Finite Group Databasebeta

← #20242434

Subgroups — #20242434

Order 6016.

240 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 49 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#15689711C211yesmaximal, characteristic
2#15689458C211yesmaximal, characteristic, complemented
3#15689441C211yesmaximal, characteristic, complemented
4#15688859C211yesmaximal, characteristic, complemented
5#15688856C211yesmaximal, characteristic, complemented
6#15688847C211yesmaximal, characteristic, complemented
7C47×#399C211yesmaximal, characteristic, complemented
8#13094017—21no—
9#13094010—21no—
10#13094006—21no—
11#13094003C2211yescharacteristic
12#13093998C2211yescharacteristic
13#13093997—21no—
14#13093993—21no—
15C4×C22⋊D47—21no—
16#13093957—21no—
17#13093955—21no—
18#13093947—21no—
19#13093944—21no—
20C22⋊(C47⋊C8)C2211yescharacteristic
21C22⋊(C47⋊C8)C2211yescharacteristic
22C2×C4⋊C4×C47—21no—
23C2×C4⋊C4×C47C2211yescharacteristic
24C2×C22⋊C4×C47—21no—
25C2×C22⋊C4×C47C2211yescharacteristic
26#95×C47C2211yescharacteristic
27C24×C47D411yescharacteristic
28C22×C4×C47—21no—
29C22×C4×C47—21no—
30C22×C4×C47D411yescharacteristic
31C22×C4×C47C2311yescharacteristic
32C2×C22⋊D47—21no—
33C2×C22⋊D47—21no—
34C2×C22⋊D47—21no—
35C2×D188D411yescharacteristic
36C2×C4×D47—21no—
37C2×Dic94D411yescharacteristic
38C4⋊C4×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—42no—
41C22⋊C4×C47—21no—
42C22⋊C4×C47—21no—
43C22⋊C4×C47—42no—
44C22⋊Dic47—21no—
45C22⋊Dic47—21no—
46C22⋊Dic47—21no—
47(C2×D47)⋊C4—21no—
48(C2×D47)⋊C4—21no—
49C4⋊Dic47D411yescharacteristic
50C4⋊Dic47D411yescharacteristic
51Dic47⋊C4—21no—
52Dic47⋊C4—21no—
53C4×Dic47—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C23×C47—21no—
57C23×C47—21no—
58C23×C47—21no—
59C23×C47—41no—
60C23×C47—41no—
61C23×C47C2×D411yescharacteristic
62C22×D47—21no—
63C2×C4×C47—22no—
64C2×C4×C47—21no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47—41no—
71C2×C4×C47—41no—
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C22⋊D47—41no—
75C22⋊D47—41no—
76C22⋊D47—81no—
77C22⋊D47—81no—
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47—21no—
81D188—41no—
82C4×D47—81no—
83Dic94—41no—
84C47⋊C8—41no—
85C47⋊C8—41no—
86C22×C47—21no—
87C22×C47—21no—
88C22×C47—42no—
89C22×C47—41no—
90C22×C47—41no—
91C22×C47—41no—
92C22×C47—81no—
93C22×C47#12011yescharacteristic
94C22×C47#13511yescharacteristic
95C22×C47#13711yescharacteristic
96C2×D47—41no—
97C2×D47—41no—
98C2×D47—41no—
99C4×C47—21no—
100C4×C47—21no—
101C4×C47—42no—
102C4×C47—41no—
103C4×C47—81no—
104Dic47—41no—
105Dic47—41no—
106Dic47—41no—
107#1618—471nomaximal, Sylow
108C2×C47—21no—
109C2×C47—21no—
110C2×C47—81no—
111C2×C47#45211yescharacteristic
112C2×C47#45311yescharacteristic
113C2×C47#45811yescharacteristic
114D47—81no—
115#538—471no—
116#484—471no—
117#481—471no—
118#399D4711yescharacteristic, complemented
119#328—471no—
120#327—471no—
121#323—471no—
122C47#161811yescharacteristic, complemented, Sylow
123#126—941no—
124#124—941no—
125#123—941no—
126C22⋊Q8—471no—
127#121—471no—
128#121—941no—
129#120—941no—
130C4×D4—941no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4C2×D4711yescharacteristic
133C2×C22⋊C4—21no—
134C2×C22⋊C4C2×D4711yescharacteristic
135#107—941no—
136#106—941no—
137#103—941no—
138#102—941no—
139C22⋊C8—471no—
140C22⋊C8—471no—
141#95C2×D4711yescharacteristic
142C24C22⋊D4711yescharacteristic
143C2×Q8—471no—
144C2×D4—471no—
145C2×D4—941no—
146C2×D4—941no—
147C2×D4—941no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—941no—
151C22×C4C22⋊D4711yescharacteristic
152C22×C4C22×D4711yescharacteristic
153C2×C8—941no—
154C2×C8—941no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—42no—
158C4⋊C4—471no—
159C4⋊C4—471no—
160C4⋊C4—941no—
161C4⋊C4—941no—
162C22⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—42no—
165C22⋊C4—941no—
166C22⋊C4—941no—
167C22⋊C4—941no—
168C22⋊C4—941no—
169C22⋊C4—941no—
170C42—941no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23—41no—
175C23—41no—
176C23—941no—
177C23C2×C22⋊D4711yescharacteristic
178Q8—1881no—
179D4—3761no—
180D4—3761no—
181D4—1881no—
182D4—1881no—
183D4—1881no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—941no—
194C2×C4—941no—
195C2×C4—941no—
196C2×C4—3761no—
197C2×C4D4×D4711yescharacteristic
198C2×C4D4×D4711yescharacteristic
199C8—1881no—
200C8—1881no—
201C22—21no—
202C22—21no—
203C22—42no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—81no—
208C22—1881no—
209C22—1881no—
210C22—1881no—
211C22#1309399211yescharacteristic
212C22#1309404411yescharacteristic
213C22#1309405511yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—41no—
218C4—81no—
219C4—1881no—
220C4—1881no—
221C4—1881no—
222C2—21no—
223C2—21no—
224C2—81no—
225C2—3761no—
226C2#1568928311yescharacteristic
227C2#1568929011yescharacteristic
228C2#1568931211yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#399C2
socleC22×C47#120
hypercenter#399D47
hypocenterC47#1618
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #15689458C2semidirect
3. #15689441C2semidirect
4. #15688859C2semidirect
5. #15688856C2semidirect
6. #15688847C2semidirect
7. C47×#399C2semidirect
118. #399D47semidirect
122. C47#1618semidirect