Finite Group Databasebeta

← #20254028

Subgroups — #20254028

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#15689746C212yesmaximal, complemented
2#15689527C211yesmaximal, characteristic, complemented
3#15689508C211yesmaximal, characteristic, complemented
4#15689484C212yesmaximal, complemented
5#15689371C212yesmaximal, complemented
6#15689359C211yesmaximal, characteristic
7#15689226C212yesmaximal, complemented
8Q16×Dic47C211yesmaximal, characteristic, complemented
9#15689205C211yesmaximal, characteristic, complemented
10#15689078C211yesmaximal, characteristic, complemented
11C47×#467C211yesmaximal, characteristic, complemented
12C2×#10625336C2212yes—
13C2×D376C2211yescharacteristic
14C2×#10625329C2211yescharacteristic
15#13094023C2212yes—
16#13094019—22no—
17#13094013C2212yes—
18#13094010—22no—
19#13094006—22no—
20#13094004—22no—
21#13093998C2212yes—
22Q8×Dic47C2212yes—
23#13093986C2212yes—
24#13093983C2211yescharacteristic
25#13093958C2211yescharacteristic
26#13093957C2212yes—
27#13093948C2212yes—
28#13093946C2212yes—
29#13093944C2212yes—
30#13093934C2211yescharacteristic
31#13093934C2211yescharacteristic
32C8×Dic47C2211yescharacteristic
33C8×Dic47C2211yescharacteristic
34C2×Q16×C47C2211yescharacteristic
35C22×C8×C47C2211yescharacteristic
36C22⋊Q8×C47C2212yes—
37#107×C47C2211yescharacteristic
38#103×C47C2212yes—
39C2×Q8×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C2×C22⋊D47—22no—
42C2×D188C2312yes—
43C2×C4×D47—22no—
44C2×Dic94—22no—
45Q16×C47—22no—
46C2×C8×C47—22no—
47C2×C8×C47C2311yescharacteristic
48C2×C8×C47C2311yescharacteristic
49C4⋊C4×C47—22no—
50C4⋊C4×C47C2312yes—
51C22⋊C4×C47—22no—
52C22⋊Dic47D411yescharacteristic
53C22⋊Dic47D411yescharacteristic
54#10625336—24no—
55(C2×D47)⋊C4—22no—
56(C2×D47)⋊C4—22no—
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—22no—
59C4⋊Dic47—22no—
60C4⋊Dic47D411yescharacteristic
61C4⋊Dic47D411yescharacteristic
62C4⋊Dic47C2312yes—
63Dic47⋊C4—22no—
64C4×Dic47—22no—
65C4×Dic47C2311yescharacteristic
66C4×Dic47C2311yescharacteristic
67#10625329—22no—
68C2×C47⋊C8C2311yescharacteristic
69C2×C47⋊C8C2311yescharacteristic
70D376—22no—
71C23×C47C2×D411yescharacteristic
72C22×D47—22no—
73Q8×C47—22no—
74Q8×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2411yescharacteristic
81C22⋊D47—82no—
82C2×Dic47—22no—
83C2×Dic47C2×D411yescharacteristic
84C2×Dic47C2×D411yescharacteristic
85C2×Dic47C2×D411yescharacteristic
86C2×Dic47C2×D411yescharacteristic
87D188—22no—
88D188—22no—
89C4×D47—82no—
90Dic94—82no—
91C8×C47—21no—
92C8×C47#4112yes—
93C47⋊C8—21no—
94C47⋊C8#4112yes—
95C22×C47—21no—
96C22×C47—21no—
97C22×C47—21no—
98C22×C47C22×D411yescharacteristic
99C2×D47—42no—
100C2×D47—42no—
101C2×D47—42no—
102C4×C47—21no—
103C4×C47—42no—
104C4×C47—42no—
105C4×C47C2×#4111yescharacteristic
106C4×C47C2×#4111yescharacteristic
107Dic47—21no—
108Dic47—21no—
109Dic47—21no—
110Dic47—21no—
111Dic47—42no—
112#3175—471nomaximal, Sylow
113C2×C47—41no—
114C2×C47#53211yescharacteristic
115C2×C47#57611yescharacteristic
116C2×C47#57811yescharacteristic
117D47—82no—
118#542—472no—
119#500—471no—
120#495—471no—
121#489—472no—
122#468—472no—
123#467D4711yescharacteristic, complemented
124#466—471no—
125#440—472no—
126C4×Q16—471no—
127C4×D8—471no—
128#405—471no—
129C47#317511yescharacteristic, complemented, Sylow
130C2×Q16C2×D4711yescharacteristic
131C2×SD16—472no—
132C2×D8—471no—
133C2×M16—471no—
134C22×C8C2×D4711yescharacteristic
135C4⋊Q8—472no—
136#126—942no—
137#124—472no—
138#124—942no—
139#123—942no—
140C22⋊Q8—942no—
141C22⋊Q8C2×D4712yes—
142#121—472no—
143C4×Q8—472no—
144C4×D4—472no—
145#117—471no—
146#107—471no—
147#107—472no—
148#107C2×D4711yescharacteristic
149#103—472no—
150#103C2×D4712yes—
151#102—472no—
152#102—472no—
153#97—471no—
154#97—471no—
155C4×C8—471no—
156C4×C8—471no—
157C2×Q8—942no—
158C2×Q8C22×D4712yes—
159C2×D4—472no—
160C2×D4—942no—
161C22×C4—942no—
162C22×C4C22×D4711yescharacteristic
163Q16—22no—
164SD16—944no—
165D8—942no—
166M16—942no—
167C2×C8—22no—
168C2×C8—471no—
169C2×C8—471no—
170C2×C8C22×D4711yescharacteristic
171C2×C8C22×D4711yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—471no—
174C4⋊C4—471no—
175C4⋊C4—472no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4C22×D4712yes—
179C22⋊C4—22no—
180C22⋊C4—471no—
181C22⋊C4—471no—
182C22⋊C4—942no—
183C22⋊C4—942no—
184C22⋊C4—942no—
185C22⋊C4—942no—
186C42—471no—
187C42—471no—
188C42—942no—
189C23—942no—
190C23D4×D4711yescharacteristic
191Q8—22no—
192Q8—22no—
193Q8—3762no—
194D4—942no—
195D4—942no—
196D4—3762no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—471no—
202C2×C4—471no—
203C2×C4—471no—
204C2×C4—471no—
205C2×C4—942no—
206C2×C4—3762no—
207C2×C4D4×D4711yescharacteristic
208C2×C4C23×D4711yescharacteristic
209C8—21no—
210C8—472no—
211C8—941no—
212C8#1062535212yes—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—1882no—
217C22—1882no—
218C22—1882no—
219C22C2×D4×D4711yescharacteristic
220C4—21no—
221C4—42no—
222C4—42no—
223C4—941no—
224C4—941no—
225C4—941no—
226C4—941no—
227C4—1882no—
228C4#41×D4711yescharacteristic
229C4C2×#1062535211yescharacteristic
230C2—41no—
231C2—3762no—
232C2#1568966811yescharacteristic
233C2#1568992511yescharacteristic
234C2#1568993611yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#467C2
socleC22×C47C22×D4
hypercenter#467D47
hypocenterC47#3175
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #15689746C2semidirect
2. #15689527C2semidirect
3. #15689508C2semidirect
4. #15689484C2semidirect
5. #15689371C2semidirect
7. #15689226C2semidirect
8. Q16×Dic47C2semidirect
9. #15689205C2semidirect
10. #15689078C2semidirect
11. C47×#467C2semidirect
123. #467D47semidirect
129. C47#3175semidirect