Finite Group Databasebeta

← C4×#22627670 #49171992

Subgroups — C4×#22627670 #49171992

Order 37504.

1660 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22627670C211yesmaximal, characteristic
2#34036612C211yesmaximal, characteristic, complemented
3#34036611C212yesmaximal, complemented
4#34036609C213yesmaximal, complemented
5#34036603C213yesmaximal, complemented
6#34036601C216yesmaximal, complemented
7C4×#17989803C212yesmaximal, complemented
8C4×#17989802C213yesmaximal, complemented
9C2×C4×D1172C213yesmaximal, complemented
10C4×D4×D293C216yesmaximal, complemented
11C4×#41×C293C211yesmaximal, characteristic, complemented
12#22627670C4116yesdirect product factor
13C2×#17989803C2212yes—
14C2×#17989802C2213yes—
15C22×D1172C2213yes—
16C2×D4×D293C2216yes—
17C22×C4×D293C2216yescomplemented
18Q8×Dic293C2212yescomplemented
19C4×Dic586C2211yescharacteristic, complemented
20C4×Dic586C2213yescomplemented
21C4×D1172C2216yescomplemented
22C4×D1172C2213yescomplemented
23C4×D1172C2216yescomplemented
24C4×D1172C2216yescomplemented
25C4×D1172C2213yescomplemented
26D4×Dic293C2216yescomplemented
27#22627586C2216yescomplemented
28#22627586C2216yescomplemented
29C4×C22⋊D293C2216yescomplemented
30C4×C22⋊D293C2216yescomplemented
31#22627584C22112yescomplemented
32#22627583C2213yescomplemented
33#22627582C2216yescomplemented
34#22627581C2216yescomplemented
35C2×C4⋊Dic293C2213yescomplemented
36C4⋊C4×D293C2216yescomplemented
37C2×#17989779C2216yescomplemented
38C22⋊C4×D293C22112yescomplemented
39C42×D293C2216yescomplemented
40C2×#41×C293C2211yescharacteristic
41C4×Q8×C293C2211yescharacteristic, complemented
42C4×Q8×C293C2211yescharacteristic, complemented
43C4×D4×C293C2213yescomplemented
44C4×D4×C293C2213yescomplemented
45#117×C293C2213yescomplemented
46C2×C42×C293C2213yescomplemented
47C23×D293C2316yes—
48#17989803C2×C4116yescomplemented
49#17989802C2×C4124yescomplemented
50C2×Dic586C2311yescharacteristic
51C2×D1172C2×C4124yescomplemented
52C2×D1172C2316yes—
53C2×D1172C2313yes—
54C2×C22⋊D293C2316yes—
55D4×D293C2×C4148yescomplemented
56C22×Dic293C2316yes—
57C2×C4×D293—412no—
58C2×C4×D293C2316yes—
59C2×C4×D293C23112yes—
60C2×C4×D293C2316yes—
61C2×C4×D293C2316yes—
62C4⋊Dic293C2316yes—
63C4⋊Dic293C2313yes—
64C4⋊Dic293C2311yescharacteristic
65#17989781C2316yes—
66#17989781C2312yes—
67C22⋊Dic293C2316yes—
68#17989779C23112yes—
69#17989779C2316yes—
70#17989779C2316yes—
71C4×Dic293C2316yes—
72C4×Dic293C2312yes—
73C4×Dic293C2316yes—
74#41×C293C2×C418yescomplemented
75C2×Q8×C293C2311yescharacteristic
76C2×D4×C293C2313yes—
77C22×C4×C293C2313yes—
78C22×C4×C293C2313yes—
79C22×C4×C293C2313yes—
80C4⋊C4×C293C2313yes—
81C4⋊C4×C293C2313yes—
82C22⋊C4×C293C2316yes—
83C42×C293C2311yescharacteristic
84C42×C293C2313yes—
85C42×C293C2313yes—
86C42×C293C2313yes—
87C22×D293—46no—
88C22×D293—46no—
89C22×D293C22×C4124yescomplemented
90C22×D293C2416yes—
91Dic586C22×C414yescomplemented
92D1172C22×C4124yescomplemented
93D1172C22×C4112yescomplemented
94C22⋊D293C22×C4124yescomplemented
95C2×Dic293—46no—
96C2×Dic293C2412yes—
97C2×Dic293C2416yes—
98C2×Dic293C2412yes—
99C4×D293—212no—
