Finite Group Databasebeta

← #21456871

Subgroups — #21456871

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#16840367C211yesmaximal, characteristic, complemented
2#16840331C211yesmaximal, characteristic, complemented
3#16840151C211yesmaximal, characteristic, complemented
4#16840139C211yesmaximal, characteristic, complemented
5#16840127C211yesmaximal, characteristic, complemented
6#16840117C211yesmaximal, characteristic, complemented
7#16839978C212yesmaximal, complemented
8#16839958C212yesmaximal, complemented
9#16839909C212yesmaximal, complemented
10#16839898C212yesmaximal, complemented
11C61×#433C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C2×#11758190C2212yescomplemented
15C2×D488C2212yes—
16C2×D488C2212yes—
17C2×D488C2212yescomplemented
18#14519774C2211yescharacteristic
19#14519774C2211yescharacteristic
20#14519774C2211yescharacteristic, complemented
21#14519769C2211yescharacteristic, complemented
22#14519765C2211yescharacteristic
23#14519765C2211yescharacteristic
24#14519762—22no—
25#14519752—22no—
26#14519751C2212yes—
27#14519750—22no—
28#14519747—22no—
29C4×D244C2212yescomplemented
30#14519702C2212yescomplemented
31#14519699C2212yes—
32#14519699C2212yes—
33#14519699C2212yescomplemented
34#117×C61C2211yescharacteristic
35C4⋊C8×C61C2212yescomplemented
36C22⋊C8×C61C2212yes—
37#97×C61C2211yescharacteristic, complemented
38C4×C8×C61C2211yescharacteristic, complemented
39C23×D61—21no—
40C22×C4×C61C2311yescharacteristic
41C2×C22⋊D61—21no—
42C2×C22⋊D61—22no—
43#11758222—42no—
44C2×D244—21no—
45C2×D244—22no—
46C2×D244—22no—
47C2×D244—22no—
48C2×D244—42no—
49C2×D244C2311yescharacteristic
50C2×D244C2311yescharacteristic
51C2×D244C2311yescharacteristic
52C2×D244C2312yes—
53C2×C4×D61—21no—
54C2×C4×D61—22no—
55C2×Dic122C2311yescharacteristic
56C2×C8×C61C2312yes—
57C2×C8×C61C2312yes—
58C4⋊C4×C61D412yes—
59C22⋊C4×C61D412yes—
60C42×C61C2311yescharacteristic
61C42×C61C2311yescharacteristic
62#11758198—22no—
63#11758198—22no—
64#11758198—22no—
65#11758198—22no—
66C4⋊Dic61C2312yes—
67#11758196—22no—
68D488—42no—
69D488—42no—
70D488—42no—
71#11758190—42no—
72C23×C61C2×D411yescharacteristic
73C22×D61—22no—
74C22×D61—21no—
75C22×D61—21no—
76C22×D61—21no—
77C22×D61—42no—
78C22×D61—82no—
79C2×C4×C61—22no—
80C2×C4×C61C2×D412yes—
81C2×C4×C61C2×D412yes—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2411yescharacteristic
84C22⋊D61—42no—
85C22⋊D61—82no—
86C2×Dic61—22no—
87C2×Dic61—21no—
88D244—22no—
89D244—22no—
90D244—22no—
91D244—22no—
92D244—22no—
93D244—42no—
94D244—82no—
95D244—82no—
96D244—82no—
97C4×D61—42no—
98C4×D61—82no—
99Dic122—22no—
100C8×C61—22no—
101C8×C61—22no—
102C22×C61—21no—
103C22×C61—22no—
104C22×C61C22×D411yescharacteristic
105C2×D61—41no—
106C2×D61—41no—
107C2×D61—41no—
108C2×D61—42no—
109C2×D61—42no—
110C2×D61—42no—
111C2×D61—42no—
112C2×D61—42no—
113C2×D61—42no—
114C2×D61—84no—
115C4×C61—21no—
116C4×C61—22no—
117C4×C61—22no—
118C4×C61H(5,𝔽2)12yes—
119Dic61—41no—
120Dic61—42no—
121#3220—611nomaximal, Sylow
122C2×C61—41no—
