Finite Group Databasebeta

← #20243712

Subgroups — #20243712

Order 6016.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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×#13094044C211yesmaximal, characteristic
2C2×#13094032C211yesmaximal, characteristic, complemented
3C2×#13093952C211yesmaximal, characteristic, complemented
4#15689090C211yesmaximal, characteristic, complemented
5#15688887C211yesmaximal, characteristic, complemented
6#15688878C211yesmaximal, characteristic, complemented
7C2×#104×C47C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094044—22no—
10#13094044—22no—
11C2×#10625337C411yescharacteristic, complemented
12C2×#10625335C411yescharacteristic, complemented
13C2×#10625336C411yescharacteristic, complemented
14C2×#10625334C411yescharacteristic, complemented
15#13094032—22no—
16#13094032—22no—
17C2×#10625329C2211yescharacteristic
18C2×#10625324—21no—
19C22×C47⋊C8C2211yescharacteristic
20C22×C47⋊C8C2211yescharacteristic
21C2×C8×D47—21no—
22#13093952—22no—
23C22⋊(C47⋊C8)—21no—
24C22⋊(C47⋊C8)—21no—
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×C47C2×C411yescharacteristic
34C2×D4×C47—21no—
35C2×D4×C47C2×C411yescharacteristic
36C22×C4×C47—21no—
37C22×C4×C47—21no—
38C22×C4×C47C2311yescharacteristic
39C2×C22⋊D47—21no—
40#10625350—21no—
41#10625350—21no—
42#10625350D412yes—
43#10625350D412yes—
44C2×D188C2×C411yescharacteristic
45C2×C4×D47—21no—
46C2×Dic94C2×C411yescharacteristic
47M16×C47—21no—
48M16×C47D412yes—
49C2×C8×C47—21no—
50C42×C47—21no—
51C42×C47—21no—
52#10625337—22no—
53#10625336—22no—
54#10625335—22no—
55#10625334—22no—
56#10625329—21no—
57#10625329—21no—
58C2×C47⋊C8—21no—
59C2×C47⋊C8—21no—
60C2×C47⋊C8—21no—
61C2×C47⋊C8—21no—
62C2×C47⋊C8—21no—
63C2×C47⋊C8C2×C411yescharacteristic
64C2×C47⋊C8C2×C411yescharacteristic
65C2×C47⋊C8D411yescharacteristic
66C2×C47⋊C8D411yescharacteristic
67#10625324—24no—
68C8×D47—24no—
69C23×C47—21no—
70C23×C47#4111yescharacteristic
71C22×D47—21no—
72Q8×C47—21no—
73Q8×C47—21no—
74D4×C47—21no—
75D4×C47—21no—
76D4×C47—41no—
77D4×C47—41no—
78C2×C4×C47—22no—
79C2×C4×C47—21no—
80C2×C4×C47—41no—
81C2×C4×C47—41no—
82C2×C4×C47—41no—
83C2×C4×C47—41no—
84C2×C4×C47C22×C411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47#4111yescharacteristic
90C22⋊D47—22no—
91C22⋊D47—22no—
92C2×Dic47—21no—
93D188—21no—
94D188C22⋊C412yes—
95C4×D47—22no—
96C4×D47—22no—
97Dic94—21no—
98Dic94C22⋊C412yes—
99C8×C47—22no—
100C47⋊C8—21no—
101C47⋊C8—21no—
102C47⋊C8—21no—
103C47⋊C8—21no—
104C47⋊C8—41no—
105C22×C47—21no—
106C22×C47—21no—
107C22×C47—41no—
108C22×C47—41no—
109C22×C47—41no—
110C22×C47C4×D411yescharacteristic
111C22×C47#12111yescharacteristic
112C22×C47#12311yescharacteristic
113C2×D47—22no—
114C2×D47—41no—
115C2×D47—41no—
116C4×C47—42no—
117C4×C47—41no—
118C4×C47C2×C22⋊C411yescharacteristic
119C4×C47C4×D411yescharacteristic
120C4×C47#12011yescharacteristic
121C4×C47#12111yescharacteristic
122Dic47—22no—
123#1876—471nomaximal, Sylow
124C2×C47—21no—
125C2×C47—21no—
126C2×C47—81no—
