Finite Group Databasebeta

← #20244603

Subgroups — #20244603

Order 6016.

278 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 67 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#15689694C211yesmaximal, characteristic
2#15689163C211yesmaximal, characteristic, complemented
3C2×#13093951C211yesmaximal, characteristic
4C2×#13093942C211yesmaximal, characteristic, complemented
5#15689028C211yesmaximal, characteristic, complemented
6#15688884C211yesmaximal, characteristic, complemented
7C47×#417C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10#13094022—21no—
11#13094011—21no—
12#13094005—22no—
13#13094003—21no—
14#13094003—21no—
15#13093983C2211yescharacteristic
16C2×C4×Dic47C2211yescharacteristic
17#13093957—21no—
18#13093955—21no—
19#13093951—22no—
20#13093942—22no—
21C47⋊#95—22no—
22C2×#41×C47C2211yescharacteristic
23C2×M16×C47C2211yescharacteristic
24C2×C4⋊C4×C47C2211yescharacteristic
25#103×C47—21no—
26#102×C47—21no—
27#41×C47—21no—
28#41×C47—21no—
29#41×C47—21no—
30#41×C47—21no—
31C2×Q8×C47D411yescharacteristic
32C2×D4×C47—21no—
33C2×D4×C47D411yescharacteristic
34C22×C4×C47—21no—
35C22×C4×C47—21no—
36C22×C4×C47C2311yescharacteristic
37C22×Dic47—21no—
38C22×Dic47D412yes—
39C2×Dic94—21no—
40C2×Dic94—21no—
41C2×Dic94—21no—
42C2×Dic94—21no—
43C2×Dic94—21no—
44C2×Dic94—21no—
45M16×C47—21no—
46M16×C47—21no—
47C2×C8×C47—21no—
48C4⋊C4×C47—21no—
49C4⋊C4×C47—21no—
50C22⋊Dic47—22no—
51C22⋊Dic47—22no—
52C22⋊Dic47—21no—
53C4⋊Dic47D411yescharacteristic
54C4⋊Dic47D411yescharacteristic
55Dic47⋊C4—22no—
56Dic47⋊C4—22no—
57C4×Dic47—21no—
58C4×Dic47—21no—
59C4×Dic47—21no—
60#10625329—21no—
61#10625329D412yes—
62C2×C47⋊C8—21no—
63C23×C47—21no—
64C23×C47C2×D411yescharacteristic
65Q8×C47—21no—
66Q8×C47—21no—
67D4×C47—21no—
68D4×C47—21no—
69D4×C47—41no—
70D4×C47—41no—
71C2×C4×C47—21no—
72C2×C4×C47—41no—
73C2×C4×C47—41no—
74C2×C4×C47—42no—
75C2×C4×C47—41no—
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47#4111yescharacteristic
80C2×C4×C47#4111yescharacteristic
81C2×C4×C47#4111yescharacteristic
82C2×Dic47—22no—
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47—41no—
89C2×Dic47—41no—
90Dic94—41no—
91Dic94—41no—
92Dic94—41no—
93Dic94—41no—
94C8×C47—41no—
95C47⋊C8—22no—
96C22×C47—21no—
97C22×C47—21no—
98C22×C47—41no—
99C22×C47—41no—
100C22×C47—41no—
101C22×C47#12011yescharacteristic
102C22×C47#12111yescharacteristic
103C22×C47#12311yescharacteristic
104C4×C47—41no—
105C4×C47—81no—
106C4×C47#12111yescharacteristic
107C4×C47#12111yescharacteristic
108C4×C47#12311yescharacteristic
109C4×C47#12411yescharacteristic
110Dic47—42no—
111Dic47—42no—
112Dic47—41no—
113Dic47—41no—
114#2038—471nomaximal, Sylow
115C2×C47—21no—
116C2×C47—21no—
117C2×C47—81no—
118C2×C47#39411yescharacteristic
119C2×C47#45411yescharacteristic
120C2×C47#45611yescharacteristic
121#536—471no—
122#428—471no—
123C2×#104—471no—
124#417D4711yescharacteristic
125C2×#101—471no—
126#391—471no—
127#339—471no—
128C47#203811yescharacteristic, complemented, Sylow
129C2×#41C2×D4711yescharacteristic
130C22×Q8—471no—
131C2×M16—471no—
132C2×M16C2×D4711yescharacteristic
133C4⋊Q8—941no—
134#124—941no—
135#123—942no—
136C22⋊Q8—941no—
137C22⋊Q8—941no—
138#117—471no—
139C2×C4⋊C4C2×D4711yescharacteristic
140C2×C42—471no—
141#107—941no—
142#106—941no—
143#104—942no—
144#103—21no—
145#102—21no—
146#101—942no—
147#95—942no—
148#41—21no—
149#41—21no—
150#41—21no—
151#41—21no—
152C2×Q8—941no—
153C2×Q8—941no—
154C2×Q8—941no—
155C2×Q8—941no—
156C2×Q8—941no—
157C2×Q8—941no—
158C2×Q8C22⋊D4711yescharacteristic
159C2×D4—21no—
160C2×D4C22⋊D4711yescharacteristic
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—472no—
164C22×C4—941no—
165C22×C4C22×D4711yescharacteristic
166M16—21no—
167M16—21no—
168M16—472no—
169M16—941no—
170C2×C8—21no—
171C2×C8—941no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—471no—
175C4⋊C4—471no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C22⋊C4—942no—
179C22⋊C4—942no—
180C22⋊C4—941no—
181C42—941no—
182C42—941no—
183C42—941no—
184C23—21no—
185C23D4×D4711yescharacteristic
186Q8—21no—
187Q8—21no—
188Q8—1881no—
189Q8—1881no—
190Q8—1881no—
191Q8—1881no—
192D4—21no—
193D4—21no—
194D4—41no—
195D4—41no—
196C2×C4—21no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—41no—
201C2×C4—942no—
202C2×C4—941no—
203C2×C4—941no—
204C2×C4—942no—
205C2×C4—942no—
206C2×C4—942no—
207C2×C4—1881no—
208C2×C4—1881no—
209C2×C4#1062535011yescharacteristic
210C2×C4#1062535011yescharacteristic
211C2×C4D4×D4711yescharacteristic
212C2×C4D4×D4711yescharacteristic
213C2×C4#1062535211yescharacteristic
214C2×C4C2×C22⋊D4711yescharacteristic
215C8—41no—
216C8—942no—
217C22—21no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22#1309399211yescharacteristic
223C22#1309399711yescharacteristic
224C22#1309400611yescharacteristic
225C4—41no—
226C4—81no—
227C4—1882no—
228C4—1882no—
229C4—1881no—
230C4—1881no—
231C4#1309399611yescharacteristic
232C4#1309399711yescharacteristic
233C4#1309400711yescharacteristic
234C4#1309401011yescharacteristic
235C2—21no—
236C2—21no—
237C2—81no—
238C2#1568903811yescharacteristic
239C2#1568929411yescharacteristic
240C2#1568930411yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#417C2
socleC22×C47#120
hypercenter#417D47
hypocenterC47#2038
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. #15689163C2semidirect
4. C2×#13093942C2semidirect
5. #15689028C2semidirect
6. #15688884C2semidirect
128. C47#2038semidirect