Finite Group Databasebeta

← #20244383

Subgroups — #20244383

Order 6016.

496 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 93 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×#13093995C212yesmaximal, complemented
2C2×#13093945C212yesmaximal, complemented
3C2×(C2×D47)⋊C8C211yesmaximal, characteristic, complemented
4#15688886C211yesmaximal, characteristic, complemented
5C22×D8×C47C211yesmaximal, characteristic, complemented
6C22×C22⋊D47—22no—
7C22×C4×D47C2211yescharacteristic
8C22×C47⋊C8C2211yescharacteristic
9#13093995—24no—
10#13093995—24no—
11C2×C4⋊Dic47C2212yes—
12C2×C22⋊Dic47—22no—
13#13093945—24no—
14(C2×D47)⋊C8—22no—
15C22×D4×C47C2212yes—
16C2×D8×C47—24no—
17C2×D8×C47—22no—
18C22×C8×C47C2211yescharacteristic
19C24×C47—22no—
20C23×D47D411yescharacteristic
21C2×D4×C47—22no—
22C2×D4×C47—22no—
23C2×D4×C47—22no—
24C2×D4×C47—22no—
25C2×D4×C47—22no—
26C2×D4×C47D414yescomplemented
27C22×C4×C47C2311yescharacteristic
28C2×C22⋊D47—28no—
29C2×C22⋊D47—44no—
30C2×C22⋊D47—44no—
31C22×Dic47—22no—
32C22×Dic47D411yescharacteristic
33C2×C4×D47—21no—
34C2×C4×D47—22no—
35C2×C4×D47—22no—
36C2×C4×D47—21no—
37D8×C47—28no—
38C2×C8×C47—22no—
39C2×C8×C47D412yescomplemented
40C22⋊Dic47—28no—
41C4⋊Dic47—22no—
42C4⋊Dic47D414yescomplemented
43C2×C47⋊C8—21no—
44C2×C47⋊C8—22no—
45C23×C47—24no—
46C23×C47—42no—
47C23×C47—42no—
48C23×C47—42no—
49C23×C47—42no—
50C23×C47—42no—
51C23×C47—42no—
52C23×C47C2×D411yescharacteristic
53C22×D47—22no—
54C22×D47—21no—
55C22×D47—21no—
56C22×D47—22no—
57C22×D47D812yescomplemented
58D4×C47—24no—
59D4×C47—24no—
60D4×C47—42no—
61D4×C47—42no—
62C2×C4×C47C2×D412yes—
63C2×C4×C47C2×D412yes—
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47#4111yescharacteristic
66C22⋊D47—416no—
67C2×Dic47—24no—
68C2×Dic47—22no—
69C2×Dic47—21no—
70C2×Dic47—42no—
71C2×Dic47—42no—
72C4×D47—41no—
73C4×D47—42no—
74C4×D47—41no—
75C8×C47—22no—
76C47⋊C8—41no—
77C22×C47—44no—
78C22×C47—44no—
79C22×C47—44no—
80C22×C47—82no—
81C22×C47—82no—
82C22×C47—82no—
83C22×C47—82no—
84C22×C47#12012yes—
85C22×C47#12111yescharacteristic
86C22×C47C2×D811yescharacteristic
87C22×C47#13511yescharacteristic
88C22×C47AGL(1,ℤ/8)12yes—
89C2×D47—24no—
90C2×D47—22no—
91C2×D47—41no—
92C2×D47—42no—
93C2×D47—41no—
94C4×C47#12011yescharacteristic
95C4×C47#12112yes—
96C4×C47#12711yescharacteristic
97Dic47—41no—
98Dic47—44no—
99#1999—471nomaximal, Sylow
100C2×C47—84no—
101C2×C47#39211yescharacteristic
102C2×C47#44712yes—
103C2×C47#44912yes—
104C2×C47#46611yescharacteristic
105C2×C47#46911yescharacteristic
106D47—42no—
107C22×D8D4711yescharacteristic, complemented
108C2×#121—472no—
109C2×#102—472no—
110C2×C22⋊C8—471no—
111#340—471no—
112C47#199911yescharacteristic, complemented, Sylow
113C22×D4—942no—
114C22×D4C2×D4712yes—
115C23×C4—471no—
116C2×D8—24no—
117C2×D8—22no—
118C22×C8—471no—
119C22×C8C2×D4711yescharacteristic
120#121—944no—
121#121—944no—
122C2×C4⋊C4—472no—
123C2×C22⋊C4—942no—
124#102—944no—
125C22⋊C8—942no—
126C24—22no—
127C24—471no—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—22no—
131C2×D4—22no—
132C2×D4—22no—
133C2×D4—948no—
134C2×D4—1884no—
135C2×D4—1884no—
136C2×D4C22⋊D4714yescomplemented
137C22×C4—471no—
138C22×C4—942no—
139C22×C4—942no—
140C22×C4—941no—
141C22×C4—941no—
142C22×C4—942no—
143C22×C4C22×D4711yescharacteristic
144D8—28no—
145C2×C8—22no—
146C2×C8—942no—
147C2×C8—941no—
148C2×C8C22⋊D4712yescomplemented
149C4⋊C4—474no—
150C4⋊C4—942no—
151C22⋊C4—948no—
152C23—24no—
153C23—42no—
154C23—42no—
155C23—42no—
156C23—42no—
157C23—42no—
158C23—42no—
159C23—472no—
160C23—942no—
161C23—941no—
162C23—941no—
163C23—942no—
164C23D4×D4711yescharacteristic
165D4—24no—
166D4—24no—
167D4—42no—
168D4—42no—
169D4—18816no—
170C2×C4—942no—
171C2×C4—944no—
172C2×C4—941no—
173C2×C4—1882no—
174C2×C4—1882no—
175C2×C4—1881no—
176C2×C4—1882no—
177C2×C4—1881no—
178C2×C4D4×D4712yes—
179C2×C4#1062535211yescharacteristic
180C2×C4C2×C22⋊D4712yes—
181C2×C4C2×C22⋊D4711yescharacteristic
182C8—22no—
183C8—1881no—
184C22—44no—
185C22—44no—
186C22—44no—
187C22—82no—
188C22—82no—
189C22—82no—
190C22—82no—
191C22—944no—
192C22—942no—
193C22—1882no—
194C22—1881no—
195C22—1881no—
196C22#1309399212yes—
197C22#1309399511yescharacteristic
198C22D8×D4711yescharacteristic
199C22#1309404311yescharacteristic
200C22#1309404812yes—
201C4—1884no—
202C4—1881no—
203C4#1309399311yescharacteristic
204C4#1309399612yes—
205C4#1309402011yescharacteristic
206C2—84no—
207C2—1882no—
208C2#1568903111yescharacteristic
209C2#1568925512yes—
210C2#1568926512yes—
211C2#1568935611yescharacteristic
212C2#1568937311yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC22×D8×C47C2
socleC23×C47C2×D4
hypercenterC22×D8D47
hypocenterC47#1999
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#13093995C2semidirect
2. C2×#13093945C2semidirect
3. C2×(C2×D47)⋊C8C2semidirect
4. #15688886C2semidirect
5. C22×D8×C47C2semidirect
26. C2×D4×C47D4semidirect
39. C2×C8×C47D4semidirect
42. C4⋊Dic47D4semidirect
57. C22×D47D8semidirect
107. C22×D8D47semidirect
112. C47#1999semidirect
136. C2×D4C22⋊D47semidirect
148. C2×C8C22⋊D47semidirect