Finite Group Databasebeta

← #20249195

Subgroups — #20249195

Order 6016.

668 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C22×(C2×D47)⋊C4C211yesmaximal, characteristic
2#15689058C212yesmaximal, complemented
3#15689045C214yesmaximal, complemented
4#15689034C212yesmaximal, complemented
5#15688995C212yesmaximal, complemented
6#15688983C211yesmaximal, characteristic, complemented
7#15688978C212yesmaximal
8C2×C22⋊Q8×C47C211yesmaximal, characteristic, complemented
9C24×D47C2211yescharacteristic
10C23×Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2212yescomplemented
12C2×Dic47⋊C4C2214yescomplemented
13C2×C22⋊Dic47C2212yes—
14C2×(C2×D47)⋊C4—24no—
15C2×(C2×D47)⋊C4C2212yes—
16C2×(C2×D47)⋊C4C2212yes—
17C2×(C2×D47)⋊C4C2214yes—
18C2×(C2×D47)⋊C4C2214yes—
19C47⋊#95C2212yescomplemented
20C47⋊#95C2214yescomplemented
21C22×Q8×C47C2211yescharacteristic, complemented
22C23×C4×C47C2211yescharacteristic
23C22⋊Q8×C47—24no—
24C2×C4⋊C4×C47C2212yescomplemented
25C2×C4⋊C4×C47C2211yescharacteristic, complemented
26C2×C22⋊C4×C47C2212yes—
27C24×C47C2311yescharacteristic
28C23×D47—22no—
29C23×D47—22no—
30C23×D47—42no—
31C23×D47—42no—
32C23×D47Q814yescomplemented
33C23×D47C2312yes—
34C2×Q8×C47—22no—
35C2×Q8×C47—42no—
36C22×C4×C47—42no—
37C22×C4×C47D414yes—
38C22×C4×C47C2312yes—
39C22×C4×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2311yescharacteristic
42C22×Dic47—22no—
43C22×Dic47—42no—
44C22×Dic47C2314yes—
45C22×Dic47C2312yes—
46C4⋊C4×C47—22no—
47C4⋊C4×C47—24no—
48C22⋊C4×C47—24no—
49C22⋊Dic47—24no—
50(C2×D47)⋊C4—24no—
51(C2×D47)⋊C4—24no—
52(C2×D47)⋊C4—44no—
53(C2×D47)⋊C4—44no—
54C4⋊Dic47—42no—
55Dic47⋊C4—44no—
56C23×C47—22no—
57C23×C47—22no—
58C23×C47C2×D412yes—
59C23×C47C2×Q812yes—
60C23×C47#4112yes—
61C23×C47C2411yescharacteristic
62C22×D47—28no—
63C22×D47—22no—
64C22×D47—22no—
65C22×D47—24no—
66C22×D47—24no—
67C22×D47—48no—
68C22×D47—44no—
69C22×D47—44no—
70C22×D47—48no—
71C22×D47C2×Q814yes—
72Q8×C47—44no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—24no—
78C2×C4×C47—24no—
79C2×C4×C47—44no—
80C2×C4×C47C2×D412yes—
81C2×C4×C47C2×D412yes—
82C2×Dic47—22no—
83C2×Dic47—24no—
84C2×Dic47—24no—
85C2×Dic47—24no—
86C2×Dic47—24no—
87C2×Dic47—44no—
88C22×C47—22no—
89C22×C47—22no—
90C22×C47—24no—
91C22×C47—24no—
92C22×C47C22⋊Q814yes—
93C22×C47C22×D411yescharacteristic
94C22×C47C22×Q811yescharacteristic
95C22×C47C2×#4111yescharacteristic
96C22×C47H(5,𝔽2)12yes—
97C22×C47H(5,𝔽2)12yes—
98C2×D47—24no—
99C2×D47—28no—
100C2×D47—416no—
101C2×D47—42no—
102C2×D47—42no—
103C2×D47—44no—
104C4×C47—22no—
105C4×C47—22no—
106C4×C47—42no—
107C4×C47—42no—
108Dic47—42no—
109Dic47—44no—
110#2626—471nomaximal, Sylow
111C2×C47—24no—
112C2×C47C2×C22⋊Q811yescharacteristic
113C2×C47#53411yescharacteristic
114C2×C47#53511yescharacteristic
115C2×C47#53812yes—
116C2×C47#54312yes—
117D47—44no—
118C2×C22⋊Q8D4711yescharacteristic, complemented
