
142C4×D181—21no—
143C4×D181—21no—
144C4×D181—21no—
145C4×D181—81no—
146C4×D181—81no—
147#13089678—21no—
148#13089678—21no—
149C23×C181—21no—
150D4×C181—21no—
151D4×C181#4112yes—
152C2×C4×C181—21no—
153C2×C4×C181—21no—
154C2×C4×C181—21no—
155C2×C4×C181—42no—
156C2×C4×C181C2×D411yescharacteristic
157C2×C4×C181C2×D411yescharacteristic
158C2×C4×C181C2411yescharacteristic
159C8×C181—21no—
160C8×C181—21no—
161C22×C181—22no—
162C22×C181—41no—
163C22×C181—41no—
164C22×C181C22×D411yescharacteristic
165C2×D181—21no—
166C2×D181—21no—
167C2×D181—21no—
168C2×D181—21no—
169C2×D181—21no—
170C2×D181—41no—
171C2×D181—41no—
172C2×D181—41no—
173C2×D181—41no—
174C2×D181—41no—
175C2×D181—41no—
176C2×D181—41no—
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×C181—41no—
186C4×C181—41no—
187C4×C181C2×#4111yescharacteristic
188C4×C181H(5,𝔽2)11yescharacteristic
189Dic181—21no—
190Dic181—21no—
191Dic181—41no—
192C2×C181—42no—
193C2×C181#54611yescharacteristic
194C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
195C2×C181#57611yescharacteristic
196D181—22no—
197D181—41no—
198D181—81no—
199D181—81no—
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#478D18111yescharacteristic, complemented
209#469—1811no—
210#466—1811no—
211#459—1811no—
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×D8—1811no—
223C2×D8—1811no—
224C2×M16—1811no—
225C22×C8—1811no—
226#127—1811no—
227#126—3621no—
228#125C2×D18111yescharacteristic, complemented
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
242#117—1811no—
243C2×C4⋊C4—1811no—
244#107C2×D18111yescharacteristic, complemented
245#106—1811no—
246#106C2×D18111yescharacteristic, complemented
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
257#102C2×D18111yescharacteristic
258C22⋊C8—1811no—
259C22⋊C8—1811no—
260#97—1811no—
261C24—3621no—
262C24—3621no—
263C2×D4—3621no—
264C2×D4—3621no—
265C2×D4—3621no—
266C2×D4—3621no—
267C2×D4—3622no—
268C2×D4—3622no—
269C2×D4—3621no—
270C2×D4—3621no—
271C2×D4—3621no—
272C2×D4—3621no—
273C2×D4—1811no—
274C2×D4—1811no—
275C2×D4—1811no—
276C2×D4—1811no—
277C2×D4—7244no—
278C2×D4—7241no—
279C2×D4—7241no—
280C2×D4C22×D18111yescharacteristic
281C22×C4—21no—
282C22×C4—3621no—
283C22×C4—3621no—
284C22×C4—1811no—
285C22×C4—1811no—
286D8—3622no—
287D8—7241no—
288D8—7241no—
289M16—7241no—
290C2×C8—1811no—
291C2×C8—1811no—
292C2×C8—7241no—
293C2×C8C22×D18111yescharacteristic
294C2×C8C22×D18111yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—3621no—
298C4⋊C4—1811no—
299C4⋊C4—1811no—
300C4⋊C4C22×D18111yescharacteristic
301C4⋊C4C22×D18111yescharacteristic
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—3621no—
316C23—3621no—
317C23—3621no—
318C23—14481no—
319C23—14481no—
320C23—1811no—
321C23—1811no—
322C23—7242no—
323C23—7242no—
324C23—7242no—
325C23—7242no—
326D4—21no—
327D4—3622no—
328D4—3621no—
329D4—3621no—
330D4—3621no—
331D4—3621no—
332D4—3621no—
333D4—3621no—
334D4—14481no—
335D4—14481no—
336D4—7242no—
337D4—7242no—
338D4—7242no—
339D4—7242no—
340D4—7242no—
341D4—7242no—
342D4#1566845012yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—42no—
347C2×C4—3621no—
348C2×C4—3621no—
349C2×C4—3621no—
350C2×C4—3621no—
351C2×C4—3621no—
352C2×C4—14481no—
353C2×C4—14481no—
354C2×C4—1811no—
355C2×C4—1811no—
356C2×C4D4×D18111yescharacteristic
357C2×C4D4×D18111yescharacteristic
358C2×C4C23×D18111yescharacteristic
359C8—21no—
360C8—21no—
361C8—3621no—
362C8—3621no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22—3621no—
367C22—3621no—
368C22—3621no—
369C22—3621no—
370C22—3621no—
371C22—14484no—
372C22—14484no—
373C22—1812no—
374C22—7241no—
375C22—7241no—
376C22—7241no—
377C22—7241no—
378C22—7241no—
379C22—7241no—
380C22—7241no—
381C22—7241no—
382C22—7241no—
383C22C2×D4×D18111yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—3621no—
390C4—3621no—
391C4—7241no—
392C4C2×#1566845011yescharacteristic
393C4#1915386211yescharacteristic
394C2—42no—
395C2—3622no—
396C2—14481no—
397C2—14481no—
398C2—14481no—
399C2—7241no—
400C2#2604192011yescharacteristic
401C2AGL(1,ℤ/8)×D18111yescharacteristic
402C2#2604208111yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#478×C181C2
socleC22×C181C22×D4
hypercenter#478D181
hypocenterC181#3318
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #26041982C2semidirect
2. D4×D724C2semidirect
3. #26041645C2semidirect
4. #26041606C2semidirect
5. #26041599C2semidirect
6. #26041533C2semidirect
7. #26041516C2semidirect
8. #26041475C2semidirect
9. #26041414C2semidirect
10. #26041414C2semidirect
11. #26041389C2semidirect
12. #26041349C2semidirect
13. #26041282C2semidirect
14. #102×D181C2semidirect
15. #478×C181C2semidirect
19. C2×D1448C22semidirect
20. C2×D1448C22semidirect
22. C2×#15668432C22semidirect
23. C2×C8×D181C22semidirect
30. #19153791C22semidirect
31. #19153791C22semidirect
36. C4×D724C22semidirect
38. #19153774C22semidirect
39. C4⋊C4×D181C22semidirect
40. #19153747C22semidirect
41. #19153738C22semidirect
42. #19153738C22semidirect
44. #19153736C22semidirect
45. #19153736C22semidirect
46. #19153736C22semidirect
47. #19153736C22semidirect
48. #19153736C22semidirect
49. #19153728C22semidirect
50. #19153728C22semidirect
51. #19153727C22semidirect
52. #125×C181C22semidirect
54. #107×C181C22semidirect
55. #106×C181C22semidirect
56. C4⋊C8×C181C22semidirect
201. C181#3318semidirect
208. #478D181semidirect
228. #125C2×D181semidirect
244. #107C2×D181semidirect
246. #106C2×D181semidirect
247. C4⋊C8C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419822
D4×D7242
#260416452
#260416062
#260415992
#260415332
#260415162
#260414752
#260414142
#260413892
#260413492
#260412822
#102×D1812
#478×C1812
#3318181