Finite Group Databasebeta

← #27194440

Subgroups — #27194440

Order 13184.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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#20268541C211yesmaximal, characteristic, complemented
2#20268155C212yesmaximal, complemented
3#20267532C212yesmaximal, complemented
4#20267531C211yesmaximal, characteristic, complemented
5#496×C103C211yesmaximal, characteristic
6#15693019—21no—
7#15693014—22no—
8#15693013C2212yes—
9#15693002—21no—
10#15692998—22no—
11#15692942—22no—
12#15692942—22no—
13#15692932C2212yes—
14C2×SD16×C103—21no—
15C2×D8×C103—21no—
16#127×C103C2211yescharacteristic
17#124×C103C2211yescharacteristic
18#97×C103C2211yescharacteristic
19C2×Dic206—21no—
20C22×Dic103—21no—
21C2×C103⋊C8—22no—
22C4⋊Dic103D412yes—
23C4⋊Dic103D412yes—
24Dic103⋊C4—22no—
25Dic103⋊C4—22no—
26Dic103⋊C4—22no—
27C22⋊Dic103—22no—
28C22⋊Dic103—21no—
29C4×Dic103—21no—
30C2×Q8×C103D411yescharacteristic
31C2×D4×C103—21no—
32C2×D4×C103—22no—
33C2×D4×C103D411yescharacteristic
34SD16×C103—42no—
35D8×C103—42no—
36C2×C8×C103—21no—
37C22⋊C4×C103—22no—
38C42×C103C2311yescharacteristic
39C23×C103—21no—
40C23×C103—41no—
41Q8×C103—41no—
42D4×C103—41no—
43D4×C103—41no—
44D4×C103—41no—
45D4×C103—44no—
46C2×C4×C103—21no—
47C2×C4×C103C2×D412yes—
48C2×C4×C103C2×D411yescharacteristic
49C2×Dic103—22no—
50C2×Dic103—22no—
51C2×Dic103—81no—
52Dic206—81no—
53C8×C103—22no—
54C103⋊C8—42no—
55C22×C103—41no—
56C22×C103—42no—
57C22×C103—81no—
58C22×C103—82no—
59C22×C103#12011yescharacteristic
60C4×C103—21no—
61C4×C103—22no—
62C4×C103—41no—
63Dic103—42no—
64Dic103—42no—
65C2×C103—81no—
66C2×C103—161no—
67C2×C103#45311yescharacteristic
68C2×C103#45412yes—
69#1657—1031nomaximal, Sylow
70C103#165711yescharacteristic, complemented, Sylow
71#563—1031no—
72#496D10311yescharacteristic
73#490—1032no—
74#330—1032no—
75#329—1031no—
76C2×SD16—21no—
77C2×D8—21no—
78C4⋊Q8—2061no—
79#127C2×D10311yescharacteristic
80#126—2062no—
81#125—1032no—
82#124C2×D10311yescharacteristic
83#123—2061no—
84C22⋊Q8—2062no—
85#102—2062no—
86#102—2062no—
87#97—1032no—
88#97C2×D10311yescharacteristic
89C2×Q8—2061no—
90C2×Q8C22⋊D10311yescharacteristic
91C2×D4—22no—
92C2×D4—21no—
93C2×D4C22⋊D10311yescharacteristic
94C22×C4—2061no—
95SD16—42no—
96D8—42no—
97C2×C8—21no—
98C2×C8—2062no—
99C4⋊C4—1032no—
100C4⋊C4—1032no—
101C4⋊C4—2062no—
102C4⋊C4—2062no—
103C4⋊C4—2062no—
104C22⋊C4—22no—
105C22⋊C4—2062no—
106C22⋊C4—2061no—
107C42—2061no—
108C42C22×D10311yescharacteristic
109C23—21no—
110C23—41no—
111Q8—41no—
112Q8—8241no—
113D4—41no—
114D4—41no—
115D4—41no—
116D4—44no—
117C2×C4—21no—
118C2×C4—8241no—
119C2×C4—2062no—
120C2×C4—2062no—
121C2×C4D4×D10312yes—
122C2×C4C2×C22⋊D10311yescharacteristic
123C8—22no—
124C8—4122no—
125C22—41no—
126C22—42no—
127C22—81no—
128C22—82no—
129C22#1569298911yescharacteristic
130C4—21no—
131C4—22no—
132C4—41no—
133C4—4122no—
134C4—4122no—
135C2—81no—
136C2—161no—
137C2#2026795811yescharacteristic
138C2#2026796212yes—
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting, prime radical#496×C103C2
socleC22×C103#120
hypercenter#496D103
hypocenterC103#1657
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #20268541C2semidirect
2. #20268155C2semidirect
3. #20267532C2semidirect
4. #20267531C2semidirect
70. C103#1657semidirect

Maximal subgroups

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

subgroupindex
#202685412
#202681552
#202675322
#202675312
#496×C1032
#1657103