Finite Group Databasebeta

← #20241801

Subgroups — #20241801

Order 6016.

234 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 85 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×C4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
2C4×#10625329C211yesmaximal, characteristic, complemented
3Q8⋊(C47⋊C8)C212yesmaximal, complemented
4D4⋊(C47⋊C8)C212yesmaximal, complemented
5C47×#529C211yesmaximal, characteristic
6C2×#10625329—21no—
7C22×C47⋊C8—21no—
8C4⋊(C47⋊C8)—21no—
9C4⋊(C47⋊C8)C2212yes—
10#13093935—21no—
11C4×C47⋊C8C2212yes—
12#126×C47—21no—
13#125×C47C411yescharacteristic
14#124×C47C411yescharacteristic
15#123×C47—21no—
16C22⋊Q8×C47C411yescharacteristic
17#121×C47C411yescharacteristic
18C4×Q8×C47C2211yescharacteristic
19C4×D4×C47—21no—
20C4×D4×C47C2211yescharacteristic
21#117×C47—21no—
22C2×C42×C47C2211yescharacteristic
23C2×Q8×C47C2×C411yescharacteristic
24C2×D4×C47—21no—
25C2×D4×C47C2×C411yescharacteristic
26C22×C4×C47—21no—
27C22×C4×C47C2×C411yescharacteristic
28C22×C4×C47D411yescharacteristic
29C22×C4×C47D411yescharacteristic
30C4⋊C4×C47—21no—
31C4⋊C4×C47—21no—
32C4⋊C4×C47—21no—
33C4⋊C4×C47—21no—
34C4⋊C4×C47C2×C411yescharacteristic
35C4⋊C4×C47C2×C411yescharacteristic
36C22⋊C4×C47—21no—
37C22⋊C4×C47—21no—
38C22⋊C4×C47—21no—
39C22⋊C4×C47—21no—
40C22⋊C4×C47—21no—
41C42×C47—21no—
42C42×C47C2×C411yescharacteristic
43C42×C47D411yescharacteristic
44C42×C47D411yescharacteristic
45C42×C47C2311yescharacteristic
46#10625329—24no—
47C2×C47⋊C8—22no—
48C2×C47⋊C8—22no—
49C2×C47⋊C8—42no—
50C23×C47—21no—
51C23×C47C22⋊C411yescharacteristic
52Q8×C47—22no—
53D4×C47—22no—
54D4×C47—42no—
55C2×C4×C47—22no—
56C2×C4×C47—22no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47C22⋊C411yescharacteristic
65C2×C4×C47C22⋊C411yescharacteristic
66C2×C4×C47C22⋊C411yescharacteristic
67C2×C4×C47C22×C411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C47⋊C8—24no—
71C47⋊C8—42no—
72C22×C47—21no—
73C22×C47—21no—
74C22×C47—41no—
75C22×C47—41no—
76C22×C47—41no—
77C22×C47#10412yes—
78C22×C47C2×C22⋊C411yescharacteristic
79C4×C47—21no—
80C4×C47—21no—
81C4×C47—21no—
82C4×C47—21no—
83C4×C47—41no—
84C4×C47—41no—
85C4×C47—41no—
86C4×C47#13112yes—
87C4×C47AGL(1,ℤ/8)11yescharacteristic
88C4×C47#13711yescharacteristic
89#1483—471nomaximal, Sylow
90C2×C47—22no—
91C2×C47—81no—
92C2×C47#40811yescharacteristic
93C2×C47#41711yescharacteristic
94C2×C47C2×#10411yescharacteristic
95#529D4711yescharacteristic
96C2×C4⋊C8—471no—
97C4×M16—471no—
98Q8⋊C8—472no—
99D4⋊C8—472no—
100C47#148311yescharacteristic, complemented, Sylow
101C2×M16—941no—
102C22×C8—941no—
103#126—21no—
104#125Dic4711yescharacteristic
105#124Dic4711yescharacteristic
106#123—21no—
107C22⋊Q8Dic4711yescharacteristic
108#121Dic4711yescharacteristic
109C4×Q8C2×D4711yescharacteristic
110C4×D4—21no—
111C4×D4C2×D4711yescharacteristic
112#117—21no—
113C2×C42C2×D4711yescharacteristic
114C4⋊C8—472no—
115C4⋊C8—941no—
116#97—941no—
117C4×C8—472no—
118C2×Q8C2×Dic4711yescharacteristic
119C2×D4—21no—
120C2×D4C2×Dic4711yescharacteristic
121C22×C4—21no—
122C22×C4C2×Dic4711yescharacteristic
123C22×C4C22⋊D4711yescharacteristic
124C22×C4C22⋊D4711yescharacteristic
125M16—944no—
126C2×C8—942no—
127C2×C8—942no—
128C2×C8—1882no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4C2×Dic4711yescharacteristic
134C4⋊C4C2×Dic4711yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—21no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C42—21no—
141C42C2×Dic4711yescharacteristic
142C42C22⋊D4711yescharacteristic
143C42C22⋊D4711yescharacteristic
144C42C22×D4711yescharacteristic
145C23—21no—
146C23C22⋊Dic4711yescharacteristic
147Q8—22no—
148D4—22no—
149D4—42no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4C22⋊Dic4711yescharacteristic
160C2×C4C22⋊Dic4711yescharacteristic
161C2×C4C22⋊Dic4711yescharacteristic
162C2×C4C22×Dic4711yescharacteristic
163C2×C4C2×C22⋊D4711yescharacteristic
164C2×C4C2×C22⋊D4711yescharacteristic
165C8—944no—
166C8—1882no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22#1309395112yes—
173C22C2×C22⋊Dic4711yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—41no—
179C4—41no—
180C4—41no—
181C4#1309403112yes—
182C4#1309404911yescharacteristic
183C4#1309405411yescharacteristic
184C2—22no—
185C2—81no—
186C2#1568909011yescharacteristic
187C2#1568912411yescharacteristic
188C2C2×#1309395111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#529C2
socleC22×C47C2×C22⋊C4
hypercenter#529D47
hypocenterC47#1483
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊(C47⋊C8)C2semidirect
2. C4×#10625329C2semidirect
3. Q8⋊(C47⋊C8)C2semidirect
4. D4⋊(C47⋊C8)C2semidirect
100. C47#1483semidirect