Finite Group Databasebeta

← C2×#15688864 #20241971

Subgroups — C2×#15688864 #20241971

Order 6016.

232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 85 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×#13094016C211yesmaximal, characteristic
2C2×#13093935C211yesmaximal, characteristic
3#15688864C214yesmaximal, direct product factor
4C2×#97×C47C211yesmaximal, characteristic
5C22×C47⋊C8—21no—
6#13094016—21no—
7#13094016—21no—
8#13094016C412yes—
9#13094016C2212yes—
10C2×C4⋊Dic47C411yescharacteristic
11C2×C4⋊Dic47C411yescharacteristic
12C2×Dic47⋊C4—21no—
13C2×Dic47⋊C4—21no—
14#13093935—21no—
15#13093935C2212yes—
16C22×C8×C47—21no—
17C2×C42×C47C2211yescharacteristic
18#97×C47—21no—
19#97×C47C2212yes—
20C22×C4×C47C2×C411yescharacteristic
21C22×C4×C47D411yescharacteristic
22C22×C4×C47D411yescharacteristic
23C22×Dic47—21no—
24C22×Dic47—21no—
25C2×C8×C47—24no—
26C2×C8×C47—22no—
27C42×C47C2×C411yescharacteristic
28C42×C47D411yescharacteristic
29C42×C47D411yescharacteristic
30C42×C47C2311yescharacteristic
31C4⋊Dic47—21no—
32C4⋊Dic47—21no—
33C4⋊Dic47C2×C412yes—
34C4⋊Dic47C2×C412yes—
35Dic47⋊C4—22no—
36Dic47⋊C4—22no—
37Dic47⋊C4—22no—
38Dic47⋊C4—22no—
39C2×C47⋊C8—24no—
40C2×C47⋊C8—22no—
41C23×C47C22⋊C411yescharacteristic
42C2×C4×C47—22no—
43C2×C4×C47—22no—
44C2×C4×C47—22no—
45C2×C4×C47C22⋊C411yescharacteristic
46C2×C4×C47C22⋊C411yescharacteristic
47C2×C4×C47C22⋊C411yescharacteristic
48C2×C4×C47C22×C411yescharacteristic
49C2×C4×C47C2×D411yescharacteristic
50C2×C4×C47C2×D411yescharacteristic
51C2×Dic47—22no—
52C2×Dic47—22no—
53C2×Dic47—42no—
54C2×Dic47—42no—
55C8×C47—24no—
56C47⋊C8—24no—
57C22×C47#10112yes—
58C22×C47#10412yes—
59C22×C47#10412yes—
60C22×C47C2×C22⋊C411yescharacteristic
61C4×C47—21no—
62C4×C47—21no—
63C4×C47—21no—
64C4×C47—21no—
65C4×C47—21no—
66C4×C47—21no—
67Dic47—42no—
68Dic47—42no—
69C2×#330—471nomaximal, Sylow
70C2×C47#33014yescomplemented
71C2×C47C2×#10111yescharacteristic
72C2×C47C2×#10411yescharacteristic
73C2×C47C2×#10411yescharacteristic
74C2×#125—471no—
75C2×#97—471no—
76C2×#97D4711yescharacteristic
77#330—474no—
78C47C2×#33011yescharacteristic, complemented, Sylow
79C22×C8—21no—
80C22×C8—941no—
81#125—472no—
82#125—472no—
83#125—941no—
84#125—941no—
85C2×C4⋊C4—471no—
86C2×C4⋊C4—471no—
87C2×C4⋊C4—941no—
88C2×C4⋊C4—941no—
89C2×C42C2×D4711yescharacteristic
90#97—21no—
91#97—472no—
92#97—941no—
93#97C2×D4712yes—
94C22×C4—941no—
95C22×C4—941no—
96C22×C4C4×D4711yescharacteristic
97C22×C4D18811yescharacteristic
98C22×C4C22⋊D4711yescharacteristic
99C2×C8—24no—
100C2×C8—22no—
101C2×C8—944no—
102C2×C8—942no—
103C4⋊C4—472no—
104C4⋊C4—472no—
105C4⋊C4—942no—
106C4⋊C4—942no—
107C4⋊C4—941no—
108C4⋊C4—941no—
109C4⋊C4—942no—
110C4⋊C4—942no—
111C42C4×D4711yescharacteristic
112C42D18811yescharacteristic
113C42C22⋊D4711yescharacteristic
114C42C22×D4711yescharacteristic
115C23(C2×D47)⋊C411yescharacteristic
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—22no—
119C2×C4—942no—
120C2×C4—942no—
121C2×C4—1882no—
122C2×C4—1882no—
123C2×C4(C2×D47)⋊C411yescharacteristic
124C2×C4(C2×D47)⋊C411yescharacteristic
125C2×C4(C2×D47)⋊C411yescharacteristic
126C2×C4C2×C4×D4711yescharacteristic
127C2×C4C2×D18811yescharacteristic
128C2×C4C2×C22⋊D4711yescharacteristic
129C8—24no—
130C8—944no—
131C22#1309394212yes—
132C22#1309395012yes—
133C22#1309395212yes—
134C22C2×(C2×D47)⋊C411yescharacteristic
135C4—21no—
136C4—21no—
137C4—21no—
138C4—21no—
139C4—21no—
140C4—21no—
141C4—1882no—
142C4—1882no—
143C2#1568886414yesdirect product factor
144C2C2×#1309394211yescharacteristic
145C2C2×#1309395011yescharacteristic
146C2C2×#1309395211yescharacteristic
subgroupG/H
centerC23(C2×D47)⋊C4
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC2×#97×C47C2
socleC23×C47C22⋊C4
hypercenterC2×#97D47
hypocenterC47C2×#330
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
3. #15688864C2direct (N × H)
70. C2×C47#330semidirect
78. C47C2×#330semidirect
143. C2#15688864direct (N × H)