Finite Group Databasebeta

← C2×#15689432 #20253167

Subgroups — C2×#15689432 #20253167

Order 6016.

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

normal subgroups only

This group has 384 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
2C2×Q8×Dic47C211yesmaximal, characteristic
3#15689432C218yesmaximal, direct product factor
4C2×#13093958C211yesmaximal, characteristic
5C2×#13093955C211yesmaximal, characteristic
6C2×Dic47⋊C8C211yesmaximal, characteristic
7C2×#13093948C211yesmaximal, characteristic
8C2×#103×C47C211yesmaximal, characteristic
9C22×C47⋊C8C2211yescharacteristic
10#13094015—22no—
11#13094015C2214yes—
12Q8×Dic47—22no—
13Q8×Dic47C2214yes—
14C2×C4⋊Dic47—21no—
15C2×C4⋊Dic47—21no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2211yescharacteristic
18C2×Dic47⋊C4—21no—
19C2×C4×Dic47—21no—
20C2×C4×Dic47C2211yescharacteristic
21#13093958C2214yes—
22#13093955C2214yes—
23Dic47⋊C8C2214yes—
24#13093948C2214yes—
25C22×Q8×C47C2211yescharacteristic
26C22×C8×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28#103×C47C2214yes—
29C2×Q8×C47—21no—
30C2×Q8×C47—22no—
31C2×Q8×C47Q814yes—
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×C8×C47—22no—
41C2×C8×C47C2312yes—
42C4⋊C4×C47—21no—
43C4⋊C4×C47C2312yes—
44C4⋊Dic47—21no—
45C4⋊Dic47—21no—
46C4⋊Dic47—24no—
47C4⋊Dic47—24no—
48C4⋊Dic47C2312yes—
49C4⋊Dic47C2312yes—
50Dic47⋊C4—24no—
51C4×Dic47—24no—
52C4×Dic47D412yes—
53C4×Dic47C2312yes—
54C2×C47⋊C8—22no—
55C2×C47⋊C8C2312yes—
56C23×C47C2×D411yescharacteristic
57Q8×C47—24no—
58Q8×C47—22no—
59Q8×C47C2×Q814yes—
60C2×C4×C47—24no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—42no—
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×Q812yes—
66C2×C4×C47#4112yes—
67C2×C4×C47C2411yescharacteristic
68C2×Dic47—22no—
69C2×Dic47—22no—
70C2×Dic47—22no—
71C2×Dic47—22no—
72C2×Dic47—42no—
73C2×Dic47—42no—
74C2×Dic47C2×D412yes—
75C2×Dic47C2×D412yes—
76C8×C47—22no—
77C47⋊C8—22no—
78C22×C47C22⋊Q812yes—
79C22×C47#13512yes—
80C22×C47#13712yes—
81C22×C47C22×D411yescharacteristic
82C4×C47—24no—
83C4×C47—42no—
84C4×C47C22⋊Q812yes—
85C4×C47C22×Q811yescharacteristic
86C4×C47C2×#4111yescharacteristic
87Dic47—22no—
88Dic47—22no—
89Dic47—42no—
90Dic47—42no—
91C2×#479—471nomaximal, Sylow
92C2×C47#47914yescomplemented
93C2×C47C2×C22⋊Q811yescharacteristic
94C2×C47C2×#13511yescharacteristic
95C2×C47C2×#13711yescharacteristic
96C2×#125—471no—
97C2×C4×Q8—471no—
98#479—478no—
99C2×#107—471no—
100C2×#106—471no—
101C2×C4⋊C8—471no—
102C2×#103—471no—
103C2×#103D4711yescharacteristic
104C47C2×#47911yescharacteristic, complemented, Sylow
105C22×Q8C2×D4711yescharacteristic
106C22×C8—471no—
107C22×C8C2×D4711yescharacteristic
108#125—474no—
109#125—942no—
110C4×Q8—474no—
111C4×Q8—942no—
112C2×C4⋊C4—471no—
113C2×C4⋊C4—471no—
114C2×C4⋊C4—941no—
115C2×C4⋊C4—941no—
116C2×C4⋊C4—941no—
117C2×C4⋊C4C2×D4711yescharacteristic
118C2×C42—471no—
119C2×C42—941no—
120#107—474no—
121#106—474no—
122C4⋊C8—474no—
123#103—474no—
124#103C2×D4714yes—
125C2×Q8—21no—
126C2×Q8—22no—
127C2×Q8Dic9414yes—
128C2×Q8C22×D4712yes—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—471no—
132C22×C4—471no—
133C22×C4—941no—
134C22×C4—941no—
135C22×C4C22×D4711yescharacteristic
136C2×C8—22no—
137C2×C8—472no—
138C2×C8—942no—
139C2×C8C22×D4712yes—
140C4⋊C4—21no—
141C4⋊C4—472no—
142C4⋊C4—472no—
143C4⋊C4—944no—
144C4⋊C4—944no—
145C4⋊C4—944no—
146C4⋊C4—941no—
147C4⋊C4—941no—
148C4⋊C4C22×D4712yes—
149C42—472no—
150C42—472no—
151C42—944no—
152C23D4×D4711yescharacteristic
153Q8—24no—
154Q8—22no—
155Q8C2×Dic9414yes—
156C2×C4—24no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—42no—
160C2×C4—472no—
161C2×C4—472no—
162C2×C4—942no—
163C2×C4—942no—
164C2×C4—942no—
165C2×C4—942no—
166C2×C4—1882no—
167C2×C4—1882no—
168C2×C4C2×Dic9412yes—
169C2×C4D4×D4711yescharacteristic
170C2×C4#1062535212yes—
171C2×C4C23×D4711yescharacteristic
172C8—22no—
173C8—942no—
174C22#1309400112yes—
175C22#1309404712yes—
176C22#1309405312yes—
177C22C2×D4×D4711yescharacteristic
178C4—24no—
179C4—42no—
180C4—942no—
181C4—942no—
182C4—1882no—
183C4—1882no—
184C4#1309400112yes—
185C4C22×Dic9411yescharacteristic
186C4C2×#1062535211yescharacteristic
187C2#1568943214yesdirect product factor
188C2C2×#1309400111yescharacteristic
189C2C2×#1309404711yescharacteristic
190C2C2×#1309405311yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47C2×#479
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. #15689432C2direct (N × H)
92. C2×C47#479semidirect
104. C47C2×#479semidirect
187. C2#15689432direct (N × H)