Finite Group Databasebeta

← C2×#15688861 #20241870

Subgroups — C2×#15688861 #20241870

Order 6016.

336 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 101 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×#13094003C211yesmaximal, characteristic
2C2×C47⋊#95C211yesmaximal, characteristic
3#15688861C214yesmaximal, direct product factor
4C2×C22⋊C8×C47C211yesmaximal, characteristic
5C22×Dic94C411yescharacteristic, complemented
6C23×Dic47—21no—
7#13094003—21no—
8#13094003—21no—
9#13094003C412yescomplemented
10#13094003C2212yes—
11C2×C4⋊Dic47C411yescharacteristic, complemented
12C2×Dic47⋊C4—21no—
13C2×C22⋊Dic47—21no—
14C47⋊#95—21no—
15C47⋊#95C2212yes—
16C23×C4×C47C2211yescharacteristic
17C22×C8×C47—21no—
18C22⋊C8×C47—21no—
19C22⋊C8×C47C2212yes—
20C24×C47D411yescharacteristic
21C22×C4×C47—42no—
22C22×C4×C47C2×C411yescharacteristic
23C22×C4×C47C2×C411yescharacteristic
24C22×C4×C47D411yescharacteristic
25C22×C4×C47D411yescharacteristic
26C22×C4×C47D411yescharacteristic
27C22×C4×C47C2311yescharacteristic
28C22×Dic47—24no—
29C22×Dic47—21no—
30C22×Dic47—21no—
31C22×Dic47—22no—
32C22×Dic47—42no—
33C22×Dic47—42no—
34C2×Dic94—21no—
35C2×Dic94—42no—
36C2×Dic94C2×C412yescomplemented
37C2×C8×C47—22no—
38C2×C8×C47—42no—
39C22⋊Dic47—22no—
40C22⋊Dic47—22no—
41C4⋊Dic47—21no—
42C4⋊Dic47C2×C412yescomplemented
43Dic47⋊C4—22no—
44Dic47⋊C4—22no—
45C23×C47—22no—
46C23×C47—22no—
47C23×C47C22⋊C411yescharacteristic
48C23×C47C22⋊C411yescharacteristic
49C23×C47SD1612yes—
50C23×C47Q1612yes—
51C23×C47C2×D411yescharacteristic
52C2×C4×C47—22no—
53C2×C4×C47—22no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47—41no—
58C2×C4×C47C22⋊C411yescharacteristic
59C2×C4×C47C22⋊C411yescharacteristic
60C2×C4×C47C22×C411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C2×Dic47—24no—
63C2×Dic47—22no—
64C2×Dic47—22no—
65C2×Dic47—48no—
66C2×Dic47—42no—
67C2×Dic47—42no—
68C2×Dic47—42no—
69C2×Dic47—42no—
70Dic94—42no—
71Dic94—42no—
72C8×C47—42no—
73C22×C47—24no—
74C22×C47—24no—
75C22×C47—21no—
76C22×C47—21no—
77C22×C47—21no—
78C22×C47—21no—
79C22×C47#9912yes—
80C22×C47#10312yes—
81C22×C47#10312yes—
82C22×C47#10412yes—
83C22×C47C2×C22⋊C411yescharacteristic
84C22×C47C2×SD1611yescharacteristic
85C22×C47C2×Q1611yescharacteristic
86C4×C47—21no—
87C4×C47—21no—
88C4×C47—21no—
89C4×C47—21no—
90Dic47—44no—
91Dic47—42no—
92Dic47—42no—
93C2×#328—471nomaximal, Sylow
94C2×C47—21no—
95C2×C47—22no—
96C2×C47—21no—
97C2×C47#32814yescomplemented
98C2×C47C2×#9911yescharacteristic
99C2×C47C2×#10311yescharacteristic
100C2×C47C2×#10411yescharacteristic
101C2×C22⋊Q8—471no—
102C2×C22⋊C8D4711yescharacteristic
103C2×#95—471no—
104#328—474no—
105C47C2×#32811yescharacteristic, complemented, Sylow
106C22×Q8—471no—
107C23×C4—941no—
108C23×C4C2×D4711yescharacteristic
109C22×C8—21no—
110C22⋊Q8—472no—
111C22⋊Q8—472no—
112C22⋊Q8—941no—
113C22⋊Q8—941no—
114C2×C4⋊C4—471no—
115C2×C4⋊C4—941no—
116C2×C22⋊C4—941no—
117C22⋊C8—21no—
118C22⋊C8C2×D4712yes—
119#95—472no—
120#95—941no—
121C24D18811yescharacteristic
122C2×Q8—472no—
123C2×Q8—941no—
124C2×Q8—1882no—
125C22×C4—42no—
126C22×C4—944no—
127C22×C4—941no—
128C22×C4—941no—
129C22×C4—942no—
130C22×C4—1882no—
131C22×C4—1882no—
132C22×C4C4×D4711yescharacteristic
133C22×C4C4×D4711yescharacteristic
134C22×C4D18811yescharacteristic
135C22×C4C22⋊D4711yescharacteristic
136C22×C4C22⋊D4711yescharacteristic
137C22×C4C22×D4711yescharacteristic
138C2×C8—22no—
139C2×C8—42no—
140C4⋊C4—472no—
141C4⋊C4—942no—
142C4⋊C4—941no—
143C4⋊C4—942no—
144C22⋊C4—942no—
145C22⋊C4—942no—
146C23—22no—
147C23—22no—
148C23#1062532512yes—
149C23Dic18812yes—
150C23(C2×D47)⋊C411yescharacteristic
151C23(C2×D47)⋊C411yescharacteristic
152C23C2×D18811yescharacteristic
153Q8—1882no—
154Q8—1882no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—944no—
162C2×C4—942no—
163C2×C4—942no—
164C2×C4—1882no—
165C2×C4—1888no—
166C2×C4—1882no—
167C2×C4—1882no—
168C2×C4—1882no—
169C2×C4(C2×D47)⋊C411yescharacteristic
170C2×C4(C2×D47)⋊C411yescharacteristic
171C2×C4C2×C4×D4711yescharacteristic
172C2×C4C2×C22⋊D4711yescharacteristic
173C8—42no—
174C22—21no—
175C22—21no—
176C22—24no—
177C22—24no—
178C22—21no—
179C22—21no—
180C22#1309393812yes—
181C22#1309394912yes—
182C22#1309394912yes—
183C22#1309395012yes—
184C22C2×(C2×D47)⋊C411yescharacteristic
185C22C2×#1062532511yescharacteristic
186C22C2×Dic18811yescharacteristic
187C4—21no—
188C4—21no—
189C4—21no—
190C4—21no—
191C4—1884no—
192C4—1882no—
193C4—1882no—
194C2—21no—
195C2—22no—
196C2—21no—
197C2#1568886114yesdirect product factor
198C2C2×#1309393811yescharacteristic
199C2C2×#1309394911yescharacteristic
200C2C2×#1309395011yescharacteristic
subgroupG/H
centerC23(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×C22⋊C8×C47C2
socleC23×C47C22⋊C4
hypercenterC2×C22⋊C8D47
hypocenterC47C2×#328
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #15688861C2direct (N × H)
5. C22×Dic94C4semidirect
9. #13094003C4semidirect
11. C2×C4⋊Dic47C4semidirect
36. C2×Dic94C2×C4semidirect
42. C4⋊Dic47C2×C4semidirect
97. C2×C47#328semidirect
105. C47C2×#328semidirect
197. C2#15688861direct (N × H)