100C4×D293—412no—
101C4×D293—46no—
102C4×D293C22×C4124yescomplemented
103C23×C293C2413yes—
104Q8×C293C22×C414yescomplemented
105D4×C293C22×C4112yescomplemented
106C2×C4×C293—26no—
107C2×C4×C293—43no—
108C2×C4×C293C22×C4112yescomplemented
109C2×C4×C293C2411yescharacteristic
110C2×C4×C293C2413yes—
111C2×C4×C293C2413yes—
112C2×C4×C293C2411yescharacteristic
113C2×C4×C293C2413yes—
114C2×C4×C293C2411yescharacteristic
115C22×C293—23no—
116C22×C293—23no—
117C22×C293C23×C416yes—
118C22×C293C2511yescharacteristic
119C2×D293—26no—
120C2×D293—26no—
121C2×D293—424no—
122C2×D293C23×C4112yes—
123C4×C293—23no—
124C4×C293—21no—
125C4×C293—23no—
126C4×C293C23×C412yes—
127C4×C293C23×C416yes—
128C4×C293H(5,𝔽2)12yescomplemented
129Dic293—26no—
130Dic293—22no—
131Dic293C23×C414yes—
132C2×C293—26no—
133C2×C293C24×C411yescharacteristic
134C2×C293C2×H(5,𝔽2)11yescharacteristic
135C2×C293#58511yescharacteristic
136D293—212no—
137C293C4×H(5,𝔽2)11yescharacteristic, complemented, Sylow
138C4×H(5,𝔽2)—2931nomaximal, Sylow
139C2×H(5,𝔽2)—2931no—
140#520—2931no—
141#520—2932no—
142#520—2933no—
143#518—2936no—
144#518—2933no—
145C4×#41—2932no—
146C4×#41—2933no—
147C4×#41D29311yescharacteristic, complemented
148C2×C4×D4—2936no—
149C2×C4×D4—2933no—
150H(5,𝔽2)—29316no—
151C2×#41—2932no—
152C2×#41—2933no—
153C2×#41C2×D29311yescharacteristic
154C22×D4—2936no—
155C22×D4—2933no—
156C23×C4—2936no—
157C4×Q8—2932no—
158C4×Q8—2931no—
159C4×Q8—2933no—
160C4×Q8C2×D29311yescharacteristic, complemented
161C4×Q8C2×D29311yescharacteristic, complemented
162C4×D4—2936no—
163C4×D4—2936no—
164C4×D4—2936no—
165C4×D4—2936no—
166C4×D4—2936no—
167C4×D4—29312no—
168C4×D4—2936no—
169C4×D4—2933no—
170C4×D4—2936no—
171C4×D4—2936no—
172C4×D4—2933no—
173C4×D4C2×D29313yescomplemented
174C4×D4C2×D29313yescomplemented
175#117—2933no—
176#117—2936no—
177#117—2936no—
178#117C2×D29313yescomplemented
179C2×C4⋊C4—2933no—
180C2×C4⋊C4—2936no—
181C2×C22⋊C4—2936no—
182C2×C22⋊C4—29312no—
183C2×C42—2936no—
184C2×C42C2×D29313yescomplemented
185C24—2936no—
186#41—29316no—
187#41—29324no—
188#41C4×D29318yescomplemented
189C2×Q8—2931no—
190C2×Q8C22×D29311yescharacteristic
191C2×D4—2936no—
192C2×D4—29348no—
193C2×D4—29324no—
194C2×D4—2936no—
195C2×D4—2933no—
196C2×D4C22×D29313yes—
197C22×C4—2936no—
198C22×C4—2936no—
199C22×C4—2936no—
200C22×C4—2936no—
201C22×C4—29312no—
202C22×C4—117212no—
203C22×C4C22×D29313yes—
204C22×C4C22×D29313yes—
205C22×C4C22×D29313yes—
206C4⋊C4—2936no—
207C4⋊C4—2936no—
208C4⋊C4—2933no—
209C4⋊C4—2932no—
210C4⋊C4—2931no—
211C4⋊C4C22×D29313yes—
212C4⋊C4C22×D29313yes—
213C22⋊C4—2936no—
214C22⋊C4—2936no—
215C22⋊C4—29312no—
216C22⋊C4—2936no—
217C22⋊C4C22×D29316yes—
218C42—2936no—
219C42—2936no—
220C42—2932no—
221C42C22×D29313yes—
222C42C22×D29313yes—
223C42C22×D29313yes—
224C42C22×D29311yescharacteristic
225C23—2936no—
226C23—29324no—
227C23—11726no—
228C23—11726no—
229C23C23×D29313yes—
230Q8—2934no—
231Q8C2×C4×D29314yescomplemented
232D4—29324no—
233D4—29324no—
234D4—29312no—
235D4C2×C4×D293112yescomplemented
236C2×C4—26no—
237C2×C4—43no—
238C2×C4—2932no—
239C2×C4—29324no—
240C2×C4—2932no—
