Finite Group Databasebeta

← #20244033

Subgroups — #20244033

Order 6016.

224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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×#13093959C211yesmaximal, characteristic, complemented
2C2×#13093951C211yesmaximal, characteristic
3#15689119C211yesmaximal, characteristic
4#15689078C211yesmaximal, characteristic, complemented
5#15688884C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C47×#408C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10#13093983C2211yescharacteristic
11C2×C4×Dic47C2211yescharacteristic
12#13093959—22no—
13#13093951—22no—
14#13093948C411yescharacteristic, complemented
15#13093948C411yescharacteristic, complemented
16#13093945C411yescharacteristic, complemented
17#13093945C411yescharacteristic, complemented
18#13093934—21no—
19C8×Dic47—21no—
20C2×#41×C47C2211yescharacteristic
21C2×M16×C47C2211yescharacteristic
22C22×C8×C47C2211yescharacteristic
23C22⋊C8×C47—21no—
24C22⋊C8×C47—21no—
25#41×C47—21no—
26#41×C47—21no—
27#41×C47—21no—
28#41×C47—21no—
29C2×Q8×C47C2×C411yescharacteristic
30C2×D4×C47—21no—
31C2×D4×C47C2×C411yescharacteristic
32C22×C4×C47—21no—
33C22×C4×C47C2311yescharacteristic
34C22×Dic47—21no—
35M16×C47—21no—
36M16×C47—21no—
37C2×C8×C47—21no—
38C2×C8×C47—21no—
39C2×C8×C47—21no—
40C2×C8×C47D411yescharacteristic
41C2×C8×C47D411yescharacteristic
42C22⋊Dic47—21no—
43C4⋊Dic47C2×C411yescharacteristic
44C4⋊Dic47C2×C411yescharacteristic
45C4×Dic47—21no—
46C4×Dic47—21no—
47C4×Dic47—21no—
48#10625329—21no—
49#10625329D412yes—
50C2×C47⋊C8—21no—
51C2×C47⋊C8—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8C2×C411yescharacteristic
54C2×C47⋊C8C2×C411yescharacteristic
55C23×C47—21no—
56C23×C47#4111yescharacteristic
57Q8×C47—21no—
58Q8×C47—21no—
59D4×C47—21no—
60D4×C47—21no—
61D4×C47—41no—
62D4×C47—41no—
63C2×C4×C47—21no—
64C2×C4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47C22×C411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47#4111yescharacteristic
70C2×C4×C47#4111yescharacteristic
71C2×C4×C47#4111yescharacteristic
72C2×Dic47—22no—
73C2×Dic47—21no—
74C2×Dic47—21no—
75C2×Dic47—41no—
76C2×Dic47—41no—
77C8×C47—21no—
78C8×C47—21no—
79C8×C47—41no—
80C47⋊C8—21no—
81C47⋊C8—21no—
82C47⋊C8—22no—
83C22×C47—21no—
84C22×C47—21no—
85C22×C47—41no—
86C22×C47—41no—
87C22×C47—41no—
88C22×C47C4×D411yescharacteristic
89C22×C47#12411yescharacteristic
90C22×C47#12611yescharacteristic
91C4×C47—41no—
92C4×C47#11711yescharacteristic
93C4×C47C4×D411yescharacteristic
94C4×C47#12111yescharacteristic
95C4×C47#12311yescharacteristic
96Dic47—42no—
97Dic47—41no—
98Dic47—41no—
99#1929—471nomaximal, Sylow
100C2×C47—21no—
101C2×C47—21no—
102C2×C47—81no—
103C2×C47#38811yescharacteristic
104C2×C47#44311yescharacteristic
105C2×C47#44411yescharacteristic
106C2×#108—471no—
107C2×#104—471no—
108#416—471no—
109#408D4711yescharacteristic
110#405—471no—
111#339—471no—
112#336—471no—
113C47#192911yescharacteristic, complemented, Sylow
114C2×#41C2×D4711yescharacteristic
115C2×M16—471no—
116C2×M16C2×D4711yescharacteristic
117C22×C8—471no—
118C22×C8C2×D4711yescharacteristic
119#117—471no—
120C2×C42—471no—
121#108—942no—
122#104—942no—
123#103—471no—
124#103—471no—
125#102—471no—
126#102—471no—
127C22⋊C8—21no—
128C22⋊C8—21no—
129#97—941no—
130C4×C8—941no—
131#41—21no—
132#41—21no—
133#41—21no—
134#41—21no—
135C2×Q8C4×D4711yescharacteristic
136C2×D4—21no—
137C2×D4C4×D4711yescharacteristic
138C22×C4—21no—
139C22×C4—941no—
140C22×C4C22×D4711yescharacteristic
141M16—21no—
142M16—21no—
143M16—472no—
144M16—941no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—471no—
149C2×C8—471no—
150C2×C8—941no—
151C2×C8—941no—
152C2×C8—941no—
153C2×C8C22⋊D4711yescharacteristic
154C2×C8C22⋊D4711yescharacteristic
155C4⋊C4—471no—
156C4⋊C4—471no—
157C22⋊C4—941no—
158C42—941no—
159C42—941no—
160C42—941no—
161C23—21no—
162C23#1062535011yescharacteristic
163Q8—21no—
164Q8—21no—
165D4—21no—
166D4—21no—
167D4—41no—
168D4—41no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—942no—
173C2×C4—941no—
174C2×C4—941no—
175C2×C4—1881no—
176C2×C4—1881no—
177C2×C4C2×C4×D4711yescharacteristic
178C2×C4D4×D4711yescharacteristic
179C2×C4#1062535211yescharacteristic
180C2×C4#1062535211yescharacteristic
181C2×C4#1062535211yescharacteristic
182C2×C4C2×C22⋊D4711yescharacteristic
183C8—21no—
184C8—21no—
185C8—41no—
186C8—941no—
187C8—941no—
188C8—942no—
189C22—21no—
190C22—21no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22C4×C22⋊D4711yescharacteristic
195C22#1309401011yescharacteristic
196C22#1309401711yescharacteristic
197C4—41no—
198C4—1882no—
199C4—1881no—
200C4—1881no—
201C4#1309398011yescharacteristic
202C4(C22⋊D47)⋊C411yescharacteristic
203C4#1309399511yescharacteristic
204C4#1309400511yescharacteristic
205C2—21no—
206C2—21no—
207C2—81no—
208C2#1568901111yescharacteristic
209C2#1568923811yescharacteristic
210C2#1568924311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#408C2
socleC22×C47C4×D4
hypercenter#408D47
hypocenterC47#1929
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C2×#13093959C2semidirect
4. #15689078C2semidirect
5. #15688884C2semidirect
6. #15688877C2semidirect
14. #13093948C4semidirect
15. #13093948C4semidirect
16. #13093945C4semidirect
17. #13093945C4semidirect
113. C47#1929semidirect