Finite Group Databasebeta

← #20244424

Subgroups — #20244424

Order 6016.

362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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×#13094055C211yesmaximal, characteristic
2#15689697C211yesmaximal, characteristic
3C2×#13093952C211yesmaximal, characteristic
4#15689132C211yesmaximal, characteristic, complemented
5C2×#13093943C211yesmaximal, characteristic, complemented
6#15688883C211yesmaximal, characteristic, complemented
7C2×C4⋊Q8×C47C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094055—22no—
10#13094055—22no—
11C2×#10625337—21no—
12C2×#10625336—21no—
13C2×#10625329C2211yescharacteristic
14C2×#10625329C2211yescharacteristic
15#13094022—21no—
16#13094013—21no—
17#13094007—22no—
18#13094000—22no—
19#13093983C2211yescharacteristic
20#13093952—22no—
21#13093948—22no—
22#13093943—22no—
23C22×Q8×C47C2211yescharacteristic
24C22×Q8×C47C2211yescharacteristic
25C4⋊Q8×C47—22no—
26C4⋊Q8×C47—22no—
27C2×C4⋊C4×C47—22no—
28C2×C42×C47C2211yescharacteristic
29C2×Q8×C47—21no—
30C2×Q8×C47—21no—
31C2×Q8×C47—21no—
32C2×Q8×C47—21no—
33C2×Q8×C47—21no—
34C2×Q8×C47—21no—
35C2×Q8×C47—21no—
36C2×Q8×C47—21no—
37C2×Q8×C47—21no—
38C2×Q8×C47—21no—
39C2×Q8×C47—21no—
40C2×Q8×C47D412yes—
41C22×C4×C47—21no—
42C22×C4×C47—21no—
43C22×C4×C47D412yes—
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—21no—
46#10625350—21no—
47#10625350—21no—
48#10625350—21no—
49#10625350—21no—
50C2×D188D411yescharacteristic
51C2×C4×D47—21no—
52C2×Dic94D411yescharacteristic
53C4⋊C4×C47—28no—
54C42×C47—21no—
55C42×C47D412yes—
56C22⋊Dic47—21no—
57#10625337—24no—
58#10625336—24no—
59(C2×D47)⋊C4—24no—
60C4⋊Dic47D412yes—
61Dic47⋊C4—24no—
62C4×Dic47—21no—
63#10625329—21no—
64#10625329—21no—
65#10625329—21no—
66#10625329D412yes—
67C2×C47⋊C8—21no—
68C2×C47⋊C8—21no—
69C23×C47C2×D411yescharacteristic
70C22×D47—21no—
71Q8×C47—22no—
72Q8×C47—22no—
73Q8×C47—41no—
74Q8×C47—41no—
75Q8×C47—41no—
76Q8×C47—41no—
77Q8×C47—41no—
78Q8×C47—41no—
79C2×C4×C47—24no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—41no—
86C2×C4×C47—41no—
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47#4111yescharacteristic
93C22⋊D47—41no—
94C22⋊D47—41no—
95C2×Dic47—22no—
96C2×Dic47—21no—
97D188—21no—
98D188—21no—
99C4×D47—41no—
100C4×D47—41no—
101Dic94—21no—
102Dic94—21no—
103C47⋊C8—22no—
104C47⋊C8—41no—
105C22×C47—22no—
106C22×C47#12011yescharacteristic
107C22×C47#12011yescharacteristic
108C22×C47#12111yescharacteristic
109C2×D47—41no—
110C2×D47—42no—
111C4×C47—24no—
112C4×C47—42no—
113C4×C47—42no—
114C4×C47#12011yescharacteristic
115C4×C47#12111yescharacteristic
116C4×C47#12111yescharacteristic
117C4×C47#12711yescharacteristic
118Dic47—41no—
119Dic47—42no—
120#2005—471nomaximal, Sylow
121C2×C47—21no—
122C2×C47—21no—
123C2×C47#39211yescharacteristic
124C2×C47#45612yes—
125D47—81no—
126C2×#137—471no—
127#536—471no—
128C2×C4⋊Q8D4711yescharacteristic, complemented
129C2×#104—471no—
130#419—471no—
131C2×#101—471no—
132#339—471no—
133C47#200511yescharacteristic, complemented, Sylow
134C2×#41—471no—
135C22×Q8C2×D4711yescharacteristic
136C22×Q8C2×D4711yescharacteristic
137#137—942no—
138#137—942no—
139C2×Q16—941no—
140C2×SD16—941no—
141C2×M16—471no—
142C2×M16—471no—
143C4⋊Q8—22no—
144C4⋊Q8—22no—
145C4⋊Q8—941no—
146#124—941no—
147#123—942no—
148C22⋊Q8—942no—
149#117—471no—
150C2×C4⋊C4—22no—
151C2×C42C2×D4711yescharacteristic
152#104—942no—
153#103—942no—
154#101—942no—
155#41—941no—
156#41—941no—
157#41—941no—
158#41—941no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—471no—
171C2×Q8C22⋊D4712yes—
172C2×D4—471no—
173C2×D4—941no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—941no—
177C22×C4C22⋊D4712yes—
178C22×C4C22×D4711yescharacteristic
179Q16—944no—
180SD16—944no—
181M16—472no—
182M16—941no—
183M16—941no—
184M16—941no—
185C2×C8—941no—
186C2×C8—941no—
187C4⋊C4—28no—
188C4⋊C4—472no—
189C4⋊C4—944no—
190C22⋊C4—944no—
191C22⋊C4—941no—
192C42—21no—
193C42—941no—
194C42C22⋊D4712yes—
195C23—941no—
196C23C2×C22⋊D4711yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201Q8—41no—
202Q8—41no—
203Q8—41no—
204Q8—41no—
205Q8—941no—
206Q8—941no—
207D4—941no—
208D4—941no—
209D4—1881no—
210D4—1881no—
211C2×C4—24no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—942no—
220C2×C4—941no—
221C2×C4—1881no—
222C2×C4—1881no—
223C2×C4D4×D4711yescharacteristic
224C2×C4D4×D4711yescharacteristic
225C2×C4D4×D4711yescharacteristic
226C2×C4#1062535211yescharacteristic
227C2×C4C2×C22⋊D4711yescharacteristic
228C2×C4C2×C22⋊D4711yescharacteristic
229C8—942no—
230C8—1881no—
231C22—22no—
232C22—1881no—
233C22—1882no—
234C22#1309399211yescharacteristic
235C22#1309399311yescharacteristic
236C22#1309399611yescharacteristic
237C4—24no—
238C4—42no—
239C4—42no—
240C4—1881no—
241C4—1882no—
242C4#1309399211yescharacteristic
243C4#1309399511yescharacteristic
244C4#1309399611yescharacteristic
245C4#1309402011yescharacteristic
246C2—21no—
247C2—21no—
248C2—3761no—
249C2#1568903111yescharacteristic
250C2#1568930512yes—
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×C4⋊Q8×C47C2
socleC22×C47#120
hypercenterC2×C4⋊Q8D47
hypocenterC47#2005
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #15689132C2semidirect
5. C2×#13093943C2semidirect
6. #15688883C2semidirect
7. C2×C4⋊Q8×C47C2semidirect
128. C2×C4⋊Q8D47semidirect
133. C47#2005semidirect