Finite Group Databasebeta

← #20256206

Subgroups — #20256206

Order 6016.

350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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
2Q8×Dic94C211yesmaximal, characteristic, complemented
3#15689481C212yesmaximal, complemented
4#15689469C211yesmaximal, characteristic
5#15689419C211yesmaximal, characteristic, complemented
6#15689401C212yesmaximal, complemented
7#15689343C212yesmaximal, complemented
8#15689250C211yesmaximal, characteristic, complemented
9#15689224C212yesmaximal, complemented
10C4×#10625337C211yesmaximal, characteristic, complemented
11C47×#460C211yesmaximal, characteristic
12C2×#10625337C2211yescharacteristic
13#13094024—21no—
14#13094024C2211yescharacteristic
15#13094023—22no—
16#13094023C2212yes—
17#13094011—21no—
18#13094011C2212yes—
19#13094005—22no—
20Q8×Dic47C2212yes—
21C4×Dic94—21no—
22C4×Dic94C2211yescharacteristic
23C4×Dic94C2211yescharacteristic
24D4×Dic47—21no—
25D4×Dic47C2212yes—
26#13093958C2212yes—
27#13093957C2211yescharacteristic
28Dic47⋊C8C2212yes—
29#13093949C2212yes—
30#13093948C2211yescharacteristic
31#13093947C2211yescharacteristic
32#13093945C2212yes—
33#13093945C2212yes—
34#13093934C2212yes—
35C4×C47⋊C8C2211yescharacteristic
36C2×SD16×C47C2212yes—
37#127×C47C2211yescharacteristic
38C4×Q8×C47C2211yescharacteristic
39C4⋊C8×C47C2211yescharacteristic
40#102×C47C2212yes—
41C2×Q8×C47C2311yescharacteristic
42C2×D4×C47—21no—
43C2×D4×C47—21no—
44C2×D4×C47C2312yes—
45C22×Dic47—22no—
46C2×Dic94—21no—
47C2×Dic94—22no—
48C2×Dic94D411yescharacteristic
49C2×Dic94C2311yescharacteristic
50SD16×C47—24no—
51C2×C8×C47C2312yes—
52C4⋊C4×C47—21no—
53C4⋊C4×C47C2311yescharacteristic
54C42×C47—21no—
55C42×C47C2311yescharacteristic
56C22⋊Dic47—22no—
57C22⋊Dic47—22no—
58C22⋊Dic47—22no—
59#10625337—22no—
60C4⋊Dic47—21no—
61C4⋊Dic47—22no—
62C4⋊Dic47D411yescharacteristic
63C4⋊Dic47C2312yes—
64C4⋊Dic47C2311yescharacteristic
65Dic47⋊C4—21no—
66Dic47⋊C4—22no—
67Dic47⋊C4D412yes—
68C4×Dic47—21no—
69C4×Dic47—22no—
70C4×Dic47C2312yes—
71C2×C47⋊C8C2311yescharacteristic
72C2×C47⋊C8C2311yescharacteristic
73C23×C47—22no—
74Q8×C47—21no—
75Q8×C47#4112yes—
76D4×C47—22no—
77D4×C47—22no—
78D4×C47—42no—
79D4×C47—81no—
80C2×C4×C47—21no—
81C2×C4×C47—21no—
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2411yescharacteristic
85C2×Dic47—22no—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—82no—
89C2×Dic47C2×D412yes—
90C2×Dic47C2×D412yes—
91Dic94—22no—
92Dic94—21no—
93Dic94—21no—
94Dic94—82no—
95Dic94—81no—
96C8×C47—22no—
97C47⋊C8—21no—
98C47⋊C8—21no—
99C22×C47—42no—
100C22×C47—42no—
101C22×C47—42no—
102C22×C47C22×D411yescharacteristic
103C4×C47—22no—
104C4×C47—21no—
105C4×C47—41no—
106C4×C47#13712yes—
107C4×C47C2×#4111yescharacteristic
108C4×C472−1+411yescharacteristic
109Dic47—22no—
110Dic47—22no—
111Dic47—41no—
112Dic47—42no—
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#486—471no—
123#477—471no—
124#474—472no—
125#464—472no—
126#460D4711yescharacteristic
127#446—471no—
128#440—472no—
129C4×Q16—471no—
130C47#337511yescharacteristic, complemented, Sylow
131C2×Q16—471no—
132C2×SD16C2×D4712yes—
133C4⋊Q8—472no—
134C4⋊Q8—471no—
135C4⋊Q8—941no—
136C4⋊Q8—942no—
137#127C2×D4711yescharacteristic
138#124—472no—
139#124—941no—
140#123—942no—
141C4×Q8—471no—
142C4×Q8—472no—
143C4×Q8—471no—
144C4×Q8—941no—
145C4×Q8C2×D4711yescharacteristic
146C4×D4—472no—
147C4×D4—941no—
148#107—472no—
149#107—471no—
150C4⋊C8—472no—
151C4⋊C8C2×D4711yescharacteristic
152#103—471no—
153#103—472no—
154#103—471no—
155#102—472no—
156#102—472no—
157#102C2×D4712yes—
158#97—472no—
159C4×C8—471no—
160C2×Q8—471no—
161C2×Q8—471no—
162C2×Q8—942no—
163C2×Q8—941no—
164C2×Q8C22×D4711yescharacteristic
165C2×D4—21no—
166C2×D4—21no—
167C2×D4C22×D4712yes—
168C22×C4—942no—
169Q16—942no—
170SD16—24no—
171C2×C8—471no—
172C2×C8—471no—
173C2×C8C22×D4712yes—
174C4⋊C4—21no—
175C4⋊C4—472no—
176C4⋊C4—471no—
177C4⋊C4—472no—
178C4⋊C4—471no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C4⋊C4—941no—
182C4⋊C4—941no—
183C4⋊C4C22×D4711yescharacteristic
184C22⋊C4—942no—
185C22⋊C4—942no—
186C22⋊C4—942no—
187C42—21no—
188C42—472no—
189C42—942no—
190C42—941no—
191C42C22×D4711yescharacteristic
192C23—22no—
193Q8—21no—
194Q8—942no—
195Q8—941no—
196Q8—941no—
197Q8—3761no—
198Q8—3762no—
199Q8#1062535212yes—
200D4—22no—
201D4—22no—
202D4—42no—
203D4—81no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—472no—
207C2×C4—472no—
208C2×C4—941no—
209C2×C4—941no—
210C2×C4—942no—
211C2×C4—3762no—
212C2×C4D4×D4711yescharacteristic
213C2×C4D4×D4711yescharacteristic
214C2×C4C23×D4711yescharacteristic
215C8—22no—
216C8—941no—
217C8—941no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22C2×D4×D4711yescharacteristic
222C4—22no—
223C4—21no—
224C4—41no—
225C4—942no—
226C4—942no—
227C4—1881no—
228C4—1881no—
229C4—1882no—
230C4#1309405312yes—
231C4C2×#1062535211yescharacteristic
232C4#1309407111yescharacteristic
233C2—82no—
234C2#1568977911yescharacteristic
235C2C2×#1309405311yescharacteristic
236C2#1568992711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#460C2
socleC22×C47C22×D4
hypercenter#460D47
hypocenterC47#3375
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. Q8×Dic94C2semidirect
3. #15689481C2semidirect
5. #15689419C2semidirect
6. #15689401C2semidirect
7. #15689343C2semidirect
8. #15689250C2semidirect
9. #15689224C2semidirect
10. C4×#10625337C2semidirect
130. C47#3375semidirect