Finite Group Databasebeta

← #21456863

Subgroups — #21456863

Order 7808.

420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840331C211yesmaximal, characteristic, complemented
2#16840149C211yesmaximal, characteristic, complemented
3#16840138C211yesmaximal, characteristic, complemented
4#16840128C211yesmaximal, characteristic, complemented
5#16840119C211yesmaximal, characteristic, complemented
6#16839977C212yesmaximal, complemented
7#16839957C212yesmaximal, complemented
8#16839905C212yesmaximal, complemented
9#16839895C212yesmaximal, complemented
10#16839823C211yesmaximal, characteristic, complemented
11C61×#540C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C2×#11758200C2212yescomplemented
15C2×#11758199C2212yes—
16C2×#11758199C2212yes—
17C2×#11758199C2212yescomplemented
18#14519774C2211yescharacteristic
19#14519774C2211yescharacteristic
20#14519765C2211yescharacteristic
21#14519765C2211yescharacteristic
22#14519752—22no—
23#14519747—22no—
24C4⋊#92418C2212yescomplemented
25#14519700C2212yescomplemented
26#14519697C2212yes—
27#14519697C2212yes—
28#14519697C2212yescomplemented
29C22⋊#92418C2212yes—
30#14519688C2211yescharacteristic, complemented
31C4×#92418C2211yescharacteristic, complemented
32#127×C61C2211yescharacteristic, complemented
33#125×C61C2211yescharacteristic, complemented
34#123×C61—22no—
35#121×C61—22no—
36#121×C61C2212yes—
37C4×D4×C61C2212yescomplemented
38#117×C61C2211yescharacteristic
39C23×D61—21no—
40C2×D4×C61—22no—
41C2×D4×C61—22no—
42C2×D4×C61C2312yes—
43C22×C4×C61—22no—
44C22×C4×C61C2311yescharacteristic
45C2×C22⋊D61—21no—
46#11758222—42no—
47C2×D244—21no—
48C2×D244—22no—
49C2×D244—22no—
50C2×D244—42no—
51C2×D244C2311yescharacteristic
52C2×D244C2311yescharacteristic
53C2×D244C2311yescharacteristic
54C2×C4×D61—21no—
55C2×Dic122C2311yescharacteristic
56C4⋊C4×C61—22no—
57C4⋊C4×C61D412yes—
58C4⋊C4×C61C2312yes—
59C22⋊C4×C61—22no—
60C22⋊C4×C61—22no—
61C22⋊C4×C61D412yes—
62C42×C61C2311yescharacteristic
63C42×C61C2311yescharacteristic
64#11758200—42no—
65#11758199—42no—
66#11758199—42no—
67#11758199—42no—
68#11758198—22no—
69#11758198—22no—
70C2×#92418C2312yes—
71C2×#92418C2312yes—
72C23×C61—22no—
73C23×C61C2×D411yescharacteristic
74C22×D61—21no—
75C22×D61—21no—
76C22×D61—21no—
77C22×D61—42no—
78C22×D61—82no—
79D4×C61—22no—
80D4×C61—22no—
81D4×C61—82no—
82D4×C61—82no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—82no—
86C2×C4×C61C2×D412yes—
87C2×C4×C61C2×D412yes—
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2411yescharacteristic
90C22⋊D61—42no—
91C2×Dic61—21no—
92D244—22no—
93D244—22no—
94D244—22no—
95D244—42no—
96D244—82no—
97D244—82no—
98C4×D61—42no—
99Dic122—22no—
100#92418—22no—
101#92418—22no—
102C22×C61—21no—
103C22×C61—22no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61—42no—
107C22×C61C22×D411yescharacteristic
108C2×D61—41no—
109C2×D61—41no—
110C2×D61—41no—
111C2×D61—42no—
112C2×D61—42no—
113C2×D61—42no—
114C2×D61—84no—
115C4×C61—21no—
116C4×C61—22no—
117C4×C61—22no—
118C4×C61—42no—
119C4×C61H(5,𝔽2)12yes—
120Dic61—41no—
121#3220—611nomaximal, Sylow
122C2×C61—41no—
123C2×C61—82no—
124C2×C61#53511yescharacteristic
125C2×C61#57612yes—
126D61—81no—
127D61—81no—
