Finite Group Databasebeta

← #20244632

Subgroups — #20244632

Order 6016.

298 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 87 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×#13094022C211yesmaximal, characteristic
2C2×#13093949C211yesmaximal, characteristic
3C2×#13093948C211yesmaximal, characteristic
4C2×#13093947C211yesmaximal, characteristic
5#15689019C211yesmaximal, characteristic
6#15688877C211yesmaximal, characteristic
7C2×#103×C47C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C22×C47⋊C8C2211yescharacteristic
10#13094022—22no—
11#13094022—22no—
12C2×C4⋊Dic47C2211yescharacteristic
13C2×Dic47⋊C4—21no—
14C2×Dic47⋊C4—21no—
15C2×Dic47⋊C4—21no—
16C2×C4×Dic47C2211yescharacteristic
17#13093949—22no—
18#13093948—22no—
19#13093947—22no—
20C47⋊#95—21no—
21C22×Q8×C47C2211yescharacteristic
22C22×C8×C47C2211yescharacteristic
23C2×C4⋊C4×C47C2211yescharacteristic
24#103×C47—22no—
25C2×Q8×C47—21no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47D412yes—
31C22×C4×C47—21no—
32C22×C4×C47—21no—
33C22×C4×C47C2311yescharacteristic
34C22×Dic47—21no—
35C22×Dic47—21no—
36C22×Dic47D411yescharacteristic
37C22×Dic47D411yescharacteristic
38C2×Dic94—21no—
39C2×Dic94—21no—
40C2×Dic94—21no—
41C2×Dic94—21no—
42C2×Dic94—21no—
43C2×Dic94D412yes—
44C2×C8×C47—21no—
45C2×C8×C47—21no—
46C2×C8×C47—21no—
47C4⋊C4×C47—21no—
48C4⋊C4×C47—21no—
49C4⋊Dic47—21no—
50C4⋊Dic47D412yes—
51Dic47⋊C4—24no—
52Dic47⋊C4—24no—
53Dic47⋊C4—42no—
54C4×Dic47—21no—
55C4×Dic47—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C2×C47⋊C8—21no—
59C23×C47C2×D411yescharacteristic
60Q8×C47—22no—
61Q8×C47—22no—
62Q8×C47—41no—
63Q8×C47—41no—
64C2×C4×C47—22no—
65C2×C4×C47—41no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47#4111yescharacteristic
74C2×C4×C47#4111yescharacteristic
75C2×C4×C47#4111yescharacteristic
76C2×Dic47—21no—
77C2×Dic47—21no—
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—41no—
83C2×Dic47—41no—
84C2×Dic47—41no—
85C2×Dic47—41no—
86C2×Dic47SD1612yes—
87C2×Dic47Q1612yes—
88Dic94—22no—
89Dic94—22no—
90Dic94—41no—
91Dic94—41no—
92C8×C47—41no—
93C47⋊C8—41no—
94C22×C47#12011yescharacteristic
95C22×C47#12111yescharacteristic
96C22×C47#12411yescharacteristic
97C22×C47C2×SD1611yescharacteristic
98C22×C47C2×Q1611yescharacteristic
99C22×C47#13711yescharacteristic
100C22×C47#13711yescharacteristic
101C4×C47—42no—
102C4×C47—81no—
103C4×C47#12111yescharacteristic
104C4×C47#12111yescharacteristic
105C4×C47#12311yescharacteristic
106C4×C47#12311yescharacteristic
107Dic47—22no—
108Dic47—22no—
109Dic47—42no—
110Dic47—42no—
111#2043—471nomaximal, Sylow
112C2×C47#39411yescharacteristic
113C2×C47#44811yescharacteristic
114C2×C47#45111yescharacteristic
115C2×C47#46111yescharacteristic
116C2×C47#46211yescharacteristic
117C2×C47#48711yescharacteristic
118C2×C47#49111yescharacteristic
119C2×C4⋊Q8—471no—
120C2×#103—471no—
121C2×#103—471no—
122C2×#103—471no—
123C2×#103D4711yescharacteristic
124#389—471no—
125#336—471no—
126C47#204311yescharacteristic, complemented, Sylow
127C22×Q8—471no—
128C22×Q8C2×D4711yescharacteristic
129C22×C8—471no—
130C22×C8C2×D4711yescharacteristic
131C4⋊Q8—942no—
132C4⋊Q8—942no—
133C2×C4⋊C4—471no—
134C2×C4⋊C4—941no—
135C2×C4⋊C4—941no—
136C2×C4⋊C4—941no—
137C2×C4⋊C4C2×D4711yescharacteristic
138C2×C42—471no—
139#103—22no—
140#103—942no—
141#103—942no—
142#103—942no—
143#95—941no—
144C2×Q8—21no—
145C2×Q8—21no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—472no—
150C2×Q8—941no—
151C2×Q8—941no—
152C2×Q8—941no—
153C2×Q8—941no—
154C2×Q8—941no—
155C2×Q8C22⋊D4712yes—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—471no—
159C22×C4—471no—
160C22×C4—941no—
161C22×C4—941no—
162C22×C4C22×D4711yescharacteristic
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—941no—
167C2×C8—941no—
168C2×C8—941no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—472no—
172C4⋊C4—944no—
173C4⋊C4—944no—
174C4⋊C4—941no—
175C4⋊C4—1882no—
176C42—941no—
177C42—941no—
178C23D4×D4711yescharacteristic
179Q8—22no—
180Q8—22no—
181Q8—41no—
182Q8—41no—
183Q8—942no—
184Q8—942no—
185Q8—1881no—
186Q8—1881no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—472no—
194C2×C4—472no—
195C2×C4—941no—
196C2×C4—941no—
197C2×C4—941no—
198C2×C4—941no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—1881no—
202C2×C4—1881no—
203C2×C4—1881no—
204C2×C4—1881no—
205C2×C4#1062535011yescharacteristic
206C2×C4#1062535011yescharacteristic
207C2×C4D4×D4711yescharacteristic
208C2×C4D4×D4711yescharacteristic
209C2×C4#1062535211yescharacteristic
210C2×C4C2×C22⋊D4711yescharacteristic
211C8—41no—
212C8—1881no—
213C22#1309399211yescharacteristic
214C22#1309399711yescharacteristic
215C22#1309401011yescharacteristic
216C22SD16×D4711yescharacteristic
217C22Q16×D4711yescharacteristic
218C22#1309405311yescharacteristic
219C22#1309405611yescharacteristic
220C4—42no—
221C4—81no—
222C4—942no—
223C4—942no—
224C4—1882no—
225C4—1882no—
226C4#1309399611yescharacteristic
227C4#1309399711yescharacteristic
228C4#1309400611yescharacteristic
229C4#1309400711yescharacteristic
230C2#1568903811yescharacteristic
231C2#1568926011yescharacteristic
232C2#1568927711yescharacteristic
233C2#1568932711yescharacteristic
234C2#1568933211yescharacteristic
235C2#1568947211yescharacteristic
236C2#1568949011yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47#2043
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
126. C47#2043semidirect