Finite Group Databasebeta

← #20246476

Subgroups — #20246476

Order 6016.

496 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 209 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×#13094022C211yesmaximal, characteristic
2#15689030C211yesmaximal, characteristic
3#15689027C212yesmaximal
4#15689020C212yesmaximal
5#15689018C212yesmaximal
6C4×Dic47⋊C4C212yesmaximal
7#15688974C212yesmaximal
8#15688974C212yesmaximal
9C47×#391C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11#13094022C418yescomplemented
12C2×C4⋊Dic47C2211yescharacteristic
13C2×Dic47⋊C4C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×C4×Dic47C2212yes—
19C2×C4×Dic47C2212yes—
20C2×C4×Dic47C2211yescharacteristic
21C2×C4×Dic47C2212yes—
22C2×C4×Dic47C2211yescharacteristic
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C47⋊#95C2212yes—
27C22×Q8×C47C2211yescharacteristic
28C2×C4⋊C4×C47C2211yescharacteristic
29C2×C42×C47C2211yescharacteristic
30#95×C47C2212yes—
31#95×C47C2212yes—
32C2×Q8×C47—41no—
33C2×Q8×C47—41no—
34C2×Q8×C47C2×C414yes—
35C22×C4×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C22×C4×C47C2311yescharacteristic
39C22×C4×C47C2312yes—
40C22×Dic47C2312yes—
41C22×Dic47C2312yes—
42C22×Dic47C2312yes—
43C22×Dic47C2312yes—
44C2×Dic94—41no—
45C2×Dic94—41no—
46C2×Dic94C2×C414yes—
47C4⋊C4×C47—41no—
48C42×C47—41no—
49C4⋊Dic47—41no—
50Dic47⋊C4—24no—
51Dic47⋊C4—42no—
52Dic47⋊C4C2×C418yes—
53Dic47⋊C4C2×C418yes—
54Dic47⋊C4Q818yescomplemented
55C4×Dic47—24no—
56C4×Dic47—24no—
57C4×Dic47—41no—
58C4×Dic47—42no—
59C4×Dic47C2×C414yes—
60C23×C47C2411yescharacteristic
61Q8×C47—44no—
62C2×C4×C47—22no—
63C2×C4×C47—22no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47C22×C412yes—
74C2×C4×C47C22×C412yes—
75C2×C4×C47C22×C412yes—
76C2×C4×C47C2×Q814yes—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47C22×C414yes—
85C2×Dic47C22×C414yes—
86C2×Dic47C2×Q814yes—
87C2×Dic47C2×Q814yes—
88C2×Dic47#4114yes—
89Dic94—44no—
90C22×C47C23×C411yescharacteristic
91C22×C47C22×Q812yes—
92C22×C47C2×#4112yes—
93C22×C47H(5,𝔽2)11yescharacteristic
94C22×C47H(5,𝔽2)11yescharacteristic
95C4×C47—22no—
96C4×C47—22no—
97C4×C47—22no—
98C4×C47—24no—
99C4×C47—42no—
100Dic47—24no—
101Dic47—24no—
102Dic47—42no—
103Dic47C4×Q818yes—
104#2369—471nomaximal, Sylow
105C2×C47C2×C4×Q812yes—
106C2×C47#51811yescharacteristic
107C2×C47#55412yes—
108C2×C47#55511yescharacteristic
109C2×C47Q8211yescharacteristic
110C2×C4⋊Q8—471no—
111#391—471no—
112#391—472no—
113#391D4711yescharacteristic
114#389—472no—
115#389—472no—
116C4×C4⋊C4—472no—
117C4×C4⋊C4—472no—
118C4×C4⋊C4—472no—
119C47#236911yescharacteristic, complemented, Sylow
120C22×Q8—471no—
121C22×Q8C2×D4711yescharacteristic
122C4⋊Q8—478no—
123C2×C4⋊C4—472no—
124C2×C4⋊C4—472no—
125C2×C4⋊C4—472no—
126C2×C4⋊C4—472no—
127C2×C4⋊C4—472no—
128C2×C4⋊C4—471no—
129C2×C4⋊C4C2×D4711yescharacteristic
130C2×C42—471no—
131C2×C42—472no—
132C2×C42—472no—
133C2×C42—471no—
134C2×C42—472no—
135C2×C42C2×D4711yescharacteristic
136#95—472no—
137#95—472no—
138#95—472no—
139#95—472no—
140#95C2×D4712yes—
141#95C2×D4712yes—
142C2×Q8—41no—
143C2×Q8—41no—
144C2×Q8—474no—
145C2×Q8—1881no—
146C2×Q8—1881no—
147C2×Q8C4×D4714yes—
148C22×C4—472no—
149C22×C4—472no—
150C22×C4—472no—
151C22×C4—472no—
152C22×C4C22×D4712yes—
153C22×C4C22×D4711yescharacteristic
154C22×C4C22×D4711yescharacteristic
155C22×C4C22×D4711yescharacteristic
156C22×C4C22×D4712yes—
157C4⋊C4—41no—
158C4⋊C4—478no—
159C4⋊C4—478no—
160C4⋊C4—478no—
161C4⋊C4—944no—
162C4⋊C4—1882no—
163C4⋊C4—1881no—
164C42—41no—
165C42—474no—
166C42—944no—
167C42—944no—
168C42—1882no—
169C42—1881no—
170C23C23×D4711yescharacteristic
171Q8—44no—
172Q8—1884no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—474no—
185C2×C4—474no—
186C2×C4—474no—
187C2×C4—474no—
188C2×C4—474no—
189C2×C4—942no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—942no—
193C2×C4—942no—
194C2×C4—942no—
195C2×C4—942no—
196C2×C4C2×C4×D4712yes—
197C2×C4C2×C4×D4712yes—
198C2×C4C2×C4×D4712yes—
199C2×C4Q8×D4714yes—
200C22C22×C4×D4711yescharacteristic
201C22C2×Q8×D4712yes—
202C22#41×D4712yes—
203C22#1309406911yescharacteristic
204C22#1309406911yescharacteristic
205C4—24no—
206C4—22no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—478no—
211C4—944no—
212C4—944no—
213C4—1882no—
214C2C4×Q8×D4712yes—
215C2#1568959611yescharacteristic
216C2#1568982712yes—
217C2#1568983511yescharacteristic
218C2#1568985311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutatorC22×C47C23×C4
FittingC47×#391C2
socleC23×C47C24
hypercenter#391D47
hypocenterC47#2369
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
11. #13094022C4semidirect
54. Dic47⋊C4Q8semidirect
119. C47#2369semidirect