128D61—81no—
129#540D6111yescharacteristic, complemented
130#535—611no—
131#496—611no—
132#493—611no—
133#490—611no—
134#488—611no—
135#463—612no—
136#459—612no—
137#449—612no—
138#447—612no—
139#433—611no—
140C61#322011yescharacteristic, complemented, Sylow
141C2×#41—611no—
142C22×D4—611no—
143C2×SD16—612no—
144C2×D8—612no—
145C2×D8—612no—
146C2×D8—612no—
147#127—611no—
148#127—611no—
149#127C2×D6111yescharacteristic, complemented
150#125C2×D6111yescharacteristic, complemented
151#124—611no—
152#124—611no—
153#123—22no—
154#121—22no—
155#121—1222no—
156#121C2×D6112yes—
157#120—1222no—
158C4×D4C2×D6112yescomplemented
159#117C2×D6111yescharacteristic
160C4⋊C8—612no—
161#103—612no—
162#102—612no—
163#102—612no—
164#102—612no—
165C22⋊C8—612no—
166#97—611no—
167C4×C8—611no—
168C24—1221no—
169#41—2442no—
170C2×Q8—611no—
171C2×D4—22no—
172C2×D4—22no—
173C2×D4—611no—
174C2×D4—611no—
175C2×D4—611no—
176C2×D4—1221no—
177C2×D4—1222no—
178C2×D4—1222no—
179C2×D4—1221no—
180C2×D4—2442no—
181C2×D4C22×D6112yes—
182C22×C4—22no—
183C22×C4—1221no—
184C22×C4C22×D6111yescharacteristic
185SD16—2442no—
186D8—2442no—
187D8—2442no—
188D8—2442no—
189C2×C8—612no—
190C2×C8—612no—
191C4⋊C4—22no—
192C4⋊C4C22⋊D6112yes—
193C4⋊C4C22×D6112yes—
194C22⋊C4—22no—
195C22⋊C4—22no—
196C22⋊C4—1222no—
197C22⋊C4—1222no—
198C22⋊C4C22⋊D6112yes—
199C42C22×D6111yescharacteristic
200C42C22×D6111yescharacteristic
201C23—22no—
202C23—1221no—
203C23—1221no—
204C23—1221no—
205C23—4882no—
206C23—2442no—
207C23C2×C22⋊D6111yescharacteristic
208Q8—1222no—
209D4—22no—
210D4—22no—
211D4—82no—
212D4—82no—
213D4—1222no—
214D4—1222no—
215D4—1222no—
216D4—4882no—
217D4—4882no—
218D4—2442no—
219D4—2442no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—82no—
223C2×C4—1221no—
224C2×C4—2442no—
225C2×C4C2×C22⋊D6112yes—
226C2×C4C2×C22⋊D6112yes—
227C2×C4C2×C22⋊D6111yescharacteristic
228C2×C4C23×D6111yescharacteristic
229C8—1222no—
230C8—1222no—
231C22—22no—
232C22—21no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—4884no—
237C22—2442no—
238C22—2442no—
239C22—2442no—
240C22—2441no—
241C22—2441no—
242C22—2441no—
243C22C22×C22⋊D6111yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—42no—
248C4—2441no—
249C4#1451982312yes—
250C2—41no—
251C2—82no—
252C2—4881no—
253C2—4881no—
254C2—4881no—
255C2#1684032611yescharacteristic
256C2#1684056512yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#540C2
socleC22×C61C22×D4
hypercenter#540D61
hypocenterC61#3220
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #16840331C2semidirect
2. #16840149C2semidirect
3. #16840138C2semidirect
4. #16840128C2semidirect
5. #16840119C2semidirect
6. #16839977C2semidirect
7. #16839957C2semidirect
8. #16839905C2semidirect
9. #16839895C2semidirect
10. #16839823C2semidirect
11. C61×#540C2semidirect
14. C2×#11758200C22semidirect
17. C2×#11758199C22semidirect
24. C4⋊#92418C22semidirect
25. #14519700C22semidirect
28. #14519697C22semidirect
30. #14519688C22semidirect
31. C4×#92418C22semidirect
32. #127×C61C22semidirect
33. #125×C61C22semidirect
37. C4×D4×C61C22semidirect
129. #540D61semidirect
140. C61#3220semidirect
149. #127C2×D61semidirect
150. #125C2×D61semidirect
158. C4×D4C2×D61semidirect