Finite Group Databasebeta

← #27196638

Subgroups — #27196638

Order 13184.

224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×Dic103⋊C8C211yesmaximal, characteristic
2#20267687C212yesmaximal
3#20267554C211yesmaximal, characteristic
4#20267553C212yesmaximal
5C2×#107×C103C211yesmaximal, characteristic
6C22×C103⋊C8C2211yescharacteristic
7C2×C4⋊Dic103C2212yes—
8C2×Dic103⋊C4—22no—
9C2×C4×Dic103C2211yescharacteristic
10Dic103⋊C8—22no—
11C103⋊#95—22no—
12C22×C8×C103C2211yescharacteristic
13C2×C4⋊C4×C103C2212yes—
14#107×C103—22no—
15C22×Dic103—22no—
16C22×Dic103D411yescharacteristic
17C22×Dic103D411yescharacteristic
18C2×C103⋊C8—21no—
19C2×C103⋊C8—22no—
20C4⋊Dic103—22no—
21C4⋊Dic103Q814yes—
22Dic103⋊C4—44no—
23C4×Dic103—21no—
24C4×Dic103—21no—
25C22×C4×C103—22no—
26C22×C4×C103C2311yescharacteristic
27C2×C8×C103—22no—
28C2×C8×C103D412yes—
29C4⋊C4×C103—22no—
30C4⋊C4×C103—22no—
31C23×C103C2×D411yescharacteristic
32C2×C4×C103—42no—
33C2×C4×C103—42no—
34C2×C4×C103—42no—
35C2×C4×C103C2×D411yescharacteristic
36C2×C4×C103C2×Q812yes—
37C2×C4×C103#4111yescharacteristic
38C2×C4×C103#4112yes—
39C2×Dic103—21no—
40C2×Dic103—21no—
41C2×Dic103—21no—
42C2×Dic103—24no—
43C2×Dic103—22no—
44C2×Dic103—42no—
45C2×Dic103—42no—
46C2×Dic103Q1612yes—
47C8×C103—22no—
48C103⋊C8—41no—
49C22×C103#12111yescharacteristic
50C22×C103C22⋊Q812yes—
51C22×C103C2×Q1611yescharacteristic
52C22×C103#13511yescharacteristic
53C22×C103AGL(1,ℤ/8)12yes—
54C4×C103—82no—
55C4×C103#12311yescharacteristic
56C4×C103#12512yes—
57C4×C103C4⋊Q811yescharacteristic
58Dic103—22no—
59Dic103—41no—
60Dic103—44no—
61C2×C103#39811yescharacteristic
62C2×C103#46711yescharacteristic
63C2×C103#46911yescharacteristic
64C2×C103#47712yes—
65C2×C103#47812yes—
66#2087—1031nomaximal, Sylow
67C103#208711yescharacteristic, complemented, Sylow
68C2×#107D10311yescharacteristic
69C2×C4⋊C8—1031no—
70#389—1032no—
71#340—1031no—
72#340—1032no—
73C22×C8—1031no—
74C22×C8C2×D10311yescharacteristic
75C2×C4⋊C4—1032no—
76C2×C4⋊C4—2062no—
77C2×C4⋊C4C2×D10312yes—
78C2×C42—1031no—
79#107—22no—
80C4⋊C8—2062no—
81#95—2062no—
82C22×C4—22no—
83C22×C4—1031no—
84C22×C4—1031no—
85C22×C4—2062no—
86C22×C4C22×D10311yescharacteristic
87C2×C8—22no—
88C2×C8—2061no—
89C2×C8—2062no—
90C2×C8C22⋊D10312yes—
91C4⋊C4—22no—
92C4⋊C4—22no—
93C4⋊C4—1034no—
94C4⋊C4—4124no—
95C4⋊C4—2062no—
96C42—2061no—
97C42—2061no—
98C23D4×D10311yescharacteristic
99C2×C4—42no—
100C2×C4—42no—
101C2×C4—42no—
102C2×C4—1032no—
103C2×C4—4122no—
104C2×C4—4122no—
105C2×C4—2061no—
106C2×C4—2064no—
107C2×C4—2062no—
108C2×C4—2061no—
109C2×C4—2061no—
110C2×C4C2×C22⋊D10311yescharacteristic
111C2×C4Q8×D10312yes—
112C2×C4#1311010411yescharacteristic
113C2×C4#1311010512yes—
114C8—22no—
115C8—4121no—
116C22#1569299211yescharacteristic
117C22#1569299912yes—
118C22Q16×D10311yescharacteristic
119C22#1569304411yescharacteristic
120C22#1569304512yes—
121C4—82no—
122C4—4121no—
123C4—4124no—
124C4—2062no—
125C4#1569300411yescharacteristic
126C4#1569301112yes—
127C4#1569301911yescharacteristic
128C2#2026772211yescharacteristic
129C2#2026802911yescharacteristic
130C2#2026804111yescharacteristic
131C2#2026808512yes—
132C2#2026809412yes—
subgroupG/H
centerC23D4×D103
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
FittingC2×#107×C103C2
socle, prime radicalC23×C103C2×D4
hypercenterC2×#107D103
hypocenterC103#2087
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
67. C103#2087semidirect

Maximal subgroups

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

subgroupindex
C2×Dic103⋊C82
#202676872
#202675542
#202675532
C2×#107×C1032
#2087103