Finite Group Databasebeta

← #20254465

Subgroups — #20254465

Order 6016.

364 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689699C211yesmaximal, characteristic
2#15689515C211yesmaximal, characteristic, complemented
3#15689502C211yesmaximal, characteristic, complemented
4#15689493C211yesmaximal, characteristic, complemented
5#15689480C211yesmaximal, characteristic, complemented
6#15689345C212yesmaximal, complemented
7#15689333C212yesmaximal, complemented
8#15689283C212yesmaximal
9#15689278C212yesmaximal, complemented
10#15689184C211yesmaximal, characteristic, complemented
11C47×#541C211yesmaximal, characteristic, complemented
12C2×#10625350C2211yescharacteristic
13C22×Dic94C2211yescharacteristic
14C2×#10625337C2212yes—
15C2×#10625337C2212yes—
16C2×#10625337C2212yes—
17C2×#10625336C2212yes—
18#13094024C2211yescharacteristic
19#13094024C2211yescharacteristic
20#13094012C2211yescharacteristic
21#13094012C2211yescharacteristic
22#13094008—22no—
23#13094004—22no—
24C4⋊(C47⋊C8)C2212yes—
25#13093947C2212yes—
26#13093947C2212yes—
27#13093947C2212yes—
28#13093944C2212yes—
29C22⋊(C47⋊C8)C2212yes—
30#13093935C2211yescharacteristic
31C4×C47⋊C8C2211yescharacteristic
32C4⋊Q8×C47C2211yescharacteristic
33#126×C47—22no—
34#125×C47—22no—
35#125×C47C2211yescharacteristic
36C22⋊Q8×C47C2212yes—
37C4×Q8×C47C2212yes—
38#117×C47C2211yescharacteristic
39C2×Q8×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C2×C22⋊D47—21no—
42C22×Dic47—21no—
43#10625350—42no—
44C2×D188C2311yescharacteristic
45C2×C4×D47—21no—
46C2×Dic94—21no—
47C2×Dic94—42no—
48C2×Dic94C2311yescharacteristic
49C2×Dic94C2311yescharacteristic
50C2×Dic94C2311yescharacteristic
51C4⋊C4×C47—22no—
52C4⋊C4×C47—22no—
53C4⋊C4×C47—22no—
54C4⋊C4×C47—22no—
55C4⋊C4×C47D412yes—
56C4⋊C4×C47C2312yes—
57C22⋊C4×C47—22no—
58C22⋊C4×C47D412yes—
59C42×C47—22no—
60C42×C47C2311yescharacteristic
61C42×C47C2311yescharacteristic
62#10625337—42no—
63#10625337—42no—
64#10625337—42no—
65#10625336—42no—
66(C2×D47)⋊C4—22no—
67(C2×D47)⋊C4—22no—
68C4⋊Dic47—22no—
69C4⋊Dic47—22no—
70C2×C47⋊C8C2312yes—
71C2×C47⋊C8C2312yes—
72C23×C47C2×D411yescharacteristic
73C22×D47—21no—
74Q8×C47—22no—
75Q8×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47C2×D412yes—
80C2×C4×C47C2×D412yes—
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2411yescharacteristic
83C22⋊D47—42no—
84C2×Dic47—21no—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—42no—
88D188—22no—
89C4×D47—42no—
90Dic94—22no—
91Dic94—22no—
92Dic94—22no—
93Dic94—42no—
94C47⋊C8—22no—
95C47⋊C8—22no—
96C22×C47—21no—
97C22×C47—22no—
98C22×C47C22×D411yescharacteristic
99C2×D47—41no—
100C2×D47—42no—
101C4×C47—21no—
102C4×C47—22no—
103C4×C47—22no—
104C4×C47—42no—
105C4×C47—42no—
106C4×C47H(5,𝔽2)12yes—
107Dic47—41no—
108Dic47—41no—
109Dic47—41no—
110#3223—471nomaximal, Sylow
111C2×C47—41no—
112C2×C47#53511yescharacteristic
113C2×C47#57812yes—
114D47—81no—
115#541D4711yescharacteristic, complemented
116#536—471no—
117#497—471no—
118#494—471no—
119#491—471no—
120#488—471no—
121#464—472no—
122#462—472no—
123#452—472no—
124#451—472no—
125#433—471no—
126C47#322311yescharacteristic, complemented, Sylow
127C2×#41—471no—
128C22×Q8—471no—
129C2×Q16—472no—
130C2×Q16—472no—
131C2×Q16—472no—
132C2×SD16—472no—
133C4⋊Q8—471no—
134C4⋊Q8—471no—
135C4⋊Q8C2×D4711yescharacteristic
136#126—22no—
137#125—22no—
138#125C2×D4711yescharacteristic
139#124—471no—
140#124—471no—
141#123—942no—
142C22⋊Q8—942no—
143C22⋊Q8C2×D4712yes—
144C4×Q8C2×D4712yes—
145#117C2×D4711yescharacteristic
146C4⋊C8—472no—
147#103—472no—
148#103—472no—
149#103—472no—
150#102—472no—
151C22⋊C8—472no—
152#97—471no—
153C4×C8—471no—
154#41—1882no—
155C2×Q8—471no—
156C2×Q8—471no—
157C2×Q8—471no—
158C2×Q8—941no—
159C2×Q8—1882no—
160C2×Q8C22×D4712yes—
161C2×D4—471no—
162C2×D4—941no—
163C22×C4—941no—
164C22×C4—941no—
165C22×C4C22×D4711yescharacteristic
166Q16—1882no—
167Q16—1882no—
168Q16—1882no—
169SD16—1882no—
170C2×C8—472no—
171C2×C8—472no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4C22⋊D4712yes—
179C4⋊C4C22×D4712yes—
180C22⋊C4—22no—
181C22⋊C4—942no—
182C22⋊C4—942no—
183C22⋊C4C22⋊D4712yes—
184C42—22no—
185C42C22×D4711yescharacteristic
186C42C22×D4711yescharacteristic
187C23—941no—
188C23C2×C22⋊D4711yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—942no—
192Q8—942no—
193Q8—942no—
194Q8—1882no—
195D4—942no—
196D4—1882no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—941no—
201C2×C4—941no—
202C2×C4—941no—
203C2×C4—1882no—
204C2×C4—1882no—
205C2×C4C2×C22⋊D4712yes—
206C2×C4C2×C22⋊D4712yes—
207C2×C4C2×C22⋊D4711yescharacteristic
208C2×C4C23×D4711yescharacteristic
209C8—942no—
210C8—942no—
211C22—22no—
212C22—21no—
213C22—1882no—
214C22—1881no—
215C22C22×C22⋊D4711yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—1881no—
222C4—1881no—
223C4—1881no—
224C4#1309407012yes—
225C2—41no—
226C2—3761no—
227C2#1568968711yescharacteristic
228C2#1568993812yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#541C2
socleC22×C47C22×D4
hypercenter#541D47
hypocenterC47#3223
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #15689515C2semidirect
3. #15689502C2semidirect
4. #15689493C2semidirect
5. #15689480C2semidirect
6. #15689345C2semidirect
7. #15689333C2semidirect
9. #15689278C2semidirect
10. #15689184C2semidirect
11. C47×#541C2semidirect
115. #541D47semidirect
126. C47#3223semidirect