Finite Group Databasebeta

← C4×#16861124 #30638518

Subgroups — C4×#16861124 #30638518

Order 16256.

412 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 129 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×#16861124C212yesmaximal
2C4×C22⋊Dic127C212yesmaximal, complemented
3#22549643C212yesmaximal, complemented
4C2×C4×D4×C127C211yesmaximal, characteristic
5C2×C22⋊Dic127C2214yes—
6C2×C4×Dic127—22no—
7#16861124C418yesdirect product factor
8C127⋊#95—22no—
9C22×D4×C127C2211yescharacteristic
10C23×C4×C127C411yescharacteristic, complemented
11C23×C4×C127C2211yescharacteristic
12C4×D4×C127—22no—
13C4×D4×C127—22no—
14C2×C4⋊C4×C127C411yescharacteristic, complemented
15C2×C22⋊C4×C127C411yescharacteristic, complemented
16C2×C22⋊C4×C127C2211yescharacteristic
17C2×C42×C127C411yescharacteristic, complemented
18C22×Dic127—24no—
19C22⋊Dic127—24no—
20C22⋊Dic127C2×C418yescomplemented
21C4×Dic127—44no—
22C24×C127C2×C411yescharacteristic
23C24×C127C2311yescharacteristic
24C2×D4×C127—22no—
25C2×D4×C127—22no—
26C2×D4×C127C2×C414yes—
27C22×C4×C127—21no—
28C22×C4×C127—21no—
29C22×C4×C127—42no—
30C22×C4×C127—42no—
31C22×C4×C127C2×C411yescharacteristic
32C22×C4×C127C2×C411yescharacteristic
33C22×C4×C127C2×C411yescharacteristic
34C22×C4×C127C2×C411yescharacteristic
35C22×C4×C127C2×C411yescharacteristic
36C22×C4×C127D412yes—
37C22×C4×C127D412yes—
38C4⋊C4×C127—22no—
39C22⋊C4×C127—22no—
40C22⋊C4×C127—22no—
41C42×C127—21no—
42C42×C127—21no—
43C2×Dic127—28no—
44C2×Dic127—44no—
45C2×Dic127—44no—
46C23×C127—21no—
47C23×C127—21no—
48C23×C127—41no—
49C23×C127—41no—
50C23×C127—41no—
51C23×C127—41no—
52C23×C127C4212yescomplemented
53C23×C127C22×C412yes—
54C23×C127C22×C411yescharacteristic
55C23×C127C2×D412yes—
56C23×C127#4112yes—
57D4×C127—28no—
58C2×C4×C127—21no—
59C2×C4×C127—21no—
60C2×C4×C127—22no—
61C2×C4×C127—24no—
62C2×C4×C127—21no—
63C2×C4×C127—21no—
64C2×C4×C127—41no—
65C2×C4×C127—42no—
66C2×C4×C127—42no—
67C2×C4×C127—42no—
68C2×C4×C127—41no—
69C2×C4×C127—41no—
70C2×C4×C127C4212yescomplemented
71C2×C4×C127C22⋊C411yescharacteristic
72C2×C4×C127C22⋊C412yes—
73C2×C4×C127C22⋊C411yescharacteristic
74C22×C127—21no—
75C22×C127—22no—
76C22×C127—21no—
77C22×C127—22no—
78C22×C127—22no—
79C22×C127—42no—
80C22×C127—42no—
81C22×C127—42no—
82C22×C127—42no—
83C22×C127—41no—
84C22×C127—41no—
85C22×C127C2×C4211yescharacteristic
86C22×C127C2×C22⋊C411yescharacteristic
87C22×C127#11711yescharacteristic
88C22×C127C4×D414yes—
89C4×C127—22no—
90C4×C127—21no—
91C4×C127—22no—
92C4×C127—41no—
93C4×C127—41no—
94C4×C127#9912yescomplemented
95Dic127—48no—
96C2×C127—24no—
97C2×C127—21no—
98C2×C127—21no—
99C2×C127—42no—
100C2×C127C4×C22⋊C411yescharacteristic
101C2×C127C2×#9911yescharacteristic
102C2×C127#41011yescharacteristic
103C4×#99—1271nomaximal, Sylow
104C127C4×#9911yescharacteristic, complemented, Sylow
105C2×C4×D4D12711yescharacteristic
106C2×#99—1272no—
107C4×C22⋊C4—1272no—
108#342—1272no—
