Finite Group Databasebeta

← #20241798

Subgroups — #20241798

Order 6016.

234 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 67 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#15689655C211yesmaximal, characteristic
2C4⋊C8×D47C211yesmaximal, characteristic, complemented
3C4×#10625324C211yesmaximal, characteristic, complemented
4#15688855C211yesmaximal, characteristic, complemented
5#15688853C211yesmaximal, characteristic, complemented
6D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
7C47×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#10625324—21no—
9C2×C8×D47—21no—
10#13094017—21no—
11#13094015C411yescharacteristic
12#13094011C411yescharacteristic
13#13094006—21no—
14#13094004C411yescharacteristic
15#13093995C411yescharacteristic
16C4×Dic94C2211yescharacteristic
17C4×C22⋊D47—21no—
18#13093983—21no—
19C42×D47C2211yescharacteristic
20C4⋊(C47⋊C8)C2211yescharacteristic
21Dic47⋊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—
30C2×C4×D47C2×C411yescharacteristic
31C2×C4×D47D411yescharacteristic
32C2×C4×D47D411yescharacteristic
33C2×Dic94C2×C411yescharacteristic
34C2×C8×C47—21no—
35C2×C8×C47—21no—
36C4⋊C4×C47C2×C411yescharacteristic
37C22⋊C4×C47—21no—
38C42×C47C2311yescharacteristic
39C22⋊Dic47—21no—
40C22⋊Dic47—21no—
41C22⋊Dic47—21no—
42(C2×D47)⋊C4—21no—
43C4⋊Dic47—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47C2×C411yescharacteristic
46Dic47⋊C4—21no—
47Dic47⋊C4—21no—
48C4×Dic47—21no—
49C4×Dic47C2×C411yescharacteristic
50C4×Dic47D411yescharacteristic
51C4×Dic47D411yescharacteristic
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54#10625324—24no—
55C8×D47—42no—
56C23×C47—21no—
57C22×D47C22⋊C411yescharacteristic
58D4×C47—21no—
59D4×C47—21no—
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—42no—
67C2×Dic47—21no—
68C2×Dic47—21no—
69C2×Dic47C22⋊C411yescharacteristic
70C2×Dic47C22⋊C411yescharacteristic
71C2×Dic47C22⋊C411yescharacteristic
72C4×D47—22no—
73C4×D47—21no—
74C4×D47—21no—
75C4×D47—21no—
76C4×D47—21no—
77Dic94—21no—
78Dic94—21no—
79C8×C47—22no—
80C8×C47—41no—
81C47⋊C8—22no—
82C47⋊C8—41no—
83C22×C47—41no—
84C22×C47—41no—
85C22×C47—41no—
86C22×C47C2×C22⋊C411yescharacteristic
87C2×D47—21no—
88C2×D47—21no—
89C2×D47#10412yes—
90C4×C47—21no—
91C4×C47—41no—
92C4×C47#13111yescharacteristic
93C4×C47#13111yescharacteristic
94C4×C47AGL(1,ℤ/8)11yescharacteristic
95C4×C47#13711yescharacteristic
96Dic47—21no—
97Dic47—21no—
98Dic47—21no—
99Dic47—41no—
100Dic47—41no—
101#1483—471nomaximal, Sylow
102C2×C47—81no—
103C2×C47#40811yescharacteristic
104C2×C47#41711yescharacteristic
105C2×C47C2×#10411yescharacteristic
106D47—22no—
107#529—471no—
108C2×C4⋊C8—471no—
109C4×M16—471no—
110Q8⋊C8—471no—
111Q8⋊C8—471no—
112D4⋊C8—471no—
113D4⋊C8D4711yescharacteristic, complemented
114C47#148311yescharacteristic, complemented, Sylow
115C2×M16—941no—
116C22×C8—941no—
117#126—941no—
118#125—471no—
119#124—471no—
120#123—941no—
121C22⋊Q8—471no—
122#121—471no—
123C4×Q8—471no—
124C4×D4—941no—
125C4×D4C2×D4711yescharacteristic
126#117—941no—
127C2×C42—471no—
128C4⋊C8—471no—
129C4⋊C8—941no—
130C4⋊C8C2×D4711yescharacteristic
131#97—941no—
132C4×C8—471no—
133C4×C8C2×D4711yescharacteristic
134C2×Q8—471no—
135C2×D4—941no—
136C2×D4C4×D4711yescharacteristic
137C22×C4—21no—
138C22×C4—471no—
139C22×C4—471no—
140C22×C4—471no—
141M16—944no—
142C2×C8—21no—
143C2×C8—21no—
144C2×C8—941no—
145C2×C8—941no—
146C2×C8—1882no—
147C4⋊C4—471no—
148C4⋊C4—941no—
149C4⋊C4—941no—
150C4⋊C4—941no—
151C4⋊C4—941no—
152C4⋊C4C4×D4711yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—941no—
155C22⋊C4—941no—
156C22⋊C4—941no—
157C22⋊C4—941no—
158C42—471no—
159C42—471no—
160C42—471no—
161C42—941no—
162C42C22×D4711yescharacteristic
163C23—21no—
164C23—471no—
165Q8—941no—
166Q8—941no—
167D4—21no—
168D4—21no—
169D4—1882no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—471no—
174C2×C4—471no—
175C2×C4—471no—
176C2×C4—942no—
177C2×C4—941no—
178C2×C4—941no—
179C2×C4—941no—
180C2×C4—941no—
181C2×C4—941no—
182C2×C4—941no—
183C2×C4C2×C4×D4711yescharacteristic
184C2×C4D4×D4711yescharacteristic
185C2×C4D4×D4711yescharacteristic
186C8—22no—
187C8—41no—
188C8—942no—
189C8—1881no—
190C22—41no—
191C22—41no—
192C22—41no—
193C22—472no—
194C22—941no—
195C22—941no—
196C22C22⋊C4×D4711yescharacteristic
197C4—21no—
198C4—41no—
199C4—941no—
200C4—941no—
201C4—941no—
202C4—1881no—
203C4—1881no—
204C4#1309403011yescharacteristic
205C4#1309403211yescharacteristic
206C4#1309404811yescharacteristic
207C4#1309405311yescharacteristic
208C2—81no—
209C2—942no—
210C2#1568908811yescharacteristic
211C2#1568912111yescharacteristic
212C2#104×D4711yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×D4⋊C8C2
socleC22×C47C2×C22⋊C4
hypercenterD4⋊C8D47
hypocenterC47#1483
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. C4⋊C8×D47C2semidirect
3. C4×#10625324C2semidirect
4. #15688855C2semidirect
5. #15688853C2semidirect
6. D4⋊(C47⋊C8)C2semidirect
7. C47×D4⋊C8C2semidirect
113. D4⋊C8D47semidirect
114. C47#1483semidirect