Finite Group Databasebeta

← #27196486

Subgroups — #27196486

Order 13184.

246 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 75 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#20267834C212yesmaximal
2#20267660C211yesmaximal, characteristic
3#20267560C211yesmaximal, characteristic
4#20267550C212yesmaximal
5#544×C103C211yesmaximal, characteristic
6C2×#13110089C2212yes—
7C2×C4⋊Dic103C2211yescharacteristic
8C2×Dic103⋊C4—22no—
9C2×C4×Dic103C2211yescharacteristic
10#15692954—22no—
11#15692952—22no—
12C4⋊Q8×C103—22no—
13#125×C103—22no—
14C22⋊Q8×C103—22no—
15#117×C103C2212yes—
16C2×C4⋊C4×C103C2211yescharacteristic
17C22×Dic103—21no—
18C22×Dic103—21no—
19#13110089—22no—
20#13110089Q814yescomplemented
21C2×C103⋊C8—22no—
22C4⋊Dic103—22no—
23Dic103⋊C4—44no—
24C4×Dic103—21no—
25C4×Dic103Q812yescomplemented
26C2×Q8×C103—22no—
27C22×C4×C103D412yes—
28C22×C4×C103C2311yescharacteristic
29C4⋊C4×C103—22no—
30C4⋊C4×C103—24no—
31C4⋊C4×C103—22no—
32C4⋊C4×C103D412yes—
33C4⋊C4×C103D412yes—
34C22⋊C4×C103—22no—
35C42×C103—22no—
36C23×C103C2×D411yescharacteristic
37Q8×C103—82no—
38C2×C4×C103—22no—
39C2×C4×C103—22no—
40C2×C4×C103—22no—
41C2×C4×C103—42no—
42C2×C4×C103C2×D412yes—
43C2×C4×C103C2×Q812yes—
44C2×C4×C103C2×Q811yescharacteristic
45C2×C4×C103#4111yescharacteristic
46C2×Dic103—22no—
47C2×Dic103—22no—
48C2×Dic103—22no—
49C2×Dic103—42no—
50C2×Dic103—41no—
51C103⋊C8—24no—
52C22×C103—21no—
53C22×C103—21no—
54C22×C103#12011yescharacteristic
55C22×C103C22⋊Q811yescharacteristic
56C22×C103C4⋊Q811yescharacteristic
57C4×C103—42no—
58C4×C103—42no—
59C4×C103—42no—
60C4×C103C22⋊Q812yes—
61C4×C103C4⋊Q812yes—
62Dic103—24no—
63Dic103—81no—
64C2×C103—21no—
65C2×C103—21no—
66C2×C103#39511yescharacteristic
67C2×C103#45311yescharacteristic
68C2×C103#45611yescharacteristic
69#2060—1031nomaximal, Sylow
70C103#206011yescharacteristic, complemented, Sylow
71#544D10311yescharacteristic
72#428—1032no—
73#384—1031no—
74#343—1031no—
75#339—1032no—
76C2×M16—1032no—
77C4⋊Q8—22no—
78#125—22no—
79C22⋊Q8—22no—
80#117C2×D10312yes—
81C2×C4⋊C4—1031no—
82C2×C4⋊C4—2062no—
83C2×C4⋊C4C2×D10311yescharacteristic
84C2×C42—1031no—
85#107—2062no—
86#106—2062no—
87C2×Q8—22no—
88C22×C4—2061no—
89C22×C4—2061no—
90C22×C4C22⋊D10312yes—
91C22×C4C22×D10311yescharacteristic
92M16—1034no—
93M16—2062no—
94C2×C8—2062no—
95C4⋊C4—22no—
96C4⋊C4—24no—
97C4⋊C4—22no—
98C4⋊C4—4124no—
99C4⋊C4—2062no—
100C4⋊C4C22⋊D10312yes—
101C4⋊C4C22⋊D10312yes—
102C22⋊C4—22no—
103C42—22no—
104C42—1032no—
105C42—2061no—
106C23C2×C22⋊D10311yescharacteristic
107Q8—82no—
108C2×C4—22no—
109C2×C4—22no—
110C2×C4—22no—
111C2×C4—42no—
112C2×C4—4122no—
113C2×C4—4121no—
114C2×C4—2062no—
115C2×C4—2062no—
116C2×C4—2062no—
117C2×C4C2×C22⋊D10312yes—
118C2×C4Q8×D10312yes—
119C2×C4Q8×D10311yescharacteristic
120C2×C4#1311010611yescharacteristic
121C8—2064no—
122C22—21no—
123C22—21no—
124C22#1569299011yescharacteristic
125C22#1569299711yescharacteristic
126C22#1569301911yescharacteristic
127C4—42no—
128C4—42no—
129C4—42no—
130C4—8241no—
131C4—2064no—
132C4#1569299712yes—
133C4#1569301912yes—
134C2—21no—
135C2—21no—
136C2#2026771011yescharacteristic
137C2#2026795911yescharacteristic
138C2#2026797411yescharacteristic
subgroupG/H
centerC22#15692990
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#544×C103C2
socleC22×C103#120
prime radicalC23×C103C2×D4
hypercenter#544D103
hypocenterC103#2060
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
20. #13110089Q8semidirect
25. C4×Dic103Q8semidirect
70. C103#2060semidirect

Maximal subgroups

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

subgroupindex
#202678342
#202676602
#202675602
#202675502
#544×C1032
#2060103