Finite Group Databasebeta

← #123×D103 #20268291

Subgroups — #123×D103 #20268291

Order 6592.

342 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 111 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×D4×D103C211yesmaximal, characteristic
2C22×C4×D103C211yesmaximal, characteristic, complemented
3#15693006C212yesmaximal, complemented
4#15693005C211yesmaximal, characteristic, complemented
5#15693004C211yesmaximal, characteristic, complemented
6#15693003C212yesmaximal, complemented
7#15693002C211yesmaximal, characteristic, complemented
8C4⋊C4×D103C212yesmaximal, complemented
9C22⋊C4×D103C212yesmaximal, complemented
10C22⋊C4×D103C211yesmaximal, characteristic, complemented
11#123×C103C211yesmaximal, characteristic, complemented
12C23×D103C2211yescharacteristic
13C23×D103C2211yescharacteristic
14C2×D412C2211yescharacteristic
15C2×C22⋊D103C2211yescharacteristic
16C2×C22⋊D103C2211yescharacteristic
17D4×D103—24no—
18C22×Dic103C2211yescharacteristic, complemented
19C2×C4×D103—24no—
20C2×C4×D103C2211yescharacteristic
21C2×C4×D103C2212yes—
22C2×C4×D103C2212yes—
23C2×C4×D103C2212yescomplemented
24C4⋊Dic103C2212yescomplemented
25Dic103⋊C4C2212yescomplemented
26Dic103⋊C4C2212yescomplemented
27C22⋊Dic103C2212yescomplemented
28C22⋊Dic103C2211yescharacteristic, complemented
29(C2×D103)⋊C4C2212yescomplemented
30(C2×D103)⋊C4C2212yescomplemented
31(C2×D103)⋊C4C2212yescomplemented
32C2×D4×C103C2211yescharacteristic
33C22×C4×C103C2211yescharacteristic, complemented
34C4⋊C4×C103C2212yescomplemented
35C22⋊C4×C103C2212yescomplemented
36C22⋊C4×C103C2211yescharacteristic, complemented
37C23×C103C2311yescharacteristic
38C23×C103C2311yescharacteristic
39C22×D103—24no—
40C22×D103—22no—
41C22×D103—24no—
42C22×D103D414yes—
43C22×D103C2311yescharacteristic
44C22×D103C2311yescharacteristic
45C22×D103C2311yescharacteristic
46D4×C103—22no—
47C2×C4×C103—22no—
48C2×C4×C103C2312yes—
49C2×C4×C103C2312yes—
50C2×C4×C103C2311yescharacteristic
51C22⋊D103—22no—
52C22⋊D103—22no—
53C2×Dic103—22no—
54C2×Dic103C2312yes—
55C2×Dic103C2312yes—
56C2×Dic103C2311yescharacteristic
57D412—22no—
58C4×D103—24no—
59C4×D103—24no—
60C4×D103—22no—
61C4×D103—24no—
62C22×C103—22no—
63C22×C103—21no—
64C22×C103—22no—
65C22×C103C2×D412yes—
66C22×C103C2411yescharacteristic
67C2×D103—22no—
68C2×D103—28no—
69C2×D103—21no—
70C2×D103—22no—
71C2×D103—44no—
72C2×D103C2×D412yes—
73C2×D103C2×D412yes—
74C2×D103#4114yes—
75C4×C103—22no—
76C4×C103—21no—
77C4×C103—22no—
78Dic103—22no—
79Dic103—21no—
80Dic103—22no—
81C2×C103—22no—
82C2×C103—41no—
83C2×C103C22×D411yescharacteristic
84C2×C103C2×#4112yes—
85D103—22no—
86D103—41no—
87D103#12314yesdirect product factor
88C103C2×#12311yescharacteristic, complemented, Sylow
