Finite Group Databasebeta

← #20243740

Subgroups — #20243740

Order 6016.

374 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#10625335C211yesmaximal, characteristic
2C2×#13093989C211yesmaximal, characteristic, complemented
3C2×#13093949C211yesmaximal, characteristic, complemented
4#15689026C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C2×#102×C47C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C2×#10625335—22no—
10C2×#10625335—22no—
11C2×#10625335C414yescomplemented
12C22×C47⋊C8C2211yescharacteristic
13#13093989—22no—
14#13093989—22no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×Dic47⋊C4—21no—
17C2×C22⋊Dic47—21no—
18C2×C22⋊Dic47—21no—
19C2×C4×Dic47—21no—
20C2×C4×Dic47C2211yescharacteristic
21#13093949—22no—
22C22×D4×C47C2211yescharacteristic
23C22×C8×C47C2211yescharacteristic
24C2×C4⋊C4×C47C2211yescharacteristic
25#102×C47—22no—
26C24×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47—21no—
30C2×D4×C47—21no—
31C2×D4×C47—21no—
32C2×D4×C47C2×C412yes—
33C22×C4×C47—21no—
34C22×C4×C47C2311yescharacteristic
35C22×Dic47—21no—
36C22×Dic47—21no—
37C22×Dic47D411yescharacteristic
38C22×Dic47D411yescharacteristic
39C2×Dic94—21no—
40C2×Dic94—21no—
41C2×Dic94—21no—
42C2×Dic94C2×C412yes—
43C2×Dic94D412yes—
44C2×Dic94D412yes—
45C2×C8×C47—21no—
46C2×C8×C47—21no—
47C2×C8×C47—21no—
48C4⋊C4×C47—21no—
49C4⋊C4×C47D412yes—
50C22⋊Dic47—42no—
51C22⋊Dic47—42no—
52#10625335—28no—
53C4⋊Dic47—21no—
54C4⋊Dic47—21no—
55Dic47⋊C4—24no—
56C4×Dic47—24no—
57C4×Dic47—21no—
58C4×Dic47—21no—
59C2×C47⋊C8—21no—
60C2×C47⋊C8—21no—
61C2×C47⋊C8C2×C412yes—
62C23×C47—22no—
63C23×C47—41no—
64C23×C47—41no—
65C23×C47—41no—
66C23×C47—41no—
67C23×C47—41no—
68C23×C47—41no—
69C23×C47C2×D411yescharacteristic
70D4×C47—22no—
71D4×C47—22no—
72D4×C47—41no—
73D4×C47—41no—
74C2×C4×C47—22no—
75C2×C4×C47—41no—
76C2×C4×C47—41no—
77C2×C4×C47C22×C411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47#4111yescharacteristic
82C2×C4×C47#4111yescharacteristic
83C2×Dic47—22no—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47—21no—
90C2×Dic47—21no—
91C2×Dic47—41no—
92C2×Dic47—41no—
93C2×Dic47—41no—
94C2×Dic47SD1612yescomplemented
95Dic94—22no—
96Dic94—22no—
97Dic94—22no—
98Dic94C22⋊C414yescomplemented
99C8×C47—41no—
100C47⋊C8—22no—
101C22×C47—42no—
102C22×C47—42no—
103C22×C47—42no—
104C22×C47—81no—
105C22×C47—81no—
106C22×C47—81no—
107C22×C47—81no—
108C22×C47C4×D411yescharacteristic
109C22×C47#12011yescharacteristic
110C22×C47#12111yescharacteristic
111C22×C47C2×SD1611yescharacteristic
112C22×C47#13511yescharacteristic
113C22×C47AGL(1,ℤ/8)11yescharacteristic
114C22×C47#13711yescharacteristic
115C4×C47—42no—
116C4×C47C2×C22⋊C411yescharacteristic
117C4×C47C4×D411yescharacteristic
118C4×C47#12111yescharacteristic
119C4×C47#12311yescharacteristic
120Dic47—24no—
121Dic47—22no—
122Dic47—41no—
123Dic47—81no—
124#1880—471nomaximal, Sylow
125C2×C47—82no—
126C2×C47#38611yescharacteristic
127C2×C47C4×SD1611yescharacteristic
128C2×C47#44011yescharacteristic
129C2×C47#44811yescharacteristic
130C2×C47#44911yescharacteristic
