Finite Group Databasebeta

← #21460598

Subgroups — #21460598

Order 7808.

1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.

normal subgroups only

This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 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
1C2×#14519823C211yesmaximal, characteristic, complemented
2#16840570C218yesmaximal, complemented
3#16840565C218yesmaximal, complemented
4#16840560C216yesmaximal, complemented
5C2×#14519802C216yesmaximal, complemented
6#16840529C211yesmaximal, characteristic, complemented
7C61×#585C211yesmaximal, characteristic, complemented
8#14519823—24no—
9#14519823C2218yescomplemented
10C2×#11758226—21no—
11C2×#11758222C2213yescomplemented
12C22×D244C2213yescomplemented
13C2×D4×D61—23no—
14#14519808C22112yescomplemented
15#14519807C2214yescomplemented
16#14519803C22112yescomplemented
17#14519802C22112yescomplemented
18#14519802C22124yescomplemented
19#14519797C22124yescomplemented
20C2×#11758201C22112yescomplemented
21C2×#11758199C22112yescomplemented
22#14519784C2218yescomplemented
23C2×#11758194C2216yescomplemented
242−1+4×C61—21no—
252−1+4×C61C2214yescomplemented
26H(5,𝔽2)×C61—23no—
27H(5,𝔽2)×C61C2214yescomplemented
28C2×#41×C61—24no—
29C2×#41×C61C2211yescharacteristic
30C2×#41×C61C2216yescomplemented
31C23×D61—23no—
32#41×C61—24no—
33#41×C61—212no—
34#41×C61—26no—
35#41×C61—26no—
36#41×C61D414yes—
37#41×C61C2314yes—
38#41×C61C2314yes—
39#41×C61C23112yescomplemented
40C2×Q8×C61—24no—
41C2×Q8×C61D411yescharacteristic
42C2×Q8×C61C2316yescomplemented
43C2×D4×C61—26no—
44C2×D4×C61—212no—
45C2×D4×C61D413yes—
46C2×D4×C61C2316yescomplemented
47C22×C4×C61—26no—
48C22×C4×C61C2313yes—
49C2×C22⋊D61—23no—
50#11758226—28no—
51D4×D61—224no—
52#11758222—26no—
53#11758222C23112yes—
54C2×D244—23no—
55C2×D244—26no—
56C2×D244C2313yes—
57C2×D244C23112yes—
58C2×C4×D61—23no—
59C2×Dic122C2311yescharacteristic
60#11758202C2318yescomplemented
61#11758201C23124yescomplemented
62#11758200C2318yescomplemented
63#11758199C23124yescomplemented
64#11758194C2314yes—
65#11758194C23112yescomplemented
66C2×#92418C23112yescomplemented
67C23×C61—26no—
68C23×C61C2×D413yes—
69C22×D61—23no—
70C22×D61—212no—
71C22×D61—86no—
72Q8×C61—26no—
73Q8×C61C2×D414yes—
74Q8×C61C2414yes—
75D4×C61—24no—
76D4×C61—212no—
77D4×C61—26no—
78D4×C61C2×D4112yes—
79D4×C61C2414yes—
80C2×C4×C61—26no—
81C2×C4×C61—24no—
82C2×C4×C61—212no—
83C2×C4×C61C2×D413yes—
84C2×C4×C61C2×D416yes—
85C2×C4×C61C2416yes—
86C2×C4×C61C2411yescharacteristic
87C22⋊D61—212no—
88C2×Dic61—21no—
89D244—23no—
90D244—212no—
91D244C2416yes—
92C4×D61—212no—
93Dic122—21no—
94Dic122C2412yes—
95#92418C2418yes—
96C22×C61—24no—
97C22×C61—43no—
98C22×C61—86no—
99C22×C61C22×D411yescharacteristic
100C22×C61C22×D416yes—
101C2×D61—26no—
102C2×D61—46no—
103C2×D61—812no—
104C4×C61—24no—
105C4×C61C22×D411yescharacteristic
106C4×C61C22×D416yes—
107C4×C61C2511yescharacteristic
108Dic61—22no—
109#3585—611nomaximal, Sylow
110C2×C61—21no—
111C2×C61—26no—
112C2×C61—44no—
113C2×C61C23×D411yescharacteristic
114D61—46no—
115#585D6111yescharacteristic, complemented
116C2×H(5,𝔽2)—611no—
117#577—618no—
118#576—618no—
119#575—616no—
120C2×AGL(1,ℤ/8)—616no—
121#568—611no—
122C61#358511yescharacteristic, complemented, Sylow
1232−1+4—21no—
1242−1+4C2×D6114yescomplemented
125H(5,𝔽2)—23no—
126H(5,𝔽2)—618no—
127H(5,𝔽2)—1224no—
128H(5,𝔽2)C2×D6114yescomplemented
129C2×#41—24no—
130C2×#41—613no—
131C2×#41—1221no—
132C2×#41C2×D6111yescharacteristic
133C2×#41C2×D6116yescomplemented
134C22×D4—613no—
135C22×D4—1223no—
136#137—614no—
137#137—6112no—
138AGL(1,ℤ/8)—6112no—
139AGL(1,ℤ/8)—6124no—
140AGL(1,ℤ/8)—6112no—
141#135—6124no—
142C2×SD16—6112no—
143C2×D8—6112no—
144#131—618no—
145C2×M16—616no—
146C24—1223no—
147#41—24no—
148#41—212no—
149#41—26no—
150#41—26no—
151#41—6112no—
152#41—1228no—
153#41—1226no—
154#41C22⋊D6114yes—
155#41C22×D6114yes—
156#41C22×D6114yes—
157#41C22×D61112yescomplemented
158C2×Q8—24no—
159C2×Q8—611no—
160C2×Q8C22⋊D6111yescharacteristic
161C2×Q8C22×D6116yescomplemented
162C2×D4—26no—
163C2×D4—212no—
164C2×D4—6112no—
165C2×D4—613no—
166C2×D4—1223no—
167C2×D4—12224no—
168C2×D4—1223no—
169C2×D4—1226no—
170C2×D4C22⋊D6113yes—
171C2×D4C22×D6116yescomplemented
172C22×C4—26no—
173C22×C4—1223no—
174C22×C4C22×D6113yes—
175Q16—618no—
176SD16—6124no—
177SD16—618no—
178D8—6124no—
179M16—614no—
180M16—6112no—
181C2×C8—6112no—
182C23—26no—
183C23—12212no—
184C23—1223no—
185C23—4886no—
186C23C2×C22⋊D6113yes—
187Q8—26no—
188Q8—612no—
189Q8—1221no—
190Q8C2×C22⋊D6114yes—
191Q8C23×D6114yes—
192D4—24no—
193D4—212no—
194D4—26no—
195D4—616no—
196D4—12212no—
197D4—1223no—
198D4—12212no—
199D4C2×C22⋊D61112yes—
200D4C23×D6114yes—
201C2×C4—26no—
202C2×C4—24no—
203C2×C4—212no—
204C2×C4—1221no—
205C2×C4—12212no—
206C2×C4C2×C22⋊D6116yes—
207C2×C4C2×C22⋊D6113yes—
208C2×C4C23×D6116yes—
209C2×C4C23×D6111yescharacteristic
210C8—618no—
211C22—24no—
212C22—43no—
213C22—86no—
214C22—1226no—
215C22—48812no—
216C22—2446no—
217C22C22×C22⋊D6116yes—
218C22C22×C22⋊D6111yescharacteristic
219C4—24no—
220C4—1222no—
221C4C22×C22⋊D6111yescharacteristic
222C4C22×C22⋊D6116yes—
223C4C24×D6111yescharacteristic
224C2—21no—
225C2—26no—
226C2—44no—
227C2—2446no—
228C2C23×C22⋊D6111yescharacteristic
subgroupG/H
centerC2C23×C22⋊D61
commutatorC4×C61C25
FrattiniC4C24×D61
FittingC61×#585C2
socleC2×C61C23×D4
hypercenter#585D61
hypocenterC61#3585
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×#41 ◁ #585

