Finite Group Databasebeta

← #20254332

Subgroups — #20254332

Order 6016.

384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689678C211yesmaximal, characteristic
2C4⋊Q8×D47C211yesmaximal, characteristic
3#15689502C211yesmaximal, characteristic, complemented
4#15689474C211yesmaximal, characteristic, complemented
5#15689473C211yesmaximal, characteristic, complemented
6#15689331C214yesmaximal, complemented
7#15689277C214yesmaximal
8#15689174C211yesmaximal, characteristic
9C47×#494C211yesmaximal, characteristic, complemented
10C2×Q8×D47C2212yes—
11C2×#10625337C2214yes—
12#13094024C2211yescharacteristic
13#13094024C2211yescharacteristic
14#13094023—21no—
15#13094023—21no—
16#13094022C2212yes—
17#13094015—21no—
18#13094004—21no—
19#13094000C2212yes—
20Q8×Dic47C2212yes—
21#13093989—21no—
22#13093982—21no—
23C4⋊C4×D47—21no—
24C4⋊C4×D47—21no—
25C42×D47C2211yescharacteristic
26Dic47⋊C8C2212yes—
27#13093949C2214yes—
28#13093948C2214yes—
29(C2×D47)⋊C8C2212yes—
30C4×C47⋊C8C2211yescharacteristic
31C2×Q16×C47C2214yes—
32C4⋊Q8×C47C2211yescharacteristic
33C4⋊Q8×C47C2211yescharacteristic
34C4×C8×C47C2211yescharacteristic
35C2×Q8×C47C2312yes—
36C2×Q8×C47C2312yes—
37Q8×D47—44no—
38C2×C4×D47—22no—
39C2×C4×D47D411yescharacteristic
40C2×C4×D47D411yescharacteristic
41C2×C4×D47C2311yescharacteristic
42C2×Dic94—21no—
43C2×Dic94—22no—
44C2×Dic94C2312yes—
45Q16×C47—44no—
46C2×C8×C47C2312yes—
47C4⋊C4×C47—21no—
48C4⋊C4×C47—21no—
49C4⋊C4×C47—21no—
50C4⋊C4×C47—21no—
51C42×C47C2311yescharacteristic
52#10625337—44no—
53(C2×D47)⋊C4—22no—
54C4⋊Dic47—21no—
55C4⋊Dic47—21no—
56C4⋊Dic47—21no—
57C4⋊Dic47—22no—
58C4⋊Dic47C2312yes—
59Dic47⋊C4—22no—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62C4×Dic47—22no—
63C4×Dic47D411yescharacteristic
64C4×Dic47D411yescharacteristic
65C4×Dic47C2311yescharacteristic
66C2×C47⋊C8C2312yes—
67C22×D47C2×D411yescharacteristic
68Q8×C47—24no—
69Q8×C47—24no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2411yescharacteristic
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47C2×D411yescharacteristic
78C2×Dic47C2×D411yescharacteristic
79C2×Dic47C2×D411yescharacteristic
80C4×D47—22no—
81C4×D47—22no—
82C4×D47—44no—
83C4×D47Q1614yescomplemented
84Dic94—24no—
85Dic94—44no—
86Dic94—42no—
87C8×C47—22no—
88C47⋊C8—22no—
89C22×C47C22×D411yescharacteristic
90C2×D47—21no—
91C2×D47—21no—
92C2×D47C2×Q1612yes—
93C4×C47—42no—
94C4×C47—42no—
95C4×C47C2×Q1612yes—
96C4×C47#13712yes—
97C4×C47H(5,𝔽2)12yes—
98Dic47—21no—
99Dic47—21no—
100Dic47—42no—
101Dic47—42no—
102Dic47C2×Q1612yes—
103#3209—471nomaximal, Sylow
104C2×C47#53511yescharacteristic
105C2×C47C22×Q1611yescharacteristic
106C2×C47C2×#13711yescharacteristic
107D47—22no—
108#533—471no—
109C2×C4⋊Q8—471no—
110#494—471no—
111#494D4711yescharacteristic, complemented
112#487—471no—
113#487—471no—
114#462—474no—
115#451—474no—
116#431—471no—
117C47#320911yescharacteristic, complemented, Sylow
118C22×Q8—472no—
119C2×Q16—474no—
120C2×Q16C2×D4714yes—
121C4⋊Q8—472no—
122C4⋊Q8—471no—
123C4⋊Q8—471no—
124C4⋊Q8—941no—
125C4⋊Q8—941no—
126C4⋊Q8C2×D4711yescharacteristic
127C4⋊Q8C2×D4711yescharacteristic
128#125—941no—
129C22⋊Q8—472no—
130C22⋊Q8—941no—
131C4×Q8—472no—
132C4×Q8—941no—
133#117—941no—
134C2×C4⋊C4—941no—
135C2×C4⋊C4—941no—
136C2×C42—471no—
137C4⋊C8—472no—
138#103—474no—
139#103—474no—
140C22⋊C8—472no—
141C4×C8—471no—
142C4×C8C2×D4711yescharacteristic
143C2×Q8—472no—
144C2×Q8—942no—
145C2×Q8—941no—
146C2×Q8—1884no—
147C2×Q8C22×D4712yes—
148C2×Q8C22×D4712yes—
149C22×C4—471no—
150C22×C4—471no—
151C22×C4—471no—
152C22×C4—942no—
153Q16—44no—
154Q16—1884no—
155C2×C8—472no—
156C2×C8C22×D4712yes—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—472no—
162C4⋊C4—942no—
163C4⋊C4—942no—
164C4⋊C4—942no—
165C4⋊C4—942no—
166C4⋊C4—941no—
167C4⋊C4—941no—
168C4⋊C4—941no—
169C22⋊C4—942no—
170C42—471no—
171C42—471no—
172C42—471no—
173C42—942no—
174C42C22×D4711yescharacteristic
175C23—471no—
176Q8—24no—
177Q8—24no—
178Q8—944no—
179Q8—1884no—
180Q8—1882no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—471no—
184C2×C4—474no—
185C2×C4—471no—
186C2×C4—471no—
187C2×C4—942no—
188C2×C4—942no—
189C2×C4—942no—
190C2×C4—942no—
191C2×C4—1884no—
192C2×C4D4×D4711yescharacteristic
193C2×C4D4×D4711yescharacteristic
194C2×C4C23×D4711yescharacteristic
195C8—22no—
196C8—942no—
197C22—472no—
198C22—941no—
199C22—941no—
200C22C2×D4×D4711yescharacteristic
201C4—42no—
202C4—42no—
203C4—472no—
204C4—941no—
205C4—941no—
206C4—1882no—
207C4—1882no—
208C4Q16×D4712yes—
209C4#1309405612yes—
210C4#1309406912yes—
211C2—942no—
212C2#1568968611yescharacteristic
213C2C2×Q16×D4711yescharacteristic
214C2C2×#1309405611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#494C2
socleC22×C47C22×D4
hypercenter#494D47
hypocenterC47#3209
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
3. #15689502C2semidirect
4. #15689474C2semidirect
5. #15689473C2semidirect
6. #15689331C2semidirect
9. C47×#494C2semidirect
83. C4×D47Q16semidirect
111. #494D47semidirect
117. C47#3209semidirect