Finite Group Databasebeta

← #27194437

Subgroups — #27194437

Order 13184.

230 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 49 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#20268181C212yesmaximal, complemented
2#20268157C211yesmaximal, characteristic, complemented
3#20267533C211yesmaximal, characteristic, complemented
4#20267531C212yesmaximal, complemented
5#562×C103C211yesmaximal, characteristic, complemented
6C2×#13110092—22no—
7C2×#13110090—22no—
8#15693018C2211yescharacteristic
9#15692941—22no—
10#15692932C2211yescharacteristic
11#15692932C2212yes—
12#125×C103C2211yescharacteristic
13#124×C103C2212yes—
14#123×C103—22no—
15C22⋊Q8×C103—22no—
16#121×C103—22no—
17C2×D412—21no—
18C2×D412—22no—
19#13110092—44no—
20#13110090—44no—
21C2×C103⋊C8—22no—
22C2×C103⋊C8—21no—
23C2×Q8×C103D412yes—
24C2×D4×C103—22no—
25C2×D4×C103D412yes—
26C22×C4×C103—22no—
27C4⋊C4×C103—22no—
28C4⋊C4×C103—22no—
29C4⋊C4×C103D412yes—
30C22⋊C4×C103—22no—
31C22⋊C4×C103—22no—
32C22⋊C4×C103—22no—
33C42×C103C2311yescharacteristic
34C23×C103—22no—
35C22×D103—41no—
36Q8×C103—42no—
37D4×C103—42no—
38D4×C103—82no—
39C2×C4×C103—22no—
40C2×C4×C103—22no—
41C2×C4×C103—82no—
42C2×C4×C103C2×D411yescharacteristic
43C2×C4×C103C2×D412yes—
44D412—42no—
45D412—42no—
46D412—42no—
47C103⋊C8—24no—
48C103⋊C8—41no—
49C22×C103—42no—
50C22×C103—42no—
51C22×C103—42no—
52C22×C103#12011yescharacteristic
53C2×D103—82no—
54C2×D103—81no—
55C4×C103—22no—
56C4×C103—21no—
57C4×C103—42no—
58C4×C103—42no—
59C2×C103—82no—
60C2×C103#45312yes—
61C2×C103#45411yescharacteristic
62D103—161no—
63#1656—1031nomaximal, Sylow
64C103#165611yescharacteristic, complemented, Sylow
65#562D10311yescharacteristic, complemented
66#496—1032no—
67#490—1031no—
68#330—1031no—
69#329—1032no—
70C2×SD16—2062no—
71C2×D8—2062no—
72#127—1031no—
73#125C2×D10311yescharacteristic
74#124C2×D10312yes—
75#123—22no—
76C22⋊Q8—22no—
77#121—22no—
78#102—2062no—
79#97—1031no—
80#97—1032no—
81C2×Q8C22⋊D10312yes—
82C2×D4—22no—
83C2×D4—2061no—
84C2×D4—2062no—
85C2×D4C22⋊D10312yes—
86C22×C4—22no—
87SD16—4124no—
88D8—4124no—
89C2×C8—2061no—
90C2×C8—2062no—
91C4⋊C4—22no—
92C4⋊C4—22no—
93C4⋊C4C22⋊D10312yes—
94C22⋊C4—22no—
95C22⋊C4—22no—
96C22⋊C4—22no—
97C42C22×D10311yescharacteristic
98C23—22no—
99C23—4121no—
100Q8—42no—
101D4—42no—
102D4—82no—
103D4—4122no—
104D4—4122no—
105D4—4122no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—82no—
109C2×C4C2×C22⋊D10311yescharacteristic
110C2×C4C2×C22⋊D10312yes—
111C8—4121no—
112C8—2064no—
113C22—42no—
114C22—42no—
115C22—42no—
116C22—8242no—
117C22—8241no—
118C22#1569299011yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C2—82no—
124C2—16481no—
125C2#2026795912yes—
126C2#2026796411yescharacteristic
subgroupG/H
centerC22#15692990
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#562×C103C2
socleC22×C103#120
hypercenter#562D103
hypocenterC103#1656
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #20268181C2semidirect
2. #20268157C2semidirect
3. #20267533C2semidirect
4. #20267531C2semidirect
5. #562×C103C2semidirect
64. C103#1656semidirect
65. #562D103semidirect

Maximal subgroups

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

subgroupindex
#202681812
#202681572
#202675332
#202675312
#562×C1032
#1656103