Complements

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

NH ≅ G/Ntype
1. C2×#14519823C2semidirect
2. #16840570C2semidirect
3. #16840565C2semidirect
4. #16840560C2semidirect
5. C2×#14519802C2semidirect
6. #16840529C2semidirect
7. C61×#585C2semidirect
9. #14519823C22semidirect
11. C2×#11758222C22semidirect
12. C22×D244C22semidirect
14. #14519808C22semidirect
15. #14519807C22semidirect
16. #14519803C22semidirect
17. #14519802C22semidirect
18. #14519802C22semidirect
19. #14519797C22semidirect
20. C2×#11758201C22semidirect
21. C2×#11758199C22semidirect
22. #14519784C22semidirect
23. C2×#11758194C22semidirect
25. 2−1+4×C61C22semidirect
27. H(5,𝔽2)×C61C22semidirect
30. C2×#41×C61C22semidirect
39. #41×C61C23semidirect
42. C2×Q8×C61C23semidirect
46. C2×D4×C61C23semidirect
60. #11758202C23semidirect
61. #11758201C23semidirect
62. #11758200C23semidirect
63. #11758199C23semidirect
65. #11758194C23semidirect
66. C2×#92418C23semidirect
115. #585D61semidirect
122. C61#3585semidirect
124. 2−1+4C2×D61semidirect
128. H(5,𝔽2)C2×D61semidirect
133. C2×#41C2×D61semidirect
157. #41C22×D61semidirect
161. C2×Q8C22×D61semidirect
171. C2×D4C22×D61semidirect