241C2×C4—2936no—
242C2×C4—58612no—
243C2×C4—117212no—
244C2×C4—11726no—
245C2×C4—11726no—
246C2×C4C2×C4×D293112yescomplemented
247C2×C4C23×D29313yes—
248C2×C4C23×D29311yescharacteristic
249C2×C4C23×D29313yes—
250C2×C4C23×D29313yes—
251C2×C4C23×D29311yescharacteristic
252C2×C4C23×D29311yescharacteristic
253C22—23no—
254C22—23no—
255C22—29312no—
256C22—5866no—
257C22—5866no—
258C22—117224no—
259C22C22×C4×D29316yes—
260C22C24×D29311yescharacteristic
261C4—23no—
262C4—21no—
263C4—23no—
264C4—2934no—
265C4—5866no—
266C4—5862no—
267C4C22×C4×D29316yes—
268C4C22×C4×D29312yes—
269C4#2262767012yesdirect product factor
270C2—26no—
271C2—58612no—
272C2C23×C4×D29311yescharacteristic
273C2C2×#2262767011yescharacteristic
274C2#3403696511yescharacteristic
subgroupG/H
centerC2×C4C23×D293
commutatorC2×C293C24×C4
FrattiniC22C24×D293
FittingC4×#41×C293C2
socle, cosocleC22×C293C25
prime radicalC2×#22627670C2
hypercenterC4×#41D293
hypocenterC293C4×H(5,𝔽2)
LCSG ▷ C2×C293 ▷ C293
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. #34036612C2semidirect
3. #34036611C2semidirect
4. #34036609C2semidirect
5. #34036603C2semidirect
6. #34036601C2semidirect
7. C4×#17989803C2semidirect
8. C4×#17989802C2semidirect
9. C2×C4×D1172C2semidirect
10. C4×D4×D293C2semidirect
11. C4×#41×C293C2semidirect
12. #22627670C4direct (N × H)
17. C22×C4×D293C22semidirect
18. Q8×Dic293C22semidirect
19. C4×Dic586C22semidirect
20. C4×Dic586C22semidirect
21. C4×D1172C22semidirect
22. C4×D1172C22semidirect
23. C4×D1172C22semidirect
24. C4×D1172C22semidirect
25. C4×D1172C22semidirect
26. D4×Dic293C22semidirect
27. #22627586C22semidirect
28. #22627586C22semidirect
29. C4×C22⋊D293C22semidirect
30. C4×C22⋊D293C22semidirect
31. #22627584C22semidirect
32. #22627583C22semidirect
33. #22627582C22semidirect
34. #22627581C22semidirect
35. C2×C4⋊Dic293C22semidirect
36. C4⋊C4×D293C22semidirect
37. C2×#17989779C22semidirect
38. C22⋊C4×D293C22semidirect
39. C42×D293C22semidirect
41. C4×Q8×C293C22semidirect
42. C4×Q8×C293C22semidirect
43. C4×D4×C293C22semidirect
44. C4×D4×C293C22semidirect
45. #117×C293C22semidirect
46. C2×C42×C293C22semidirect
48. #17989803C2×C4semidirect
49. #17989802C2×C4semidirect
51. C2×D1172C2×C4semidirect
55. D4×D293C2×C4semidirect
74. #41×C293C2×C4semidirect
89. C22×D293C22×C4semidirect
91. Dic586C22×C4semidirect
92. D1172C22×C4semidirect
93. D1172C22×C4semidirect
94. C22⋊D293C22×C4semidirect
102. C4×D293C22×C4semidirect
104. Q8×C293C22×C4semidirect
105. D4×C293C22×C4semidirect
108. C2×C4×C293C22×C4semidirect
128. C4×C293H(5,𝔽2)semidirect
137. C293C4×H(5,𝔽2)semidirect
147. C4×#41D293semidirect
160. C4×Q8C2×D293semidirect
161. C4×Q8C2×D293semidirect
173. C4×D4C2×D293semidirect
174. C4×D4C2×D293semidirect
178. #117C2×D293semidirect
184. C2×C42C2×D293semidirect
188. #41C4×D293semidirect
231. Q8C2×C4×D293semidirect
235. D4C2×C4×D293semidirect
246. C2×C4C2×C4×D293semidirect
269. C4#22627670direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#226276702
#340366122
#340366112
#340366092
#340366032
#340366012
C4×#179898032
C4×#179898022
C2×C4×D11722
C4×D4×D2932
C4×#41×C2932
C4×H(5,𝔽2)293