Finite Group Databasebeta

← #20243665

Subgroups — #20243665

Order 6016.

270 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 97 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×#13094031C211yesmaximal, characteristic
2C2×#13093960C211yesmaximal, characteristic, complemented
3#15689150C211yesmaximal, characteristic, complemented
4C2×#13093951C211yesmaximal, characteristic
5#15688882C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C47×#416C211yesmaximal, characteristic
8#13094031—22no—
9#13094031—22no—
10C2×#10625329—21no—
11C2×#10625329C2211yescharacteristic
12C2×#10625329C2211yescharacteristic
13C22×C47⋊C8—21no—
14C22×C47⋊C8C2211yescharacteristic
15C2×C4×Dic47C2211yescharacteristic
16#13093960—22no—
17C4⋊(C47⋊C8)—21no—
18C4⋊(C47⋊C8)—21no—
19#13093951—22no—
20C2×#41×C47C2211yescharacteristic
21C22×C8×C47C2211yescharacteristic
22#117×C47C2211yescharacteristic
23#103×C47C411yescharacteristic, complemented
24#103×C47C411yescharacteristic, complemented
25#102×C47C411yescharacteristic, complemented
26#102×C47C411yescharacteristic, complemented
27#41×C47—21no—
28#41×C47—21no—
29#41×C47D412yes—
30#41×C47Q812yes—
31C2×Q8×C47C2×C411yescharacteristic
32C2×D4×C47—21no—
33C2×D4×C47C2×C411yescharacteristic
34C22×C4×C47—21no—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47—21no—
37C2×C8×C47—21no—
38C2×C8×C47—21no—
39C2×C8×C47C2×C411yescharacteristic
40C2×C8×C47C2×C411yescharacteristic
41C4⋊C4×C47C2×C411yescharacteristic
42C4⋊C4×C47C2×C411yescharacteristic
43C22⋊C4×C47—21no—
44C42×C47—21no—
45C4×Dic47—21no—
46C4×Dic47—21no—
47#10625329—24no—
48#10625329—21no—
49#10625329—21no—
50#10625329—21no—
51#10625329D412yes—
52C2×C47⋊C8—24no—
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8D411yescharacteristic
58C2×C47⋊C8D411yescharacteristic
59C23×C47—21no—
60C23×C47#4111yescharacteristic
61Q8×C47—21no—
62Q8×C47C4⋊C412yes—
63D4×C47—22no—
64D4×C47—22no—
65D4×C47—21no—
66D4×C47C4⋊C412yes—
67C2×C4×C47—21no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—21no—
71C2×C4×C47—21no—
72C2×C4×C47C22×C411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×Q811yescharacteristic
77C2×C4×C47#4111yescharacteristic
78C2×Dic47—22no—
79C2×Dic47—41no—
80C2×Dic47—41no—
81C8×C47—21no—
82C8×C47—21no—
83C47⋊C8—21no—
84C47⋊C8—22no—
85C47⋊C8—21no—
86C47⋊C8—41no—
87C22×C47—21no—
88C22×C47—21no—
89C22×C47—22no—
90C22×C47—41no—
91C22×C47—41no—
92C22×C47C4×D411yescharacteristic
93C22×C47C22⋊Q811yescharacteristic
94C22×C47#12311yescharacteristic
95C4×C47—22no—
96C4×C47—41no—
97C4×C47—41no—
98C4×C47C2×C4⋊C411yescharacteristic
99C4×C47C4×D411yescharacteristic
100C4×C47#12011yescharacteristic
101C4×C47C22⋊Q811yescharacteristic
102Dic47—42no—
103#1866—471nomaximal, Sylow
104C2×C47—21no—
105C2×C47—21no—
106C2×C47—42no—
107C2×C47#38511yescharacteristic
108C2×C47#44311yescharacteristic
109C2×C47#44411yescharacteristic
110C2×#131—471no—
111C2×#108—471no—
112#424—471no—
113C2×#104—471no—
114#416D4711yescharacteristic
115#339—471no—
116#336—471no—
117C47#186611yescharacteristic, complemented, Sylow
118C2×#41C2×D4711yescharacteristic
119#131—942no—
120#131—942no—
121C2×M16—471no—
122C2×M16—471no—
123C2×M16—941no—
124C22×C8—471no—
125C22×C8—941no—
126C22×C8C2×D4711yescharacteristic
127#117C2×D4711yescharacteristic
128C2×C42—471no—
129#108—942no—
130C4⋊C8—941no—
131C4⋊C8—941no—
132#104—942no—
133#103Dic4711yescharacteristic, complemented
134#103Dic4711yescharacteristic, complemented
135#102Dic4711yescharacteristic, complemented
136#102Dic4711yescharacteristic, complemented
137#41—21no—
138#41—21no—
139#41Dic9412yes—
140#41D18812yes—
141C2×Q8C2×Dic4711yescharacteristic
142C2×D4—21no—
143C2×D4C2×Dic4711yescharacteristic
144C22×C4—21no—
145C22×C4—941no—
146C22×C4C22×D4711yescharacteristic
147M16—472no—
148M16—944no—
149M16—941no—
150M16—941no—
151M16—941no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—471no—
155C2×C8—471no—
156C2×C8—944no—
157C2×C8—941no—
158C2×C8—941no—
159C2×C8—941no—
160C2×C8—941no—
161C2×C8C2×Dic4711yescharacteristic
162C2×C8C2×Dic4711yescharacteristic
163C4⋊C4C2×Dic4711yescharacteristic
164C4⋊C4C2×Dic4711yescharacteristic
165C22⋊C4—21no—
166C42—21no—
167C42—941no—
168C42—941no—
169C23—21no—
170C23#1062535211yescharacteristic
171Q8—21no—
172Q8C4⋊Dic4712yes—
173D4—22no—
174D4—22no—
175D4—21no—
176D4C4⋊Dic4712yes—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—942no—
183C2×C4—1881no—
184C2×C4—1881no—
185C2×C4C2×Dic9411yescharacteristic
186C2×C4C2×D18811yescharacteristic
187C2×C4D4×D4711yescharacteristic
188C2×C4D4×D4711yescharacteristic
189C2×C4#1062535211yescharacteristic
190C2×C4C22×Dic4711yescharacteristic
191C8—21no—
192C8—21no—
193C8—941no—
194C8—941no—
195C8—942no—
196C8—1881no—
197C22—21no—
198C22—21no—
199C22—22no—
200C22—41no—
201C22—41no—
202C22D4×Dic4711yescharacteristic
203C22#1309400111yescharacteristic
204C22#1309400811yescharacteristic
205C4—22no—
206C4—41no—
207C4—41no—
208C4—1882no—
209C4C2×C4⋊Dic4711yescharacteristic
210C4D4×Dic4711yescharacteristic
211C4#1309399411yescharacteristic
212C4#1309400111yescharacteristic
213C2—21no—
214C2—21no—
215C2—42no—
216C2#1568899811yescharacteristic
217C2#1568924011yescharacteristic
218C2#1568924511yescharacteristic
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#416C2
socleC22×C47C4×D4
hypercenter#416D47
hypocenterC47#1866
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. C2×#13093960C2semidirect
3. #15689150C2semidirect
5. #15688882C2semidirect
6. #15688877C2semidirect
23. #103×C47C4semidirect
24. #103×C47C4semidirect
25. #102×C47C4semidirect
26. #102×C47C4semidirect
117. C47#1866semidirect
133. #103Dic47semidirect
134. #103Dic47semidirect
135. #102Dic47semidirect
136. #102Dic47semidirect