Finite Group Databasebeta

← C4×#16812155 #28349668

Subgroups — C4×#16812155 #28349668

Order 13696.

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×#16812155C211yesmaximal, characteristic
2#20293110C211yesmaximal, characteristic, complemented
3#20293109C212yesmaximal, complemented
4#20293107C213yesmaximal, complemented
5#20293101C213yesmaximal, complemented
6#20293099C216yesmaximal, complemented
7C4×#13133819C212yesmaximal, complemented
8C4×#13133818C213yesmaximal, complemented
9C2×C4×D428C213yesmaximal, complemented
10C4×D4×D107C216yesmaximal, complemented
11C4×#41×C107C211yesmaximal, characteristic, complemented
12#16812155C4116yesdirect product factor
13C2×#13133819C2212yes—
14C2×#13133818C2213yes—
15C22×D428C2213yes—
16C2×D4×D107C2216yes—
17C22×C4×D107C2216yescomplemented
18Q8×Dic107C2212yescomplemented
19C4×Dic214C2211yescharacteristic, complemented
20C4×Dic214C2213yescomplemented
21C4×D428C2216yescomplemented
22C4×D428C2213yescomplemented
23C4×D428C2216yescomplemented
24C4×D428C2216yescomplemented
25C4×D428C2213yescomplemented
26D4×Dic107C2216yescomplemented
27#16812071C2216yescomplemented
28#16812071C2216yescomplemented
29C4×C22⋊D107C2216yescomplemented
30C4×C22⋊D107C2216yescomplemented
31(C22⋊D107)⋊C4C22112yescomplemented
32#16812068C2213yescomplemented
33#16812067C2216yescomplemented
34#16812066C2216yescomplemented
35C2×C4⋊Dic107C2213yescomplemented
36C4⋊C4×D107C2216yescomplemented
37C2×(C2×D107)⋊C4C2216yescomplemented
38C22⋊C4×D107C22112yescomplemented
39C42×D107C2216yescomplemented
40C2×#41×C107C2211yescharacteristic
41C4×Q8×C107C2211yescharacteristic, complemented
42C4×Q8×C107C2211yescharacteristic, complemented
43C4×D4×C107C2213yescomplemented
44C4×D4×C107C2213yescomplemented
45#117×C107C2213yescomplemented
46C2×C42×C107C2213yescomplemented
47C23×D107C2316yes—
48#13133819C2×C4116yescomplemented
49#13133818C2×C4124yescomplemented
50C2×Dic214C2311yescharacteristic
51C2×D428C2×C4124yescomplemented
52C2×D428C2316yes—
53C2×D428C2313yes—
54C2×C22⋊D107C2316yes—
55D4×D107C2×C4148yescomplemented
56C22×Dic107C2316yes—
57C2×C4×D107—412no—
58C2×C4×D107C2316yes—
59C2×C4×D107C2316yes—
60C2×C4×D107C23112yes—
61C2×C4×D107C2316yes—
62C4⋊Dic107C2316yes—
63C4⋊Dic107C2313yes—
64C4⋊Dic107C2311yescharacteristic
65Dic107⋊C4C2316yes—
66Dic107⋊C4C2312yes—
67C22⋊Dic107C2316yes—
68(C2×D107)⋊C4C2316yes—
69(C2×D107)⋊C4C23112yes—
70(C2×D107)⋊C4C2316yes—
71C4×Dic107C2312yes—
72C4×Dic107C2316yes—
73C4×Dic107C2316yes—
74#41×C107C2×C418yescomplemented
75C2×Q8×C107C2311yescharacteristic
76C2×D4×C107C2313yes—
77C22×C4×C107C2313yes—
78C22×C4×C107C2313yes—
79C22×C4×C107C2313yes—
80C4⋊C4×C107C2313yes—
81C4⋊C4×C107C2313yes—
82C22⋊C4×C107C2316yes—
83C42×C107C2313yes—
84C42×C107C2313yes—
85C42×C107C2311yescharacteristic
86C42×C107C2313yes—
87C23×C107C2413yes—
88C22×D107—46no—
89C22×D107—46no—
90C22×D107C22×C4124yescomplemented
91C22×D107C2416yes—
92Q8×C107C22×C414yescomplemented
93D4×C107C22×C4112yescomplemented
94C2×C4×C107—26no—
95C2×C4×C107—43no—
96C2×C4×C107C22×C4112yescomplemented
97C2×C4×C107C2411yescharacteristic
98C2×C4×C107C2413yes—
