Finite Group Databasebeta

← C2×#22550046 #30648056

Subgroups — C2×#22550046 #30648056

Order 16256.

844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16861254C211yesmaximal, characteristic, complemented
2C2×#16861237C212yesmaximal, complemented
3C2×#16861205C211yesmaximal, characteristic, complemented
4#22550046C218yesmaximal, direct product factor
5C2×#16861135C212yesmaximal, complemented
6C2×#100×C127C211yesmaximal, characteristic, complemented
7#16861254—24no—
8#16861254—22no—
9#16861254C2214yescomplemented
10C2×#14523248C2212yes—
11C2×#14523247—22no—
12C22×D508C2211yescharacteristic, complemented
13C22×C22⋊D127—22no—
14C22×C22⋊D127—22no—
15C2×D4×D127—22no—
16#16861237—24no—
17#16861237C2218yescomplemented
18C2×#14523237—22no—
19C2×D1016—22no—
20#16861205—22no—
21#16861205C2214yescomplemented
22C2×C4×Dic127C2211yescharacteristic, complemented
23#16861135C2218yescomplemented
24C22×D4×C127C2211yescharacteristic
25C2×M16×C127C2212yescomplemented
26#100×C127C2214yescomplemented
27C23×D127—22no—
28C23×D127—21no—
29#14523248—22no—
30#14523248—22no—
31#14523248D414yescomplemented
32#14523248C2314yes—
33#14523247—28no—
34#14523247—28no—
35C2×Dic254D412yescomplemented
36C2×D508—22no—
37C2×D508—22no—
38C2×D508—21no—
39C2×D508D412yescomplemented
40C2×D508C2312yescomplemented
41C2×C22⋊D127—24no—
42C2×C22⋊D127—28no—
43C2×C22⋊D127—22no—
44C2×C22⋊D127—28no—
45C2×C22⋊D127—28no—
46C2×C22⋊D127—48no—
47D4×D127—28no—
48D4×D127—28no—
49C22×Dic127—22no—
50C22×Dic127—21no—
51C2×C4×D127—22no—
52#14523237—28no—
53D1016—28no—
54C4×Dic127—21no—
55C4×Dic127C2312yescomplemented
56C24×C127D412yes—
57C2×D4×C127—22no—
58C2×D4×C127—22no—
59C2×D4×C127D412yes—
60C2×D4×C127C2312yes—
61C22×C4×C127C2311yescharacteristic
62M16×C127—22no—
63M16×C127C2314yescomplemented
64C2×C8×C127—22no—
65C22×D127—22no—
66C22×D127—28no—
67C22×D127—22no—
68C22×D127—44no—
69C22×D127—41no—
70C22×D127—41no—
71C22×D127—84no—
72Dic254—22no—
73Dic254C2×D414yescomplemented
74D508—22no—
75D508—24no—
76D508—42no—
77D508C2×D414yescomplemented
78C22⋊D127—216no—
79C22⋊D127—24no—
80C22⋊D127—24no—
81C22⋊D127—416no—
82C2×Dic127—28no—
83C2×Dic127—24no—
84C2×Dic127—22no—
85C2×Dic127—22no—
86C4×D127—24no—
87C4×D127—24no—
88C23×C127—22no—
89C23×C127—22no—
90C23×C127—44no—
91C23×C127C2×D411yescharacteristic
92C23×C127C2×D414yes—
93D4×C127—24no—
94D4×C127—24no—
95C2×C4×C127C2×D412yes—
96C2×C4×C127C2×D412yes—
97C2×C4×C127C2×D411yescharacteristic
98C2×C4×C127C2411yescharacteristic
99C8×C127—24no—
100C22×C127—22no—
101C22×C127—24no—
102C22×C127—44no—
103C22×C127—44no—
104C22×C127—82no—
105C22×C127#12011yescharacteristic
106C22×C127#12011yescharacteristic
107C22×C127C22×D411yescharacteristic
108C2×D127—24no—
109C2×D127—44no—
110C2×D127—44no—
111C2×D127—42no—
112C2×D127—88no—
113C2×D127—82no—
114C2×D127—82no—
115C4×C127#12012yes—
116C4×C127C22×D412yes—
117Dic127—24no—
118Dic127—24no—
119C2×C127—21no—
120C2×C127—21no—
121C2×C127—44no—
122C2×C127#45312yescomplemented
123C2×C127C2×#12011yescharacteristic
124D127—44no—
125D127—82no—
126C2×#453—1271nomaximal, Sylow
127C127C2×#45311yescharacteristic, complemented, Sylow
128C2×H(5,𝔽2)—1271no—
129C2×AGL(1,ℤ/8)—1272no—
130C2×#127—1271no—
131#453—1278no—
132C2×#104—1272no—
133C2×#100D12711yescharacteristic, complemented
134H(5,𝔽2)—1274no—
