Finite Group Databasebeta

← #20265984

Subgroups — #20265984

Order 6464.

258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 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#15692302C211yesmaximal, characteristic, complemented
2#15692301C211yesmaximal, characteristic, complemented
3#15692287C212yesmaximal, complemented
4#15692285C211yesmaximal, characteristic, complemented
5#15692280C211yesmaximal, characteristic, complemented
6#15692279C212yesmaximal, complemented
7#15692276C212yesmaximal, complemented
8C2×#13108063C211yesmaximal, characteristic, complemented
9SD16×D101C212yesmaximal, complemented
10#15692261C211yesmaximal, characteristic, complemented
11#135×C101C211yesmaximal, characteristic, complemented
12#13108075C2212yes—
13#13108074—21no—
14#13108074—21no—
15#13108074C2211yescharacteristic
16#13108073—22no—
17#13108073C2212yescomplemented
18C2×Dic202—21no—
19C2×Dic202C2211yescharacteristic, complemented
20Q8×D101C2212yescomplemented
21C2×D404—21no—
22C2×D404C2211yescharacteristic
23D4×D101—22no—
24D4×D101C2212yes—
25#13108064C2212yescomplemented
26#13108063C2212yescomplemented
27#13108063C2212yescomplemented
28#13108062C2212yescomplemented
29#13108061C2212yescomplemented
30#13108059C2212yescomplemented
31#13108058C2211yescharacteristic, complemented
32#13108057C2212yescomplemented
33C8×D101C2212yescomplemented
34#41×C101C2211yescharacteristic
35#41×C101C2211yescharacteristic, complemented
36Q16×C101C2211yescharacteristic, complemented
37SD16×C101C2211yescharacteristic, complemented
38SD16×C101C2211yescharacteristic, complemented
39D8×C101C2211yescharacteristic, complemented
40C2×C8×C101C2211yescharacteristic, complemented
41C22×D101—21no—
42C22×D101—22no—
43Q8×C101C2311yescharacteristic
44Q8×C101C2311yescharacteristic
45D4×C101—21no—
46D4×C101—21no—
47D4×C101C2311yescharacteristic
48D4×C101C2311yescharacteristic
49C2×C4×C101—21no—
50C2×C4×C101—21no—
51C2×C4×C101C2311yescharacteristic
52C22⋊D101—22no—
53C22⋊D101—22no—
54C22⋊D101D412yes—
55C2×Dic101—21no—
56C2×Dic101—22no—
57D404—22no—
58D404—21no—
59D404D411yescharacteristic
60D404C2312yes—
61C4×D101—22no—
62C4×D101—22no—
63C4×D101C2312yes—
64Dic202—21no—
65Dic202—22no—
66Dic202D411yescharacteristic
67Dic202C2312yes—
68C8×C101C2311yescharacteristic
69C8×C101C2311yescharacteristic
70#11717579C2312yes—
71C22×C101—21no—
72C22×C101—21no—
73C22×C101C2×D411yescharacteristic
74C2×D101—22no—
75C2×D101—82no—
76C2×D101—81no—
77C2×D101C2×D412yes—
78C4×C101—21no—
79C4×C101—21no—
80C4×C101C2×D411yescharacteristic
81C4×C101C2411yescharacteristic
82Dic101—22no—
83Dic101C2×D412yes—
84C2×C101—21no—
85C2×C101—41no—
86C2×C101—41no—
87C2×C101C22×D411yescharacteristic
88D101—22no—
89D101—42no—
90C101#57711yescharacteristic, complemented, Sylow
91#577—1011nomaximal, Sylow
922−1+4—1011no—
93H(5,𝔽2)—1011no—
94#137—1011no—
95#137—1012no—
96AGL(1,ℤ/8)—1011no—
97AGL(1,ℤ/8)—1012no—
98#135—1012no—
99#135D10111yescharacteristic, complemented
100C2×SD16—1012no—
101C2×SD16—1011no—
102#131—1011no—
103#41—1011no—
104#41—1012no—
105#41—1012no—
106#41—2021no—
107#41—2021no—
108#41—2022no—
109#41C2×D10111yescharacteristic
110#41C2×D10111yescharacteristic, complemented
111C2×Q8—1012no—
112C2×Q8—1011no—
113C2×Q8—2021no—
114C2×D4—1012no—
115C2×D4—1011no—
116C2×D4—2021no—
117C2×D4—2022no—
118Q16—1012no—
119Q16C2×D10111yescharacteristic, complemented
120SD16—1012no—
121SD16—1012no—
122SD16—1012no—
123SD16—1012no—
124SD16C2×D10111yescharacteristic, complemented
125SD16C2×D10111yescharacteristic, complemented
126D8—1012no—
127D8C2×D10111yescharacteristic, complemented
128M16—1011no—
129M16—1012no—
130C2×C8—1012no—
131C2×C8C2×D10111yescharacteristic, complemented
132C23—2022no—
133C23—2021no—
134Q8—1011no—
135Q8—1012no—
136Q8—2022no—
137Q8—2021no—
138Q8C22×D10111yescharacteristic
139Q8C22×D10111yescharacteristic
140D4—21no—
141D4—21no—
142D4—1012no—
143D4—1011no—
144D4—1012no—
145D4—2022no—
146D4—2022no—
147D4—2022no—
148D4—2021no—
149D4C22×D10111yescharacteristic
150D4C22×D10111yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—1012no—
154C2×C4—2022no—
155C2×C4—2022no—
156C2×C4—2022no—
157C2×C4—2021no—
158C2×C4C22×D10111yescharacteristic
159C8—1012no—
160C8C22×D10111yescharacteristic
161C8C22×D10111yescharacteristic
162C22—21no—
163C22—21no—
164C22—8081no—
165C22—8082no—
166C22—1012no—
167C22—2022no—
168C22D4×D10111yescharacteristic
169C4—21no—
170C4—21no—
171C4—1012no—
172C4—2022no—
173C4D4×D10111yescharacteristic
174C4C23×D10111yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—4042no—
179C2—2022no—
180C2C2×D4×D10111yescharacteristic
subgroupG/H
centerC2C2×D4×D101
commutatorC4×C101C24
FrattiniC4C23×D101
Fitting#135×C101C2
socleC2×C101C22×D4
hypercenter#135D101
hypocenterC101#577
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #15692302C2semidirect
2. #15692301C2semidirect
3. #15692287C2semidirect
4. #15692285C2semidirect
5. #15692280C2semidirect
6. #15692279C2semidirect
7. #15692276C2semidirect
8. C2×#13108063C2semidirect
9. SD16×D101C2semidirect
10. #15692261C2semidirect
11. #135×C101C2semidirect
17. #13108073C22semidirect
19. C2×Dic202C22semidirect
20. Q8×D101C22semidirect
25. #13108064C22semidirect
26. #13108063C22semidirect
27. #13108063C22semidirect
28. #13108062C22semidirect
29. #13108061C22semidirect
30. #13108059C22semidirect
31. #13108058C22semidirect
32. #13108057C22semidirect
33. C8×D101C22semidirect
35. #41×C101C22semidirect
36. Q16×C101C22semidirect
37. SD16×C101C22semidirect
38. SD16×C101C22semidirect
39. D8×C101C22semidirect
40. C2×C8×C101C22semidirect
90. C101#577semidirect
99. #135D101semidirect
110. #41C2×D101semidirect
119. Q16C2×D101semidirect
124. SD16C2×D101semidirect
125. SD16C2×D101semidirect
127. D8C2×D101semidirect
131. C2×C8C2×D101semidirect