131C2×C47#46011yescharacteristic
132C2×C47#46411yescharacteristic
133C22×SD16—471no—
134C2×C4×Q8—471no—
135C2×#103—471no—
136C2×#102D4711yescharacteristic
137#390—471no—
138#340—471no—
139#336—471no—
140C47#188011yescharacteristic, complemented, Sylow
141C22×Q8—471no—
142C22×D4C2×D4711yescharacteristic
143C2×SD16—474no—
144C2×SD16—942no—
145C2×SD16—942no—
146C22×C8—471no—
147C22×C8C2×D4711yescharacteristic
148C4×Q8—942no—
149C4×Q8—942no—
150C2×C4⋊C4—471no—
151C2×C4⋊C4—941no—
152C2×C4⋊C4C2×D4711yescharacteristic
153C2×C22⋊C4—941no—
154C2×C22⋊C4—941no—
155C2×C42—471no—
156C2×C42—941no—
157#103—942no—
158#102—22no—
159C24—21no—
160C2×Q8—472no—
161C2×Q8—472no—
162C2×Q8—472no—
163C2×Q8—941no—
164C2×Q8—941no—
165C2×Q8—941no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4C4×D4712yes—
172C22×C4—21no—
173C22×C4—471no—
174C22×C4—471no—
175C22×C4—941no—
176C22×C4—941no—
177C22×C4C22×D4711yescharacteristic
178SD16—948no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—472no—
183C2×C8—941no—
184C2×C8—941no—
185C4⋊C4—21no—
186C4⋊C4—944no—
187C4⋊C4—941no—
188C4⋊C4—941no—
189C4⋊C4C22⋊D4712yes—
190C22⋊C4—1882no—
191C22⋊C4—1882no—
192C42—944no—
193C42—941no—
194C42—941no—
195C23—22no—
196C23—41no—
197C23—41no—
198C23—41no—
199C23—41no—
200C23—41no—
201C23—41no—
202C23D4×D4711yescharacteristic
203Q8—474no—
204Q8—942no—
205Q8—942no—
206Q8—942no—
207D4—22no—
208D4—22no—
209D4—41no—
210D4—41no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—472no—
215C2×C4—942no—
216C2×C4—941no—
217C2×C4—942no—
218C2×C4—942no—
219C2×C4—941no—
220C2×C4—941no—
221C2×C4—941no—
222C2×C4—941no—
223C2×C4—1881no—
224C2×C4—1881no—
225C2×C4—1881no—
226C2×C4C2×C4×D4711yescharacteristic
227C2×C4#1062535011yescharacteristic
228C2×C4D4×D4711yescharacteristic
229C2×C4D4×D4711yescharacteristic
230C2×C4#1062535211yescharacteristic
231C2×C4C2×C22⋊D4711yescharacteristic
232C8—41no—
233C8—942no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—81no—
238C22—81no—
239C22—81no—
240C22—81no—
241C22(C22⋊D47)⋊C411yescharacteristic
242C22#1309399211yescharacteristic
243C22#1309399711yescharacteristic
244C22SD16×D4711yescharacteristic
245C22#1309404311yescharacteristic
246C22#1309404811yescharacteristic
247C22#1309405311yescharacteristic
248C4—42no—
249C4—944no—
250C4—942no—
251C4—3761no—
252C4—1881no—
253C4C22⋊C4×D4711yescharacteristic
254C4C4×C22⋊D4711yescharacteristic
255C4#1309399511yescharacteristic
256C4#1309400611yescharacteristic
257C2—82no—
258C2#1568899911yescharacteristic
259C2#1568921411yescharacteristic
260C2#1568922011yescharacteristic
261C2#1568926011yescharacteristic
262C2#1568926511yescharacteristic
263C2#1568932211yescharacteristic
264C2#1568934411yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#102×C47C2
socleC23×C47C2×D4
hypercenterC2×#102D47
hypocenterC47#1880
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#13093989C2semidirect
3. C2×#13093949C2semidirect
5. #15688885C2semidirect
6. #15688877C2semidirect
11. C2×#10625335C4semidirect
94. C2×Dic47SD16semidirect
98. Dic94C22⋊C4semidirect
140. C47#1880semidirect