Finite Group Databasebeta

← C2×#15689472 #20253697

Subgroups — C2×#15689472 #20253697

Order 6016.

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

normal subgroups only

This group has 424 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×#13094023C211yesmaximal, characteristic
2C2×#13094022C211yesmaximal, characteristic
3#15689472C218yesmaximal, direct product factor
4C2×#13093949C211yesmaximal, characteristic
5C2×#13093948C211yesmaximal, characteristic
6C2×#13093947C211yesmaximal, characteristic
7C2×C8×Dic47C211yesmaximal, characteristic
8C2×#103×C47C211yesmaximal, characteristic
9C22×Dic94—21no—
10C22×Dic94C2211yescharacteristic
11C22×C47⋊C8C2211yescharacteristic
12#13094023—22no—
13#13094023C2214yes—
14#13094022—22no—
15#13094022C2214yes—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4—21no—
18C2×Dic47⋊C4—21no—
19C2×Dic47⋊C4—21no—
20C2×C4×Dic47C2211yescharacteristic
21#13093949C2214yes—
22#13093948C2214yes—
23#13093947C2214yes—
24C8×Dic47C2214yes—
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×Dic94—24no—
44C2×Dic94—44no—
45C2×Dic94C2312yes—
46C2×C8×C47—22no—
47C2×C8×C47C2312yes—
48C4⋊C4×C47—21no—
49C4⋊C4×C47C2312yes—
50C4⋊Dic47—21no—
51C4⋊Dic47C2312yes—
52Dic47⋊C4—24no—
53Dic47⋊C4—24no—
54Dic47⋊C4—24no—
55C4×Dic47D412yes—
56C4×Dic47C2312yes—
57C2×C47⋊C8—22no—
58C2×C47⋊C8C2312yes—
59C23×C47C2×D411yescharacteristic
60Q8×C47—22no—
61Q8×C47—22no—
62Q8×C47—42no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—42no—
66C2×C4×C47—42no—
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47#4112yes—
69C2×C4×C47#4112yes—
70C2×C4×C47C2411yescharacteristic
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—42no—
74C2×Dic47—42no—
75C2×Dic47SD1614yes—
76C2×Dic47Q1614yes—
77C2×Dic47C2×D412yes—
78C2×Dic47C2×D412yes—
79Dic94—22no—
80Dic94—22no—
81Dic94—42no—
82Dic94—48no—
83C8×C47—22no—
84C47⋊C8—22no—
85C22×C47#12412yes—
86C22×C47C2×SD1612yes—
87C22×C47C2×Q1612yes—
88C22×C47C22×D411yescharacteristic
89C4×C47—42no—
90C4×C47—42no—
91C4×C47#12412yes—
92C4×C47C2×#4111yescharacteristic
93C4×C47C2×#4111yescharacteristic
94Dic47—42no—
95Dic47—42no—
96Dic47C2×SD1614yes—
97Dic47C2×Q1614yes—
98C2×#487—471nomaximal, Sylow
99C2×C47#48714yescomplemented
100C2×C47C2×#12411yescharacteristic
101C2×C47C22×SD1611yescharacteristic
102C2×C47C22×Q1611yescharacteristic
103C2×C4⋊Q8—471no—
104C2×C4⋊Q8—471no—
105#487—478no—
106C2×#103—471no—
107C2×#103—471no—
108C2×#103—471no—
109C2×#103D4711yescharacteristic
110C2×C4×C8—471no—
111C47C2×#48711yescharacteristic, complemented, Sylow
112C22×Q8—471no—
113C22×Q8—941no—
114C22×Q8C2×D4711yescharacteristic
115C22×C8—471no—
116C22×C8C2×D4711yescharacteristic
117C4⋊Q8—474no—
118C4⋊Q8—474no—
119C4⋊Q8—942no—
120C4⋊Q8—942no—
121C2×C4⋊C4—471no—
122C2×C4⋊C4—941no—
123C2×C4⋊C4—941no—
124C2×C4⋊C4—941no—
125C2×C4⋊C4C2×D4711yescharacteristic
126C2×C42—471no—
127#103—474no—
128#103—474no—
129#103—474no—
130#103C2×D4714yes—
131C4×C8—474no—
132C2×Q8—21no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—472no—
136C2×Q8—944no—
137C2×Q8—941no—
138C2×Q8—942no—
139C2×Q8—942no—
140C2×Q8—1884no—
141C2×Q8C22×D4712yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—471no—
145C22×C4—471no—
146C22×C4—941no—
147C22×C4—941no—
148C22×C4C22×D4711yescharacteristic
149C2×C8—22no—
150C2×C8—472no—
151C2×C8—942no—
152C2×C8C22×D4712yes—
153C4⋊C4—21no—
154C4⋊C4—472no—
155C4⋊C4—944no—
156C4⋊C4—944no—
157C4⋊C4—944no—
158C4⋊C4—941no—
159C4⋊C4C22×D4712yes—
160C42—472no—
161C42—472no—
162C23D4×D4711yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—42no—
166Q8—942no—
167Q8—942no—
168Q8—1888no—
169Q8—1882no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—474no—
175C2×C4—474no—
176C2×C4—472no—
177C2×C4—472no—
178C2×C4—942no—
179C2×C4—942no—
180C2×C4—1882no—
181C2×C4—1882no—
182C2×C4#1062535012yes—
183C2×C4D4×D4711yescharacteristic
184C2×C4#1062535212yes—
185C2×C4C23×D4711yescharacteristic
186C8—22no—
187C8—942no—
188C22#1309401012yes—
189C22SD16×D4712yes—
190C22Q16×D4712yes—
191C22C2×D4×D4711yescharacteristic
192C4—42no—
193C4—42no—
194C4—474no—
195C4—474no—
196C4—1882no—
197C4—1882no—
198C4#1309401012yes—
199C4C2×#1062535211yescharacteristic
200C4C2×#1062535011yescharacteristic
201C2#1568947214yesdirect product factor
202C2C2×#1309401011yescharacteristic
203C2C2×SD16×D4711yescharacteristic
204C2C2×Q16×D4711yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47C2×#487
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. #15689472C2direct (N × H)
99. C2×C47#487semidirect
111. C47C2×#487semidirect
201. C2#15689472direct (N × H)