Finite Group Databasebeta

← #21459597

Subgroups — #21459597

Order 7808.

1748 conjugacy classes of subgroups; only the 557 normal subgroups are shown.

normal subgroups only

This group has 1748 conjugacy classes of subgroups — too many to draw. Only its 557 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×#14519823C212yesmaximal, complemented
2#16840434C214yesmaximal, complemented
3D4×D244C2112yesmaximal, complemented
4#16840331C216yesmaximal, complemented
5#16840312C213yesmaximal, complemented
6C2×#14519774C213yesmaximal, complemented
7C4×#41×C61C211yesmaximal, characteristic, complemented
8#14519823—216no—
9C2×#11758226C2214yescomplemented
10C2×#11758222C2216yescomplemented
11C22×D244C2216yescomplemented
12C22×D244C22112yescomplemented
13C2×D4×D61C22112yescomplemented
14#14519777C2211yescharacteristic, complemented
15#14519774C2213yescomplemented
16#14519774C2216yescomplemented
17#14519774C22112yescomplemented
18#14519765C2216yescomplemented
19#14519752C22124yescomplemented
20#14519751C22112yescomplemented
21#14519747C22124yescomplemented
22C4×D244C22112yescomplemented
23C2×#41×C61C2211yescharacteristic
24C4×Q8×C61C2212yescomplemented
25C4×D4×C61C2216yescomplemented
26#117×C61C2213yescomplemented
27C2×C42×C61C2213yescomplemented
28C23×D61C23112yes—
29#41×C61D418yescomplemented
30C2×Q8×C61C2311yescharacteristic
31C2×D4×C61C2313yes—
32C22×C4×C61C2316yes—
33C22×C4×C61C2313yes—
34C2×C22⋊D61C23112yes—
35#11758226—216no—
36D4×D61—248no—
37#11758222—224no—
38C2×D244—224no—
39C2×D244—424no—
40C2×D244C23112yes—
41C2×D244C2316yes—
42C2×D244C23112yes—
43C2×D244C23124yes—
44C2×C4×D61C23112yes—
45C2×Dic122C2312yes—
46C4⋊C4×C61C2316yes—
47C22⋊C4×C61C2316yes—
48C42×C61C2311yescharacteristic
49C42×C61C2313yes—
50C42×C61C2316yes—
51#11758198C23124yes—
52C4⋊Dic61C2314yes—
53C23×C61C2413yes—
54C22×D61—224no—
55C22×D61—424no—
56C22×D61C24112yes—
57Q8×C61C2×D414yescomplemented
58D4×C61C2×D4112yescomplemented
59C2×C4×C61—212no—
60C2×C4×C61C2×D4112yescomplemented
61C2×C4×C61C2416yes—
62C2×C4×C61C2411yescharacteristic
63C2×C4×C61C2413yes—
64C2×C4×C61C2412yes—
65C22⋊D61—224no—
66C2×Dic61C2414yes—
67D244—212no—
68D244—224no—
69D244—224no—
70D244—424no—
71C4×D61—224no—
72Dic122—24no—
73C22×C61—26no—
74C22×C61C22×D416yes—
75C22×C61C2511yescharacteristic
76C2×D61—212no—
77C2×D61—224no—
78C2×D61—824no—
79C4×C61—26no—
80C4×C61C22×D412yes—
81C4×C61C22×D416yes—
82C4×C61H(5,𝔽2)14yescomplemented
83Dic61—24no—
84#3498—611nomaximal, Sylow
85C2×C61—26no—
86C2×C61C23×D411yescharacteristic
87C2×C61C2×H(5,𝔽2)12yes—
88D61—412no—
89C2×H(5,𝔽2)—612no—
90#550—614no—
91D42—6112no—
92#535—616no—
93#532—613no—
94C2×#127—613no—
95C4×#41D6111yescharacteristic, complemented
96C61#349811yescharacteristic, complemented, Sylow
97H(5,𝔽2)—12216no—
98C2×#41—614no—
99C2×#41—616no—
