Finite Group Databasebeta

← #27192983

Subgroups — #27192983

Order 13184.

208 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 109 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×C4×C103⋊C8C211yesmaximal, characteristic
2C4×C4⋊Dic103C211yesmaximal, characteristic
3C2×C4⋊C8×C103C211yesmaximal, characteristic
4C22×C103⋊C8—21no—
5C2×C4⋊Dic103C412yes—
6C2×C4×Dic103—21no—
7C4×C103⋊C8—21no—
8C4×C103⋊C8C412yescomplemented
9C103⋊#95—21no—
10C22×C8×C103—21no—
11C2×C42×C103C2211yescharacteristic
12C4⋊C8×C103—21no—
13C4⋊C8×C103C412yescomplemented
14C22×Dic103—22no—
15C2×C103⋊C8—24no—
16C2×C103⋊C8—22no—
17C4⋊Dic103—22no—
18C4⋊Dic103C814yescomplemented
19C4×Dic103—41no—
20C4×Dic103—41no—
21C22×C4×C103C2×C411yescharacteristic
22C22×C4×C103D411yescharacteristic
23C22×C4×C103D411yescharacteristic
24C2×C8×C103—22no—
25C2×C8×C103—41no—
26C2×C8×C103—41no—
27C42×C103C2×C411yescharacteristic
28C42×C103C2×C411yescharacteristic
29C42×C103D411yescharacteristic
30C42×C103Q811yescharacteristic
31C23×C103C22⋊C411yescharacteristic
32C2×C4×C103—22no—
33C2×C4×C103C4211yescharacteristic
34C2×C4×C103C22⋊C411yescharacteristic
35C2×C4×C103C22⋊C411yescharacteristic
36C2×C4×C103C4⋊C411yescharacteristic
37C2×C4×C103C4⋊C411yescharacteristic
38C2×C4×C103C4⋊C411yescharacteristic
39C2×C4×C103C2×C812yes—
40C2×C4×C103M1612yes—
41C2×C4×C103D811yescharacteristic
42C2×C4×C103SD1611yescharacteristic
43C2×C4×C103SD1611yescharacteristic
44C2×C4×C103Q1611yescharacteristic
45C2×Dic103—24no—
46C2×Dic103—42no—
47C2×Dic103—42no—
48C8×C103—42no—
49C103⋊C8—24no—
50C22×C103#9511yescharacteristic
51C22×C103C22⋊C812yes—
52C22×C103#10211yescharacteristic
53C22×C103#10311yescharacteristic
54C22×C103#10412yes—
55C4×C103—21no—
56C4×C103—21no—
57C4×C103C4×C811yescharacteristic
58C4×C103#9711yescharacteristic
59C4×C103#10211yescharacteristic
60C4×C103#10311yescharacteristic
61C4×C103C4⋊C812yes—
62C4×C103#10611yescharacteristic
63C4×C103#10711yescharacteristic
64Dic103—44no—
65C2×C103D4⋊C812yes—
66C2×C103Q8⋊C812yes—
67C2×C103#33611yescharacteristic
68C2×C103#33911yescharacteristic
69C2×C103#34011yescharacteristic
70#1279—1031nomaximal, Sylow
71C103#127911yescharacteristic, complemented, Sylow
72C2×C4⋊C8D10311yescharacteristic
73C2×C4×C8—1031no—
74C4×C4⋊C4—1031no—
75C22×C8—21no—
76C22×C8—2061no—
77C2×C4⋊C4—1032no—
78C2×C42—2061no—
79C2×C42C2×D10311yescharacteristic
80C4⋊C8—21no—
81C4⋊C8Dic10312yescomplemented
82C4×C8—1032no—
83C4×C8—2061no—
84#95—2061no—
85C22×C4—2062no—
86C22×C4C4×D10311yescharacteristic
87C22×C4D41211yescharacteristic
88C22×C4C22⋊D10311yescharacteristic
89C2×C8—22no—
90C2×C8—41no—
91C2×C8—41no—
92C2×C8—2064no—
93C2×C8—2062no—
94C4⋊C4—1034no—
95C4⋊C4—2062no—
96C42—4121no—
97C42—4121no—
98C42Dic20611yescharacteristic
99C42C4×D10311yescharacteristic
100C42C2×Dic10311yescharacteristic
101C42C22⋊D10311yescharacteristic
102C23(C2×D103)⋊C411yescharacteristic
103C2×C4—22no—
104C2×C4—4122no—
105C2×C4—4122no—
106C2×C4—2064no—
107C2×C4C4×Dic10311yescharacteristic
108C2×C4(C2×D103)⋊C411yescharacteristic
109C2×C4C22⋊Dic10311yescharacteristic
110C2×C4Dic103⋊C411yescharacteristic
111C2×C4Dic103⋊C411yescharacteristic
112C2×C4C4⋊Dic10311yescharacteristic
113C2×C4C8×D10312yes—
114C2×C4#1311008812yes—
115C2×C4#1311009011yescharacteristic
116C2×C4#1311009211yescharacteristic
117C2×C4#1311009311yescharacteristic
118C2×C4#1311009511yescharacteristic
119C8—42no—
120C8—2064no—
121C22C103⋊#9511yescharacteristic
122C22(C2×D103)⋊C812yes—
123C22#1569294111yescharacteristic
124C22#1569294411yescharacteristic
125C22#1569294712yes—
126C4—21no—
127C4—21no—
128C4—4124no—
129C4C8×Dic10311yescharacteristic
130C4#1569293111yescharacteristic
131C4#1569294211yescharacteristic
132C4#1569294511yescharacteristic
133C4Dic103⋊C812yes—
134C4#1569295211yescharacteristic
135C4#1569295411yescharacteristic
136C2#2026751812yes—
137C2#2026752112yes—
138C2#2026754511yescharacteristic
139C2#2026755211yescharacteristic
140C2#2026755311yescharacteristic
subgroupG/H
centerC22×C4C22⋊D103
commutatorC4×C103C4×C8
FrattiniC2×C42C2×D103
FittingC2×C4⋊C8×C103C2
socle, prime radicalC23×C103C22⋊C4
cosocleC2×C42×C103C22
hypercenterC2×C4⋊C8D103
hypocenterC103#1279
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
8. C4×C103⋊C8C4semidirect
13. C4⋊C8×C103C4semidirect
18. C4⋊Dic103C8semidirect
71. C103#1279semidirect
81. C4⋊C8Dic103semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C103⋊C82
C4×C4⋊Dic1032
C2×C4⋊C8×C1032
#1279103