Finite Group Databasebeta

← #20254510

Subgroups — #20254510

Order 6016.

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

normal subgroups only

This group has 404 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#15689674C211yesmaximal, characteristic
2C4⋊Q8×D47C211yesmaximal, characteristic, complemented
3#15689526C211yesmaximal, characteristic, complemented
4#15689471C211yesmaximal, characteristic, complemented
5#15689470C211yesmaximal, characteristic, complemented
6#15689438C214yesmaximal, complemented
7#15689402C214yesmaximal, complemented
8#15689174C211yesmaximal, characteristic, complemented
9C47×#500C211yesmaximal, characteristic, complemented
10C2×#10625354—21no—
11C2×Q8×D47—21no—
12#13094024C2211yescharacteristic
13#13094023—21no—
14#13094023C2212yes—
15#13094022—21no—
16#13094021C2211yescharacteristic
17#13094013—21no—
18#13093999—21no—
19#13093999C2212yes—
20#13093986—21no—
21#13093986C2212yes—
22C4⋊C4×D47—21no—
23C4⋊C4×D47C2212yes—
24C42×D47C2211yescharacteristic
25#13093957C2214yes—
26Dic47⋊C8C2212yes—
27#13093946C2214yes—
28#13093944C2214yes—
29(C2×D47)⋊C8C2212yes—
30C4×C47⋊C8C2211yescharacteristic
31C4⋊Q8×C47C2211yescharacteristic
32C4⋊Q8×C47C2211yescharacteristic
33#107×C47C2214yes—
34C4×C8×C47C2211yescharacteristic
35C2×Q8×C47—21no—
36C2×Q8×C47—21no—
37#10625354—44no—
38Q8×D47—44no—
39C2×D188—22no—
40C2×D188—21no—
41C2×D188—21no—
42C2×D188C2312yes—
43C2×C4×D47—22no—
44C2×C4×D47—22no—
45C2×C4×D47D411yescharacteristic
46C2×C4×D47D411yescharacteristic
47C2×C4×D47C2311yescharacteristic
48C2×Dic94—21no—
49C2×Dic94—22no—
50C2×C8×C47C2312yes—
51C4⋊C4×C47—21no—
52C4⋊C4×C47—21no—
53C4⋊C4×C47C2312yes—
54C4⋊C4×C47C2312yes—
55C42×C47C2311yescharacteristic
56(C2×D47)⋊C4—22no—
57(C2×D47)⋊C4—22no—
58C4⋊Dic47—21no—
59C4⋊Dic47C2312yes—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62C4×Dic47D411yescharacteristic
63C4×Dic47D411yescharacteristic
64C4×Dic47C2311yescharacteristic
65C2×C47⋊C8C2312yes—
66C22×D47—22no—
67C22×D47C2×D411yescharacteristic
68Q8×C47—42no—
69Q8×C47—42no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2411yescharacteristic
75C2×Dic47—22no—
76C2×Dic47C2×D411yescharacteristic
77C2×Dic47C2×D411yescharacteristic
78C2×Dic47C2×D411yescharacteristic
79D188—24no—
80D188—44no—
81D188—42no—
82D188—42no—
83C4×D47—22no—
84C4×D47—22no—
85C4×D47—44no—
86C4×D47—44no—
87C4×D47D814yes—
88Dic94—42no—
89Dic94—44no—
90C8×C47—22no—
91C47⋊C8—22no—
92C22×C47C22×D411yescharacteristic
93C2×D47—21no—
94C2×D47—21no—
95C2×D47—42no—
96C2×D47—42no—
97C2×D47—42no—
98C2×D47C2×D812yes—
99C4×C47—42no—
100C4×C47—42no—
101C4×C47C2×D812yes—
102C4×C47#13712yes—
103C4×C472−1+412yes—
104Dic47—21no—
105Dic47—21no—
106Dic47—42no—
107Dic47C2×D812yes—
108#3226—471nomaximal, Sylow
109C2×C47#53611yescharacteristic
110C2×C47C22×D811yescharacteristic
111C2×C47C2×#13711yescharacteristic
112D47—22no—
113D47—82no—
114#532—471no—
115C2×C4⋊Q8—471no—
116#500—471no—
117#500D4711yescharacteristic, complemented
118#486—471no—
119#486—471no—
120#480—474no—
121#474—474no—
122#431—471no—
123C47#322611yescharacteristic, complemented, Sylow
124C2×#41—941no—
125C22×Q8—941no—
126C4⋊Q8—472no—
127C4⋊Q8—471no—
128C4⋊Q8—941no—
129C4⋊Q8—941no—
130C4⋊Q8C2×D4711yescharacteristic
131C4⋊Q8C2×D4711yescharacteristic
132#127—471no—
133#124—941no—
134#121—472no—
135#121—941no—
136C4×D4—472no—
137C4×D4—941no—
138C2×C4⋊C4—472no—
139C2×C4⋊C4—941no—
140C2×C42—471no—
141#107—474no—
142#107C2×D4714yes—
143C4⋊C8—472no—
144#102—474no—
145#102—474no—
146C22⋊C8—472no—
147C4×C8—471no—
148C4×C8C2×D4711yescharacteristic
149#41—1884no—
150C2×Q8—21no—
151C2×Q8—21no—
152C2×Q8—942no—
153C2×Q8—941no—
154C2×Q8—1884no—
155C2×D4—472no—
156C2×D4—942no—
157C2×D4—941no—
158C2×D4—941no—
159C22×C4—471no—
160C22×C4—471no—
161C22×C4—471no—
162C22×C4—942no—
163C22×C4—942no—
164C2×C8—472no—
165C2×C8C22×D4712yes—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—472no—
169C4⋊C4—942no—
170C4⋊C4—942no—
171C4⋊C4—941no—
172C4⋊C4C22×D4712yes—
173C4⋊C4C22×D4712yes—
174C22⋊C4—942no—
175C22⋊C4—942no—
176C42—471no—
177C42—471no—
178C42—471no—
179C42C22×D4711yescharacteristic
180C23—471no—
181C23—942no—
182Q8—42no—
183Q8—42no—
184Q8—1884no—
185Q8—1882no—
186D4—944no—
187D4—1884no—
188D4—1882no—
189D4—1882no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—471no—
193C2×C4—474no—
194C2×C4—471no—
195C2×C4—471no—
196C2×C4—942no—
197C2×C4—942no—
198C2×C4—942no—
199C2×C4—1884no—
200C2×C4—1884no—
201C2×C4D4×D4711yescharacteristic
202C2×C4D4×D4711yescharacteristic
203C2×C4C23×D4711yescharacteristic
204C8—22no—
205C8—942no—
206C22—472no—
207C22—941no—
208C22—941no—
209C22—1882no—
210C22—1882no—
211C22—1882no—
212C22C2×D4×D4711yescharacteristic
213C4—42no—
214C4—42no—
215C4—472no—
216C4—941no—
217C4—941no—
218C4—1882no—
219C4D8×D4712yes—
220C4#1309405612yes—
221C4#1309407212yes—
222C2—942no—
223C2—3762no—
224C2#1568969811yescharacteristic
225C2C2×D8×D4711yescharacteristic
226C2C2×#1309405611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#500C2
socleC22×C47C22×D4
hypercenter#500D47
hypocenterC47#3226
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D47C2semidirect
3. #15689526C2semidirect
4. #15689471C2semidirect
5. #15689470C2semidirect
6. #15689438C2semidirect
7. #15689402C2semidirect
8. #15689174C2semidirect
9. C47×#500C2semidirect
117. #500D47semidirect
123. C47#3226semidirect