Finite Group Databasebeta

← #37545862

Subgroups — #37545862

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#26041975C211yesmaximal, characteristic, complemented
2#26041643C211yesmaximal, characteristic, complemented
3#26041600C211yesmaximal, characteristic, complemented
4#26041595C211yesmaximal, characteristic, complemented
5#26041579C211yesmaximal, characteristic, complemented
6#26041530C211yesmaximal, characteristic, complemented
7#26041513C211yesmaximal, characteristic, complemented
8#26041471C211yesmaximal, characteristic, complemented
9#26041413C211yesmaximal, characteristic, complemented
10#26041413C211yesmaximal, characteristic, complemented
11#26041389C211yesmaximal, characteristic, complemented
12#26041351C211yesmaximal, characteristic, complemented
13#26041284C211yesmaximal, characteristic, complemented
14C2×#19153737C211yesmaximal, characteristic, complemented
15D42×C181C211yesmaximal, characteristic, complemented
16C2×#15668434C2211yescharacteristic
17C2×#15668434C2211yescharacteristic, complemented
18C2×#15668434C2211yescharacteristic, complemented
19C2×#15668433C2211yescharacteristic, complemented
20C22×#13089678C2211yescharacteristic, complemented
21#19153811—21no—
22#19153808C2211yescharacteristic, complemented
23#19153798—21no—
24#19153790C2211yescharacteristic, complemented
25#19153790C2211yescharacteristic, complemented
26#19153788—21no—
27C4×D724C2211yescharacteristic, complemented
28#19153776—21no—
29#19153775C2211yescharacteristic, complemented
30C2×C4⋊Dic181C2211yescharacteristic, complemented
31#19153749C2211yescharacteristic, complemented
32#19153747C2211yescharacteristic, complemented
33#19153747C2211yescharacteristic, complemented
34C4⋊#13089678C2211yescharacteristic, complemented
35#19153737C2211yescharacteristic
36#19153737C2211yescharacteristic
37#19153737C2211yescharacteristic
38#19153737C2211yescharacteristic, complemented
39#19153737C2211yescharacteristic, complemented
40#19153737C2211yescharacteristic, complemented
41#19153737C2211yescharacteristic, complemented
42#19153737C2211yescharacteristic, complemented
43#19153737C2211yescharacteristic, complemented
44#19153736C2211yescharacteristic, complemented
45C22⋊#13089678C2211yescharacteristic, complemented
46C22⋊#13089678C2211yescharacteristic, complemented
47#19153727C2211yescharacteristic, complemented
48C22×D4×C181—21no—
49C22×D4×C181C2211yescharacteristic
50C22×D4×C181C2211yescharacteristic
51#127×C181C2211yescharacteristic
52#121×C181—21no—
53#121×C181C2211yescharacteristic
54#121×C181C2211yescharacteristic
55#120×C181—21no—
56#120×C181—21no—
57C4×D4×C181C2211yescharacteristic
58C4×D4×C181C2211yescharacteristic
59C2×D724C2311yescharacteristic
60C2×C22⋊D181—21no—
61C2×C22⋊D181—21no—
62C22×Dic181—21no—
63C2×C4×D181—21no—
64#15668434—22no—
65#15668434—41no—
66#15668434—41no—
67#15668433—41no—
68C2×#13089678—41no—
69C2×#13089678C2311yescharacteristic
70C2×#13089678C2311yescharacteristic
71C2×#13089678C2311yescharacteristic
72C2×#13089678C2311yescharacteristic
73C4⋊Dic181—21no—
74C4⋊Dic181C2311yescharacteristic
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77#15668428—21no—
78#15668428—21no—
79C22⋊Dic181—21no—
80#15668426—21no—
81#15668426—21no—
82#15668426—21no—
83C4×Dic181—21no—
84C24×C181—21no—
85C24×C181—21no—
86C2×D4×C181—22no—
87C2×D4×C181—22no—
88C2×D4×C181—21no—
89C2×D4×C181—21no—
90C2×D4×C181—21no—
91C2×D4×C181—21no—
92C2×D4×C181—21no—
93C2×D4×C181—21no—
94C2×D4×C181—41no—
95C2×D4×C181—41no—
96C2×D4×C181—44no—
