Finite Group Databasebeta

← #21457431

Subgroups — #21457431

Order 7808.

520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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×#14519805C212yesmaximal, complemented
2#16840408C212yesmaximal, complemented
3#16840146C211yesmaximal, characteristic, complemented
4#16840008C212yesmaximal, complemented
5#16839978C212yesmaximal, complemented
6#16839926C212yesmaximal, complemented
7#16839898C212yesmaximal, complemented
8C4×D488C211yesmaximal, characteristic, complemented
9C61×#436C211yesmaximal, characteristic, complemented
10C2×#11758222C2212yes—
11C22×D244C2212yescomplemented
12#14519805—28no—
13C2×Dic244C2211yescharacteristic, complemented
14C2×#11758190C2212yescomplemented
15C2×#11758190C2212yescomplemented
16C2×D488C2212yes—
17C2×D488C2211yescharacteristic
18C2×D488C2211yescharacteristic
19#14519765C2212yescomplemented
20#14519762—22no—
21#14519756C2212yescomplemented
22#14519751C2212yes—
23#14519750—22no—
24#14519745—22no—
25C4×D244C2212yescomplemented
26C22⋊C4×D61—22no—
27#14519711C2211yescharacteristic, complemented
28#14519702C2212yescomplemented
29#14519699C2212yescomplemented
30#14519699C2212yescomplemented
31C2×M16×C61C2212yescomplemented
32C4×D4×C61C2211yescharacteristic
33C4⋊C8×C61C2211yescharacteristic, complemented
34C22⋊C8×C61C2212yescomplemented
35C4×C8×C61C2211yescharacteristic, complemented
36C23×D61—22no—
37C2×D4×C61D411yescharacteristic
38C22×C4×C61C2312yes—
39C2×C22⋊D61—22no—
40C2×C22⋊D61—22no—
41#11758222—24no—
42#11758222—42no—
43C2×D244—24no—
44C2×D244—22no—
45C2×D244—42no—
46C2×D244C2312yes—
47C2×D244C2312yes—
48C2×C4×D61—22no—
49C2×C4×D61—22no—
50C2×Dic122C2312yes—
51M16×C61—24no—
52C2×C8×C61C2311yescharacteristic
53C2×C8×C61C2312yes—
54C2×C8×C61C2311yescharacteristic
55C4⋊C4×C61D411yescharacteristic
56C22⋊C4×C61D412yes—
57C42×C61C2311yescharacteristic
58C22⋊Dic61—22no—
59#11758198—22no—
60#11758198—22no—
61#11758198—22no—
62#11758198—22no—
63C4⋊Dic61C2312yes—
64#11758196—22no—
65Dic244—41no—
66D488—24no—
67D488—41no—
68D488D414yescomplemented
69#11758190—24no—
70#11758190—24no—
71C23×C61C2×D412yes—
72C22×D61—22no—
73C22×D61—22no—
74C22×D61—44no—
75C22×D61—44no—
76C22×D61—82no—
77D4×C61—41no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61C2×D412yes—
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2411yescharacteristic
84C22⋊D61—44no—
85C22⋊D61—82no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88D244—22no—
89D244—22no—
90D244—22no—
91D244—44no—
92D244C2×D414yes—
93C4×D61—44no—
94C4×D61—82no—
95Dic122—22no—
96Dic122—22no—
97C8×C61—22no—
98C8×C61—21no—
99C8×C61C2×D412yes—
100C22×C61—22no—
101C22×C61—22no—
102C22×C61—22no—
103C22×C61C22×D411yescharacteristic
104C2×D61—24no—
105C2×D61—42no—
106C2×D61—42no—
107C2×D61—42no—
108C2×D61—42no—
109C2×D61—42no—
110C2×D61—88no—
111C4×C61—22no—
112C4×C61—21no—
113C4×C61—21no—
114C4×C61C22×D411yescharacteristic
115C4×C61H(5,𝔽2)11yescharacteristic
116Dic61—42no—
117Dic61—42no—
118#3273—611nomaximal, Sylow
119C2×C61—42no—
120C2×C61D4211yescharacteristic
121C2×C61#57511yescharacteristic
122C2×C61#57611yescharacteristic
123D61—44no—
124D61—82no—
125C2×AGL(1,ℤ/8)—612no—
126#546—612no—
127#495—611no—
128#468—612no—
129#463—612no—
130#452—612no—
