Finite Group Databasebeta

← #20243741

Subgroups — #20243741

Order 6016.

374 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 107 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×#10625336C211yesmaximal, characteristic
2C2×Q8×Dic47C211yesmaximal, characteristic, complemented
3C2×#13093946C211yesmaximal, characteristic
4#15689024C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C2×#103×C47C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C2×#10625336—22no—
10C2×#10625336—22no—
11C2×#10625336C414yescomplemented
12C22×C47⋊C8C2211yescharacteristic
13Q8×Dic47—22no—
14Q8×Dic47—22no—
15C2×C4⋊Dic47—21no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×(C2×D47)⋊C4—21no—
18C2×(C2×D47)⋊C4—21no—
19C2×C4×Dic47—21no—
20C2×C4×Dic47C2211yescharacteristic
21#13093946—22no—
22C22×Q8×C47C2211yescharacteristic
23C22×C8×C47C2211yescharacteristic
24C2×C4⋊C4×C47C2211yescharacteristic
25#103×C47—22no—
26C23×D47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47C2×C412yes—
31C2×Q8×C47D412yes—
32C2×Q8×C47D412yes—
33C22×C4×C47—21no—
34C22×C4×C47—21no—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47—21no—
37C22×Dic47D411yescharacteristic
38C22×Dic47D411yescharacteristic
39C2×D188—21no—
40C2×D188—21no—
41C2×D188—21no—
42C2×D188—21no—
43C2×D188—21no—
44C2×D188C2×C412yes—
45C2×C8×C47—21no—
46C2×C8×C47—21no—
47C2×C8×C47—21no—
48C4⋊C4×C47—21no—
49C4⋊C4×C47—21no—
50#10625336—28no—
51(C2×D47)⋊C4—42no—
52(C2×D47)⋊C4—42no—
53C4⋊Dic47—24no—
54C4⋊Dic47—21no—
55C4⋊Dic47D412yes—
56C4×Dic47—24no—
57C4×Dic47—21no—
58C4×Dic47—21no—
59C2×C47⋊C8—21no—
60C2×C47⋊C8—21no—
61C2×C47⋊C8C2×C412yes—
62C23×C47C2×D411yescharacteristic
63C22×D47—22no—
64C22×D47—41no—
65C22×D47—41no—
66C22×D47—41no—
67C22×D47—41no—
68C22×D47—41no—
69C22×D47—41no—
70Q8×C47—22no—
71Q8×C47—22no—
72Q8×C47—22no—
73Q8×C47C22⋊C414yescomplemented
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—41no—
78C2×C4×C47—41no—
79C2×C4×C47—41no—
80C2×C4×C47C22×C411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47#4111yescharacteristic
85C2×C4×C47#4111yescharacteristic
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47—22no—
90C2×Dic47—21no—
91C2×Dic47—21no—
92C2×Dic47—41no—
93C2×Dic47—41no—
94C2×Dic47SD1612yescomplemented
95D188—22no—
96D188—22no—
97D188—41no—
98D188—41no—
99C8×C47—41no—
100C47⋊C8—22no—
101C22×C47C4×D411yescharacteristic
102C22×C47#12011yescharacteristic
103C22×C47#12111yescharacteristic
104C22×C47C2×SD1611yescharacteristic
105C22×C47#13511yescharacteristic
106C22×C47AGL(1,ℤ/8)11yescharacteristic
107C22×C47#13711yescharacteristic
108C2×D47—42no—
109C2×D47—42no—
110C2×D47—42no—
111C2×D47—81no—
112C2×D47—81no—
113C2×D47—81no—
114C2×D47—81no—
115C4×C47—24no—
116C4×C47—81no—
117C4×C47C2×C22⋊C411yescharacteristic
118C4×C47C4×D411yescharacteristic
119C4×C47#12111yescharacteristic
120C4×C47#12311yescharacteristic
121Dic47—22no—
122Dic47—41no—
123Dic47—42no—
124#1880—471nomaximal, Sylow
