Finite Group Databasebeta

← #20253197

Subgroups — #20253197

Order 6016.

416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C4×#10625350C211yesmaximal, characteristic
2#15689415C212yesmaximal, complemented
3#15689410C212yesmaximal, complemented
4#15689405C212yesmaximal, complemented
5#15689400C212yesmaximal, complemented
6#15689163C212yesmaximal, complemented
7#15689147C211yesmaximal, characteristic, complemented
8#15689122C212yesmaximal
9C2×C4⋊Q8×C47C211yesmaximal, characteristic, complemented
10C2×#10625350C2211yescharacteristic
11C2×#10625329C2212yes—
12C4×Dic94C2211yescharacteristic
13C4×Dic94C2211yescharacteristic
14C4×D188C2211yescharacteristic
15C4×D188C2211yescharacteristic
16C4×C22⋊D47—21no—
17C4×C22⋊D47—21no—
18#13093983C2211yescharacteristic
19#13093981—21no—
20C42×D47—21no—
21#13093957C2214yes—
22#13093955C2214yes—
23C4⋊(C47⋊C8)C2212yes—
24C4⋊(C47⋊C8)C2212yes—
25#13093947C2214yes—
26#13093944C2214yes—
27C22×Q8×C47—21no—
28C4⋊Q8×C47—21no—
29C4⋊Q8×C47—21no—
30C4⋊Q8×C47C2212yes—
31C4⋊Q8×C47C2212yes—
32C2×C4⋊C4×C47—21no—
33C2×C4⋊C4×C47C2212yes—
34C2×C42×C47C2211yescharacteristic
35C2×Q8×C47—22no—
36C2×Q8×C47—22no—
37C2×Q8×C47—44no—
38C22×C4×C47—22no—
39C22×C4×C47D411yescharacteristic
40C22×C4×C47D411yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C2×C22⋊D47—21no—
43#10625350—22no—
44#10625350Q814yescomplemented
45C2×D188C2311yescharacteristic
46C2×C4×D47—21no—
47C2×C4×D47—21no—
48C2×C4×D47—21no—
49C2×Dic94C2311yescharacteristic
50C4⋊C4×C47—22no—
51C4⋊C4×C47—22no—
52C4⋊C4×C47—22no—
53C4⋊C4×C47C2314yes—
54C42×C47D411yescharacteristic
55C42×C47D411yescharacteristic
56C42×C47C2311yescharacteristic
57C42×C47C2311yescharacteristic
58C22⋊Dic47—21no—
59(C2×D47)⋊C4—21no—
60(C2×D47)⋊C4—21no—
61C4⋊Dic47C2311yescharacteristic
62C4⋊Dic47C2311yescharacteristic
63Dic47⋊C4—21no—
64Dic47⋊C4—21no—
65C4×Dic47—21no—
66C4×Dic47—21no—
67C4×Dic47—21no—
68#10625329—24no—
69C2×C47⋊C8C2314yes—
70C23×C47C2×D411yescharacteristic
71C22×D47—21no—
72Q8×C47—44no—
73Q8×C47—44no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—24no—
77C2×C4×C47—44no—
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×Q812yes—
84C2×C4×C47#4112yes—
85C2×C4×C47C2411yescharacteristic
86C22⋊D47—24no—
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47—21no—
90D188—21no—
91D188C2×Q812yescomplemented
92C4×D47—24no—
93C4×D47—42no—
94C4×D47—42no—
95Dic94—21no—
96Dic94C2×Q812yescomplemented
97C47⋊C8—24no—
98C22×C47—21no—
99C22×C47—21no—
100C22×C47C22⋊Q812yes—
101C22×C47C22×D411yescharacteristic
102C2×D47—22no—
103C2×D47—41no—
104C2×D47—41no—
105C4×C47—21no—
106C4×C47—21no—
107C4×C47—44no—
108C4×C47C22⋊Q812yes—
109C4×C47AGL(1,ℤ/8)12yes—
110C4×C47#13712yes—
111C4×C47C22×Q811yescharacteristic
112C4×C47C2×#4111yescharacteristic
113Dic47—22no—
114Dic47—41no—
115Dic47—41no—
116#3079—471nomaximal, Sylow
117C2×C47—22no—
118C2×C47C2×C22⋊Q811yescharacteristic
119C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
