Finite Group Databasebeta

← #21455332

Subgroups — #21455332

Order 7808.

494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519805C211yesmaximal, characteristic
2C22×#11758190C211yesmaximal, characteristic, complemented
3#16840338C211yesmaximal, characteristic, complemented
4#16840236C211yesmaximal, characteristic, complemented
5#16839978C214yesmaximal, complemented
6#16839968C214yesmaximal, complemented
7#16839772C211yesmaximal, characteristic, complemented
8#16839759C211yesmaximal, characteristic, complemented
9C61×#424C211yesmaximal, characteristic, complemented
10C2×#11758222C2211yescharacteristic
11C22×Dic122C2211yescharacteristic
12C22×D244C2211yescharacteristic
13#14519805—24no—
14C2×#11758190—24no—
15C2×#11758190C2212yes—
16C2×#11758190C2214yes—
17C2×D488C2212yes—
18#14519777C2212yescomplemented
19#14519765C2212yescomplemented
20#14519761—22no—
21#14519757—22no—
22C4×D244C2214yes—
23#14519739—22no—
24#14519736C2211yescharacteristic
25C22⋊C4×D61—22no—
26#14519702C2212yescomplemented
27#14519702C2214yescomplemented
28#14519699C2212yescomplemented
29C2×M16×C61C2211yescharacteristic
30C22×C8×C61C2211yescharacteristic
31#117×C61C2211yescharacteristic
32C4⋊C8×C61C2214yescomplemented
33C23×D61—21no—
34C22×C4×C61C2311yescharacteristic
35C2×C22⋊D61—21no—
36C22×Dic61—21no—
37#11758222—22no—
38#11758222—22no—
39C2×D244—21no—
40C2×D244—22no—
41C2×D244D414yes—
42C2×D244C2311yescharacteristic
43C2×D244C2312yes—
44C2×C4×D61—21no—
45C2×C4×D61—24no—
46C2×Dic122—22no—
47C2×Dic122—22no—
48C2×Dic122—21no—
49C2×Dic122C2312yes—
50C2×Dic122C2311yescharacteristic
51M16×C61—22no—
52C2×C8×C61—22no—
53C2×C8×C61C2312yes—
54C2×C8×C61C2312yes—
55C4⋊C4×C61D412yes—
56C22⋊C4×C61D412yes—
57C42×C61C2312yes—
58C22⋊Dic61—21no—
59#11758198—24no—
60#11758198—24no—
61C4⋊Dic61—24no—
62C4⋊Dic61C2312yes—
63C4×Dic61—21no—
64D488—24no—
65#11758190—28no—
66#11758190—24no—
67C23×C61C2×D411yescharacteristic
68C22×D61—22no—
69C22×D61—24no—
70C22×D61—21no—
71C22×D61—82no—
72C2×C4×C61C2×D414yes—
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D412yes—
75C2×C4×C61#4112yes—
76C2×C4×C61C2411yescharacteristic
77C22⋊D61—42no—
78C2×Dic61—22no—
79C2×Dic61—21no—
80C2×Dic61—22no—
81C2×Dic61—42no—
82D244—24no—
83D244—21no—
84D244—22no—
85D244—21no—
86D244C2×D414yes—
87C4×D61—42no—
88C4×D61—84no—
89Dic122—22no—
90Dic122—21no—
91Dic122—22no—
92Dic122—21no—
93Dic122—42no—
94C8×C61—22no—
95C8×C61—22no—
96C22×C61—22no—
97C22×C61#12112yes—
98C22×C61C22×D411yescharacteristic
99C2×D61—24no—
100C2×D61—44no—
101C2×D61—41no—
102C2×D61—42no—
103C2×D61—84no—
104C4×C61—24no—
105C4×C61#12112yes—
106C4×C61C22×D411yescharacteristic
107C4×C61C2×#4111yescharacteristic
108Dic61—42no—
109Dic61—41no—
110Dic61—42no—
111#3042—611nomaximal, Sylow
112C2×C61—22no—
113C2×C61C2×#12111yescharacteristic
114C2×C61#57712yes—
115D61—44no—
