Finite Group Databasebeta

← #20243492

Subgroups — #20243492

Order 6016.

262 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 89 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#15689107C211yesmaximal, characteristic
2#15689097C211yesmaximal, characteristic
3#15688883C212yesmaximal, complemented
4#15688879C212yesmaximal, complemented
5C4×#41×C47C211yesmaximal, characteristic
6C2×#10625329C2212yes—
7#13093983C2212yes—
8#13093943—21no—
9#13093941—21no—
10#13093939—22no—
11C2×#41×C47C2211yescharacteristic
12C4×Q8×C47—21no—
13C4×D4×C47—22no—
14C4×D4×C47—21no—
15#117×C47C412yescomplemented
16#117×C47C2211yescharacteristic
17C2×C42×C47C412yescomplemented
18C2×C42×C47C2211yescharacteristic
19#41×C47—22no—
20#41×C47—22no—
21C2×Q8×C47D411yescharacteristic
22C2×D4×C47D412yes—
23C2×D4×C47D411yescharacteristic
24C22×C4×C47—22no—
25C22×C4×C47—21no—
26C22×C4×C47C2×C412yes—
27C22×C4×C47C2311yescharacteristic
28C4⋊C4×C47—22no—
29C4⋊C4×C47—21no—
30C22⋊C4×C47—22no—
31C22⋊C4×C47—21no—
32C42×C47—22no—
33C42×C47—21no—
34C42×C47C2×C411yescharacteristic
35C42×C47C2×C412yes—
36C42×C47C2×C411yescharacteristic
37C22⋊Dic47—22no—
38C4⋊Dic47—22no—
39C4×Dic47—22no—
40#10625329—22no—
41#10625329—22no—
42C2×C47⋊C8—22no—
43C23×C47C22⋊C412yes—
44C23×C47C2×D411yescharacteristic
45Q8×C47—22no—
46D4×C47—24no—
47D4×C47—22no—
48C2×C4×C47—21no—
49C2×C4×C47—22no—
50C2×C4×C47—22no—
51C2×C4×C47—22no—
52C2×C4×C47—21no—
53C2×C4×C47—42no—
54C2×C4×C47—44no—
55C2×C4×C47C22⋊C412yes—
56C2×C4×C47C22×C411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47#4112yes—
59C2×C4×C47#4112yes—
60C2×Dic47—42no—
61C47⋊C8—42no—
62C22×C47—22no—
63C22×C47—41no—
64C22×C47—42no—
65C22×C47C2×C22⋊C411yescharacteristic
66C22×C47#12312yes—
67C4×C47—22no—
68C4×C47—22no—
69C4×C47—42no—
70C4×C47—41no—
71C4×C47#11711yescharacteristic
72C4×C47#11711yescharacteristic
73C4×C47#12312yes—
74Dic47—82no—
75#1827—471nomaximal, Sylow
76C2×C47—22no—
77C2×C47—21no—
78C2×C47—42no—
79C2×C47#38111yescharacteristic
80C4×#41D4711yescharacteristic
81#413—471no—
82#410—471no—
83#339—472no—
84H(3,ℤ/4)—472no—
85C47#182711yescharacteristic, complemented, Sylow
86C2×#41C2×D4711yescharacteristic
87C2×M16—472no—
88C4×Q8—21no—
89C4×D4—22no—
90C4×D4—21no—
91#117—472no—
92#117Dic4712yescomplemented
93#117C2×D4711yescharacteristic
94C2×C42Dic4712yescomplemented
95C2×C42C2×D4711yescharacteristic
96#101—941no—
97#100—941no—
98#99—942no—
99#41—22no—
100#41—22no—
101C2×Q8C22⋊D4711yescharacteristic
102C2×D4C22⋊D4712yes—
103C2×D4C22⋊D4711yescharacteristic
104C22×C4—22no—
105C22×C4—21no—
106C22×C4C2×Dic4712yes—
107C22×C4C22×D4711yescharacteristic
108M16—942no—
109M16—942no—
110C2×C8—942no—
111C4⋊C4—22no—
112C4⋊C4—21no—
113C4⋊C4—942no—
114C22⋊C4—22no—
115C22⋊C4—21no—
116C22⋊C4—942no—
117C42—22no—
118C42—21no—
119C42—942no—
120C42C2×Dic4711yescharacteristic
121C42C2×Dic4712yes—
122C42C2×Dic4711yescharacteristic
123C23C22⋊Dic4712yes—
124C23C2×C22⋊D4711yescharacteristic
125Q8—22no—
126D4—24no—
127D4—22no—
128C2×C4—21no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—21no—
133C2×C4—42no—
134C2×C4—44no—
135C2×C4—1882no—
136C2×C4C22⋊Dic4712yes—
137C2×C4#1062535012yes—
138C2×C4#1062535012yes—
139C2×C4C22×Dic4711yescharacteristic
140C2×C4C2×C22⋊D4711yescharacteristic
141C8—1882no—
142C22—22no—
143C22—41no—
144C22—42no—
145C22C2×C22⋊Dic4711yescharacteristic
146C22#1309400712yes—
147C4—22no—
148C4—22no—
149C4—42no—
150C4—41no—
151C4—3762no—
152C4#1309398311yescharacteristic
153C4#1309398311yescharacteristic
154C4#1309400712yes—
155C2—21no—
156C2—22no—
157C2—42no—
158C2#1568898611yescharacteristic
subgroupG/H
centerC4#13093983
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC4×#41×C47C2
socleC2×C47#381
hypercenterC4×#41D47
hypocenterC47#1827
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ #117 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
3. #15688883C2semidirect
4. #15688879C2semidirect
15. #117×C47C4semidirect
17. C2×C42×C47C4semidirect
85. C47#1827semidirect
92. #117Dic47semidirect
94. C2×C42Dic47semidirect