Finite Group Databasebeta

← #21460600

Subgroups — #21460600

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
1#16840598C211yesmaximal, characteristic, complemented
2C2×#14519823C211yesmaximal, characteristic, complemented
3#16840574C218yesmaximal, complemented
4#16840567C218yesmaximal, complemented
5#16840562C216yesmaximal, complemented
6C2×#14519805C216yesmaximal, complemented
7C61×#568C211yesmaximal, characteristic, complemented
8#14519825—21no—
9#14519824C2214yescomplemented
10#14519823—24no—
11#14519823C2218yescomplemented
12#14519823C2214yescomplemented
13#14519822—23no—
14C2×#11758226—21no—
15C2×#11758222C2213yescomplemented
16C2×#11758222C2216yescomplemented
17#41×D61—24no—
18C22×D244C2213yescomplemented
19C2×D4×D61—23no—
20#14519810C2214yescomplemented
21#14519810C22112yescomplemented
22#14519805C22112yescomplemented
23#14519805C22124yescomplemented
24#14519805C22112yescomplemented
25#14519799C22124yescomplemented
26C2×#11758190C22112yescomplemented
27C2×D488C22112yescomplemented
28C2×#41×C61C2211yescharacteristic
29#131×C61C2218yescomplemented
30C2×M16×C61C2216yescomplemented
31C23×D61—23no—
32#41×C61D414yes—
33#41×C61C2314yes—
34C2×Q8×C61D411yescharacteristic
35C2×D4×C61D413yes—
36C22×C4×C61C2313yes—
37C2×C22⋊D61—23no—
38C2×C22⋊D61—26no—
39#11758226—24no—
40#11758226—28no—
41Q8×D61—24no—
42#11758224—212no—
43D4×D61—224no—
44D4×D61—212no—
45#11758222—26no—
46#11758222—26no—
47#11758222—26no—
48#11758222C2314yes—
49#11758222C23112yes—
50#11758222C23112yescomplemented
51C2×D244—23no—
52C2×D244—26no—
53C2×D244C2313yes—
54C2×D244C23112yes—
55C2×D244C2316yescomplemented
56C2×C4×D61—23no—
57C2×C4×D61—26no—
58C2×Dic122C2311yescharacteristic
59C2×Dic122C2316yescomplemented
60M16×C61C2314yes—
61M16×C61C23112yescomplemented
62C2×C8×C61C23112yescomplemented
63Dic244C2318yescomplemented
64D488C23124yescomplemented
65#11758190C23124yescomplemented
66#11758190C2318yescomplemented
67C23×C61C2×D413yes—
68C22×D61—23no—
69C22×D61—26no—
70C22×D61—212no—
71C22×D61—86no—
72Q8×C61C2×D414yes—
73D4×C61C2×D4112yes—
74C2×C4×C61C2×D413yes—
75C2×C4×C61C2×D416yes—
76C2×C4×C61C2416yes—
77C2×C4×C61C2411yescharacteristic
78C22⋊D61—24no—
79C22⋊D61—212no—
80C22⋊D61—212no—
81C2×Dic61—21no—
82C2×Dic61—26no—
83D244—23no—
84D244—212no—
85D244—26no—
86D244C2416yes—
87D244C2414yes—
88C4×D61—24no—
89C4×D61—212no—
90C4×D61—212no—
91Dic122—21no—
92Dic122—26no—
93Dic122C2414yes—
94Dic122C2412yes—
95C8×C61C2418yes—
96C22×C61—43no—
97C22×C61C22×D411yescharacteristic
98C22×C61C22×D416yes—
99C2×D61—24no—
100C2×D61—26no—
101C2×D61—46no—
102C2×D61—86no—
103C2×D61—812no—
104C4×C61C22×D411yescharacteristic
105C4×C61C22×D416yes—
106C4×C61C2511yescharacteristic
107Dic61—24no—
108Dic61—22no—
109#3585—611nomaximal, Sylow
110C2×C61—21no—
111C2×C61—26no—
112C2×C61C23×D411yescharacteristic
113D61—46no—
114D61—44no—
115#585—611no—
116C2×H(5,𝔽2)—611no—
117#577—618no—
118#576—618no—
119#575—616no—
120C2×AGL(1,ℤ/8)—616no—
121#568D6111yescharacteristic, complemented
122C61#358511yescharacteristic, complemented, Sylow
1232−1+4—614no—
1242−1+4—1221no—
125H(5,𝔽2)—614no—
126H(5,𝔽2)—618no—
127H(5,𝔽2)—1224no—
128H(5,𝔽2)—1223no—
129C2×#41—616no—
130C2×#41—613no—
131C2×#41—1224no—
132C2×#41—1221no—
133C2×#41C2×D6111yescharacteristic
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#131C2×D6118yescomplemented
145C2×M16C2×D6116yescomplemented
146C24—1223no—
147#41—6112no—
148#41—6112no—
149#41—614no—
150#41—1228no—
151#41—1224no—
152#41—12212no—
153#41—1226no—
154#41—1226no—
155#41—1226no—
156#41D24414yes—
157#41C22×D6114yes—
158C2×Q8—616no—
159C2×Q8—611no—
160C2×Q8—1224no—
161C2×Q8D24411yescharacteristic
162C2×D4—616no—
163C2×D4—6112no—
164C2×D4—613no—
165C2×D4—1223no—
166C2×D4—1226no—
167C2×D4—12224no—
168C2×D4—12212no—
169C2×D4—1223no—
170C2×D4—1226no—
171C2×D4D24413yes—
172C22×C4—1223no—
173C22×C4—1226no—
174C22×C4C22×D6113yes—
175Q16—618no—
176SD16—6124no—
177SD16—618no—
178D8—6124no—
179M16C22×D6114yes—
180M16C22×D61112yescomplemented
181C2×C8C22×D61112yescomplemented
182C23—1226no—
183C23—12212no—
184C23—1223no—
185C23—4886no—
186C23C2×D24413yes—
187Q8—614no—
188Q8—612no—
189Q8—1226no—
190Q8—1221no—
191Q8C2×D24414yes—
192D4—614no—
193D4—616no—
194D4—12212no—
195D4—1224no—
196D4—12212no—
197D4—1223no—
198D4—12212no—
199D4—1226no—
200D4C2×D244112yes—
201C2×C4—1221no—
202C2×C4—1226no—
203C2×C4—1224no—
204C2×C4—12212no—
205C2×C4—12212no—
206C2×C4C2×D24413yes—
207C2×C4C2×D24416yes—
208C2×C4C23×D6116yes—
209C2×C4C23×D6111yescharacteristic
210C8C23×D6118yes—
211C22—43no—
212C22—1224no—
213C22—1226no—
214C22—4886no—
215C22—48812no—
216C22—2446no—
217C22C22×D24411yescharacteristic
218C22C22×D24416yes—
219C4—1222no—
220C4—1224no—
221C4C22×D24411yescharacteristic
222C4C22×D24416yes—
223C4C24×D6111yescharacteristic
224C2—21no—
225C2—26no—
226C2—2446no—
227C2—2444no—
228C2C23×D24411yescharacteristic
subgroupG/H
centerC2C23×D244
commutatorC4×C61C25
FrattiniC4C24×D61
FittingC61×#568C2
socleC2×C61C23×D4
hypercenter#568D61
hypocenterC61#3585
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×#41 ◁ #568

