Finite Group Databasebeta

← #27196120

Subgroups — #27196120

Order 13184.

284 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 97 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#20268348C211yesmaximal, characteristic
2C42×Dic103C211yesmaximal, characteristic
3#20267552C214yesmaximal
4#423×C103C211yesmaximal, characteristic
5#15693021C412yescomplemented
6#15693013C412yescomplemented
7#15693000—22no—
8C4×Dic206—22no—
9#15692980C2212yes—
10C2×C4×Dic103—22no—
11C2×C4×Dic103C2212yes—
12C2×M16×C103C2212yes—
13C2×C42×C103C2211yescharacteristic
14C4⋊C8×C103—22no—
15C2×Dic206—22no—
16C22×Dic103—22no—
17C4⋊Dic103—22no—
18C4⋊Dic103C2×C414yes—
19Dic103⋊C4—24no—
20C22⋊Dic103—22no—
21C4×Dic103—28no—
22C4×Dic103—22no—
23C4×Dic103—22no—
24C4×Dic103Q814yescomplemented
25C22×C4×C103D412yes—
26C22×C4×C103C2311yescharacteristic
27M16×C103—24no—
28C2×C8×C103—22no—
29C42×C103C2×C411yescharacteristic
30C42×C103C2×C411yescharacteristic
31C42×C103D412yes—
32C23×C103C2×D411yescharacteristic
33C2×C4×C103—24no—
34C2×C4×C103C22⋊C412yes—
35C2×C4×C103C22⋊C412yes—
36C2×C4×C103C22×C411yescharacteristic
37C2×C4×C103C2×D411yescharacteristic
38C2×C4×C103C2×Q812yes—
39C2×C4×C103#4112yes—
40C2×Dic103—28no—
41C2×Dic103—24no—
42C2×Dic103—24no—
43Dic206—44no—
44C8×C103—42no—
45C22×C103—22no—
46C22×C103C2×C22⋊C411yescharacteristic
47C22×C103C22⋊Q812yes—
48C4×C103—22no—
49C4×C103#10414yes—
50C4×C103C4×Q812yes—
51C4×C103#12411yescharacteristic
52C4×C103C4⋊Q811yescharacteristic
53Dic103—28no—
54Dic103—44no—
55C2×C103—22no—
56C2×C103#39111yescharacteristic
57C2×C103C2×#10412yes—
58#1994—1031nomaximal, Sylow
59C103#199411yescharacteristic, complemented, Sylow
60#533—1031no—
61#423D10311yescharacteristic
62C43—1031no—
63#339—1034no—
64C2×M16C2×D10312yes—
65C4⋊Q8—1032no—
66#125—1032no—
67C22⋊Q8—2062no—
68C4×Q8—2062no—
69#117—1032no—
70C2×C42—1032no—
71C2×C42—2062no—
72C2×C42C2×D10311yescharacteristic
73C4⋊C8—22no—
74C2×Q8—2062no—
75C22×C4—2062no—
76C22×C4D41212yes—
77C22×C4C22×D10311yescharacteristic
78M16—24no—
79C2×C8—22no—
80C4⋊C4—1034no—
81C4⋊C4—2064no—
82C4⋊C4—2062no—
83C22⋊C4—2062no—
84C42—1034no—
85C42—2068no—
86C42—2062no—
87C42—2062no—
88C42C4×D10311yescharacteristic
89C42C4×D10311yescharacteristic
90C42C22⋊D10312yes—
91C23C2×D41211yescharacteristic
92Q8—4124no—
93C2×C4—24no—
94C2×C4—2064no—
95C2×C4—2068no—
96C2×C4—2064no—
97C2×C4(C2×D103)⋊C412yes—
98C2×C4(C2×D103)⋊C412yes—
99C2×C4C2×C4×D10311yescharacteristic
100C2×C4C2×C22⋊D10311yescharacteristic
101C2×C4Q8×D10312yes—
102C2×C4#1311010412yes—
103C8—42no—
104C22—22no—
105C22C2×(C2×D103)⋊C411yescharacteristic
106C22#1569300112yes—
107C4—22no—
108C4—4124no—
109C4—2068no—
110C4#1569294714yes—
111C4#1569298612yes—
112C4#1569300811yescharacteristic
113C4#1569301911yescharacteristic
114C2—22no—
115C2#2026769611yescharacteristic
116C2C2×#1569294712yes—
subgroupG/H
centerC2×C4C2×C22⋊D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#423×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC23×C103C2×D4
cosocleC22×C4×C103C23
hypercenter#423D103
hypocenterC103#1994
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
5. #15693021C4semidirect
6. #15693013C4semidirect
24. C4×Dic103Q8semidirect
59. C103#1994semidirect

Maximal subgroups

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

subgroupindex
#202683482
C42×Dic1032
#202675522
#423×C1032
#1994103