Finite Group Databasebeta

← #20256245

Subgroups — #20256245

Order 6016.

370 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 133 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#15689853C211yesmaximal, characteristic, complemented
2#15689788C211yesmaximal, characteristic
3#15689520C212yesmaximal, complemented
4#15689412C212yesmaximal
5#15689410C211yesmaximal, characteristic
6#15689407C212yesmaximal, complemented
7#15689405C211yesmaximal, characteristic, complemented
8C8×Dic94C211yesmaximal, characteristic, complemented
9C4×#10625325C211yesmaximal, characteristic
10#15689210C212yesmaximal
11C47×#498C211yesmaximal, characteristic, complemented
12C2×Q8×D47—21no—
13C2×#10625325C2211yescharacteristic
14#13094023—21no—
15#13094023C2212yes—
16#13094023C2212yes—
17#13094022—22no—
18#13094002—22no—
19#13094000—21no—
20C4×Dic94C2211yescharacteristic
21C4×Dic94C2211yescharacteristic
22#13093989—21no—
23#13093989C2212yes—
24C4×D188C2211yescharacteristic
25#13093986C2212yes—
26#13093956C2211yescharacteristic
27#13093955C2212yes—
28#13093955C2212yes—
29C4⋊(C47⋊C8)C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093949C2211yescharacteristic
32#13093947C2212yes—
33#13093946C2211yescharacteristic
34#13093944C2212yes—
35C8×Dic47C2212yes—
36C4⋊Q8×C47C2211yescharacteristic
37C4⋊Q8×C47C2211yescharacteristic
38#106×C47C2212yes—
39#106×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47—21no—
42C2×Q8×C47—21no—
43Q8×D47—44no—
44C2×D188C2311yescharacteristic
45C2×C4×D47—21no—
46C2×C4×D47—22no—
47C2×Dic94—22no—
48C2×Dic94—22no—
49C2×Dic94D411yescharacteristic
50C2×Dic94C2311yescharacteristic
51C2×C8×C47C2311yescharacteristic
52C2×C8×C47C2311yescharacteristic
53C4⋊C4×C47—21no—
54C4⋊C4×C47—21no—
55C4⋊C4×C47C2312yes—
56C4⋊C4×C47C2312yes—
57C42×C47C2311yescharacteristic
58(C2×D47)⋊C4—21no—
59(C2×D47)⋊C4—22no—
60C4⋊Dic47D411yescharacteristic
61C4⋊Dic47C2311yescharacteristic
62C4⋊Dic47C2311yescharacteristic
63Dic47⋊C4—21no—
64Dic47⋊C4—22no—
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67Dic47⋊C4D412yes—
68C4×Dic47—21no—
69C4×Dic47—22no—
70C4×Dic47C2312yes—
71C2×C47⋊C8C2312yes—
72#10625325Q814yescomplemented
73C22×D47—21no—
74Q8×C47—42no—
75Q8×C47—81no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2411yescharacteristic
81C2×Dic47—21no—
82C2×Dic47—21no—
83C2×Dic47—21no—
84C2×Dic47C2×D412yes—
85C2×Dic47C2×D412yes—
86D188—21no—
87D188C2×Q812yes—
88C4×D47—42no—
89C4×D47—44no—
90Dic94—21no—
91Dic94—44no—
92Dic94—82no—
93Dic94SD1614yescomplemented
94Dic94C2×Q812yescomplemented
95C8×C47—21no—
96C8×C47C2×Q812yescomplemented
97C47⋊C8—22no—
98C22×C47C22×D411yescharacteristic
99C2×D47—22no—
100C2×D47—41no—
101C2×D47—41no—
102C4×C47—21no—
103C4×C47—42no—
104C4×C47—42no—
105C4×C47C2×SD1612yes—
106C4×C47C22×Q811yescharacteristic
107C4×C472−1+411yescharacteristic
108Dic47—22no—
109Dic47—22no—
110Dic47—41no—
111Dic47—41no—
