Finite Group Databasebeta

← #27197217

Subgroups — #27197217

Order 13184.

170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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#20268227C212yesmaximal, complemented
2#20267909C211yesmaximal, characteristic, complemented
3#20267612C211yesmaximal, characteristic, complemented
4#20267604C212yesmaximal, complemented
5#493×C103C211yesmaximal, characteristic, complemented
6#15693043C2211yescharacteristic
7#15693027—21no—
8#15692965—22no—
9#15692962—22no—
10#15692961C2212yes—
11#15692957C2211yescharacteristic
12#15692949—21no—
13C2×D8×C103—21no—
14C2×D8×C103C2212yes—
15#127×C103—21no—
16C4×C8×C103C2211yescharacteristic
17#13110105—21no—
18Dic412D411yescharacteristic, complemented
19#13110094—21no—
20D824D411yescharacteristic, complemented
21#13110089—21no—
22#13110088—41no—
23C8×D103—41no—
24C103⋊C16—22no—
25C2×D4×C103—22no—
26C2×D4×C103—42no—
27D8×C103—22no—
28D8×C103—22no—
29D8×C103—41no—
30D8×C103—41no—
31C2×C8×C103D411yescharacteristic
32C2×C8×C103C2311yescharacteristic
33C42×C103D411yescharacteristic
34C23×C103—42no—
35D4×C103—42no—
36D4×C103—42no—
37D4×C103—84no—
38C2×C4×C103—21no—
39C2×C4×C103C2×D411yescharacteristic
40C22⋊D103—41no—
41D412—21no—
42C4×D103—41no—
43Dic206—21no—
44C8×C103D811yescharacteristic
45C8×C103D811yescharacteristic
46C8×C103C2×D411yescharacteristic
47C8×C103#4111yescharacteristic
48C103⋊C8—41no—
49C22×C103—84no—
50C22×C103—82no—
51C22×C103AGL(1,ℤ/8)11yescharacteristic
52C2×D103—41no—
53C4×C103—22no—
54C4×C103#12111yescharacteristic
55C4×C103C2×D811yescharacteristic
56Dic103—41no—
57C2×C103—21no—
58C2×C103—162no—
59C2×C103#45911yescharacteristic
60D103—81no—
61#2213—1031nomaximal, Sylow
62C103#221311yescharacteristic, complemented, Sylow
63#509—1032no—
64#493D10311yescharacteristic, complemented
65#443—1031no—
66#364—1031no—
67#361—1032no—
68#135—1031no—
69C2×D8—21no—
70C2×D8C2×D10312yes—
71#131—2061no—
72#127—21no—
73SD32—2062no—
74D16—2062no—
75M32—1032no—
76#108—1031no—
77#104—2061no—
78C4×C8C2×D10311yescharacteristic
79#41—2061no—
80C2×D4—22no—
81C2×D4—42no—
82Q16—1031no—
83SD16—2061no—
84D8—22no—
85D8—22no—
86D8—41no—
87D8—41no—
88D8—1031no—
89M16—4121no—
90M16—2061no—
91C2×C8—4121no—
92C2×C8C22⋊D10311yescharacteristic
93C2×C8C22×D10311yescharacteristic
94C42C22⋊D10311yescharacteristic
95C16—2062no—
96C23—42no—
97Q8—2061no—
98D4—42no—
99D4—42no—
100D4—84no—
101D4—4121no—
102D4—2061no—
103C2×C4—21no—
104C2×C4—4121no—
105C2×C4C2×C22⋊D10311yescharacteristic
106C8—4121no—
107C8#1311009011yescharacteristic
108C8#1311009011yescharacteristic
109C8D4×D10311yescharacteristic
110C8#1311010411yescharacteristic
111C22—84no—
112C22—82no—
113C22—4121no—
114C22#1569304711yescharacteristic
115C4—22no—
116C4—4121no—
117C4#1569299211yescharacteristic
118C4C2×#1311009011yescharacteristic
119C2—21no—
120C2—162no—
121C2—8241no—
122C2#2026798311yescharacteristic
subgroupG/H
centerC2#20267983
commutator, cosocleC2×C8×C103C23
FrattiniC2×C8C22×D103
Fitting#493×C103C2
socleC2×C103#459
hypercenter#493D103
hypocenterC103#2213
LCSG ▷ C2×C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #20268227C2semidirect
2. #20267909C2semidirect
3. #20267612C2semidirect
4. #20267604C2semidirect
5. #493×C103C2semidirect
18. Dic412D4semidirect
20. D824D4semidirect
62. C103#2213semidirect
64. #493D103semidirect

Maximal subgroups

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

subgroupindex
#202682272
#202679092
#202676122
#202676042
#493×C1032
#2213103