Finite Group Databasebeta

← #20247699

Subgroups — #20247699

Order 6016.

584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 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×C22⋊D47C211yesmaximal, characteristic
2#15689061C212yesmaximal, complemented
3#15689058C212yesmaximal, complemented
4#15689019C212yesmaximal, complemented
5#15689002C212yesmaximal
6#15688996C212yesmaximal, complemented
7#15688983C211yesmaximal, characteristic, complemented
8#15688980C212yesmaximal, complemented
9C22×C4⋊C4×C47C211yesmaximal, characteristic, complemented
10C22×C22⋊D47C2211yescharacteristic
11C22×C4×D47C2211yescharacteristic
12C4×C22⋊D47—24no—
13C2×C4⋊Dic47C2212yes—
14C2×Dic47⋊C4C2211yescharacteristic
15C2×Dic47⋊C4C2214yes—
16C2×C22⋊Dic47C2212yes—
17C2×C22⋊Dic47C2211yescharacteristic
18C2×(C2×D47)⋊C4C2211yescharacteristic
19C2×(C2×D47)⋊C4C2214yes—
20C2×C4×Dic47C2211yescharacteristic
21C47⋊#95C2214yes—
22C47⋊#95C2212yes—
23C47⋊#95C2214yes—
24C23×C4×C47C2211yescharacteristic
25C23×C4×C47C2212yes—
26C2×C4⋊C4×C47—24no—
27C2×C4⋊C4×C47C2212yes—
28C2×C4⋊C4×C47C2212yes—
29C24×C47C2311yescharacteristic
30C23×D47C2311yescharacteristic
31C22×C4×C47—24no—
32C22×C4×C47—24no—
33C22×C4×C47—44no—
34C22×C4×C47D414yes—
35C22×C4×C47C2314yes—
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C2×C22⋊D47—22no—
39C2×C22⋊D47—22no—
40C2×C22⋊D47Q814yes—
41C22×Dic47C2311yescharacteristic
42C22×Dic47C2314yes—
43C22×Dic47C2311yescharacteristic
44C22×Dic47C2311yescharacteristic
45C2×C4×D47—22no—
46C2×C4×D47—24no—
47C4⋊C4×C47—24no—
48C4⋊C4×C47—24no—
49C22⋊Dic47—22no—
50C22⋊Dic47—24no—
51(C2×D47)⋊C4—22no—
52(C2×D47)⋊C4—44no—
53C4⋊Dic47—24no—
54Dic47⋊C4—22no—
55Dic47⋊C4—44no—
56C4×Dic47—22no—
57C23×C47—22no—
58C23×C47—22no—
59C23×C47C2×D412yes—
60C23×C47C2×Q812yes—
61C23×C47#4112yes—
62C23×C47C2411yescharacteristic
63C22×D47—21no—
64C22×D47—22no—
65C22×D47—21no—
66C22×D47—22no—
67C22×D47C2×Q812yes—
68C2×C4×C47—22no—
69C2×C4×C47—28no—
70C2×C4×C47—24no—
71C2×C4×C47—24no—
72C2×C4×C47—24no—
73C2×C4×C47—48no—
74C2×C4×C47C2×D412yes—
75C2×C4×C47C2×D412yes—
76C2×C4×C47#4114yes—
77C22⋊D47—28no—
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47—21no—
81C2×Dic47—21no—
82C2×Dic47—24no—
83C2×Dic47—24no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—24no—
87C2×Dic47C2×Q812yes—
88C4×D47—44no—
89C22×C47—22no—
90C22×C47—22no—
91C22×C47—24no—
92C22×C47—24no—
93C22×C47C22⋊Q814yes—
94C22×C47C22×D411yescharacteristic
95C22×C47C22×Q811yescharacteristic
96C22×C47C2×#4112yes—
97C22×C47C2×#4111yescharacteristic
98C22×C47H(5,𝔽2)12yes—
99C2×D47—22no—
100C2×D47—24no—
101C2×D47—41no—
102C2×D47—41no—
103C2×D47—42no—
104C4×C47—22no—
105C4×C47—44no—
106C4×C47#12314yes—
107Dic47—22no—
108Dic47—41no—
109Dic47—41no—
110Dic47—44no—
111#2487—471nomaximal, Sylow
112C2×C47—24no—
113C2×C47C2×C22⋊Q811yescharacteristic
