Finite Group Databasebeta

← #20248340

Subgroups — #20248340

Order 6016.

676 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 177 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×#13094023C211yesmaximal, characteristic, complemented
2C2×#13094002C214yesmaximal, complemented
3C2×#13093986C211yesmaximal, characteristic
4#15689058C214yesmaximal, complemented
5#15689025C211yesmaximal, characteristic
6#15689024C211yesmaximal, characteristic
7#15688992C211yesmaximal, characteristic, complemented
8C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
9C47×#384C211yesmaximal, characteristic, complemented
10C22×Dic94C2212yes—
11C22×D188C2211yescharacteristic
12C22×C4×D47C2212yes—
13#13094023—24no—
14#13094002—216no—
15#13093986—24no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2214yes—
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2214yes—
21C2×(C2×D47)⋊C4C2214yes—
22C2×(C2×D47)⋊C4C2212yes—
23C2×C4×Dic47C2211yescharacteristic
24C2×C4×Dic47C2211yescharacteristic
25C47⋊#95C2212yes—
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2214yes—
29C2×C42×C47C2211yescharacteristic
30C23×D47C2312yes—
31C22×C4×C47C2312yes—
32C22×C4×C47C2312yes—
33C22×C4×C47C2312yes—
34C22×C4×C47C2311yescharacteristic
35C22×Dic47C2312yes—
36C22×Dic47C2311yescharacteristic
37C22×Dic47C2312yes—
38C22×Dic47C2311yescharacteristic
39C2×D188—22no—
40C2×D188—22no—
41C2×D188Q814yescomplemented
42C2×C4×D47—24no—
43C2×C4×D47—28no—
44C2×Dic94—28no—
45C2×Dic94—24no—
46C4⋊C4×C47—22no—
47C4⋊C4×C47—28no—
48C4⋊C4×C47—22no—
49C42×C47—22no—
50(C2×D47)⋊C4—28no—
51(C2×D47)⋊C4—24no—
52(C2×D47)⋊C4—28no—
53C4⋊Dic47—22no—
54Dic47⋊C4—28no—
55Dic47⋊C4—24no—
56Dic47⋊C4D418yescomplemented
57C4×Dic47—22no—
58C4×Dic47D414yes—
59C23×C47C2411yescharacteristic
60C22×D47—24no—
61C22×D47—22no—
62C22×D47—22no—
63C22×D47—24no—
64C22×D47C2×Q814yes—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—24no—
69C2×C4×C47—24no—
70C2×C4×C47—22no—
71C2×C4×C47C2×D414yes—
72C2×C4×C47C2×D412yes—
73C2×C4×C47C2×Q812yes—
74C2×C4×C47#4112yes—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—24no—
80C2×Dic47C2×D412yes—
81C2×Dic47C2×D414yes—
82C2×Dic47C2×D412yes—
83C2×Dic47C2×D414yes—
84D188—28no—
85C4×D47—48no—
86Dic94—48no—
87C22×C47C22×D411yescharacteristic
88C22×C47C22×D412yes—
89C22×C47C22×Q811yescharacteristic
90C22×C47C2×#4111yescharacteristic
91C22×C472−1+412yes—
92C2×D47—24no—
93C2×D47—28no—
94C2×D47—42no—
95C2×D47—42no—
96C2×D47—44no—
97C4×C47—24no—
98C4×C47—42no—
99C4×C47—42no—
100C4×C47C22⋊Q814yescomplemented
101Dic47—22no—
102Dic47—24no—
103Dic47—42no—
104Dic47#12714yes—
105#2542—471nomaximal, Sylow
106C2×C47C2×C22⋊Q811yescharacteristic
107C2×C47C2×#12711yescharacteristic
108C2×C47#53611yescharacteristic
109C2×C47#54712yes—
110C2×C47D4×Q812yes—
111D47—44no—
112C2×C4⋊Q8—471no—
113C2×C22⋊Q8—474no—
114C2×C4×D4—471no—
115#399—474no—
116#390—471no—
117#390—471no—
118#384—471no—
119#384D4711yescharacteristic, complemented
120C4×C4⋊C4—471no—
121C47#254211yescharacteristic, complemented, Sylow
122C22×Q8—472no—
123C22×D4—471no—
124C23×C4—472no—
125C4⋊Q8—944no—
126C22⋊Q8—9416no—
127C4×D4—944no—
128C2×C4⋊C4—472no—
129C2×C4⋊C4—474no—
130C2×C4⋊C4—472no—
131C2×C4⋊C4—471no—
132C2×C4⋊C4C2×D4711yescharacteristic
133C2×C4⋊C4C2×D4714yes—
134C2×C4⋊C4C2×D4711yescharacteristic
135C2×C22⋊C4—472no—
136C2×C22⋊C4—474no—
137C2×C22⋊C4—474no—
138C2×C42—471no—
139C2×C42—471no—
140C2×C42C2×D4711yescharacteristic
141#95—472no—
142C24—472no—
143C2×Q8—948no—
144C2×Q8—944no—
145C2×D4—474no—
146C2×D4—942no—
147C2×D4—942no—
148C22×C4—471no—
149C22×C4—471no—
150C22×C4—472no—
151C22×C4—472no—
152C22×C4—944no—
153C22×C4—948no—
154C22×C4C22×D4712yes—
155C22×C4C22×D4712yes—
156C22×C4C22×D4712yes—
157C22×C4C22×D4711yescharacteristic
158C4⋊C4—22no—
159C4⋊C4—28no—
160C4⋊C4—22no—
161C4⋊C4—478no—
162C4⋊C4—948no—
163C4⋊C4—944no—
164C4⋊C4—942no—
165C22⋊C4—944no—
166C22⋊C4—948no—
167C22⋊C4—948no—
168C42—22no—
169C42—474no—
170C42—942no—
171C23—474no—
172C23—944no—
173C23—942no—
174C23—942no—
175C23—944no—
176C23C23×D4711yescharacteristic
177Q8—1888no—
178D4—948no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—24no—
184C2×C4—22no—
185C2×C4—472no—
186C2×C4—474no—
187C2×C4—472no—
188C2×C4—474no—
189C2×C4—942no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—944no—
193C2×C4—942no—
194C2×C4—1888no—
195C2×C4#1062535012yes—
196C2×C4D4×D4714yes—
197C2×C4D4×D4712yes—
198C2×C4Q8×D4712yes—
199C22—948no—
200C22—944no—
201C22—1884no—
202C22—1882no—
203C22—1882no—
204C22C2×D4×D4712yes—
205C22C2×D4×D4711yescharacteristic
206C22C2×Q8×D4711yescharacteristic
207C22C2×#1062535011yescharacteristic
208C22#1309407212yes—
209C4—24no—
210C4—42no—
211C4—42no—
212C4—474no—
213C4—944no—
214C4—942no—
215C4—1882no—
216C4#1309400214yescomplemented
217C2—1884no—
218C2C2×#1309400211yescharacteristic
219C2#127×D4711yescharacteristic
220C2#1568969811yescharacteristic
221C2#1568977412yes—
222C2#1568978812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#384C2
hypercenter#384D47
hypocenterC47#2542
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
1. C2×#13094023C2semidirect
2. C2×#13094002C2semidirect
4. #15689058C2semidirect
7. #15688992C2semidirect
8. C4×Dic47⋊C4C2semidirect
9. C47×#384C2semidirect
41. C2×D188Q8semidirect
56. Dic47⋊C4D4semidirect
100. C4×C47C22⋊Q8semidirect
119. #384D47semidirect
121. C47#2542semidirect
216. C4#13094002semidirect