Finite Group Databasebeta

← #20242349

Subgroups — #20242349

Order 6016.

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

normal subgroups only

This group has 244 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#15689720C211yesmaximal, characteristic
2#15689279C211yesmaximal, characteristic, complemented
3#15689262C211yesmaximal, characteristic
4#15688859C211yesmaximal, characteristic, complemented
5#15688856C211yesmaximal, characteristic
6#15688849C211yesmaximal, characteristic, complemented
7C47×#395C211yesmaximal, characteristic, complemented
8C2×#10625337—21no—
9C2×#10625336—21no—
10#13094019—21no—
11#13094014—21no—
12#13094009—21no—
13#13094007—21no—
14#13094003C2211yescharacteristic
15#13094002—21no—
16#13093998C2211yescharacteristic
17C4×C22⋊D47—21no—
18#13093948—21no—
19#13093948—21no—
20C22⋊(C47⋊C8)C2211yescharacteristic
21C22⋊(C47⋊C8)C2211yescharacteristic
22C22×Q8×C47C2211yescharacteristic
23C2×C4⋊C4×C47—21no—
24C2×C4⋊C4×C47C2211yescharacteristic
25#95×C47—21no—
26#95×C47C2211yescharacteristic
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—42no—
30C22×C4×C47—21no—
31C22×C4×C47—21no—
32C22×C4×C47D411yescharacteristic
33C22×C4×C47D411yescharacteristic
34C22×C4×C47C2311yescharacteristic
35C2×C22⋊D47—21no—
36C2×D188D411yescharacteristic
37C2×C4×D47—21no—
38C2×Dic94D411yescharacteristic
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C4⋊C4×C47—42no—
42C22⋊Dic47—21no—
43#10625337—42no—
44#10625336—42no—
45(C2×D47)⋊C4—21no—
46(C2×D47)⋊C4—21no—
47(C2×D47)⋊C4—21no—
48(C2×D47)⋊C4—21no—
49C4⋊Dic47D411yescharacteristic
50C4⋊Dic47D411yescharacteristic
51Dic47⋊C4—21no—
52Dic47⋊C4—21no—
53Dic47⋊C4—21no—
54Dic47⋊C4—21no—
55C4×Dic47—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C23×C47C2×D411yescharacteristic
59C22×D47—21no—
60Q8×C47—22no—
61Q8×C47—22no—
62Q8×C47—41no—
63Q8×C47—41no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—41no—
71C2×C4×C47—41no—
72C2×C4×C47—41no—
73C2×C4×C47—41no—
74C2×C4×C47—41no—
75C2×C4×C47—41no—
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C22⋊D47—41no—
79C22⋊D47—41no—
80C2×Dic47—21no—
81C2×Dic47—21no—
82C2×Dic47—21no—
83D188—41no—
84C4×D47—81no—
85Dic94—41no—
86C47⋊C8—41no—
87C47⋊C8—41no—
88C22×C47—21no—
89C22×C47—21no—
90C22×C47#12011yescharacteristic
91C22×C47#13511yescharacteristic
92C22×C47#13711yescharacteristic
93C2×D47—41no—
94C2×D47—41no—
95C2×D47—41no—
96C4×C47—21no—
97C4×C47—21no—
98C4×C47—42no—
99C4×C47—41no—
100C4×C47—41no—
101C4×C47—42no—
102Dic47—41no—
103Dic47—41no—
104Dic47—41no—
105#1603—471nomaximal, Sylow
106C2×C47—21no—
107C2×C47—21no—
108C2×C47#45211yescharacteristic
109C2×C47#45611yescharacteristic
110C2×C47B(4,𝔽2)11yescharacteristic
111D47—81no—
112#539—471no—
113#451—471no—
114#448—471no—
115#395D4711yescharacteristic, complemented
116#328—471no—
117#327—471no—
118#324—471no—
119C47#160311yescharacteristic, complemented, Sylow
120C22×Q8C2×D4711yescharacteristic
121C2×Q16—941no—
122C2×SD16—941no—
123#126—941no—
124#125—941no—
125#123—941no—
126#123—941no—
127C22⋊Q8—471no—
128C22⋊Q8—941no—
129#121—471no—
130C4×D4—941no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4C2×D4711yescharacteristic
133#103—941no—
134#103—941no—
135C22⋊C8—471no—
136C22⋊C8—471no—
137#95—21no—
138#95C2×D4711yescharacteristic
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—42no—
142C2×Q8—471no—
143C2×D4—471no—
144C2×D4—941no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—941no—
148C22×C4C22⋊D4711yescharacteristic
149C22×C4C22⋊D4711yescharacteristic
150C22×C4C22×D4711yescharacteristic
151Q16—1882no—
152SD16—1882no—
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—
162C4⋊C4—941no—
163C4⋊C4—941no—
164C22⋊C4—941no—
165C22⋊C4—941no—
166C22⋊C4—941no—
167C22⋊C4—941no—
168C22⋊C4—941no—
169C42—941no—
170C23—941no—
171C23C2×C22⋊D4711yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—1881no—
177D4—1881no—
178D4—1881no—
179D4—1881no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—941no—
193C2×C4—941no—
194C2×C4—941no—
195C2×C4—3761no—
196C2×C4D4×D4711yescharacteristic
197C2×C4D4×D4711yescharacteristic
198C8—1881no—
199C8—1881no—
200C22—21no—
201C22—21no—
202C22—1881no—
203C22—1881no—
204C22—1881no—
205C22#1309399211yescharacteristic
206C22#1309404411yescharacteristic
207C22#1309405511yescharacteristic
208C4—21no—
209C4—21no—
210C4—42no—
211C4—41no—
212C4—42no—
213C4—41no—
214C4—1881no—
215C4—1881no—
216C4—1881no—
217C2—21no—
218C2—21no—
219C2—3761no—
220C2#1568928311yescharacteristic
221C2#1568930511yescharacteristic
222C2#1568930911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#395C2
socleC22×C47#120
hypercenter#395D47
hypocenterC47#1603
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
2. #15689279C2semidirect
4. #15688859C2semidirect
6. #15688849C2semidirect
7. C47×#395C2semidirect
115. #395D47semidirect
119. C47#1603semidirect