97C2×D4×C181D411yescharacteristic
98C2×D4×C181C2311yescharacteristic
99C2×D4×C181C2311yescharacteristic
100C2×D4×C181C2311yescharacteristic
101C22×C4×C181—21no—
102C22×C4×C181C2311yescharacteristic
103C22×C4×C181C2311yescharacteristic
104C4⋊C4×C181D411yescharacteristic
105C4⋊C4×C181C2311yescharacteristic
106C22⋊C4×C181—21no—
107C22⋊C4×C181—21no—
108C22⋊C4×C181—21no—
109C22⋊C4×C181D411yescharacteristic
110C22⋊C4×C181D411yescharacteristic
111C42×C181C2311yescharacteristic
112C22×D181—21no—
113D724—21no—
114D724—21no—
115C22⋊D181—42no—
116C22⋊D181—81no—
117C2×Dic181—21no—
118C2×Dic181—21no—
119C2×Dic181—21no—
120C2×Dic181—81no—
121C4×D181—81no—
122#13089678—21no—
123#13089678—21no—
124#13089678—21no—
125#13089678—21no—
126C23×C181—21no—
127C23×C181—21no—
128C23×C181—21no—
129C23×C181—42no—
130C23×C181—42no—
131C23×C181—42no—
132C23×C181—42no—
133C23×C181—81no—
134C23×C181—81no—
135C23×C181C2×D411yescharacteristic
136C23×C181C2×D411yescharacteristic
137D4×C181—22no—
138D4×C181—21no—
139D4×C181—21no—
140D4×C181—21no—
141D4×C181—21no—
142D4×C181—21no—
143D4×C181—42no—
144D4×C181—42no—
145D4×C181—42no—
146D4×C181—42no—
147D4×C181—42no—
148D4×C181—81no—
149D4×C181#4112yes—
150C2×C4×C181—21no—
151C2×C4×C181—21no—
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×C181C2×D411yescharacteristic
159C2×C4×C181C2×D411yescharacteristic
160C2×C4×C181C2411yescharacteristic
161C22×C181—21no—
162C22×C181—21no—
163C22×C181—21no—
164C22×C181—22no—
165C22×C181—21no—
166C22×C181—21no—
167C22×C181—41no—
168C22×C181—41no—
169C22×C181—41no—
170C22×C181—41no—
171C22×C181—41no—
172C22×C181—41no—
173C22×C181—41no—
174C22×C181—41no—
175C22×C181—84no—
176C22×C181—84no—
177C22×C181AGL(1,ℤ/8)12yes—
178C22×C181C22×D411yescharacteristic
179C2×D181—41no—
180C2×D181—41no—
181C2×D181—41no—
182C4×C181—21no—
183C4×C181—21no—
184C4×C181—21no—
185C4×C181—21no—
186C4×C181—41no—
187C4×C181C2×#4111yescharacteristic
188C4×C181H(5,𝔽2)11yescharacteristic
189Dic181—41no—
190Dic181—41no—
191Dic181—41no—
192C2×C181—22no—
193C2×C181—41no—
194C2×C181—42no—
195C2×C181—81no—
196C2×C181—81no—
197C2×C181#54611yescharacteristic
198C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
199C2×C181#57611yescharacteristic
200D181—81no—
201C181#331811yescharacteristic, complemented, Sylow
202#3318—1811nomaximal, Sylow
203#553—1811no—
204D42D18111yescharacteristic, complemented
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#447—1811no—
214#442—1811no—
215#435—1811no—
216#418—1811no—
217C2×#102—1811no—
218C22×D4—21no—
219C22×D4C2×D18111yescharacteristic
220C22×D4C2×D18111yescharacteristic
221C2×D8—1811no—
222C2×D8—1811no—
223C2×D8—1811no—
224C2×M16—1811no—
225C22×C8—1811no—
226#127C2×D18111yescharacteristic
227#126—3621no—
228#125—1811no—
229#123—3621no—
230#121—21no—
231#121—3621no—
232#121—1811no—
233#121—1811no—
234#121C2×D18111yescharacteristic
235#121C2×D18111yescharacteristic
236#120—21no—
237#120—21no—
238C4×D4—3621no—
239C4×D4—1811no—
240C4×D4C2×D18111yescharacteristic
241C4×D4C2×D18111yescharacteristic
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#102—1811no—
257#102—1811no—
258C22⋊C8—1811no—
259C22⋊C8—1811no—
260#97—1811no—
261C24—21no—
262C24—21no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—44no—
274C2×D4—3621no—
275C2×D4—3621no—
276C2×D4—1811no—
277C2×D4C22⋊D18111yescharacteristic
278C2×D4C22×D18111yescharacteristic
279C2×D4C22×D18111yescharacteristic
280C2×D4C22×D18111yescharacteristic
281C22×C4—21no—
282C22×C4—3621no—
283C22×C4—3621no—
