Finite Group Databasebeta

← #20244423

Subgroups — #20244423

Order 6016.

362 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 73 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×#13094054C211yesmaximal, characteristic
2#15689694C211yesmaximal, characteristic
3C2×#13094024C211yesmaximal, characteristic, complemented
4#15689133C211yesmaximal, characteristic, complemented
5C2×#13093942C211yesmaximal, characteristic, complemented
6#15688883C211yesmaximal, characteristic, complemented
7C2×#104×C47C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C22×Dic94C2211yescharacteristic
10#13094054—22no—
11#13094054—22no—
12C2×#10625337—21no—
13C2×#10625335—21no—
14C2×#10625329C2211yescharacteristic
15#13094024—22no—
16#13094024—22no—
17#13094022—21no—
18#13094011—21no—
19#13094005—22no—
20#13094003—22no—
21#13093983C2211yescharacteristic
22C2×C4⋊Dic47—22no—
23#13093949—22no—
24#13093942—22no—
25C2×#41×C47C2211yescharacteristic
26C2×M16×C47C2211yescharacteristic
27C2×C42×C47C2211yescharacteristic
28#104×C47—22no—
29#41×C47—21no—
30#41×C47—21no—
31#41×C47—21no—
32#41×C47—21no—
33C2×Q8×C47D411yescharacteristic
34C2×D4×C47—21no—
35C2×D4×C47D411yescharacteristic
36C22×C4×C47—21no—
37C22×C4×C47—21no—
38C22×C4×C47C2311yescharacteristic
39C22×Dic47—21no—
40C22×Dic47D412yes—
41C2×Dic94—21no—
42C2×Dic94—21no—
43C2×Dic94—21no—
44C2×Dic94—21no—
45C2×Dic94—21no—
46C2×Dic94—21no—
47C2×Dic94—21no—
48C2×Dic94—21no—
49C2×Dic94—21no—
50C2×Dic94—21no—
51C2×Dic94—21no—
52C2×Dic94D412yes—
53M16×C47—21no—
54M16×C47—21no—
55C2×C8×C47—21no—
56C42×C47—21no—
57C42×C47D412yes—
58C22⋊Dic47—24no—
59C22⋊Dic47—21no—
60#10625337—24no—
61#10625335—24no—
62C4⋊Dic47—28no—
63C4⋊Dic47D412yes—
64Dic47⋊C4—24no—
65C4×Dic47—21no—
66#10625329—21no—
67#10625329D412yes—
68C2×C47⋊C8—21no—
69C23×C47—21no—
70C23×C47C2×D411yescharacteristic
71Q8×C47—21no—
72Q8×C47—21no—
73D4×C47—21no—
74D4×C47—21no—
75D4×C47—41no—
76D4×C47—41no—
77C2×C4×C47—24no—
78C2×C4×C47—22no—
79C2×C4×C47—21no—
80C2×C4×C47—41no—
81C2×C4×C47—41no—
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47#4111yescharacteristic
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—41no—
94C2×Dic47—41no—
95Dic94—22no—
96Dic94—22no—
97Dic94—41no—
98Dic94—41no—
99Dic94—41no—
100Dic94—41no—
101Dic94—41no—
102Dic94—41no—
103C8×C47—41no—
104C47⋊C8—22no—
105C22×C47—22no—
106C22×C47—41no—
107C22×C47—42no—
108C22×C47#12011yescharacteristic
109C22×C47#12011yescharacteristic
110C22×C47#12111yescharacteristic
111C4×C47—24no—
112C4×C47—41no—
113C4×C47#12011yescharacteristic
114C4×C47#12111yescharacteristic
115C4×C47#12111yescharacteristic
116C4×C47#12711yescharacteristic
117Dic47—42no—
118Dic47—42no—
119Dic47—42no—
120#2005—471nomaximal, Sylow
121C2×C47—21no—
122C2×C47—21no—
123C2×C47—81no—
124C2×C47#39211yescharacteristic
125C2×C47#45612yes—
126C2×#137—471no—
127#536—471no—
128C2×C4⋊Q8—471no—
129C2×#104D4711yescharacteristic
130#419—471no—
131C2×#101—471no—
132#339—471no—
133C47#200511yescharacteristic, complemented, Sylow
134C2×#41C2×D4711yescharacteristic
135C22×Q8—471no—
136C22×Q8—471no—
137#137—942no—
138#137—942no—
139C2×Q16—941no—
140C2×SD16—941no—
141C2×M16—471no—
142C2×M16C2×D4711yescharacteristic
143C4⋊Q8—942no—
144C4⋊Q8—941no—
145C4⋊Q8—942no—
146#124—941no—
147#123—942no—
148C22⋊Q8—942no—
149#117—471no—
150C2×C4⋊C4—942no—
151C2×C42C2×D4711yescharacteristic
152#104—22no—
153#103—942no—
154#101—942no—
155#41—21no—
156#41—21no—
157#41—21no—
158#41—21no—
159C2×Q8—472no—
160C2×Q8—941no—
161C2×Q8—941no—
162C2×Q8—941no—
163C2×Q8—941no—
164C2×Q8—941no—
165C2×Q8—941no—
166C2×Q8—941no—
167C2×Q8—941no—
168C2×Q8—941no—
169C2×Q8—941no—
170C2×Q8—941no—
171C2×Q8D18811yescharacteristic
172C2×D4—21no—
173C2×D4D18811yescharacteristic
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—472no—
177C22×C4—941no—
178C22×C4C22×D4711yescharacteristic
179Q16—944no—
180SD16—944no—
181M16—21no—
182M16—21no—
183M16—472no—
184M16—941no—
185C2×C8—21no—
186C2×C8—941no—
187C4⋊C4—472no—
188C4⋊C4—944no—
189C4⋊C4—948no—
190C22⋊C4—944no—
191C22⋊C4—941no—
192C42—21no—
193C42—941no—
194C42C22⋊D4712yes—
195C23—21no—
196C23D4×D4711yescharacteristic
197Q8—21no—
198Q8—21no—
199Q8—942no—
200Q8—942no—
201Q8—1881no—
202Q8—1881no—
203Q8—1881no—
204Q8—1881no—
205Q8—1881no—
206Q8—1881no—
207D4—21no—
208D4—21no—
209D4—41no—
210D4—41no—
211C2×C4—24no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—942no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4—1881no—
222C2×C4—1881no—
223C2×C4C2×D18811yescharacteristic
224C2×C4#1062535011yescharacteristic
225C2×C4D4×D4711yescharacteristic
226C2×C4D4×D4711yescharacteristic
227C2×C4D4×D4711yescharacteristic
228C2×C4C2×C22⋊D4711yescharacteristic
229C8—41no—
230C8—942no—
231C22—22no—
232C22—41no—
233C22—42no—
234C22#1309399211yescharacteristic
235C22#1309399411yescharacteristic
236C22#1309399711yescharacteristic
237C4—24no—
238C4—41no—
239C4—1882no—
240C4—1882no—
241C4—1882no—
242C4#1309399411yescharacteristic
243C4#1309399711yescharacteristic
244C4#1309399811yescharacteristic
245C4#1309402011yescharacteristic
246C2—21no—
247C2—21no—
248C2—81no—
249C2#1568903211yescharacteristic
250C2#1568930712yes—
subgroupG/H
centerC22#13093994
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#104×C47C2
socleC22×C47#120
hypercenterC2×#104D47
hypocenterC47#2005
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
3. C2×#13094024C2semidirect
4. #15689133C2semidirect
5. C2×#13093942C2semidirect
6. #15688883C2semidirect
133. C47#2005semidirect