Finite Group Databasebeta

← #27194227

Subgroups — #27194227

Order 13184.

240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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#20268165C211yesmaximal, characteristic, complemented
2#20267986C212yesmaximal, complemented
3#20267540C211yesmaximal, characteristic, complemented
4D4⋊(C103⋊C8)C212yesmaximal, complemented
5#555×C103C211yesmaximal, characteristic, complemented
6C2×#13110092—22no—
7C2×#13110090—22no—
8#15693018C2211yescharacteristic
9C4⋊(C103⋊C8)C2212yes—
10#15692941—22no—
11C4×C103⋊C8C2211yescharacteristic
12C4⋊Q8×C103C2211yescharacteristic
13#124×C103—22no—
14#121×C103—22no—
15C4×D4×C103C2212yes—
16#117×C103—22no—
17C2×D412—22no—
18C2×D412—21no—
19#13110092—44no—
20#13110090—44no—
21C2×C103⋊C8—21no—
22C2×C103⋊C8—22no—
23C2×Q8×C103D412yes—
24C2×D4×C103—22no—
25C2×D4×C103D412yes—
26C22×C4×C103—22no—
27C4⋊C4×C103—22no—
28C4⋊C4×C103D412yes—
29C22⋊C4×C103—24no—
30C22⋊C4×C103—22no—
31C42×C103—22no—
32C42×C103C2311yescharacteristic
33C23×C103—22no—
34C22×D103—41no—
35Q8×C103—42no—
36D4×C103—22no—
37D4×C103—22no—
38D4×C103—82no—
39C2×C4×C103—22no—
40C2×C4×C103—22no—
41C2×C4×C103—42no—
42C2×C4×C103—42no—
43C2×C4×C103C2×D411yescharacteristic
44C2×C4×C103C2×D412yes—
45D412—42no—
46D412—42no—
47D412—42no—
48C103⋊C8—22no—
49C103⋊C8—42no—
50C22×C103—42no—
51C22×C103—42no—
52C22×C103—42no—
53C22×C103#12011yescharacteristic
54C2×D103—82no—
55C2×D103—81no—
56C4×C103—21no—
57C4×C103—42no—
58C4×C103—42no—
59C4×C103#13512yes—
60C4×C103AGL(1,ℤ/8)12yes—
61C2×C103—82no—
62C2×C103#44912yes—
63C2×C103#45311yescharacteristic
64D103—161no—
65#1624—1031nomaximal, Sylow
66C103#162411yescharacteristic, complemented, Sylow
67#555D10311yescharacteristic, complemented
68#492—1031no—
69#459—1032no—
70#333—1031no—
71D4⋊C8—1032no—
72C2×SD16—2062no—
73C2×D8—2062no—
74C4⋊Q8C2×D10311yescharacteristic
75#127—1031no—
76#124—22no—
77#121—22no—
78C4×D4C2×D10312yes—
79#117—22no—
80C4⋊C8—1032no—
81#102—2062no—
82C4×C8—1031no—
83C2×Q8C22⋊D10312yes—
84C2×D4—22no—
85C2×D4—2062no—
86C2×D4—2061no—
87C2×D4C22⋊D10312yes—
88C22×C4—22no—
89SD16—4124no—
90D8—4124no—
91C2×C8—2062no—
92C2×C8—2061no—
93C4⋊C4—22no—
94C4⋊C4C22⋊D10312yes—
95C22⋊C4—24no—
96C22⋊C4—22no—
97C42—22no—
98C42C22×D10311yescharacteristic
99C23—22no—
100C23—4121no—
101Q8—42no—
102D4—22no—
103D4—22no—
104D4—82no—
105D4—4122no—
106D4—4122no—
107D4—4122no—
108C2×C4—22no—
109C2×C4—22no—
110C2×C4—42no—
111C2×C4—42no—
112C2×C4C2×C22⋊D10311yescharacteristic
113C2×C4C2×C22⋊D10312yes—
114C8—4122no—
115C8—2062no—
116C22—42no—
117C22—42no—
118C22—42no—
119C22—8242no—
120C22—8241no—
121C22#1569299011yescharacteristic
122C4—21no—
123C4—42no—
124C4—42no—
125C4#1569304112yes—
126C4#1569304612yes—
127C2—82no—
128C2—16481no—
129C2#2026793612yes—
130C2#2026795911yescharacteristic
subgroupG/H
centerC22#15692990
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#555×C103C2
socleC22×C103#120
hypercenter#555D103
hypocenterC103#1624
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #20268165C2semidirect
2. #20267986C2semidirect
3. #20267540C2semidirect
4. D4⋊(C103⋊C8)C2semidirect
5. #555×C103C2semidirect
66. C103#1624semidirect
67. #555D103semidirect

Maximal subgroups

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

subgroupindex
#202681652
#202679862
#202675402
D4⋊(C103⋊C8)2
#555×C1032
#1624103