Finite Group Databasebeta

← #20251350

Subgroups — #20251350

Order 6016.

392 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 149 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#15689056C212yesmaximal
2#15689055C212yesmaximal
3#15689043C212yesmaximal
4#15689029C211yesmaximal, characteristic
5#15689029C211yesmaximal, characteristic
6#15689027C212yesmaximal
7#15689022C212yesmaximal
8#15689009C212yesmaximal
9C47×#389C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11C22×Dic94C2211yescharacteristic
12C2×C4⋊Dic47C2212yes—
13C2×C4⋊Dic47C2211yescharacteristic
14C2×C4⋊Dic47C2212yes—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×C4×Dic47C2212yes—
19C47⋊#95C2212yes—
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C2×C4⋊C4×C47C2212yes—
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C42×C47C2211yescharacteristic
30#95×C47C2212yes—
31C22×C4×C47C2312yes—
32C22×C4×C47C2311yescharacteristic
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2312yes—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47C2312yes—
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C2×Dic94—22no—
41C2×Dic94—41no—
42C2×Dic94—41no—
43C2×Dic94—41no—
44C2×Dic94—41no—
45C2×Dic94Q814yescomplemented
46C4⋊C4×C47—24no—
47C4⋊C4×C47—41no—
48C4⋊C4×C47Q814yescomplemented
49C42×C47—41no—
50C4⋊Dic47—42no—
51C4⋊Dic47—42no—
52C4⋊Dic47—41no—
53C4⋊Dic47—41no—
54Dic47⋊C4—42no—
55Dic47⋊C4—42no—
56C4×Dic47—42no—
57C23×C47C2411yescharacteristic
58C2×C4×C47—22no—
59C2×C4×C47—22no—
60C2×C4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47C2×Q812yes—
70C2×C4×C47C2×Q814yes—
71C2×C4×C47C2×Q812yes—
72C2×C4×C47#4112yes—
73C2×Dic47—22no—
74C2×Dic47—22no—
75C2×Dic47—22no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47C2×Q814yes—
85Dic94—44no—
86Dic94—44no—
87C22×C47C22×Q811yescharacteristic
88C22×C47C22×Q811yescharacteristic
89C22×C47C2×#4111yescharacteristic
90C22×C47H(5,𝔽2)11yescharacteristic
91C22×C47H(5,𝔽2)11yescharacteristic
92C22×C47H(5,𝔽2)11yescharacteristic
93C22×C472−1+411yescharacteristic
94C4×C47—22no—
95C4×C47—22no—
96C4×C47—22no—
97C4×C47—24no—
98C4×C47—42no—
99Dic47—24no—
100Dic47—42no—
101Dic47—42no—
102Dic47—42no—
103#2806—471nomaximal, Sylow
104C2×C47#53811yescharacteristic
105C2×C47#54311yescharacteristic
106C2×C47#54411yescharacteristic
107C2×C47#55411yescharacteristic
108C2×C47#55711yescharacteristic
109C2×C47Q8211yescharacteristic
110C2×C47#56211yescharacteristic
111#398—472no—
112#398—472no—
113#395—472no—
114#391—471no—
115#391—471no—
116#391—472no—
117#389—472no—
118#389D4711yescharacteristic
119#387—472no—
120C47#280611yescharacteristic, complemented, Sylow
121C22×Q8—471no—
122C22×Q8—471no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4—472no—
125C2×C4⋊C4—472no—
126C2×C4⋊C4—471no—
127C2×C4⋊C4—472no—
128C2×C4⋊C4—471no—
129C2×C4⋊C4C2×D4712yes—
130C2×C4⋊C4C2×D4711yescharacteristic
131C2×C4⋊C4C2×D4711yescharacteristic
132C2×C42—472no—
133C2×C42C2×D4711yescharacteristic
134#95—472no—
135#95—472no—
136#95—472no—
137#95—472no—
138#95—472no—
139#95—472no—
140#95—472no—
141#95C2×D4712yes—
142C2×Q8—474no—
143C2×Q8—942no—
144C2×Q8—1881no—
145C2×Q8—1881no—
146C2×Q8—1881no—
147C2×Q8—1881no—
148C22×C4—472no—
149C22×C4—472no—
150C22×C4—472no—
151C22×C4—472no—
152C22×C4C22×D4712yes—
153C22×C4C22×D4711yescharacteristic
154C22×C4C22×D4712yes—
155C22×C4C22×D4711yescharacteristic
156C22×C4C22×D4711yescharacteristic
157C4⋊C4—24no—
158C4⋊C4—41no—
159C4⋊C4—1882no—
160C4⋊C4—1882no—
161C4⋊C4—1882no—
162C4⋊C4—1881no—
163C4⋊C4—1881no—
164C4⋊C4—1882no—
165C4⋊C4Dic9414yescomplemented
166C42—41no—
167C42—1882no—
168C23C23×D4711yescharacteristic
169Q8—1884no—
170Q8—1884no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—474no—
183C2×C4—942no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4—942no—
187C2×C4—942no—
188C2×C4—942no—
189C2×C4—942no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—942no—
193C2×C4—942no—
194C2×C4C2×Dic9412yes—
195C2×C4C2×Dic9414yes—
196C2×C4#1062535212yes—
197C2×C4Q8×D4712yes—
198C22C2×Q8×D4711yescharacteristic
199C22C22×Dic9411yescharacteristic
200C22C2×#1062535211yescharacteristic
201C22#1309406911yescharacteristic
202C22#1309407011yescharacteristic
203C22#1309407011yescharacteristic
204C22#1309407211yescharacteristic
205C4—22no—
206C4—22no—
207C4—24no—
208C4—22no—
209C4—42no—
210C4—944no—
211C4—1882no—
212C4—1882no—
213C4—1882no—
214C2#1568971011yescharacteristic
215C2#1568974811yescharacteristic
216C2#1568975411yescharacteristic
217C2#1568983011yescharacteristic
218C2#1568984811yescharacteristic
219C2Q8×Dic9411yescharacteristic
220C2#1568987111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#389C2
hypercenter#389D47
hypocenterC47#2806
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
45. C2×Dic94Q8semidirect
48. C4⋊C4×C47Q8semidirect
120. C47#2806semidirect
165. C4⋊C4Dic94semidirect