Finite Group Databasebeta

← #20256088

Subgroups — #20256088

Order 6016.

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

normal subgroups only

This group has 348 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
2#15689852C211yesmaximal, characteristic, complemented
3#15689476C212yesmaximal, complemented
4#15689469C211yesmaximal, characteristic
5#15689425C212yesmaximal, complemented
6#15689409C211yesmaximal, characteristic, complemented
7#15689343C212yesmaximal, complemented
8#15689247C211yesmaximal, characteristic, complemented
9C4×#10625337C211yesmaximal, characteristic, complemented
10SD16×Dic47C212yesmaximal, complemented
11C47×#460C211yesmaximal, characteristic
12C2×#10625337C2211yescharacteristic
13#13094024—21no—
14#13094024C2211yescharacteristic
15#13094015—22no—
16#13094015C2212yes—
17#13094011—21no—
18#13094011C2212yes—
19#13094005—22no—
20Q8×Dic47C2212yes—
21C4×Dic94—21no—
22C4×Dic94C2211yescharacteristic
23C4×Dic94C2211yescharacteristic
24D4×Dic47—21no—
25D4×Dic47C2212yes—
26#13093957C2211yescharacteristic
27#13093956C2212yes—
28Dic47⋊C8C2212yes—
29#13093949C2212yes—
30#13093948C2211yescharacteristic
31#13093947C2211yescharacteristic
32#13093945C2212yes—
33#13093945C2212yes—
34C4×C47⋊C8C2211yescharacteristic
35C8×Dic47C2212yes—
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×Dic94D411yescharacteristic
48C2×Dic94C2311yescharacteristic
49SD16×C47—24no—
50C2×C8×C47C2312yes—
51C4⋊C4×C47—21no—
52C4⋊C4×C47C2311yescharacteristic
53C42×C47—21no—
54C42×C47C2311yescharacteristic
55C22⋊Dic47—22no—
56C22⋊Dic47—22no—
57C22⋊Dic47—22no—
58#10625337—22no—
59C4⋊Dic47—21no—
60C4⋊Dic47—22no—
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—42no—
95C8×C47—22no—
96C47⋊C8—21no—
97C47⋊C8—21no—
98C22×C47—42no—
99C22×C47—42no—
100C22×C47—42no—
101C22×C47C22×D411yescharacteristic
102C4×C47—22no—
103C4×C47—21no—
104C4×C47—41no—
105C4×C47#13512yes—
106C4×C47C2×#4111yescharacteristic
107C4×C472−1+411yescharacteristic
108Dic47—22no—
109Dic47—22no—
110Dic47—41no—
111Dic47—42no—
112Dic47—41no—
113#3365—471nomaximal, Sylow
114C2×C47—82no—
115C2×C47#54811yescharacteristic
116C2×C47C2×#13511yescharacteristic
117C2×C47#57711yescharacteristic
118#559—471no—
119#557—471no—
120#488—472no—
121#486—471no—
122#478—472no—
123#475—471no—
124#464—472no—
125#460D4711yescharacteristic
126C8×Q8—471no—
127C4×Q16—471no—
128C4×SD16—472no—
129C47#336511yescharacteristic, complemented, Sylow
130C2×Q16—471no—
131C2×SD16C2×D4712yes—
132C4⋊Q8—471no—
133C4⋊Q8—941no—
134#127C2×D4711yescharacteristic
135#125—472no—
136#125—942no—
137#124—472no—
138#124—941no—
139#123—942no—
140C4×Q8—471no—
141C4×Q8—472no—
142C4×Q8—471no—
143C4×Q8—941no—
144C4×Q8C2×D4711yescharacteristic
145C4×D4—472no—
146C4×D4—941no—
147#107—471no—
148#106—472no—
149C4⋊C8—472no—
150C4⋊C8C2×D4711yescharacteristic
151#103—471no—
152#103—472no—
153#103—471no—
154#102—472no—
155#102—472no—
156#102C2×D4712yes—
157C4×C8—472no—
158C4×C8—471no—
159C2×Q8—471no—
160C2×Q8—471no—
161C2×Q8—941no—
162C2×Q8C22×D4711yescharacteristic
163C2×D4—21no—
164C2×D4—21no—
165C2×D4C22×D4712yes—
166C22×C4—942no—
167Q16—942no—
168SD16—24no—
169C2×C8—471no—
170C2×C8—471no—
171C2×C8C22×D4712yes—
172C4⋊C4—21no—
173C4⋊C4—472no—
174C4⋊C4—471no—
175C4⋊C4—472no—
176C4⋊C4—471no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—942no—
180C4⋊C4—941no—
181C4⋊C4—941no—
182C4⋊C4C22×D4711yescharacteristic
183C22⋊C4—942no—
184C22⋊C4—942no—
185C22⋊C4—942no—
186C42—21no—
187C42—472no—
188C42—942no—
189C42—941no—
190C42C22×D4711yescharacteristic
191C23—22no—
192Q8—21no—
193Q8—942no—
194Q8—941no—
195Q8—941no—
196Q8—1882no—
197Q8#1062535212yes—
198D4—22no—
199D4—22no—
200D4—42no—
201D4—81no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—472no—
205C2×C4—472no—
206C2×C4—941no—
207C2×C4—941no—
208C2×C4—942no—
209C2×C4—3762no—
210C2×C4D4×D4711yescharacteristic
211C2×C4D4×D4711yescharacteristic
212C2×C4C23×D4711yescharacteristic
213C8—22no—
214C8—941no—
215C8—941no—
216C22—42no—
217C22—42no—
218C22—42no—
219C22C2×D4×D4711yescharacteristic
220C4—22no—
221C4—21no—
222C4—41no—
223C4—942no—
224C4—942no—
225C4—1881no—
226C4—1882no—
227C4—1881no—
228C4#1309404512yes—
229C4C2×#1062535211yescharacteristic
230C4#1309407111yescharacteristic
231C2—82no—
232C2#1568977911yescharacteristic
233C2C2×#1309404511yescharacteristic
234C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#460C2
socleC22×C47C22×D4
hypercenter#460D47
hypocenterC47#3365
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. #15689852C2semidirect
3. #15689476C2semidirect
5. #15689425C2semidirect
6. #15689409C2semidirect
7. #15689343C2semidirect
8. #15689247C2semidirect
9. C4×#10625337C2semidirect
10. SD16×Dic47C2semidirect
129. C47#3365semidirect