125C2×C47#38611yescharacteristic
126C2×C47C4×SD1611yescharacteristic
127C2×C47#44011yescharacteristic
128C2×C47#44811yescharacteristic
129C2×C47#44911yescharacteristic
130C2×C47#46011yescharacteristic
131C2×C47#46411yescharacteristic
132D47—82no—
133C22×SD16—471no—
134C2×C4×Q8—471no—
135C2×#103D4711yescharacteristic, complemented
136C2×#102—471no—
137#390—471no—
138#340—471no—
139#336—471no—
140C47#188011yescharacteristic, complemented, Sylow
141C22×Q8C2×D4711yescharacteristic
142C22×D4—471no—
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—22no—
158#102—942no—
159C24—941no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8C4×D4712yes—
164C2×Q8D18812yes—
165C2×Q8C22⋊D4712yes—
166C2×D4—472no—
167C2×D4—941no—
168C2×D4—941no—
169C2×D4—941no—
170C2×D4—941no—
171C2×D4—941no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—471no—
175C22×C4—471no—
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—21no—
187C4⋊C4—472no—
188C4⋊C4—944no—
189C4⋊C4—941no—
190C22⋊C4—1882no—
191C22⋊C4—1882no—
192C42—944no—
193C42—941no—
194C42—941no—
195C23—942no—
196C23—1881no—
197C23—1881no—
198C23—1881no—
199C23—1881no—
200C23—1881no—
201C23—1881no—
202C23D4×D4711yescharacteristic
203Q8—22no—
204Q8—22no—
205Q8—22no—
206Q8(C2×D47)⋊C414yescomplemented
207D4—942no—
208D4—942no—
209D4—1881no—
210D4—1881no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—472no—
218C2×C4—941no—
219C2×C4—941no—
220C2×C4—942no—
221C2×C4—941no—
222C2×C4—941no—
223C2×C4—941no—
224C2×C4—1881no—
225C2×C4—1881no—
226C2×C4C2×C4×D4711yescharacteristic
227C2×C4C2×D18811yescharacteristic
228C2×C4D4×D4711yescharacteristic
229C2×C4#1062535211yescharacteristic
230C2×C4#1062535211yescharacteristic
231C2×C4C2×C22⋊D4711yescharacteristic
232C8—41no—
233C8—942no—
234C22—3761no—
235C22—3761no—
236C22—3761no—
237C22—3761no—
238C22—1882no—
239C22—1882no—
240C22—1882no—
241C22(C22⋊D47)⋊C411yescharacteristic
242C22#1309399411yescharacteristic
243C22#1309399611yescharacteristic
244C22SD16×D4711yescharacteristic
245C22#1309404711yescharacteristic
246C22#1309405111yescharacteristic
247C22#1309405611yescharacteristic
248C4—24no—
249C4—81no—
250C4—942no—
251C4—1881no—
252C4—1882no—
253C4C2×(C2×D47)⋊C411yescharacteristic
254C4(C22⋊D47)⋊C411yescharacteristic
255C4#1309399611yescharacteristic
256C4#1309400811yescharacteristic
257C2—3762no—
258C2#1568900011yescharacteristic
259C2#1568920811yescharacteristic
260C2#1568922611yescharacteristic
261C2#1568926311yescharacteristic
262C2#1568927111yescharacteristic
263C2#1568932111yescharacteristic
264C2#1568934711yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47#1880
LCSG ▷ C2×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
2. C2×Q8×Dic47C2semidirect
5. #15688885C2semidirect
6. #15688877C2semidirect
7. C2×#103×C47C2semidirect
11. C2×#10625336C4semidirect
73. Q8×C47C22⋊C4semidirect
94. C2×Dic47SD16semidirect
135. C2×#103D47semidirect
140. C47#1880semidirect
206. Q8(C2×D47)⋊C4semidirect