Finite Group Databasebeta

← #20256207

Subgroups — #20256207

Order 6016.

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

normal subgroups only

This group has 350 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#15689859C211yesmaximal, characteristic
2#15689853C211yesmaximal, characteristic, complemented
3#15689481C212yesmaximal, complemented
4#15689415C211yesmaximal, characteristic, complemented
5#15689401C212yesmaximal, complemented
6#15689344C212yesmaximal, complemented
7#15689320C211yesmaximal, characteristic
8#15689253C211yesmaximal, characteristic, complemented
9#15689220C212yesmaximal, complemented
10C4×Dic188C211yesmaximal, characteristic, complemented
11C47×#486C211yesmaximal, characteristic
12C2×Dic188C2211yescharacteristic
13C2×#10625335C2212yes—
14#13094023—21no—
15#13094023C2212yes—
16#13094022—22no—
17#13094011—21no—
18#13094011C2212yes—
19#13094005—22no—
20C4×Dic94C2211yescharacteristic
21C4×Dic94C2211yescharacteristic
22C4×Dic94C2211yescharacteristic
23#13093989—21no—
24#13093989C2212yes—
25D4×Dic47—21no—
26D4×Dic47C2212yes—
27#13093958C2211yescharacteristic
28#13093957C2212yes—
29C4⋊(C47⋊C8)C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093949C2211yescharacteristic
32#13093949C2211yescharacteristic
33#13093947C2212yes—
34#13093945C2212yes—
35#13093934C2212yes—
36C4⋊Q8×C47C2211yescharacteristic
37#127×C47C2211yescharacteristic
38#102×C47C2212yes—
39#102×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47—21no—
42C2×D4×C47—21no—
43C2×D4×C47—21no—
44C2×D4×C47C2312yes—
45C22×Dic47—22no—
46C2×Dic94—22no—
47C2×Dic94D411yescharacteristic
48C2×Dic94C2311yescharacteristic
49C2×Dic94C2311yescharacteristic
50C2×C8×C47C2311yescharacteristic
51C2×C8×C47C2311yescharacteristic
52C4⋊C4×C47—21no—
53C4⋊C4×C47C2312yes—
54C42×C47C2311yescharacteristic
55C22⋊Dic47—22no—
56C22⋊Dic47—22no—
57C22⋊Dic47—22no—
58#10625335—24no—
59C4⋊Dic47D411yescharacteristic
60C4⋊Dic47C2311yescharacteristic
61C4⋊Dic47C2311yescharacteristic
62Dic47⋊C4—21no—
63Dic47⋊C4—21no—
64Dic47⋊C4—22no—
65Dic47⋊C4—22no—
66Dic47⋊C4D412yes—
67C4×Dic47—21no—
68C4×Dic47—21no—
69C4×Dic47—22no—
70C4×Dic47C2312yes—
71C2×C47⋊C8C2312yes—
72Dic188—22no—
73C23×C47—22no—
74Q8×C47—81no—
75D4×C47—22no—
76D4×C47—22no—
77D4×C47—42no—
78D4×C47—81no—
79C2×C4×C47—22no—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2411yescharacteristic
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—82no—
88C2×Dic47C2×D412yes—
89C2×Dic47C2×D412yes—
90Dic94—22no—
91Dic94—21no—
92Dic94—21no—
93Dic94—21no—
94Dic94—82no—
95Dic94#4112yes—
96C8×C47—21no—
97C8×C47—21no—
98C47⋊C8—22no—
99C22×C47—42no—
100C22×C47—42no—
101C22×C47—42no—
102C22×C47C22×D411yescharacteristic
103C4×C47—21no—
104C4×C47—42no—
105C4×C47#13712yes—
106C4×C47C2×#4111yescharacteristic
107C4×C472−1+411yescharacteristic
108Dic47—22no—
109Dic47—22no—
110Dic47—22no—
111Dic47—41no—
112Dic47—41no—
113Dic47—41no—
114#3375—471nomaximal, Sylow
115C2×C47—82no—
116C2×C47#54811yescharacteristic
117C2×C47C2×#13711yescharacteristic
118C2×C47#57611yescharacteristic
119#559—471no—
120Q82—471no—
121#489—472no—
122#486D4711yescharacteristic
123#477—471no—
124#474—472no—
125#464—472no—
126#460—471no—
127#446—471no—
128#440—472no—
129C4×Q16—471no—
130C47#337511yescharacteristic, complemented, Sylow
131C2×Q16—471no—
132C2×SD16—472no—
133C4⋊Q8—472no—
134C4⋊Q8—941no—
135C4⋊Q8—942no—
136C4⋊Q8C2×D4711yescharacteristic
137#127C2×D4711yescharacteristic
138#124—472no—
139#124—941no—
140#123—942no—
141C4×Q8—471no—
142C4×Q8—472no—
143C4×Q8—471no—
144C4×Q8—471no—
145C4×Q8—941no—
146C4×D4—472no—
147C4×D4—941no—
148#107—471no—
149#107—472no—
150C4⋊C8—472no—
151C4⋊C8—471no—
152#103—471no—
153#103—471no—
154#103—472no—
155#102—472no—
156#102C2×D4712yes—
157#102C2×D4712yes—
158#97—472no—
159C4×C8C2×D4711yescharacteristic
160C2×Q8—21no—
161C2×Q8—471no—
162C2×Q8—471no—
163C2×Q8—471no—
164C2×Q8—942no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4C22×D4712yes—
168C22×C4—942no—
169Q16—942no—
170SD16—944no—
171C2×C8—472no—
172C2×C8C22×D4711yescharacteristic
173C2×C8C22×D4711yescharacteristic
174C4⋊C4—21no—
175C4⋊C4—472no—
176C4⋊C4—471no—
177C4⋊C4—471no—
178C4⋊C4—471no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C4⋊C4—941no—
182C4⋊C4—941no—
183C4⋊C4C22×D4712yes—
184C22⋊C4—942no—
185C22⋊C4—942no—
186C22⋊C4—942no—
187C42—472no—
188C42—942no—
189C42—941no—
190C42—941no—
191C42C22×D4711yescharacteristic
192C23—22no—
193Q8—81no—
194Q8—472no—
195Q8—942no—
196Q8—941no—
197Q8—941no—
198Q8—941no—
199Q8—3762no—
200D4—22no—
201D4—22no—
202D4—42no—
203D4—81no—
204C2×C4—22no—
205C2×C4—472no—
206C2×C4—472no—
207C2×C4—941no—
208C2×C4—941no—
209C2×C4—941no—
210C2×C4—941no—
211C2×C4—3762no—
212C2×C4D4×D4711yescharacteristic
213C2×C4D4×D4711yescharacteristic
214C2×C4C23×D4711yescharacteristic
215C8—21no—
216C8—21no—
217C8—942no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22C2×D4×D4711yescharacteristic
222C4—21no—
223C4—42no—
224C4—942no—
225C4—942no—
226C4—942no—
227C4—1881no—
228C4—1881no—
229C4—1881no—
230C4#1309405312yes—
231C4#41×D4711yescharacteristic
232C4#1309407111yescharacteristic
233C2—82no—
234C2#1568978111yescharacteristic
235C2C2×#1309405311yescharacteristic
236C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#486C2
socleC22×C47C22×D4
hypercenter#486D47
hypocenterC47#3375
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #15689853C2semidirect
3. #15689481C2semidirect
4. #15689415C2semidirect
5. #15689401C2semidirect
6. #15689344C2semidirect
8. #15689253C2semidirect
9. #15689220C2semidirect
10. C4×Dic188C2semidirect
130. C47#3375semidirect