Finite Group Databasebeta

← #27196495

Subgroups — #27196495

Order 13184.

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

normal subgroups only

This group has 230 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#20268422C211yesmaximal, characteristic
2#20267833C212yesmaximal
3#20267656C211yesmaximal, characteristic
4#20267552C212yesmaximal
5#343×C103C211yesmaximal, characteristic
6#15693020—22no—
7#15693012—22no—
8#15693000—22no—
9#15692980C2212yes—
10C2×C4⋊Dic103C2211yescharacteristic
11C2×C4×Dic103C2211yescharacteristic
12#15692955—22no—
13#15692953—22no—
14C103⋊#95—22no—
15C2×M16×C103C2212yes—
16C2×C4⋊C4×C103C2211yescharacteristic
17C2×Dic206—22no—
18C22×Dic103—21no—
19C22×Dic103—21no—
20C4⋊Dic103—22no—
21C4⋊Dic103—22no—
22C4⋊Dic103D412yes—
23C4⋊Dic103D412yes—
24Dic103⋊C4—24no—
25C22⋊Dic103—22no—
26C4×Dic103—22no—
27C4×Dic103—21no—
28C4×Dic103Q812yescomplemented
29C22×C4×C103D412yes—
30C22×C4×C103C2311yescharacteristic
31M16×C103—22no—
32M16×C103Q814yescomplemented
33C2×C8×C103—22no—
34C4⋊C4×C103—22no—
35C23×C103C2×D411yescharacteristic
36C2×C4×C103—22no—
37C2×C4×C103—42no—
38C2×C4×C103C2×D412yes—
39C2×C4×C103C2×Q811yescharacteristic
40C2×C4×C103C2×Q812yes—
41C2×C4×C103#4111yescharacteristic
42C2×Dic103—22no—
43C2×Dic103—22no—
44C2×Dic103—22no—
45C2×Dic103—41no—
46C2×Dic103—41no—
47C2×Dic103—42no—
48C2×Dic103—41no—
49Dic206—82no—
50C8×C103—24no—
51C22×C103—21no—
52C22×C103—21no—
53C22×C103#12011yescharacteristic
54C22×C103C22⋊Q811yescharacteristic
55C22×C103C4⋊Q811yescharacteristic
56C4×C103—42no—
57C4×C103C22⋊Q812yes—
58C4×C103C4⋊Q812yes—
59Dic103—42no—
60Dic103—42no—
61Dic103—42no—
62Dic103—81no—
63C2×C103—21no—
64C2×C103—21no—
65C2×C103#39511yescharacteristic
66C2×C103#45411yescharacteristic
67C2×C103#45511yescharacteristic
68#2061—1031nomaximal, Sylow
69C103#206111yescharacteristic, complemented, Sylow
70#544—1031no—
71#428—1032no—
72#382—1031no—
73#343D10311yescharacteristic
74#339—1032no—
75C2×M16C2×D10312yes—
76C4⋊Q8—2062no—
77#125—2062no—
78C22⋊Q8—2062no—
79#117—1032no—
80C2×C4⋊C4—1031no—
81C2×C4⋊C4C2×D10311yescharacteristic
82C2×C42—1031no—
83#107—2062no—
84#106—2062no—
85#95—2062no—
86C2×Q8—2062no—
87C22×C4—2061no—
88C22×C4—2061no—
89C22×C4D41212yes—
90C22×C4C22×D10311yescharacteristic
91M16—22no—
92M16Dic20614yescomplemented
93C2×C8—22no—
94C4⋊C4—22no—
95C4⋊C4—1032no—
96C4⋊C4—1032no—
97C4⋊C4—2064no—
98C4⋊C4—2062no—
99C4⋊C4—2062no—
100C22⋊C4—2062no—
101C42—1032no—
102C42—2062no—
103C42—2061no—
104C23C2×D41211yescharacteristic
105Q8—8242no—
106C2×C4—22no—
107C2×C4—42no—
108C2×C4—4122no—
109C2×C4—4121no—
110C2×C4—4121no—
111C2×C4—4121no—
112C2×C4—2062no—
113C2×C4—2062no—
114C2×C4—2062no—
115C2×C4D4×D10312yes—
116C2×C4Q8×D10311yescharacteristic
117C2×C4C2×Dic20612yes—
118C2×C4#1311010411yescharacteristic
119C8—24no—
120C22—21no—
121C22—21no—
122C22#1569299111yescharacteristic
123C22#1569300111yescharacteristic
124C22#1569302111yescharacteristic
125C4—42no—
126C4—8241no—
127C4—4122no—
128C4—4122no—
129C4—4122no—
130C4#1569299812yes—
131C4#1569302012yes—
132C2—21no—
133C2—21no—
134C2#2026771211yescharacteristic
135C2#2026796611yescharacteristic
136C2#2026797111yescharacteristic
subgroupG/H
centerC22#15692991
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#343×C103C2
socleC22×C103#120
prime radicalC23×C103C2×D4
hypercenter#343D103
hypocenterC103#2061
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
28. C4×Dic103Q8semidirect
32. M16×C103Q8semidirect
69. C103#2061semidirect
92. M16Dic206semidirect

Maximal subgroups

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

subgroupindex
#202684222
#202678332
#202676562
#202675522
#343×C1032
#2061103