Finite Group Databasebeta

← #27196727

Subgroups — #27196727

Order 13184.

148 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 59 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#20267839C211yesmaximal, characteristic
2#20267818C211yesmaximal, characteristic
3#20267561C211yesmaximal, characteristic
4#20267555C211yesmaximal, characteristic
5#20267555C211yesmaximal, characteristic
6C103⋊#338C211yesmaximal, characteristic
7#344×C103C211yesmaximal, characteristic
8C2×#13110089C2211yescharacteristic
9C2×#13110089C2211yescharacteristic
10C2×#13110089C2211yescharacteristic
11C22×C103⋊C8C2211yescharacteristic
12#15692956—22no—
13C4⋊(C103⋊C8)—22no—
14C2×M16×C103C2211yescharacteristic
15C2×M16×C103C2211yescharacteristic
16#117×C103C2211yescharacteristic
17#13110089—21no—
18#13110089—21no—
19#13110089—21no—
20#13110089—21no—
21#13110089—21no—
22#13110089—21no—
23C2×C103⋊C8—21no—
24C2×C103⋊C8—21no—
25C2×C103⋊C8—21no—
26C2×C103⋊C8—21no—
27C2×C103⋊C8—21no—
28C2×C103⋊C8D412yes—
29C22×C4×C103C2311yescharacteristic
30M16×C103—21no—
31M16×C103—21no—
32M16×C103—21no—
33M16×C103—21no—
34C2×C8×C103—21no—
35C2×C8×C103—21no—
36C4⋊C4×C103—21no—
37C22⋊C4×C103Q812yes—
38C42×C103—21no—
39C23×C103C2×Q811yescharacteristic
40C2×C4×C103—22no—
41C2×C4×C103C2×D411yescharacteristic
42C2×C4×C103#4111yescharacteristic
43C2×C4×C103#4111yescharacteristic
44C2×C4×C103#4111yescharacteristic
45C2×C4×C103#4111yescharacteristic
46C2×C4×C103#4111yescharacteristic
47C8×C103—41no—
48C8×C103—41no—
49C103⋊C8—22no—
50C103⋊C8—41no—
51C103⋊C8—41no—
52C103⋊C8—41no—
53C22×C103—41no—
54C22×C103C22⋊Q811yescharacteristic
55C22×C103#12511yescharacteristic
56C22×C103#12511yescharacteristic
57C4×C103—42no—
58C4×C103#12311yescharacteristic
59C4×C103#12411yescharacteristic
60C4×C103#12611yescharacteristic
61C4×C103#12611yescharacteristic
62C2×C103—21no—
63C2×C103—21no—
64C2×C103—21no—
65C2×C103#40011yescharacteristic
66#2103—1031nomaximal, Sylow
67C103#210311yescharacteristic, complemented, Sylow
68#430—1031no—
69#424—1031no—
70#344—1031no—
71#344D10311yescharacteristic
72#341—1031no—
73#341—1031no—
74#338—1031no—
75C2×M16—1031no—
76C2×M16—1031no—
77C2×M16—1031no—
78C2×M16C2×D10311yescharacteristic
79C2×M16C2×D10311yescharacteristic
80C22×C8—1031no—
81#117C2×D10311yescharacteristic
82#108—2062no—
83C4⋊C8—2062no—
84C22×C4C22×D10311yescharacteristic
85M16—21no—
86M16—21no—
87M16—21no—
88M16—21no—
89M16—2061no—
90M16—2061no—
91M16—2061no—
92M16—2061no—
93M16—2061no—
94M16—2061no—
95C2×C8—21no—
96C2×C8—21no—
97C2×C8—1032no—
98C2×C8—2061no—
99C2×C8—2061no—
100C2×C8—2061no—
101C2×C8—2061no—
102C2×C8—2061no—
103C4⋊C4—21no—
104C22⋊C4Dic20612yes—
105C42—21no—
106C23C2×Dic20611yescharacteristic
107C2×C4—22no—
108C2×C4D4×D10311yescharacteristic
109C2×C4#1311010411yescharacteristic
110C2×C4#1311010411yescharacteristic
111C2×C4#1311010511yescharacteristic
112C2×C4#1311010511yescharacteristic
113C2×C4#1311010611yescharacteristic
114C8—41no—
115C8—41no—
116C8—4121no—
117C8—4121no—
118C8—4121no—
119C8—2062no—
120C22—41no—
121C22#1569299811yescharacteristic
122C22#1569301211yescharacteristic
123C22#1569301311yescharacteristic
124C4—42no—
125C4#1569300611yescharacteristic
126C4#1569300711yescharacteristic
127C4#1569301411yescharacteristic
128C4#1569301611yescharacteristic
129C2—21no—
130C2—21no—
131C2—21no—
132C2#2026773311yescharacteristic
subgroupG/H
centerC4#15693007
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#344×C103C2
socleC2×C103#400
prime radicalC23×C103C2×Q8
hypercenter#344D103
hypocenterC103#2103
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
67. C103#2103semidirect

Maximal subgroups

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

subgroupindex
#202678392
#202678182
#202675612
#202675552
C103⋊#3382
#344×C1032
#2103103