Finite Group Databasebeta

← #21456808

Subgroups — #21456808

Order 7808.

444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#16840312C211yesmaximal, characteristic, complemented
2C2×#14519765C211yesmaximal, characteristic, complemented
3#16840151C212yesmaximal, complemented
4#16840122C212yesmaximal, complemented
5#16839978C214yesmaximal, complemented
6#16839903C212yesmaximal, complemented
7#16839898C212yesmaximal, complemented
8C61×#432C211yesmaximal, characteristic, complemented
9C2×#11758222—21no—
10C22×Dic122C2211yescharacteristic
11C22×D244C2211yescharacteristic
12C2×#11758190C2214yescomplemented
13C2×D488C2214yes—
14#14519777C2211yescharacteristic, complemented
15#14519774C2211yescharacteristic, complemented
16#14519765—21no—
17#14519765—21no—
18#14519765—21no—
19#14519765C2212yes—
20#14519765C2212yes—
21#14519751—21no—
22#14519751C2212yes—
23C4×D244—21no—
24C4×D244C2212yescomplemented
25C2×#11758198—21no—
26C2×#11758198—21no—
27#14519702C2214yescomplemented
28#14519699C2214yes—
29C2×C42×C61C2211yescharacteristic
30C4⋊C8×C61C2212yescomplemented
31C22⋊C8×C61C2212yes—
32#97×C61C2212yescomplemented
33C23×D61—21no—
34C22×C4×C61D411yescharacteristic
35C22×C4×C61D411yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C2×C22⋊D61—22no—
38C22×Dic61—21no—
39#11758222—44no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244—21no—
43C2×D244—42no—
44C2×D244C2312yes—
45C2×D244C2312yes—
46C2×C4×D61—22no—
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122—42no—
50C2×Dic122C2312yes—
51C2×C8×C61C2314yes—
52C42×C61D411yescharacteristic
53C42×C61D411yescharacteristic
54C42×C61C2311yescharacteristic
55C42×C61C2311yescharacteristic
56#11758198—22no—
57#11758198—22no—
58#11758198—22no—
59#11758198—22no—
60#11758198—22no—
61#11758198—22no—
62C4⋊Dic61—21no—
63C4⋊Dic61C2312yes—
64D488—44no—
65#11758190—44no—
66C23×C61C2×D411yescharacteristic
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—42no—
70C22×D61—42no—
71C22×D61—42no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—41no—
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2411yescharacteristic
81C22⋊D61—44no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—42no—
85D244—24no—
86D244—24no—
87D244—42no—
88D244—42no—
89D244—42no—
90C4×D61—44no—
91Dic122—24no—
92Dic122—42no—
93Dic122—42no—
94C8×C61—24no—
95C22×C61—21no—
96C22×C61—21no—
97C22×C61AGL(1,ℤ/8)12yes—
98C22×C61C22×D411yescharacteristic
99C2×D61—42no—
100C2×D61—42no—
101C2×D61—42no—
102C2×D61—42no—
103C2×D61—42no—
104C2×D61—42no—
105C2×D61—84no—
106C4×C61—21no—
107C4×C61—21no—
108C4×C61—21no—
109C4×C61—21no—
110C4×C61—21no—
111C4×C61H(5,𝔽2)12yes—
112Dic61—42no—
113Dic61—42no—
114#3213—611nomaximal, Sylow
115C2×C61—22no—
116C2×C61#53511yescharacteristic
117C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
118C2×C61#57511yescharacteristic
119D61—82no—
120D61—82no—
121#532—611no—
122C2×#124—611no—
123#496—612no—
124#489—612no—
125#463—614no—
126#448—612no—
127#447—612no—
128#432D6111yescharacteristic, complemented
129C61#321311yescharacteristic, complemented, Sylow
130C2×#41—1221no—
131C22×Q8—611no—
132C22×D4—611no—
133C2×SD16—614no—
134C2×D8—614no—
135C4⋊Q8—611no—
136#127—611no—
137#124—612no—
138#124—612no—
139#124—1221no—
140#124—1221no—
141#124—1221no—
142#121—612no—
143#121—1221no—
144C4×D4—612no—
145C4×D4—1221no—
146C2×C22⋊C4—1221no—
147C2×C22⋊C4—1221no—
148C2×C42C2×D6111yescharacteristic
149C4⋊C8C2×D6112yescomplemented
150#103—614no—
151#102—614no—
152C22⋊C8C2×D6112yes—
153#97C2×D6112yescomplemented
154C24—1221no—
155#41—2444no—
156C2×Q8—612no—
157C2×Q8—1221no—
158C2×Q8—1221no—
159C2×Q8—2442no—
160C2×D4—612no—
161C2×D4—612no—
162C2×D4—1222no—
163C2×D4—1221no—
164C2×D4—1221no—
165C2×D4—1221no—
166C2×D4—2442no—
167C22×C4—1221no—
168C22×C4—1222no—
169C22×C4D24411yescharacteristic
170C22×C4D24411yescharacteristic
171C22×C4C22×D6111yescharacteristic
172SD16—2444no—
173D8—2444no—
174C2×C8C22×D6114yes—
175C4⋊C4—612no—
176C4⋊C4—1221no—
177C22⋊C4—1222no—
178C22⋊C4—1222no—
179C22⋊C4—1222no—
180C22⋊C4—1222no—
181C22⋊C4—1222no—
182C22⋊C4—1222no—
183C42D24411yescharacteristic
184C42D24411yescharacteristic
185C42C22×D6111yescharacteristic
186C42C22×D6111yescharacteristic
187C23—1222no—
188C23—1222no—
189C23—2442no—
190C23—2442no—
191C23—2442no—
192C23C2×D24411yescharacteristic
193Q8—1224no—
194Q8—2442no—
195Q8—2442no—
196D4—1224no—
197D4—1224no—
198D4—2442no—
199D4—2442no—
200D4—2442no—
201D4—2444no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4—2444no—
208C2×C4—2442no—
209C2×C4C2×D24411yescharacteristic
210C2×C4C2×D24411yescharacteristic
211C2×C4C2×D24411yescharacteristic
212C2×C4C2×D24411yescharacteristic
213C2×C4C2×D24411yescharacteristic
214C2×C4C23×D6111yescharacteristic
215C8—24no—
216C22—21no—
217C22—21no—
218C22—4884no—
219C22—2442no—
220C22—2442no—
221C22—2442no—
222C22—2442no—
223C22—2442no—
224C22—2442no—
225C22#1451980512yes—
226C22C22×D24411yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—21no—
232C4—2442no—
233C4—2442no—
234C4#1451982312yes—
235C2—22no—
236C2—4882no—
237C2—4882no—
238C2#1684033111yescharacteristic
239C2C2×#1451980511yescharacteristic
240C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#432C2
socleC22×C61C22×D4
hypercenter#432D61
hypocenterC61#3213
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #16840312C2semidirect
2. C2×#14519765C2semidirect
3. #16840151C2semidirect
4. #16840122C2semidirect
5. #16839978C2semidirect
6. #16839903C2semidirect
7. #16839898C2semidirect
8. C61×#432C2semidirect
12. C2×#11758190C22semidirect
14. #14519777C22semidirect
15. #14519774C22semidirect
24. C4×D244C22semidirect
27. #14519702C22semidirect
30. C4⋊C8×C61C22semidirect
32. #97×C61C22semidirect
128. #432D61semidirect
129. C61#3213semidirect
149. C4⋊C8C2×D61semidirect
153. #97C2×D61semidirect