Complements

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

NH ≅ G/Ntype
1. #16840598C2semidirect
2. C2×#14519823C2semidirect
3. #16840574C2semidirect
4. #16840567C2semidirect
5. #16840562C2semidirect
6. C2×#14519805C2semidirect
7. C61×#568C2semidirect
9. #14519824C22semidirect
11. #14519823C22semidirect
12. #14519823C22semidirect
15. C2×#11758222C22semidirect
16. C2×#11758222C22semidirect
18. C22×D244C22semidirect
20. #14519810C22semidirect
21. #14519810C22semidirect
22. #14519805C22semidirect
23. #14519805C22semidirect
24. #14519805C22semidirect
25. #14519799C22semidirect
26. C2×#11758190C22semidirect
27. C2×D488C22semidirect
29. #131×C61C22semidirect
30. C2×M16×C61C22semidirect
50. #11758222C23semidirect
55. C2×D244C23semidirect
59. C2×Dic122C23semidirect
61. M16×C61C23semidirect
62. C2×C8×C61C23semidirect
63. Dic244C23semidirect
64. D488C23semidirect
65. #11758190C23semidirect
66. #11758190C23semidirect
121. #568D61semidirect
122. C61#3585semidirect
144. #131C2×D61semidirect
145. C2×M16C2×D61semidirect
180. M16C22×D61semidirect
181. C2×C8C22×D61semidirect