Finite Group Databasebeta

← #37545861

Subgroups — #37545861

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
2#26041914C211yesmaximal, characteristic, complemented
3#26041602C211yesmaximal, characteristic, complemented
4#26041596C211yesmaximal, characteristic, complemented
5#26041576C211yesmaximal, characteristic, complemented
6#26041531C211yesmaximal, characteristic, complemented
7#26041514C211yesmaximal, characteristic, complemented
8#26041471C211yesmaximal, characteristic, complemented
9#26041414C211yesmaximal, characteristic, complemented
10#26041414C211yesmaximal, characteristic, complemented
11#26041392C211yesmaximal, characteristic, complemented
12#26041352C211yesmaximal, characteristic, complemented
13#26041282C211yesmaximal, characteristic, complemented
14#102×D181C211yesmaximal, characteristic, complemented
15#490×C181C211yesmaximal, characteristic, complemented
16C2×D4×D181—21no—
17C2×D4×D181C2211yescharacteristic
18C2×D4×D181C2211yescharacteristic
19C2×D1448C2211yescharacteristic
20C2×#15668434C2211yescharacteristic, complemented
21C2×#15668434C2211yescharacteristic, complemented
22C2×#15668432C2211yescharacteristic, complemented
23C2×C8×D181C2211yescharacteristic, complemented
24#19153811—21no—
25#19153801—21no—
26#19153791—21no—
27#19153791C2211yescharacteristic, complemented
28#19153791C2211yescharacteristic, complemented
29#19153787—21no—
30#19153787C2211yescharacteristic
31#19153787C2211yescharacteristic
32#19153784—21no—
33#19153784—21no—
34C4×D724C2211yescharacteristic
35C4×D724C2211yescharacteristic
36C4×D724C2211yescharacteristic, complemented
37#19153778—21no—
38#19153774C2211yescharacteristic, complemented
39C4⋊C4×D181C2211yescharacteristic, complemented
40#19153749C2211yescharacteristic, complemented
41#19153748C2211yescharacteristic, complemented
42#19153747C2211yescharacteristic, complemented
43C4⋊#13089678C2211yescharacteristic, complemented
44#19153738C2211yescharacteristic
45#19153738C2211yescharacteristic, complemented
46#19153737C2211yescharacteristic, complemented
47#19153737C2211yescharacteristic, complemented
48#19153736C2211yescharacteristic
49#19153736C2211yescharacteristic
50#19153728C2211yescharacteristic, complemented
51#19153728C2211yescharacteristic, complemented
52#127×C181C2211yescharacteristic
53#125×C181C2211yescharacteristic, complemented
54#102×C181C2211yescharacteristic, complemented
55#102×C181C2211yescharacteristic, complemented
56#102×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic, complemented
58#97×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60C23×D181—21no—
61C2×D724—21no—
62C2×D724—21no—
63C2×D724D411yescharacteristic
64C2×D724C2311yescharacteristic
65C2×D724C2311yescharacteristic
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70D4×D181—22no—
71D4×D181—22no—
72D4×D181—41no—
73D4×D181—41no—
74D4×D181—44no—
75C2×C4×D181—21no—
76C2×C4×D181—21no—
77C2×C4×D181—21no—
78C2×C4×D181C2311yescharacteristic
79C2×C4×D181C2311yescharacteristic
80D1448—22no—
81#15668434—41no—
82#15668434—41no—
83#15668432—41no—
84C2×#13089678C2311yescharacteristic
85C2×#13089678C2311yescharacteristic
86C8×D181—41no—
87C4⋊Dic181D411yescharacteristic
88C4⋊Dic181C2311yescharacteristic
89C4⋊Dic181C2311yescharacteristic
90#15668428—21no—
91C22⋊Dic181—21no—
92C22⋊Dic181—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×C181—21no—
102C2×D4×C181—21no—
103C2×D4×C181C2311yescharacteristic
104C2×D4×C181C2311yescharacteristic
105C2×C8×C181C2311yescharacteristic
106C2×C8×C181C2311yescharacteristic
107C4⋊C4×C181—21no—
108C4⋊C4×C181—21no—
109C4⋊C4×C181C2311yescharacteristic
110C4⋊C4×C181C2311yescharacteristic
111C42×C181C2311yescharacteristic
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
121C22×D181C2×D411yescharacteristic
122D724—22no—
123D724—21no—
124D724—21no—
125D724—21no—
126D724—42no—
127D724—81no—
128D724#4112yes—
129C22⋊D181—42no—
130C22⋊D181—42no—
131C22⋊D181—42no—
132C22⋊D181—42no—
133C2×Dic181—21no—
134C2×Dic181—21no—
135C2×Dic181C2×D411yescharacteristic
136C2×Dic181C2×D411yescharacteristic
137C4×D181—21no—
138C4×D181—21no—
139C4×D181—21no—
140C4×D181—21no—
141C4×D181—42no—
142C4×D181—81no—
143C4×D181—81no—
144#13089678—21no—
145#13089678—21no—
146C23×C181—21no—
147C23×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—21no—
