Finite Group Databasebeta

← C2×#22550063 #30648114

Subgroups — C2×#22550063 #30648114

Order 16256.

1018 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 165 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×#16861177C213yesmaximal, complemented
2#22550063C218yesmaximal, direct product factor
3C2×#16861124C213yesmaximal, complemented
4C2×H(5,𝔽2)×C127C211yesmaximal, characteristic, complemented
5C24×D127C2211yescharacteristic, complemented
6C22×C22⋊D127—23no—
7#16861177—26no—
8#16861177C22112yescomplemented
9C2×C22⋊Dic127C2213yescomplemented
10C2×(C2×D127)⋊C4—23no—
11#16861124C22112yescomplemented
12H(5,𝔽2)×C127—26no—
13H(5,𝔽2)×C127C2214yescomplemented
14C2×#41×C127—23no—
15C22×D4×C127—23no—
16C22×D4×C127C2213yes—
17C23×D127—23no—
18C23×D127—23no—
19C23×D127—44no—
20C23×D127C2312yescomplemented
21C2×C22⋊D127—212no—
22C2×C22⋊D127—412no—
23C22×Dic127—23no—
24C22⋊Dic127—23no—
25C22⋊Dic127C2316yescomplemented
26(C2×D127)⋊C4—212no—
27C24×C127—21no—
28C24×C127D413yescomplemented
29C24×C127C2311yescharacteristic
30#41×C127—212no—
31#41×C127—212no—
32C2×Q8×C127—21no—
33C2×D4×C127—23no—
34C2×D4×C127—212no—
35C2×D4×C127—26no—
36C2×D4×C127—26no—
37C2×D4×C127—212no—
38C2×D4×C127D416yescomplemented
39C2×D4×C127C2316yes—
40C22×C4×C127—23no—
41C22×C4×C127D413yescomplemented
42C22×D127—212no—
43C22×D127—26no—
44C22×D127—44no—
45C22×D127—412no—
46C22×D127—46no—
47C22×D127—43no—
48C22×D127—41no—
49C22⋊D127—424no—
50C2×Dic127—26no—
51C2×Dic127—46no—
52C23×C127—24no—
53C23×C127—23no—
54C23×C127—23no—
55C23×C127—42no—
56C23×C127—46no—
57C23×C127—82no—
58C23×C127C2×D413yes—
59C23×C127C2×D413yes—
60C23×C127C2×D416yescomplemented
61C23×C127C2411yescharacteristic
62Q8×C127—24no—
63D4×C127—212no—
64D4×C127—212no—
65D4×C127—212no—
66C2×C4×C127—212no—
67C2×C4×C127—23no—
68C2×C4×C127—23no—
69C2×C4×C127C2×D416yescomplemented
70C22×C127—26no—
71C22×C127—26no—
72C22×C127—43no—
73C22×C127—41no—
74C22×C127—46no—
75C22×C127—46no—
76C22×C127—83no—
77C22×C127—84no—
78C22×C127#12013yes—
79C22×C127#12011yescharacteristic
80C22×C127C22×D413yes—
81C2×D127—212no—
82C2×D127—46no—
83C2×D127—412no—
84C2×D127—42no—
85C2×D127—44no—
86C4×C127—26no—
87Dic127—46no—
88C2×C127—23no—
89C2×C127—23no—
90C2×C127—46no—
91C2×C127B(4,𝔽2)12yescomplemented
92C2×C127C2×#12011yescharacteristic
93D127—44no—
94C2×B(4,𝔽2)—1271nomaximal, Sylow
95C127C2×B(4,𝔽2)11yescharacteristic, complemented, Sylow
96C2×H(5,𝔽2)D12711yescharacteristic, complemented
97C2×#120—1273no—
98B(4,𝔽2)—1278no—
99C2×#99—1273no—
100C25—1271no—
101H(5,𝔽2)—26no—
102H(5,𝔽2)C2×D12714yescomplemented
103C2×#41—23no—
104C22×D4—23no—
105C22×D4—2543no—
106C22×D4C2×D12713yes—
