Finite Group Databasebeta

← C4×#16861130 #30638545

Subgroups — C4×#16861130 #30638545

Order 16256.

396 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 157 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×#16861130C212yesmaximal
2C2×C4×C127⋊C8C211yesmaximal, characteristic, complemented
3C4×C4⋊Dic127C211yesmaximal, characteristic, complemented
4#22549638C212yesmaximal, complemented
5C2×C4×D4×C127C211yesmaximal, characteristic
6C22×C127⋊C8C2212yes—
7C2×C4⋊Dic127C2212yes—
8C2×C4×Dic127—21no—
9#16861130C418yesdirect product factor
10C4×C127⋊C8—22no—
11C127⋊#95—21no—
12C22×D4×C127C2211yescharacteristic
13C23×C4×C127—21no—
14C4×D4×C127—22no—
15C4×D4×C127C414yescomplemented
16C2×C4⋊C4×C127C2211yescharacteristic
17C2×C22⋊C4×C127—21no—
18C2×C42×C127C2211yescharacteristic
19C22×Dic127—22no—
20C2×C127⋊C8—22no—
21C2×C127⋊C8—22no—
22C2×C127⋊C8C2×C414yescomplemented
23C4⋊Dic127—22no—
24C4⋊Dic127C2×C414yescomplemented
25C4×Dic127—42no—
26C24×C127—21no—
27C2×D4×C127—21no—
28C2×D4×C127—22no—
29C2×D4×C127C2×C414yes—
30C2×D4×C127C2×C412yes—
31C22×C4×C127—21no—
32C22×C4×C127—24no—
33C22×C4×C127—42no—
34C22×C4×C127—42no—
35C22×C4×C127D411yescharacteristic
36C22×C4×C127D411yescharacteristic
37C22×C4×C127C2311yescharacteristic
38C4⋊C4×C127—21no—
39C4⋊C4×C127C2×C412yes—
40C22⋊C4×C127—24no—
41C42×C127C2×C412yes—
42C42×C127D412yes—
43C2×Dic127—24no—
44C2×Dic127—42no—
45C2×Dic127—42no—
46C127⋊C8—24no—
47C23×C127—22no—
48C23×C127—24no—
49C23×C127—41no—
50C23×C127—41no—
51C23×C127—42no—
52C23×C127C2×D411yescharacteristic
53D4×C127—22no—
54D4×C127—24no—
55D4×C127C4214yescomplemented
56C2×C4×C127—22no—
57C2×C4×C127—22no—
58C2×C4×C127—41no—
59C2×C4×C127—41no—
60C2×C4×C127—48no—
61C2×C4×C127C22⋊C412yes—
62C2×C4×C127C22⋊C412yes—
63C2×C4×C127D812yes—
64C2×C4×C127SD1612yes—
65C2×C4×C127C22×C412yes—
66C2×C4×C127C22×C411yescharacteristic
67C2×C4×C127C2×D411yescharacteristic
68C2×C4×C127#4112yes—
69C22×C127—24no—
70C22×C127—42no—
71C22×C127—42no—
72C22×C127—44no—
73C22×C127—44no—
74C22×C127C2×C22⋊C411yescharacteristic
75C22×C127C4×D412yes—
76C22×C127C2×D811yescharacteristic
77C22×C127C2×SD1611yescharacteristic
78C22×C127#13512yes—
79C4×C127—22no—
80C4×C127—42no—
81C4×C127#10214yescomplemented
82C4×C127C2×C4211yescharacteristic
83C4×C127#11711yescharacteristic
84C4×C127C4×D412yes—
85Dic127—44no—
86C2×C127—44no—
87C2×C127C4×C22⋊C411yescharacteristic
88C2×C127C2×#10211yescharacteristic
89C2×C127#41611yescharacteristic
90C2×C127C4×D812yes—
91C2×C127C4×SD1612yes—
92C4×#102—1271nomaximal, Sylow
93C127C4×#10211yescharacteristic, complemented, Sylow
94C2×C4×D4D12711yescharacteristic
95C2×#102—1272no—
96C2×C4×C8—1271no—
