Finite Group Databasebeta

← #20256017

Subgroups — #20256017

Order 6016.

354 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#15689838C211yesmaximal, characteristic
2#15689834C211yesmaximal, characteristic, complemented
3#15689526C211yesmaximal, characteristic, complemented
4#15689467C212yesmaximal, complemented
5#15689435C212yesmaximal, complemented
6#15689419C211yesmaximal, characteristic, complemented
7#15689368C212yesmaximal, complemented
8C4×#10625335C211yesmaximal, characteristic, complemented
9#15689200C211yesmaximal, characteristic, complemented
10#15689162C212yesmaximal, complemented
11C47×#476C211yesmaximal, characteristic, complemented
12C2×#10625335C2211yescharacteristic
13C2×#10625324C2212yes—
14#13094024C2211yescharacteristic
15#13094015—21no—
16#13094010—22no—
17#13094004C2212yes—
18#13094000—22no—
19#13093998—21no—
20#13093995C2212yes—
21C4×Dic94C2211yescharacteristic
22C4×D188C2211yescharacteristic
23#13093986—21no—
24#13093983—21no—
25#13093982C2212yes—
26C4⋊C4×D47C2212yes—
27#13093958C2212yes—
28#13093957C2212yes—
29#13093957C2212yes—
30#13093955C2211yescharacteristic
31#13093949C2212yes—
32#13093947C2211yescharacteristic
33#13093945C2211yescharacteristic
34(C2×D47)⋊C8C2212yes—
35C4×C47⋊C8C2211yescharacteristic
36C4⋊Q8×C47C2211yescharacteristic
37C4×D4×C47C2211yescharacteristic
38#106×C47C2212yes—
39C4⋊C8×C47C2211yescharacteristic
40#102×C47C2212yes—
41C2×Q8×C47—21no—
42C2×D4×C47C2311yescharacteristic
43C22×C4×C47—21no—
44C2×C22⋊D47—22no—
45C2×D188D411yescharacteristic
46C2×C4×D47—22no—
47C2×C4×D47C2312yes—
48C2×Dic94—21no—
49C2×Dic94C2311yescharacteristic
50C2×C8×C47C2312yes—
51C4⋊C4×C47—21no—
52C4⋊C4×C47C2311yescharacteristic
53C4⋊C4×C47C2312yes—
54C22⋊C4×C47—21no—
55C42×C47C2311yescharacteristic
56C22⋊Dic47—22no—
57#10625335—22no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4D412yes—
61C4⋊Dic47—21no—
62C4⋊Dic47—22no—
63C4⋊Dic47D411yescharacteristic
64C4⋊Dic47C2311yescharacteristic
65C4⋊Dic47C2312yes—
66Dic47⋊C4—21no—
67Dic47⋊C4—22no—
68C4×Dic47—21no—
69C4×Dic47—22no—
70C2×C47⋊C8C2311yescharacteristic
71C2×C47⋊C8C2311yescharacteristic
72#10625324—24no—
73C23×C47—21no—
74C22×D47C2×D412yes—
75Q8×C47—81no—
76D4×C47—21no—
77D4×C47—21no—
78C2×C4×C47—21no—
79C2×C4×C47—22no—
80C2×C4×C47—42no—
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2411yescharacteristic
84C22⋊D47—82no—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—22no—
88C2×Dic47C2×D412yes—
89D188—22no—
90C4×D47—22no—
91C4×D47—22no—
92C4×D47—82no—
93Dic94—21no—
94Dic94—21no—
95Dic94—81no—
96C8×C47—22no—
97C47⋊C8—21no—
98C47⋊C8#4112yes—
99C22×C47—41no—
100C22×C47—41no—
101C22×C47—41no—
102C22×C47C22×D411yescharacteristic
103C2×D47—22no—
104C2×D47—22no—
105C2×D47—22no—
106C4×C47—21no—
107C4×C47—41no—
108C4×C47—42no—
109C4×C47#13712yes—
110C4×C47C2×#4111yescharacteristic
111C4×C472−1+411yescharacteristic
112Dic47—22no—
