Finite Group Databasebeta

← #21456655

Subgroups — #21456655

Order 7808.

418 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 109 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#16840272C212yesmaximal, complemented
2#16840106C212yesmaximal, complemented
3#16840085C212yesmaximal, complemented
4#16840020C211yesmaximal, characteristic, complemented
5#16840006C212yesmaximal, complemented
6#16839925C212yesmaximal, complemented
7#16839904C212yesmaximal, complemented
8#16839725C211yesmaximal, characteristic, complemented
9C61×#469C211yesmaximal, characteristic, complemented
10C2×#11758224C2212yes—
11C22×C4×D61C2211yescharacteristic
12C2×Dic244C2211yescharacteristic, complemented
13C2×#11758200C2212yescomplemented
14C2×#11758194C2211yescharacteristic
15#14519759—22no—
16#14519757C2212yes—
17#14519756C2212yes—
18#14519748C2212yes—
19#14519745—22no—
20D4×Dic61—22no—
21#14519737—22no—
22#14519735C2212yes—
23#14519710C2212yescomplemented
24#14519709C2211yescharacteristic, complemented
25#14519702C2212yescomplemented
26#14519700C2212yescomplemented
27#14519698C2212yescomplemented
28#14519689C2212yes—
29#14519689C2212yes—
30C2×D8×C61C2211yescharacteristic, complemented
31C2×M16×C61C2211yescharacteristic
32#121×C61C2212yes—
33#106×C61C2211yescharacteristic, complemented
34#102×C61C2212yescomplemented
35C23×D61D411yescharacteristic
36C2×D4×C61—22no—
37C2×D4×C61C2312yes—
38C22×C4×C61C2311yescharacteristic
39C2×C22⋊D61—22no—
40C2×C22⋊D61—22no—
41C22×Dic61—22no—
42C22×Dic61D411yescharacteristic
43#11758224—42no—
44#11758224—42no—
45C2×C4×D61—41no—
46C2×C4×D61—41no—
47C2×C4×D61D412yes—
48C2×C4×D61C2312yes—
49C2×Dic122C2312yes—
50D8×C61—41no—
51M16×C61—41no—
52C2×C8×C61C2311yescharacteristic
53C2×C8×C61C2311yescharacteristic
54C4⋊C4×C61C2312yes—
55C22⋊C4×C61—22no—
56C22⋊Dic61—22no—
57C22⋊Dic61—22no—
58#11758200—42no—
59#11758198—22no—
60#11758198—22no—
61C4⋊Dic61—22no—
62C4⋊Dic61C2312yes—
63#11758196—22no—
64C4×Dic61—22no—
65#11758194—41no—
66C2×#92418C2312yes—
67Dic244—41no—
68C23×C61—22no—
69C23×C61C2×D411yescharacteristic
70C22×D61—41no—
71C22×D61—42no—
72C22×D61C2×D412yes—
73D4×C61—22no—
74D4×C61—22no—
75D4×C61—44no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2411yescharacteristic
81C22⋊D61—44no—
82C22⋊D61—44no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—41no—
86C2×Dic61—44no—
87C2×Dic61C2×D412yes—
88C4×D61—22no—
89C4×D61—22no—
90C4×D61—42no—
91Dic122—22no—
92Dic122—22no—
93C8×C61—21no—
94C8×C61—21no—
95#92418—22no—
96C22×C61—21no—
97C22×C61—22no—
98C22×C61—42no—
99C22×C61—42no—
100C22×C61—42no—
101C22×C61C22×D411yescharacteristic
102C2×D61—22no—
103C2×D61—22no—
104C2×D61—22no—
105C2×D61—44no—
106C4×C61—21no—
107C4×C61—42no—
108C4×C61H(5,𝔽2)11yescharacteristic
109C4×C61H(5,𝔽2)11yescharacteristic
110Dic61—22no—
111Dic61—42no—
112Dic61—42no—
113#3197—611nomaximal, Sylow
114C2×C61—41no—
115C2×C61—82no—
116C2×C61#53411yescharacteristic
117C2×C61#57512yes—
118D61—42no—