135H(5,𝔽2)—2544no—
136H(5,𝔽2)—2542no—
137C2×#41—1272no—
138C2×#41—2542no—
139C22×D4—1271no—
140C22×D4—2542no—
141C22×D4—2542no—
142C22×D4—2542no—
143C22×D4C2×D12711yescharacteristic
144AGL(1,ℤ/8)—1278no—
145AGL(1,ℤ/8)—2544no—
146C2×SD16—2542no—
147C2×D8—2542no—
148C2×M16C2×D12712yescomplemented
149#127—1274no—
150#127—2542no—
151C2×C42—1271no—
152#104—1278no—
153#100C2×D12714yescomplemented
154C24—2542no—
155C24—2541no—
156C24D50812yes—
157#41—1274no—
158#41—1274no—
159#41—2548no—
160#41—2548no—
161#41—2542no—
162#41—2542no—
163C2×Q8—1272no—
164C2×D4—22no—
165C2×D4—22no—
166C2×D4—1272no—
167C2×D4—1272no—
168C2×D4—5088no—
169C2×D4—2548no—
170C2×D4—2548no—
171C2×D4—2548no—
172C2×D4—2544no—
173C2×D4—2548no—
174C2×D4—2542no—
175C2×D4—2548no—
176C2×D4—2542no—
177C2×D4—2542no—
178C2×D4—2541no—
179C2×D4D50812yes—
180C2×D4C22×D12712yes—
181C22×C4—2542no—
182C22×C4—2541no—
183C22×C4—2542no—
184C22×C4C22×D12711yescharacteristic
185SD16—2548no—
186D8—2548no—
187M16—22no—
188M16C22×D12714yescomplemented
189C2×C8—22no—
190C42—1272no—
191C42—2541no—
192C23—22no—
193C23—22no—
194C23—44no—
195C23—10164no—
196C23—5084no—
197C23—5081no—
198C23—5081no—
199C23—2548no—
200C23—2542no—
201C23—2542no—
202C23C2×D50811yescharacteristic
203C23C2×D50814yes—
204Q8—1274no—
205Q8—2542no—
206D4—24no—
207D4—24no—
208D4—1274no—
209D4—50816no—
210D4—5082no—
211D4—25416no—
212D4—2544no—
213D4—2544no—
214D4—2544no—
215D4—2542no—
216C2×C4—2544no—
217C2×C4—2548no—
218C2×C4—2542no—
219C2×C4—2542no—
220C2×C4—2544no—
221C2×C4—2544no—
222C2×C4D4×D12712yes—
223C2×C4D4×D12712yes—
224C2×C4C2×D50811yescharacteristic
225C2×C4C23×D12711yescharacteristic
226C8—24no—
227C22—22no—
228C22—24no—
229C22—44no—
230C22—44no—
231C22—82no—
232C22—10162no—
233C22—10168no—
234C22—10162no—
235C22—5084no—
236C22—5082no—
237C22—5084no—
238C22—2544no—
239C22#1686117911yescharacteristic
240C22#1686117911yescharacteristic
241C22C22×D50811yescharacteristic
242C4—2544no—
243C4—2544no—
244C4#1686117912yes—
245C4C2×D4×D12712yes—
246C2—21no—
247C2—21no—
248C2—44no—
249C2—10162no—
250C2—5084no—
251C2#2255004612yesdirect product factor
252C2C2×#1686117911yescharacteristic
subgroupG/H
centerC22#16861179
commutator, cosocleC2×C4×C127C24
FrattiniC2×C4C23×D127
FittingC2×#100×C127C2
socleC22×C127#120
hypercenterC2×#100D127
hypocenterC127C2×#453
LCSG ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#16861254C2semidirect
2. C2×#16861237C2semidirect
3. C2×#16861205C2semidirect
4. #22550046C2direct (N × H)
5. C2×#16861135C2semidirect
6. C2×#100×C127C2semidirect
9. #16861254C22semidirect
12. C22×D508C22semidirect
17. #16861237C22semidirect
21. #16861205C22semidirect
22. C2×C4×Dic127C22semidirect
23. #16861135C22semidirect
25. C2×M16×C127C22semidirect
26. #100×C127C22semidirect
31. #14523248D4semidirect
35. C2×Dic254D4semidirect
39. C2×D508D4semidirect
40. C2×D508C23semidirect
55. C4×Dic127C23semidirect
63. M16×C127C23semidirect
73. Dic254C2×D4semidirect
77. D508C2×D4semidirect
122. C2×C127#453semidirect
127. C127C2×#453semidirect
133. C2×#100D127semidirect
148. C2×M16C2×D127semidirect
153. #100C2×D127semidirect
188. M16C22×D127semidirect
251. C2#22550046direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168612542
C2×#168612372
C2×#168612052
#225500462
C2×#168611352
C2×#100×C1272
C2×#453127