127C2×C47#38611yescharacteristic
128C2×C47#44311yescharacteristic
129C2×C47#44411yescharacteristic
130D47—42no—
131C2×#135—471no—
132C2×#131—471no—
133C2×#104—471no—
134C2×#104D4711yescharacteristic, complemented
135#408—471no—
136#341—471no—
137#336—471no—
138C47#187611yescharacteristic, complemented, Sylow
139C2×#41—471no—
140C2×#41C2×D4711yescharacteristic
141#135—942no—
142#135—942no—
143C2×Q16—471no—
144C2×SD16—471no—
145C2×SD16—471no—
146C2×D8—471no—
147#131—942no—
148#131—942no—
149C2×M16—471no—
150C2×M16—941no—
151C2×M16C2×D4711yescharacteristic
152C22×C8—471no—
153C22×C8—471no—
154C22×C8—941no—
155C2×C42C2×D4711yescharacteristic
156#104—22no—
157#104—942no—
158C22⋊C8—941no—
159C22⋊C8—941no—
160#41—21no—
161#41—21no—
162#41—21no—
163#41—21no—
164#41—472no—
165#41—472no—
166#41—941no—
167#41—941no—
168C2×Q8—471no—
169C2×Q8C4×D4711yescharacteristic
170C2×D4—21no—
171C2×D4—471no—
172C2×D4—941no—
173C2×D4C4×D4711yescharacteristic
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—941no—
177C22×C4C22×D4711yescharacteristic
178Q16—942no—
179SD16—942no—
180SD16—942no—
181D8—942no—
182M16—21no—
183M16—944no—
184M16—941no—
185M16—941no—
186M16C22⋊D4712yes—
187C2×C8—21no—
188C2×C8—471no—
189C2×C8—471no—
190C2×C8—471no—
191C2×C8—471no—
192C2×C8—944no—
193C2×C8—941no—
194C2×C8—941no—
195C2×C8—941no—
196C2×C8—941no—
197C2×C8—941no—
198C42—21no—
199C42—21no—
200C23—21no—
201C23—941no—
202C23#1062535211yescharacteristic
203Q8—21no—
204Q8—21no—
205Q8—472no—
206Q8—941no—
207D4—21no—
208D4—21no—
209D4—41no—
210D4—41no—
211D4—472no—
212D4—942no—
213D4—942no—
214D4—941no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—941no—
222C2×C4—942no—
223C2×C4—942no—
224C2×C4C2×C4×D4711yescharacteristic
225C2×C4#1062535011yescharacteristic
226C2×C4D4×D4711yescharacteristic
227C2×C4D4×D4711yescharacteristic
228C2×C4D4×D4711yescharacteristic
229C2×C4C2×C22⋊D4711yescharacteristic
230C8—22no—
231C8—941no—
232C8—941no—
233C8—941no—
234C8—941no—
235C8—1881no—
236C22—21no—
237C22—21no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—942no—
242C22—1881no—
243C22—1881no—
244C22(C22⋊D47)⋊C411yescharacteristic
245C22#1309399511yescharacteristic
246C22#1309400611yescharacteristic
247C4—42no—
248C4—41no—
249C4—942no—
250C4C22⋊C4×D4711yescharacteristic
251C4C4×C22⋊D4711yescharacteristic
252C4#1309399211yescharacteristic
253C4#1309399711yescharacteristic
254C2—21no—
255C2—21no—
256C2—81no—
257C2—1882no—
258C2#1568899911yescharacteristic
259C2#1568923711yescharacteristic
260C2#1568924211yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#104×C47C2
socleC22×C47C4×D4
hypercenterC2×#104D47
hypocenterC47#1876
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#13094032C2semidirect
3. C2×#13093952C2semidirect
4. #15689090C2semidirect
5. #15688887C2semidirect
6. #15688878C2semidirect
7. C2×#104×C47C2semidirect
11. C2×#10625337C4semidirect
12. C2×#10625335C4semidirect
13. C2×#10625336C4semidirect
14. C2×#10625334C4semidirect
134. C2×#104D47semidirect
138. C47#1876semidirect