Finite Group Databasebeta

← #20265976

Subgroups — #20265976

Order 6464.

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

normal subgroups only

This group has 262 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
1C2×#13108075C211yesmaximal, characteristic, complemented
2#41×D101C211yesmaximal, characteristic, complemented
3#15692287C212yesmaximal, complemented
4#15692286C211yesmaximal, characteristic, complemented
5#15692283C211yesmaximal, characteristic, complemented
6#15692282C212yesmaximal, complemented
7#15692280C211yesmaximal, characteristic, complemented
8#15692278C212yesmaximal, complemented
9#15692276C212yesmaximal, complemented
10M16×D101C211yesmaximal, characteristic, complemented
11#137×C101C211yesmaximal, characteristic, complemented
12#13108075—21no—
13#13108075—21no—
14#13108075C2212yes—
15#13108075C2211yescharacteristic, complemented
16#13108075C2212yescomplemented
17#13108074—21no—
18#13108074C2211yescharacteristic
19#13108073—21no—
20#13108073C2211yescharacteristic, complemented
21Q8×D101C2211yescharacteristic, complemented
22C2×D404—21no—
23C2×D404C2211yescharacteristic, complemented
24D4×D101—21no—
25D4×D101C2211yescharacteristic, complemented
26C2×C4×D101—21no—
27C2×C4×D101—21no—
28C2×C4×D101C2211yescharacteristic
29#13108064C2212yescomplemented
30#13108063C2212yescomplemented
31#13108061C2212yescomplemented
32#13108061C2212yescomplemented
33D808C2212yescomplemented
34#13108059C2212yescomplemented
35#13108058C2211yescharacteristic, complemented
36#13108057C2212yescomplemented
37C8×D101C2212yescomplemented
38#41×C101C2211yescharacteristic
39C2×Q8×C101C2211yescharacteristic, complemented
40Q16×C101C2212yescomplemented
41SD16×C101C2212yescomplemented
42M16×C101C2211yescharacteristic, complemented
43C22×D101—21no—
44C22×D101—21no—
45C22×D101D411yescharacteristic
46Q8×C101—21no—
47Q8×C101C2312yes—
48Q8×C101C2311yescharacteristic
49D4×C101—21no—
50D4×C101C2311yescharacteristic
51C2×C4×C101—21no—
52C2×C4×C101—21no—
53C2×C4×C101C2311yescharacteristic
54C22⋊D101—21no—
55C22⋊D101—21no—
56C22⋊D101—21no—
57C2×Dic101—21no—
58C2×Dic101D411yescharacteristic
59D404—21no—
60D404—22no—
61D404—22no—
62D404—21no—
63D404C2312yes—
64D404C2311yescharacteristic
65C4×D101—21no—
66C4×D101—21no—
67C4×D101—21no—
68C4×D101—22no—
69C4×D101—22no—
70C4×D101D411yescharacteristic
71C4×D101D411yescharacteristic
72C4×D101C2311yescharacteristic
73C4×D101C2311yescharacteristic
74Dic202—21no—
75Dic202C2311yescharacteristic
76C8×C101C2312yes—
77#11717579C2312yes—
78C22×C101—21no—
79C22×C101C2×D411yescharacteristic
80C2×D101—22no—
81C2×D101—21no—
82C2×D101—41no—
83C2×D101—42no—
84C2×D101—42no—
85C2×D101C2×D411yescharacteristic
86C2×D101C2×D411yescharacteristic
87C4×C101—21no—
88C4×C101—22no—
89C4×C101C2×D411yescharacteristic
90C4×C101C2411yescharacteristic
91Dic101—21no—
92Dic101C2×D411yescharacteristic
93Dic101C2×D411yescharacteristic
94C2×C101—21no—
95C2×C101—41no—
96C2×C101C22×D411yescharacteristic
97D101—21no—
98D101—21no—
99D101—42no—
100D101—41no—
