Finite Group Databasebeta

← #20268590

Subgroups — #20268590

Order 6592.

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×#13110106C211yesmaximal, characteristic, complemented
2#41×D103C211yesmaximal, characteristic, complemented
3#15693053C212yesmaximal, complemented
4#15693052C211yesmaximal, characteristic, complemented
5#15693049C211yesmaximal, characteristic, complemented
6#15693048C212yesmaximal, complemented
7#15693046C211yesmaximal, characteristic, complemented
8#15693044C212yesmaximal, complemented
9#15693042C212yesmaximal, complemented
10M16×D103C211yesmaximal, characteristic, complemented
11#137×C103C211yesmaximal, characteristic, complemented
12#13110106—21no—
13#13110106—21no—
14#13110106C2212yes—
15#13110106C2211yescharacteristic, complemented
16#13110106C2212yescomplemented
17#13110105—21no—
18#13110105C2211yescharacteristic
19#13110104—21no—
20#13110104C2211yescharacteristic, complemented
21Q8×D103C2211yescharacteristic, complemented
22C2×D412—21no—
23C2×D412C2211yescharacteristic, complemented
24D4×D103—21no—
25D4×D103C2211yescharacteristic, complemented
26C2×C4×D103—21no—
27C2×C4×D103—21no—
28C2×C4×D103C2211yescharacteristic
29#13110095C2212yescomplemented
30#13110094C2212yescomplemented
31#13110092C2212yescomplemented
32#13110092C2212yescomplemented
33D824C2212yescomplemented
34#13110090C2212yescomplemented
35#13110089C2211yescharacteristic, complemented
36#13110088C2212yescomplemented
37C8×D103C2212yescomplemented
38#41×C103C2211yescharacteristic
39C2×Q8×C103C2211yescharacteristic, complemented
40Q16×C103C2212yescomplemented
41SD16×C103C2212yescomplemented
42M16×C103C2211yescharacteristic, complemented
43C22×D103—21no—
44C22×D103—21no—
45C22×D103D411yescharacteristic
46Q8×C103—21no—
47Q8×C103C2312yes—
48Q8×C103C2311yescharacteristic
49D4×C103—21no—
50D4×C103C2311yescharacteristic
51C2×C4×C103—21no—
52C2×C4×C103—21no—
53C2×C4×C103C2311yescharacteristic
54C22⋊D103—21no—
55C22⋊D103—21no—
56C22⋊D103—21no—
57C2×Dic103—21no—
58C2×Dic103D411yescharacteristic
59D412—21no—
60D412—22no—
61D412—22no—
62D412—21no—
63D412C2312yes—
64D412C2311yescharacteristic
65C4×D103—21no—
66C4×D103—21no—
67C4×D103—21no—
68C4×D103—22no—
69C4×D103—22no—
70C4×D103D411yescharacteristic
71C4×D103D411yescharacteristic
72C4×D103C2311yescharacteristic
73C4×D103C2311yescharacteristic
74Dic206—21no—
75Dic206C2311yescharacteristic
76C8×C103C2312yes—
77C103⋊C8C2312yes—
78C22×C103—21no—
79C22×C103C2×D411yescharacteristic
80C2×D103—22no—
81C2×D103—21no—
82C2×D103—41no—
83C2×D103—42no—
84C2×D103—42no—
85C2×D103C2×D411yescharacteristic
86C2×D103C2×D411yescharacteristic
87C4×C103—21no—
88C4×C103—22no—
89C4×C103C2×D411yescharacteristic
90C4×C103C2411yescharacteristic
91Dic103—21no—
92Dic103C2×D411yescharacteristic
93Dic103C2×D411yescharacteristic
94C2×C103—21no—
95C2×C103—41no—
96C2×C103C22×D411yescharacteristic
97D103—21no—
98D103—21no—
99D103—42no—
100D103—41no—
101C103#57511yescharacteristic, complemented, Sylow
102#575—1031nomaximal, Sylow
