Finite Group Databasebeta

← #20248399

Subgroups — #20248399

Order 6016.

544 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 173 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×#13094003C212yesmaximal
2#15689057C212yesmaximal, complemented
3#15689044C212yesmaximal, complemented
4#15689027C212yesmaximal, complemented
5#15689020C212yesmaximal, complemented
6#15688996C212yesmaximal
7#15688983C211yesmaximal, characteristic
8C4×C22⋊Dic47C211yesmaximal, characteristic
9C2×#95×C47C211yesmaximal, characteristic
10C22×Dic94C2212yes—
11#13094003—28no—
12C2×C4⋊Dic47C2212yes—
13C2×C4⋊Dic47C2212yes—
14C2×Dic47⋊C4C2212yes—
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×C22⋊Dic47C2212yes—
19C2×C22⋊Dic47C2211yescharacteristic
20C2×C22⋊Dic47C2211yescharacteristic
21C2×C4×Dic47C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2211yescharacteristic
24C47⋊#95C2211yescharacteristic
25C47⋊#95C2212yes—
26C47⋊#95C2212yes—
27C23×C4×C47C2212yes—
28C23×C4×C47C2211yescharacteristic
29#95×C47C2212yes—
30#95×C47C2211yescharacteristic
31#95×C47C2211yescharacteristic
32C24×C47C2311yescharacteristic
33C22×C4×C47—24no—
34C22×C4×C47—24no—
35C22×C4×C47—42no—
36C22×C4×C47—42no—
37C22×C4×C47Q814yescomplemented
38C22×C4×C47C2312yes—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×Dic47C2312yes—
43C22×Dic47C2312yes—
44C22×Dic47C2312yes—
45C22×Dic47C2312yes—
46C2×Dic94—24no—
47C2×Dic94—24no—
48C2×Dic94—42no—
49C22⋊Dic47—24no—
50C22⋊Dic47D414yes—
51C22⋊Dic47Q814yescomplemented
52C4⋊Dic47—24no—
53C4⋊Dic47—42no—
54Dic47⋊C4—24no—
55Dic47⋊C4—24no—
56Dic47⋊C4—24no—
57Dic47⋊C4—42no—
58C4×Dic47—42no—
59C23×C47—22no—
60C23×C47—22no—
61C23×C47C2×D412yes—
62C23×C47C2×Q812yes—
63C23×C47C2×Q812yes—
64C23×C47C2411yescharacteristic
65C2×C4×C47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—44no—
73C2×C4×C47—48no—
74C2×C4×C47C2×Q812yes—
75C2×C4×C47C2×Q812yes—
76C2×C4×C47#4114yes—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47C2×D414yes—
88C2×Dic47C2×Q814yes—
89Dic94—48no—
90C22×C47—22no—
91C22×C47—22no—
92C22×C47—24no—
93C22×C47—24no—
94C22×C47C4⋊Q814yes—
95C22×C47C22×D411yescharacteristic
96C22×C47C22×Q811yescharacteristic
97C22×C47C22×Q811yescharacteristic
98C22×C47C2×#4112yes—
99C22×C47H(5,𝔽2)12yes—
100C4×C47—22no—
101C4×C47—22no—
102C4×C47—24no—
103C4×C47—42no—
104Dic47—24no—
105Dic47—24no—
106Dic47—42no—
107Dic47—42no—
108#2549—471nomaximal, Sylow
109C2×C47—24no—
110C2×C47C2×C4⋊Q811yescharacteristic
111C2×C47#53311yescharacteristic
112C2×C47#54311yescharacteristic
113C2×C47#54612yes—
114C2×C47#55412yes—
115C2×C22⋊Q8—472no—
116#398—472no—
117#395—472no—
118#391—472no—
119#389—472no—
120#385—472no—
121#380—471no—
122C4×C22⋊C4—471no—
123C2×#95D4711yescharacteristic
124C47#254911yescharacteristic, complemented, Sylow
125C22×Q8—472no—
126C23×C4C2×D4712yes—
127C23×C4C2×D4711yescharacteristic
128C22⋊Q8—948no—
129C2×C4⋊C4—472no—
130C2×C4⋊C4—472no—
131C2×C4⋊C4—472no—
132C2×C4⋊C4—472no—
133C2×C4⋊C4—472no—
134C2×C4⋊C4—472no—
135C2×C22⋊C4—471no—
136C2×C22⋊C4—471no—
137C2×C22⋊C4—472no—
138C2×C42—472no—
139#95—472no—
140#95—471no—
141#95—471no—
142#95—472no—
143#95—472no—
144#95C2×D4712yes—
145#95C2×D4711yescharacteristic
146#95C2×D4711yescharacteristic
147C24C22×D4711yescharacteristic
148C2×Q8—944no—
149C2×Q8—944no—
150C2×Q8—1882no—
151C22×C4—24no—
152C22×C4—24no—
153C22×C4—42no—
154C22×C4—42no—
155C22×C4—472no—
156C22×C4—472no—
157C22×C4—472no—
158C22×C4—472no—
159C22×C4Dic9414yescomplemented
160C22×C4C22×D4712yes—
161C22×C4C22×D4711yescharacteristic
162C22×C4C22×D4711yescharacteristic
163C22×C4C22×D4712yes—
164C4⋊C4—944no—
165C4⋊C4—944no—
166C4⋊C4—944no—
167C4⋊C4—944no—
168C4⋊C4—1882no—
169C4⋊C4—1882no—
170C22⋊C4—474no—
171C22⋊C4—474no—
172C22⋊C4—944no—
173C42—1882no—
174C23—22no—
175C23—22no—
176C23C2×Dic9412yes—
177C23D4×D4712yes—
178C23Q8×D4712yes—
179C23C23×D4711yescharacteristic
180Q8—1888no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—44no—
189C2×C4—48no—
190C2×C4—474no—
191C2×C4—474no—
192C2×C4—942no—
193C2×C4—942no—
194C2×C4—942no—
195C2×C4—942no—
196C2×C4—942no—
197C2×C4—942no—
198C2×C4—942no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—942no—
202C2×C4C2×Dic9412yes—
203C2×C4C2×Dic9412yes—
204C2×C4#1062535014yes—
205C22—22no—
206C22—24no—
207C22—24no—
208C22—22no—
209C22#1309402314yes—
210C22C2×D4×D4711yescharacteristic
211C22C2×Q8×D4711yescharacteristic
212C22C22×Dic9411yescharacteristic
213C22C2×#1062535012yes—
214C22#1309406912yes—
215C4—22no—
216C4—22no—
217C4—24no—
218C4—42no—
219C4—944no—
220C4—944no—
221C4—1882no—
222C4—1882no—
223C2—24no—
224C2C2×#1309402311yescharacteristic
225C2#1568968011yescharacteristic
226C2#1568974911yescharacteristic
227C2#1568976312yes—
228C2#1568982812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#95×C47C2
hypercenterC2×#95D47
hypocenterC47#2549
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
2. #15689057C2semidirect
3. #15689044C2semidirect
4. #15689027C2semidirect
5. #15689020C2semidirect
37. C22×C4×C47Q8semidirect
51. C22⋊Dic47Q8semidirect
124. C47#2549semidirect
159. C22×C4Dic94semidirect