Finite Group Databasebeta

← #20244506

Subgroups — #20244506

Order 6016.

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

normal subgroups only

This group has 342 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×#13094054C211yesmaximal, characteristic
2C22×#10625337C211yesmaximal, characteristic, complemented
3C2×#13093943C211yesmaximal, characteristic, complemented
4C2×#13093942C211yesmaximal, characteristic, complemented
5#15689090C211yesmaximal, characteristic
6#15688887C211yesmaximal, characteristic, complemented
7C2×#137×C47C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9#13094054—22no—
10#13094054—22no—
11C2×#10625337—22no—
12C2×#10625337—21no—
13C2×#10625337—22no—
14C2×#10625337—22no—
15C2×#10625335—21no—
16C2×#10625329C2211yescharacteristic
17C2×#10625329C2211yescharacteristic
18C22×C47⋊C8C2211yescharacteristic
19#13093943—22no—
20#13093942—22no—
21C22⋊(C47⋊C8)—22no—
22C2×#41×C47C2211yescharacteristic
23C22×Q8×C47C2211yescharacteristic
24#137×C47—22no—
25#137×C47—22no—
26C2×Q16×C47—21no—
27C2×SD16×C47—21no—
28C2×M16×C47C2211yescharacteristic
29#41×C47—21no—
30#41×C47—21no—
31#41×C47—21no—
32#41×C47—21no—
33C2×Q8×C47—21no—
34C2×Q8×C47—21no—
35C2×Q8×C47—21no—
36C2×Q8×C47—21no—
37C2×Q8×C47—21no—
38C2×Q8×C47D411yescharacteristic
39C2×Q8×C47D412yes—
40C2×D4×C47—21no—
41C2×D4×C47D411yescharacteristic
42C22×C4×C47—21no—
43C22×C4×C47—21no—
44C22×C4×C47C2311yescharacteristic
45C22×Dic47—21no—
46C2×Dic94—21no—
47C2×Dic94—21no—
48C2×Dic94—21no—
49C2×Dic94—21no—
50C2×Dic94—21no—
51C2×Dic94D412yes—
52Q16×C47—24no—
53SD16×C47—24no—
54M16×C47—21no—
55M16×C47D412yes—
56C2×C8×C47—21no—
57#10625337—28no—
58#10625337—24no—
59#10625335—24no—
60#10625329—21no—
61#10625329—21no—
62#10625329—21no—
63#10625329D412yes—
64C2×C47⋊C8—21no—
65C2×C47⋊C8—21no—
66C2×C47⋊C8—21no—
67C2×C47⋊C8—21no—
68C2×C47⋊C8D412yes—
69C23×C47—21no—
70C23×C47#4111yescharacteristic
71Q8×C47—22no—
72Q8×C47—21no—
73Q8×C47—22no—
74Q8×C47—21no—
75Q8×C47—41no—
76Q8×C47—41no—
77D4×C47—21no—
78D4×C47—21no—
79D4×C47—41no—
80D4×C47—41no—
81C2×C4×C47—21no—
82C2×C4×C47—22no—
83C2×C4×C47—41no—
84C2×C4×C47—41no—
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×C47C2×D411yescharacteristic
93C2×Dic47—22no—
94C2×Dic47—41no—
95C2×Dic47—41no—
96Dic94—22no—
97Dic94—22no—
98Dic94—41no—
99Dic94—41no—
100C8×C47—22no—
101C47⋊C8—22no—
102C47⋊C8—22no—
103C47⋊C8—41no—
104C22×C47—22no—
105C22×C47—41no—
106C22×C47—42no—
107C22×C47#12111yescharacteristic
108C22×C47#12111yescharacteristic
109C22×C47#12111yescharacteristic
110C4×C47—41no—
111C4×C47—42no—
112C4×C47#12011yescharacteristic
113C4×C47#12011yescharacteristic
114C4×C47#12011yescharacteristic
115C4×C47#12711yescharacteristic
116Dic47—42no—
117#2020—471nomaximal, Sylow
118C2×C47—21no—
119C2×C47—21no—
120C2×C47—81no—
121C2×C47#39211yescharacteristic
122C2×C47#47312yes—
123C2×#137—471no—
124C2×#137D4711yescharacteristic
125C22×Q16—471no—
126C2×#101—471no—
127C2×#101—471no—
128#408—471no—
129#341—471no—
130C47#202011yescharacteristic, complemented, Sylow
131C2×#41C2×D4711yescharacteristic
132C22×Q8—471no—
133C22×Q8C2×D4711yescharacteristic
134#137—22no—
135#137—22no—
136#137—942no—
137#137—942no—
138C2×Q16—21no—
139C2×Q16—942no—
140C2×Q16—942no—
141C2×Q16—942no—
142C2×Q16—941no—
143C2×SD16—21no—
144C2×SD16—941no—
145C2×M16—471no—
146C2×M16—471no—
147C2×M16C2×D4711yescharacteristic
148C22×C8—471no—
149#101—942no—
150#101—942no—
151C22⋊C8—942no—
152#41—21no—
153#41—21no—
154#41—21no—
155#41—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—472no—
162C2×Q8—941no—
163C2×Q8—941no—
164C2×Q8—941no—
165C2×Q8—941no—
166C2×Q8—941no—
167C2×Q8C22⋊D4711yescharacteristic
168C2×Q8C22⋊D4712yes—
169C2×D4—21no—
170C2×D4C22⋊D4711yescharacteristic
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—941no—
174C22×C4C22×D4711yescharacteristic
175Q16—24no—
176Q16—948no—
177Q16—944no—
178SD16—24no—
179SD16—944no—
180M16—21no—
181M16—472no—
182M16—941no—
183M16—941no—
184M16—941no—
185M16C22⋊D4712yes—
186C2×C8—21no—
187C2×C8—472no—
188C2×C8—941no—
189C2×C8—941no—
190C2×C8—941no—
191C2×C8—941no—
192C23—21no—
193C23#1062535211yescharacteristic
194Q8—22no—
195Q8—21no—
196Q8—22no—
197Q8—21no—
198Q8—41no—
199Q8—41no—
200Q8—942no—
201Q8—942no—
202Q8—1881no—
203Q8—1881no—
204D4—21no—
205D4—21no—
206D4—41no—
207D4—41no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—942no—
215C2×C4—1881no—
216C2×C4—1881no—
217C2×C4D4×D4711yescharacteristic
218C2×C4D4×D4711yescharacteristic
219C2×C4D4×D4711yescharacteristic
220C2×C4C2×C22⋊D4711yescharacteristic
221C2×C4C2×C22⋊D4711yescharacteristic
222C2×C4C2×C22⋊D4711yescharacteristic
223C8—22no—
224C8—942no—
225C8—942no—
226C8—1881no—
227C22—22no—
228C22—41no—
229C22—42no—
230C22#1309399511yescharacteristic
231C22#1309399611yescharacteristic
232C22#1309399611yescharacteristic
233C4—41no—
234C4—42no—
235C4—1882no—
236C4#1309399211yescharacteristic
237C4#1309399211yescharacteristic
238C4#1309399311yescharacteristic
239C4#1309402011yescharacteristic
240C2—21no—
241C2—21no—
242C2—81no—
243C2#1568903111yescharacteristic
244C2#1568939612yes—
subgroupG/H
centerC22#13093996
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#137×C47C2
socleC22×C47#121
hypercenterC2×#137D47
hypocenterC47#2020
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C22×#10625337C2semidirect
3. C2×#13093943C2semidirect
4. C2×#13093942C2semidirect
6. #15688887C2semidirect
130. C47#2020semidirect