100C2×#41C2×D6111yescharacteristic
101C22×D4—6112no—
102C22×D4—616no—
103C22×D4—6112no—
104C4⋊Q8—611no—
105#127—613no—
106#127—616no—
107#127—6112no—
108#124—616no—
109#121—6112no—
110#121—6124no—
111#120—6124no—
112C4×Q8C2×D6112yescomplemented
113C4×D4—6112no—
114C4×D4C2×D6116yescomplemented
115#117C2×D6113yescomplemented
116C2×C42C2×D6113yescomplemented
117C24—6112no—
118#41—12216no—
119#41—12224no—
120#41D24418yescomplemented
121C2×Q8—612no—
122C2×Q8C22×D6111yescharacteristic
123C2×D4—6112no—
124C2×D4—6112no—
125C2×D4—6112no—
126C2×D4—616no—
127C2×D4—6124no—
128C2×D4—12248no—
129C2×D4—12224no—
130C2×D4—24424no—
131C2×D4C22×D6113yes—
132C22×C4—6112no—
133C22×C4C22×D6116yes—
134C22×C4C22×D6113yes—
135C4⋊C4—614no—
136C4⋊C4C22×D6116yes—
137C22⋊C4—6124no—
138C22⋊C4C22×D6116yes—
139C42C22×D6111yescharacteristic
140C42C22×D6113yes—
141C42C22×D6116yes—
142C23—6112no—
143C23—12224no—
144C23—24424no—
145C23C23×D6113yes—
146Q8—1224no—
147Q8C2×D24414yescomplemented
148D4—12224no—
149D4—12224no—
150D4—12212no—
151D4—12224no—
152D4—24424no—
153D4C2×D244112yescomplemented
154C2×C4—212no—
155C2×C4—614no—
156C2×C4—12224no—
157C2×C4C2×D244112yescomplemented
158C2×C4C23×D6116yes—
159C2×C4C23×D6111yescharacteristic
160C2×C4C23×D6113yes—
161C2×C4C23×D6112yes—
162C22—26no—
163C22—12212no—
164C22—12224no—
165C22—48824no—
166C22C22×D24416yes—
167C22C24×D6111yescharacteristic
168C4—26no—
169C4—1224no—
170C4C22×D24416yes—
171C4C22×D24412yes—
172C4#1451982314yescomplemented
173C2—26no—
174C2—24412no—
175C2C23×D24411yescharacteristic
176C2C2×#1451982312yes—
subgroupG/H
center, FrattiniC22C24×D61
commutator, socleC22×C61C25
FittingC4×#41×C61C2
hypercenterC4×#41D61
hypocenterC61#3498
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#14519823C2semidirect
2. #16840434C2semidirect
3. D4×D244C2semidirect
4. #16840331C2semidirect
5. #16840312C2semidirect
6. C2×#14519774C2semidirect
7. C4×#41×C61C2semidirect
9. C2×#11758226C22semidirect
10. C2×#11758222C22semidirect
11. C22×D244C22semidirect
12. C22×D244C22semidirect
13. C2×D4×D61C22semidirect
14. #14519777C22semidirect
15. #14519774C22semidirect
16. #14519774C22semidirect
17. #14519774C22semidirect
18. #14519765C22semidirect
19. #14519752C22semidirect
20. #14519751C22semidirect
21. #14519747C22semidirect
22. C4×D244C22semidirect
24. C4×Q8×C61C22semidirect
25. C4×D4×C61C22semidirect
26. #117×C61C22semidirect
27. C2×C42×C61C22semidirect
29. #41×C61D4semidirect
57. Q8×C61C2×D4semidirect
58. D4×C61C2×D4semidirect
60. C2×C4×C61C2×D4semidirect
82. C4×C61H(5,𝔽2)semidirect
95. C4×#41D61semidirect
96. C61#3498semidirect
112. C4×Q8C2×D61semidirect
114. C4×D4C2×D61semidirect
115. #117C2×D61semidirect
116. C2×C42C2×D61semidirect
120. #41D244semidirect
147. Q8C2×D244semidirect
153. D4C2×D244semidirect
157. C2×C4C2×D244semidirect
172. C4#14519823semidirect