Finite Group Databasebeta

← #20244122

Subgroups — #20244122

Order 6016.

248 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 117 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×#13093958C211yesmaximal, characteristic
2C2×C8×Dic47C211yesmaximal, characteristic
3#15689022C212yesmaximal
4#15688885C212yesmaximal
5C2×#107×C47C211yesmaximal, characteristic
6C22×C47⋊C8C2211yescharacteristic
7C2×C4⋊Dic47—22no—
8C2×C4⋊Dic47C2212yes—
9C2×C4×Dic47C2211yescharacteristic
10#13093958—22no—
11C8×Dic47—22no—
12C47⋊#95—22no—
13C22×C8×C47C2211yescharacteristic
14C2×C4⋊C4×C47C2212yes—
15#107×C47C414yescomplemented
16C22×C4×C47—22no—
17C22×C4×C47C2311yescharacteristic
18C22×Dic47—22no—
19C22×Dic47D411yescharacteristic
20C22×Dic47D411yescharacteristic
21C2×C8×C47C2×C412yes—
22C2×C8×C47D412yes—
23C2×C8×C47Q812yes—
24C4⋊C4×C47—22no—
25C4⋊C4×C47C2×C414yes—
26C4⋊Dic47—22no—
27C4⋊Dic47—22no—
28C4⋊Dic47—44no—
29C4×Dic47—21no—
30C4×Dic47—21no—
31C2×C47⋊C8—21no—
32C2×C47⋊C8—21no—
33C2×C47⋊C8Q812yes—
34C23×C47C2×D411yescharacteristic
35C2×C4×C47—24no—
36C2×C4×C47—42no—
37C2×C4×C47—42no—
38C2×C4×C47C22×C411yescharacteristic
39C2×C4×C47C2×D411yescharacteristic
40C2×C4×C47C2×Q811yescharacteristic
41C2×C4×C47C2×Q811yescharacteristic
42C2×C4×C47#4111yescharacteristic
43C2×C4×C47#4111yescharacteristic
44C2×Dic47—21no—
45C2×Dic47—21no—
46C2×Dic47—21no—
47C2×Dic47—21no—
48C2×Dic47—42no—
49C2×Dic47—42no—
50C2×Dic47—42no—
51C2×Dic47D812yes—
52C2×Dic47Q1612yes—
53C8×C47C4⋊C414yescomplemented
54C47⋊C8—22no—
55C22×C47C4×D411yescharacteristic
56C22×C47#12111yescharacteristic
57C22×C47C4⋊Q811yescharacteristic
58C22×C47C2×D811yescharacteristic
59C22×C47C2×Q1611yescharacteristic
60C22×C47#13511yescharacteristic
61C22×C47#13511yescharacteristic
62C4×C47—44no—
63C4×C47C2×C4⋊C411yescharacteristic
64C4×C47C4×Q811yescharacteristic
65C4×C47C22⋊Q811yescharacteristic
66C4×C47#12511yescharacteristic
67Dic47—22no—
68Dic47—22no—
69Dic47—82no—
70#1942—471nomaximal, Sylow
71C2×C47#38911yescharacteristic
72C2×C47C4×D811yescharacteristic
73C2×C47C4×Q1611yescharacteristic
74C2×C47#46611yescharacteristic
75C2×C47#46711yescharacteristic
76C2×C47#49911yescharacteristic
77C2×C47#50011yescharacteristic
78C2×#107—471no—
79C2×#107D4711yescharacteristic
80C2×C4×C8—471no—
81#389—472no—
82#340—472no—
83C47#194211yescharacteristic, complemented, Sylow
84C22×C8—471no—
85C22×C8C2×D4711yescharacteristic
86C2×C4⋊C4—472no—
87C2×C4⋊C4—942no—
88C2×C4⋊C4C2×D4712yes—
89C2×C42—471no—
90#107—942no—
91#107Dic4714yescomplemented
92C4×C8—942no—
93#95—942no—
94C22×C4—22no—
95C22×C4—471no—
96C22×C4—471no—
97C22×C4—942no—
98C22×C4C22×D4711yescharacteristic
99C2×C8—472no—
100C2×C8—941no—
101C2×C8—941no—
102C2×C8Dic9412yes—
103C2×C8D18812yes—
104C2×C8C2×Dic4712yes—
105C4⋊C4—22no—
106C4⋊C4—942no—
107C4⋊C4—942no—
108C4⋊C4—1884no—
109C4⋊C4C2×Dic4714yes—
110C42—941no—
111C42—941no—
112C23D4×D4711yescharacteristic
113C2×C4—24no—
114C2×C4—42no—
115C2×C4—42no—
116C2×C4—472no—
117C2×C4—472no—
118C2×C4—941no—
119C2×C4—941no—
120C2×C4—941no—
121C2×C4—941no—
122C2×C4—1882no—
123C2×C4—1882no—
124C2×C4—1882no—
125C2×C4C2×Dic9411yescharacteristic
126C2×C4C2×D18811yescharacteristic
127C2×C4#1062535211yescharacteristic
128C2×C4Q8×D4711yescharacteristic
129C2×C4#1062535411yescharacteristic
130C2×C4C22×Dic4711yescharacteristic
131C8—942no—
132C8C4⋊Dic4714yescomplemented
133C22D4×Dic4711yescharacteristic
134C22#1309399911yescharacteristic
135C22#1309402311yescharacteristic
136C22D8×D4711yescharacteristic
137C22Q16×D4711yescharacteristic
138C22#1309404311yescharacteristic
139C22#1309404711yescharacteristic
140C4—44no—
141C4—942no—
142C4—942no—
143C4—3762no—
144C4C2×C4⋊Dic4711yescharacteristic
145C4Q8×Dic4711yescharacteristic
146C4#1309400411yescharacteristic
147C4#1309401511yescharacteristic
148C2#1568902211yescharacteristic
149C2D8×Dic4711yescharacteristic
150C2Q16×Dic4711yescharacteristic
151C2#1568936011yescharacteristic
152C2#1568936511yescharacteristic
153C2#1568952411yescharacteristic
154C2#1568952711yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#107×C47C2
socleC23×C47C2×D4
hypercenterC2×#107D47
hypocenterC47#1942
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
15. #107×C47C4semidirect
53. C8×C47C4⋊C4semidirect
83. C47#1942semidirect
91. #107Dic47semidirect
132. C8C4⋊Dic47semidirect