Finite Group Databasebeta

← #20245043

Subgroups — #20245043

Order 6016.

234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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#15689694C211yesmaximal, characteristic
2#15689097C211yesmaximal, characteristic
3#15688914C214yesmaximal, complemented
4C47×#413C211yesmaximal, characteristic
5C22×Dic94C411yescharacteristic, complemented
6#13094022—21no—
7#13094011—21no—
8#13094005C412yescomplemented
9#13094005C2212yes—
10#13094003—21no—
11#13094003—21no—
12#13093983—21no—
13#13093983C411yescharacteristic, complemented
14#13093939—21no—
15#13093939C2212yes—
16C2×#41×C47C2211yescharacteristic
17C2×M16×C47—21no—
18#101×C47—21no—
19#100×C47C2212yes—
20#41×C47—41no—
21#41×C47—41no—
22C2×Q8×C47D411yescharacteristic
23C2×D4×C47C2×C411yescharacteristic
24C2×D4×C47D411yescharacteristic
25C2×D4×C47C2311yescharacteristic
26C22×C4×C47C2×C411yescharacteristic
27C22×C4×C47D411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×Dic47C2×C412yes—
30C2×Dic94—21no—
31C2×Dic94—21no—
32C2×Dic94—41no—
33C2×Dic94—41no—
34M16×C47—22no—
35M16×C47—41no—
36C2×C8×C47—41no—
37C22⋊Dic47—22no—
38C22⋊Dic47—22no—
39C22⋊Dic47—22no—
40C22⋊Dic47C2×C412yes—
41C4⋊Dic47—21no—
42C4⋊Dic47—41no—
43Dic47⋊C4—22no—
44Dic47⋊C4—22no—
45C4×Dic47—21no—
46C4×Dic47—41no—
47C23×C47C22⋊C411yescharacteristic
48C23×C47C22×C411yescharacteristic
49C23×C47C2×D411yescharacteristic
50Q8×C47—41no—
51D4×C47—41no—
52D4×C47—41no—
53D4×C47—41no—
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47C22⋊C411yescharacteristic
61C2×C4×C47C22⋊C411yescharacteristic
62C2×C4×C47C22⋊C411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×Dic47—22no—
65C2×Dic47—22no—
66C2×Dic47—42no—
67C2×Dic47—42no—
68Dic94—42no—
69Dic94—41no—
70Dic94—41no—
71C8×C47—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#9911yescharacteristic
83C4×C47#9911yescharacteristic
84Dic47—42no—
85Dic47—42no—
86Dic47—82no—
87#2123—471nomaximal, Sylow
88C2×C47—21no—
89C2×C47—41no—
90C2×C47—41no—
91C2×C47—41no—
92C2×C47C2×#9911yescharacteristic
93#536—471no—
94#413D4711yescharacteristic
95#410—471no—
96#352—474no—
97C47#212311yescharacteristic, complemented, Sylow
98C2×#41C2×D4711yescharacteristic
99C22×Q8—471no—
100C2×M16—21no—
101C4⋊Q8—941no—
102#124—941no—
103#123—472no—
104#123—472no—
105C22⋊Q8—941no—
106C22⋊Q8—941no—
107#117—471no—
108#117—941no—
109#101—21no—
110#100C2×D4712yes—
111#99—472no—
112#99—941no—
113#41—41no—
114#41—41no—
115C2×Q8—941no—
116C2×Q8—941no—
117C2×Q8—1881no—
118C2×Q8—1881no—
119C2×Q8C22⋊D4711yescharacteristic
120C2×D4C4×D4711yescharacteristic
121C2×D4D18811yescharacteristic
122C2×D4C22×D4711yescharacteristic
123C22×C4—472no—
124C22×C4C4×D4711yescharacteristic
125C22×C4D18811yescharacteristic
126C22×C4C22⋊D4711yescharacteristic
127M16—22no—
128M16—41no—
129C2×C8—41no—
130C4⋊C4—942no—
131C4⋊C4—941no—
132C4⋊C4—942no—
133C4⋊C4—1881no—
134C22⋊C4—472no—
135C22⋊C4—942no—
136C22⋊C4—942no—
137C22⋊C4—942no—
138C42—941no—
139C42—1881no—
140C23(C2×D47)⋊C411yescharacteristic
141C23C2×C4×D4711yescharacteristic
142C23C2×D18811yescharacteristic
143Q8—41no—
144Q8—1882no—
145Q8—1881no—
146Q8—1881no—
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—942no—
157C2×C4—942no—
158C2×C4—1882no—
159C2×C4—1882no—
160C2×C4(C2×D47)⋊C411yescharacteristic
161C2×C4(C2×D47)⋊C411yescharacteristic
162C2×C4(C2×D47)⋊C411yescharacteristic
163C2×C4C2×C22⋊D4711yescharacteristic
164C8—42no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22C2×(C2×D47)⋊C411yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—3762no—
176C4—1882no—
177C4—1882no—
178C4#1309393811yescharacteristic
179C4#1309393811yescharacteristic
180C2—21no—
181C2—41no—
182C2—41no—
183C2—41no—
184C2C2×#1309393811yescharacteristic
subgroupG/H
centerC2C2×#13093938
commutatorC23×C47C22×C4
FrattiniC2×D4C22×D47
FittingC47×#413C2
socleC2×C47C2×#99
hypercenter#413D47
hypocenterC47#2123
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #15688914C2semidirect
5. C22×Dic94C4semidirect
8. #13094005C4semidirect
13. #13093983C4semidirect
97. C47#2123semidirect