Finite Group Databasebeta

← #20247865

Subgroups — #20247865

Order 6016.

544 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 169 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
1C2×#13094000C211yesmaximal, characteristic
2C2×C4⋊C4×D47C211yesmaximal, characteristic
3#15689057C214yesmaximal, complemented
4#15689030C211yesmaximal, characteristic, complemented
5#15688997C214yesmaximal
6#15688993C211yesmaximal, characteristic, complemented
7#15688992C211yesmaximal, characteristic, complemented
8C4×(C2×D47)⋊C4C211yesmaximal, characteristic
9C47×#391C211yesmaximal, characteristic, complemented
10C22×C4×D47C2211yescharacteristic
11C22×C4×D47C2212yes—
12#13094000—24no—
13C2×C4⋊Dic47C2211yescharacteristic
14C2×C4⋊Dic47C2211yescharacteristic
15C2×C4⋊Dic47C2214yes—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×Dic47⋊C4C2214yes—
19C4⋊C4×D47—24no—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×C4×Dic47C2211yescharacteristic
23C47⋊#95C2212yes—
24C47⋊#95C2214yes—
25C22×Q8×C47C2211yescharacteristic
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×C42×C47C2211yescharacteristic
28#95×C47C2214yes—
29C23×D47C2311yescharacteristic
30C2×Q8×C47—22no—
31C2×Q8×C47—22no—
32C2×Q8×C47—22no—
33C22×C4×C47C2312yes—
34C22×C4×C47C2312yes—
35C22×C4×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2311yescharacteristic
40C22×Dic47C2312yes—
41C2×C4×D47—22no—
42C2×C4×D47—22no—
43C2×C4×D47—24no—
44C2×C4×D47—44no—
45C2×C4×D47D414yes—
46C4⋊C4×C47—22no—
47C42×C47—22no—
48(C2×D47)⋊C4—24no—
49(C2×D47)⋊C4Q818yescomplemented
50C4⋊Dic47—22no—
51C4⋊Dic47—22no—
52C4⋊Dic47—44no—
53Dic47⋊C4—24no—
54Dic47⋊C4—24no—
55Dic47⋊C4—44no—
56C4×Dic47—22no—
57C23×C47C2411yescharacteristic
58C22×D47—21no—
59C22×D47—21no—
60C22×D47—22no—
61C22×D47C2×D412yes—
62C22×D47C2×Q814yes—
63Q8×C47—44no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—24no—
71C2×C4×C47C2×D412yes—
72C2×C4×C47C2×Q814yes—
73C2×C4×C47#4112yes—
74C2×C4×C47#4112yes—
75C2×Dic47—22no—
76C2×Dic47—21no—
77C2×Dic47—21no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—24no—
82C2×Dic47—24no—
83C2×Dic47C2×D412yes—
84C2×Dic47C2×Q814yes—
85C4×D47—28no—
86C4×D47—48no—
87C22×C47C22×D411yescharacteristic
88C22×C47C22×Q812yes—
89C22×C47C2×#4111yescharacteristic
90C22×C47C2×#4111yescharacteristic
91C22×C47H(5,𝔽2)12yes—
92C2×D47—22no—
93C2×D47—22no—
94C2×D47—24no—
95C2×D47—24no—
96C2×D47C4⋊Q814yes—
97C4×C47—24no—
98C4×C47—42no—
99C4×C47—42no—
100C4×C47#12314yes—
101Dic47—22no—
102Dic47—24no—
103Dic47—42no—
104Dic47—42no—
105#2502—471nomaximal, Sylow
106C2×C47C2×#12311yescharacteristic
107C2×C47C2×C4⋊Q811yescharacteristic
108C2×C47#53511yescharacteristic
109C2×C47#55412yes—
110C2×C47#55412yes—
111D47—24no—
112C2×C22⋊Q8—471no—
113C22×C4⋊C4—471no—
114#398—474no—
115#391—471no—
116#391D4711yescharacteristic, complemented
117#385—474no—
118#384—471no—
119#384—471no—
120C4×C22⋊C4—471no—
121C47#250211yescharacteristic, complemented, Sylow
122C22×Q8C2×D4711yescharacteristic
123C23×C4—471no—
124C23×C4—472no—
125C22⋊Q8—944no—
126C2×C4⋊C4—472no—
127C2×C4⋊C4—471no—
128C2×C4⋊C4—472no—
129C2×C4⋊C4—471no—
130C2×C4⋊C4—474no—
131C2×C4⋊C4—474no—
132C2×C4⋊C4—944no—
133C2×C4⋊C4C2×D4711yescharacteristic
134C2×C22⋊C4—472no—
135C2×C22⋊C4—472no—
136C2×C42—471no—
137C2×C42C2×D4711yescharacteristic
138#95—472no—
139#95—474no—
140#95C2×D4714yes—
141C24—471no—
142C2×Q8—22no—
143C2×Q8—22no—
144C2×Q8—22no—
145C22×C4—472no—
146C22×C4—471no—
147C22×C4—474no—
148C22×C4—472no—
149C22×C4—472no—
150C22×C4—944no—
151C22×C4—942no—
152C22×C4—942no—
153C22×C4—1884no—
154C22×C4C22×D4712yes—
155C22×C4C22×D4712yes—
156C22×C4C22×D4712yes—
157C22×C4C22×D4711yescharacteristic
158C4⋊C4—22no—
159C4⋊C4—944no—
160C4⋊C4—944no—
161C4⋊C4—942no—
162C4⋊C4—942no—
163C4⋊C4—1884no—
164C4⋊C4—1884no—
165C22⋊C4—478no—
166C22⋊C4—944no—
167C42—22no—
168C42—942no—
169C23—472no—
170C23—474no—
171C23—941no—
172C23—941no—
173C23—942no—
174C23C23×D4711yescharacteristic
175Q8—44no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—472no—
184C2×C4—474no—
185C2×C4—941no—
186C2×C4—942no—
187C2×C4—941no—
188C2×C4—942no—
189C2×C4—948no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—944no—
193C2×C4—944no—
194C2×C4—1888no—
195C2×C4#1062535012yes—
196C2×C4D4×D4712yes—
197C2×C4#1062535212yes—
198C2×C4Q8×D4714yes—
199C22—474no—
200C22—944no—
201C22—944no—
202C22—942no—
203C22—942no—
204C22C2×D4×D4711yescharacteristic
205C22C2×Q8×D4712yes—
206C22C2×#1062535211yescharacteristic
207C22C2×#1062535011yescharacteristic
208C22#1309407012yes—
209C4—24no—
210C4—42no—
211C4—42no—
212C4—944no—
213C4—942no—
214C4—1882no—
215C4—1882no—
216C4#1309400614yes—
217C2—944no—
218C2C2×#1309400611yescharacteristic
219C2C4⋊Q8×D4711yescharacteristic
220C2#1568969111yescharacteristic
221C2#1568983112yes—
222C2#1568983312yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#391C2
hypercenter#391D47
hypocenterC47#2502
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
3. #15689057C2semidirect
4. #15689030C2semidirect
6. #15688993C2semidirect
7. #15688992C2semidirect
9. C47×#391C2semidirect
49. (C2×D47)⋊C4Q8semidirect
116. #391D47semidirect
121. C47#2502semidirect