131#447—612no—
132C4×D8—611no—
133#436D6111yescharacteristic, complemented
134C61#327311yescharacteristic, complemented, Sylow
135C2×#41—612no—
136C22×D4—612no—
137AGL(1,ℤ/8)—1228no—
138C2×Q16—611no—
139C2×SD16—612no—
140C2×SD16—612no—
141C2×D8—611no—
142C2×D8—612no—
143C2×D8—611no—
144C2×M16C2×D6112yescomplemented
145#124—612no—
146#123—1222no—
147C22⋊Q8—612no—
148#121—612no—
149#121—1222no—
150#120—1222no—
151C4×D4—612no—
152C4×D4C2×D6111yescharacteristic
153C2×C22⋊C4—1222no—
154#107—611no—
155C4⋊C8C2×D6111yescharacteristic, complemented
156#103—612no—
157#102—612no—
158#102—612no—
159C22⋊C8C2×D6112yescomplemented
160C4×C8C2×D6111yescharacteristic, complemented
161C24—1222no—
162#41—1224no—
163#41—2442no—
164C2×Q8—612no—
165C2×D4—612no—
166C2×D4—612no—
167C2×D4—1224no—
168C2×D4—1222no—
169C2×D4—1222no—
170C2×D4—1222no—
171C2×D4—2442no—
172C2×D4D24411yescharacteristic
173C22×C4—1222no—
174C22×C4—1222no—
175C22×C4C22×D6112yes—
176Q16—2441no—
177SD16—1224no—
178SD16—1224no—
179D8—614no—
180D8—1224no—
181D8—2441no—
182M16—24no—
183C2×C8C22×D6111yescharacteristic
184C2×C8C22×D6112yes—
185C2×C8C22×D6111yescharacteristic
186C4⋊C4—612no—
187C4⋊C4—1222no—
188C4⋊C4D24411yescharacteristic
189C22⋊C4—1222no—
190C22⋊C4—1222no—
191C22⋊C4—1222no—
192C22⋊C4—1222no—
193C22⋊C4—1222no—
194C22⋊C4D24412yes—
195C42C22×D6111yescharacteristic
196C23—1222no—
197C23—1222no—
198C23—4882no—
199C23—2444no—
200C23—2444no—
201C23C2×D24412yes—
202Q8—1222no—
203Q8—1222no—
204D4—41no—
205D4—614no—
206D4—1222no—
207D4—1222no—
208D4—1222no—
209D4—4882no—
210D4—2444no—
211D4—2444no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—4882no—
217C2×C4—2444no—
218C2×C4C2×D24411yescharacteristic
219C2×C4C2×D24411yescharacteristic
220C2×C4C2×D24412yes—
221C2×C4C23×D6111yescharacteristic
222C8—22no—
223C8—21no—
224C8D4×D6112yes—
225C22—22no—
226C22—22no—
227C22—22no—
228C22—1224no—
229C22—4888no—
230C22—2442no—
231C22—2442no—
232C22—2442no—
233C22—2442no—
234C22—2442no—
235C22C22×D24411yescharacteristic
236C4—21no—
237C4—21no—
238C4—22no—
239C4—2442no—
240C4—2442no—
241C4C2×D4×D6111yescharacteristic
242C4#1451982311yescharacteristic
243C2—42no—
244C2—4882no—
245C2—2444no—
246C2D4×D24411yescharacteristic
247C2#1684056211yescharacteristic
248C2#1684056711yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#436C2
socleC22×C61C22×D4
hypercenter#436D61
hypocenterC61#3273
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#14519805C2semidirect
2. #16840408C2semidirect
3. #16840146C2semidirect
4. #16840008C2semidirect
5. #16839978C2semidirect
6. #16839926C2semidirect
7. #16839898C2semidirect
8. C4×D488C2semidirect
9. C61×#436C2semidirect
11. C22×D244C22semidirect
13. C2×Dic244C22semidirect
14. C2×#11758190C22semidirect
15. C2×#11758190C22semidirect
19. #14519765C22semidirect
21. #14519756C22semidirect
25. C4×D244C22semidirect
27. #14519711C22semidirect
28. #14519702C22semidirect
29. #14519699C22semidirect
30. #14519699C22semidirect
31. C2×M16×C61C22semidirect
33. C4⋊C8×C61C22semidirect
34. C22⋊C8×C61C22semidirect
35. C4×C8×C61C22semidirect
68. D488D4semidirect
133. #436D61semidirect
134. C61#3273semidirect
144. C2×M16C2×D61semidirect
155. C4⋊C8C2×D61semidirect
159. C22⋊C8C2×D61semidirect
160. C4×C8C2×D61semidirect