284C22×C4C22×D18111yescharacteristic
285C22×C4C22×D18111yescharacteristic
286D8—3622no—
287D8—7241no—
288D8—7241no—
289M16—7241no—
290C2×C8—1811no—
291C2×C8—1811no—
292C2×C8—1811no—
293C2×C8—1811no—
294C2×C8—7241no—
295C4⋊C4—3621no—
296C4⋊C4—3621no—
297C4⋊C4—3621no—
298C4⋊C4—1811no—
299C4⋊C4—1811no—
300C4⋊C4—1811no—
301C4⋊C4C22⋊D18111yescharacteristic
302C4⋊C4C22×D18111yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—3621no—
307C22⋊C4—3621no—
308C22⋊C4—3621no—
309C22⋊C4—3621no—
310C22⋊C4C22⋊D18111yescharacteristic
311C22⋊C4C22⋊D18111yescharacteristic
312C42—3621no—
313C42C22×D18111yescharacteristic
314C23—21no—
315C23—21no—
316C23—21no—
317C23—42no—
318C23—42no—
319C23—42no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—3621no—
324C23C2×C22⋊D18111yescharacteristic
325C23C2×C22⋊D18111yescharacteristic
326D4—22no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—42no—
334D4—42no—
335D4—42no—
336D4—42no—
337D4—81no—
338D4—3621no—
339D4—3621no—
340D4—14481no—
341D4—7242no—
342D4#1566844812yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—3621no—
350C2×C4—3621no—
351C2×C4—3621no—
352C2×C4—14481no—
353C2×C4—14481no—
354C2×C4C2×C22⋊D18111yescharacteristic
355C2×C4C2×C22⋊D18111yescharacteristic
356C2×C4C2×C22⋊D18111yescharacteristic
357C2×C4C2×C22⋊D18111yescharacteristic
358C2×C4C23×D18111yescharacteristic
359C8—3621no—
360C8—3621no—
361C8—3621no—
362C8—3621no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—22no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—84no—
378C22—84no—
379C22—7241no—
380C22—7241no—
381C22—7241no—
382C22#1915384212yes—
383C22C22×C22⋊D18111yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—7241no—
390C4—7241no—
391C4—7241no—
392C4C2×#1566844811yescharacteristic
393C4#1915386111yescharacteristic
394C2—22no—
395C2—41no—
396C2—42no—
397C2—81no—
398C2—81no—
399C2—14481no—
400C2#2604192311yescharacteristic
401C2C2×#1915384211yescharacteristic
402C2#2604208211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingD42×C181C2
socleC22×C181C22×D4
hypercenterD42D181
hypocenterC181#3318
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #26041975C2semidirect
2. #26041643C2semidirect
3. #26041600C2semidirect
4. #26041595C2semidirect
5. #26041579C2semidirect
6. #26041530C2semidirect
7. #26041513C2semidirect
8. #26041471C2semidirect
9. #26041413C2semidirect
10. #26041413C2semidirect
11. #26041389C2semidirect
12. #26041351C2semidirect
13. #26041284C2semidirect
14. C2×#19153737C2semidirect
15. D42×C181C2semidirect
17. C2×#15668434C22semidirect
18. C2×#15668434C22semidirect
19. C2×#15668433C22semidirect
20. C22×#13089678C22semidirect
22. #19153808C22semidirect
24. #19153790C22semidirect
25. #19153790C22semidirect
27. C4×D724C22semidirect
29. #19153775C22semidirect
30. C2×C4⋊Dic181C22semidirect
31. #19153749C22semidirect
32. #19153747C22semidirect
33. #19153747C22semidirect
34. C4⋊#13089678C22semidirect
38. #19153737C22semidirect
39. #19153737C22semidirect
40. #19153737C22semidirect
41. #19153737C22semidirect
42. #19153737C22semidirect
43. #19153737C22semidirect
44. #19153736C22semidirect
45. C22⋊#13089678C22semidirect
46. C22⋊#13089678C22semidirect
47. #19153727C22semidirect
201. C181#3318semidirect
204. D42D181semidirect

Maximal subgroups

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

subgroupindex
#260419752
#260416432
#260416002
#260415952
#260415792
#260415302
#260415132
#260414712
#260414132
#260413892
#260413512
#260412842
C2×#191537372
D42×C1812
#3318181