Finite Group Databasebeta

← #20255817

Subgroups — #20255817

Order 6016.

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

normal subgroups only

This group has 340 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#15689847C211yesmaximal, characteristic
2#15689846C211yesmaximal, characteristic
3#15689526C211yesmaximal, characteristic, complemented
4#15689467C212yesmaximal, complemented
5#15689462C212yesmaximal, complemented
6#15689409C211yesmaximal, characteristic, complemented
7#15689363C212yesmaximal, complemented
8C4×#10625337C211yesmaximal, characteristic, complemented
9#15689188C211yesmaximal, characteristic
10#15689158C212yesmaximal, complemented
11C47×#475C211yesmaximal, characteristic, complemented
12C2×#10625337C2211yescharacteristic
13C2×C8×D47C2212yes—
14#13094024C2211yescharacteristic
15#13094019—22no—
16#13094019—22no—
17#13094013—21no—
18#13094012—21no—
19#13094004C2212yes—
20#13094000C2212yes—
21Q8×Dic47—21no—
22C4×Dic94—21no—
23C4×Dic94C2211yescharacteristic
24C4×D188C2211yescharacteristic
25#13093982C2212yes—
26#13093982C2212yes—
27#13093957C2211yescharacteristic
28#13093957C2212yes—
29#13093957C2212yes—
30#13093956C2212yes—
31#13093949C2212yes—
32#13093948C2211yescharacteristic
33#13093947C2211yescharacteristic
34(C2×D47)⋊C8C2212yes—
35C4×C47⋊C8C2211yescharacteristic
36C4⋊Q8×C47C2211yescharacteristic
37C4×Q8×C47C2211yescharacteristic
38#106×C47C2212yes—
39C4⋊C8×C47C2211yescharacteristic
40#103×C47C2212yes—
41C2×Q8×C47—21no—
42C2×Q8×C47C2311yescharacteristic
43C2×D188D411yescharacteristic
44C2×C4×D47C2312yes—
45C2×Dic94—21no—
46C2×Dic94C2311yescharacteristic
47C2×C8×C47C2312yes—
48C4⋊C4×C47—21no—
49C4⋊C4×C47—21no—
50C4⋊C4×C47C2312yes—
51C4⋊C4×C47C2311yescharacteristic
52C42×C47—21no—
53C42×C47C2311yescharacteristic
54#10625337—22no—
55(C2×D47)⋊C4—22no—
56(C2×D47)⋊C4—22no—
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4D412yes—
60C4⋊Dic47—21no—
61C4⋊Dic47—22no—
62C4⋊Dic47D411yescharacteristic
63C4⋊Dic47C2311yescharacteristic
64C4⋊Dic47C2312yes—
65Dic47⋊C4—21no—
66Dic47⋊C4—22no—
67C4×Dic47—21no—
68C4×Dic47—22no—
69C4×Dic47—22no—
70C2×C47⋊C8C2311yescharacteristic
71C2×C47⋊C8C2311yescharacteristic
72C8×D47—24no—
73C22×D47C2×D412yes—
74Q8×C47—21no—
75Q8×C47—21no—
76Q8×C47—42no—
77C2×C4×C47—21no—
78C2×C4×C47—22no—
79C2×C4×C47—21no—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2411yescharacteristic
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47C2×D412yes—
87D188—22no—
88C4×D47—22no—
89C4×D47—22no—
90Dic94—21no—
91Dic94—21no—
92Dic94—42no—
93C8×C47—22no—
94C47⋊C8—21no—
95C47⋊C8#4112yes—
96C22×C47C22×D411yescharacteristic
97C2×D47—22no—
98C2×D47—22no—
99C2×D47—22no—
100C4×C47—21no—
101C4×C47—41no—
102C4×C47—42no—
103C4×C47—41no—
104C4×C47#13512yes—
105C4×C47C2×#4111yescharacteristic
106C4×C472−1+411yescharacteristic
107Dic47—22no—
108Dic47—41no—
109Dic47—42no—
110Dic47—41no—
111#3342—471nomaximal, Sylow
112C2×C47#54711yescharacteristic
113C2×C47C2×#13511yescharacteristic
114C2×C47#57811yescharacteristic
115D47—42no—
116#556—471no—
117#556—471no—
118#500—471no—
119#485—472no—
120#485—472no—
121#475—471no—
122#475D4711yescharacteristic, complemented
123#467—472no—
124C4×Q16—471no—
125C8×D4—471no—
126#427—472no—
127C47#334211yescharacteristic, complemented, Sylow
128C2×Q16—471no—
129C22×C8—472no—
130C4⋊Q8—471no—
131C4⋊Q8C2×D4711yescharacteristic
132#126—942no—
133#126—942no—
134#124—941no—
135#124—941no—
136C22⋊Q8—472no—
137C22⋊Q8—472no—
138C4×Q8—471no—
139C4×Q8—941no—
140C4×Q8—941no—
141C4×Q8C2×D4711yescharacteristic
142C4×D4—471no—
143#117—472no—
144#117—472no—
145#107—471no—
146#107—472no—
147#107—472no—
148#106—472no—
149#106C2×D4712yes—
150C4⋊C8C2×D4711yescharacteristic
151#103—471no—
152#103—472no—
153#103—471no—
154#103C2×D4712yes—
155C22⋊C8—472no—
156C4×C8—471no—
157C2×Q8—21no—
158C2×Q8—471no—
159C2×Q8—941no—
160C2×Q8C22×D4711yescharacteristic
161C2×D4—471no—
162C22×C4—472no—
163Q16—942no—
164C2×C8—471no—
165C2×C8—471no—
166C2×C8—944no—
167C2×C8C22×D4712yes—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—471no—
171C4⋊C4—471no—
172C4⋊C4—472no—
173C4⋊C4—942no—
174C4⋊C4—942no—
175C4⋊C4—941no—
176C4⋊C4—941no—
177C4⋊C4C22×D4711yescharacteristic
178C4⋊C4C22×D4712yes—
179C22⋊C4—472no—
180C22⋊C4—942no—
181C22⋊C4—942no—
182C22⋊C4—942no—
183C22⋊C4—942no—
184C42—21no—
185C42—942no—
186C42—942no—
187C42—941no—
188C42C22×D4711yescharacteristic
189C23—472no—
190Q8—21no—
191Q8—21no—
192Q8—42no—
193Q8—941no—
194Q8—941no—
195Q8—1882no—
196D4—942no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—472no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4—941no—
204C2×C4—942no—
205C2×C4—941no—
206C2×C4D4×D4711yescharacteristic
207C2×C4D4×D4711yescharacteristic
208C2×C4C23×D4711yescharacteristic
209C8—22no—
210C8—472no—
211C8—941no—
212C22—942no—
213C22—942no—
214C22—942no—
215C22C2×D4×D4711yescharacteristic
216C4—21no—
217C4—41no—
218C4—42no—
219C4—41no—
220C4—942no—
221C4—1881no—
222C4—1882no—
223C4—1881no—
224C4#1309404512yes—
225C4#41×D4711yescharacteristic
226C4#1309407211yescharacteristic
227C2—1882no—
228C2#1568977511yescharacteristic
229C2C2×#1309404511yescharacteristic
230C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#475C2
socleC22×C47C22×D4
hypercenter#475D47
hypocenterC47#3342
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. #15689526C2semidirect
4. #15689467C2semidirect
5. #15689462C2semidirect
6. #15689409C2semidirect
7. #15689363C2semidirect
8. C4×#10625337C2semidirect
10. #15689158C2semidirect
11. C47×#475C2semidirect
122. #475D47semidirect
127. C47#3342semidirect