Finite Group Databasebeta

← #21456661

Subgroups — #21456661

Order 7808.

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

normal subgroups only

This group has 418 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#16840273C212yesmaximal, complemented
2#16840104C212yesmaximal, complemented
3#16840087C212yesmaximal, complemented
4#16840020C211yesmaximal, characteristic, complemented
5#16840015C211yesmaximal, characteristic, complemented
6#16840008C212yesmaximal, complemented
7#16839926C212yesmaximal, complemented
8#16839909C212yesmaximal, complemented
9C61×#407C211yesmaximal, characteristic, complemented
10C2×#11758222C2212yes—
11C2×Dic244C2211yescharacteristic, complemented
12C2×#11758190C2212yescomplemented
13C2×D488C2211yescharacteristic, complemented
14#14519760—22no—
15#14519756C2212yes—
16#14519756C2212yes—
17#14519751C2212yes—
18#14519751C2212yes—
19#14519746—22no—
20C4×C22⋊D61—22no—
21C4×C22⋊D61—22no—
22#14519736C2212yes—
23#14519711C2212yescomplemented
24#14519709C2211yescharacteristic, complemented
25#14519709C2211yescharacteristic, complemented
26#14519702C2212yescomplemented
27#14519702C2212yescomplemented
28#14519699C2212yescomplemented
29#14519699C2212yescomplemented
30C23×C4×C61C2211yescharacteristic
31C2×M16×C61C2211yescharacteristic
32C2×M16×C61C2211yescharacteristic
33C22⋊C8×C61C2212yes—
34C22⋊C8×C61C2212yes—
35C24×C61D411yescharacteristic
36C22×C4×C61—41no—
37C22×C4×C61—41no—
38C22×C4×C61D411yescharacteristic
39C22×C4×C61D412yes—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C2×C22⋊D61—22no—
43C2×C22⋊D61—22no—
44C2×C22⋊D61—22no—
45#11758222—42no—
46#11758222—42no—
47C2×D244C2312yes—
48C2×C4×D61—22no—
49C2×Dic122C2312yes—
50M16×C61—41no—
51M16×C61—41no—
52C2×C8×C61C2311yescharacteristic
53C2×C8×C61C2312yes—
54C2×C8×C61C2311yescharacteristic
55C22⋊Dic61—22no—
56C22⋊Dic61—22no—
57C22⋊Dic61—22no—
58#11758198—22no—
59#11758198—22no—
60C4⋊Dic61C2312yes—
61C4⋊Dic61C2312yes—
62#11758196—22no—
63#11758196—22no—
64C4×Dic61—22no—
65Dic244—41no—
66D488—41no—
67#11758190—42no—
68C23×C61—41no—
69C23×C61—42no—
70C23×C61C2×D412yes—
71C23×C61C2×D411yescharacteristic
72C22×D61—22no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—41no—
78C2×C4×C61—42no—
79C2×C4×C61C2×D412yes—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2411yescharacteristic
82C22⋊D61—44no—
83C22⋊D61—44no—
84C22⋊D61—44no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88D244—22no—
89D244—22no—
90C4×D61—44no—
91Dic122—22no—
92Dic122—22no—
93C8×C61—22no—
94C8×C61—21no—
95C8×C61—21no—
96C22×C61—22no—
97C22×C61—21no—
98C22×C61—22no—
99C22×C61—22no—
100C22×C61—22no—
101C22×C61—44no—
102C22×C61C22×D411yescharacteristic
103C2×D61—42no—
104C2×D61—42no—
105C2×D61—42no—
106C4×C61—22no—
107C4×C61—21no—
108C4×C61H(5,𝔽2)11yescharacteristic
109C4×C61H(5,𝔽2)11yescharacteristic
110Dic61—42no—
111Dic61—42no—
112Dic61—42no—
113#3197—611nomaximal, Sylow
114C2×C61—42no—
