Finite Group Databasebeta

← #20251868

Subgroups — #20251868

Order 6016.

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

normal subgroups only

This group has 704 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×#13094072C211yesmaximal, characteristic
2#15689889C212yesmaximal, complemented
3#15689106C214yesmaximal, complemented
4#15689105C212yesmaximal, complemented
5C2×#13093943C211yesmaximal, characteristic, complemented
6#101×D47C214yesmaximal, complemented
7C2×#101×C47C211yesmaximal, characteristic, complemented
8#13094072—24no—
9#13094072—24no—
10C2×#10625354C412yes—
11C2×#10625354C2212yes—
12C2×#10625350C414yes—
13C2×#10625350C2211yescharacteristic
14C2×#10625350C2211yescharacteristic
15C2×Q8×D47C412yes—
16C2×Q8×D47C2212yes—
17#13094032—24no—
18#13094030—24no—
19C2×#10625329C2212yes—
20M16×D47C2218yes—
21#13093943C2214yes—
22#13093942C2214yes—
23#13093940C2214yes—
24C22×Q8×C47C2211yescharacteristic
25C2×M16×C47C2212yes—
26#101×C47C2214yes—
27C2×Q8×C47—22no—
28C2×Q8×C47—22no—
29C2×Q8×C47C2×C412yes—
30C2×Q8×C47C2312yes—
31C22×C4×C47C2×C412yes—
32C22×C4×C47C2311yescharacteristic
33C2×C22⋊D47C2×C412yes—
34C2×C22⋊D47C2×C412yes—
35#10625354—28no—
36#10625354—28no—
37Q8×D47—28no—
38Q8×D47—28no—
39#10625350—22no—
40#10625350—22no—
41#10625350—28no—
42#10625350—28no—
43#10625350D414yes—
44#10625350D414yes—
45C2×D188C2×C414yes—
46C2×D188C2×C411yescharacteristic
47C2×D188C2311yescharacteristic
48C2×C4×D47C2×C414yes—
49C2×C4×D47C2×C412yes—
50C2×C4×D47C2×C414yes—
51C2×C4×D47C2312yes—
52C2×Dic94C2×C414yes—
53C2×Dic94C2×C411yescharacteristic
54C2×Dic94C2311yescharacteristic
55M16×C47—22no—
56M16×C47C2314yes—
57C2×C8×C47—22no—
58#10625329—22no—
59#10625329C2314yes—
60C2×C47⋊C8—22no—
61#10625324—28no—
62C8×D47—28no—
63C23×C47C22×C411yescharacteristic
64C22×D47C22×C412yes—
65C22×D47C22×C412yes—
66Q8×C47—24no—
67Q8×C47—24no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47C22×C414yes—
71C2×C4×C47C22×C411yescharacteristic
72C2×C4×C47C2×D412yes—
73C2×C4×C47C2×D412yes—
74C2×C4×C47C2411yescharacteristic
75C22⋊D47—22no—
76C22⋊D47—22no—
77C22⋊D47C22⋊C414yes—
78C22⋊D47C22⋊C414yes—
79C2×Dic47C22×C412yes—
80C2×Dic47C22×C412yes—
81D188—28no—
82D188—22no—
83D188C22⋊C414yes—
84C4×D47—28no—
85C4×D47—24no—
86C4×D47—28no—
87C4×D47C2×D418yes—
88Dic94—22no—
89Dic94—28no—
90Dic94C22⋊C414yes—
91C8×C47—24no—
92C47⋊C8—24no—
93C22×C47—41no—
94C22×C47C2×C22⋊C411yescharacteristic
95C22×C47C2×C22⋊C411yescharacteristic
96C22×C47C23×C411yescharacteristic
97C2×D47—22no—
98C2×D47—42no—
99C2×D47—42no—
100C2×D47C2×C22⋊C414yes—
101C4×C47—24no—
102C4×C47C2×C22⋊C412yes—
103C4×C47C22×D412yes—
104Dic47—22no—
105Dic47C2×C22⋊C414yes—
106#2889—471nomaximal, Sylow
107C2×C47—21no—
108C2×C47—21no—
109C2×C47—21no—
110C2×C47C22×C22⋊C411yescharacteristic
111D47—24no—
112D47—42no—
113C2×2−1+4—471no—
114#568—472no—
115#413—472no—
116#413—474no—
117C2×#101—471no—
118C2×#101—474no—
119C2×#101D4711yescharacteristic, complemented
120C47#288911yescharacteristic, complemented, Sylow
1212−1+4—944no—
1222−1+4—944no—
123C2×#41—472no—
124C2×#41—472no—
125C2×#41—474no—
126C2×#41—471no—
127C2×#41—471no—
128C22×Q8—472no—
129C22×Q8—472no—
130C22×Q8C2×D4711yescharacteristic
131#131—944no—
132#131—944no—
133C2×M16—472no—
134C2×M16—478no—
135C2×M16C2×D4712yes—
136#101—474no—
137#101—474no—
138#101C2×D4714yes—
139#100—474no—
140#41—474no—
141#41—474no—
142#41—948no—
143#41—948no—
144#41—948no—
145#41—948no—
146#41—942no—
147#41—942no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—471no—
151C2×Q8—474no—
152C2×Q8—471no—
153C2×Q8—948no—
154C2×Q8—948no—
155C2×Q8C4×D4712yes—
156C2×Q8C22×D4712yes—
157C2×D4—472no—
158C2×D4—472no—
159C2×D4—471no—
160C2×D4—474no—
161C2×D4—471no—
162C22×C4—472no—
163C22×C4—474no—
164C22×C4—474no—
165C22×C4—472no—
166C22×C4C4×D4712yes—
167C22×C4C22×D4711yescharacteristic
168M16—22no—
169M16—474no—
170M16—948no—
171M16—942no—
172M16C22×D4714yes—
173C2×C8—22no—
174C2×C8—948no—
175C2×C8—942no—
176C23—472no—
177C23—472no—
178C23C2×C4×D4711yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—474no—
182Q8—948no—
183Q8—942no—
184D4—474no—
185D4—474no—
186D4—474no—
187D4—948no—
188D4—942no—
189D4—942no—
190D4—942no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—472no—
194C2×C4—478no—
195C2×C4—472no—
196C2×C4—948no—
197C2×C4—948no—
198C2×C4—944no—
199C2×C4C2×C4×D4714yes—
200C2×C4C2×C4×D4711yescharacteristic
201C2×C4D4×D4712yes—
202C2×C4D4×D4712yes—
203C2×C4C23×D4711yescharacteristic
204C8—24no—
205C8—944no—
206C22—41no—
207C22—474no—
208C22—942no—
209C22—1882no—
210C22—1882no—
211C22C22⋊C4×D4711yescharacteristic
212C22C22⋊C4×D4711yescharacteristic
213C22C22×C4×D4711yescharacteristic
214C4—24no—
215C4—474no—
216C4—942no—
217C4C22⋊C4×D4712yes—
218C4C2×D4×D4712yes—
219C2—21no—
220C2—21no—
221C2—21no—
222C2—944no—
223C2—1882no—
224C2C2×C22⋊C4×D4711yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D47
commutatorC22×C47C23×C4
FrattiniC2×C4C23×D47
FittingC2×#101×C47C2
socleC2×C47C22×C22⋊C4
hypercenterC2×#101D47
hypocenterC47#2889
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #15689889C2semidirect
3. #15689106C2semidirect
4. #15689105C2semidirect
5. C2×#13093943C2semidirect
6. #101×D47C2semidirect
7. C2×#101×C47C2semidirect
119. C2×#101D47semidirect
120. C47#2889semidirect