Finite Group Databasebeta

← #27196494

Subgroups — #27196494

Order 13184.

230 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 73 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#20267831C212yesmaximal
3#20267560C211yesmaximal, characteristic
4#20267551C212yesmaximal
5#382×C103C211yesmaximal, characteristic
6C2×#13110089C2212yes—
7#15693020—22no—
8#15693012—22no—
9#15693000—22no—
10#15692980C2212yes—
11#15692954—22no—
12#15692952—22no—
13C2×C4⋊C4×C103C2211yescharacteristic
14C2×C4⋊C4×C103C2211yescharacteristic
15C2×C42×C103C2211yescharacteristic
16#95×C103—22no—
17C2×Dic206—22no—
18#13110089—22no—
19#13110089Q814yescomplemented
20C2×C103⋊C8—22no—
21C4⋊Dic103—22no—
22C4⋊Dic103D412yes—
23C4⋊Dic103D412yes—
24Dic103⋊C4—24no—
25C22⋊Dic103—22no—
26C4×Dic103—22no—
27C22×C4×C103—21no—
28C22×C4×C103—21no—
29C22×C4×C103D412yes—
30C22×C4×C103C2311yescharacteristic
31C4⋊C4×C103—22no—
32C4⋊C4×C103—22no—
33C42×C103—21no—
34C42×C103Q812yescomplemented
35C23×C103C2×D411yescharacteristic
36C2×C4×C103—22no—
37C2×C4×C103—22no—
38C2×C4×C103—41no—
39C2×C4×C103—41no—
40C2×C4×C103—42no—
41C2×C4×C103—42no—
42C2×C4×C103—41no—
43C2×C4×C103C2×D412yes—
44C2×C4×C103C2×Q812yes—
45C2×C4×C103C2×Q811yescharacteristic
46C2×C4×C103#4111yescharacteristic
47C2×Dic103—22no—
48C2×Dic103—22no—
49Dic206—82no—
50C103⋊C8—24no—
51C22×C103—21no—
52C22×C103—21no—
53C22×C103#12011yescharacteristic
54C22×C103C22⋊Q811yescharacteristic
55C22×C103C4⋊Q811yescharacteristic
56C4×C103—42no—
57C4×C103—42no—
58C4×C103—81no—
59C4×C103C22⋊Q812yes—
60C4×C103C4⋊Q812yes—
61Dic103—42no—
62Dic103—42no—
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#382D10311yescharacteristic
73#343—1031no—
74#339—1032no—
75C2×M16—1032no—
76C4⋊Q8—2062no—
77#125—2062no—
78C22⋊Q8—2062no—
79#117—1032no—
80C2×C4⋊C4C2×D10311yescharacteristic
81C2×C4⋊C4C2×D10311yescharacteristic
82C2×C42C2×D10311yescharacteristic
83#107—2062no—
84#106—2062no—
85#95—22no—
86C2×Q8—2062no—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4C22⋊D10312yes—
90C22×C4C22×D10311yescharacteristic
91M16—1034no—
92M16—2062no—
93C2×C8—2062no—
94C4⋊C4—22no—
95C4⋊C4—22no—
96C4⋊C4—1032no—
97C4⋊C4—1032no—
98C4⋊C4—2064no—
99C4⋊C4—2062no—
100C22⋊C4—2062no—
101C42—21no—
102C42—2062no—
103C42Dic20612yescomplemented
104C23C2×C22⋊D10311yescharacteristic
105Q8—8242no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—42no—
111C2×C4—42no—
112C2×C4—41no—
113C2×C4—2062no—
114C2×C4—2062no—
115C2×C4D4×D10312yes—
116C2×C4Q8×D10312yes—
117C2×C4C2×Dic20611yescharacteristic
118C2×C4#1311010511yescharacteristic
119C8—2064no—
120C22—21no—
121C22—21no—
122C22#1569298911yescharacteristic
123C22#1569300011yescharacteristic
124C22#1569301911yescharacteristic
125C4—42no—
126C4—42no—
127C4—81no—
128C4—4122no—
129C4—4122no—
130C4#1569299912yes—
131C4#1569302012yes—
132C2—21no—
133C2—21no—
134C2#2026771111yescharacteristic
135C2#2026796311yescharacteristic
136C2#2026796811yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#382×C103C2
socleC22×C103#120
prime radicalC23×C103C2×D4
hypercenter#382D103
hypocenterC103#2061
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #382

Complements

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

NH ≅ G/Ntype
19. #13110089Q8semidirect
34. C42×C103Q8semidirect
69. C103#2061semidirect
103. C42Dic206semidirect

Maximal subgroups

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

subgroupindex
#202684222
#202678312
#202675602
#202675512
#382×C1032
#2061103