89C2×#123—1031nomaximal, Sylow
90C22×D4—1031no—
91C23×C4—1031no—
92#123—1031no—
93#123—1031no—
94#123—1032no—
95#123—1032no—
96#123—1031no—
97#123D10311yescharacteristic, direct product factor
98C2×C4⋊C4—1032no—
99C2×C22⋊C4—1031no—
100C2×C22⋊C4—1032no—
101C24—1031no—
102C24—1031no—
103C2×D4—1031no—
104C2×D4—1031no—
105C2×D4—1031no—
106C2×D4—2064no—
107C2×D4C2×D10311yescharacteristic
108C22×C4—1031no—
109C22×C4—1032no—
110C22×C4—1032no—
111C22×C4—1031no—
112C22×C4—1032no—
113C22×C4—2064no—
114C22×C4C2×D10311yescharacteristic, complemented
115C4⋊C4—1032no—
116C4⋊C4—1032no—
117C4⋊C4—1032no—
118C4⋊C4C2×D10312yescomplemented
119C22⋊C4—1031no—
120C22⋊C4—1032no—
121C22⋊C4—1032no—
122C22⋊C4—1032no—
123C22⋊C4—1032no—
124C22⋊C4C2×D10311yescharacteristic, complemented
125C22⋊C4C2×D10312yescomplemented
126C23—1031no—
127C23—1034no—
128C23—1031no—
129C23—1031no—
130C23—2062no—
131C23—2064no—
132C23—2064no—
133C23C22×D10311yescharacteristic
134C23C22×D10311yescharacteristic
135D4—22no—
136D4—2062no—
137D4—2062no—
138D4—2062no—
139C2×C4—22no—
140C2×C4—1032no—
141C2×C4—1032no—
142C2×C4—1031no—
143C2×C4—2064no—
144C2×C4—2064no—
145C2×C4—2062no—
146C2×C4—2064no—
147C2×C4—2062no—
148C2×C4C22×D10312yes—
149C2×C4C22×D10312yes—
150C2×C4C22×D10311yescharacteristic
151C22—22no—
152C22—21no—
153C22—22no—
154C22—1032no—
155C22—1034no—
156C22—1032no—
157C22—4124no—
158C22—2068no—
159C22—2061no—
160C22—2062no—
161C22—2062no—
162C22D4×D10312yes—
163C22C23×D10311yescharacteristic
164C4—22no—
165C4—21no—
166C4—22no—
167C4—2062no—
168C4—2061no—
169C4—2062no—
170C2—22no—
171C2—41no—
172C2—1034no—
173C2—4121no—
174C2—2062no—
175C2C2×D4×D10311yescharacteristic
176C2#41×D10312yes—
subgroupG/H
center, FrattiniC22C23×D103
commutator, socleC22×C103C24
Fitting#123×C103C2
hypercenter#123D103
hypocenterC103C2×#123
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
2. C22×C4×D103C2semidirect
3. #15693006C2semidirect
4. #15693005C2semidirect
5. #15693004C2semidirect
6. #15693003C2semidirect
7. #15693002C2semidirect
8. C4⋊C4×D103C2semidirect
9. C22⋊C4×D103C2semidirect
10. C22⋊C4×D103C2semidirect
11. #123×C103C2semidirect
18. C22×Dic103C22semidirect
23. C2×C4×D103C22semidirect
24. C4⋊Dic103C22semidirect
25. Dic103⋊C4C22semidirect
26. Dic103⋊C4C22semidirect
27. C22⋊Dic103C22semidirect
28. C22⋊Dic103C22semidirect
29. (C2×D103)⋊C4C22semidirect
30. (C2×D103)⋊C4C22semidirect
31. (C2×D103)⋊C4C22semidirect
33. C22×C4×C103C22semidirect
34. C4⋊C4×C103C22semidirect
35. C22⋊C4×C103C22semidirect
36. C22⋊C4×C103C22semidirect
87. D103#123direct (N × H)
88. C103C2×#123semidirect
97. #123D103direct (N × H)
114. C22×C4C2×D103semidirect
118. C4⋊C4C2×D103semidirect
124. C22⋊C4C2×D103semidirect
125. C22⋊C4C2×D103semidirect