Finite Group Databasebeta

← C2×#15688921 #20245068

Subgroups — C2×#15688921 #20245068

Order 6016.

240 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 69 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×#13094022C211yesmaximal, characteristic
2C2×#13093943C211yesmaximal, characteristic
3#15688921C214yesmaximal, direct product factor
4C2×#101×C47C211yesmaximal, characteristic
5C22×Dic94C411yescharacteristic
6C2×#10625329—21no—
7#13094022—21no—
8#13094022—21no—
9#13094022C412yes—
10#13094022C2212yes—
11C2×Dic47⋊C4—21no—
12C2×Dic47⋊C4—21no—
13C2×C4×Dic47C411yescharacteristic
14#13093943—21no—
15#13093943C2212yes—
16C22×Q8×C47C2211yescharacteristic
17C2×M16×C47—21no—
18#101×C47—21no—
19#101×C47C2212yes—
20C2×Q8×C47—41no—
21C2×Q8×C47—41no—
22C2×Q8×C47C2×C411yescharacteristic
23C2×Q8×C47D411yescharacteristic
24C2×Q8×C47D411yescharacteristic
25C2×Q8×C47C2311yescharacteristic
26C22×C4×C47C2×C411yescharacteristic
27C22×C4×C47D411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×Dic47—21no—
30C22×Dic47—21no—
31C2×Dic94—21no—
32C2×Dic94—41no—
33C2×Dic94—41no—
34C2×Dic94C2×C412yes—
35M16×C47—22no—
36M16×C47—41no—
37C2×C8×C47—41no—
38Dic47⋊C4—22no—
39Dic47⋊C4—22no—
40Dic47⋊C4—22no—
41Dic47⋊C4—22no—
42C4×Dic47—21no—
43C4×Dic47C2×C412yes—
44#10625329—22no—
45#10625329—41no—
46C2×C47⋊C8—41no—
47C23×C47C22⋊C411yescharacteristic
48Q8×C47—41no—
49Q8×C47—41no—
50Q8×C47—41no—
51Q8×C47—41no—
52C2×C4×C47—21no—
53C2×C4×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47C22⋊C411yescharacteristic
59C2×C4×C47C22⋊C411yescharacteristic
60C2×C4×C47C22⋊C411yescharacteristic
61C2×C4×C47C22×C411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×Dic47—24no—
65C2×Dic47—22no—
66C2×Dic47—22no—
67C2×Dic47—41no—
68C2×Dic47—41no—
69Dic94—42no—
70Dic94—42no—
71C8×C47—42no—
72C47⋊C8—42no—
73C22×C47—22no—
74C22×C47#9911yescharacteristic
75C22×C47#9911yescharacteristic
76C22×C47C2×C22⋊C411yescharacteristic
77C4×C47—21no—
78C4×C47—21no—
79C4×C47—21no—
80C4×C47—21no—
81C4×C47—21no—
82C4×C47—21no—
83Dic47—24no—
84Dic47—42no—
85C2×#356—471nomaximal, Sylow
86C2×C47—21no—
87C2×C47—21no—
88C2×C47#35612yescomplemented
89C2×C47C2×#9911yescharacteristic
90C2×C4⋊Q8—471no—
91C2×#101—471no—
92C2×#101D4711yescharacteristic
93#356—474no—
94C47C2×#35611yescharacteristic, complemented, Sylow
95C22×Q8—471no—
96C22×Q8C2×D4711yescharacteristic
97C2×M16—21no—
98C2×M16—941no—
99C4⋊Q8—472no—
100C4⋊Q8—472no—
101C4⋊Q8—941no—
102C4⋊Q8—941no—
103C2×C4⋊C4—941no—
104C2×C4⋊C4—941no—
105C2×C42—471no—
106#101—21no—
107#101—472no—
108#101—941no—
109#101C2×D4712yes—
110C2×Q8—41no—
111C2×Q8—41no—
112C2×Q8—472no—
113C2×Q8—941no—
114C2×Q8—1881no—
115C2×Q8—1881no—
116C2×Q8C4×D4711yescharacteristic
117C2×Q8D18811yescharacteristic
118C2×Q8C22⋊D4711yescharacteristic
119C2×Q8C22×D4711yescharacteristic
120C22×C4—941no—
121C22×C4—941no—
122C22×C4C4×D4711yescharacteristic
123C22×C4D18811yescharacteristic
124C22×C4C22⋊D4711yescharacteristic
125M16—22no—
126M16—41no—
127M16—942no—
128M16—1881no—
129C2×C8—41no—
130C2×C8—1881no—
131C4⋊C4—942no—
132C4⋊C4—942no—
133C4⋊C4—942no—
134C4⋊C4—942no—
135C42—472no—
136C42—941no—
137C23(C2×D47)⋊C411yescharacteristic
138Q8—41no—
139Q8—41no—
140Q8—41no—
141Q8—41no—
142Q8—1882no—
143Q8—1882no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—944no—
151C2×C4—942no—
152C2×C4—942no—
153C2×C4—1881no—
154C2×C4—1881no—
155C2×C4(C2×D47)⋊C411yescharacteristic
156C2×C4(C2×D47)⋊C411yescharacteristic
157C2×C4(C2×D47)⋊C411yescharacteristic
158C2×C4C2×C4×D4711yescharacteristic
159C2×C4C2×D18811yescharacteristic
160C2×C4C2×C22⋊D4711yescharacteristic
161C8—42no—
162C8—1882no—
163C22—22no—
164C22#1309393811yescharacteristic
165C22#1309393811yescharacteristic
166C22C2×(C2×D47)⋊C411yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—944no—
174C4—1882no—
175C2—21no—
176C2—21no—
177C2#1568892112yesdirect product factor
178C2C2×#1309393811yescharacteristic
subgroupG/H
centerC22#13093938
commutatorC2×C4×C47C22×C4
FrattiniC2×Q8C22×D47
FittingC2×#101×C47C2
socleC22×C47#99
hypercenterC2×#101D47
hypocenterC47C2×#356
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
3. #15688921C2direct (N × H)
88. C2×C47#356semidirect
94. C47C2×#356semidirect
177. C2#15688921direct (N × H)