Finite Group Databasebeta

← C2×#15689416 #20253157

Subgroups — C2×#15689416 #20253157

Order 6016.

416 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 165 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×Q8×Dic47C211yesmaximal, characteristic
3#15689416C218yesmaximal, direct product factor
4C2×#13093958C211yesmaximal, characteristic
5C2×#13093957C211yesmaximal, characteristic
6C2×Dic47⋊C8C211yesmaximal, characteristic
7C2×#13093948C211yesmaximal, characteristic
8C2×#103×C47C211yesmaximal, characteristic
9C22×Dic94—21no—
10C22×C47⋊C8C2211yescharacteristic
11#13094023—22no—
12#13094023C2214yes—
13Q8×Dic47—22no—
14Q8×Dic47C2214yes—
15C2×C4⋊Dic47—21no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2211yescharacteristic
18C2×Dic47⋊C4—21no—
19C2×C4×Dic47—21no—
20C2×C4×Dic47C2211yescharacteristic
21#13093958C2214yes—
22#13093957C2214yes—
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×C47Q814yescomplemented
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—24no—
41C2×Dic94—44no—
42C2×C8×C47—22no—
43C2×C8×C47C2312yes—
44C4⋊C4×C47—21no—
45C4⋊C4×C47C2312yes—
46C4⋊Dic47—21no—
47C4⋊Dic47—21no—
48C4⋊Dic47—24no—
49C4⋊Dic47C2312yes—
50C4⋊Dic47C2312yes—
51Dic47⋊C4—24no—
52C4×Dic47—24no—
53C4×Dic47D412yes—
54C4×Dic47C2312yes—
55C2×C47⋊C8—22no—
56C2×C47⋊C8C2312yes—
57C23×C47C2×D411yescharacteristic
58Q8×C47—24no—
59Q8×C47—22no—
60Q8×C47C2×Q814yescomplemented
61C2×C4×C47—24no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—42no—
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×Q812yes—
67C2×C4×C47#4112yes—
68C2×C4×C47C2411yescharacteristic
69C2×Dic47—22no—
70C2×Dic47—22no—
71C2×Dic47—22no—
72C2×Dic47—42no—
73C2×Dic47—42no—
74C2×Dic47Q1614yes—
75C2×Dic47C2×D412yes—
76C2×Dic47C2×D412yes—
77Dic94—48no—
78C8×C47—22no—
79C47⋊C8—22no—
80C22×C47C22⋊Q812yes—
81C22×C47C2×Q1612yes—
82C22×C47AGL(1,ℤ/8)12yes—
83C22×C47C22×D411yescharacteristic
84C4×C47—24no—
85C4×C47—42no—
86C4×C47C22⋊Q812yes—
87C4×C47C22×Q811yescharacteristic
88C4×C47C2×#4111yescharacteristic
89Dic47—22no—
90Dic47—42no—
91Dic47—42no—
92Dic47C2×Q1614yes—
93C2×#477—471nomaximal, Sylow
94C2×C47#47714yescomplemented
95C2×C47C2×C22⋊Q811yescharacteristic
96C2×C47C22×Q1611yescharacteristic
97C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
98C2×C4⋊Q8—471no—
99C2×C4×Q8—471no—
100#477—478no—
101C2×#107—471no—
102C2×#107—471no—
103C2×C4⋊C8—471no—
104C2×#103—471no—
105C2×#103D4711yescharacteristic
106C47C2×#47711yescharacteristic, complemented, Sylow
107C22×Q8—941no—
108C22×Q8C2×D4711yescharacteristic
109C22×C8—471no—
110C22×C8C2×D4711yescharacteristic
111C4⋊Q8—474no—
112C4⋊Q8—942no—
113C4×Q8—474no—
114C4×Q8—942no—
115C2×C4⋊C4—471no—
116C2×C4⋊C4—471no—
117C2×C4⋊C4—941no—
118C2×C4⋊C4—941no—
119C2×C4⋊C4C2×D4711yescharacteristic
120C2×C42—471no—
121C2×C42—941no—
122#107—474no—
123#107—474no—
124C4⋊C8—474no—
125#103—474no—
126#103C2×D4714yes—
127C2×Q8—21no—
128C2×Q8—22no—
129C2×Q8—944no—
130C2×Q8—1884no—
131C2×Q8Dic9414yescomplemented
132C2×Q8C22×D4712yes—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—471no—
136C22×C4—471no—
137C22×C4—941no—
138C22×C4—941no—
139C22×C4C22×D4711yescharacteristic
140C2×C8—22no—
141C2×C8—472no—
142C2×C8—942no—
143C2×C8C22×D4712yes—
144C4⋊C4—21no—
145C4⋊C4—472no—
146C4⋊C4—472no—
147C4⋊C4—944no—
148C4⋊C4—944no—
149C4⋊C4—941no—
150C4⋊C4—941no—
151C4⋊C4C22×D4712yes—
152C42—472no—
153C42—472no—
154C42—944no—
155C23D4×D4711yescharacteristic
156Q8—24no—
157Q8—22no—
158Q8—1888no—
159Q8C2×Dic9414yescomplemented
160C2×C4—24no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—474no—
165C2×C4—472no—
166C2×C4—472no—
167C2×C4—942no—
168C2×C4—942no—
169C2×C4—942no—
170C2×C4—1882no—
171C2×C4—1882no—
172C2×C4C2×Dic9412yes—
173C2×C4D4×D4711yescharacteristic
174C2×C4#1062535212yes—
175C2×C4C23×D4711yescharacteristic
176C8—22no—
177C8—942no—
178C22#1309400112yes—
179C22Q16×D4712yes—
180C22#1309405112yes—
181C22C2×D4×D4711yescharacteristic
182C4—24no—
183C4—42no—
184C4—474no—
185C4—942no—
186C4—1882no—
187C4—1882no—
188C4#1309400112yes—
189C4C22×Dic9411yescharacteristic
190C4C2×#1062535211yescharacteristic
191C2#1568941614yesdirect product factor
192C2C2×#1309400111yescharacteristic
193C2C2×Q16×D4711yescharacteristic
194C2C2×#1309405111yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47C2×#477
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. #15689416C2direct (N × H)
31. C2×Q8×C47Q8semidirect
60. Q8×C47C2×Q8semidirect
94. C2×C47#477semidirect
106. C47C2×#477semidirect
131. C2×Q8Dic94semidirect
159. Q8C2×Dic94semidirect
191. C2#15689416direct (N × H)