97C4×C4⋊C4—1271no—
98#340—1272no—
99C22×D4C2×D12711yescharacteristic
100C23×C4—21no—
101C22×C8—1272no—
102C4×D4—22no—
103C4×D4Dic12714yescomplemented
104C2×C4⋊C4—1272no—
105C2×C4⋊C4C2×D12711yescharacteristic
106C2×C22⋊C4—21no—
107C2×C42—2541no—
108C2×C42C2×D12711yescharacteristic
109#102—1278no—
110C4×C8—2542no—
111#95—2541no—
112C24—21no—
113C2×D4—21no—
114C2×D4—22no—
115C2×D4C4×D12714yes—
116C2×D4C2×Dic12712yes—
117C22×C4—21no—
118C22×C4—24no—
119C22×C4—42no—
120C22×C4—42no—
121C22×C4—2542no—
122C22×C4C22⋊D12711yescharacteristic
123C22×C4C22⋊D12711yescharacteristic
124C22×C4C22×D12711yescharacteristic
125C2×C8—1274no—
126C2×C8—2542no—
127C2×C8—2542no—
128C4⋊C4—21no—
129C4⋊C4—1274no—
130C4⋊C4—2542no—
131C4⋊C4C2×Dic12712yes—
132C22⋊C4—24no—
133C42—5082no—
134C42C2×Dic12712yes—
135C42C22⋊D12712yes—
136C23—22no—
137C23—24no—
138C23—41no—
139C23—41no—
140C23—42no—
141C23C2×C22⋊D12711yescharacteristic
142D4—22no—
143D4—24no—
144D4C4×Dic12714yescomplemented
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—48no—
150C2×C4—5082no—
151C2×C4—5082no—
152C2×C4—2544no—
153C2×C4C22⋊Dic12712yes—
154C2×C4C22⋊Dic12712yes—
155C2×C4#1452323312yes—
156C2×C4#1452323612yes—
157C2×C4C2×C4×D12712yes—
158C2×C4C22×Dic12711yescharacteristic
159C2×C4C2×C22⋊D12711yescharacteristic
160C2×C4#1452324812yes—
161C8—2544no—
162C22—24no—
163C22—42no—
164C22—42no—
165C22—44no—
166C22—44no—
167C22C2×C22⋊Dic12711yescharacteristic
168C22C4×C22⋊D12712yes—
169C22C2×#1452323311yescharacteristic
170C22C2×#1452323611yescharacteristic
171C22#1686122912yes—
172C4—22no—
173C4—42no—
174C4—5084no—
175C4#1686113014yesdirect product factor
176C4C2×C4×Dic12711yescharacteristic
177C4#1686116811yescharacteristic
178C4C4×C22⋊D12712yes—
179C2—44no—
180C2C4×C22⋊Dic12711yescharacteristic
181C2C2×#1686113011yescharacteristic
182C2#2254987211yescharacteristic
183C2C4×#1452323312yes—
184C2C4×#1452323612yes—
subgroupG/H
centerC22×C4C22⋊D127
commutatorC4×C127C2×C42
FrattiniC22×C4C22×D127
FittingC2×C4×D4×C127C2
socleC23×C127C2×D4
prime radicalC22×D4×C127C22
cosocleC22×C4×C127C23
hypercenterC2×C4×D4D127
hypocenterC127C4×#102
LCSG ▷ C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C127⋊C8C2semidirect
3. C4×C4⋊Dic127C2semidirect
4. #22549638C2semidirect
9. #16861130C4direct (N × H)
15. C4×D4×C127C4semidirect
22. C2×C127⋊C8C2×C4semidirect
24. C4⋊Dic127C2×C4semidirect
55. D4×C127C42semidirect
81. C4×C127#102semidirect
93. C127C4×#102semidirect
103. C4×D4Dic127semidirect
144. D4C4×Dic127semidirect
175. C4#16861130direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168611302
C2×C4×C127⋊C82
C4×C4⋊Dic1272
#225496382
C2×C4×D4×C1272
C4×#102127