Finite Group Databasebeta

← C2×#15689425 #20253147

Subgroups — C2×#15689425 #20253147

Order 6016.

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

normal subgroups only

This group has 448 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×#13094015C211yesmaximal, characteristic, complemented
2C2×D4×Dic47C211yesmaximal, characteristic
3#15689425C218yesmaximal, direct product factor
4C2×#13093957C211yesmaximal, characteristic, complemented
5C2×#13093956C211yesmaximal, characteristic, complemented
6C2×Dic47⋊C8C211yesmaximal, characteristic, complemented
7C2×#13093945C211yesmaximal, characteristic
8C2×#102×C47C211yesmaximal, characteristic
9C23×Dic47—21no—
10C22×C47⋊C8C2211yescharacteristic
11#13094015—22no—
12#13094015C2214yescomplemented
13D4×Dic47—22no—
14D4×Dic47C2214yes—
15C2×C4⋊Dic47—21no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2211yescharacteristic
18C2×Dic47⋊C4—21no—
19C2×C22⋊Dic47—21no—
20C2×C4×Dic47C2211yescharacteristic
21#13093957C2214yescomplemented
22#13093956C2214yescomplemented
23Dic47⋊C8C2214yescomplemented
24#13093945C2214yes—
25C22×D4×C47C2211yescharacteristic
26C22×C8×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28#102×C47C2214yes—
29C24×C47—21no—
30C2×D4×C47—21no—
31C2×D4×C47—22no—
32C2×D4×C47Q814yes—
33C2×D4×C47C2312yes—
34C22×C4×C47—21no—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47—21no—
37C22×Dic47—21no—
38C22×Dic47—24no—
39C22×Dic47—44no—
40C22×Dic47D411yescharacteristic
41C22×Dic47D411yescharacteristic
42C2×C8×C47—22no—
43C2×C8×C47C2312yes—
44C4⋊C4×C47—21no—
45C4⋊C4×C47C2312yes—
46C22⋊Dic47—24no—
47C4⋊Dic47—21no—
48C4⋊Dic47—21no—
49C4⋊Dic47—24no—
50C4⋊Dic47C2312yes—
51C4⋊Dic47C2312yes—
52Dic47⋊C4—24no—
53C4×Dic47D412yes—
54C4×Dic47C2312yes—
55C2×C47⋊C8—22no—
56C2×C47⋊C8C2312yes—
57C23×C47—24no—
58C23×C47—22no—
59C23×C47—42no—
60C23×C47—42no—
61C23×C47C2×D411yescharacteristic
62D4×C47—24no—
63D4×C47—22no—
64D4×C47C2×Q814yes—
65C2×C4×C47—22no—
66C2×C4×C47—42no—
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×Q812yes—
69C2×C4×C47#4112yes—
70C2×C4×C47C2411yescharacteristic
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—48no—
76C2×Dic47—42no—
77C2×Dic47—42no—
78C2×Dic47C2×D412yes—
79C2×Dic47C2×D412yes—
80C8×C47—22no—
81C47⋊C8—22no—
82C22×C47—24no—
83C22×C47—42no—
84C22×C47—42no—
85C22×C47—48no—
86C22×C47C22⋊Q812yes—
87C22×C47#13512yes—
88C22×C47AGL(1,ℤ/8)12yes—
89C22×C47C22×D411yescharacteristic
90C4×C47—42no—
91C4×C47C22⋊Q812yes—
92C4×C47C22×Q811yescharacteristic
93C4×C47C2×#4111yescharacteristic
94Dic47—22no—
95Dic47—22no—
96Dic47—42no—
97Dic47—42no—
98C2×#478—471nomaximal, Sylow
99C2×C47—44no—
100C2×C47#47814yescomplemented
101C2×C47C2×C22⋊Q811yescharacteristic
102C2×C47C2×#13511yescharacteristic
103C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
104C2×#125—471no—
105C2×C4×D4—471no—
106#478—478no—
107C2×#107—471no—
108C2×#106—471no—
109C2×C4⋊C8—471no—
110C2×#102—471no—
111C2×#102D4711yescharacteristic
112C47C2×#47811yescharacteristic, complemented, Sylow
113C22×D4C2×D4711yescharacteristic
114C23×C4—941no—
115C22×C8—471no—
116C22×C8C2×D4711yescharacteristic
117#125—474no—
118#125—942no—
119C4×D4—474no—
120C4×D4—942no—
121C2×C4⋊C4—471no—
122C2×C4⋊C4—471no—
123C2×C4⋊C4—941no—
124C2×C4⋊C4—941no—
125C2×C4⋊C4C2×D4711yescharacteristic
126C2×C22⋊C4—941no—
127C2×C42—471no—
128#107—474no—
129#106—474no—
130C4⋊C8—474no—
131#102—474no—
132#102C2×D4714yes—
133C24—21no—
134C2×D4—21no—
135C2×D4—22no—
136C2×D4Dic9414yes—
137C2×D4C22×D4712yes—
138C22×C4—21no—
139C22×C4—471no—
140C22×C4—471no—
141C22×C4—944no—
142C22×C4—941no—
143C22×C4—941no—
144C22×C4—1884no—
145C22×C4C22×D4711yescharacteristic
146C2×C8—22no—
147C2×C8—472no—
148C2×C8—942no—
149C2×C8C22×D4712yes—
150C4⋊C4—21no—
151C4⋊C4—472no—
152C4⋊C4—472no—
153C4⋊C4—944no—
154C4⋊C4—944no—
155C4⋊C4—941no—
156C4⋊C4—941no—
157C4⋊C4C22×D4712yes—
158C22⋊C4—944no—
159C42—472no—
160C42—472no—
161C23—24no—
162C23—22no—
163C23—42no—
164C23—42no—
165C23D4×D4711yescharacteristic
166D4—24no—
167D4—22no—
168D4C2×Dic9414yes—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—472no—
172C2×C4—472no—
173C2×C4—942no—
174C2×C4—942no—
175C2×C4—942no—
176C2×C4—942no—
177C2×C4—1888no—
178C2×C4—1882no—
179C2×C4—1882no—
180C2×C4C2×Dic9412yes—
181C2×C4D4×D4711yescharacteristic
182C2×C4#1062535212yes—
183C2×C4C23×D4711yescharacteristic
184C8—22no—
185C8—942no—
186C22—24no—
187C22—42no—
188C22—42no—
189C22—48no—
190C22#1309400112yes—
191C22#1309404512yes—
192C22#1309404812yes—
193C22C2×D4×D4711yescharacteristic
194C4—42no—
195C4—942no—
196C4—942no—
197C4—1882no—
198C4—1882no—
199C4#1309400112yes—
200C4C22×Dic9411yescharacteristic
201C4C2×#1062535211yescharacteristic
202C2—44no—
203C2#1568942514yesdirect product factor
204C2C2×#1309400111yescharacteristic
205C2C2×#1309404511yescharacteristic
206C2C2×#1309404811yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#102×C47C2
socleC23×C47C2×D4
hypercenterC2×#102D47
hypocenterC47C2×#478
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#13094015C2semidirect
3. #15689425C2direct (N × H)
4. C2×#13093957C2semidirect
5. C2×#13093956C2semidirect
6. C2×Dic47⋊C8C2semidirect
12. #13094015C22semidirect
21. #13093957C22semidirect
22. #13093956C22semidirect
23. Dic47⋊C8C22semidirect
100. C2×C47#478semidirect
112. C47C2×#478semidirect
203. C2#15689425direct (N × H)