Finite Group Databasebeta

← #20256277

Subgroups — #20256277

Order 6016.

324 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 133 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#15689852C212yesmaximal
2#15689528C211yesmaximal, characteristic
3#15689524C212yesmaximal
4#15689432C214yesmaximal
5#15689408C212yesmaximal
6C8×Dic94C211yesmaximal, characteristic
7Q16×Dic47C212yesmaximal
8C4×Q16×C47C211yesmaximal, characteristic
9#13094024—22no—
10#13094024C2212yes—
11#13094015—24no—
12#13094015C2214yes—
13Q8×Dic47C2214yes—
14C4×Dic94—22no—
15C4×Dic94C2211yescharacteristic
16#13093958C2212yes—
17#13093958C2212yes—
18#13093955C2214yes—
19C4⋊(C47⋊C8)C2211yescharacteristic
20Dic47⋊C8C2212yes—
21#13093948C2214yes—
22C8×Dic47C2212yes—
23C2×Q16×C47C2211yescharacteristic
24C4×Q8×C47C2212yes—
25#107×C47C2211yescharacteristic
26#103×C47C2212yes—
27C4×C8×C47C2211yescharacteristic
28C2×Q8×C47C2312yes—
29C2×Dic94—22no—
30C2×Dic94D411yescharacteristic
31Q16×C47Q814yescomplemented
32C2×C8×C47C2311yescharacteristic
33C2×C8×C47C2311yescharacteristic
34C4⋊C4×C47—22no—
35C4⋊C4×C47C2312yes—
36C42×C47—22no—
37C42×C47C2311yescharacteristic
38C4⋊Dic47—22no—
39C4⋊Dic47—24no—
40C4⋊Dic47—24no—
41C4⋊Dic47D411yescharacteristic
42C4⋊Dic47C2314yes—
43Dic47⋊C4—24no—
44Dic47⋊C4D412yes—
45C4×Dic47—24no—
46C4×Dic47C2312yes—
47C2×C47⋊C8C2312yes—
48Q8×C47—22no—
49Q8×C47C2×Q814yes—
50C2×C4×C47—22no—
51C2×C4×C47—22no—
52C2×C4×C47C2×D411yescharacteristic
53C2×C4×C47C2×D411yescharacteristic
54C2×C4×C47C2411yescharacteristic
55C2×Dic47—24no—
56C2×Dic47C2×D412yes—
57C2×Dic47C2×D412yes—
58Dic94—22no—
59Dic94—44no—
60C8×C47—21no—
61C8×C47C2×Q812yes—
62C47⋊C8—22no—
63C22×C47C22×D411yescharacteristic
64C4×C47—24no—
65C4×C47—21no—
66C4×C47—42no—
67C4×C47#13512yes—
68C4×C47C22×Q811yescharacteristic
69C4×C472−1+411yescharacteristic
70Dic47—22no—
71Dic47—22no—
72Dic47—44no—
73#3383—471nomaximal, Sylow
74C2×C47D4×Q811yescharacteristic
75C2×C47C2×#13511yescharacteristic
76C2×C47#57811yescharacteristic
77#557—472no—
78#500—471no—
79#499—472no—
80#479—474no—
81#475—472no—
82C8×Q8—471no—
83C4×Q16—472no—
84C4×Q16D4711yescharacteristic
85C47#338311yescharacteristic, complemented, Sylow
86C2×Q16C2×D4711yescharacteristic
87C4⋊Q8—472no—
88C4⋊Q8—942no—
89#125—474no—
90#125—944no—
91C4×Q8—471no—
92C4×Q8—474no—
93C4×Q8—942no—
94C4×Q8C2×D4712yes—
95#107—472no—
96#107—472no—
97#107C2×D4711yescharacteristic
98#106—474no—
99C4⋊C8—472no—
100C4⋊C8—471no—
101#103—474no—
102#103C2×D4712yes—
103C4×C8—472no—
104C4×C8C2×D4711yescharacteristic
105C2×Q8—471no—
106C2×Q8—942no—
107C2×Q8C22×D4712yes—
108Q16Dic9414yescomplemented
109C2×C8—472no—
110C2×C8C22×D4711yescharacteristic
111C2×C8C22×D4711yescharacteristic
112C4⋊C4—22no—
113C4⋊C4—472no—
114C4⋊C4—471no—
115C4⋊C4—474no—
116C4⋊C4—944no—
117C4⋊C4—944no—
118C4⋊C4—944no—
119C4⋊C4—942no—
120C4⋊C4C22×D4712yes—
121C42—22no—
122C42—472no—
123C42—944no—
124C42C22×D4711yescharacteristic
125Q8—22no—
126Q8—942no—
127Q8—1884no—
128Q8C2×Dic9414yes—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—472no—
132C2×C4—472no—
133C2×C4—944no—
134C2×C4D4×D4711yescharacteristic
135C2×C4D4×D4711yescharacteristic
136C2×C4C23×D4711yescharacteristic
137C8—21no—
138C8—942no—
139C8C2×Dic9412yes—
140C22C2×D4×D4711yescharacteristic
141C4—24no—
142C4—21no—
143C4—42no—
144C4—942no—
145C4—942no—
146C4—1884no—
147C4#1309404712yes—
148C4C22×Dic9411yescharacteristic
149C4#1309407111yescharacteristic
150C2D4×Dic9411yescharacteristic
151C2C2×#1309404711yescharacteristic
152C2#1568993711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×Q16×C47C2
socleC22×C47C22×D4
hypercenterC4×Q16D47
hypocenterC47#3383
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
31. Q16×C47Q8semidirect
85. C47#3383semidirect
108. Q16Dic94semidirect