115C2×C61—41no—
116C2×C61#53411yescharacteristic
117C2×C61#57512yes—
118D61—82no—
119#525—612no—
120#485—612no—
121#482—612no—
122#470—611no—
123#469—611no—
124#468—612no—
125#452—612no—
126#449—612no—
127#407D6111yescharacteristic, complemented
128C61#319711yescharacteristic, complemented, Sylow
129C2×#41—612no—
130C23×C4C2×D6111yescharacteristic
131C2×Q16—611no—
132C2×SD16—612no—
133C2×D8—611no—
134C2×M16C2×D6111yescharacteristic
135C2×M16C2×D6111yescharacteristic
136#123—1222no—
137C22⋊Q8—612no—
138C22⋊Q8—612no—
139#121—612no—
140#121—612no—
141#120—1222no—
142C4×D4—1222no—
143C4×D4—1222no—
144#117—612no—
145#107—612no—
146#106—611no—
147#106—611no—
148#103—612no—
149#103—612no—
150#102—612no—
151#102—612no—
152C22⋊C8C2×D6112yes—
153C22⋊C8C2×D6112yes—
154C24D24411yescharacteristic
155#41—2442no—
156#41—2442no—
157C2×Q8—612no—
158C2×D4—612no—
159C2×D4—1222no—
160C2×D4—1222no—
161C2×D4—1222no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—1222no—
165C22×C4D24411yescharacteristic
166C22×C4D24412yes—
167C22×C4C22×D6112yes—
168C22×C4C22×D6111yescharacteristic
169Q16—2441no—
170SD16—2442no—
171D8—2441no—
172M16—41no—
173M16—41no—
174C2×C8C22×D6111yescharacteristic
175C2×C8C22×D6112yes—
176C2×C8C22×D6111yescharacteristic
177C4⋊C4—612no—
178C4⋊C4—612no—
179C4⋊C4—1222no—
180C4⋊C4—1222no—
181C22⋊C4—1222no—
182C22⋊C4—1222no—
183C22⋊C4—1222no—
184C22⋊C4—1222no—
185C22⋊C4—1222no—
186C42—1222no—
187C23—41no—
188C23—42no—
189C23—1222no—
190C23C2×D24411yescharacteristic
191C23C2×D24412yes—
192Q8—1222no—
193Q8—1222no—
194D4—1222no—
195D4—1222no—
196D4—2444no—
197D4—2444no—
198D4—2444no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4—1222no—
208C2×C4—2444no—
209C2×C4C2×D24412yes—
210C2×C4C2×D24411yescharacteristic
211C2×C4C23×D6111yescharacteristic
212C8—21no—
213C8—22no—
214C8—21no—
215C22—22no—
216C22—22no—
217C22—22no—
218C22—22no—
219C22—21no—
220C22—44no—
221C22—2442no—
222C22—2442no—
223C22—2442no—
224C22C22×D24411yescharacteristic
225C4—22no—
226C4—21no—
227C4—2442no—
228C4—2442no—
229C4—2442no—
230C4#1451982211yescharacteristic
231C4#1451982211yescharacteristic
232C2—41no—
233C2—42no—
234C2—4882no—
235C2#1684032411yescharacteristic
236C2#1684056212yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#407C2
socleC22×C61C22×D4
hypercenter#407D61
hypocenterC61#3197
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #16840273C2semidirect
2. #16840104C2semidirect
3. #16840087C2semidirect
4. #16840020C2semidirect
5. #16840015C2semidirect
6. #16840008C2semidirect
7. #16839926C2semidirect
8. #16839909C2semidirect
9. C61×#407C2semidirect
11. C2×Dic244C22semidirect
12. C2×#11758190C22semidirect
13. C2×D488C22semidirect
23. #14519711C22semidirect
24. #14519709C22semidirect
25. #14519709C22semidirect
26. #14519702C22semidirect
27. #14519702C22semidirect
28. #14519699C22semidirect
29. #14519699C22semidirect
127. #407D61semidirect
128. C61#3197semidirect