Finite Group Databasebeta

← #28334608

Subgroups — #28334608

Order 13696.

112 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 23 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#20292804C211yesmaximal, characteristic
2#20292367C211yesmaximal, characteristic, complemented
3#355×C107C211yesmaximal, characteristic, complemented
4#16812154C411yescharacteristic
5#16812140—21no—
6#16812037—21no—
7#16812026C411yescharacteristic
8#16812020—21no—
9#124×C107C2211yescharacteristic
10#101×C107—21no—
11#13133818—21no—
12#13133817—41no—
13C2×C22⋊D107—41no—
14D4×D107—41no—
15#13133808—41no—
16#13133805—41no—
17#13133802—21no—
18C2×C107⋊C8—41no—
19C2×Q8×C107D411yescharacteristic
20C2×D4×C107C2×C411yescharacteristic
21M16×C107—41no—
22C22⋊C4×C107—41no—
23C42×C107D411yescharacteristic
24C23×C107—21no—
25C22×D107—41no—
26Q8×C107—41no—
27D4×C107—41no—
28C2×C4×C107—21no—
29C2×C4×C107—21no—
30C2×C4×C107C22⋊C411yescharacteristic
31C22⋊D107—42no—
32C22⋊D107—41no—
33C2×Dic107—41no—
34D428—21no—
35C4×D107—41no—
36Dic214—21no—
37C8×C107—81no—
38C107⋊C8—41no—
39C107⋊C8—42no—
40C22×C107—41no—
41C22×C107—81no—
42C22×C107#9911yescharacteristic
43C2×D107—41no—
44C2×D107—161no—
45C4×C107—21no—
46C4×C107—41no—
47C4×C107—41no—
48Dic107—41no—
49C2×C107—21no—
50C2×C107—81no—
51C2×C107AΣL(1,𝔽16)11yescharacteristic
52D107—81no—
53#1403—1071nomaximal, Sylow
54C107#140311yescharacteristic, complemented, Sylow
55#455—1071no—
56#355D10711yescharacteristic, complemented
57#329—1071no—
58H(5,𝔽2)—1071no—
59#137—2141no—
60#124C2×D10711yescharacteristic
61#104—2141no—
62#101—21no—
63#100—1071no—
64#97—2141no—
65#41—4281no—
66#41—2141no—
67C2×Q8C22⋊D10711yescharacteristic
68C2×D4—4281no—
69C2×D4—4281no—
70C2×D4C4×D10711yescharacteristic
71Q16—4281no—
72SD16—4281no—
73M16—41no—
74M16—2141no—
75C2×C8—4281no—
76C22⋊C4—41no—
77C42D42811yescharacteristic
78C23—21no—
79C23—4281no—
80Q8—41no—
81Q8—2141no—
82D4—41no—
83D4—4282no—
84D4—4281no—
85D4—2141no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—4281no—
89C2×C4—4281no—
90C2×C4(C2×D107)⋊C411yescharacteristic
91C8—81no—
92C8—4281no—
93C8—4282no—
94C22—41no—
95C22—81no—
96C22—4281no—
97C22—17121no—
98C22#1681202311yescharacteristic
99C4—21no—
100C4—41no—
101C4—41no—
102C4—4281no—
103C2—21no—
104C2—81no—
105C2—8561no—
106C2#2029241311yescharacteristic
subgroupG/H
centerC2#20292413
commutatorC2×D4×C107C2×C4
Frattini#124C2×D107
Fitting#355×C107C2
socleC2×C107AΣL(1,𝔽16)
prime radical#16812154C4
cosocle#124×C107C22
hypercenter#355D107
hypocenterC107#1403
LCSG ▷ C2×D4×C107 ▷ C2×C4×C107 ▷ C22×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #20292367C2semidirect
3. #355×C107C2semidirect
54. C107#1403semidirect
56. #355D107semidirect

Maximal subgroups

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

subgroupindex
#202928042
#202923672
#355×C1072
#1403107