Finite Group Databasebeta

← C2×C4×#14523236 #30647485

Subgroups — C2×C4×#14523236 #30647485

Order 16256.

552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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
1C22×#14523236C211yesmaximal, characteristic
2C2×C4×Dic254C211yesmaximal, characteristic, complemented
3C4×#14523236C218yesmaximal, direct product factor
4C2×#16861140C211yesmaximal, characteristic, complemented
5C2×#16861132C211yesmaximal, characteristic, complemented
6C2×#16861130C211yesmaximal, characteristic
7C2×C4×C127⋊C8C211yesmaximal, characteristic, complemented
8C2×C4×D4×C127C211yesmaximal, characteristic
9C22×Dic254C2211yescharacteristic
10C2×#14523236C418yesdirect product factor
11C2×#14523236C2214yes—
12C22×C127⋊C8C2211yescharacteristic
13C22×C127⋊C8C2211yescharacteristic
14C4×Dic254—22no—
15C4×Dic254C2214yescomplemented
16C2×C4⋊Dic127C2211yescharacteristic
17C2×Dic127⋊C4—21no—
18C2×C4×Dic127—21no—
19#16861140C2214yescomplemented
20#16861132C2214yescomplemented
21#16861130C2214yes—
22C4×C127⋊C8C2214yescomplemented
23C22×D4×C127C2211yescharacteristic
24C23×C4×C127—21no—
25C4×D4×C127—22no—
26C4×D4×C127C2214yes—
27C2×C4⋊C4×C127C2211yescharacteristic
28C2×C22⋊C4×C127—21no—
29C2×C42×C127C2211yescharacteristic
30C2×Dic254—21no—
31C2×Dic254—22no—
32C2×Dic254C2×C414yescomplemented
33C2×Dic254C2312yes—
34C22×Dic127—21no—
35C22×Dic127—21no—
36#14523236C2×C4116yesdirect product factor
37C2×C127⋊C8—22no—
38C2×C127⋊C8C2×C414yescomplemented
39C2×C127⋊C8C2312yes—
40C2×C127⋊C8C2312yes—
41C4⋊Dic127—21no—
42C4⋊Dic127C2312yes—
43Dic127⋊C4—24no—
44C4×Dic127—24no—
45C24×C127—21no—
46C2×D4×C127—21no—
47C2×D4×C127—22no—
48C2×D4×C127C2×C414yes—
49C2×D4×C127C2312yes—
50C22×C4×C127—21no—
51C22×C4×C127—24no—
52C22×C4×C127—44no—
53C22×C4×C127D411yescharacteristic
54C22×C4×C127D411yescharacteristic
55C22×C4×C127C2311yescharacteristic
56C4⋊C4×C127—21no—
57C4⋊C4×C127C2312yes—
58C22⋊C4×C127—24no—
59C42×C127D412yes—
60C42×C127C2312yes—
61Dic254—24no—
62Dic254—22no—
63Dic254C22×C414yescomplemented
64C2×Dic127—24no—
65C2×Dic127—22no—
66C2×Dic127—22no—
67C2×Dic127—42no—
68C127⋊C8—22no—
69C127⋊C8C22×C414yescomplemented
70C23×C127—24no—
71C23×C127—22no—
72C23×C127—42no—
73C23×C127—42no—
74C23×C127C2×D411yescharacteristic
75D4×C127—24no—
76D4×C127—22no—
77D4×C127C22×C414yes—
78C2×C4×C127—22no—
79C2×C4×C127—22no—
80C2×C4×C127—42no—
81C2×C4×C127—48no—
82C2×C4×C127SD1614yescomplemented
83C2×C4×C127C22×C412yes—
84C2×C4×C127C2×D412yes—
85C2×C4×C127C2×D411yescharacteristic
86C2×C4×C127C2×D412yes—
87C2×C4×C127#4112yes—
88C2×C4×C127C2411yescharacteristic
89C22×C127—24no—
90C22×C127—42no—
91C22×C127—42no—
92C22×C127—48no—
93C22×C127C4×D412yes—
94C22×C127C2×SD1612yes—
95C22×C127#13512yes—
96C22×C127C22×D411yescharacteristic
97C4×C127—22no—
98C4×C127—42no—
99C4×C127C4×D412yes—
100C4×C127C2×SD1614yescomplemented
101C4×C127C23×C411yescharacteristic
102C4×C127C2×#4111yescharacteristic
103Dic127—24no—
104Dic127—42no—
105C2×C127—44no—
106C2×C127C4×SD1614yescomplemented
107C2×C127C2×C4×D411yescharacteristic
108C2×C127C22×SD1611yescharacteristic
109C2×C127C2×#13511yescharacteristic
110C2×C4×SD16—1271nomaximal, Sylow
111C127C2×C4×SD1611yescharacteristic, complemented, Sylow
112C22×SD16—1271no—
113C2×C4×Q8—1271no—
114C2×C4×D4D12711yescharacteristic
115C4×SD16—1278no—
