Finite Group Databasebeta

← #20256440

Subgroups — #20256440

Order 6016.

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

normal subgroups only

This group has 362 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#15689851C211yesmaximal, characteristic, complemented
3#15689514C212yesmaximal, complemented
4#15689495C211yesmaximal, characteristic
5#15689344C212yesmaximal, complemented
6#15689334C211yesmaximal, characteristic, complemented
7#15689326C212yesmaximal, complemented
8#15689250C211yesmaximal, characteristic, complemented
9#15689220C212yesmaximal, complemented
10C4×#10625337C211yesmaximal, characteristic, complemented
11C47×#460C211yesmaximal, characteristic
12C2×Dic188C2212yes—
13C2×#10625337C2211yescharacteristic
14C2×#10625335C2212yes—
15C2×#10625335C2212yes—
16#13094024C2211yescharacteristic
17#13094022C2212yes—
18#13094016—21no—
19#13094014—22no—
20#13094011—21no—
21#13094011C2212yes—
22#13094005—22no—
23C4×Dic94—21no—
24C4×Dic94C2211yescharacteristic
25C4×Dic94C2211yescharacteristic
26#13093989C2212yes—
27D4×Dic47—21no—
28D4×Dic47C2212yes—
29#13093957C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093949C2212yes—
32#13093948C2211yescharacteristic
33#13093947C2211yescharacteristic
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×Dic94D411yescharacteristic
47C2×Dic94C2311yescharacteristic
48C2×Dic94C2312yes—
49SD16×C47—42no—
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—
59#10625335—24no—
60#10625335—42no—
61C4⋊Dic47—21no—
62C4⋊Dic47—21no—
63C4⋊Dic47D411yescharacteristic
64C4⋊Dic47C2311yescharacteristic
65Dic47⋊C4—21no—
66Dic47⋊C4—22no—
67Dic47⋊C4—22no—
68Dic47⋊C4—22no—
69Dic47⋊C4D412yes—
70C4×Dic47—21no—
71C4×Dic47—22no—
72C4×Dic47C2312yes—
73C2×C47⋊C8C2311yescharacteristic
74C2×C47⋊C8C2311yescharacteristic
75Dic188—42no—
76C23×C47—22no—
77Q8×C47—21no—
78Q8×C47—21no—
79D4×C47—22no—
80D4×C47—22no—
81D4×C47—42no—
82D4×C47—81no—
83C2×C4×C47—21no—
84C2×C4×C47—21no—
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2411yescharacteristic
88C2×Dic47—22no—
89C2×Dic47—21no—
90C2×Dic47—21no—
91C2×Dic47—82no—
92C2×Dic47C2×D412yes—
93C2×Dic47C2×D412yes—
94Dic94—22no—
95Dic94—22no—
96Dic94—21no—
97Dic94—21no—
98Dic94—22no—
99C8×C47—22no—
100C47⋊C8—21no—
101C47⋊C8#4112yes—
102C22×C47—42no—
103C22×C47—42no—
104C22×C47—42no—
105C22×C47C22×D411yescharacteristic
106C4×C47—21no—
107C4×C47—41no—
108C4×C47—41no—
109C4×C47#13712yes—
110C4×C47C2×#4111yescharacteristic
111C4×C47H(5,𝔽2)11yescharacteristic
112Dic47—22no—
113Dic47—22no—
114Dic47—42no—
115Dic47—41no—
116Dic47—41no—
117#3400—471nomaximal, Sylow
118C2×C47—82no—
119C2×C47#55011yescharacteristic
120C2×C47C2×#13711yescharacteristic
121C2×C47#57711yescharacteristic
122#559—471no—
123#557—471no—
124#497—472no—
125#492—471no—
126#464—472no—
127#462—471no—
128#461—472no—
129#460D4711yescharacteristic
130#446—471no—
131#440—472no—
132C4×Q16—471no—
133C47#340011yescharacteristic, complemented, Sylow
134C2×Q16—471no—
135C2×Q16—472no—
136C2×SD16—472no—
137C2×SD16—472no—
138C2×SD16C2×D4712yes—
139C4⋊Q8—472no—
140C4⋊Q8—471no—
141#127C2×D4711yescharacteristic
142#125—941no—
143#125—942no—
144#124—472no—
145#124—941no—
146#123—942no—
147C4×Q8—471no—
148C4×Q8—472no—
149C4×Q8—471no—
150C4×Q8—941no—
151C4×Q8C2×D4711yescharacteristic
152C4×D4—472no—
153C4×D4—941no—
154#107—471no—
155C4⋊C8—472no—
156C4⋊C8C2×D4711yescharacteristic
157#103—471no—
158#103—472no—
159#103—471no—
160#102C2×D4712yes—
161#97—472no—
162C4×C8—471no—
163C2×Q8—471no—
164C2×Q8—471no—
165C2×Q8—472no—
166C2×Q8C22×D4711yescharacteristic
167C2×D4—21no—
168C2×D4—21no—
169C2×D4C22×D4712yes—
170C22×C4—942no—
171Q16—942no—
172Q16—1882no—
173SD16—42no—
174SD16—944no—
175SD16—1882no—
176C2×C8—471no—
177C2×C8—471no—
178C2×C8C22×D4712yes—
179C4⋊C4—21no—
180C4⋊C4—472no—
181C4⋊C4—471no—
182C4⋊C4—471no—
183C4⋊C4—942no—
184C4⋊C4—942no—
185C4⋊C4—942no—
186C4⋊C4—941no—
187C4⋊C4—941no—
188C4⋊C4—941no—
189C4⋊C4C22×D4711yescharacteristic
190C22⋊C4—942no—
191C22⋊C4—942no—
192C22⋊C4—942no—
193C42—21no—
194C42—472no—
195C42—942no—
196C42—941no—
197C42C22×D4711yescharacteristic
198C23—22no—
199Q8—21no—
200Q8—21no—
201Q8—942no—
202Q8—942no—
203Q8—941no—
204Q8—942no—
205Q8—941no—
206D4—22no—
207D4—22no—
208D4—42no—
209D4—81no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—472no—
213C2×C4—472no—
214C2×C4—941no—
215C2×C4—941no—
216C2×C4—942no—
217C2×C4—3762no—
218C2×C4D4×D4711yescharacteristic
219C2×C4D4×D4711yescharacteristic
220C2×C4C23×D4711yescharacteristic
221C8—22no—
222C8—472no—
223C8—941no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22C2×D4×D4711yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—942no—
232C4—942no—
233C4—1881no—
234C4—1882no—
235C4—1881no—
236C4#1309405312yes—
237C4#41×D4711yescharacteristic
238C4#1309406911yescharacteristic
239C2—82no—
240C2#1568979111yescharacteristic
241C2C2×#1309405311yescharacteristic
242C2#1568993311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#460C2
socleC22×C47C22×D4
hypercenter#460D47
hypocenterC47#3400
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. #15689851C2semidirect
3. #15689514C2semidirect
5. #15689344C2semidirect
6. #15689334C2semidirect
7. #15689326C2semidirect
8. #15689250C2semidirect
9. #15689220C2semidirect
10. C4×#10625337C2semidirect
133. C47#3400semidirect