123C2×C61#53511yescharacteristic
124C2×C61#57612yes—
125D61—81no—
126D61—82no—
127D61—81no—
128D61—81no—
129#540—611no—
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#433D6111yescharacteristic, complemented
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#127—611no—
150#125—611no—
151#124—611no—
152#124—611no—
153#123—1222no—
154#121—612no—
155#121—1222no—
156#121—1222no—
157#120—1222no—
158C4×D4—612no—
159#117C2×D6111yescharacteristic
160C4⋊C8C2×D6112yescomplemented
161#103—612no—
162#102—612no—
163#102—612no—
164#102—612no—
165C22⋊C8C2×D6112yes—
166#97C2×D6111yescharacteristic, complemented
167C4×C8C2×D6111yescharacteristic, complemented
168C24—1221no—
169#41—2442no—
170C2×Q8—611no—
171C2×D4—611no—
172C2×D4—611no—
173C2×D4—611no—
174C2×D4—612no—
175C2×D4—1222no—
176C2×D4—1221no—
177C2×D4—1222no—
178C2×D4—1222no—
179C2×D4—1222no—
180C2×D4—1221no—
181C2×D4—2442no—
182C22×C4—1222no—
183C22×C4—1221no—
184C22×C4C22×D6111yescharacteristic
185SD16—2442no—
186D8—2442no—
187D8—2442no—
188D8—2442no—
189C2×C8C22×D6112yes—
190C2×C8C22×D6112yes—
191C4⋊C4—612no—
192C4⋊C4—1222no—
193C4⋊C4D24412yes—
194C22⋊C4—1222no—
195C22⋊C4—1222no—
196C22⋊C4—1222no—
197C22⋊C4—1222no—
198C22⋊C4D24412yes—
199C42C22×D6111yescharacteristic
200C42C22×D6111yescharacteristic
201C23—1222no—
202C23—1221no—
203C23—1221no—
204C23—1221no—
205C23—4882no—
206C23—2442no—
207C23C2×D24411yescharacteristic
208Q8—1222no—
209D4—1222no—
210D4—1222no—
211D4—1222no—
212D4—1222no—
213D4—1222no—
214D4—4882no—
215D4—4882no—
216D4—4882no—
217D4—4882no—
218D4—2442no—
219D4—2442no—
220C2×C4—22no—
221C2×C4—1221no—
222C2×C4—1222no—
223C2×C4—4882no—
224C2×C4—2442no—
225C2×C4C2×D24412yes—
226C2×C4C2×D24412yes—
227C2×C4C2×D24411yescharacteristic
228C2×C4C23×D6111yescharacteristic
229C8—22no—
230C8—22no—
231C22—22no—
232C22—21no—
233C22—4884no—
234C22—2442no—
235C22—2442no—
236C22—2442no—
237C22—2442no—
238C22—2442no—
239C22—2441no—
240C22—2441no—
241C22—2441no—
242C22—2442no—
243C22C22×D24411yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—2442no—
248C4—2441no—
249C4#1451982312yes—
250C2—41no—
251C2—4881no—
252C2—4881no—
253C2—4882no—
254C2—4881no—
255C2#1684033111yescharacteristic
256C2#1684056712yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#433C2
socleC22×C61C22×D4
hypercenter#433D61
hypocenterC61#3220
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #16840367C2semidirect
2. #16840331C2semidirect
3. #16840151C2semidirect
4. #16840139C2semidirect
5. #16840127C2semidirect
6. #16840117C2semidirect
7. #16839978C2semidirect
8. #16839958C2semidirect
9. #16839909C2semidirect
10. #16839898C2semidirect
11. C61×#433C2semidirect
14. C2×#11758190C22semidirect
17. C2×D488C22semidirect
20. #14519774C22semidirect
21. #14519769C22semidirect
29. C4×D244C22semidirect
30. #14519702C22semidirect
33. #14519699C22semidirect
35. C4⋊C8×C61C22semidirect
37. #97×C61C22semidirect
38. C4×C8×C61C22semidirect
139. #433D61semidirect
140. C61#3220semidirect
160. C4⋊C8C2×D61semidirect
166. #97C2×D61semidirect
167. C4×C8C2×D61semidirect