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×C181C22×D411yescharacteristic
168C2×D181—21no—
169C2×D181—21no—
170C2×D181—21no—
171C2×D181—22no—
172C2×D181—21no—
173C2×D181—21no—
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×C181C2×#4111yescharacteristic
187C4×C181H(5,𝔽2)11yescharacteristic
188Dic181—21no—
189Dic181—21no—
190Dic181—41no—
191Dic181—41no—
192C2×C181—81no—
193C2×C181—81no—
194C2×C181#54611yescharacteristic
195C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
196C2×C181#57611yescharacteristic
197D181—22no—
198D181—41no—
199D181—42no—
200D181—81no—
201C181#331811yescharacteristic, complemented, Sylow
202#3318—1811nomaximal, Sylow
203#553—1811no—
204D42—1811no—
205#490D18111yescharacteristic, complemented
206#482—1811no—
207#481—1811no—
208#478—1811no—
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#127C2×D18111yescharacteristic
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×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#102C2×D18111yescharacteristic, complemented
255#102C2×D18111yescharacteristic, complemented
256#102C2×D18111yescharacteristic, complemented
257#102C2×D18111yescharacteristic, complemented
258C22⋊C8—1811no—
259C22⋊C8—1811no—
260#97C2×D18111yescharacteristic, complemented
261C24—3621no—
262C24—3621no—
263C2×D4—21no—
264C2×D4—21no—
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—7241no—
277C2×D4—7241no—
278C2×D4—7244no—
279C2×D4C22×D18111yescharacteristic
280C2×D4C22×D18111yescharacteristic
281C22×C4—3621no—
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⋊C4—1811no—
301C4⋊C4C22×D18111yescharacteristic
302C4⋊C4C22×D18111yescharacteristic
303C22⋊C4—3621no—
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—3621no—
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—42no—
331D4—81no—
332D4—3622no—
333D4—3621no—
334D4—3621no—
335D4—3621no—
336D4—14481no—
337D4—1812no—
338D4—7242no—
339D4—7242no—
340D4—7242no—
341D4—7242no—
342D4—7242no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—3621no—
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—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—3621no—
370C22—3621no—
371C22—3621no—
372C22—3622no—
373C22—3621no—
374C22—3621no—
375C22—14484no—
376C22—14484no—
377C22—1812no—
378C22—7241no—
379C22—7241no—
380C22—7241no—
381C22—7241no—
382C22—7241no—
383C22C2×D4×D18111yescharacteristic
384C4—21no—
385C4—21no—
386C4—41no—
387C4—41no—
388C4—3621no—
389C4—3621no—
390C4—7241no—
391C4—7241no—
392C4#41×D18111yescharacteristic
393C4#1915386211yescharacteristic
394C2—81no—
395C2—81no—
396C2—3622no—
397C2—14481no—
398C2—7241no—
399C2—7242no—
400C2#2604192211yescharacteristic
401C2AGL(1,ℤ/8)×D18111yescharacteristic
402C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#490×C181C2
socleC22×C181C22×D4
hypercenter#490D181
hypocenterC181#3318
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #26041982C2semidirect
2. #26041914C2semidirect
3. #26041602C2semidirect
4. #26041596C2semidirect
5. #26041576C2semidirect
6. #26041531C2semidirect
7. #26041514C2semidirect
8. #26041471C2semidirect
9. #26041414C2semidirect
10. #26041414C2semidirect
11. #26041392C2semidirect
12. #26041352C2semidirect
13. #26041282C2semidirect
14. #102×D181C2semidirect
15. #490×C181C2semidirect
20. C2×#15668434C22semidirect
21. C2×#15668434C22semidirect
22. C2×#15668432C22semidirect
23. C2×C8×D181C22semidirect
27. #19153791C22semidirect
28. #19153791C22semidirect
36. C4×D724C22semidirect
38. #19153774C22semidirect
39. C4⋊C4×D181C22semidirect
40. #19153749C22semidirect
41. #19153748C22semidirect
42. #19153747C22semidirect
43. C4⋊#13089678C22semidirect
45. #19153738C22semidirect
46. #19153737C22semidirect
47. #19153737C22semidirect
50. #19153728C22semidirect
51. #19153728C22semidirect
53. #125×C181C22semidirect
54. #102×C181C22semidirect
55. #102×C181C22semidirect
56. #102×C181C22semidirect
57. #102×C181C22semidirect
58. #97×C181C22semidirect
201. C181#3318semidirect
205. #490D181semidirect
228. #125C2×D181semidirect
254. #102C2×D181semidirect
255. #102C2×D181semidirect
256. #102C2×D181semidirect
257. #102C2×D181semidirect
260. #97C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419822
#260419142
#260416022
#260415962
#260415762
#260415312
#260415142
#260414712
#260414142
#260413922
#260413522
#260412822
#102×D1812
#490×C1812
#3318181