Finite Group Databasebeta

← #21457613

Subgroups — #21457613

Order 7808.

460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840574C212yesmaximal, complemented
2#16840569C212yesmaximal, complemented
3#16840135C211yesmaximal, characteristic, complemented
4#16840026C212yesmaximal, complemented
5#16840025C212yesmaximal, complemented
6#16839946C212yesmaximal, complemented
7#16839931C212yesmaximal, complemented
8#16839880C211yesmaximal, characteristic, complemented
9C61×#443C211yesmaximal, characteristic, complemented
10#14519824C2212yes—
11#14519823C2212yescomplemented
12#14519810—22no—
13#14519810C2212yescomplemented
14#14519809—22no—
15#14519807C2212yescomplemented
16#14519805—22no—
17#14519805C2212yes—
18#14519802C2212yes—
19#14519801—22no—
20#14519799—22no—
21#14519799C2211yescharacteristic
22#14519798—22no—
23C2×#11758190—22no—
24C2×#11758190C2212yescomplemented
25C2×#11758190C2212yescomplemented
26SD16×D61—22no—
27#14519783C2212yescomplemented
28#14519777C2211yescharacteristic, complemented
29#14519774C2211yescharacteristic
30#14519713C2211yescharacteristic, complemented
31#14519705C2212yescomplemented
32#14519695C2212yescomplemented
33#14519693C2212yescomplemented
34#135×C61C2211yescharacteristic
35#131×C61C2212yescomplemented
36#108×C61C2211yescharacteristic, complemented
37#104×C61C2212yescomplemented
38C4×C8×C61C2211yescharacteristic, complemented
39#41×C61C2312yes—
40#11758226—22no—
41Q8×D61—22no—
42#11758224—22no—
43#11758224—42no—
44D4×D61—22no—
45D4×D61—42no—
46#11758222—22no—
47#11758222—22no—
48#11758222C2312yes—
49C2×D244—22no—
50C2×D244—41no—
51C2×D244C2312yes—
52C2×Dic122—22no—
53C2×Dic122C2312yes—
54Q16×C61D411yescharacteristic, complemented
55SD16×C61D412yescomplemented
56D8×C61D411yescharacteristic, complemented
57M16×C61—22no—
58M16×C61C2312yes—
59C2×C8×C61—22no—
60C2×C8×C61C2311yescharacteristic
61C2×C8×C61C2311yescharacteristic
62C42×C61C2311yescharacteristic
63#11758202—22no—
64#11758201—22no—
65#11758200—22no—
66#11758199—22no—
67C4⋊Dic61—41no—
68#11758194C2312yes—
69Dic244—22no—
70Dic244D411yescharacteristic, complemented
71D488—22no—
72D488D411yescharacteristic, complemented
73#11758190—22no—
74#11758190—22no—
75#11758190—22no—
76#11758190—22no—
77#11758190—22no—
78#11758190—22no—
79#11758190D412yescomplemented
80#11758189—22no—
81C8×D61—22no—
82C22×D61—22no—
83C22×D61—42no—
84Q8×C61C2×D412yes—
85D4×C61—22no—
86D4×C61C2×D412yes—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61C2411yescharacteristic
90C22⋊D61—22no—
91C22⋊D61—42no—
92C22⋊D61—42no—
93C2×Dic61—22no—
94C2×Dic61—42no—
95D244—22no—
96D244—22no—
97D244—42no—
98D244—82no—
99D244C2×D412yes—
100C4×D61—22no—
101C4×D61—42no—
102C4×D61—42no—
103Dic122—22no—
104Dic122—22no—
105Dic122—42no—
106Dic122C2×D412yes—
107C8×C61—22no—
108C8×C61C2×D411yescharacteristic
109C8×C61C2×D411yescharacteristic
110C8×C61C2×D411yescharacteristic
111C8×C61C2×D411yescharacteristic
112#92418—22no—
113C22×C61—22no—
114C22×C61H(5,𝔽2)11yescharacteristic
115C2×D61—22no—
116C2×D61—42no—
117C2×D61—82no—
118C2×D61—162no—
119C4×C61—22no—
120C4×C61—22no—
121C4×C61C22×D411yescharacteristic
122C4×C61C22×D411yescharacteristic
123Dic61—22no—
124Dic61—42no—
125#3291—611nomaximal, Sylow
126C2×C61—21no—
127C2×C61—42no—
128C2×C61D4211yescharacteristic
129D61—42no—
130D61—82no—
131#577—612no—
132#577—612no—
133#492—611no—
134#471—612no—
135#471—612no—
136#456—612no—
137#453—612no—
138#443—611no—
139#443D6111yescharacteristic, complemented
