Finite Group Databasebeta

← #21455458

Subgroups — #21455458

Order 7808.

492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11758190C211yesmaximal, characteristic, complemented
2#16840333C211yesmaximal, characteristic, complemented
3#16840326C211yesmaximal, characteristic
4#16840008C214yesmaximal, complemented
5#16839991C214yesmaximal, complemented
6#16839800C211yesmaximal, characteristic, complemented
7#16839772C211yesmaximal, characteristic, complemented
8#16839768C211yesmaximal, characteristic, complemented
9C2×#131×C61C211yesmaximal, characteristic, complemented
10C22×Dic122C2211yescharacteristic
11C22×D244C2211yescharacteristic
12C2×#11758190—24no—
13C2×#11758190C2212yes—
14C2×#11758190C2212yes—
15#14519775—21no—
16#14519773—21no—
17#14519766—21no—
18#14519764—21no—
19#14519758—22no—
20#14519756C2214yescomplemented
21#14519751C2214yes—
22#14519745—22no—
23#14519736C2211yescharacteristic
24#14519736C2211yescharacteristic
25#14519711C2212yescomplemented
26#14519709C2212yescomplemented
27#14519702C2214yescomplemented
28#14519699C2214yes—
29C2×#41×C61C2211yescharacteristic
30#131×C61—24no—
31C2×M16×C61C2211yescharacteristic
32C2×M16×C61C2212yescomplemented
33C22×C8×C61C2211yescharacteristic
34C22×C8×C61C2212yescomplemented
35C23×D61—21no—
36#41×C61—22no—
37#41×C61—22no—
38C2×Q8×C61D411yescharacteristic
39C2×D4×C61D412yes—
40C2×D4×C61D411yescharacteristic
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C2×C22⋊D61—24no—
44C22×Dic61—21no—
45C2×D244—22no—
46C2×D244—22no—
47C2×D244—21no—
48C2×D244C2312yes—
49C2×Dic122—22no—
50C2×Dic122—22no—
51C2×Dic122—21no—
52C2×Dic122C2312yes—
53M16×C61—22no—
54M16×C61—24no—
55C2×C8×C61—24no—
56C2×C8×C61D414yescomplemented
57C2×C8×C61C2312yes—
58C2×C8×C61C2311yescharacteristic
59C2×C8×C61C2311yescharacteristic
60C22⋊Dic61—21no—
61C22⋊Dic61—21no—
62C22⋊Dic61—24no—
63#11758198—24no—
64C4⋊Dic61C2312yes—
65C4⋊Dic61C2312yes—
66#11758196—24no—
67C4×Dic61—21no—
68C4×Dic61—21no—
69#11758190—24no—
70#11758190—24no—
71C23×C61C2×D412yes—
72C23×C61C2×D411yescharacteristic
73C22×D61—22no—
74C22×D61—42no—
75C22×D61—82no—
76Q8×C61—22no—
77D4×C61—24no—
78D4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61C2×D412yes—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D412yes—
84C2×C4×C61#4112yes—
85C2×C4×C61C2411yescharacteristic
86C22⋊D61—84no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—42no—
91D244—22no—
92D244—22no—
93D244—42no—
94Dic122—22no—
95Dic122—22no—
96Dic122—42no—
97C8×C61—22no—
98C8×C61C2×D412yes—
99C8×C61C2×D412yes—
100C22×C61—22no—
101C22×C61—22no—
102C22×C61—24no—
103C22×C61#12112yes—
104C22×C61C22×D411yescharacteristic
105C2×D61—42no—
106C2×D61—44no—
107C2×D61—84no—
108C4×C61—22no—
109C4×C61#12112yes—
110C4×C61C22×D411yescharacteristic
111C4×C61C2×#4111yescharacteristic
112Dic61—42no—
113Dic61—42no—
114Dic61—42no—
115#3057—611nomaximal, Sylow
116C2×C61—22no—
117C2×C61—42no—
118C2×C61C2×#12111yescharacteristic
119C2×C61#57712yes—
120D61—82no—
121C22×SD16—611no—
122C2×#131D6111yescharacteristic, complemented
