Finite Group Databasebeta

← #20244373

Subgroups — #20244373

Order 6016.

324 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 97 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×#13094003C211yesmaximal, characteristic
2#15688983C211yesmaximal, characteristic
3#15688889C214yesmaximal
4C4×C22⋊C4×C47C211yesmaximal, characteristic
5C22×Dic94C411yescharacteristic, complemented
6#13094003—21no—
7#13094003—21no—
8#13094003—21no—
9#13094003—21no—
10C2×C4⋊Dic47—21no—
11C2×C4⋊Dic47C411yescharacteristic, complemented
12C2×Dic47⋊C4C412yescomplemented
13C2×C22⋊Dic47C2212yes—
14C2×C22⋊Dic47C2212yes—
15C47⋊#95—21no—
16C23×C4×C47C2211yescharacteristic
17C2×C22⋊C4×C47C2212yes—
18C2×C42×C47—21no—
19#95×C47—21no—
20C24×C47C2311yescharacteristic
21C22×C4×C47—22no—
22C22×C4×C47—42no—
23C22×C4×C47C2×C411yescharacteristic
24C22×C4×C47C2×C411yescharacteristic
25C22×C4×C47D411yescharacteristic
26C22×C4×C47D411yescharacteristic
27C22×C4×C47D411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×Dic47—22no—
30C22×Dic47C2×C412yes—
31C22×Dic47C2×C412yes—
32C2×Dic94—21no—
33C2×Dic94—21no—
34C2×Dic94—42no—
35C22⋊C4×C47—22no—
36C22⋊C4×C47Q814yescomplemented
37C42×C47—42no—
38C22⋊Dic47—22no—
39C22⋊Dic47—22no—
40C22⋊Dic47—24no—
41C4⋊Dic47—21no—
42C4⋊Dic47—21no—
43C4⋊Dic47—42no—
44Dic47⋊C4—22no—
45Dic47⋊C4—22no—
46C23×C47—41no—
47C23×C47—41no—
48C23×C47C22×C411yescharacteristic
49C23×C47C2×D411yescharacteristic
50C23×C47C2×D411yescharacteristic
51C23×C47C2×Q812yes—
52C23×C47#4112yes—
53C2×C4×C47—22no—
54C2×C4×C47—22no—
55C2×C4×C47—22no—
56C2×C4×C47—24no—
57C2×C4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47—42no—
61C2×C4×C47—42no—
62C2×C4×C47C22⋊C411yescharacteristic
63C2×C4×C47C22⋊C411yescharacteristic
64C2×C4×C47C22⋊C411yescharacteristic
65C2×C4×C47C22⋊C411yescharacteristic
66C2×Dic47—22no—
67C2×Dic47—22no—
68C2×Dic47—42no—
69C2×Dic47—42no—
70C2×Dic47—42no—
71C2×Dic47—42no—
72C2×Dic47—42no—
73Dic94—42no—
74Dic94—42no—
75C22×C47—21no—
76C22×C47—21no—
77C22×C47—21no—
78C22×C47—21no—
79C22×C47—21no—
80C22×C47—21no—
81C22×C47—42no—
82C22×C47—42no—
83C22×C47C2×C22⋊C411yescharacteristic
84C22×C47C4×Q812yes—
85C22×C47C22⋊Q812yes—
86C22×C47#12411yescharacteristic
87C22×C47C4⋊Q811yescharacteristic
88C4×C47—21no—
89C4×C47—21no—
90C4×C47—21no—
91C4×C47—44no—
92C4×C47#9912yes—
93Dic47—42no—
94Dic47—42no—
95Dic47—82no—
96#1996—471nomaximal, Sylow
97C2×C47—21no—
98C2×C47—22no—
99C2×C47—22no—
100C2×C47—21no—
101C2×C47#39111yescharacteristic
102C2×C47C2×#9911yescharacteristic
103C2×C47#41011yescharacteristic
104C2×C22⋊Q8—471no—
105#380—471no—
106C4×C22⋊C4D4711yescharacteristic
107#342—474no—
108C47#199611yescharacteristic, complemented, Sylow
109C22×Q8—471no—
110C23×C4C2×D4711yescharacteristic
111C22⋊Q8—941no—
112C22⋊Q8—941no—
113C22⋊Q8—941no—
114C22⋊Q8—941no—
115C2×C4⋊C4—472no—
116C2×C4⋊C4—471no—
117C2×C4⋊C4—941no—
118C2×C22⋊C4—472no—
119C2×C22⋊C4—472no—
120C2×C22⋊C4C2×D4712yes—
121C2×C42—21no—
122#95—21no—
123#95—941no—
124C24C22×D4711yescharacteristic
125C2×Q8—941no—
126C2×Q8—941no—
127C2×Q8—1882no—
128C22×C4—22no—
129C22×C4—42no—
130C22×C4—472no—
131C22×C4—472no—
132C22×C4—942no—
133C22×C4C4×D4711yescharacteristic
134C22×C4C4×D4711yescharacteristic
135C22×C4D18811yescharacteristic
136C22×C4D18811yescharacteristic
137C22×C4C22⋊D4711yescharacteristic
138C22×C4C22⋊D4711yescharacteristic
139C4⋊C4—942no—
140C4⋊C4—942no—
141C4⋊C4—941no—
142C4⋊C4—941no—
143C4⋊C4—1882no—
144C22⋊C4—22no—
145C22⋊C4—942no—
146C22⋊C4—942no—
147C22⋊C4—944no—
148C22⋊C4Dic9414yescomplemented
149C42—42no—
150C23—41no—
151C23—41no—
152C23C2×Dic9412yes—
153C23C2×C4×D4711yescharacteristic
154C23C2×D18811yescharacteristic
155C23#1062535012yes—
156C23C2×C22⋊D4711yescharacteristic
157Q8—1882no—
158Q8—1882no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—24no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—942no—
169C2×C4—942no—
170C2×C4—1882no—
171C2×C4—1882no—
172C2×C4—1882no—
173C2×C4—1882no—
174C2×C4—1882no—
175C2×C4(C2×D47)⋊C411yescharacteristic
176C2×C4(C2×D47)⋊C411yescharacteristic
177C2×C4(C2×D47)⋊C411yescharacteristic
178C2×C4(C2×D47)⋊C411yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—42no—
186C22—42no—
187C22C2×(C2×D47)⋊C411yescharacteristic
188C22C4×Dic9412yes—
189C22#1309400312yes—
190C22#1309401211yescharacteristic
191C22#1309402411yescharacteristic
192C4—21no—
193C4—21no—
194C4—21no—
195C4—44no—
196C4—3762no—
197C4—1882no—
198C4—1882no—
199C4#1309393812yes—
200C2—22no—
201C2—21no—
202C2—22no—
203C2—21no—
204C2#1568902911yescharacteristic
205C2C2×#1309393811yescharacteristic
206C2#1568909611yescharacteristic
subgroupG/H
centerC22C2×(C2×D47)⋊C4
commutatorC23×C47C22×C4
FrattiniC24C22×D47
FittingC4×C22⋊C4×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC4×C22⋊C4D47
hypocenterC47#1996
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. C22×Dic94C4semidirect
11. C2×C4⋊Dic47C4semidirect
12. C2×Dic47⋊C4C4semidirect
36. C22⋊C4×C47Q8semidirect
108. C47#1996semidirect
148. C22⋊C4Dic94semidirect