120C2×C47C2×#13711yescharacteristic
121D47—42no—
122C2×C4⋊Q8D4711yescharacteristic, complemented
123C4×#41—471no—
124#477—472no—
125#476—472no—
126#475—472no—
127#474—472no—
128#428—472no—
129#423—471no—
130#417—472no—
131C47#307911yescharacteristic, complemented, Sylow
132C2×#41—471no—
133C22×Q8—21no—
134C2×M16—472no—
135C4⋊Q8—21no—
136C4⋊Q8—21no—
137C4⋊Q8C2×D4712yes—
138C4⋊Q8C2×D4712yes—
139C4×Q8—471no—
140C4×Q8—471no—
141C4×D4—471no—
142C4×D4—471no—
143C4×D4—941no—
144C4×D4—941no—
145#117—471no—
146#117—941no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4C2×D4712yes—
149C2×C42—941no—
150C2×C42C2×D4711yescharacteristic
151#107—474no—
152#106—474no—
153C4⋊C8—472no—
154C4⋊C8—472no—
155#103—474no—
156#102—474no—
157#41—474no—
158#41—942no—
159C2×Q8—22no—
160C2×Q8—22no—
161C2×Q8—44no—
162C2×Q8—471no—
163C2×D4—471no—
164C2×D4—941no—
165C22×C4—22no—
166C22×C4—941no—
167C22×C4—941no—
168C22×C4—941no—
169C22×C4C22⋊D4711yescharacteristic
170C22×C4C22⋊D4711yescharacteristic
171C22×C4C22×D4711yescharacteristic
172M16—944no—
173C2×C8—474no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—471no—
178C4⋊C4—471no—
179C4⋊C4—941no—
180C4⋊C4—941no—
181C4⋊C4C22×D4714yes—
182C22⋊C4—941no—
183C22⋊C4—941no—
184C22⋊C4—941no—
185C42—941no—
186C42—941no—
187C42—941no—
188C42C22⋊D4711yescharacteristic
189C42C22⋊D4711yescharacteristic
190C42C22×D4711yescharacteristic
191C42C22×D4711yescharacteristic
192C23—941no—
193C23C2×C22⋊D4711yescharacteristic
194Q8—44no—
195Q8—44no—
196Q8—472no—
197Q8—941no—
198D4—472no—
199D4—944no—
200D4—941no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—24no—
204C2×C4—44no—
205C2×C4—941no—
206C2×C4—944no—
207C2×C4—941no—
208C2×C4—941no—
209C2×C4—1882no—
210C2×C4—1882no—
211C2×C4Q8×D4712yes—
212C2×C4#1062535412yes—
213C2×C4C2×C22⋊D4711yescharacteristic
214C2×C4C2×C22⋊D4711yescharacteristic
215C2×C4C2×C22⋊D4711yescharacteristic
216C2×C4C2×C22⋊D4711yescharacteristic
217C2×C4C2×C22⋊D4711yescharacteristic
218C2×C4C23×D4711yescharacteristic
219C8—944no—
220C22—21no—
221C22—21no—
222C22—942no—
223C22—1881no—
224C22—1881no—
225C22#1309400012yes—
226C22C22×C22⋊D4711yescharacteristic
227C4—21no—
228C4—21no—
229C4—44no—
230C4—942no—
231C4—1881no—
232C4—1881no—
233C4#1309400012yes—
234C4#1309405012yes—
235C4#1309405512yes—
236C4C2×Q8×D4711yescharacteristic
237C4C2×#1062535411yescharacteristic
238C2—22no—
239C2—1882no—
240C2C2×#1309400011yescharacteristic
241C2C2×#1309405011yescharacteristic
242C2C2×#1309405511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×C4⋊Q8×C47C2
socleC22×C47C22×D4
hypercenterC2×C4⋊Q8D47
hypocenterC47#3079
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #15689415C2semidirect
3. #15689410C2semidirect
4. #15689405C2semidirect
5. #15689400C2semidirect
6. #15689163C2semidirect
7. #15689147C2semidirect
9. C2×C4⋊Q8×C47C2semidirect
44. #10625350Q8semidirect
91. D188C2×Q8semidirect
96. Dic94C2×Q8semidirect
122. C2×C4⋊Q8D47semidirect
131. C47#3079semidirect