119C22×C22⋊C4—471no—
120#399—472no—
121#396—474no—
122#393—472no—
123#385—472no—
124#380—471no—
125#379—472no—
126C47#262611yescharacteristic, complemented, Sylow
127C25—471no—
128C22×Q8C2×D4711yescharacteristic, complemented
129C23×C4—471no—
130C23×C4C2×D4711yescharacteristic
131C22⋊Q8—24no—
132C2×C4⋊C4—474no—
133C2×C4⋊C4—472no—
134C2×C4⋊C4C2×D4712yescomplemented
135C2×C4⋊C4C2×D4711yescharacteristic, complemented
136C2×C22⋊C4—472no—
137C2×C22⋊C4—472no—
138C2×C22⋊C4—472no—
139C2×C22⋊C4—474no—
140C2×C22⋊C4—474no—
141C2×C22⋊C4—944no—
142C2×C22⋊C4C2×D4712yes—
143#95—472no—
144#95—474no—
145C24—472no—
146C24—474no—
147C24—942no—
148C24—942no—
149C24—1882no—
150C24—1882no—
151C24C22×D4711yescharacteristic
152C2×Q8—22no—
153C2×Q8—42no—
154C22×C4—42no—
155C22×C4—474no—
156C22×C4—472no—
157C22×C4—942no—
158C22×C4—1882no—
159C22×C4C22⋊D4714yes—
160C22×C4C22×D4712yes—
161C22×C4C22×D4712yes—
162C22×C4C22×D4711yescharacteristic
163C22×C4C22×D4711yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—24no—
166C4⋊C4—1884no—
167C4⋊C4—1882no—
168C22⋊C4—24no—
169C22⋊C4—944no—
170C22⋊C4—944no—
171C22⋊C4—944no—
172C22⋊C4—1884no—
173C22⋊C4—1884no—
174C23—22no—
175C23—22no—
176C23—474no—
177C23—948no—
178C23—942no—
179C23—942no—
180C23—944no—
181C23—944no—
182C23—1888no—
183C23—1884no—
184C23—1884no—
185C23—1888no—
186C23Q8×D4712yes—
187C23#1062535412yes—
188C23C2×C22⋊D4712yes—
189C23C23×D4711yescharacteristic
190Q8—44no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—44no—
198C2×C4—942no—
199C2×C4—944no—
200C2×C4—944no—
201C2×C4—944no—
202C2×C4—944no—
203C2×C4—1884no—
204C2×C4C2×C22⋊D4712yes—
205C2×C4C2×C22⋊D4712yes—
206C22—24no—
207C22—22no—
208C22—22no—
209C22—24no—
210C22—948no—
211C22—944no—
212C22—18816no—
213C22—1882no—
214C22—1882no—
215C22—1884no—
216C22#1309400014yes—
217C22C22×C22⋊D4711yescharacteristic
218C22C2×Q8×D4711yescharacteristic
219C22C2×#1062535411yescharacteristic
220C22#1309406912yes—
221C22#1309407012yes—
222C4—22no—
223C4—22no—
224C4—42no—
225C4—42no—
226C4—1882no—
227C4—1884no—
228C2—24no—
229C2—1884no—
230C2C2×#1309400011yescharacteristic
231C2#1568968211yescharacteristic
232C2#1568968711yescharacteristic
233C2#1568971312yes—
234C2#1568974812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C22⋊Q8×C47C2
hypercenterC2×C22⋊Q8D47
hypocenterC47#2626
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #15689058C2semidirect
3. #15689045C2semidirect
4. #15689034C2semidirect
5. #15688995C2semidirect
6. #15688983C2semidirect
8. C2×C22⋊Q8×C47C2semidirect
11. C2×C4⋊Dic47C22semidirect
12. C2×Dic47⋊C4C22semidirect
19. C47⋊#95C22semidirect
20. C47⋊#95C22semidirect
21. C22×Q8×C47C22semidirect
24. C2×C4⋊C4×C47C22semidirect
25. C2×C4⋊C4×C47C22semidirect
32. C23×D47Q8semidirect
118. C2×C22⋊Q8D47semidirect
126. C47#2626semidirect
128. C22×Q8C2×D47semidirect
134. C2×C4⋊C4C2×D47semidirect
135. C2×C4⋊C4C2×D47semidirect