Finite Group Databasebeta

← #20244703

Subgroups — #20244703

Order 6016.

324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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×C4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
3C2×#13093948C211yesmaximal, characteristic, complemented
4C2×#13093944C211yesmaximal, characteristic
5#15689025C211yesmaximal, characteristic
6#15688885C211yesmaximal, characteristic, complemented
7C47×#391C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C2×#10625336—22no—
10C2×#10625336—22no—
11C2×#10625336—22no—
12C22×C47⋊C8C2211yescharacteristic
13C22×C47⋊C8C2211yescharacteristic
14C2×C4⋊Dic47C2211yescharacteristic
15C2×(C2×D47)⋊C4—21no—
16C2×(C2×D47)⋊C4—21no—
17C4⋊(C47⋊C8)—22no—
18#13093948—22no—
19#13093944—22no—
20C22×Q8×C47C2211yescharacteristic
21C2×C4⋊C4×C47C2211yescharacteristic
22C2×C42×C47C2211yescharacteristic
23#95×C47—21no—
24#95×C47—21no—
25C23×D47—21no—
26C2×Q8×C47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47—21no—
31C2×Q8×C47D412yes—
32C22×C4×C47—21no—
33C22×C4×C47—21no—
34C22×C4×C47D411yescharacteristic
35C22×C4×C47D411yescharacteristic
36C22×C4×C47C2311yescharacteristic
37C22×Dic47—21no—
38C2×D188—21no—
39C2×D188—21no—
40C2×D188—21no—
41C2×D188—21no—
42C2×D188—21no—
43C2×D188D412yes—
44C4⋊C4×C47—21no—
45C4⋊C4×C47—21no—
46C42×C47—21no—
47C42×C47—21no—
48#10625336—28no—
49(C2×D47)⋊C4—42no—
50(C2×D47)⋊C4—42no—
51C4⋊Dic47—21no—
52C4⋊Dic47—21no—
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C2×C47⋊C8D412yes—
59C23×C47C2×D411yescharacteristic
60C22×D47—22no—
61C22×D47—41no—
62C22×D47—41no—
63C22×D47—41no—
64C22×D47—41no—
65C22×D47—41no—
66C22×D47—41no—
67Q8×C47—22no—
68Q8×C47—22no—
69Q8×C47—41no—
70Q8×C47—41no—
71C2×C4×C47—21no—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—41no—
78C2×C4×C47—41no—
79C2×C4×C47—41no—
80C2×C4×C47—41no—
81C2×C4×C47—41no—
82C2×C4×C47SD1612yescomplemented
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47#4111yescharacteristic
87C2×C4×C47#4111yescharacteristic
88C2×C4×C47#4111yescharacteristic
89C2×Dic47—41no—
90C2×Dic47—41no—
91C2×Dic47—41no—
92D188—22no—
93D188—22no—
94D188—41no—
95D188—41no—
96C47⋊C8—22no—
97C47⋊C8—41no—
98C22×C47#12111yescharacteristic
99C22×C47#12111yescharacteristic
100C22×C47#12111yescharacteristic
101C22×C47C2×SD1611yescharacteristic
102C22×C47#13511yescharacteristic
103C22×C47AGL(1,ℤ/8)11yescharacteristic
104C22×C47#13711yescharacteristic
105C2×D47—42no—
106C2×D47—42no—
107C2×D47—42no—
108C2×D47—81no—
109C2×D47—81no—
110C2×D47—81no—
111C2×D47—81no—
112C4×C47—22no—
113C4×C47—42no—
114C4×C47—41no—
115C4×C47—81no—
116C4×C47#12011yescharacteristic
117C4×C47#12311yescharacteristic
118C4×C47#12311yescharacteristic
119C4×C47#12411yescharacteristic
120Dic47—81no—
121#2055—471nomaximal, Sylow
122C2×C47#39411yescharacteristic
123C2×C47#46011yescharacteristic
124C2×C47#46111yescharacteristic
125C2×C47#46311yescharacteristic
126C2×C47#46411yescharacteristic
127C2×C47#46511yescharacteristic