114C2×C47C2×#12311yescharacteristic
115C2×C47#53511yescharacteristic
116C2×C47#55312yes—
117C2×C47#55412yes—
118D47—42no—
119C2×C4×D4—471no—
120C22×C4⋊C4D4711yescharacteristic, complemented
121#400—472no—
122#399—472no—
123#389—472no—
124#386—472no—
125#385—472no—
126#380—471no—
127#380—472no—
128C47#248711yescharacteristic, complemented, Sylow
129C22×D4—471no—
130C23×C4—471no—
131C23×C4C2×D4711yescharacteristic
132C23×C4C2×D4712yes—
133C4×D4—944no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4—471no—
136C2×C4⋊C4—472no—
137C2×C4⋊C4—474no—
138C2×C4⋊C4C2×D4712yes—
139C2×C4⋊C4C2×D4712yes—
140C2×C22⋊C4—471no—
141C2×C22⋊C4—472no—
142C2×C22⋊C4—471no—
143C2×C22⋊C4—474no—
144C2×C42—471no—
145#95—474no—
146#95—472no—
147#95—474no—
148C24—471no—
149C24C22×D4711yescharacteristic
150C2×D4—474no—
151C2×D4—942no—
152C2×D4—942no—
153C22×C4—24no—
154C22×C4—24no—
155C22×C4—44no—
156C22×C4—471no—
157C22×C4—471no—
158C22×C4—474no—
159C22×C4—471no—
160C22×C4—944no—
161C22×C4—942no—
162C22×C4C22⋊D4714yes—
163C22×C4C22×D4714yes—
164C22×C4C22×D4711yescharacteristic
165C22×C4C22×D4711yescharacteristic
166C4⋊C4—24no—
167C4⋊C4—24no—
168C4⋊C4—944no—
169C4⋊C4—942no—
170C4⋊C4—1884no—
171C22⋊C4—944no—
172C22⋊C4—942no—
173C22⋊C4—942no—
174C22⋊C4—1884no—
175C42—942no—
176C23—22no—
177C23—22no—
178C23—472no—
179C23—941no—
180C23—942no—
181C23—941no—
182C23—942no—
183C23Q8×D4712yes—
184C23#1062535412yes—
185C23C2×C22⋊D4712yes—
186C23C23×D4711yescharacteristic
187D4—948no—
188C2×C4—22no—
189C2×C4—28no—
190C2×C4—24no—
191C2×C4—24no—
192C2×C4—24no—
193C2×C4—48no—
194C2×C4—472no—
195C2×C4—941no—
196C2×C4—941no—
197C2×C4—941no—
198C2×C4—941no—
199C2×C4—944no—
200C2×C4—942no—
201C2×C4—944no—
202C2×C4—944no—
203C2×C4—942no—
204C2×C4—1884no—
205C2×C4#1062535014yes—
206C2×C4C2×C22⋊D4712yes—
207C2×C4C2×C22⋊D4712yes—
208C22—24no—
209C22—24no—
210C22—22no—
211C22—22no—
212C22—944no—
213C22—942no—
214C22—1882no—
215C22—1881no—
216C22—1881no—
217C22#1309400014yes—
218C22C22×C22⋊D4711yescharacteristic
219C22C2×Q8×D4711yescharacteristic
220C22C2×#1062535012yes—
221C22C2×#1062535411yescharacteristic
222C22#1309406912yes—
223C4—22no—
224C4—44no—
225C4—942no—
226C4—1884no—
227C4—1881no—
228C4—1881no—
229C4#1309400714yes—
230C2—24no—
231C2—1882no—
232C2C2×#1309400011yescharacteristic
233C2C2×#1309400711yescharacteristic
234C2#1568969011yescharacteristic
235C2#1568982112yes—
236C2#1568982812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC22×C4⋊C4×C47C2
hypercenterC22×C4⋊C4D47
hypocenterC47#2487
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #15689061C2semidirect
3. #15689058C2semidirect
4. #15689019C2semidirect
6. #15688996C2semidirect
7. #15688983C2semidirect
8. #15688980C2semidirect
9. C22×C4⋊C4×C47C2semidirect
120. C22×C4⋊C4D47semidirect
128. C47#2487semidirect