140C61#329111yescharacteristic, complemented, Sylow
1412−1+4—612no—
142H(5,𝔽2)—612no—
143#137—612no—
144#137—612no—
145#137—1222no—
146#137—1222no—
147AGL(1,ℤ/8)—612no—
148AGL(1,ℤ/8)—612no—
149AGL(1,ℤ/8)—1222no—
150AGL(1,ℤ/8)—1222no—
151#135—611no—
152#135—1222no—
153#135—1222no—
154#135C2×D6111yescharacteristic
155C2×SD16—612no—
156C2×SD16—612no—
157C2×SD16—1222no—
158C2×SD16—1222no—
159#131—612no—
160#131C2×D6112yescomplemented
161C4⋊Q8—611no—
162#127—611no—
163#108—611no—
164#108C2×D6111yescharacteristic, complemented
165#104—612no—
166#104C2×D6112yescomplemented
167#101—612no—
168#100—612no—
169C4×C8C2×D6111yescharacteristic, complemented
170#41—612no—
171#41—1222no—
172#41—1222no—
173#41—1222no—
174#41—1222no—
175#41—2442no—
176#41C22×D6112yes—
177C2×Q8—612no—
178C2×Q8—1222no—
179C2×Q8—1222no—
180C2×D4—612no—
181C2×D4—1222no—
182C2×D4—1222no—
183C2×D4—2441no—
184C2×D4—2442no—
185Q16—611no—
186Q16—1222no—
187Q16—1222no—
188Q16D24411yescharacteristic, complemented
189SD16—612no—
190SD16—1222no—
191SD16—1222no—
192SD16—1222no—
193SD16—1222no—
194SD16—1222no—
195SD16—1222no—
196SD16—1222no—
197SD16—1222no—
198SD16D24412yescomplemented
199D8—611no—
200D8—1222no—
201D8—1222no—
202D8D24411yescharacteristic, complemented
203M16—22no—
204M16—612no—
205M16—1222no—
206M16C22×D6112yes—
207C2×C8—22no—
208C2×C8—1222no—
209C2×C8C22×D6111yescharacteristic
210C2×C8C22×D6111yescharacteristic
211C4⋊C4—2441no—
212C42C22×D6111yescharacteristic
213C23—1222no—
214C23—2442no—
215Q8—612no—
216Q8—1222no—
217Q8—1222no—
218Q8—2442no—
219Q8C2×D24412yes—
220D4—22no—
221D4—612no—
222D4—1222no—
223D4—1222no—
224D4—1222no—
225D4—4882no—
226D4—2442no—
227D4—2442no—
228D4—2442no—
229D4C2×D24412yes—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4—2442no—
235C2×C4—2442no—
236C2×C4—2442no—
237C2×C4C23×D6111yescharacteristic
238C8—22no—
239C8—1222no—
240C8C2×D24411yescharacteristic
241C8C2×D24411yescharacteristic
242C8D4×D6111yescharacteristic
243C8D4×D6111yescharacteristic
244C22—22no—
245C22—1222no—
246C22—9762no—
247C22—4882no—
248C22—2442no—
249C22#1451982311yescharacteristic
250C4—22no—
251C4—22no—
252C4—1222no—
253C4—2442no—
254C4C2×D4×D6111yescharacteristic
255C4C22×D24411yescharacteristic
256C2—21no—
257C2—42no—
258C2—4882no—
259C2—2442no—
260C2D4×D24411yescharacteristic
subgroupG/H
centerC2D4×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#443C2
socleC2×C61D42
hypercenter#443D61
hypocenterC61#3291
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #16840574C2semidirect
2. #16840569C2semidirect
3. #16840135C2semidirect
4. #16840026C2semidirect
5. #16840025C2semidirect
6. #16839946C2semidirect
7. #16839931C2semidirect
8. #16839880C2semidirect
9. C61×#443C2semidirect
11. #14519823C22semidirect
13. #14519810C22semidirect
15. #14519807C22semidirect
24. C2×#11758190C22semidirect
25. C2×#11758190C22semidirect
27. #14519783C22semidirect
28. #14519777C22semidirect
30. #14519713C22semidirect
31. #14519705C22semidirect
32. #14519695C22semidirect
33. #14519693C22semidirect
35. #131×C61C22semidirect
36. #108×C61C22semidirect
37. #104×C61C22semidirect
38. C4×C8×C61C22semidirect
54. Q16×C61D4semidirect
55. SD16×C61D4semidirect
56. D8×C61D4semidirect
70. Dic244D4semidirect
72. D488D4semidirect
79. #11758190D4semidirect
139. #443D61semidirect
140. C61#3291semidirect
160. #131C2×D61semidirect
164. #108C2×D61semidirect
166. #104C2×D61semidirect
169. C4×C8C2×D61semidirect
188. Q16D244semidirect
198. SD16D244semidirect
202. D8D244semidirect