Finite Group Databasebeta

← #34102304

Subgroups — #34102304

Order 20096.

126 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 47 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#23757391C211yesmaximal, characteristic
2#23757095C212yesmaximal, complemented
3#23757094C211yesmaximal, characteristic, complemented
4#23757082C212yesmaximal
5#498×C157C211yesmaximal, characteristic, complemented
6#19097793C2211yescharacteristic
7#19097777—21no—
8#19097711C2212yes—
9#19097707C2211yescharacteristic
10#19097699—21no—
11C4⋊Q8×C157—21no—
12#106×C157—21no—
13#106×C157C2212yes—
14C4×C8×C157C2211yescharacteristic
15#14578954—21no—
16Dic628Q811yescharacteristic, complemented
17#14578943—21no—
18D1256Q811yescharacteristic, complemented
19#14578938—21no—
20#14578937—41no—
21C8×D157—41no—
22#14578929—22no—
23C2×Q8×C157—41no—
24C2×C8×C157D411yescharacteristic
25C2×C8×C157C2311yescharacteristic
26C4⋊C4×C157—22no—
27C4⋊C4×C157—41no—
28C42×C157D411yescharacteristic
29Dic314—21no—
30D628—21no—
31C22⋊D157—41no—
32C4×D157—41no—
33#11929434—41no—
34Q8×C157—82no—
35C2×C4×C157—21no—
36C2×C4×C157—42no—
37C2×C4×C157C2×D411yescharacteristic
38C8×C157SD1611yescharacteristic
39C8×C157SD1611yescharacteristic
40C8×C157C2×Q811yescharacteristic
41C8×C157#4111yescharacteristic
42C22×C157AGL(1,ℤ/8)11yescharacteristic
43C2×D157—41no—
44C4×C157—22no—
45C4×C157—82no—
46C4×C157C22⋊Q811yescharacteristic
47C4×C157C2×SD1611yescharacteristic
48Dic157—41no—
49C2×C157—21no—
50C2×C157#47611yescharacteristic
51D157—81no—
52C157#223011yescharacteristic, complemented, Sylow
53#2230—1571nomaximal, Sylow
54#498D15711yescharacteristic, complemented
55#443—1571no—
56#365—1572no—
57#364—1571no—
58#360—1572no—
59#135—1571no—
60#131—3141no—
61C4⋊Q8—21no—
62M32—1572no—
63#108—1571no—
64#106—21no—
65#106C2×D15712yes—
66#104—3141no—
67C4×C8C2×D15711yescharacteristic
68#41—3141no—
69C2×Q8—41no—
70Q16—1571no—
71SD16—3141no—
72D8—1571no—
73M16—3141no—
74M16—6281no—
75C2×C8—6281no—
76C2×C8C22⋊D15711yescharacteristic
77C2×C8C22×D15711yescharacteristic
78C4⋊C4—22no—
79C4⋊C4—41no—
80C42C22⋊D15711yescharacteristic
81C16—3142no—
82Q8—82no—
83Q8—3141no—
84D4—3141no—
85D4—6281no—
86C2×C4—21no—
87C2×C4—42no—
88C2×C4—6281no—
89C2×C4C2×C22⋊D15711yescharacteristic
90C8—6281no—
91C8#1457894111yescharacteristic
92C8#1457894111yescharacteristic
93C8Q8×D15711yescharacteristic
94C8#1457895511yescharacteristic
95C22—6281no—
96C22#1909779711yescharacteristic
97C4—22no—
98C4—82no—
99C4—6281no—
100C4#1909774711yescharacteristic
101C4C2×#1457894111yescharacteristic
102C2—21no—
103C2—12561no—
104C2#2375756011yescharacteristic
subgroupG/H
centerC2#23757560
commutator, cosocleC2×C8×C157C23
FrattiniC2×C8C22×D157
Fitting#498×C157C2
socleC2×C157#476
prime radical#19097793C22
hypercenter#498D157
hypocenterC157#2230
LCSG ▷ C2×C8×C157 ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #498

Complements

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

NH ≅ G/Ntype
2. #23757095C2semidirect
3. #23757094C2semidirect
5. #498×C157C2semidirect
16. Dic628Q8semidirect
18. D1256Q8semidirect
52. C157#2230semidirect
54. #498D157semidirect

Maximal subgroups

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

subgroupindex
#237573912
#237570952
#237570942
#237570822
#498×C1572
#2230157