Finite Group Databasebeta

← C4×#13093942 #20243185

Subgroups — C4×#13093942 #20243185

Order 6016.

296 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 117 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×C4×Dic94C211yesmaximal, characteristic
2C2×#13093942C212yesmaximal
3C4×#10625329C211yesmaximal, characteristic
4#15688891C212yesmaximal
5C4×M16×C47C211yesmaximal, characteristic
6C22×Dic94C2211yescharacteristic
7C2×#10625329C2212yes—
8C4×Dic94—21no—
9C4×Dic94—21no—
10C4×Dic94—21no—
11C4×Dic94—21no—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×Dic47⋊C4C412yes—
14C2×C4×Dic47C412yes—
15#13093942C418yesdirect product factor
16#13093935—21no—
17C4×C47⋊C8—21no—
18C2×M16×C47C2212yes—
19C2×C42×C47C2211yescharacteristic
20#97×C47—21no—
21C4×C8×C47—21no—
22C22×C4×C47C2×C411yescharacteristic
23C22×C4×C47C2×C411yescharacteristic
24C22×C4×C47C2311yescharacteristic
25C22×Dic47C2×C412yes—
26C22×Dic47C2×C412yes—
27C2×Dic94—21no—
28C2×Dic94—21no—
29C2×Dic94—22no—
30C2×Dic94C2×C414yes—
31M16×C47—22no—
32M16×C47C2×C414yes—
33C2×C8×C47—22no—
34C42×C47D411yescharacteristic
35C42×C47D411yescharacteristic
36C42×C47D411yescharacteristic
37C42×C47D411yescharacteristic
38C4⋊Dic47—21no—
39C4⋊Dic47—21no—
40Dic47⋊C4—22no—
41Dic47⋊C4—22no—
42C4×Dic47—22no—
43C4×Dic47—22no—
44#10625329—22no—
45#10625329C2×C414yes—
46C2×C47⋊C8—22no—
47C23×C47C22×C411yescharacteristic
48C2×C4×C47—22no—
49C2×C4×C47—41no—
50C2×C4×C47C22⋊C411yescharacteristic
51C2×C4×C47C22⋊C411yescharacteristic
52C2×C4×C47C22⋊C411yescharacteristic
53C2×C4×C47C22⋊C411yescharacteristic
54C2×C4×C47C22×C412yes—
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47#4112yes—
58C2×Dic47—22no—
59C2×Dic47—22no—
60C2×Dic47—22no—
61C2×Dic47—42no—
62C2×Dic47C4214yes—
63Dic94—24no—
64Dic94—24no—
65C8×C47—24no—
66C47⋊C8—24no—
67C22×C47—21no—
68C22×C47—21no—
69C22×C47C2×C4211yescharacteristic
70C22×C47C2×C22⋊C411yescharacteristic
71C22×C47#11711yescharacteristic
72C4×C47—21no—
73C4×C47—21no—
74C4×C47—21no—
75C4×C47#10112yescomplemented
76C4×C47C4×D412yes—
77C4×C47C4×D412yes—
78Dic47—24no—
79Dic47—42no—
80C4×#101—471nomaximal, Sylow
81C2×C47—21no—
82C2×C47—21no—
83C2×C47C4×C22⋊C411yescharacteristic
84C2×C47C2×#10111yescharacteristic
85C2×C47#41311yescharacteristic
86C2×C4×Q8—471no—
87C2×#101—472no—
88C4×M16—471no—
89C4×M16D4711yescharacteristic
90#343—472no—
91C47C4×#10111yescharacteristic, complemented, Sylow
92C22×Q8—471no—
93C2×M16—472no—
94C2×M16C2×D4712yes—
95C4×Q8—941no—
96C4×Q8—941no—
97C4×Q8—941no—
98C4×Q8—941no—
99C2×C4⋊C4—472no—
100C2×C4⋊C4—471no—
101C2×C42—472no—
102C2×C42C2×D4711yescharacteristic
103#101—478no—
104#97—21no—
105#97—941no—
106C4×C8—21no—
107C4×C8—941no—
108C2×Q8—474no—
109C2×Q8—941no—
110C2×Q8—942no—
111C2×Q8—941no—
112C22×C4—472no—
113C22×C4—472no—
114C22×C4C4×D4711yescharacteristic
115C22×C4C4×D4711yescharacteristic
116C22×C4C22×D4711yescharacteristic
117M16—22no—
118M16—474no—
119M16—942no—
120M16C4×D4714yes—
121C2×C8—22no—
122C2×C8—942no—
123C4⋊C4—942no—
124C4⋊C4—942no—
125C4⋊C4—941no—
126C4⋊C4—941no—
127C42—942no—
128C42—942no—
129C42D18811yescharacteristic
130C42D18811yescharacteristic
131C42C22⋊D4711yescharacteristic
132C42C22⋊D4711yescharacteristic
133C23C2×C4×D4711yescharacteristic
134Q8—944no—
135Q8—944no—
136C2×C4—22no—
137C2×C4—41no—
138C2×C4—474no—
139C2×C4—942no—
140C2×C4—942no—
141C2×C4—942no—
142C2×C4—1882no—
143C2×C4(C2×D47)⋊C411yescharacteristic
144C2×C4(C2×D47)⋊C411yescharacteristic
145C2×C4(C2×D47)⋊C411yescharacteristic
146C2×C4(C2×D47)⋊C411yescharacteristic
147C2×C4C2×C4×D4712yes—
148C2×C4C2×D18811yescharacteristic
149C2×C4#1062535012yes—
150C2×C4C2×C22⋊D4711yescharacteristic
151C8—24no—
152C8—944no—
153C22—21no—
154C22—21no—
155C22C42×D4711yescharacteristic
156C22C2×(C2×D47)⋊C411yescharacteristic
157C22#1309398111yescharacteristic
158C4—21no—
159C4—21no—
160C4—21no—
161C4—944no—
162C4—1882no—
163C4#1309394212yesdirect product factor
164C4C4×C22⋊D4712yes—
165C4C4×D18812yes—
166C2—21no—
167C2—21no—
168C2C4×(C2×D47)⋊C411yescharacteristic
169C2C2×#1309394211yescharacteristic
170C2#1568910511yescharacteristic
subgroupG/H
centerC2×C4(C2×D47)⋊C4
commutatorC22×C47C2×C42
FrattiniC22×C4C22×D47
FittingC4×M16×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC4×M16D47
hypocenterC47C4×#101
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
15. #13093942C4direct (N × H)
75. C4×C47#101semidirect
91. C47C4×#101semidirect
163. C4#13093942direct (N × H)