Finite Group Databasebeta

← #20242377

Subgroups — #20242377

Order 6016.

228 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 51 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#15689748C211yesmaximal, characteristic
2#15689453C211yesmaximal, characteristic, complemented
3#15689049C211yesmaximal, characteristic
4#15688861C211yesmaximal, characteristic, complemented
5#15688860C211yesmaximal, characteristic, complemented
6#15688846C211yesmaximal, characteristic
7C47×#483C211yesmaximal, characteristic, complemented
8#13094004—21no—
9#13094003C2211yescharacteristic
10#13094002—21no—
11#13094002—21no—
12#13094001—21no—
13#13094000—21no—
14C2×(C2×D47)⋊C4—21no—
15C2×(C2×D47)⋊C4C2211yescharacteristic
16C22⋊C4×D47—21no—
17#13093955—21no—
18#13093947—21no—
19C22⋊(C47⋊C8)C2211yescharacteristic
20C47⋊#95—21no—
21C47⋊#95C2211yescharacteristic
22C22⋊Q8×C47C2211yescharacteristic
23C2×C4⋊C4×C47C2211yescharacteristic
24#106×C47—21no—
25#103×C47—21no—
26C22⋊C8×C47C2211yescharacteristic
27C23×D47D411yescharacteristic
28C2×Q8×C47D411yescharacteristic
29C22×C4×C47—21no—
30C22×C4×C47C2311yescharacteristic
31C22×Dic47—21no—
32C22×Dic47D411yescharacteristic
33C2×C4×D47—21no—
34C2×C4×D47—21no—
35C2×Dic94—21no—
36C2×Dic94D411yescharacteristic
37C2×C8×C47—21no—
38C4⋊C4×C47—21no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C4⋊C4×C47D411yescharacteristic
42C22⋊C4×C47—21no—
43C22⋊Dic47—21no—
44(C2×D47)⋊C4—21no—
45(C2×D47)⋊C4—21no—
46(C2×D47)⋊C4—21no—
47(C2×D47)⋊C4—21no—
48(C2×D47)⋊C4—42no—
49C4⋊Dic47—21no—
50C4⋊Dic47D411yescharacteristic
51Dic47⋊C4—21no—
52Dic47⋊C4—21no—
53Dic47⋊C4—21no—
54C2×C47⋊C8—21no—
55C23×C47C2×D411yescharacteristic
56C22×D47—21no—
57C22×D47—21no—
58C22×D47—41no—
59C22×D47—41no—
60C22×D47SD1612yes—
61Q8×C47—41no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—41no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47C2×D411yescharacteristic
70C2×Dic47—21no—
71C2×Dic47—21no—
72C2×Dic47—21no—
73C2×Dic47—41no—
74C2×Dic47—41no—
75C2×Dic47—41no—
76C2×Dic47—41no—
77C4×D47—81no—
78C4×D47—81no—
79Dic94—41no—
80Dic94—81no—
81C8×C47—41no—
82C47⋊C8—41no—
83C22×C47—21no—
84C22×C47—21no—
85C22×C47#12011yescharacteristic
86C22×C47C2×SD1611yescharacteristic
87C22×C47#13711yescharacteristic
88C2×D47—22no—
89C2×D47—41no—
90C2×D47—41no—
91C2×D47—42no—
92C2×D47—81no—
93C4×C47—21no—
94C4×C47—21no—
95C4×C47—41no—
96C4×C47—41no—
97C4×C47—81no—
98Dic47—41no—
99Dic47—41no—
100Dic47—41no—
101Dic47—81no—
102#1608—471nomaximal, Sylow
103C2×C47—21no—
104C2×C47—21no—
105C2×C47#44811yescharacteristic
106C2×C47#45511yescharacteristic
107C2×C47#45811yescharacteristic
108D47—42no—
109#543—471no—
110#483—471no—
111#483D4711yescharacteristic, complemented
112#397—471no—
113#328—471no—
114#328—471no—
115#323—471no—
116C47#160811yescharacteristic, complemented, Sylow
117C22⋊Q8—471no—
118C22⋊Q8—941no—
119C22⋊Q8—941no—
120C22⋊Q8—941no—
121C22⋊Q8—941no—
122C22⋊Q8—941no—
123C22⋊Q8C2×D4711yescharacteristic
124C2×C4⋊C4C2×D4711yescharacteristic
125C2×C22⋊C4—471no—
126C2×C22⋊C4—941no—
127C2×C22⋊C4—941no—
128#106—21no—
129#106—941no—
130#103—21no—
131#103—941no—
132C22⋊C8—471no—
133C22⋊C8C2×D4711yescharacteristic
134#95—471no—
135#95—941no—
136C24—471no—
137C2×Q8—471no—
138C2×Q8—941no—
139C2×Q8C22⋊D4711yescharacteristic
140C22×C4—21no—
141C22×C4—471no—
142C22×C4—941no—
143C22×C4—941no—
144C22×C4—941no—
145C22×C4C22×D4711yescharacteristic
146C2×C8—21no—
147C2×C8—941no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—471no—
152C4⋊C4—941no—
153C4⋊C4—941no—
154C4⋊C4—941no—
155C4⋊C4—941no—
156C4⋊C4C22⋊D4711yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—941no—
159C22⋊C4—941no—
160C22⋊C4—941no—
161C22⋊C4—941no—
162C22⋊C4—941no—
163C22⋊C4—1882no—
164C23—472no—
165C23—941no—
166C23—941no—
167C23—1881no—
168C23—1881no—
169C23D4×D4711yescharacteristic
170Q8—41no—
171Q8—3761no—
172Q8—1881no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—941no—
180C2×C4—941no—
181C2×C4—941no—
182C2×C4—3761no—
183C2×C4—3761no—
184C2×C4—1881no—
185C2×C4—1881no—
186C2×C4—1881no—
187C2×C4—1881no—
188C2×C4D4×D4711yescharacteristic
189C2×C4C2×C22⋊D4711yescharacteristic
190C8—41no—
191C8—1881no—
192C22—21no—
193C22—21no—
194C22—942no—
195C22—3761no—
196C22—1882no—
197C22—1881no—
198C22—1881no—
199C22#1309399211yescharacteristic
200C22SD16×D4711yescharacteristic
201C22#1309405311yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—81no—
207C4—3761no—
208C4—1881no—
209C4—1881no—
210C4—1881no—
211C2—21no—
212C2—21no—
213C2—1882no—
214C2#1568926011yescharacteristic
215C2#1568929911yescharacteristic
216C2#1568931211yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#483C2
socleC22×C47#120
hypercenter#483D47
hypocenterC47#1608
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. #15689453C2semidirect
4. #15688861C2semidirect
5. #15688860C2semidirect
7. C47×#483C2semidirect
111. #483D47semidirect
116. C47#1608semidirect