Finite Group Databasebeta

← #21456679

Subgroups — #21456679

Order 7808.

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

normal subgroups only

This group has 442 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#16840328C212yesmaximal, complemented
2#16840089C212yesmaximal, complemented
3#16840084C212yesmaximal, complemented
4#16840013C212yesmaximal, complemented
5#16839998C211yesmaximal, characteristic, complemented
6#16839897C212yesmaximal, complemented
7#16839894C212yesmaximal, complemented
8#16839728C211yesmaximal, characteristic, complemented
9C61×#466C211yesmaximal, characteristic, complemented
10C2×#11758222C2211yescharacteristic
11C2×D4×D61C2212yescomplemented
12C2×D488C2211yescharacteristic
13C2×#11758199C2212yes—
14C2×#11758194C2211yescharacteristic, complemented
15#14519773—22no—
16#14519763—22no—
17#14519752C2212yes—
18#14519751C2212yescomplemented
19#14519748C2212yes—
20#14519747—22no—
21#14519745—22no—
22#14519735C2212yescomplemented
23#14519711C2211yescharacteristic, complemented
24#14519708C2212yescomplemented
25#14519699C2212yescomplemented
26#14519698C2212yescomplemented
27#14519697C2212yescomplemented
28#14519689C2212yescomplemented
29#14519689C2212yescomplemented
30C2×D8×C61C2211yescharacteristic
31C22×C8×C61C2211yescharacteristic, complemented
32#121×C61C2212yescomplemented
33#107×C61C2211yescharacteristic, complemented
34#102×C61C2212yescomplemented
35C23×D61—22no—
36C2×D4×C61—22no—
37C2×D4×C61C2312yes—
38C22×C4×C61C2311yescharacteristic
39C2×C22⋊D61—22no—
40C2×C22⋊D61—22no—
41C2×C22⋊D61—22no—
42C2×C22⋊D61D412yes—
43D4×D61—42no—
44D4×D61—42no—
45#11758222—41no—
46#11758222—41no—
47C2×D244—22no—
48C2×D244D411yescharacteristic
49C2×D244C2312yes—
50C2×C4×D61C2312yes—
51C2×Dic122D411yescharacteristic
52D8×C61—41no—
53C2×C8×C61—41no—
54C2×C8×C61C2311yescharacteristic
55C2×C8×C61C2311yescharacteristic
56C4⋊C4×C61C2312yes—
57C22⋊C4×C61—22no—
58C22⋊Dic61—22no—
59#11758199—42no—
60#11758198—22no—
61#11758198—22no—
62#11758198—22no—
63C4⋊Dic61C2312yes—
64C4×Dic61—22no—
65#11758194—41no—
66C2×#92418C2312yes—
67D488—41no—
68C23×C61—22no—
69C23×C61C2×D411yescharacteristic
70C22×D61—22no—
71C22×D61—44no—
72C22×D61—82no—
73C22×D61—82no—
74C22×D61C2×D412yes—
75D4×C61—22no—
76D4×C61—22no—
77D4×C61—82no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2411yescharacteristic
83C22⋊D61—42no—
84C22⋊D61—44no—
85C22⋊D61—82no—
86C22⋊D61—82no—
87C2×Dic61—22no—
88C2×Dic61C2×D412yes—
89D244—22no—
90D244—22no—
91D244—41no—
92D244—82no—
93C4×D61—22no—
94C4×D61—22no—
95Dic122—41no—
96C8×C61—21no—
97C8×C61—21no—
98#92418—22no—
99C22×C61—21no—
100C22×C61—21no—
101C22×C61—21no—
102C22×C61—42no—
103C22×C61—42no—
104C22×C61—42no—
105C22×C61C22×D411yescharacteristic
106C2×D61—22no—
107C2×D61—22no—
108C2×D61—22no—
109C2×D61—42no—
110C2×D61—42no—
111C2×D61—42no—
112C2×D61—88no—
113C4×C61—21no—
114C4×C61—42no—
115C4×C61H(5,𝔽2)11yescharacteristic
116C4×C61H(5,𝔽2)11yescharacteristic
117Dic61—22no—
118Dic61—42no—
119#3199—611nomaximal, Sylow
120C2×C61—41no—
121C2×C61—82no—
122C2×C61#53411yescharacteristic
123C2×C61#57611yescharacteristic
124C2×C61#57611yescharacteristic
125D61—42no—
126D61—82no—
127#535—612no—
128#482—612no—
129#482—612no—
