Finite Group Databasebeta

← #20254280

Subgroups — #20254280

Order 6016.

378 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 109 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#15689696C212yesmaximal
2#15689467C212yesmaximal, complemented
3#15689462C212yesmaximal, complemented
4#15689381C211yesmaximal, characteristic, complemented
5#15689362C212yesmaximal, complemented
6#15689280C212yesmaximal, complemented
7#15689277C212yesmaximal, complemented
8#15689091C211yesmaximal, characteristic
9C47×#470C211yesmaximal, characteristic, complemented
10C2×#10625350C2211yescharacteristic
11C2×Q8×D47C2212yes—
12C2×Dic188C2211yescharacteristic
13C2×#10625337C2212yes—
14C22×C47⋊C8C2211yescharacteristic
15#13094023—22no—
16#13094010—22no—
17#13094009—22no—
18#13094006—22no—
19#13094004C2212yes—
20#13094003C2212yes—
21#13094000C2212yes—
22#13093982C2212yes—
23#13093957C2212yes—
24#13093956C2211yescharacteristic
25#13093949C2212yes—
26#13093948C2212yes—
27#13093947C2212yes—
28(C2×D47)⋊C8C2212yes—
29(C2×D47)⋊C8C2212yes—
30C2×Q16×C47C2211yescharacteristic
31C2×M16×C47C2211yescharacteristic
32C22⋊Q8×C47C2212yes—
33#106×C47C2211yescharacteristic
34#103×C47C2212yes—
35C2×Q8×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C2×C22⋊D47D412yes—
38Q8×D47—42no—
39Q8×D47—42no—
40#10625350—41no—
41#10625350—41no—
42C2×D188D411yescharacteristic
43C2×C4×D47—22no—
44C2×C4×D47C2312yes—
45C2×Dic94—22no—
46C2×Dic94D411yescharacteristic
47C2×Dic94C2312yes—
48Q16×C47—41no—
49M16×C47—41no—
50C2×C8×C47C2311yescharacteristic
51C2×C8×C47C2311yescharacteristic
52C4⋊C4×C47—22no—
53C4⋊C4×C47C2312yes—
54C22⋊C4×C47—22no—
55C22⋊Dic47—22no—
56#10625337—42no—
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60C4⋊Dic47—22no—
61C4⋊Dic47C2312yes—
62Dic47⋊C4—22no—
63Dic47⋊C4—22no—
64C4×Dic47—22no—
65C2×C47⋊C8—41no—
66C2×C47⋊C8C2312yes—
67Dic188—41no—
68C23×C47C2×D411yescharacteristic
69C22×D47C2×D412yes—
70Q8×C47—22no—
71Q8×C47—22no—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2411yescharacteristic
78C22⋊D47—42no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47C2×D412yes—
82D188—41no—
83C4×D47—22no—
84C4×D47—22no—
85C4×D47—44no—
86Dic94—22no—
87Dic94—22no—
88Dic94—41no—
89Dic94—44no—
90C8×C47—21no—
91C8×C47—21no—
92C47⋊C8—22no—
93C22×C47—21no—
94C22×C47—22no—
95C22×C47C22×D411yescharacteristic
96C2×D47—22no—
97C2×D47—24no—
98C4×C47—21no—
99C4×C47—42no—
100C4×C47—42no—
101C4×C47H(5,𝔽2)11yescharacteristic
102C4×C47H(5,𝔽2)11yescharacteristic
103Dic47—22no—
104Dic47—42no—
105Dic47—42no—
106#3202—471nomaximal, Sylow
107C2×C47—41no—
108C2×C47#53411yescharacteristic
109C2×C47#57812yes—
110D47—42no—
111#536—472no—
112#485—472no—
113#485—472no—
114#470—471no—
115#470D4711yescharacteristic, complemented
116#467—472no—
117#451—472no—
118#451—472no—
119#408—471no—
120C47#320211yescharacteristic, complemented, Sylow
121C2×#41—471no—
122C22×Q8—472no—
123C2×Q16—472no—
124C2×Q16—471no—
125C2×Q16C2×D4711yescharacteristic
126C2×M16C2×D4711yescharacteristic
127C22×C8—471no—
128C4⋊Q8—942no—
129#124—942no—
130#123—942no—
131#123—942no—
132C22⋊Q8—472no—
133C22⋊Q8—472no—
134C22⋊Q8—472no—
135C22⋊Q8C2×D4712yes—
136#117—472no—
137#107—472no—
138#106—471no—
139#106C2×D4711yescharacteristic
140#103—472no—
141#103—472no—
142#103—472no—
143#103C2×D4712yes—
144C22⋊C8—472no—
145C22⋊C8—472no—
146#41—1881no—
147#41—1881no—
148C2×Q8—471no—
149C2×Q8—472no—
150C2×Q8—942no—
151C2×Q8—1882no—
152C2×Q8—1882no—
153C2×Q8C22×D4712yes—
154C2×D4—472no—
155C2×D4—471no—
156C22×C4—472no—
157C22×C4—942no—
158C22×C4C22×D4711yescharacteristic
159Q16—41no—
160Q16—1881no—
161Q16—1882no—
162M16—41no—
163C2×C8—472no—
164C2×C8—1881no—
165C2×C8C22×D4711yescharacteristic
166C2×C8C22×D4711yescharacteristic
167C4⋊C4—22no—
168C4⋊C4—472no—
169C4⋊C4—942no—
170C4⋊C4—942no—
171C4⋊C4—942no—
172C4⋊C4C22×D4712yes—
173C22⋊C4—22no—
174C22⋊C4—942no—
175C22⋊C4—942no—
176C22⋊C4—942no—
177C22⋊C4—942no—
178C42—942no—
179C23—472no—
180C23D4×D4711yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—942no—
184Q8—942no—
185Q8—1881no—
186Q8—1884no—
187D4—1881no—
188D4—1882no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—472no—
194C2×C4—942no—
195C2×C4—942no—
196C2×C4—942no—
197C2×C4—942no—
198C2×C4—1884no—
199C2×C4D4×D4711yescharacteristic
200C2×C4C23×D4711yescharacteristic
201C8—21no—
202C8—21no—
203C8—942no—
204C22—21no—
205C22—22no—
206C22—942no—
207C22—944no—
208C22C2×D4×D4711yescharacteristic
209C4—21no—
210C4—42no—
211C4—42no—
212C4—942no—
213C4—1882no—
214C4—1882no—
215C4#1309406911yescharacteristic
216C4#1309407011yescharacteristic
217C2—41no—
218C2—1882no—
219C2#1568968111yescharacteristic
220C2#1568993912yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#470C2
socleC22×C47C22×D4
hypercenter#470D47
hypocenterC47#3202
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #15689467C2semidirect
3. #15689462C2semidirect
4. #15689381C2semidirect
5. #15689362C2semidirect
6. #15689280C2semidirect
7. #15689277C2semidirect
9. C47×#470C2semidirect
115. #470D47semidirect
120. C47#3202semidirect