Finite Group Databasebeta

← #28338534

Subgroups — #28338534

Order 13696.

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#20293063C212yesmaximal, complemented
2#20292745C211yesmaximal, characteristic, complemented
3#20292448C211yesmaximal, characteristic, complemented
4#20292440C212yesmaximal, complemented
5#493×C107C211yesmaximal, characteristic, complemented
6#16812131C2211yescharacteristic
7#16812115—21no—
8#16812053—22no—
9#16812050—22no—
10#16812049C2212yes—
11#16812045C2211yescharacteristic
12#16812037—21no—
13C2×D8×C107—21no—
14C2×D8×C107C2212yes—
15#127×C107—21no—
16C4×C8×C107C2211yescharacteristic
17#13133818—21no—
18Dic428D411yescharacteristic, complemented
19#13133807—21no—
20D856D411yescharacteristic, complemented
21#13133802—21no—
22#13133801—41no—
23C8×D107—41no—
24C107⋊C16—22no—
25C2×D4×C107—22no—
26C2×D4×C107—42no—
27D8×C107—22no—
28D8×C107—22no—
29D8×C107—41no—
30D8×C107—41no—
31C2×C8×C107D411yescharacteristic
32C2×C8×C107C2311yescharacteristic
33C42×C107D411yescharacteristic
34C23×C107—42no—
35D4×C107—42no—
36D4×C107—42no—
37D4×C107—84no—
38C2×C4×C107—21no—
39C2×C4×C107C2×D411yescharacteristic
40C22⋊D107—41no—
41D428—21no—
42C4×D107—41no—
43Dic214—21no—
44C8×C107D811yescharacteristic
45C8×C107D811yescharacteristic
46C8×C107C2×D411yescharacteristic
47C8×C107#4111yescharacteristic
48C107⋊C8—41no—
49C22×C107—84no—
50C22×C107—82no—
51C22×C107AGL(1,ℤ/8)11yescharacteristic
52C2×D107—41no—
53C4×C107—22no—
54C4×C107#12111yescharacteristic
55C4×C107C2×D811yescharacteristic
56Dic107—41no—
57C2×C107—21no—
58C2×C107—162no—
59C2×C107#45911yescharacteristic
60D107—81no—
61#2213—1071nomaximal, Sylow
62C107#221311yescharacteristic, complemented, Sylow
63#509—1072no—
64#493D10711yescharacteristic, complemented
65#443—1071no—
66#364—1071no—
67#361—1072no—
68#135—1071no—
69C2×D8—21no—
70C2×D8C2×D10712yes—
71#131—2141no—
72#127—21no—
73SD32—2142no—
74D16—2142no—
75M32—1072no—
76#108—1071no—
77#104—2141no—
78C4×C8C2×D10711yescharacteristic
79#41—2141no—
80C2×D4—22no—
81C2×D4—42no—
82Q16—1071no—
83SD16—2141no—
84D8—22no—
85D8—22no—
86D8—41no—
87D8—41no—
88D8—1071no—
89M16—4281no—
90M16—2141no—
91C2×C8—4281no—
92C2×C8C22⋊D10711yescharacteristic
93C2×C8C22×D10711yescharacteristic
94C42C22⋊D10711yescharacteristic
95C16—2142no—
96C23—42no—
97Q8—2141no—
98D4—42no—
99D4—42no—
100D4—84no—
101D4—4281no—
102D4—2141no—
103C2×C4—21no—
104C2×C4—4281no—
105C2×C4C2×C22⋊D10711yescharacteristic
106C8—4281no—
107C8#1313380311yescharacteristic
108C8#1313380311yescharacteristic
109C8D4×D10711yescharacteristic
110C8#1313381711yescharacteristic
111C22—84no—
112C22—82no—
113C22—4281no—
114C22#1681213511yescharacteristic
115C4—22no—
116C4—4281no—
117C4#1681208011yescharacteristic
118C4C2×#1313380311yescharacteristic
119C2—21no—
120C2—162no—
121C2—8561no—
122C2#2029281911yescharacteristic
subgroupG/H
centerC2#20292819
commutator, cosocleC2×C8×C107C23
FrattiniC2×C8C22×D107
Fitting#493×C107C2
socleC2×C107#459
hypercenter#493D107
hypocenterC107#2213
LCSG ▷ C2×C8×C107 ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #20293063C2semidirect
2. #20292745C2semidirect
3. #20292448C2semidirect
4. #20292440C2semidirect
5. #493×C107C2semidirect
18. Dic428D4semidirect
20. D856D4semidirect
62. C107#2213semidirect
64. #493D107semidirect

Maximal subgroups

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

subgroupindex
#202930632
#202927452
#202924482
#202924402
#493×C1072
#2213107