128C2×C47#46811yescharacteristic
129D47—82no—
130C22×SD16—471no—
131C2×C4⋊C8—471no—
132C2×#103—471no—
133C2×#102—471no—
134#391D4711yescharacteristic, complemented
135#390—471no—
136#340—471no—
137C47#205511yescharacteristic, complemented, Sylow
138C22×Q8C2×D4711yescharacteristic
139C22×D4—471no—
140C2×SD16—942no—
141C2×SD16—942no—
142C2×SD16—942no—
143C22×C8—471no—
144C22×C8—471no—
145C2×C4⋊C4—471no—
146C2×C4⋊C4C2×D4711yescharacteristic
147C2×C22⋊C4—941no—
148C2×C22⋊C4—941no—
149C2×C42C2×D4711yescharacteristic
150C4⋊C8—942no—
151#103—942no—
152#102—942no—
153#95—21no—
154#95—21no—
155C24—941no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8D18812yes—
162C2×D4—472no—
163C2×D4—941no—
164C2×D4—941no—
165C2×D4—941no—
166C2×D4—941no—
167C2×D4—941no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—941no—
171C22×C4C22⋊D4711yescharacteristic
172C22×C4C22⋊D4711yescharacteristic
173C22×C4C22×D4711yescharacteristic
174SD16—948no—
175C2×C8—472no—
176C2×C8—941no—
177C2×C8—941no—
178C2×C8—941no—
179C2×C8—941no—
180C2×C8—941no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—941no—
184C4⋊C4—941no—
185C22⋊C4—1882no—
186C22⋊C4—1882no—
187C42—21no—
188C42—21no—
189C23—942no—
190C23—1881no—
191C23—1881no—
192C23—1881no—
193C23—1881no—
194C23—1881no—
195C23—1881no—
196C23C2×C22⋊D4711yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201D4—942no—
202D4—942no—
203D4—1881no—
204D4—1881no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—1881no—
217C2×C4—1881no—
218C2×C4—1881no—
219C2×C4#1062533612yescomplemented
220C2×C4C2×D18811yescharacteristic
221C2×C4#1062535011yescharacteristic
222C2×C4D4×D4711yescharacteristic
223C2×C4D4×D4711yescharacteristic
224C2×C4#1062535211yescharacteristic
225C2×C4#1062535211yescharacteristic
226C8—942no—
227C8—1881no—
228C22—3761no—
229C22—3761no—
230C22—3761no—
231C22—3761no—
232C22—1882no—
233C22—1882no—
234C22—1882no—
235C22#1309399511yescharacteristic
236C22#1309399611yescharacteristic
237C22#1309399811yescharacteristic
238C22C2×#1062533611yescharacteristic
239C22#1309404411yescharacteristic
240C22#1309404911yescharacteristic
241C22#1309405511yescharacteristic
242C4—22no—
243C4—42no—
244C4—41no—
245C4—81no—
246C4—3761no—
247C4#1309399411yescharacteristic
248C4#1309400611yescharacteristic
249C4#1309400811yescharacteristic
250C4#1309401011yescharacteristic
251C2—3762no—
252C2#1568903911yescharacteristic
253C2#1568932311yescharacteristic
254C2#1568932511yescharacteristic
255C2#1568933511yescharacteristic
256C2#1568934511yescharacteristic
257C2#1568935411yescharacteristic
258C2#1568937111yescharacteristic
subgroupG/H
centerC23C2×C22⋊D47
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#391C2
socleC23×C47C2×D4
hypercenter#391D47
hypocenterC47#2055
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊(C47⋊C8)C2semidirect
3. C2×#13093948C2semidirect
6. #15688885C2semidirect
7. C47×#391C2semidirect
82. C2×C4×C47SD16semidirect
134. #391D47semidirect
137. C47#2055semidirect
219. C2×C4#10625336semidirect