Finite Group Databasebeta

← #20254609

Subgroups — #20254609

Order 6016.

362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689657C211yesmaximal, characteristic
2#15689529C212yesmaximal, complemented
3#15689485C212yesmaximal, complemented
4#15689453C212yesmaximal, complemented
5#15689436C212yesmaximal
6#15689415C212yesmaximal, complemented
7#15689410C212yesmaximal, complemented
8#15689180C211yesmaximal, characteristic, complemented
9C2×C4⋊Q8×C47C211yesmaximal, characteristic, complemented
10#13094018—21no—
11#13094016C2211yescharacteristic
12#13094012C2211yescharacteristic
13#13094007—21no—
14#13094003C2211yescharacteristic
15#13093998C2211yescharacteristic
16C4×Dic94C2211yescharacteristic
17C4×D188C2211yescharacteristic
18C4×C22⋊D47—21no—
19#13093981—21no—
20#13093957C2214yes—
21#13093955C2214yes—
22C4⋊(C47⋊C8)C2212yes—
23#13093947C2214yes—
24#13093944C2214yes—
25C22⋊(C47⋊C8)C2212yes—
26#13093935C2212yes—
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—
43C2×D188C2311yescharacteristic
44C2×C4×D47—21no—
45C2×Dic94C2311yescharacteristic
46C4⋊C4×C47—22no—
47C4⋊C4×C47—22no—
48C4⋊C4×C47—22no—
49C4⋊C4×C47C2314yes—
50C42×C47D411yescharacteristic
51C42×C47D411yescharacteristic
52C42×C47C2311yescharacteristic
53C42×C47C2311yescharacteristic
54C22⋊Dic47—21no—
55(C2×D47)⋊C4—21no—
56(C2×D47)⋊C4—21no—
57(C2×D47)⋊C4—21no—
58(C2×D47)⋊C4—21no—
59C4⋊Dic47C2311yescharacteristic
60C4⋊Dic47C2311yescharacteristic
61Dic47⋊C4—21no—
62Dic47⋊C4—21no—
63Dic47⋊C4—21no—
64Dic47⋊C4—21no—
65C4×Dic47—21no—
66C2×C47⋊C8C2314yes—
67C23×C47C2×D411yescharacteristic
68C22×D47—21no—
69Q8×C47—44no—
70Q8×C47—44no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—24no—
75C2×C4×C47—44no—
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2411yescharacteristic
82C22⋊D47—42no—
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47—21no—
86D188—22no—
87C4×D47—42no—
88Dic94—22no—
89C47⋊C8—24no—
90C22×C47—21no—
91C22×C47—21no—
92C22×C47AGL(1,ℤ/8)12yes—
93C22×C47C22×D411yescharacteristic
94C2×D47—41no—
95C2×D47—41no—
96C2×D47—41no—
97C4×C47—21no—
98C4×C47—21no—
99C4×C47—21no—
100C4×C47—21no—
101C4×C47—44no—
102C4×C47#13712yes—
103C4×C472−1+412yes—
104Dic47—41no—
105Dic47—41no—
106Dic47—41no—
107#3238—471nomaximal, Sylow
108C2×C47—22no—
109C2×C47#53611yescharacteristic
110C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C47C2×#13711yescharacteristic
112D47—81no—
113C2×C4⋊Q8D4711yescharacteristic, complemented
114#529—471no—
115#501—472no—
116#489—472no—
117#483—472no—
118#480—472no—
119#477—472no—
120#476—472no—
121#432—471no—
122C47#323811yescharacteristic, complemented, Sylow
123C22×Q8—21no—
124C4⋊Q8—21no—
125C4⋊Q8—21no—
126C4⋊Q8C2×D4712yes—
127C4⋊Q8C2×D4712yes—
128#126—941no—
129#125—471no—
130#124—471no—
131#123—941no—
132C22⋊Q8—471no—
133#121—471no—
134C4×Q8—471no—
135C4×D4—471no—
136C4×D4—941no—
137#117—941no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4C2×D4712yes—
140C2×C42C2×D4711yescharacteristic
141#107—474no—
142#106—474no—
143C4⋊C8—472no—
144#103—474no—
145#102—474no—
146C22⋊C8—472no—
147#97—472no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—44no—
151C2×Q8—471no—
152C2×D4—471no—
153C2×D4—941no—
154C22×C4—22no—
155C22×C4—941no—
156C22×C4C22⋊D4711yescharacteristic
157C22×C4C22⋊D4711yescharacteristic
158C22×C4C22×D4711yescharacteristic
159C2×C8—474no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—471no—
164C4⋊C4—471no—
165C4⋊C4—941no—
166C4⋊C4—941no—
167C4⋊C4—941no—
168C4⋊C4—941no—
169C4⋊C4C22×D4714yes—
170C22⋊C4—941no—
171C22⋊C4—941no—
172C22⋊C4—941no—
173C22⋊C4—941no—
174C22⋊C4—941no—
175C42—941no—
176C42C22⋊D4711yescharacteristic
177C42C22⋊D4711yescharacteristic
178C42C22×D4711yescharacteristic
179C42C22×D4711yescharacteristic
180C23—941no—
181C23C2×C22⋊D4711yescharacteristic
182Q8—44no—
183Q8—44no—
184Q8—942no—
185D4—942no—
186D4—1882no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—44no—
192C2×C4—941no—
193C2×C4—941no—
194C2×C4—941no—
195C2×C4—1882no—
196C2×C4C2×C22⋊D4711yescharacteristic
197C2×C4C2×C22⋊D4711yescharacteristic
198C2×C4C2×C22⋊D4711yescharacteristic
199C2×C4C2×C22⋊D4711yescharacteristic
200C2×C4C2×C22⋊D4711yescharacteristic
201C2×C4C23×D4711yescharacteristic
202C8—944no—
203C22—21no—
204C22—21no—
205C22—1881no—
206C22—1881no—
207C22—1881no—
208C22#1309405012yes—
209C22C22×C22⋊D4711yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—21no—
214C4—44no—
215C4—1881no—
216C4—1881no—
217C4—1881no—
218C4#1309405512yes—
219C4#1309407212yes—
220C2—22no—
221C2—3761no—
222C2#1568969711yescharacteristic
223C2C2×#1309405011yescharacteristic
224C2C2×#1309405511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×C4⋊Q8×C47C2
socleC22×C47C22×D4
hypercenterC2×C4⋊Q8D47
hypocenterC47#3238
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. #15689529C2semidirect
3. #15689485C2semidirect
4. #15689453C2semidirect
6. #15689415C2semidirect
7. #15689410C2semidirect
8. #15689180C2semidirect
9. C2×C4⋊Q8×C47C2semidirect
113. C2×C4⋊Q8D47semidirect
122. C47#3238semidirect