Finite Group Databasebeta

← #20243780

Subgroups — #20243780

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×#13094024C211yesmaximal, characteristic
2#15689600C211yesmaximal, characteristic
3#15689133C211yesmaximal, characteristic
4#15689131C211yesmaximal, characteristic
5C2×#13093942C211yesmaximal, characteristic
6#15688883C211yesmaximal, characteristic
7C47×#339C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C22×Dic94C2211yescharacteristic
10C2×#10625329C2211yescharacteristic
11#13094024—22no—
12#13094024C414yescomplemented
13C4×Dic94—22no—
14#13093989—22no—
15#13093983C2211yescharacteristic
16#13093980—22no—
17C2×C4⋊Dic47—22no—
18#13093949—22no—
19#13093947—22no—
20#13093942—22no—
21C2×M16×C47C2211yescharacteristic
22#117×C47C2211yescharacteristic
23C2×C42×C47C2211yescharacteristic
24C22×C4×C47—21no—
25C22×C4×C47C2311yescharacteristic
26C22×Dic47—21no—
27C22×Dic47D412yes—
28C2×Dic94—21no—
29C2×Dic94—21no—
30C2×Dic94—21no—
31C2×Dic94—21no—
32C2×Dic94—21no—
33C2×Dic94—21no—
34C2×Dic94—21no—
35C2×Dic94—21no—
36C2×Dic94—21no—
37C2×Dic94C2×C412yes—
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—
46C42×C47—21no—
47C42×C47C2×C412yes—
48C22⋊Dic47—21no—
49C4⋊Dic47—28no—
50C4⋊Dic47D412yes—
51Dic47⋊C4—24no—
52C4×Dic47—24no—
53C4×Dic47—21no—
54#10625329—21no—
55#10625329—21no—
56C2×C47⋊C8—21no—
57C23×C47C2×D411yescharacteristic
58C2×C4×C47—24no—
59C2×C4×C47—22no—
60C2×C4×C47—22no—
61C2×C4×C47C22×C411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47#4111yescharacteristic
66C2×C4×C47#4111yescharacteristic
67C2×Dic47—22no—
68C2×Dic47—22no—
69C2×Dic47—22no—
70C2×Dic47—22no—
71C2×Dic47—41no—
72C2×Dic47—41no—
73C2×Dic47C22⋊C414yes—
74Dic94—22no—
75Dic94—22no—
76Dic94—22no—
77Dic94—22no—
78Dic94—22no—
79Dic94—22no—
80Dic94—41no—
81Dic94—41no—
82C8×C47—41no—
83C47⋊C8—41no—
84C22×C47—22no—
85C22×C47C2×C22⋊C411yescharacteristic
86C22×C47#12011yescharacteristic
87C22×C47#12311yescharacteristic
88C4×C47—24no—
89C4×C47—42no—
90C4×C47C4×D411yescharacteristic
91C4×C47C4×D411yescharacteristic
92C4×C47#12111yescharacteristic
93C4×C47#12111yescharacteristic
94Dic47—24no—
95Dic47—42no—
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#419—471no—
106C2×#101—471no—
107#339—471no—
108#339D4711yescharacteristic
109C47#188611yescharacteristic, complemented, Sylow
110C22×Q8—471no—
111C22×Q8—471no—
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×C42C2×D4711yescharacteristic
123#103—942no—
124#103—942no—
125#101—942no—
126C2×Q8—472no—
127C2×Q8—472no—
128C2×Q8—472no—
129C2×Q8—941no—
130C2×Q8—941no—
131C2×Q8—941no—
132C2×Q8—941no—
133C2×Q8—941no—
134C2×Q8—941no—
135C2×Q8—941no—
136C2×Q8—941no—
137C2×Q8—941no—
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⋊C4D18812yes—
152C22⋊C4—21no—
153C22⋊C4—941no—
154C42—21no—
155C42—21no—
156C42—944no—
157C42—941no—
158C42C4×D4712yes—
159C23D4×D4711yescharacteristic
160Q8—942no—
161Q8—942no—
162Q8—942no—
163Q8—942no—
164Q8—942no—
165Q8—942no—
166Q8—1881no—
167Q8—1881no—
168C2×C4—24no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—474no—
172C2×C4—942no—
173C2×C4—942no—
174C2×C4—942no—
175C2×C4—942no—
176C2×C4—1881no—
177C2×C4—1881no—
178C2×C4C2×C4×D4711yescharacteristic
179C2×C4C2×D18811yescharacteristic
180C2×C4#1062535011yescharacteristic
181C2×C4D4×D4711yescharacteristic
182C2×C4D4×D4711yescharacteristic
183C2×C4#1062535411yescharacteristic
184C8—41no—
185C8—1881no—
186C22—22no—
187C22C22⋊C4×D4711yescharacteristic
188C22#1309399411yescharacteristic
189C22#1309400911yescharacteristic
190C4—24no—
191C4—42no—
192C4—944no—
193C4—1882no—
194C4—1882no—
195C4#1309398611yescharacteristic
196C4C4×D18811yescharacteristic
197C4#1309399711yescharacteristic
198C4#1309399911yescharacteristic
199C2—21no—
200C2—21no—
201C2#1568900111yescharacteristic
202C2#1568930712yes—
subgroupG/H
centerC22#13093994
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#339C2
socleC22×C47#120
hypercenter#339D47
hypocenterC47#1886
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
12. #13094024C4semidirect
109. C47#1886semidirect