Finite Group Databasebeta

← #27193296

Subgroups — #27193296

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#20267963C211yesmaximal, characteristic
2#20267586C211yesmaximal, characteristic, complemented
3#329×C103C211yesmaximal, characteristic, complemented
4#15693069C411yescharacteristic, complemented
5#15693047—21no—
6#15692949—21no—
7#15692940C411yescharacteristic, complemented
8#15692936—21no—
9#124×C103C2211yescharacteristic
10#97×C103—21no—
11#13110106—41no—
12#13110105—21no—
13#13110105—41no—
14Q8×D103—41no—
15#13110093—41no—
16#13110090—41no—
17#13110089—21no—
18C22⋊Dic103—41no—
19C2×Q8×C103C2×C411yescharacteristic
20C2×D4×C103D411yescharacteristic
21C2×C8×C103—41no—
22C22⋊C4×C103—41no—
23C42×C103D411yescharacteristic
24C23×C103—21no—
25Q8×C103—41no—
26D4×C103—41no—
27C2×C4×C103—21no—
28C2×C4×C103—21no—
29C2×C4×C103C22⋊C411yescharacteristic
30C22⋊D103—41no—
31C2×Dic103—81no—
32D412—21no—
33D412—41no—
34C4×D103—41no—
35C4×D103—42no—
36Dic206—21no—
37Dic206—41no—
38C8×C103—42no—
39C103⋊C8—41no—
40C22×C103—41no—
41C22×C103—81no—
42C22×C103#9911yescharacteristic
43C2×D103—41no—
44C4×C103—21no—
45C4×C103—41no—
46C4×C103—41no—
47Dic103—41no—
48Dic103—161no—
49C2×C103—21no—
50C2×C103—81no—
51C2×C103AΣL(1,𝔽16)11yescharacteristic
52D103—81no—
53#1404—1031nomaximal, Sylow
54C103#140411yescharacteristic, complemented, Sylow
55#454—1031no—
56#354—1031no—
57#329D10311yescharacteristic, complemented
582−1+4—1031no—
59AGL(1,ℤ/8)—2061no—
60#124C2×D10311yescharacteristic
61#104—2061no—
62#101—1031no—
63#99—2061no—
64#97—21no—
65#41—4121no—
66#41—4121no—
67#41—2061no—
68C2×Q8—4121no—
69C2×Q8C4×D10311yescharacteristic
70C2×D4D41211yescharacteristic
71SD16—4121no—
72D8—4121no—
73M16—2061no—
74C2×C8—41no—
75C22⋊C4—41no—
76C22⋊C4—4121no—
77C42C22⋊D10311yescharacteristic
78C23—21no—
79Q8—41no—
80Q8—4121no—
81Q8—2061no—
82D4—41no—
83D4—4121no—
84D4—4121no—
85D4—2061no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—8241no—
89C2×C4—4121no—
90C2×C4—4122no—
91C2×C4(C2×D103)⋊C411yescharacteristic
92C8—42no—
93C8—4121no—
94C22—41no—
95C22—81no—
96C22—4121no—
97C22#1569293511yescharacteristic
98C4—21no—
99C4—41no—
100C4—41no—
101C4—16481no—
102C4—4121no—
103C2—21no—
104C2—81no—
105C2—8241no—
106C2#2026757911yescharacteristic
subgroupG/H
centerC2#20267579
commutatorC2×Q8×C103C2×C4
Frattini#124C2×D103
Fitting#329×C103C2
socleC2×C103AΣL(1,𝔽16)
prime radical#20267963C2
cosocle#124×C103C22
hypercenter#329D103
hypocenterC103#1404
LCSG ▷ C2×Q8×C103 ▷ C2×C4×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #20267586C2semidirect
3. #329×C103C2semidirect
4. #15693069C4semidirect
7. #15692940C4semidirect
54. C103#1404semidirect
57. #329D103semidirect

Maximal subgroups

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

subgroupindex
#202679632
#202675862
#329×C1032
#1404103