Finite Group Databasebeta

← #27193291

Subgroups — #27193291

Order 13184.

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#20267968C211yesmaximal, characteristic
2#20267531C211yesmaximal, characteristic, complemented
3#355×C103C211yesmaximal, characteristic, complemented
4#15693066C411yescharacteristic
5#15693052—21no—
6#15692949—21no—
7#15692938C411yescharacteristic
8#15692932—21no—
9#124×C103C2211yescharacteristic
10#101×C103—21no—
11#13110105—21no—
12#13110104—41no—
13C2×C22⋊D103—41no—
14D4×D103—41no—
15#13110095—41no—
16#13110092—41no—
17#13110089—21no—
18C2×C103⋊C8—41no—
19C2×Q8×C103D411yescharacteristic
20C2×D4×C103C2×C411yescharacteristic
21M16×C103—41no—
22C22⋊C4×C103—41no—
23C42×C103D411yescharacteristic
24C23×C103—21no—
25C22×D103—41no—
26Q8×C103—41no—
27D4×C103—41no—
28C2×C4×C103—21no—
29C2×C4×C103—21no—
30C2×C4×C103C22⋊C411yescharacteristic
31C22⋊D103—42no—
32C22⋊D103—41no—
33C2×Dic103—41no—
34D412—21no—
35C4×D103—41no—
36Dic206—21no—
37C8×C103—81no—
38C103⋊C8—41no—
39C103⋊C8—42no—
40C22×C103—41no—
41C22×C103—81no—
42C22×C103#9911yescharacteristic
43C2×D103—41no—
44C2×D103—161no—
45C4×C103—21no—
46C4×C103—41no—
47C4×C103—41no—
48Dic103—41no—
49C2×C103—21no—
50C2×C103—81no—
51C2×C103AΣL(1,𝔽16)11yescharacteristic
52D103—81no—
53#1403—1031nomaximal, Sylow
54C103#140311yescharacteristic, complemented, Sylow
55#455—1031no—
56#355D10311yescharacteristic, complemented
57#329—1031no—
58H(5,𝔽2)—1031no—
59#137—2061no—
60#124C2×D10311yescharacteristic
61#104—2061no—
62#101—21no—
63#100—1031no—
64#97—2061no—
65#41—4121no—
66#41—2061no—
67C2×Q8C22⋊D10311yescharacteristic
68C2×D4—4121no—
69C2×D4—4121no—
70C2×D4C4×D10311yescharacteristic
71Q16—4121no—
72SD16—4121no—
73M16—41no—
74M16—2061no—
75C2×C8—4121no—
76C22⋊C4—41no—
77C42D41211yescharacteristic
78C23—21no—
79C23—4121no—
80Q8—41no—
81Q8—2061no—
82D4—41no—
83D4—4122no—
84D4—4121no—
85D4—2061no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—4121no—
89C2×C4—4121no—
90C2×C4(C2×D103)⋊C411yescharacteristic
91C8—81no—
92C8—4121no—
93C8—4122no—
94C22—41no—
95C22—81no—
96C22—16481no—
97C22—4121no—
98C22#1569293511yescharacteristic
99C4—21no—
100C4—41no—
101C4—41no—
102C4—4121no—
103C2—21no—
104C2—81no—
105C2—8241no—
106C2#2026757711yescharacteristic
subgroupG/H
centerC2#20267577
commutatorC2×D4×C103C2×C4
Frattini#124C2×D103
Fitting#355×C103C2
socleC2×C103AΣL(1,𝔽16)
prime radical#15693066C4
cosocle#124×C103C22
hypercenter#355D103
hypocenterC103#1403
LCSG ▷ C2×D4×C103 ▷ C2×C4×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #20267531C2semidirect
3. #355×C103C2semidirect
54. C103#1403semidirect
56. #355D103semidirect

Maximal subgroups

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

subgroupindex
#202679682
#202675312
#355×C1032
#1403103