123#536—611no—
124#535—611no—
125#468—614no—
126#465—614no—
127#427—611no—
128#419—611no—
129#418—611no—
130C61#305711yescharacteristic, complemented, Sylow
131C2×#41C2×D6111yescharacteristic
132C22×Q8—611no—
133C22×D4—611no—
134C2×SD16—612no—
135C2×SD16—612no—
136C2×SD16—1224no—
137#131—24no—
138C2×M16C2×D6111yescharacteristic
139C2×M16C2×D6112yescomplemented
140C22×C8C2×D6111yescharacteristic
141C22×C8C2×D6112yescomplemented
142C4⋊Q8—1221no—
143#127—1221no—
144#124—1221no—
145#124—1221no—
146#123—1222no—
147C22⋊Q8—614no—
148#121—614no—
149#120—1222no—
150#117—611no—
151#117—611no—
152#107—612no—
153#106—612no—
154#103—614no—
155#102—614no—
156C24—1221no—
157#41—22no—
158#41—22no—
159C2×Q8—612no—
160C2×Q8—1221no—
161C2×Q8—1222no—
162C2×Q8—1222no—
163C2×Q8D24411yescharacteristic
164C2×D4—612no—
165C2×D4—1224no—
166C2×D4—1221no—
167C2×D4—1222no—
168C2×D4—1222no—
169C2×D4D24412yes—
170C2×D4D24411yescharacteristic
171C22×C4—1221no—
172C22×C4C22×D6112yes—
173C22×C4C22×D6111yescharacteristic
174SD16—1224no—
175SD16—1224no—
176M16—22no—
177M16—24no—
178C2×C8—24no—
179C2×C8C22⋊D6114yescomplemented
180C2×C8C22×D6112yes—
181C2×C8C22×D6111yescharacteristic
182C2×C8C22×D6111yescharacteristic
183C4⋊C4—612no—
184C4⋊C4—612no—
185C4⋊C4—1224no—
186C22⋊C4—1221no—
187C22⋊C4—1221no—
188C22⋊C4—1224no—
189C22⋊C4—1224no—
190C42—1221no—
191C42—1221no—
192C23—1222no—
193C23—4882no—
194C23—2442no—
195C23C2×D24412yes—
196C23C2×D24411yescharacteristic
197Q8—22no—
198Q8—1222no—
199Q8—1222no—
200Q8—2442no—
201D4—24no—
202D4—22no—
203D4—1222no—
204D4—1222no—
205D4—4884no—
206D4—2442no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—1222no—
210C2×C4—1222no—
211C2×C4—1222no—
212C2×C4—2442no—
213C2×C4C2×D24412yes—
214C2×C4C2×D24411yescharacteristic
215C2×C4#1175822212yes—
216C2×C4C2×C22⋊D6112yes—
217C2×C4C23×D6111yescharacteristic
218C8—22no—
219C8C2×C22⋊D6112yes—
220C8C2×C22⋊D6112yes—
221C22—22no—
222C22—22no—
223C22—24no—
224C22—4884no—
225C22—2442no—
226C22—2444no—
227C22#1451975112yes—
228C22C22×D24411yescharacteristic
229C4—22no—
230C4—2442no—
231C4—2442no—
232C4—2442no—
233C4#1451975112yes—
234C4C22×C22⋊D6111yescharacteristic
235C4C2×#1175822211yescharacteristic
236C2—22no—
237C2—42no—
238C2—4882no—
239C2C2×#1451975111yescharacteristic
240C2#1684057412yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#131×C61C2
socleC22×C61C22×D4
hypercenterC2×#131D61
hypocenterC61#3057
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. C22×#11758190C2semidirect
2. #16840333C2semidirect
4. #16840008C2semidirect
5. #16839991C2semidirect
6. #16839800C2semidirect
7. #16839772C2semidirect
8. #16839768C2semidirect
9. C2×#131×C61C2semidirect
20. #14519756C22semidirect
25. #14519711C22semidirect
26. #14519709C22semidirect
27. #14519702C22semidirect
32. C2×M16×C61C22semidirect
34. C22×C8×C61C22semidirect
56. C2×C8×C61D4semidirect
122. C2×#131D61semidirect
130. C61#3057semidirect
139. C2×M16C2×D61semidirect
141. C22×C8C2×D61semidirect
179. C2×C8C22⋊D61semidirect