Finite Group Databasebeta

← #27194776

Subgroups — #27194776

Order 13184.

176 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 61 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#20268187C211yesmaximal, characteristic
2#20268187C211yesmaximal, characteristic
3#20268170C211yesmaximal, characteristic
4#20268142C211yesmaximal, characteristic
5#20268141C211yesmaximal, characteristic
6#20267513C211yesmaximal, characteristic
7#498×C103C211yesmaximal, characteristic
8C2×#13110095—22no—
9#15693021C2211yescharacteristic
10#15693021C2211yescharacteristic
11#15692952—22no—
12#15692952—22no—
13#15692946—22no—
14#15692945—22no—
15C4×C103⋊C8C2211yescharacteristic
16C4×C103⋊C8C2211yescharacteristic
17C4⋊Q8×C103C2211yescharacteristic
18C4⋊Q8×C103C2211yescharacteristic
19#106×C103—22no—
20C4×C8×C103C2211yescharacteristic
21C2×Dic206—21no—
22C2×Dic206—21no—
23#13110095—44no—
24C2×C103⋊C8D412yes—
25C2×C103⋊C8D412yes—
26C4⋊Dic103—21no—
27C4⋊Dic103—21no—
28C4⋊Dic103—21no—
29C4⋊Dic103—21no—
30C2×Q8×C103—21no—
31C2×Q8×C103—21no—
32C2×C8×C103D412yes—
33C4⋊C4×C103—21no—
34C4⋊C4×C103—21no—
35C4⋊C4×C103—21no—
36C4⋊C4×C103—21no—
37C42×C103C2311yescharacteristic
38Q8×C103—42no—
39Q8×C103—42no—
40C2×C4×C103—41no—
41C2×C4×C103—41no—
42C2×C4×C103C2×D411yescharacteristic
43C2×C4×C103C2×D411yescharacteristic
44C2×C4×C103C2×D411yescharacteristic
45C2×Dic103—41no—
46C2×Dic103—41no—
47Dic206—42no—
48Dic206—42no—
49C8×C103—22no—
50C103⋊C8—22no—
51C103⋊C8SD1614yes—
52C22×C103#12711yescharacteristic
53C4×C103—81no—
54C4×C103—81no—
55C4×C103C2×SD1612yes—
56C4×C103#13712yes—
57C4×C103#13712yes—
58Dic103—81no—
59Dic103—81no—
60C2×C103#49211yescharacteristic
61C2×C103#49711yescharacteristic
62C2×C103#49711yescharacteristic
63#1716—1031nomaximal, Sylow
64C103#171611yescharacteristic, complemented, Sylow
65#498—1031no—
66#498—1031no—
67#498D10311yescharacteristic
68#494—1031no—
69#487—1031no—
70#487—1031no—
71#322—1031no—
72C2×Q16—2062no—
73C4⋊Q8—1031no—
74C4⋊Q8—1031no—
75C4⋊Q8C2×D10311yescharacteristic
76C4⋊Q8C2×D10311yescharacteristic
77#106—22no—
78#106—2062no—
79#106—2062no—
80#103—2062no—
81#103—2062no—
82C4×C8—1031no—
83C4×C8—1031no—
84C4×C8C2×D10311yescharacteristic
85C2×Q8—21no—
86C2×Q8—21no—
87C2×Q8—2061no—
88C2×Q8—2061no—
89Q16—4124no—
90C2×C8—1032no—
91C2×C8—1032no—
92C2×C8C22⋊D10312yes—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—21no—
97C4⋊C4—2061no—
98C4⋊C4—2061no—
99C4⋊C4—2061no—
100C4⋊C4—2061no—
101C42C22×D10311yescharacteristic
102Q8—42no—
103Q8—42no—
104Q8—4122no—
105Q8—4122no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—4121no—
109C2×C4—4121no—
110C2×C4D4×D10311yescharacteristic
111C2×C4D4×D10311yescharacteristic
112C2×C4C2×C22⋊D10311yescharacteristic
113C8—22no—
114C8—1034no—
115C8—2062no—
116C22#1569301711yescharacteristic
117C4—81no—
118C4—81no—
119C4—8241no—
120C4—8241no—
121C4SD16×D10312yes—
122C4#1569305012yes—
123C4#1569305212yes—
124C2#2026816211yescharacteristic
125C2#2026818211yescharacteristic
126C2#2026818311yescharacteristic
subgroupG/H
centerC22#15693017
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#498×C103C2
socle, prime radicalC22×C103#127
hypercenter#498D103
hypocenterC103#1716
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
64. C103#1716semidirect

Maximal subgroups

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

subgroupindex
#202681872
#202681702
#202681422
#202681412
#202675132
#498×C1032
#1716103