109C22×D4C2×D12711yescharacteristic
110C23×C4Dic12711yescharacteristic, complemented
111C23×C4C2×D12711yescharacteristic
112C4×D4—22no—
113C4×D4—22no—
114C2×C4⋊C4Dic12711yescharacteristic, complemented
115C2×C22⋊C4—1274no—
116C2×C22⋊C4Dic12711yescharacteristic, complemented
117C2×C22⋊C4C2×D12711yescharacteristic
118C2×C42—2542no—
119C2×C42Dic12711yescharacteristic, complemented
120#99—1278no—
121#95—2542no—
122C24C2×Dic12711yescharacteristic
123C24C22×D12711yescharacteristic
124C2×D4—22no—
125C2×D4—22no—
126C2×D4C4×D12714yes—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—42no—
130C22×C4—42no—
131C22×C4—2544no—
132C22×C4C2×Dic12711yescharacteristic
133C22×C4C2×Dic12711yescharacteristic
134C22×C4C2×Dic12711yescharacteristic
135C22×C4C2×Dic12711yescharacteristic
136C22×C4C2×Dic12711yescharacteristic
137C22×C4C22⋊D12712yes—
138C22×C4C22⋊D12712yes—
139C4⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4—1278no—
143C22⋊C4—2544no—
144C42—21no—
145C42—21no—
146C42—5084no—
147C23—21no—
148C23—21no—
149C23—41no—
150C23—41no—
151C23—41no—
152C23—41no—
153C23C4×Dic12712yescomplemented
154C23C2×C4×D12712yes—
155C23C22×Dic12711yescharacteristic
156C23C2×C22⋊D12712yes—
157C23#1452324812yes—
158D4—28no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—5084no—
172C2×C4—5084no—
173C2×C4—2548no—
174C2×C4C4×Dic12712yescomplemented
175C2×C4C22⋊Dic12711yescharacteristic
176C2×C4C22⋊Dic12712yes—
177C2×C4C22⋊Dic12711yescharacteristic
178C22—21no—
179C22—22no—
180C22—21no—
181C22—22no—
182C22—22no—
183C22—42no—
184C22—42no—
185C22—42no—
186C22—42no—
187C22—41no—
188C22—41no—
189C22C2×C4×Dic12711yescharacteristic
190C22C2×C22⋊Dic12711yescharacteristic
191C22#1686116811yescharacteristic
192C22C4×C22⋊D12714yes—
193C4—21no—
194C4—22no—
195C4—22no—
196C4—41no—
197C4—41no—
198C4—5088no—
199C4#1686112412yesdirect product factor
200C2—24no—
201C2—21no—
202C2—21no—
203C2—42no—
204C2C4×C22⋊Dic12711yescharacteristic
205C2C2×#1686112411yescharacteristic
206C2#2254985011yescharacteristic
subgroupG/H
centerC2×C4C22⋊Dic127
commutatorC22×C127C2×C42
FrattiniC24C22×D127
FittingC2×C4×D4×C127C2
socleC22×C127C2×C22⋊C4
prime radicalC22×D4×C127C22
cosocleC24×C127C23
hypercenterC2×C4×D4D127
hypocenterC127C4×#99
LCSG ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊Dic127C2semidirect
3. #22549643C2semidirect
7. #16861124C4direct (N × H)
10. C23×C4×C127C4semidirect
14. C2×C4⋊C4×C127C4semidirect
15. C2×C22⋊C4×C127C4semidirect
17. C2×C42×C127C4semidirect
20. C22⋊Dic127C2×C4semidirect
52. C23×C127C42semidirect
70. C2×C4×C127C42semidirect
94. C4×C127#99semidirect
104. C127C4×#99semidirect
110. C23×C4Dic127semidirect
114. C2×C4⋊C4Dic127semidirect
116. C2×C22⋊C4Dic127semidirect
119. C2×C42Dic127semidirect
153. C23C4×Dic127semidirect
174. C2×C4C4×Dic127semidirect
199. C4#16861124direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168611242
C4×C22⋊Dic1272
#225496432
C2×C4×D4×C1272
C4×#99127