Finite Group Databasebeta

← C2×#15689490 #20253726

Subgroups — C2×#15689490 #20253726

Order 6016.

384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13094022C211yesmaximal, characteristic
2C2×#13094015C211yesmaximal, characteristic
3#15689490C218yesmaximal, direct product factor
4C2×#13093949C211yesmaximal, characteristic
5C2×#13093948C211yesmaximal, characteristic
6C2×#13093947C211yesmaximal, characteristic
7C2×#13093934C211yesmaximal, characteristic
8C2×#103×C47C211yesmaximal, characteristic
9C22×Dic94C2211yescharacteristic
10C22×C47⋊C8C2211yescharacteristic
11#13094022—22no—
12#13094022C2214yes—
13#13094015—22no—
14#13094015C2214yes—
15C2×C4⋊Dic47—21no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4—21no—
18C2×Dic47⋊C4—21no—
19C2×Dic47⋊C4—21no—
20C2×C4×Dic47C2211yescharacteristic
21#13093949C2214yes—
22#13093948C2214yes—
23#13093947C2214yes—
24#13093934C2214yes—
25C22×Q8×C47C2211yescharacteristic
26C22×C8×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28#103×C47C2214yes—
29C2×Q8×C47—21no—
30C2×Q8×C47—22no—
31C2×Q8×C47—22no—
32C2×Q8×C47C2312yes—
33C22×C4×C47—21no—
34C22×C4×C47—21no—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47—21no—
37C22×Dic47—21no—
38C22×Dic47D411yescharacteristic
39C22×Dic47D411yescharacteristic
40C2×Dic94—22no—
41C2×Dic94—22no—
42C2×Dic94—21no—
43C2×Dic94C2312yes—
44C2×C8×C47—22no—
45C2×C8×C47C2312yes—
46C4⋊C4×C47—21no—
47C4⋊C4×C47C2312yes—
48C4⋊Dic47—21no—
49C4⋊Dic47—24no—
50C4⋊Dic47C2312yes—
51Dic47⋊C4—24no—
52Dic47⋊C4—24no—
53Dic47⋊C4—24no—
54C4×Dic47D412yes—
55C4×Dic47C2312yes—
56C2×C47⋊C8—22no—
57C2×C47⋊C8C2312yes—
58C23×C47C2×D411yescharacteristic
59Q8×C47—22no—
60Q8×C47—22no—
61Q8×C47—42no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—42no—
65C2×C4×C47—42no—
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47#4112yes—
68C2×C4×C47#4112yes—
69C2×C4×C47C2411yescharacteristic
70C2×Dic47—22no—
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—42no—
75C2×Dic47—42no—
76C2×Dic47C2×D412yes—
77C2×Dic47C2×D412yes—
78Dic94—22no—
79Dic94—22no—
80Dic94—42no—
81C8×C47—22no—
82C47⋊C8—22no—
83C22×C47#12412yes—
84C22×C47#13712yes—
85C22×C47#13712yes—
86C22×C47C22×D411yescharacteristic
87C4×C47—42no—
88C4×C47—42no—
89C4×C47#12412yes—
90C4×C47C2×#4111yescharacteristic
91C4×C47C2×#4111yescharacteristic
92Dic47—22no—
93Dic47—22no—
94Dic47—42no—
95Dic47—42no—
96C2×#491—471nomaximal, Sylow
97C2×C47#49114yescomplemented
98C2×C47C2×#12411yescharacteristic
99C2×C47C2×#13711yescharacteristic
100C2×C47C2×#13711yescharacteristic
101C2×C4⋊Q8—471no—
102C2×#125—471no—
103#491—478no—
104C2×#103—471no—
105C2×#103—471no—
106C2×#103—471no—
107C2×#103D4711yescharacteristic
108C2×#97—471no—
109C47C2×#49111yescharacteristic, complemented, Sylow
110C22×Q8—471no—
111C22×Q8C2×D4711yescharacteristic
112C22×C8—471no—
113C22×C8C2×D4711yescharacteristic
114C4⋊Q8—474no—
115C4⋊Q8—942no—
116#125—474no—
117#125—942no—
118C2×C4⋊C4—471no—
119C2×C4⋊C4—941no—
120C2×C4⋊C4—941no—
121C2×C4⋊C4—941no—
122C2×C4⋊C4—941no—
123C2×C4⋊C4C2×D4711yescharacteristic
124C2×C42—471no—
125#103—474no—
126#103—474no—
127#103—474no—
128#103C2×D4714yes—
129#97—474no—
130C2×Q8—21no—
131C2×Q8—22no—
132C2×Q8—22no—
133C2×Q8—472no—
134C2×Q8—941no—
135C2×Q8—942no—
136C2×Q8—942no—
137C2×Q8C22×D4712yes—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—471no—
141C22×C4—471no—
142C22×C4—941no—
143C22×C4—941no—
144C22×C4C22×D4711yescharacteristic
145C2×C8—22no—
146C2×C8—472no—
147C2×C8—942no—
148C2×C8C22×D4712yes—
149C4⋊C4—21no—
150C4⋊C4—472no—
151C4⋊C4—944no—
152C4⋊C4—944no—
153C4⋊C4—944no—
154C4⋊C4—944no—
155C4⋊C4—941no—
156C4⋊C4C22×D4712yes—
157C42—472no—
158C42—472no—
159C23D4×D4711yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—42no—
163Q8—942no—
164Q8—942no—
165Q8—1882no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—472no—
171C2×C4—472no—
172C2×C4—942no—
173C2×C4—942no—
174C2×C4—942no—
175C2×C4—942no—
176C2×C4—1882no—
177C2×C4—1882no—
178C2×C4#1062535012yes—
179C2×C4D4×D4711yescharacteristic
180C2×C4#1062535212yes—
181C2×C4C23×D4711yescharacteristic
182C8—22no—
183C8—942no—
184C22#1309401012yes—
185C22#1309405312yes—
186C22#1309405612yes—
187C22C2×D4×D4711yescharacteristic
188C4—42no—
189C4—42no—
190C4—942no—
191C4—942no—
192C4—1882no—
193C4—1882no—
194C4#1309401012yes—
195C4C2×#1062535211yescharacteristic
196C4C2×#1062535011yescharacteristic
197C2#1568949014yesdirect product factor
198C2C2×#1309401011yescharacteristic
199C2C2×#1309405311yescharacteristic
200C2C2×#1309405611yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47C2×#491
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. #15689490C2direct (N × H)
97. C2×C47#491semidirect
109. C47C2×#491semidirect
197. C2#15689490direct (N × H)