Finite Group Databasebeta

← #20255781

Subgroups — #20255781

Order 6016.

356 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 141 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#15689830C212yesmaximal
2#15689528C211yesmaximal, characteristic, complemented
3#15689459C214yesmaximal, complemented
4#15689419C212yesmaximal, complemented
5#15689364C212yesmaximal, complemented
6C4×Dic188C211yesmaximal, characteristic, complemented
7C2×#13093958C212yesmaximal, complemented
8C8×D4×C47C211yesmaximal, characteristic
9C2×Dic188C2211yescharacteristic
10#13094024C2212yes—
11#13094015—22no—
12#13094003C2214yes—
13#13094001—24no—
14C4×Dic94C2212yes—
15D4×Dic47—22no—
16C2×C4⋊Dic47C2214yes—
17#13093958C2211yescharacteristic
18#13093958C2212yes—
19#13093958C2212yes—
20#13093958C2214yes—
21#13093949C2212yes—
22#13093949C2214yes—
23C22×C8×C47C2212yes—
24C4×D4×C47C2211yescharacteristic
25C4⋊C8×C47C2211yescharacteristic
26C22⋊C8×C47C2212yes—
27C4×C8×C47C2211yescharacteristic
28C2×D4×C47D411yescharacteristic
29C22×C4×C47C2312yes—
30C22×Dic47—24no—
31C2×Dic94—22no—
32C2×Dic94C2312yes—
33C2×C8×C47—24no—
34C2×C8×C47C2312yes—
35C2×C8×C47C2311yescharacteristic
36C2×C8×C47C2311yescharacteristic
37C4⋊C4×C47D411yescharacteristic
38C22⋊C4×C47D412yes—
39C42×C47C2311yescharacteristic
40C22⋊Dic47—24no—
41C4⋊Dic47—24no—
42C4⋊Dic47—22no—
43C4⋊Dic47C2312yes—
44C4⋊Dic47C2314yes—
45Dic47⋊C4—22no—
46Dic47⋊C4—24no—
47C4×Dic47—22no—
48Dic188—22no—
49C23×C47C2×D412yes—
50D4×C47Q1614yescomplemented
51C2×C4×C47—22no—
52C2×C4×C47—22no—
53C2×C4×C47C2×D412yes—
54C2×C4×C47C2×D411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2411yescharacteristic
57C2×Dic47—22no—
58C2×Dic47—22no—
59C2×Dic47—24no—
60C2×Dic47—84no—
61Dic94—22no—
62Dic94—22no—
63Dic94—82no—
64C8×C47—22no—
65C8×C47—21no—
66C8×C47#4112yes—
67C22×C47—22no—
68C22×C47—22no—
69C22×C47C2×Q1614yes—
70C22×C47C22×D411yescharacteristic
71C4×C47—22no—
72C4×C47—21no—
73C4×C47C2×Q1612yes—
74C4×C47C2×#4111yescharacteristic
75C4×C472−1+411yescharacteristic
76Dic47—42no—
77Dic47—44no—
78Dic47—42no—
79#3338—471nomaximal, Sylow
80C2×C47—24no—
81C2×C47#54711yescharacteristic
82C2×C47C22×Q1611yescharacteristic
83C2×C47#57611yescharacteristic
84#554—472no—
85#500—471no—
86#484—474no—
87#477—472no—
88#467—472no—
89C4×Q16—471no—
90C8×D4D4711yescharacteristic
91C2×#107—472no—
92C47#333811yescharacteristic, complemented, Sylow
93C2×Q16—471no—
94C22×C8C2×D4712yes—
95C4⋊Q8—472no—
96#125—942no—
97C22⋊Q8—474no—
98C22⋊Q8—944no—
99C4×Q8—472no—
100C4×D4—942no—
101C4×D4C2×D4711yescharacteristic
102C2×C4⋊C4—474no—
103#107—471no—
104#107—472no—
105#107—474no—
106#107—472no—
107C4⋊C8C2×D4711yescharacteristic
108#103—472no—
109#103—474no—
110C22⋊C8C2×D4712yes—
111C4×C8C2×D4711yescharacteristic
112C2×Q8—472no—
113C2×Q8—942no—
114C2×D4D18811yescharacteristic
115C22×C4—944no—
116C22×C4C22×D4712yes—
117Q16—942no—
118C2×C8—24no—
119C2×C8C22×D4711yescharacteristic
120C2×C8C22×D4712yes—
121C2×C8C22×D4711yescharacteristic
122C4⋊C4—472no—
123C4⋊C4—474no—
124C4⋊C4—942no—
125C4⋊C4—944no—
126C4⋊C4—944no—
127C4⋊C4—942no—
128C4⋊C4D18811yescharacteristic
129C22⋊C4—944no—
130C22⋊C4D18812yes—
131C42—942no—
132C42C22×D4711yescharacteristic
133C23C2×D18812yes—
134Q8—942no—
135Q8—942no—
136Q8—3762no—
137D4Dic18814yescomplemented
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—942no—
141C2×C4—942no—
142C2×C4—944no—
143C2×C4—3764no—
144C2×C4C2×D18811yescharacteristic
145C2×C4C2×D18812yes—
146C2×C4C2×D18811yescharacteristic
147C2×C4C23×D4711yescharacteristic
148C8—22no—
149C8—21no—
150C8#1062535212yes—
151C22—22no—
152C22—22no—
153C22C2×Dic18814yes—
154C22C22×D18811yescharacteristic
155C4—22no—
156C4—21no—
157C4—1882no—
158C4—1882no—
159C4—1884no—
160C4C2×Dic18812yes—
161C4C2×#1062535211yescharacteristic
162C4#1309407111yescharacteristic
163C2—24no—
164C2#1568977711yescharacteristic
165C2C22×Dic18811yescharacteristic
166C2#1568992811yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC8×D4×C47C2
socleC22×C47C22×D4
hypercenterC8×D4D47
hypocenterC47#3338
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
2. #15689528C2semidirect
3. #15689459C2semidirect
4. #15689419C2semidirect
5. #15689364C2semidirect
6. C4×Dic188C2semidirect
7. C2×#13093958C2semidirect
50. D4×C47Q16semidirect
92. C47#3338semidirect
137. D4Dic188semidirect