Finite Group Databasebeta

← #20241819

Subgroups — #20241819

Order 6016.

246 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C4×#10625352C211yesmaximal, characteristic
2#15689179C211yesmaximal, characteristic, complemented
3#15689174C211yesmaximal, characteristic, complemented
4#15688855C211yesmaximal, characteristic, complemented
5#15688853C211yesmaximal, characteristic, complemented
6D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
7C47×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10625352C411yescharacteristic
9C4×Dic94C2211yescharacteristic
10#13093989C411yescharacteristic
11D4×Dic47C411yescharacteristic
12C4×C22⋊D47—21no—
13(C22⋊D47)⋊C4—21no—
14#13093982C411yescharacteristic
15#13093980—21no—
16C2×C4×Dic47—21no—
17C42×D47C2211yescharacteristic
18C4⋊(C47⋊C8)C2211yescharacteristic
19Dic47⋊C8—21no—
20(C2×D47)⋊C8—21no—
21(C2×D47)⋊C8—21no—
22#13093934—21no—
23C4×C47⋊C8C2211yescharacteristic
24C4×D4×C47C2211yescharacteristic
25C4⋊C8×C47C2211yescharacteristic
26C4×C8×C47C2211yescharacteristic
27C2×D4×C47C2×C411yescharacteristic
28C22×C4×C47—21no—
29C2×C22⋊D47—21no—
30C22×Dic47—21no—
31C22×Dic47—21no—
32#10625352—22no—
33#10625352—22no—
34C2×C4×D47C2×C411yescharacteristic
35C2×C4×D47D411yescharacteristic
36C2×C4×D47D411yescharacteristic
37C2×Dic94C2×C411yescharacteristic
38C2×C8×C47—21no—
39C2×C8×C47—21no—
40C4⋊C4×C47C2×C411yescharacteristic
41C22⋊C4×C47—21no—
42C42×C47C2311yescharacteristic
43C22⋊Dic47—21no—
44(C2×D47)⋊C4—21no—
45C4⋊Dic47C2×C411yescharacteristic
46Dic47⋊C4—21no—
47Dic47⋊C4—21no—
48C4×Dic47—21no—
49C4×Dic47—21no—
50C4×Dic47—21no—
51C4×Dic47C2×C411yescharacteristic
52C4×Dic47D411yescharacteristic
53C4×Dic47D411yescharacteristic
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C23×C47—21no—
57C22×D47C22⋊C411yescharacteristic
58D4×C47—21no—
59D4×C47M1612yes—
60C2×C4×C47—21no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47C22×C411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C22⋊D47—24no—
67C2×Dic47—24no—
68C2×Dic47—21no—
69C2×Dic47—21no—
70C2×Dic47—42no—
71C2×Dic47C22⋊C411yescharacteristic
72C2×Dic47C22⋊C411yescharacteristic
73C2×Dic47C22⋊C411yescharacteristic
74C4×D47—21no—
75C4×D47—21no—
76C4×D47—21no—
77C4×D47—21no—
78C4×D47—41no—
79Dic94—21no—
80Dic94M1612yes—
81C8×C47—41no—
82C8×C47—41no—
83C47⋊C8—41no—
84C47⋊C8—41no—
85C22×C47—22no—
86C22×C47—41no—
87C22×C47—41no—
88C22×C47C2×C22⋊C411yescharacteristic
89C2×D47—21no—
90C2×D47—21no—
91C2×D47—21no—
92C4×C47—21no—
93C4×C47—41no—
94C4×C47C2×M1611yescharacteristic
95C4×C47C2×M1611yescharacteristic
96C4×C47#13511yescharacteristic
97C4×C47#13511yescharacteristic
98Dic47—22no—
99Dic47—21no—
100Dic47—21no—
101Dic47—21no—
102Dic47—41no—
103#1488—471nomaximal, Sylow
104C2×C47—42no—
105C2×C47#40711yescharacteristic
106C2×C47#41611yescharacteristic
107C2×C47#42111yescharacteristic
108D47—41no—
109C4×#41—471no—
110#432—471no—
111#431—471no—
112Q8⋊C8—471no—
113Q8⋊C8—471no—
114D4⋊C8—471no—
115D4⋊C8D4711yescharacteristic, complemented
116C47#148811yescharacteristic, complemented, Sylow
117C2×#41—471no—
118C4×Q8—471no—
119C4×Q8—471no—
120C4×D4—471no—
121C4×D4—941no—
122C4×D4—941no—
123C4×D4C2×D4711yescharacteristic
124#117—471no—
125#117—941no—
126C2×C42—471no—
127C2×C42—941no—
128C4⋊C8—471no—
129C4⋊C8—941no—
130C4⋊C8C2×D4711yescharacteristic
131C22⋊C8—941no—
132C22⋊C8—941no—
133#97—941no—
134C4×C8—471no—
135C4×C8C2×D4711yescharacteristic
136#41—942no—
137#41—942no—
138C2×Q8—471no—
139C2×D4—941no—
140C2×D4C4×D4711yescharacteristic
141C22×C4—21no—
142C22×C4—471no—
143C22×C4—471no—
144C22×C4—471no—
145C22×C4—941no—
146C22×C4—941no—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—941no—
150C2×C8—941no—
151C4⋊C4—471no—
152C4⋊C4—941no—
153C4⋊C4—941no—
154C4⋊C4C4×D4711yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—941no—
157C22⋊C4—941no—
158C42—471no—
159C42—471no—
160C42—471no—
161C42—941no—
162C42—941no—
163C42—941no—
164C42C22×D4711yescharacteristic
165C23—21no—
166C23—471no—
167Q8—472no—
168Q8—941no—
169D4—21no—
170D4—944no—
171D4#1062532412yes—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—471no—
176C2×C4—471no—
177C2×C4—471no—
178C2×C4—944no—
179C2×C4—941no—
180C2×C4—941no—
181C2×C4—941no—
182C2×C4—941no—
183C2×C4—941no—
184C2×C4—941no—
185C2×C4—1881no—
186C2×C4—1882no—
187C2×C4C2×C4×D4711yescharacteristic
188C2×C4D4×D4711yescharacteristic
189C2×C4D4×D4711yescharacteristic
190C8—41no—
191C8—41no—
192C8—1881no—
193C8—1881no—
194C22—22no—
195C22—41no—
196C22—41no—
197C22—941no—
198C22—941no—
199C22—941no—
200C22C22⋊C4×D4711yescharacteristic
201C4—21no—
202C4—41no—
203C4—941no—
204C4—942no—
205C4—941no—
206C4—941no—
207C4—1881no—
208C4M16×D4711yescharacteristic
209C4C2×#1062532411yescharacteristic
210C4#1309404311yescharacteristic
211C4#1309404511yescharacteristic
212C2—42no—
213C2—1881no—
214C2#1568908511yescharacteristic
215C2#1568911611yescharacteristic
216C2#1568913811yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×D4⋊C8C2
socleC22×C47C2×C22⋊C4
hypercenterD4⋊C8D47
hypocenterC47#1488
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #15689179C2semidirect
3. #15689174C2semidirect
4. #15688855C2semidirect
5. #15688853C2semidirect
6. D4⋊(C47⋊C8)C2semidirect
7. C47×D4⋊C8C2semidirect
115. D4⋊C8D47semidirect
116. C47#1488semidirect