Finite Group Databasebeta

← #27194442

Subgroups — #27194442

Order 13184.

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

normal subgroups only

This group has 206 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#20268181C211yesmaximal, characteristic
2#20268157C212yesmaximal, complemented
3#20267533C212yesmaximal, complemented
4#20267531C211yesmaximal, characteristic, complemented
5#563×C103C211yesmaximal, characteristic, complemented
6C2×#13110092—21no—
7C2×#13110090—21no—
8#15693018C2211yescharacteristic
9#15692941—22no—
10#15692941—22no—
11#15692932C2212yes—
12#15692932C2211yescharacteristic
13C4⋊Q8×C103—21no—
14#126×C103—22no—
15#125×C103C2212yes—
16#124×C103C2211yescharacteristic
17#123×C103—21no—
18C22⋊Q8×C103—22no—
19C2×D412—22no—
20C2×D412—21no—
21#13110092—42no—
22#13110090—42no—
23C2×C103⋊C8—21no—
24C2×C103⋊C8—22no—
25C2×Q8×C103—21no—
26C2×Q8×C103D411yescharacteristic
27C2×D4×C103D411yescharacteristic
28C22×C4×C103—21no—
29C4⋊C4×C103—22no—
30C4⋊C4×C103—22no—
31C4⋊C4×C103—22no—
32C4⋊C4×C103D412yes—
33C4⋊C4×C103D412yes—
34C22⋊C4×C103—22no—
35C22⋊C4×C103—21no—
36C22⋊C4×C103—22no—
37C42×C103—21no—
38C42×C103C2311yescharacteristic
39C23×C103—21no—
40C22×D103—41no—
41Q8×C103—41no—
42Q8×C103—81no—
43D4×C103—41no—
44C2×C4×C103—22no—
45C2×C4×C103—21no—
46C2×C4×C103—22no—
47C2×C4×C103—81no—
48C2×C4×C103C2×D412yes—
49C2×C4×C103C2×D411yescharacteristic
50D412—41no—
51D412—41no—
52D412—44no—
53C103⋊C8—22no—
54C103⋊C8—42no—
55C22×C103—41no—
56C22×C103—42no—
57C22×C103#12011yescharacteristic
58C2×D103—81no—
59C2×D103—82no—
60C4×C103—21no—
61C4×C103—22no—
62C4×C103—42no—
63C4×C103—41no—
64C4×C103—42no—
65C2×C103—81no—
66C2×C103#45311yescharacteristic
67C2×C103#45412yes—
68D103—161no—
69#1657—1031nomaximal, Sylow
70C103#165711yescharacteristic, complemented, Sylow
71#563D10311yescharacteristic, complemented
72#496—1031no—
73#490—1032no—
74#330—1032no—
75#329—1031no—
76C2×SD16—2061no—
77C2×D8—2061no—
78C4⋊Q8—21no—
79#127—1031no—
80#126—22no—
81#125C2×D10312yes—
82#124C2×D10311yescharacteristic
83#123—21no—
84C22⋊Q8—22no—
85#102—2062no—
86#102—2062no—
87#97—1032no—
88#97—1031no—
89C2×Q8—21no—
90C2×Q8C22⋊D10311yescharacteristic
91C2×D4—2062no—
92C2×D4—2061no—
93C2×D4C22⋊D10311yescharacteristic
94C22×C4—21no—
95SD16—4122no—
96D8—4122no—
97C2×C8—2062no—
98C2×C8—2061no—
99C4⋊C4—22no—
100C4⋊C4—22no—
101C4⋊C4—22no—
102C4⋊C4C22⋊D10312yes—
103C4⋊C4C22⋊D10312yes—
104C22⋊C4—22no—
105C22⋊C4—21no—
106C22⋊C4—22no—
107C42—21no—
108C42C22×D10311yescharacteristic
109C23—21no—
110C23—4121no—
111Q8—41no—
112Q8—81no—
113D4—41no—
114D4—4121no—
115D4—4121no—
116D4—4124no—
117C2×C4—22no—
118C2×C4—21no—
119C2×C4—22no—
120C2×C4—81no—
121C2×C4C2×C22⋊D10312yes—
122C2×C4C2×C22⋊D10311yescharacteristic
123C8—4122no—
124C8—2062no—
125C22—41no—
126C22—42no—
127C22—8241no—
128C22—8242no—
129C22#1569299011yescharacteristic
130C4—21no—
131C4—22no—
132C4—42no—
133C4—41no—
134C4—42no—
135C2—81no—
136C2—16481no—
137C2#2026795911yescharacteristic
138C2#2026796412yes—
subgroupG/H
centerC22#15692990
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#563×C103C2
socleC22×C103#120
prime radical#20268181C2
hypercenter#563D103
hypocenterC103#1657
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
2. #20268157C2semidirect
3. #20267533C2semidirect
4. #20267531C2semidirect
5. #563×C103C2semidirect
70. C103#1657semidirect
71. #563D103semidirect

Maximal subgroups

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

subgroupindex
#202681812
#202681572
#202675332
#202675312
#563×C1032
#1657103