Finite Group Databasebeta

← #20254580

Subgroups — #20254580

Order 6016.

368 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 121 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×#13094016C211yesmaximal, characteristic, complemented
3#15689532C212yesmaximal, complemented
4#15689488C212yesmaximal, complemented
5#15689442C212yesmaximal, complemented
6#15689437C212yesmaximal, complemented
7#15689424C214yesmaximal, complemented
8C47×#432C211yesmaximal, characteristic, complemented
9C2×#10625350—21no—
10#13094024C2211yescharacteristic
11#13094021C2211yescharacteristic
12#13094016—21no—
13#13094016—21no—
14#13094016C2212yes—
15#13094016C2212yes—
16#13094012—21no—
17#13093998—21no—
18#13093998C2212yes—
19C4×D188—21no—
20C4×D188C2212yes—
21C2×C4⋊Dic47C2211yescharacteristic
22C2×C4⋊Dic47C2211yescharacteristic
23C2×Dic47⋊C4—21no—
24C2×Dic47⋊C4—21no—
25#13093958C2214yes—
26#13093956C2214yes—
27#13093946C2214yes—
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×C8×C47C2314yes—
46C42×C47D411yescharacteristic
47C42×C47D411yescharacteristic
48C42×C47C2311yescharacteristic
49C42×C47C2311yescharacteristic
50(C2×D47)⋊C4—22no—
51(C2×D47)⋊C4—22no—
52C4⋊Dic47—21no—
53C4⋊Dic47—21no—
54C4⋊Dic47—21no—
55C4⋊Dic47C2312yes—
56C4⋊Dic47C2312yes—
57C4⋊Dic47C2312yes—
58Dic47⋊C4—22no—
59Dic47⋊C4—22no—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62C23×C47C2×D411yescharacteristic
63C22×D47—22no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—41no—
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2411yescharacteristic
73C22⋊D47—44no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—42no—
78C2×Dic47—42no—
79D188—24no—
80D188—42no—
81D188—42no—
82C4×D47—44no—
83Dic94—42no—
84C8×C47—24no—
85C22×C47—21no—
86C22×C47—21no—
87C22×C47AGL(1,ℤ/8)12yes—
88C22×C47C22×D411yescharacteristic
89C2×D47—42no—
90C2×D47—42no—
91C2×D47—42no—
92C4×C47—21no—
93C4×C47—21no—
94C4×C47—21no—
95C4×C47—21no—
96C4×C47—21no—
97C4×C472−1+412yes—
98Dic47—42no—
99Dic47—42no—
100Dic47—42no—
101#3234—471nomaximal, Sylow
102C2×C47—22no—
103C2×C47#53611yescharacteristic
104C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
105C2×C47#57511yescharacteristic
106D47—82no—
107#532—471no—
108C2×#125—471no—
109#501—472no—
110#490—472no—
111#481—472no—
112#480—472no—
113#478—474no—
114#432D4711yescharacteristic, complemented
115C47#323411yescharacteristic, complemented, Sylow
116C2×#41—941no—
117C4⋊Q8—471no—
118#127—471no—
119#125—472no—
120#125—472no—
121#125—941no—
122#125—941no—
123#124—941no—
124#121—472no—
125#121—941no—
126C4×D4—472no—
127C4×D4—941no—
128C2×C4⋊C4—471no—
129C2×C4⋊C4—471no—
130C2×C4⋊C4—941no—
131C2×C4⋊C4—941no—
132C2×C42C2×D4711yescharacteristic
133#107—474no—
134#106—474no—
135C4⋊C8C2×D4712yes—
136#102—474no—
137#102—474no—
138C22⋊C8C2×D4712yes—
139#97C2×D4712yes—
140#41—1884no—
141C2×Q8—941no—
142C2×D4—472no—
143C2×D4—942no—
144C2×D4—941no—
145C2×D4—941no—
146C22×C4—941no—
147C22×C4—941no—
148C22×C4—942no—
149C22×C4D18811yescharacteristic
150C22×C4D18811yescharacteristic
151C22×C4C22×D4711yescharacteristic
152C2×C8C22×D4714yes—
153C4⋊C4—472no—
154C4⋊C4—472no—
155C4⋊C4—472no—
156C4⋊C4—942no—
157C4⋊C4—942no—
158C4⋊C4—942no—
159C4⋊C4—942no—
160C4⋊C4—941no—
161C4⋊C4—941no—
162C4⋊C4—941no—
163C22⋊C4—942no—
164C22⋊C4—942no—
165C42D18811yescharacteristic
166C42D18811yescharacteristic
167C42C22×D4711yescharacteristic
168C42C22×D4711yescharacteristic
169C23—942no—
170C23C2×D18811yescharacteristic
171Q8—1882no—
172D4—944no—
173D4—1882no—
174D4—1882no—
175D4—1884no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—942no—
180C2×C4—942no—
181C2×C4—942no—
182C2×C4—1884no—
183C2×C4—1882no—
184C2×C4—1882no—
185C2×C4C2×D18811yescharacteristic
186C2×C4C2×D18811yescharacteristic
187C2×C4C2×D18811yescharacteristic
188C2×C4C2×D18811yescharacteristic
189C2×C4C2×D18811yescharacteristic
190C2×C4C23×D4711yescharacteristic
191C8—24no—
192C22—21no—
193C22—21no—
194C22—1882no—
195C22—1882no—
196C22—1882no—
197C22#1309405212yes—
198C22C22×D18811yescharacteristic
199C4—21no—
200C4—21no—
201C4—21no—
202C4—21no—
203C4—21no—
204C4—1882no—
205C4—1882no—
206C4—1882no—
207C4#1309407112yes—
208C2—22no—
209C2—3762no—
210C2#1568969911yescharacteristic
211C2C2×#1309405211yescharacteristic
212C2#1568992311yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#432C2
socleC22×C47C22×D4
hypercenter#432D47
hypocenterC47#3234
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×#13094016C2semidirect
3. #15689532C2semidirect
4. #15689488C2semidirect
5. #15689442C2semidirect
6. #15689437C2semidirect
7. #15689424C2semidirect
8. C47×#432C2semidirect
114. #432D47semidirect
115. C47#3234semidirect