Finite Group Databasebeta

← #20252875

Subgroups — #20252875

Order 6016.

480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13094054C212yesmaximal
2C2×#13094024C211yesmaximal, characteristic, complemented
3#15689333C214yesmaximal, complemented
4#15689328C214yesmaximal, complemented
5#15689147C211yesmaximal, characteristic, complemented
6#15689131C212yesmaximal, complemented
7C4×#41×C47C211yesmaximal, characteristic
8C22×Dic94C2212yes—
9#13094054—28no—
10C2×#10625337C2214yes—
11C2×#10625335C2214yes—
12C2×#10625329C2212yes—
13#13094024—21no—
14#13094024—21no—
15#13094024C2214yes—
16C2×C4⋊Dic47—22no—
17C4⋊(C47⋊C8)C2214yes—
18#13093947C2218yes—
19C2×#41×C47C2211yescharacteristic
20C4×Q8×C47C2212yes—
21C4×D4×C47—22no—
22C4×D4×C47C2212yes—
23#117×C47—21no—
24#117×C47C2211yescharacteristic
25C2×C42×C47—21no—
26C2×C42×C47C2211yescharacteristic
27#41×C47—22no—
28#41×C47D414yes—
29C2×Q8×C47C2311yescharacteristic
30C2×D4×C47—21no—
31C2×D4×C47C2311yescharacteristic
32C22×C4×C47—21no—
33C22×C4×C47—22no—
34C22×C4×C47D412yes—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47—22no—
37C2×Dic94—24no—
38C2×Dic94—24no—
39C2×Dic94—22no—
40C2×Dic94C2314yes—
41C4⋊C4×C47—22no—
42C4⋊C4×C47C2312yes—
43C22⋊C4×C47—21no—
44C22⋊C4×C47—22no—
45C42×C47—21no—
46C42×C47—22no—
47C42×C47D411yescharacteristic
48C42×C47D411yescharacteristic
49C42×C47C2312yes—
50#10625337—28no—
51#10625335—28no—
52C4⋊Dic47—24no—
53C4⋊Dic47—24no—
54#10625329—24no—
55C2×C47⋊C8C2314yes—
56C23×C47—21no—
57C23×C47C2×D411yescharacteristic
58Q8×C47—21no—
59Q8×C47C2×D412yes—
60D4×C47—24no—
61D4×C47—21no—
62D4×C47C2×D412yes—
63C2×C4×C47—21no—
64C2×C4×C47—24no—
65C2×C4×C47—24no—
66C2×C4×C47—22no—
67C2×C4×C47—44no—
68C2×C4×C47C2×D412yes—
69C2×C4×C47C2×D412yes—
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D412yes—
72C2×C4×C47#4112yes—
73C2×C4×C47C2411yescharacteristic
74C2×Dic47—24no—
75C2×Dic47—44no—
76Dic94—24no—
77Dic94—24no—
78Dic94—44no—
79C47⋊C8—24no—
80C22×C47—22no—
81C22×C47—22no—
82C22×C47—42no—
83C22×C47#12112yes—
84C22×C47C22×D411yescharacteristic
85C4×C47—22no—
86C4×C47—22no—
87C4×C47—42no—
88C4×C47#12112yes—
89C4×C47#13714yescomplemented
90C4×C47C22×D411yescharacteristic
91C4×C47C2×#4111yescharacteristic
92Dic47—44no—
93#3039—471nomaximal, Sylow
94C2×C47—22no—
95C2×C47—42no—
96C2×C47C2×#12111yescharacteristic
97C2×C47C2×#13712yes—
98C2×#137—472no—
99C2×C4⋊Q8—471no—
100C4×#41D4711yescharacteristic
101#462—474no—
102#461—474no—
103#423—471no—
104#419—472no—
105C47#303911yescharacteristic, complemented, Sylow
106C2×#41C2×D4711yescharacteristic
107C22×Q8—472no—
108#137—948no—
109C2×Q16—474no—
110C2×SD16—474no—
111C2×M16—472no—
112C4⋊Q8—474no—
113C4⋊Q8—941no—
114C4⋊Q8—941no—
115C4×Q8C2×D4712yes—
116C4×D4—22no—
117C4×D4C2×D4712yes—
118#117—21no—
119#117C2×D4711yescharacteristic
120C2×C4⋊C4—942no—
121C2×C42—21no—
122C2×C42C2×D4711yescharacteristic
123C4⋊C8—474no—
124#103—478no—
125#41—22no—
126#41D18814yes—
127C2×Q8—474no—
128C2×Q8—942no—
129C2×Q8—944no—
130C2×Q8—944no—
131C2×Q8C22×D4711yescharacteristic
132C2×D4—21no—
133C2×D4C22×D4711yescharacteristic
134C22×C4—21no—
135C22×C4—22no—
136C22×C4—942no—
137C22×C4C22⋊D4712yes—
138C22×C4C22×D4711yescharacteristic
139Q16—948no—
140SD16—948no—
141M16—944no—
142C2×C8—474no—
143C4⋊C4—22no—
144C4⋊C4—944no—
145C4⋊C4—944no—
146C4⋊C4C22×D4712yes—
147C22⋊C4—21no—
148C22⋊C4—22no—
149C42—21no—
150C42—22no—
151C42C22⋊D4711yescharacteristic
152C42C22⋊D4711yescharacteristic
153C42C22×D4712yes—
154C23—21no—
155C23C2×C22⋊D4711yescharacteristic
156Q8—21no—
157Q8—944no—
158Q8—944no—
159Q8—1884no—
160Q8C2×D18812yes—
161D4—24no—
162D4—21no—
163D4C2×D18812yes—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—24no—
167C2×C4—22no—
168C2×C4—44no—
169C2×C4—944no—
170C2×C4—1884no—
171C2×C4C2×D18812yes—
172C2×C4#1062535012yes—
173C2×C4C2×C22⋊D4712yes—
174C2×C4C2×C22⋊D4711yescharacteristic
175C2×C4C2×C22⋊D4712yes—
176C2×C4C23×D4711yescharacteristic
177C8—944no—
178C22—22no—
179C22—22no—
180C22—42no—
181C22#1309399812yes—
182C22C22×C22⋊D4711yescharacteristic
183C4—22no—
184C4—22no—
185C4—42no—
186C4—1884no—
187C4#1309399812yes—
188C4#1309405414yescomplemented
189C4C22×D18811yescharacteristic
190C4C2×#1062535011yescharacteristic
191C2—22no—
192C2—42no—
193C2C2×#1309399811yescharacteristic
194C2C2×#1309405412yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×#41×C47C2
socleC22×C47C22×D4
hypercenterC4×#41D47
hypocenterC47#3039
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. C2×#13094024C2semidirect
3. #15689333C2semidirect
4. #15689328C2semidirect
5. #15689147C2semidirect
6. #15689131C2semidirect
89. C4×C47#137semidirect
105. C47#3039semidirect
188. C4#13094054semidirect