Finite Group Databasebeta

← #20245042

Subgroups — #20245042

Order 6016.

234 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 73 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
1#15689107C211yesmaximal, characteristic
2#15689097C211yesmaximal, characteristic
3#15688913C214yesmaximal, complemented
4C47×#536C211yesmaximal, characteristic
5C2×#10625329—21no—
6#13093983—21no—
7#13093943—21no—
8#13093941C2212yes—
9#13093939—21no—
10#13093939C2212yes—
11C2×#41×C47C2211yescharacteristic
12C22×Q8×C47C411yescharacteristic, complemented
13C4⋊Q8×C47—21no—
14#124×C47—21no—
15#123×C47C412yescomplemented
16#123×C47C2212yes—
17C22⋊Q8×C47—21no—
18C22⋊Q8×C47—21no—
19#117×C47C411yescharacteristic, complemented
20#41×C47—41no—
21#41×C47—41no—
22C2×Q8×C47—21no—
23C2×Q8×C47—21no—
24C2×Q8×C47—41no—
25C2×Q8×C47—41no—
26C2×Q8×C47D411yescharacteristic
27C2×D4×C47C2×C411yescharacteristic
28C2×D4×C47D411yescharacteristic
29C2×D4×C47C2311yescharacteristic
30C22×C4×C47C2×C411yescharacteristic
31C22×C4×C47C2×C412yes—
32C22×C4×C47D411yescharacteristic
33C22×C4×C47D411yescharacteristic
34C4⋊C4×C47—21no—
35C4⋊C4×C47—22no—
36C4⋊C4×C47—22no—
37C22⋊C4×C47—22no—
38C22⋊C4×C47—22no—
39C22⋊C4×C47C2×C412yes—
40C42×C47—21no—
41C22⋊Dic47—22no—
42C4⋊Dic47—41no—
43C4×Dic47—41no—
44#10625329—22no—
45#10625329—41no—
46C2×C47⋊C8—41no—
47C23×C47C22⋊C411yescharacteristic
48C23×C47C22×C411yescharacteristic
49C23×C47C2×D411yescharacteristic
50Q8×C47—41no—
51Q8×C47—42no—
52Q8×C47—41no—
53Q8×C47—41no—
54D4×C47—41no—
55D4×C47—41no—
56D4×C47—41no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47—21no—
63C2×C4×C47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—42no—
66C2×C4×C47C22⋊C411yescharacteristic
67C2×C4×C47C22⋊C411yescharacteristic
68C2×C4×C47C22⋊C411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×Dic47—42no—
71C47⋊C8—42no—
72C22×C47—21no—
73C22×C47—21no—
74C22×C47—21no—
75C22×C47—41no—
76C22×C47—41no—
77C22×C47—41no—
78C22×C47C2×C22⋊C411yescharacteristic
79C4×C47—21no—
80C4×C47—21no—
81C4×C47—21no—
82C4×C47—42no—
83C4×C47—42no—
84C4×C47#9911yescharacteristic
85C4×C47#9911yescharacteristic
86Dic47—82no—
87#2123—471nomaximal, Sylow
88C2×C47—21no—
89C2×C47—41no—
90C2×C47—41no—
91C2×C47—41no—
92C2×C47C2×#9911yescharacteristic
93#536D4711yescharacteristic
94#413—471no—
95#410—471no—
96#352—474no—
97C47#212311yescharacteristic, complemented, Sylow
98C2×#41C2×D4711yescharacteristic
99C22×Q8Dic4711yescharacteristic, complemented
100C2×M16—941no—
101C4⋊Q8—21no—
102#124—21no—
103#123Dic4712yescomplemented
104#123C2×D4712yes—
105C22⋊Q8—21no—
106C22⋊Q8—21no—
107#117—941no—
108#117Dic4711yescharacteristic, complemented
109#101—941no—
110#100—472no—
111#99—472no—
112#99—941no—
113#41—41no—
114#41—41no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8—41no—
118C2×Q8—41no—
119C2×Q8C22⋊D4711yescharacteristic
120C2×D4C2×Dic4711yescharacteristic
121C2×D4C22⋊D4711yescharacteristic
122C2×D4C22×D4711yescharacteristic
123C22×C4C2×Dic4711yescharacteristic
124C22×C4C2×Dic4712yes—
125C22×C4C22⋊D4711yescharacteristic
126C22×C4C22⋊D4711yescharacteristic
127M16—942no—
128M16—1881no—
129C2×C8—1881no—
130C4⋊C4—22no—
131C4⋊C4—21no—
132C4⋊C4—22no—
133C4⋊C4—1881no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—942no—
137C22⋊C4C2×Dic4712yes—
138C42—21no—
139C42—1881no—
140C23C22⋊Dic4711yescharacteristic
141C23C22×Dic4711yescharacteristic
142C23C2×C22⋊D4711yescharacteristic
143Q8—41no—
144Q8—42no—
145Q8—41no—
146Q8—41no—
147D4—41no—
148D4—41no—
149D4—41no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—1882no—
160C2×C4C22⋊Dic4711yescharacteristic
161C2×C4C22⋊Dic4711yescharacteristic
162C2×C4C22⋊Dic4711yescharacteristic
163C2×C4C2×C22⋊D4711yescharacteristic
164C8—1882no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22C2×C22⋊Dic4711yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—42no—
176C4—42no—
177C4—3762no—
178C4#1309393911yescharacteristic
179C4#1309393911yescharacteristic
180C2—21no—
181C2—41no—
182C2—41no—
183C2—41no—
184C2C2×#1309393911yescharacteristic
subgroupG/H
centerC2C2×#13093939
commutatorC23×C47C22×C4
FrattiniC2×D4C22×D47
FittingC47×#536C2
socleC2×C47C2×#99
hypercenter#536D47
hypocenterC47#2123
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
3. #15688913C2semidirect
12. C22×Q8×C47C4semidirect
15. #123×C47C4semidirect
19. #117×C47C4semidirect
97. C47#2123semidirect
99. C22×Q8Dic47semidirect
103. #123Dic47semidirect
108. #117Dic47semidirect