Finite Group Databasebeta

← #27205791

Subgroups — #27205791

Order 13184.

386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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#20268395C212yesmaximal, complemented
2#20268193C211yesmaximal, characteristic, complemented
3#20268155C212yesmaximal, complemented
4#20268041C212yesmaximal, complemented
5#20268024C212yesmaximal, complemented
6#20267903C212yesmaximal, complemented
7D8×Dic103C212yesmaximal, complemented
8#20267745C211yesmaximal, characteristic, complemented
9#493×C103C211yesmaximal, characteristic, complemented
10C2×#13110088C2211yescharacteristic
11C2×C8×D103C2211yescharacteristic
12#15693013C2212yes—
13#15693002—24no—
14#15692993—24no—
15#15692992C2214yes—
16D4×Dic103C2214yes—
17#15692978C2211yescharacteristic
18#15692955C2212yes—
19#15692953C2212yes—
20#15692942C2214yes—
21#15692942C2214yes—
22#15692932C2211yescharacteristic
23#15692931C2211yescharacteristic
24C8×Dic103C2211yescharacteristic
25C2×D8×C103C2212yes—
26C2×D8×C103C2212yes—
27#127×C103C2212yes—
28C4×C8×C103C2211yescharacteristic
29C2×C22⋊D103—24no—
30C22×Dic103—24no—
31C2×C4×D103C2311yescharacteristic
32#13110088—22no—
33C2×C103⋊C8C2311yescharacteristic
34C2×C103⋊C8C2311yescharacteristic
35C8×D103—22no—
36C4⋊Dic103C2314yes—
37Dic103⋊C4—24no—
38Dic103⋊C4D412yes—
39C22⋊Dic103—24no—
40C22⋊Dic103—24no—
41(C2×D103)⋊C4D412yes—
42C4×Dic103C2311yescharacteristic
43C2×D4×C103—24no—
44C2×D4×C103C2314yes—
45D8×C103—24no—
46D8×C103—24no—
47C2×C8×C103C2311yescharacteristic
48C2×C8×C103C2311yescharacteristic
49C42×C103C2311yescharacteristic
50C23×C103—24no—
51C22×D103C2×D411yescharacteristic
52D4×C103—24no—
53D4×C103—24no—
54D4×C103—84no—
55C2×C4×C103C2×D412yes—
56C2×C4×C103C2411yescharacteristic
57C22⋊D103—84no—
58C2×Dic103—24no—
59C2×Dic103—84no—
60C2×Dic103C2×D412yes—
61C2×Dic103C2×D411yescharacteristic
62C4×D103—21no—
63C4×D103—21no—
64C8×C103#4112yes—
65C8×C103#4112yes—
66C103⋊C8—21no—
67C103⋊C8—21no—
68C22×C103—44no—
69C22×C103—44no—
70C22×C103—44no—
71C22×C103C22×D411yescharacteristic
72C2×D103—21no—
73C2×D103—22no—
74C4×C103—22no—
75C4×C103C2×#4111yescharacteristic
76C4×C103C2×#4111yescharacteristic
77Dic103—21no—
78Dic103—22no—
79Dic103—44no—
80C2×C103—84no—
81C2×C103#53211yescharacteristic
82C2×C103#57612yes—
83D103—41no—
84#3176—1031nomaximal, Sylow
85C103#317611yescharacteristic, complemented, Sylow
86#540—1032no—
87#499—1031no—
88#493D10311yescharacteristic, complemented
89#490—1032no—
90#469—1032no—
91#466—1032no—
92#442—1032no—
93C4×D8—1032no—
94#405—1031no—
95C2×D8C2×D10312yes—
96C2×D8C2×D10312yes—
97C2×M16—1031no—
98C22×C8—1031no—
99#127C2×D10312yes—
100#125—1032no—
101#123—2064no—
102#121—1034no—
103#121—2064no—
104C4×D4—1034no—
105#117—1031no—
106#107—1032no—
107#106—1032no—
108#102—1034no—
109#102—1034no—
110#97—1031no—
111#97—1031no—
112C4×C8—1031no—
113C4×C8C2×D10311yescharacteristic
114C2×D4—24no—
115C2×D4—2064no—
116C2×D4C22×D10314yes—
117C22×C4—1031no—
118C22×C4—2064no—
119D8—24no—
120D8—24no—
121M16—2062no—
122C2×C8—1031no—
123C2×C8—1031no—
124C2×C8—2062no—
125C2×C8C22×D10311yescharacteristic
126C2×C8C22×D10311yescharacteristic
127C4⋊C4—1032no—
128C4⋊C4—1034no—
129C4⋊C4—2064no—
130C22⋊C4—1032no—
131C22⋊C4—2064no—
132C22⋊C4—2064no—
133C42—1031no—
134C42C22×D10311yescharacteristic
135C23—24no—
136C23—1031no—
137D4—24no—
138D4—24no—
139D4—84no—
140D4—8244no—
141C2×C4—8244no—
142C2×C4—1032no—
143C2×C4—1031no—
144C2×C4—2064no—
145C2×C4—2061no—
146C2×C4—2061no—
147C2×C4D4×D10312yes—
148C2×C4C23×D10311yescharacteristic
149C8—2061no—
150C8—2061no—
151C8#1311010412yes—
152C8#1311010412yes—
153C22—44no—
154C22—44no—
155C22—44no—
156C22—2062no—
157C22—2061no—
158C22C2×D4×D10311yescharacteristic
159C4—22no—
160C4—4124no—
161C4—2062no—
162C4—2061no—
163C4C2×#1311010411yescharacteristic
164C4C2×#1311010411yescharacteristic
165C2—84no—
166C2—4121no—
167C2#2026833911yescharacteristic
168C2#2026859212yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#493×C103C2
socleC22×C103C22×D4
hypercenter#493D103
hypocenterC103#3176
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #20268395C2semidirect
2. #20268193C2semidirect
3. #20268155C2semidirect
4. #20268041C2semidirect
5. #20268024C2semidirect
6. #20267903C2semidirect
7. D8×Dic103C2semidirect
8. #20267745C2semidirect
9. #493×C103C2semidirect
85. C103#3176semidirect
88. #493D103semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202683952
#202681932
#202681552
#202680412
#202680242
#202679032
D8×Dic1032
#202677452
#493×C1032
#3176103