116C2×#106—1271no—
117C2×#103—1271no—
118C2×#102—1271no—
119C2×C4×C8—1271no—
120C22×Q8—1271no—
121C22×D4C2×D12711yescharacteristic
122C23×C4—21no—
123C2×SD16—1278no—
124C2×SD16—1274no—
125C22×C8—1271no—
126C22×C8—1271no—
127C4×Q8—1274no—
128C4×Q8—2542no—
129C4×D4—22no—
130C4×D4C2×D12714yes—
131C2×C4⋊C4—1271no—
132C2×C4⋊C4—2541no—
133C2×C4⋊C4C2×D12711yescharacteristic
134C2×C22⋊C4—21no—
135C2×C42—2541no—
136C2×C42C2×D12711yescharacteristic
137#106—1274no—
138#103—1274no—
139#102—1274no—
140C4×C8—1274no—
141C24—21no—
142C2×Q8—1274no—
143C2×Q8—1272no—
144C2×Q8—2541no—
145C2×Q8—2542no—
146C2×D4—21no—
147C2×D4—22no—
148C2×D4C4×D12714yes—
149C2×D4C22×D12712yes—
150C22×C4—21no—
151C22×C4—24no—
152C22×C4—44no—
153C22×C4—2541no—
154C22×C4—2541no—
155C22×C4C22⋊D12711yescharacteristic
156C22×C4C22⋊D12711yescharacteristic
157C22×C4C22×D12711yescharacteristic
158SD16—12716no—
159C2×C8—1274no—
160C2×C8—1272no—
161C2×C8—1272no—
162C2×C8—2542no—
163C4⋊C4—21no—
164C4⋊C4—1272no—
165C4⋊C4—2544no—
166C4⋊C4—2541no—
167C4⋊C4C22×D12712yes—
168C22⋊C4—24no—
169C42—2544no—
170C42C22⋊D12712yes—
171C42C22×D12712yes—
172C23—22no—
173C23—24no—
174C23—42no—
175C23—42no—
176C23C2×C22⋊D12711yescharacteristic
177Q8—1274no—
178Q8—2542no—
179Q8—2544no—
180D4—22no—
181D4—24no—
182D4C2×C4×D12714yes—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—42no—
186C2×C4—48no—
187C2×C4—5082no—
188C2×C4—2542no—
189C2×C4—2542no—
190C2×C4—2544no—
191C2×C4#1452323614yesdirect product factor
192C2×C4C2×C4×D12712yes—
193C2×C4C2×C22⋊D12712yes—
194C2×C4C2×C22⋊D12712yes—
195C2×C4C2×C22⋊D12711yescharacteristic
196C2×C4#1452324812yes—
197C2×C4C23×D12711yescharacteristic
198C8—1274no—
199C8—2542no—
200C22—24no—
201C22—42no—
202C22—42no—
203C22—48no—
204C22C4×C22⋊D12712yes—
205C22C2×#1452323612yes—
206C22#1686122912yes—
207C22C22×C22⋊D12711yescharacteristic
208C4—22no—
209C4—42no—
210C4—5082no—
211C4—2544no—
212C4C4×C22⋊D12712yes—
213C4C2×#1452323614yesdirect product factor
214C4C22×C4×D12711yescharacteristic
215C4C2×#1452324811yescharacteristic
216C2—44no—
217C2C4×#1452323614yesdirect product factor
218C2C2×C4×C22⋊D12711yescharacteristic
219C2C22×#1452323611yescharacteristic
220C2C2×#1686122911yescharacteristic
subgroupG/H
centerC22×C4C22⋊D127
commutatorC4×C127C23×C4
FrattiniC2×C4C23×D127
FittingC2×C4×D4×C127C2
socleC23×C127C2×D4
prime radicalC22×D4×C127C22
cosocleC2×C4×C127C24
hypercenterC2×C4×D4D127
hypocenterC127C2×C4×SD16
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×Dic254C2semidirect
3. C4×#14523236C2direct (N × H)
4. C2×#16861140C2semidirect
5. C2×#16861132C2semidirect
7. C2×C4×C127⋊C8C2semidirect
10. C2×#14523236C4direct (N × H)
15. C4×Dic254C22semidirect
19. #16861140C22semidirect
20. #16861132C22semidirect
22. C4×C127⋊C8C22semidirect
32. C2×Dic254C2×C4semidirect
36. #14523236C2×C4direct (N × H)
38. C2×C127⋊C8C2×C4semidirect
63. Dic254C22×C4semidirect
69. C127⋊C8C22×C4semidirect
82. C2×C4×C127SD16semidirect
100. C4×C127C2×SD16semidirect
106. C2×C127C4×SD16semidirect
111. C127C2×C4×SD16semidirect
191. C2×C4#14523236direct (N × H)
213. C4C2×#14523236direct (N × H)
217. C2C4×#14523236direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145232362
C2×C4×Dic2542
C4×#145232362
C2×#168611402
C2×#168611322
C2×#168611302
C2×C4×C127⋊C82
C2×C4×D4×C1272
C2×C4×SD16127