116D61—81no—
117C2×AGL(1,ℤ/8)—611no—
118C22×SD16—611no—
119#536—611no—
120#518—611no—
121#463—614no—
122#461—614no—
123#424D6111yescharacteristic, complemented
124#419—611no—
125#416—611no—
126C61#304211yescharacteristic, complemented, Sylow
127C2×#41—611no—
128C22×Q8—611no—
129C22×D4—611no—
130AGL(1,ℤ/8)—1224no—
131C2×SD16—614no—
132C2×SD16—612no—
133C2×SD16—1224no—
134C2×D8—612no—
135C2×M16C2×D6111yescharacteristic
136C22×C8C2×D6111yescharacteristic
137C4⋊Q8—612no—
138#124—612no—
139#123—1222no—
140C22⋊Q8—1222no—
141C4×D4—614no—
142C4×D4—1222no—
143#117—611no—
144#117C2×D6111yescharacteristic
145C2×C22⋊C4—1222no—
146C4⋊C8C2×D6114yescomplemented
147#103—612no—
148#103—614no—
149#102—612no—
150C24—1221no—
151#41—1222no—
152#41—1222no—
153C2×Q8—612no—
154C2×Q8—611no—
155C2×Q8—1221no—
156C2×Q8—1222no—
157C2×Q8—1222no—
158C2×D4—614no—
159C2×D4—612no—
160C2×D4—611no—
161C2×D4—1221no—
162C2×D4—1221no—
163C2×D4—1222no—
164C22×C4—1221no—
165C22×C4—1224no—
166C22×C4—1221no—
167C22×C4C22×D6111yescharacteristic
168SD16—1228no—
169SD16—1224no—
170D8—1224no—
171M16—22no—
172C2×C8—22no—
173C2×C8C22×D6112yes—
174C2×C8C22×D6112yes—
175C4⋊C4—612no—
176C4⋊C4—1224no—
177C4⋊C4D24412yes—
178C22⋊C4—1221no—
179C22⋊C4—1224no—
180C22⋊C4—1224no—
181C22⋊C4D24412yes—
182C42—1221no—
183C42C22×D6112yes—
184C23—1224no—
185C23—1222no—
186C23—1221no—
187C23—4882no—
188C23C2×D24411yescharacteristic
189Q8—1222no—
190Q8—1221no—
191Q8—1222no—
192Q8—1221no—
193Q8—2442no—
194D4—614no—
195D4—1221no—
196D4—1222no—
197D4—1221no—
198D4—1224no—
199D4—2442no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—1221no—
203C2×C4—4884no—
204C2×C4—2442no—
205C2×C4—2442no—
206C2×C4C2×D24414yes—
207C2×C4C2×D24411yescharacteristic
208C2×C4D4×D6112yes—
209C2×C4#1175822612yes—
210C2×C4C23×D6111yescharacteristic
211C8—22no—
212C8—22no—
213C22—22no—
214C22—1224no—
215C22—4884no—
216C22—2441no—
217C22—2442no—
218C22—2444no—
219C22#1451975212yes—
220C22C22×D24411yescharacteristic
221C4—24no—
222C4—2441no—
223C4—2442no—
224C4—2442no—
225C4#1451975212yes—
226C4C2×D4×D6111yescharacteristic
227C4C2×#1175822611yescharacteristic
228C2—22no—
229C2—4881no—
230C2—2444no—
231C2C2×#1451975211yescharacteristic
232C2#1684057412yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#424C2
socleC22×C61C22×D4
hypercenter#424D61
hypocenterC61#3042
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
2. C22×#11758190C2semidirect
3. #16840338C2semidirect
4. #16840236C2semidirect
5. #16839978C2semidirect
6. #16839968C2semidirect
7. #16839772C2semidirect
8. #16839759C2semidirect
9. C61×#424C2semidirect
18. #14519777C22semidirect
19. #14519765C22semidirect
26. #14519702C22semidirect
27. #14519702C22semidirect
28. #14519699C22semidirect
32. C4⋊C8×C61C22semidirect
123. #424D61semidirect
126. C61#3042semidirect
146. C4⋊C8C2×D61semidirect