99C2×C4×C107C2413yes—
100C2×C4×C107C2411yescharacteristic
101C2×C4×C107C2413yes—
102C2×C4×C107C2411yescharacteristic
103C22⋊D107C22×C4124yescomplemented
104C2×Dic107—46no—
105C2×Dic107C2412yes—
106C2×Dic107C2416yes—
107C2×Dic107C2412yes—
108D428C22×C4124yescomplemented
109D428C22×C4112yescomplemented
110C4×D107—212no—
111C4×D107—412no—
112C4×D107—46no—
113C4×D107C22×C4124yescomplemented
114Dic214C22×C414yescomplemented
115C22×C107—23no—
116C22×C107—23no—
117C22×C107C23×C416yes—
118C22×C107C2511yescharacteristic
119C2×D107—26no—
120C2×D107—26no—
121C2×D107—424no—
122C2×D107C23×C4112yes—
123C4×C107—23no—
124C4×C107—23no—
125C4×C107—21no—
126C4×C107C23×C412yes—
127C4×C107C23×C416yes—
128C4×C107H(5,𝔽2)12yescomplemented
129Dic107—26no—
130Dic107—22no—
131Dic107C23×C414yes—
132C2×C107—26no—
133C2×C107C24×C411yescharacteristic
134C2×C107C2×H(5,𝔽2)11yescharacteristic
135C2×C107#58511yescharacteristic
136D107—212no—
137C4×H(5,𝔽2)—1071nomaximal, Sylow
138C107C4×H(5,𝔽2)11yescharacteristic, complemented, Sylow
139C2×H(5,𝔽2)—1071no—
140#520—1071no—
141#520—1072no—
142#520—1073no—
143#518—1076no—
144#518—1073no—
145C4×#41—1072no—
146C4×#41—1073no—
147C4×#41D10711yescharacteristic, complemented
148C2×C4×D4—1076no—
149C2×C4×D4—1073no—
150H(5,𝔽2)—10716no—
151C2×#41—1072no—
152C2×#41—1073no—
153C2×#41C2×D10711yescharacteristic
154C22×D4—1076no—
155C22×D4—1073no—
156C23×C4—1076no—
157C4×Q8—1072no—
158C4×Q8—1071no—
159C4×Q8—1073no—
160C4×Q8C2×D10711yescharacteristic, complemented
161C4×Q8C2×D10711yescharacteristic, complemented
162C4×D4—1076no—
163C4×D4—1076no—
164C4×D4—1076no—
165C4×D4—1076no—
166C4×D4—1076no—
167C4×D4—10712no—
168C4×D4—1076no—
169C4×D4—1073no—
170C4×D4—1076no—
171C4×D4—1076no—
172C4×D4—1073no—
173C4×D4C2×D10713yescomplemented
174C4×D4C2×D10713yescomplemented
175#117—1073no—
176#117—1076no—
177#117—1076no—
178#117C2×D10713yescomplemented
179C2×C4⋊C4—1073no—
180C2×C4⋊C4—1076no—
181C2×C22⋊C4—1076no—
182C2×C22⋊C4—10712no—
183C2×C42—1076no—
184C2×C42C2×D10713yescomplemented
185C24—1076no—
186#41—10716no—
187#41—10724no—
188#41C4×D10718yescomplemented
189C2×Q8—1071no—
190C2×Q8C22×D10711yescharacteristic
191C2×D4—1076no—
192C2×D4—10748no—
193C2×D4—10724no—
194C2×D4—1076no—
195C2×D4—1073no—
196C2×D4C22×D10713yes—
197C22×C4—1076no—
198C22×C4—1076no—
199C22×C4—1076no—
200C22×C4—10712no—
201C22×C4—1076no—
202C22×C4—42812no—
203C22×C4C22×D10713yes—
204C22×C4C22×D10713yes—
205C22×C4C22×D10713yes—
206C4⋊C4—1076no—
207C4⋊C4—1076no—
208C4⋊C4—1073no—
209C4⋊C4—1072no—
210C4⋊C4—1071no—
211C4⋊C4C22×D10713yes—
212C4⋊C4C22×D10713yes—
213C22⋊C4—1076no—
214C22⋊C4—1076no—
215C22⋊C4—10712no—
216C22⋊C4—1076no—
217C22⋊C4C22×D10716yes—
218C42—1076no—
219C42—1076no—
220C42—1072no—
221C42C22×D10713yes—
222C42C22×D10713yes—
223C42C22×D10713yes—
224C42C22×D10711yescharacteristic
225C23—10724no—
226C23—1076no—
227C23—4286no—
228C23—4286no—
229C23C23×D10713yes—
230Q8—1074no—
231Q8C2×C4×D10714yescomplemented
232D4—10724no—
233D4—10724no—
234D4—10712no—
235D4C2×C4×D107112yescomplemented
236C2×C4—26no—
237C2×C4—43no—
238C2×C4—1072no—
239C2×C4—10724no—
240C2×C4—1072no—