113Dic47—41no—
114Dic47—42no—
115Dic47—41no—
116#3357—471nomaximal, Sylow
117C2×C47—81no—
118C2×C47#54711yescharacteristic
119C2×C47C2×#13711yescharacteristic
120C2×C47#57611yescharacteristic
121D47—42no—
122#555—471no—
123#554—471no—
124#500—471no—
125#485—472no—
126#480—472no—
127#477—471no—
128#476D4711yescharacteristic, complemented
129#468—472no—
130C4×SD16—471no—
131#436—471no—
132#428—472no—
133C47#335711yescharacteristic, complemented, Sylow
134C2×SD16—471no—
135C2×M16—472no—
136C4⋊Q8—471no—
137C4⋊Q8C2×D4711yescharacteristic
138#125—941no—
139#124—942no—
140C22⋊Q8—472no—
141C22⋊Q8—942no—
142#121—472no—
143#121—941no—
144C4×Q8—471no—
145C4×D4—471no—
146C4×D4—941no—
147C4×D4C2×D4711yescharacteristic
148#117—472no—
149#117—941no—
150C2×C4⋊C4—472no—
151#107—472no—
152#107—472no—
153#107—472no—
154#106—471no—
155#106C2×D4712yes—
156C4⋊C8C2×D4711yescharacteristic
157#103—472no—
158#103—471no—
159#102—471no—
160#102C2×D4712yes—
161C22⋊C8—472no—
162C4×C8—471no—
163C2×Q8—21no—
164C2×Q8—471no—
165C2×Q8—941no—
166C2×D4—471no—
167C2×D4—942no—
168C2×D4C22×D4711yescharacteristic
169C22×C4—21no—
170C22×C4—472no—
171C22×C4—942no—
172SD16—942no—
173M16—944no—
174C2×C8—471no—
175C2×C8—471no—
176C2×C8C22×D4712yes—
177C4⋊C4—21no—
178C4⋊C4—471no—
179C4⋊C4—471no—
180C4⋊C4—472no—
181C4⋊C4—942no—
182C4⋊C4—942no—
183C4⋊C4—941no—
184C4⋊C4—941no—
185C4⋊C4C22×D4712yes—
186C4⋊C4C22×D4711yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—472no—
189C22⋊C4—942no—
190C22⋊C4—942no—
191C22⋊C4—942no—
192C42—942no—
193C42—941no—
194C42C22×D4711yescharacteristic
195C23—21no—
196C23—472no—
197Q8—81no—
198Q8—941no—
199Q8—941no—
200Q8—3761no—
201D4—21no—
202D4—21no—
203D4—942no—
204D4—3762no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—472no—
209C2×C4—942no—
210C2×C4—942no—
211C2×C4—942no—
212C2×C4—941no—
213C2×C4—941no—
214C2×C4—3762no—
215C2×C4D4×D4711yescharacteristic
216C2×C4D4×D4711yescharacteristic
217C2×C4C23×D4711yescharacteristic
218C8—22no—
219C8—472no—
220C8—941no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—942no—
225C22—942no—
226C22—942no—
227C22C2×D4×D4711yescharacteristic
228C4—21no—
229C4—41no—
230C4—42no—
231C4—942no—
232C4—1881no—
233C4—1881no—
234C4—1882no—
235C4#1309405312yes—
236C4#41×D4711yescharacteristic
237C4#1309407211yescharacteristic
238C2—81no—
239C2—1882no—
240C2#1568977511yescharacteristic
241C2C2×#1309405311yescharacteristic
242C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#476C2
socleC22×C47C22×D4
hypercenter#476D47
hypocenterC47#3357
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #15689834C2semidirect
3. #15689526C2semidirect
4. #15689467C2semidirect
5. #15689435C2semidirect
6. #15689419C2semidirect
7. #15689368C2semidirect
8. C4×#10625335C2semidirect
9. #15689200C2semidirect
10. #15689162C2semidirect
11. C47×#476C2semidirect
128. #476D47semidirect
133. C47#3357semidirect