Finite Group Databasebeta

← #27196490

Subgroups — #27196490

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#20268422C211yesmaximal, characteristic
2#20267833C212yesmaximal
3#20267660C211yesmaximal, characteristic
4#20267552C212yesmaximal
5#343×C103C211yesmaximal, characteristic
6#15693020—22no—
7#15693012—22no—
8#15693000—22no—
9#15692980C2212yes—
10C2×C4⋊Dic103C2211yescharacteristic
11C2×Dic103⋊C4—22no—
12C2×C4×Dic103C2211yescharacteristic
13#15692955—22no—
14#15692953—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—
25Dic103⋊C4—44no—
26C22⋊Dic103—22no—
27C4×Dic103—22no—
28C4×Dic103—21no—
29C4×Dic103Q812yescomplemented
30C22×C4×C103D412yes—
31C22×C4×C103C2311yescharacteristic
32M16×C103—22no—
33M16×C103Q814yescomplemented
34C2×C8×C103—22no—
35C4⋊C4×C103—22no—
36C23×C103C2×D411yescharacteristic
37C2×C4×C103—22no—
38C2×C4×C103—42no—
39C2×C4×C103C2×D412yes—
40C2×C4×C103C2×Q811yescharacteristic
41C2×C4×C103C2×Q812yes—
42C2×C4×C103#4111yescharacteristic
43C2×Dic103—22no—
44C2×Dic103—22no—
45C2×Dic103—22no—
46C2×Dic103—22no—
47C2×Dic103—22no—
48C2×Dic103—42no—
49C2×Dic103—41no—
50Dic206—82no—
51C8×C103—24no—
52C22×C103—21no—
53C22×C103—21no—
54C22×C103#12011yescharacteristic
55C22×C103C22⋊Q811yescharacteristic
56C22×C103C4⋊Q811yescharacteristic
57C4×C103—42no—
58C4×C103C22⋊Q812yes—
59C4×C103C4⋊Q812yes—
60Dic103—24no—
61Dic103—42no—
62Dic103—42no—
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#544—1031no—
72#428—1032no—
73#384—1031no—
74#343D10311yescharacteristic
75#339—1032no—
76C2×M16C2×D10312yes—
77C4⋊Q8—2062no—
78#125—2062no—
79C22⋊Q8—2062no—
80#117—1032no—
81C2×C4⋊C4—1031no—
82C2×C4⋊C4—2062no—
83C2×C4⋊C4C2×D10311yescharacteristic
84C2×C42—1031no—
85#107—2062no—
86#106—2062no—
87C2×Q8—2062no—
88C22×C4—2061no—
89C22×C4—2061no—
90C22×C4D41212yes—
91C22×C4C22×D10311yescharacteristic
92M16—22no—
93M16Dic20614yescomplemented
94C2×C8—22no—
95C4⋊C4—22no—
96C4⋊C4—1032no—
97C4⋊C4—1032no—
98C4⋊C4—4124no—
99C4⋊C4—2064no—
100C4⋊C4—2062no—
101C4⋊C4—2062no—
102C22⋊C4—2062no—
103C42—1032no—
104C42—2062no—
105C42—2061no—
106C23C2×D41211yescharacteristic
107Q8—8242no—
108C2×C4—22no—
109C2×C4—42no—
110C2×C4—4122no—
111C2×C4—4121no—
112C2×C4—2062no—
113C2×C4—2062no—
114C2×C4—2062no—
115C2×C4—2062no—
116C2×C4—2062no—
117C2×C4D4×D10312yes—
118C2×C4Q8×D10311yescharacteristic
119C2×C4C2×Dic20612yes—
120C2×C4#1311010411yescharacteristic
121C8—24no—
122C22—21no—
123C22—21no—
124C22#1569299111yescharacteristic
125C22#1569300111yescharacteristic
126C22#1569302111yescharacteristic
127C4—42no—
128C4—8241no—
129C4—4122no—
130C4—4122no—
131C4—2064no—
132C4#1569299812yes—
133C4#1569302012yes—
134C2—21no—
135C2—21no—
136C2#2026771211yescharacteristic
137C2#2026796111yescharacteristic
138C2#2026797611yescharacteristic
subgroupG/H
centerC22#15692991
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#343×C103C2
socleC22×C103#120
prime radicalC23×C103C2×D4
hypercenter#343D103
hypocenterC103#2060
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
29. C4×Dic103Q8semidirect
33. M16×C103Q8semidirect
70. C103#2060semidirect
93. M16Dic206semidirect

Maximal subgroups

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

subgroupindex
#202684222
#202678332
#202676602
#202675522
#343×C1032
#2060103