130#469—612no—
131#466—611no—
132#466D6111yescharacteristic, complemented
133#447—612no—
134#447—612no—
135#408—611no—
136C61#319911yescharacteristic, complemented, Sylow
137C2×#41—611no—
138C22×D4—612no—
139C2×D8—612no—
140C2×D8—611no—
141C2×D8C2×D6111yescharacteristic
142C2×M16—611no—
143C22×C8C2×D6111yescharacteristic, complemented
144#127—1222no—
145#124—1222no—
146#121—612no—
147#121—612no—
148#121—612no—
149#121C2×D6112yescomplemented
150#120—1222no—
151#120—1222no—
152#117—612no—
153#107—611no—
154#107C2×D6111yescharacteristic, complemented
155#106—612no—
156#102—612no—
157#102—612no—
158#102—612no—
159#102C2×D6112yescomplemented
160C22⋊C8—612no—
161C22⋊C8—612no—
162C24—1222no—
163#41—2441no—
164#41—2441no—
165C2×Q8—611no—
166C2×D4—22no—
167C2×D4—612no—
168C2×D4—611no—
169C2×D4—612no—
170C2×D4—1222no—
171C2×D4—1222no—
172C2×D4—1222no—
173C2×D4—1222no—
174C2×D4—2442no—
175C2×D4—2442no—
176C2×D4C22×D6112yes—
177C22×C4—612no—
178C22×C4C22×D6111yescharacteristic
179D8—41no—
180D8—2441no—
181D8—2442no—
182M16—2441no—
183C2×C8—41no—
184C2×C8—612no—
185C2×C8C22×D6111yescharacteristic
186C2×C8C22×D6111yescharacteristic
187C4⋊C4—612no—
188C4⋊C4C22×D6112yes—
189C22⋊C4—22no—
190C22⋊C4—1222no—
191C22⋊C4—1222no—
192C22⋊C4—1222no—
193C22⋊C4—1222no—
194C42—1222no—
195C23—22no—
196C23—612no—
197C23—1222no—
198C23—4882no—
199C23—4882no—
200C23—2444no—
201C23D4×D6111yescharacteristic
202Q8—2441no—
203D4—22no—
204D4—22no—
205D4—82no—
206D4—1222no—
207D4—1222no—
208D4—4882no—
209D4—4882no—
210D4—4882no—
211D4—2441no—
212D4—2442no—
213D4—2444no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—612no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4D4×D6111yescharacteristic
222C2×C4C23×D6111yescharacteristic
223C8—21no—
224C8—21no—
225C8—1222no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—42no—
230C22—42no—
231C22—42no—
232C22—1222no—
233C22—1222no—
234C22—1222no—
235C22—4888no—
236C22—2442no—
237C22—2442no—
238C22—2442no—
239C22C2×D4×D6111yescharacteristic
240C4—21no—
241C4—42no—
242C4—1222no—
243C4—2442no—
244C4#1451982211yescharacteristic
245C4#1451982311yescharacteristic
246C2—41no—
247C2—82no—
248C2—4882no—
249C2—2442no—
250C2#1684032011yescharacteristic
251C2#1684056311yescharacteristic
252C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#466C2
socleC22×C61C22×D4
hypercenter#466D61
hypocenterC61#3199
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #16840328C2semidirect
2. #16840089C2semidirect
3. #16840084C2semidirect
4. #16840013C2semidirect
5. #16839998C2semidirect
6. #16839897C2semidirect
7. #16839894C2semidirect
8. #16839728C2semidirect
9. C61×#466C2semidirect
11. C2×D4×D61C22semidirect
14. C2×#11758194C22semidirect
18. #14519751C22semidirect
22. #14519735C22semidirect
23. #14519711C22semidirect
24. #14519708C22semidirect
25. #14519699C22semidirect
26. #14519698C22semidirect
27. #14519697C22semidirect
28. #14519689C22semidirect
29. #14519689C22semidirect
31. C22×C8×C61C22semidirect
32. #121×C61C22semidirect
33. #107×C61C22semidirect
34. #102×C61C22semidirect
132. #466D61semidirect
136. C61#3199semidirect
143. C22×C8C2×D61semidirect
149. #121C2×D61semidirect
154. #107C2×D61semidirect
159. #102C2×D61semidirect