Finite Group Databasebeta

← #20244036

Subgroups — #20244036

Order 6016.

224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 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×#13093950C211yesmaximal, characteristic
3#15689117C211yesmaximal, characteristic
4#15689089C211yesmaximal, characteristic
5#15688882C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C47×#405C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C22×C47⋊C8C2211yescharacteristic
11C2×C4×Dic47C2211yescharacteristic
12#13093959—22no—
13#13093950—22no—
14#13093947C411yescharacteristic, complemented
15#13093947C411yescharacteristic, complemented
16#13093944C411yescharacteristic, complemented
17#13093944C411yescharacteristic, complemented
18(C2×D47)⋊C8—21no—
19(C2×D47)⋊C8—21no—
20C2×M16×C47C2211yescharacteristic
21C22×C8×C47C2211yescharacteristic
22#117×C47C2211yescharacteristic
23#97×C47—21no—
24C4×C8×C47—21no—
25C22×C4×C47C2311yescharacteristic
26C2×C22⋊D47—21no—
27C22×Dic47—21no—
28#10625350—21no—
29#10625350—21no—
30#10625350—21no—
31#10625350—21no—
32C2×D188C2×C411yescharacteristic
33C2×C4×D47—21no—
34C2×Dic94C2×C411yescharacteristic
35M16×C47—21no—
36M16×C47D412yes—
37C2×C8×C47—21no—
38C2×C8×C47—21no—
39C2×C8×C47—21no—
40C2×C8×C47D411yescharacteristic
41C2×C8×C47D411yescharacteristic
42C4⋊C4×C47C2×C411yescharacteristic
43C4⋊C4×C47C2×C411yescharacteristic
44C22⋊C4×C47—21no—
45C42×C47—21no—
46C4×Dic47—21no—
47C4×Dic47—21no—
48#10625329—21no—
49#10625329—21no—
50C2×C47⋊C8—21no—
51C2×C47⋊C8—21no—
52C2×C47⋊C8—21no—
53C2×C47⋊C8C2×C411yescharacteristic
54C2×C47⋊C8C2×C411yescharacteristic
55C23×C47#4111yescharacteristic
56C22×D47—21no—
57C2×C4×C47—21no—
58C2×C4×C47—21no—
59C2×C4×C47C22×C411yescharacteristic
60C2×C4×C47C2×D411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47#4111yescharacteristic
63C2×C4×C47#4111yescharacteristic
64C2×C4×C47#4111yescharacteristic
65C22⋊D47—41no—
66C22⋊D47—41no—
67C2×Dic47—22no—
68C2×Dic47—21no—
69C2×Dic47—41no—
70C2×Dic47—41no—
71D188—21no—
72D188—21no—
73C4×D47—41no—
74C4×D47—41no—
75Dic94—21no—
76Dic94—21no—
77C8×C47—22no—
78C8×C47—21no—
79C8×C47—21no—
80C47⋊C8—21no—
81C47⋊C8—21no—
82C47⋊C8—41no—
83C22×C47—21no—
84C22×C47—21no—
85C22×C47C4×D411yescharacteristic
86C22×C47#12411yescharacteristic
87C22×C47#12611yescharacteristic
88C2×D47—41no—
89C2×D47—41no—
90C2×D47—41no—
91C4×C47—41no—
92C4×C47—41no—
93C4×C47#11711yescharacteristic
94C4×C47C4×D411yescharacteristic
95C4×C47#12111yescharacteristic
96C4×C47#12311yescharacteristic
97Dic47—42no—
98Dic47—41no—
99#1929—471nomaximal, Sylow
100C2×C47—21no—
101C2×C47—21no—
102C2×C47#38811yescharacteristic
103C2×C47#44311yescharacteristic
104C2×C47#44411yescharacteristic
105D47—81no—
106C2×#108—471no—
107C2×#104—471no—
108#416—471no—
109#408—471no—
110#405D4711yescharacteristic, complemented
111#339—471no—
112#336—471no—
113C47#192911yescharacteristic, complemented, Sylow
114C2×#41—471no—
115C2×M16—471no—
116C2×M16C2×D4711yescharacteristic
117C22×C8—471no—
118C22×C8C2×D4711yescharacteristic
119#117C2×D4711yescharacteristic
120C2×C42—471no—
121#108—942no—
122#104—942no—
123#103—471no—
124#103—471no—
125#102—471no—
126#102—471no—
127C22⋊C8—941no—
128C22⋊C8—941no—
129#97—21no—
130C4×C8—21no—
131#41—941no—
132#41—941no—
133#41—941no—
134#41—941no—
135C2×Q8—471no—
136C2×D4—471no—
137C2×D4—941no—
138C22×C4—941no—
139C22×C4—941no—
140C22×C4C22×D4711yescharacteristic
141M16—21no—
142M16—941no—
143M16—941no—
144M16D18812yes—
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⋊C4C4×D4711yescharacteristic
156C4⋊C4C4×D4711yescharacteristic
157C22⋊C4—21no—
158C42—21no—
159C42—941no—
160C42—941no—
161C23—941no—
162C23#1062535011yescharacteristic
163Q8—941no—
164Q8—941no—
165D4—941no—
166D4—941no—
167D4—1881no—
168D4—1881no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—942no—
172C2×C4—941no—
173C2×C4—1881no—
174C2×C4—1881no—
175C2×C4—1881no—
176C2×C4—1881no—
177C2×C4C2×C4×D4711yescharacteristic
178C2×C4C2×D18811yescharacteristic
179C2×C4#1062535011yescharacteristic
180C2×C4#1062535011yescharacteristic
181C2×C4#1062535011yescharacteristic
182C2×C4C2×C22⋊D4711yescharacteristic
183C8—22no—
184C8—21no—
185C8—21no—
186C8—941no—
187C8—941no—
188C8—1881no—
189C22—21no—
190C22—21no—
191C22—1881no—
192C22—1881no—
193C22—1881no—
194C22C4×C22⋊D4711yescharacteristic
195C22#1309401211yescharacteristic
196C22#1309401811yescharacteristic
197C4—41no—
198C4—41no—
199C4—1882no—
200C4—1881no—
201C4#1309398111yescharacteristic
202C4C4×D18811yescharacteristic
203C4#1309399811yescharacteristic
204C4#1309400711yescharacteristic
205C2—21no—
206C2—21no—
207C2—3761no—
208C2#1568901411yescharacteristic
209C2#1568923811yescharacteristic
210C2#1568924311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#405C2
socleC22×C47C4×D4
hypercenter#405D47
hypocenterC47#1929
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #405

Complements

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

NH ≅ G/Ntype
1. C2×#13093959C2semidirect
5. #15688882C2semidirect
6. #15688877C2semidirect
7. C47×#405C2semidirect
14. #13093947C4semidirect
15. #13093947C4semidirect
16. #13093944C4semidirect
17. #13093944C4semidirect
110. #405D47semidirect
113. C47#1929semidirect