241C2×C4—1076no—
242C2×C4—42812no—
243C2×C4—4286no—
244C2×C4—4286no—
245C2×C4—21412no—
246C2×C4C2×C4×D107112yescomplemented
247C2×C4C23×D10713yes—
248C2×C4C23×D10711yescharacteristic
249C2×C4C23×D10713yes—
250C2×C4C23×D10713yes—
251C2×C4C23×D10711yescharacteristic
252C2×C4C23×D10711yescharacteristic
253C22—23no—
254C22—23no—
255C22—10712no—
256C22—42824no—
257C22—2146no—
258C22—2146no—
259C22C22×C4×D10716yes—
260C22C24×D10711yescharacteristic
261C4—23no—
262C4—21no—
263C4—23no—
264C4—1074no—
265C4—2146no—
266C4—2142no—
267C4C22×C4×D10716yes—
268C4C22×C4×D10712yes—
269C4#1681215512yesdirect product factor
270C2—26no—
271C2—21412no—
272C2C23×C4×D10711yescharacteristic
273C2C2×#1681215511yescharacteristic
274C2#2029346311yescharacteristic
subgroupG/H
centerC2×C4C23×D107
commutatorC2×C107C24×C4
FrattiniC22C24×D107
FittingC4×#41×C107C2
socle, cosocleC22×C107C25
prime radicalC2×#16812155C2
hypercenterC4×#41D107
hypocenterC107C4×H(5,𝔽2)
LCSG ▷ C2×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. #20293110C2semidirect
3. #20293109C2semidirect
4. #20293107C2semidirect
5. #20293101C2semidirect
6. #20293099C2semidirect
7. C4×#13133819C2semidirect
8. C4×#13133818C2semidirect
9. C2×C4×D428C2semidirect
10. C4×D4×D107C2semidirect
11. C4×#41×C107C2semidirect
12. #16812155C4direct (N × H)
17. C22×C4×D107C22semidirect
18. Q8×Dic107C22semidirect
19. C4×Dic214C22semidirect
20. C4×Dic214C22semidirect
21. C4×D428C22semidirect
22. C4×D428C22semidirect
23. C4×D428C22semidirect
24. C4×D428C22semidirect
25. C4×D428C22semidirect
26. D4×Dic107C22semidirect
27. #16812071C22semidirect
28. #16812071C22semidirect
29. C4×C22⋊D107C22semidirect
30. C4×C22⋊D107C22semidirect
31. (C22⋊D107)⋊C4C22semidirect
32. #16812068C22semidirect
33. #16812067C22semidirect
34. #16812066C22semidirect
35. C2×C4⋊Dic107C22semidirect
36. C4⋊C4×D107C22semidirect
37. C2×(C2×D107)⋊C4C22semidirect
38. C22⋊C4×D107C22semidirect
39. C42×D107C22semidirect
41. C4×Q8×C107C22semidirect
42. C4×Q8×C107C22semidirect
43. C4×D4×C107C22semidirect
44. C4×D4×C107C22semidirect
45. #117×C107C22semidirect
46. C2×C42×C107C22semidirect
48. #13133819C2×C4semidirect
49. #13133818C2×C4semidirect
51. C2×D428C2×C4semidirect
55. D4×D107C2×C4semidirect
74. #41×C107C2×C4semidirect
90. C22×D107C22×C4semidirect
92. Q8×C107C22×C4semidirect
93. D4×C107C22×C4semidirect
96. C2×C4×C107C22×C4semidirect
103. C22⋊D107C22×C4semidirect
108. D428C22×C4semidirect
109. D428C22×C4semidirect
113. C4×D107C22×C4semidirect
114. Dic214C22×C4semidirect
128. C4×C107H(5,𝔽2)semidirect
138. C107C4×H(5,𝔽2)semidirect
147. C4×#41D107semidirect
160. C4×Q8C2×D107semidirect
161. C4×Q8C2×D107semidirect
173. C4×D4C2×D107semidirect
174. C4×D4C2×D107semidirect
178. #117C2×D107semidirect
184. C2×C42C2×D107semidirect
188. #41C4×D107semidirect
231. Q8C2×C4×D107semidirect
235. D4C2×C4×D107semidirect
246. C2×C4C2×C4×D107semidirect
269. C4#16812155direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168121552
#202931102
#202931092
#202931072
#202931012
#202930992
C4×#131338192
C4×#131338182
C2×C4×D4282
C4×D4×D1072
C4×#41×C1072
C4×H(5,𝔽2)107