Finite Group Databasebeta

← #27197369

Subgroups — #27197369

Order 13184.

160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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#20268168C211yesmaximal, characteristic
2#20267591C214yesmaximal, complemented
3C4×C103⋊C16C211yesmaximal, characteristic, complemented
4#500×C103C211yesmaximal, characteristic, complemented
5C2×D824—21no—
6C2×D824C2212yes—
7#15693018—21no—
8C2×C103⋊C16C2212yes—
9C4⋊Q8×C103—21no—
10#107×C103—21no—
11#107×C103C2212yes—
12C4×C8×C103C2211yescharacteristic
13C2×D412—22no—
14C2×D412—41no—
15C2×D412—41no—
16D824—24no—
17D824—42no—
18C103⋊C16—22no—
19C2×Q8×C103—41no—
20C2×C8×C103D411yescharacteristic
21C2×C8×C103C2311yescharacteristic
22C4⋊C4×C103—22no—
23C4⋊C4×C103—41no—
24C42×C103D411yescharacteristic
25C22×D103—42no—
26Q8×C103—82no—
27C2×C4×C103—42no—
28C2×C4×C103D811yescharacteristic
29C2×C4×C103D811yescharacteristic
30C2×C4×C103C2×D411yescharacteristic
31D412—42no—
32D412—42no—
33D412—82no—
34D412—82no—
35C8×C103SD1612yes—
36C8×C103#4112yes—
37C22×C103C2×D811yescharacteristic
38C2×D103—82no—
39C2×D103—82no—
40C2×D103—82no—
41C4×C103—82no—
42C4×C103D1612yes—
43C4×C103SD3212yes—
44C4×C103#12411yescharacteristic
45C4×C103C2×SD1611yescharacteristic
46C2×C103#48611yescharacteristic
47C2×C103C2×D1611yescharacteristic
48C2×C103C2×SD3211yescharacteristic
49D103—162no—
50#2240—1031nomaximal, Sylow
51C103#224011yescharacteristic, complemented, Sylow
52#500D10311yescharacteristic, complemented
53#493—1031no—
54#357—1034no—
55C4×C16—1031no—
56C2×D8—1032no—
57C2×D8—2061no—
58C4⋊Q8—21no—
59#127—2061no—
60C2×C16—1032no—
61#107—21no—
62#107C2×D10312yes—
63C4×C8C2×D10311yescharacteristic
64C2×Q8—41no—
65C2×D4—4121no—
66C2×D4—4121no—
67C2×D4—2062no—
68D8—4122no—
69D8—2064no—
70C2×C8C22⋊D10311yescharacteristic
71C2×C8C22×D10311yescharacteristic
72C4⋊C4—22no—
73C4⋊C4—41no—
74C42C22⋊D10311yescharacteristic
75C16—2062no—
76C23—4122no—
77Q8—82no—
78D4—8242no—
79D4—8242no—
80D4—4122no—
81D4—4122no—
82C2×C4—42no—
83C2×C4#1311009011yescharacteristic
84C2×C4#1311009011yescharacteristic
85C2×C4C2×C22⋊D10311yescharacteristic
86C8#1311009212yes—
87C8#1311010612yes—
88C22—8242no—
89C22—8242no—
90C22—8242no—
91C22C2×#1311009011yescharacteristic
92C4—82no—
93C4#1569296212yes—
94C4#1569296412yes—
95C4#1569301011yescharacteristic
96C4C2×#1311009211yescharacteristic
97C2—16482no—
98C2#2026813911yescharacteristic
99C2C2×#1569296211yescharacteristic
100C2C2×#1569296411yescharacteristic
subgroupG/H
centerC22C2×#13110090
commutator, cosocleC2×C8×C103C23
FrattiniC2×C8C22×D103
Fitting#500×C103C2
socleC22×C103C2×D8
prime radical#20268168C2
hypercenter#500D103
hypocenterC103#2240
LCSG ▷ C2×C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
2. #20267591C2semidirect
3. C4×C103⋊C16C2semidirect
4. #500×C103C2semidirect
51. C103#2240semidirect
52. #500D103semidirect

Maximal subgroups

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

subgroupindex
#202681682
#202675912
C4×C103⋊C162
#500×C1032
#2240103