107#120—12712no—
108#120—2546no—
109C2×C22⋊C4—1273no—
110C2×C22⋊C4—2543no—
111#99—12712no—
112C24—21no—
113C24—1272no—
114C24—5084no—
115C24—2543no—
116C24—2543no—
117C24C22⋊D12713yescomplemented
118C24C22×D12711yescharacteristic
119#41—212no—
120#41—212no—
121C2×Q8—21no—
122C2×D4—23no—
123C2×D4—212no—
124C2×D4—26no—
125C2×D4—26no—
126C2×D4—212no—
127C2×D4—50812no—
128C2×D4—25412no—
129C2×D4C22⋊D12716yescomplemented
130C2×D4C22×D12716yes—
131C22×C4—23no—
132C22×C4—2543no—
133C22×C4C22⋊D12713yescomplemented
134C22⋊C4—1276no—
135C22⋊C4—2543no—
136C22⋊C4—25412no—
137C23—24no—
138C23—23no—
139C23—23no—
140C23—42no—
141C23—46no—
142C23—82no—
143C23—5086no—
144C23—50812no—
145C23—5084no—
146C23—5083no—
147C23—5081no—
148C23—25412no—
149C23—2546no—
150C23C2×C22⋊D12713yes—
151C23C2×C22⋊D12713yes—
152C23C2×C22⋊D12716yescomplemented
153C23C23×D12711yescharacteristic
154Q8—24no—
155D4—212no—
156D4—212no—
157D4—212no—
158D4—50824no—
159C2×C4—212no—
160C2×C4—23no—
161C2×C4—23no—
162C2×C4—5086no—
163C2×C4—2546no—
164C2×C4C2×C22⋊D12716yescomplemented
165C22—26no—
166C22—26no—
167C22—43no—
168C22—41no—
169C22—46no—
170C22—46no—
171C22—83no—
172C22—84no—
173C22—5086no—
174C22—50812no—
175C22—5084no—
176C22—5082no—
177C22—25412no—
178C22#1686117813yes—
179C22#1686117811yescharacteristic
180C22C22×C22⋊D12713yes—
181C4—26no—
182C4—5086no—
183C2—23no—
184C2—23no—
185C2—46no—
186C2—5084no—
187C2#2255006312yesdirect product factor
188C2C2×#1686117811yescharacteristic
subgroupG/H
centerC22#16861178
commutator, cosocleC23×C127C24
FrattiniC23C23×D127
FittingC2×H(5,𝔽2)×C127C2
socleC22×C127#120
hypercenterC2×H(5,𝔽2)D127
hypocenterC127C2×B(4,𝔽2)
LCSG ▷ C23×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C24 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×#16861177C2semidirect
2. #22550063C2direct (N × H)
3. C2×#16861124C2semidirect
4. C2×H(5,𝔽2)×C127C2semidirect
5. C24×D127C22semidirect
8. #16861177C22semidirect
9. C2×C22⋊Dic127C22semidirect
11. #16861124C22semidirect
13. H(5,𝔽2)×C127C22semidirect
20. C23×D127C23semidirect
25. C22⋊Dic127C23semidirect
28. C24×C127D4semidirect
38. C2×D4×C127D4semidirect
41. C22×C4×C127D4semidirect
60. C23×C127C2×D4semidirect
69. C2×C4×C127C2×D4semidirect
91. C2×C127B(4,𝔽2)semidirect
95. C127C2×B(4,𝔽2)semidirect
96. C2×H(5,𝔽2)D127semidirect
102. H(5,𝔽2)C2×D127semidirect
117. C24C22⋊D127semidirect
129. C2×D4C22⋊D127semidirect
133. C22×C4C22⋊D127semidirect
152. C23C2×C22⋊D127semidirect
164. C2×C4C2×C22⋊D127semidirect
187. C2#22550063direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168611772
#225500632
C2×#168611242
C2×H(5,𝔽2)×C1272
C2×B(4,𝔽2)127