Finite Group Databasebeta

← #27193297

Subgroups — #27193297

Order 13184.

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

normal subgroups only

This group has 106 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#20267973C211yesmaximal, characteristic
2#20267540C211yesmaximal, characteristic, complemented
3#356×C103C211yesmaximal, characteristic, complemented
4#15693069C411yescharacteristic
5#15693052—21no—
6C4⋊(C103⋊C8)—21no—
7#15692949—21no—
8#15692940C411yescharacteristic
9C4⋊Q8×C103C2211yescharacteristic
10#101×C103—21no—
11#13110106—41no—
12#13110105—21no—
13#13110105—41no—
14Q8×D103—41no—
15#13110095—41no—
16#13110092—41no—
17#13110089—21no—
18C2×C103⋊C8—41no—
19C2×Q8×C103C2×C411yescharacteristic
20C2×Q8×C103D411yescharacteristic
21M16×C103—41no—
22C4⋊C4×C103—41no—
23C42×C103D411yescharacteristic
24Q8×C103—41no—
25Q8×C103—41no—
26C2×C4×C103—21no—
27C2×C4×C103—21no—
28C2×C4×C103—21no—
29C2×C4×C103C22⋊C411yescharacteristic
30C22⋊D103—41no—
31D412—21no—
32D412—41no—
33C4×D103—41no—
34C4×D103—42no—
35Dic206—21no—
36Dic206—41no—
37C8×C103—81no—
38C103⋊C8—41no—
39C103⋊C8—81no—
40C22×C103#9911yescharacteristic
41C2×D103—41no—
42C4×C103—21no—
43C4×C103—21no—
44C4×C103—21no—
45C4×C103—41no—
46C4×C103—41no—
47Dic103—41no—
48C2×C103—21no—
49C2×C103AΣL(1,𝔽16)11yescharacteristic
50D103—81no—
51#1405—1031nomaximal, Sylow
52C103#140511yescharacteristic, complemented, Sylow
53#456—1031no—
54#356D10311yescharacteristic, complemented
55#333—1031no—
562−1+4—1031no—
57#137—2061no—
58C4⋊Q8C2×D10311yescharacteristic
59C4⋊C8—2061no—
60#104—2061no—
61#101—21no—
62#101—1031no—
63#41—4121no—
64#41—4121no—
65#41—2061no—
66C2×Q8—4121no—
67C2×Q8C4×D10311yescharacteristic
68C2×Q8C22⋊D10311yescharacteristic
69Q16—4121no—
70SD16—4121no—
71M16—41no—
72M16—2061no—
73C2×C8—4121no—
74C4⋊C4—41no—
75C42D41211yescharacteristic
76Q8—41no—
77Q8—41no—
78Q8—4121no—
79Q8—2061no—
80D4—4121no—
81D4—4121no—
82D4—2061no—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—4121no—
87C2×C4—4122no—
88C2×C4(C2×D103)⋊C411yescharacteristic
89C8—81no—
90C8—8241no—
91C8—4121no—
92C22—4121no—
93C22#1569293511yescharacteristic
94C4—21no—
95C4—21no—
96C4—21no—
97C4—41no—
98C4—41no—
99C4—4121no—
100C2—21no—
101C2—8241no—
102C2#2026757711yescharacteristic
subgroupG/H
centerC2#20267577
commutatorC2×Q8×C103C2×C4
FrattiniC4⋊Q8C2×D103
Fitting#356×C103C2
socleC2×C103AΣL(1,𝔽16)
prime radical#15693069C4
cosocleC4⋊Q8×C103C22
hypercenter#356D103
hypocenterC103#1405
LCSG ▷ C2×Q8×C103 ▷ C2×C4×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #20267540C2semidirect
3. #356×C103C2semidirect
52. C103#1405semidirect
54. #356D103semidirect

Maximal subgroups

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

subgroupindex
#202679732
#202675402
#356×C1032
#1405103