Finite Group Databasebeta

← #20249335

Subgroups — #20249335

Order 6016.

416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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
2C2×#13094014C211yesmaximal, characteristic
3#15689065C212yesmaximal
4#15689064C212yesmaximal
5#15689063C211yesmaximal, characteristic
6#15689062C211yesmaximal, characteristic
7#15689061C211yesmaximal, characteristic
8#15689027C212yesmaximal
9#15689027C212yesmaximal
10#15688968C211yesmaximal, characteristic
11C47×#400C211yesmaximal, characteristic
12C22×Dic94C2212yes—
13#13094023—24no—
14#13094014—24no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4⋊Dic47C2211yescharacteristic
17C2×Dic47⋊C4C2211yescharacteristic
18C2×Dic47⋊C4C2211yescharacteristic
19C2×Dic47⋊C4C2211yescharacteristic
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2212yes—
22C2×C4×Dic47C2212yes—
23C2×C4×Dic47C2211yescharacteristic
24C47⋊#95C2211yescharacteristic
25C47⋊#95C2212yes—
26C47⋊#95C2212yes—
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34#95×C47C2211yescharacteristic
35#95×C47C2212yes—
36#95×C47C2212yes—
37C22×C4×C47C2311yescharacteristic
38C22×C4×C47C2311yescharacteristic
39C22×C4×C47C2312yes—
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×Dic47C2312yes—
43C22×Dic47C2311yescharacteristic
44C22×Dic47C2311yescharacteristic
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2311yescharacteristic
48C2×Dic94—24no—
49C2×Dic94—28no—
50C4⋊C4×C47—22no—
51C4⋊C4×C47—22no—
52C4⋊Dic47—22no—
53C4⋊Dic47—22no—
54Dic47⋊C4—22no—
55Dic47⋊C4—22no—
56Dic47⋊C4—22no—
57Dic47⋊C4—22no—
58Dic47⋊C4—24no—
59C4×Dic47—24no—
60C4×Dic47D414yes—
61C23×C47C2411yescharacteristic
62C2×C4×C47—22no—
63C2×C4×C47—21no—
64C2×C4×C47—21no—
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—24no—
68C2×C4×C47—21no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—21no—
73C2×C4×C47C2×D412yes—
74C2×Dic47—21no—
75C2×Dic47—21no—
76C2×Dic47—21no—
77C2×Dic47—21no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—24no—
81C2×Dic47—22no—
82C2×Dic47—21no—
83C2×Dic47—22no—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47C2×D412yes—
87C2×Dic47C2×D412yes—
88C2×Dic47#4114yes—
89Dic94—48no—
90C22×C47C22×D411yescharacteristic
91C22×C47C2×#4112yes—
92C22×C472−1+411yescharacteristic
93C22×C472−1+412yes—
94C22×C472−1+411yescharacteristic
95C4×C47—22no—
96C4×C47—42no—
97C4×C47—41no—
98C4×C47—41no—
99C4×C47—42no—
100Dic47—22no—
101Dic47—42no—
102Dic47—41no—
103Dic47—41no—
104Dic47—42no—
105Dic47#12414yes—
106#2642—471nomaximal, Sylow
107C2×C47C2×#12411yescharacteristic
108C2×C47#53611yescharacteristic
109C2×C47#53611yescharacteristic
110C2×C47#54112yes—
111C2×C47#54112yes—
112C2×C4⋊Q8—471no—
113C2×#125—471no—
114#400—471no—
115#400—471no—
116#400—471no—
117#400—472no—
118#400—472no—
119#400D4711yescharacteristic
120#391—472no—
121#391—472no—
122#376—471no—
123C47#264211yescharacteristic, complemented, Sylow
124C22×Q8—472no—
125C4⋊Q8—944no—
126#125—944no—
127C2×C4⋊C4—471no—
128C2×C4⋊C4—471no—
129C2×C4⋊C4—471no—
130C2×C4⋊C4—471no—
131C2×C4⋊C4—471no—
132C2×C4⋊C4—472no—
133C2×C4⋊C4—471no—
134C2×C4⋊C4C2×D4711yescharacteristic
135C2×C4⋊C4C2×D4711yescharacteristic
136C2×C42—471no—
137C2×C42—472no—
138#95—472no—
139#95—471no—
140#95—472no—
141#95—472no—
142#95—472no—
143#95—472no—
144#95—472no—
145#95—472no—
146#95C2×D4711yescharacteristic
147#95C2×D4712yes—
148#95C2×D4712yes—
149C2×Q8—944no—
150C2×Q8—948no—
151C22×C4—471no—
152C22×C4—471no—
153C22×C4—472no—
154C22×C4—471no—
155C22×C4—471no—
156C22×C4—472no—
157C22×C4C22×D4712yes—
158C22×C4C22×D4711yescharacteristic
159C22×C4C22×D4711yescharacteristic
160C22×C4C22×D4712yes—
161C22×C4C22×D4711yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—942no—
165C4⋊C4—942no—
166C4⋊C4—942no—
167C4⋊C4—944no—
168C4⋊C4—942no—
169C4⋊C4—942no—
170C4⋊C4—942no—
171C42—474no—
172C42—944no—
173C23C23×D4711yescharacteristic
174Q8—1888no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—472no—
187C2×C4—474no—
188C2×C4—472no—
189C2×C4—941no—
190C2×C4—941no—
191C2×C4—941no—
192C2×C4—941no—
193C2×C4—942no—
194C2×C4—942no—
195C2×C4—944no—
196C2×C4—942no—
197C2×C4—942no—
198C2×C4—941no—
199C2×C4—942no—
200C2×C4—941no—
201C2×C4D4×D4712yes—
202C22C2×D4×D4711yescharacteristic
203C22#41×D4712yes—
204C22#1309407111yescharacteristic
205C22#1309407112yes—
206C22#1309407211yescharacteristic
207C4—22no—
208C4—42no—
209C4—42no—
210C4—41no—
211C4—41no—
212C4—474no—
213C4—942no—
214C4—1882no—
215C4—1882no—
216C4—1881no—
217C4—1881no—
218C2#124×D4711yescharacteristic
219C2#1568969511yescharacteristic
220C2#1568969611yescharacteristic
221C2#1568973012yes—
222C2#1568973212yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#400C2
hypercenter#400D47
hypocenterC47#2642
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
123. C47#2642semidirect