Finite Group Databasebeta

← #20241925

Subgroups — #20241925

Order 6016.

222 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 61 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#15689659C211yesmaximal, characteristic
2#15689177C211yesmaximal, characteristic, complemented
3#15688987C211yesmaximal, characteristic, complemented
4#15688860C211yesmaximal, characteristic, complemented
5#15688858C211yesmaximal, characteristic
6#15688856C211yesmaximal, characteristic
7C47×#328C211yesmaximal, characteristic, complemented
8#13094019—21no—
9#13094015C411yescharacteristic, complemented
10#13094013C411yescharacteristic, complemented
11#13094008—21no—
12#13093998C2211yescharacteristic
13Q8×Dic47C411yescharacteristic, complemented
14#13093986C411yescharacteristic, complemented
15(C22⋊D47)⋊C4—21no—
16#13093982—21no—
17C2×Dic47⋊C4—21no—
18C2×C4×Dic47C2211yescharacteristic
19Dic47⋊C8—21no—
20C22⋊(C47⋊C8)C2211yescharacteristic
21#13093934—21no—
22C47⋊#95—21no—
23C47⋊#95C2211yescharacteristic
24C22⋊Q8×C47C2211yescharacteristic
25C22⋊C8×C47C2211yescharacteristic
26#95×C47C2211yescharacteristic
27C2×Q8×C47C2×C411yescharacteristic
28C22×C4×C47—21no—
29C22×C4×C47C2311yescharacteristic
30C2×C22⋊D47—21no—
31C22×Dic47—21no—
32C22×Dic47D411yescharacteristic
33C22×Dic47D411yescharacteristic
34C2×D188C2×C411yescharacteristic
35C2×C4×D47—21no—
36C2×C8×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47C2×C411yescharacteristic
39C22⋊C4×C47—21no—
40(C2×D47)⋊C4—21no—
41(C2×D47)⋊C4—21no—
42(C2×D47)⋊C4—21no—
43(C2×D47)⋊C4—21no—
44C4⋊Dic47—21no—
45C4⋊Dic47—21no—
46C4⋊Dic47C2×C411yescharacteristic
47Dic47⋊C4—21no—
48Dic47⋊C4—42no—
49C4×Dic47—21no—
50C4×Dic47C2×C411yescharacteristic
51C4×Dic47C2×C411yescharacteristic
52C4×Dic47D411yescharacteristic
53C4×Dic47D411yescharacteristic
54C2×C47⋊C8—21no—
55C23×C47C2×D411yescharacteristic
56C22×D47—21no—
57Q8×C47—41no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47C22×C411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C22⋊D47—41no—
67C22⋊D47—41no—
68C2×Dic47—21no—
69C2×Dic47—21no—
70C2×Dic47—21no—
71C2×Dic47—41no—
72C2×Dic47—41no—
73C2×Dic47—41no—
74C2×Dic47—41no—
75C2×Dic47C22⋊C411yescharacteristic
76C2×Dic47C22⋊C411yescharacteristic
77C2×Dic47C22⋊C411yescharacteristic
78C2×Dic47C22⋊C411yescharacteristic
79D188—41no—
80C4×D47—42no—
81C8×C47—41no—
82C47⋊C8—41no—
83C22×C47—21no—
84C22×C47—21no—
85C22×C47C2×C22⋊C411yescharacteristic
86C22×C47AGL(1,ℤ/8)11yescharacteristic
87C22×C47#13711yescharacteristic
88C2×D47—41no—
89C2×D47—41no—
90C2×D47—41no—
91C4×C47—21no—
92C4×C47—21no—
93C4×C47—41no—
94C4×C47—41no—
95C4×C47—81no—
96Dic47—21no—
97Dic47—21no—
98Dic47—21no—
99Dic47—21no—
100Dic47—41no—
101Dic47—81no—
102#1512—471nomaximal, Sylow
103C2×C47—21no—
104C2×C47—21no—
105C2×C47#41011yescharacteristic
106C2×C47#41711yescharacteristic
107C2×C47#42111yescharacteristic
108D47—81no—
109#529—471no—
110#432—471no—
111#382—471no—
112#328—471no—
113#328D4711yescharacteristic, complemented
114#327—471no—
115#327—471no—
116C47#151211yescharacteristic, complemented, Sylow
117#126—941no—
118#125—471no—
119#124—471no—
120#123—941no—
121C22⋊Q8C2×D4711yescharacteristic
122#121—471no—
123C4×Q8—471no—
124C4×D4—471no—
125C4×D4—941no—
126#117—941no—
127C2×C4⋊C4—941no—
128C2×C42—471no—
129C4⋊C8—941no—
130C22⋊C8—471no—
131C22⋊C8C2×D4711yescharacteristic
132#97—941no—
133#95—471no—
134#95—941no—
135#95C2×D4711yescharacteristic
136C2×Q8C4×D4711yescharacteristic
137C2×D4—471no—
138C2×D4—941no—
139C22×C4—21no—
140C22×C4—471no—
141C22×C4—471no—
142C22×C4—941no—
143C22×C4—941no—
144C22×C4C22×D4711yescharacteristic
145C2×C8—21no—
146C2×C8—941no—
147C4⋊C4—21no—
148C4⋊C4—471no—
149C4⋊C4—941no—
150C4⋊C4—941no—
151C4⋊C4—941no—
152C4⋊C4—1882no—
153C4⋊C4C4×D4711yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—941no—
156C22⋊C4—941no—
157C22⋊C4—941no—
158C22⋊C4—941no—
159C42—471no—
160C42—471no—
161C42—471no—
162C42—471no—
163C42—941no—
164C23—941no—
165C23D4×D4711yescharacteristic
166Q8—41no—
167D4—1881no—
168D4—1881no—
169D4—1881no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—471no—
177C2×C4—471no—
178C2×C4—471no—
179C2×C4—471no—
180C2×C4—941no—
181C2×C4—941no—
182C2×C4—941no—
183C2×C4—1882no—
184C2×C4—1881no—
185C2×C4—1881no—
186C2×C4—1881no—
187C2×C4—1881no—
188C2×C4C2×C4×D4711yescharacteristic
189C2×C4D4×D4711yescharacteristic
190C8—41no—
191C8—1881no—
192C22—21no—
193C22—21no—
194C22—1881no—
195C22—1881no—
196C22—1881no—
197C22C22⋊C4×D4711yescharacteristic
198C22#1309405111yescharacteristic
199C22#1309405611yescharacteristic
200C4—21no—
201C4—21no—
202C4—41no—
203C4—41no—
204C4—81no—
205C4—941no—
206C4—941no—
207C4—941no—
208C4—941no—
209C4—3761no—
210C4—1881no—
211C2—21no—
212C2—21no—
213C2—3761no—
214C2#1568909511yescharacteristic
215C2#1568912311yescharacteristic
216C2#1568913811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#328C2
socleC22×C47C2×C22⋊C4
hypercenter#328D47
hypocenterC47#1512
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #15689177C2semidirect
3. #15688987C2semidirect
4. #15688860C2semidirect
7. C47×#328C2semidirect
9. #13094015C4semidirect
10. #13094013C4semidirect
13. Q8×Dic47C4semidirect
14. #13093986C4semidirect
113. #328D47semidirect
116. C47#1512semidirect