Finite Group Databasebeta

← #20253511

Subgroups — #20253511

Order 6016.

424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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#15689673C211yesmaximal, characteristic
2C2×C4×Dic94C211yesmaximal, characteristic, complemented
3#15689437C212yesmaximal, complemented
4#15689419C212yesmaximal, complemented
5#15689324C212yesmaximal, complemented
6#15689264C212yesmaximal, complemented
7#15689225C214yesmaximal, complemented
8C47×#432C211yesmaximal, characteristic, complemented
9C2×#10625350—21no—
10C22×Dic94C2211yescharacteristic
11C2×#10625325C2214yes—
12#13094024C2211yescharacteristic
13#13094021C2211yescharacteristic
14#13094012—21no—
15#13093998—21no—
16#13093998C2212yes—
17C4×Dic94—21no—
18C4×Dic94—21no—
19C4×Dic94C2212yes—
20C4×Dic94C2212yes—
21C4×D188—21no—
22C4×D188C2212yes—
23C2×C4⋊Dic47C2211yescharacteristic
24C2×Dic47⋊C4—21no—
25C2×C4×Dic47—21no—
26#13093958C2214yes—
27#13093949C2214yes—
28#13093946C2214yes—
29C2×C42×C47C2211yescharacteristic
30C4⋊C8×C47C2212yes—
31C22⋊C8×C47C2212yes—
32#97×C47C2212yes—
33C22×C4×C47D411yescharacteristic
34C22×C4×C47D411yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C2×C22⋊D47—22no—
37C22×Dic47—21no—
38C22×Dic47—21no—
39#10625350—44no—
40C2×D188—21no—
41C2×D188—21no—
42C2×D188C2312yes—
43C2×C4×D47—22no—
44C2×Dic94—21no—
45C2×Dic94—24no—
46C2×Dic94—21no—
47C2×Dic94C2312yes—
48C2×C8×C47C2314yes—
49C42×C47D411yescharacteristic
50C42×C47D411yescharacteristic
51C42×C47C2311yescharacteristic
52C42×C47C2311yescharacteristic
53(C2×D47)⋊C4—22no—
54(C2×D47)⋊C4—22no—
55C4⋊Dic47—21no—
56C4⋊Dic47—21no—
57C4⋊Dic47C2312yes—
58C4⋊Dic47C2312yes—
59Dic47⋊C4—22no—
60Dic47⋊C4—22no—
61C4×Dic47—22no—
62C4×Dic47—22no—
63#10625325—28no—
64C23×C47C2×D411yescharacteristic
65C22×D47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2411yescharacteristic
75C22⋊D47—44no—
76C2×Dic47—24no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—42no—
81D188—24no—
82D188—42no—
83D188—42no—
84C4×D47—44no—
85Dic94—24no—
86Dic94—22no—
87Dic94—42no—
88Dic94#4114yescomplemented
89C8×C47—24no—
90C22×C47—21no—
91C22×C47—21no—
92C22×C47AGL(1,ℤ/8)12yes—
93C22×C47C22×D411yescharacteristic
94C2×D47—42no—
95C2×D47—42no—
96C2×D47—42no—
97C4×C47—21no—
98C4×C47—21no—
99C4×C47—21no—
100C4×C47—21no—
101C4×C47#13712yes—
102C4×C47C2×#4112yes—
103Dic47—24no—
104Dic47—42no—
105Dic47—42no—
106#3112—471nomaximal, Sylow
107C2×C47—22no—
108C2×C47#52511yescharacteristic
109C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
110C2×C47C2×#13711yescharacteristic
111D47—82no—
112#532—471no—
113C2×C4×Q8—471no—
114#480—472no—
115#477—472no—
116#460—472no—
117#448—472no—
118#440—474no—
119#432D4711yescharacteristic, complemented
120C47#311211yescharacteristic, complemented, Sylow
121C2×#41—941no—
122C22×Q8—471no—
123C2×SD16—474no—
124C4⋊Q8—471no—
125#127—471no—
126#124—941no—
127#121—472no—
128#121—941no—
129C4×Q8—472no—
130C4×Q8—472no—
131C4×Q8—941no—
132C4×Q8—941no—
133C4×D4—472no—
134C4×D4—941no—
135C2×C4⋊C4—471no—
136C2×C4⋊C4—941no—
137C2×C42—941no—
138C2×C42C2×D4711yescharacteristic
139#107—474no—
140C4⋊C8C2×D4712yes—
141#103—474no—
142#102—474no—
143C22⋊C8C2×D4712yes—
144#97C2×D4712yes—
145#41—1884no—
146C2×Q8—472no—
147C2×Q8—944no—
148C2×Q8—941no—
149C2×Q8—941no—
150C2×D4—472no—
151C2×D4—942no—
152C2×D4—941no—
153C2×D4—941no—
154C22×C4—941no—
155C22×C4—941no—
156C22×C4—942no—
157C22×C4D18811yescharacteristic
158C22×C4D18811yescharacteristic
159C22×C4C22×D4711yescharacteristic
160SD16—948no—
161C2×C8C22×D4714yes—
162C4⋊C4—472no—
163C4⋊C4—472no—
164C4⋊C4—942no—
165C4⋊C4—942no—
166C4⋊C4—941no—
167C4⋊C4—941no—
168C22⋊C4—942no—
169C22⋊C4—942no—
170C42—942no—
171C42—942no—
172C42D18811yescharacteristic
173C42D18811yescharacteristic
174C42C22×D4711yescharacteristic
175C42C22×D4711yescharacteristic
176C23—942no—
177C23C2×D18811yescharacteristic
178Q8—474no—
179Q8—944no—
180Q8—942no—
181Q8—1882no—
182D4—944no—
183D4—1882no—
184D4—1884no—
185D4—1882no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—944no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—942no—
193C2×C4—1884no—
194C2×C4—1882no—
195C2×C4C2×D18811yescharacteristic
196C2×C4C2×D18811yescharacteristic
197C2×C4C2×D18811yescharacteristic
198C2×C4C2×D18811yescharacteristic
199C2×C4C2×D18811yescharacteristic
200C2×C4C23×D4711yescharacteristic
201C8—24no—
202C22—21no—
203C22—21no—
204C22—1882no—
205C22—1882no—
206C22—1882no—
207C22#1309405212yes—
208C22C22×D18811yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—944no—
214C4—1882no—
215C4—1882no—
216C4#1309405712yes—
217C4#41×D4712yes—
218C2—22no—
219C2—3762no—
220C2#1568963511yescharacteristic
221C2C2×#1309405211yescharacteristic
222C2C2×#1309405711yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#432C2
socleC22×C47C22×D4
hypercenter#432D47
hypocenterC47#3112
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic94C2semidirect
3. #15689437C2semidirect
4. #15689419C2semidirect
5. #15689324C2semidirect
6. #15689264C2semidirect
7. #15689225C2semidirect
8. C47×#432C2semidirect
88. Dic94#41semidirect
119. #432D47semidirect
120. C47#3112semidirect