103C2×#41—1031no—
104C2×#41—1031no—
105#137—1031no—
106#137—1032no—
107#137D10311yescharacteristic, complemented
108AGL(1,ℤ/8)—1031no—
109AGL(1,ℤ/8)—1032no—
110AGL(1,ℤ/8)—1031no—
111#135—1032no—
112#135—1032no—
113C2×M16—1031no—
114#41—1032no—
115#41—1031no—
116#41—1032no—
117#41—1031no—
118#41—1031no—
119#41—2061no—
120#41—2061no—
121#41—2061no—
122#41—2061no—
123#41C2×D10311yescharacteristic
124C2×Q8—1031no—
125C2×Q8C2×D10311yescharacteristic, complemented
126C2×D4—1031no—
127C2×D4—1031no—
128C2×D4—2061no—
129C2×D4—2061no—
130C22×C4—1031no—
131C22×C4—2061no—
132C22×C4—2061no—
133Q16—1032no—
134Q16C2×D10312yescomplemented
135SD16—1032no—
136SD16—1032no—
137SD16—1032no—
138SD16C2×D10312yescomplemented
139D8—1032no—
140D8—1032no—
141M16—1031no—
142M16—1032no—
143M16C2×D10311yescharacteristic, complemented
144C2×C8—1032no—
145C23—1031no—
146C23—2061no—
147C23—2061no—
148Q8—21no—
149Q8—1031no—
150Q8—2061no—
151Q8C22×D10311yescharacteristic
152Q8C22×D10312yes—
153D4—21no—
154D4—1032no—
155D4—1031no—
156D4—2061no—
157D4—2062no—
158D4—2062no—
159D4—2061no—
160D4—2061no—
161D4—2061no—
162D4—2061no—
163D4C22×D10311yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—1031no—
167C2×C4—1031no—
168C2×C4—1031no—
169C2×C4—1031no—
170C2×C4—1031no—
171C2×C4—2061no—
172C2×C4—2062no—
173C2×C4—2062no—
174C2×C4—2061no—
175C2×C4—2061no—
176C2×C4—2061no—
177C2×C4C22×D10311yescharacteristic
178C8—1032no—
179C8C22×D10312yes—
180C22—21no—
181C22—1031no—
182C22—1031no—
183C22—4122no—
184C22—4121no—
185C22—4122no—
186C22—2062no—
187C22—2061no—
188C22D4×D10311yescharacteristic
189C4—21no—
190C4—22no—
191C4—1031no—
192C4—1031no—
193C4—2061no—
194C4D4×D10311yescharacteristic
195C4C23×D10311yescharacteristic
196C2—21no—
197C2—41no—
198C2—4122no—
199C2—4121no—
200C2—2061no—
201C2—2061no—
202C2C2×D4×D10311yescharacteristic
subgroupG/H
centerC2C2×D4×D103
commutatorC4×C103C24
FrattiniC4C23×D103
Fitting#137×C103C2
socleC2×C103C22×D4
hypercenter#137D103
hypocenterC103#575
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C2×#13110106C2semidirect
2. #41×D103C2semidirect
3. #15693053C2semidirect
4. #15693052C2semidirect
5. #15693049C2semidirect
6. #15693048C2semidirect
7. #15693046C2semidirect
8. #15693044C2semidirect
9. #15693042C2semidirect
10. M16×D103C2semidirect
11. #137×C103C2semidirect
15. #13110106C22semidirect
16. #13110106C22semidirect
20. #13110104C22semidirect
21. Q8×D103C22semidirect
23. C2×D412C22semidirect
25. D4×D103C22semidirect
29. #13110095C22semidirect
30. #13110094C22semidirect
31. #13110092C22semidirect
32. #13110092C22semidirect
33. D824C22semidirect
34. #13110090C22semidirect
35. #13110089C22semidirect
36. #13110088C22semidirect
37. C8×D103C22semidirect
39. C2×Q8×C103C22semidirect
40. Q16×C103C22semidirect
41. SD16×C103C22semidirect
42. M16×C103C22semidirect
101. C103#575semidirect
107. #137D103semidirect
125. C2×Q8C2×D103semidirect
134. Q16C2×D103semidirect
138. SD16C2×D103semidirect
143. M16C2×D103semidirect