101C101#57511yescharacteristic, complemented, Sylow
102#575—1011nomaximal, Sylow
103C2×#41—1011no—
104C2×#41—1011no—
105#137—1011no—
106#137—1012no—
107#137D10111yescharacteristic, complemented
108AGL(1,ℤ/8)—1011no—
109AGL(1,ℤ/8)—1012no—
110AGL(1,ℤ/8)—1011no—
111#135—1012no—
112#135—1012no—
113C2×M16—1011no—
114#41—1012no—
115#41—1011no—
116#41—1012no—
117#41—1011no—
118#41—1011no—
119#41—2021no—
120#41—2021no—
121#41—2021no—
122#41—2021no—
123#41C2×D10111yescharacteristic
124C2×Q8—1011no—
125C2×Q8C2×D10111yescharacteristic, complemented
126C2×D4—1011no—
127C2×D4—1011no—
128C2×D4—2021no—
129C2×D4—2021no—
130C22×C4—1011no—
131C22×C4—2021no—
132C22×C4—2021no—
133Q16—1012no—
134Q16C2×D10112yescomplemented
135SD16—1012no—
136SD16—1012no—
137SD16—1012no—
138SD16C2×D10112yescomplemented
139D8—1012no—
140D8—1012no—
141M16—1011no—
142M16—1012no—
143M16C2×D10111yescharacteristic, complemented
144C2×C8—1012no—
145C23—1011no—
146C23—2021no—
147C23—2021no—
148Q8—21no—
149Q8—1011no—
150Q8—2021no—
151Q8C22×D10111yescharacteristic
152Q8C22×D10112yes—
153D4—21no—
154D4—1012no—
155D4—1011no—
156D4—2021no—
157D4—2022no—
158D4—2022no—
159D4—2021no—
160D4—2021no—
161D4—2021no—
162D4—2021no—
163D4C22×D10111yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—1011no—
167C2×C4—1011no—
168C2×C4—1011no—
169C2×C4—1011no—
170C2×C4—1011no—
171C2×C4—2021no—
172C2×C4—2022no—
173C2×C4—2022no—
174C2×C4—2021no—
175C2×C4—2021no—
176C2×C4—2021no—
177C2×C4C22×D10111yescharacteristic
178C8—1012no—
179C8C22×D10112yes—
180C22—21no—
181C22—1011no—
182C22—1011no—
183C22—4042no—
184C22—4041no—
185C22—4042no—
186C22—2022no—
187C22—2021no—
188C22D4×D10111yescharacteristic
189C4—21no—
190C4—22no—
191C4—1011no—
192C4—1011no—
193C4—2021no—
194C4D4×D10111yescharacteristic
195C4C23×D10111yescharacteristic
196C2—21no—
197C2—41no—
198C2—4042no—
199C2—4041no—
200C2—2021no—
201C2—2021no—
202C2C2×D4×D10111yescharacteristic
subgroupG/H
centerC2C2×D4×D101
commutatorC4×C101C24
FrattiniC4C23×D101
Fitting#137×C101C2
socleC2×C101C22×D4
hypercenter#137D101
hypocenterC101#575
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C2×#13108075C2semidirect
2. #41×D101C2semidirect
3. #15692287C2semidirect
4. #15692286C2semidirect
5. #15692283C2semidirect
6. #15692282C2semidirect
7. #15692280C2semidirect
8. #15692278C2semidirect
9. #15692276C2semidirect
10. M16×D101C2semidirect
11. #137×C101C2semidirect
15. #13108075C22semidirect
16. #13108075C22semidirect
20. #13108073C22semidirect
21. Q8×D101C22semidirect
23. C2×D404C22semidirect
25. D4×D101C22semidirect
29. #13108064C22semidirect
30. #13108063C22semidirect
31. #13108061C22semidirect
32. #13108061C22semidirect
33. D808C22semidirect
34. #13108059C22semidirect
35. #13108058C22semidirect
36. #13108057C22semidirect
37. C8×D101C22semidirect
39. C2×Q8×C101C22semidirect
40. Q16×C101C22semidirect
41. SD16×C101C22semidirect
42. M16×C101C22semidirect
101. C101#575semidirect
107. #137D101semidirect
125. C2×Q8C2×D101semidirect
134. Q16C2×D101semidirect
138. SD16C2×D101semidirect
143. M16C2×D101semidirect