Finite Group Databasebeta

← #20243778

Subgroups — #20243778

Order 6016.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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
2#15689600C211yesmaximal, characteristic
3#15689132C211yesmaximal, characteristic
4C2×#13093942C211yesmaximal, characteristic
5#15688884C211yesmaximal, characteristic
6#15688882C211yesmaximal, characteristic
7C47×#419C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10#13094022—22no—
11#13094022C414yescomplemented
12C4×Dic94—22no—
13#13093989—22no—
14#13093983C2211yescharacteristic
15#13093980—22no—
16C2×Dic47⋊C4—22no—
17C2×C4×Dic47C2211yescharacteristic
18#13093948—22no—
19#13093942—22no—
20C22×Q8×C47C2211yescharacteristic
21C2×M16×C47C2211yescharacteristic
22#117×C47C2211yescharacteristic
23#103×C47—22no—
24C2×Q8×C47—21no—
25C2×Q8×C47—21no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47C2×C412yes—
30C22×C4×C47—21no—
31C22×C4×C47C2311yescharacteristic
32C22×Dic47—21no—
33C22×Dic47D412yes—
34C2×Dic94—21no—
35C2×Dic94—21no—
36C2×Dic94—21no—
37C2×Dic94—21no—
38C2×Dic94C2×C412yes—
39C2×Dic94D412yes—
40M16×C47—21no—
41M16×C47—21no—
42C2×C8×C47—21no—
43C4⋊C4×C47D412yes—
44C22⋊C4×C47—21no—
45C42×C47—21no—
46C22⋊Dic47—21no—
47C4⋊Dic47D412yes—
48Dic47⋊C4—24no—
49Dic47⋊C4—28no—
50C4×Dic47—24no—
51C4×Dic47—21no—
52C4×Dic47—21no—
53C4×Dic47C2×C412yes—
54#10625329—21no—
55#10625329—21no—
56C2×C47⋊C8—21no—
57C23×C47C2×D411yescharacteristic
58Q8×C47—22no—
59Q8×C47—22no—
60Q8×C47—41no—
61Q8×C47—41no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47C22×C411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47#4111yescharacteristic
71C2×C4×C47#4111yescharacteristic
72C2×Dic47—24no—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47C22⋊C414yes—
78Dic94—22no—
79Dic94—22no—
80Dic94—22no—
81Dic94—22no—
82C8×C47—41no—
83C47⋊C8—41no—
84C22×C47—22no—
85C22×C47C2×C22⋊C411yescharacteristic
86C22×C47#12011yescharacteristic
87C22×C47#12311yescharacteristic
88C4×C47—42no—
89C4×C47—42no—
90C4×C47C4×D411yescharacteristic
91C4×C47C4×D411yescharacteristic
92C4×C47#12111yescharacteristic
93C4×C47#12111yescharacteristic
94Dic47—24no—
95Dic47—24no—
96Dic47—42no—
97#1886—471nomaximal, Sylow
98C2×C47—21no—
99C2×C47—21no—
100C2×C47#38611yescharacteristic
101C2×C47#45612yes—
102C2×C4⋊Q8—471no—
103#519—471no—
104#419—471no—
105#419D4711yescharacteristic
106C2×#101—471no—
107#339—471no—
108#339—471no—
109C47#188611yescharacteristic, complemented, Sylow
110C22×Q8—471no—
111C22×Q8C2×D4711yescharacteristic
112C2×M16—471no—
113C2×M16C2×D4711yescharacteristic
114C4⋊Q8—474no—
115C4⋊Q8—942no—
116C4×Q8—942no—
117C4×Q8—942no—
118#117—471no—
119#117—942no—
120#117C2×D4711yescharacteristic
121C2×C4⋊C4—942no—
122C2×C42—471no—
123#103—22no—
124#103—942no—
125#101—942no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—472no—
132C2×Q8—472no—
133C2×Q8—941no—
134C2×Q8—941no—
135C2×Q8—941no—
136C2×Q8—941no—
137C2×Q8C4×D4712yes—
138C22×C4—21no—
139C22×C4—472no—
140C22×C4—941no—
141C22×C4C22×D4711yescharacteristic
142M16—21no—
143M16—21no—
144M16—941no—
145M16—941no—
146C2×C8—21no—
147C2×C8—941no—
148C4⋊C4—472no—
149C4⋊C4—948no—
150C4⋊C4—944no—
151C4⋊C4C22⋊D4712yes—
152C22⋊C4—21no—
153C22⋊C4—941no—
154C42—21no—
155C42—472no—
156C42—944no—
157C42—941no—
158C42—941no—
159C23D4×D4711yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164Q8—942no—
165Q8—942no—
166Q8—942no—
167Q8—942no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—474no—
173C2×C4—944no—
174C2×C4—942no—
175C2×C4—942no—
176C2×C4—942no—
177C2×C4—942no—
178C2×C4C2×C4×D4711yescharacteristic
179C2×C4#1062535011yescharacteristic
180C2×C4D4×D4711yescharacteristic
181C2×C4D4×D4711yescharacteristic
182C2×C4#1062535211yescharacteristic
183C2×C4C2×C22⋊D4711yescharacteristic
184C8—41no—
185C8—1881no—
186C22—22no—
187C22C22⋊C4×D4711yescharacteristic
188C22#1309399211yescharacteristic
189C22#1309400611yescharacteristic
190C4—42no—
191C4—42no—
192C4—944no—
193C4—944no—
194C4—1882no—
195C4(C22⋊D47)⋊C411yescharacteristic
196C4C4×C22⋊D4711yescharacteristic
197C4#1309399511yescharacteristic
198C4#1309399711yescharacteristic
199C2—21no—
200C2—21no—
201C2#1568899911yescharacteristic
202C2#1568930412yes—
subgroupG/H
centerC22#13093992
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#419C2
socleC22×C47#120
hypercenter#419D47
hypocenterC47#1886
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
11. #13094022C4semidirect
109. C47#1886semidirect