112Dic47C2×SD1614yes—
113Q8×SD16—471nomaximal, Sylow
114C2×C47D4×Q811yescharacteristic
115C2×C47C22×SD1611yescharacteristic
116C2×C47#57711yescharacteristic
117D47—42no—
118Q82—471no—
119D4×Q8—471no—
120#498—472no—
121#498D4711yescharacteristic, complemented
122#476—471no—
123#476—472no—
124#475—471no—
125#475—472no—
126C8×Q8—471no—
127C4×SD16—472no—
128C4×SD16—471no—
129C47Q8×SD1611yescharacteristic, complemented, Sylow
130C22×Q8—941no—
131C2×SD16—471no—
132C4⋊Q8—472no—
133C4⋊Q8—472no—
134C4⋊Q8—941no—
135C4⋊Q8—942no—
136C4⋊Q8C2×D4711yescharacteristic
137C4⋊Q8C2×D4711yescharacteristic
138C22⋊Q8—942no—
139C22⋊Q8—941no—
140C4×Q8—471no—
141C4×Q8—472no—
142C4×Q8—471no—
143C4×Q8—941no—
144C4×D4—472no—
145C4×D4—471no—
146#106—471no—
147#106—472no—
148#106—472no—
149#106C2×D4712yes—
150#106C2×D4712yes—
151C4⋊C8—472no—
152C4⋊C8—471no—
153#103—471no—
154#103—472no—
155#102—471no—
156#102—472no—
157C4×C8—472no—
158C4×C8C2×D4711yescharacteristic
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—471no—
162C2×Q8—471no—
163C2×Q8—942no—
164C2×Q8—942no—
165C2×Q8—1884no—
166C2×D4—471no—
167C22×C4—942no—
168C22×C4—941no—
169SD16—474no—
170C2×C8—472no—
171C2×C8C22×D4711yescharacteristic
172C2×C8C22×D4711yescharacteristic
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—472no—
176C4⋊C4—471no—
177C4⋊C4—471no—
178C4⋊C4—471no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C4⋊C4—942no—
182C4⋊C4—941no—
183C4⋊C4C22×D4712yes—
184C4⋊C4C22×D4712yes—
185C22⋊C4—942no—
186C22⋊C4—941no—
187C42—472no—
188C42—942no—
189C42—941no—
190C42C22×D4711yescharacteristic
191C23—941no—
192Q8—42no—
193Q8—81no—
194Q8—474no—
195Q8—472no—
196Q8—941no—
197Q8—3762no—
198Q8—1884no—
199D4—472no—
200D4—941no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—472no—
204C2×C4—472no—
205C2×C4—941no—
206C2×C4—941no—
207C2×C4—941no—
208C2×C4—1884no—
209C2×C4—1882no—
210C2×C4D4×D4711yescharacteristic
211C2×C4D4×D4711yescharacteristic
212C2×C4C23×D4711yescharacteristic
213C8—21no—
214C8—942no—
215C8Q8×D4712yescomplemented
216C22—942no—
217C22—1881no—
218C22—1881no—
219C22C2×D4×D4711yescharacteristic
220C4—21no—
221C4—42no—
222C4—42no—
223C4—474no—
224C4—942no—
225C4—942no—
226C4—1881no—
227C4—1881no—
228C4SD16×D4712yes—
229C4C2×Q8×D4711yescharacteristic
230C4#1309407211yescharacteristic
231C2—1882no—
232C2#1568978811yescharacteristic
233C2C2×SD16×D4711yescharacteristic
234C2#1568992911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#498C2
socleC22×C47C22×D4
hypercenter#498D47
hypocenterC47Q8×SD16
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
1. #15689853C2semidirect
3. #15689520C2semidirect
6. #15689407C2semidirect
7. #15689405C2semidirect
8. C8×Dic94C2semidirect
11. C47×#498C2semidirect
72. #10625325Q8semidirect
93. Dic94SD16semidirect
94. Dic94C2×Q8semidirect
96. C8×C47C2×Q8semidirect
121. #498D47semidirect
129. C47Q8×SD16semidirect
215. C8Q8×D47semidirect