119#525—612no—
120#485—612no—
121#482—612no—
122#470—611no—
123#469D6111yescharacteristic, complemented
124#468—612no—
125#452—612no—
126#449—612no—
127#407—611no—
128C61#319711yescharacteristic, complemented, Sylow
129C2×#41—612no—
130C23×C4—611no—
131C2×Q16—611no—
132C2×SD16—612no—
133C2×D8C2×D6111yescharacteristic, complemented
134C2×M16—611no—
135C2×M16C2×D6111yescharacteristic
136#123—1222no—
137C22⋊Q8—612no—
138C22⋊Q8—612no—
139#121—612no—
140#121C2×D6112yes—
141#120—1222no—
142C4×D4—1222no—
143C4×D4—1222no—
144#117—612no—
145#107—612no—
146#106—611no—
147#106C2×D6111yescharacteristic, complemented
148#103—612no—
149#103—612no—
150#102—612no—
151#102C2×D6112yescomplemented
152C22⋊C8—612no—
153C22⋊C8—612no—
154C24—611no—
155#41—2442no—
156#41—2442no—
157C2×Q8—612no—
158C2×D4—22no—
159C2×D4—1222no—
160C2×D4—1222no—
161C2×D4C22×D6112yes—
162C22×C4—611no—
163C22×C4—612no—
164C22×C4—612no—
165C22×C4—1222no—
166C22×C4—2441no—
167C22×C4—2441no—
168C22×C4C22×D6111yescharacteristic
169Q16—2441no—
170SD16—2442no—
171D8—41no—
172M16—41no—
173M16—2441no—
174C2×C8—612no—
175C2×C8C22×D6111yescharacteristic
176C2×C8C22×D6111yescharacteristic
177C4⋊C4—612no—
178C4⋊C4—1222no—
179C4⋊C4—1222no—
180C4⋊C4C22×D6112yes—
181C22⋊C4—22no—
182C22⋊C4—1222no—
183C22⋊C4—1222no—
184C22⋊C4—1222no—
185C22⋊C4—1222no—
186C42—1222no—
187C23—22no—
188C23—612no—
189C23—2441no—
190C23—2442no—
191C23D4×D6111yescharacteristic
192Q8—1222no—
193Q8—1222no—
194D4—22no—
195D4—22no—
196D4—44no—
197D4—2444no—
198D4—2444no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—612no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4—2442no—
208C2×C4—2441no—
209C2×C4—2444no—
210C2×C4D4×D6111yescharacteristic
211C2×C4C23×D6111yescharacteristic
212C8—21no—
213C8—21no—
214C8—1222no—
215C22—22no—
216C22—21no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—1222no—
221C22—1222no—
222C22—1222no—
223C22—2444no—
224C22C2×D4×D6111yescharacteristic
225C4—21no—
226C4—42no—
227C4—1222no—
228C4—2442no—
229C4—2442no—
230C4#1451982211yescharacteristic
231C4#1451982311yescharacteristic
232C2—41no—
233C2—82no—
234C2—2442no—
235C2#1684032011yescharacteristic
236C2#1684055812yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#469C2
socleC22×C61C22×D4
hypercenter#469D61
hypocenterC61#3197
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #16840272C2semidirect
2. #16840106C2semidirect
3. #16840085C2semidirect
4. #16840020C2semidirect
5. #16840006C2semidirect
6. #16839925C2semidirect
7. #16839904C2semidirect
8. #16839725C2semidirect
9. C61×#469C2semidirect
12. C2×Dic244C22semidirect
13. C2×#11758200C22semidirect
23. #14519710C22semidirect
24. #14519709C22semidirect
25. #14519702C22semidirect
26. #14519700C22semidirect
27. #14519698C22semidirect
30. C2×D8×C61C22semidirect
33. #106×C61C22semidirect
34. #102×C61C22semidirect
123. #469D61semidirect
128. C61#3197semidirect
133. C2×D8C2×D61semidirect
147. #106C2×D61semidirect
151. #102C2×D61semidirect