Finite Group Databasebeta

← #34088078

Subgroups — #34088078

Order 19648.

160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 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#23754305C211yesmaximal, characteristic
2#23754244C212yesmaximal, complemented
3#23754241C211yesmaximal, characteristic, complemented
4#23754174C212yesmaximal, complemented
5#99×C307C211yesmaximal, characteristic, complemented
6#19096826—21no—
7#19096825—22no—
8C2×C22⋊D307—21no—
9C2×C22⋊D307C2212yes—
10D4×D307—22no—
11C22×Dic307C2211yescharacteristic, complemented
12C4⋊Dic307—22no—
13Dic307⋊C4—21no—
14C22⋊Dic307—21no—
15C22⋊Dic307C2211yescharacteristic, complemented
16(C2×D307)⋊C4—22no—
17C2×D4×C307C2211yescharacteristic
18C22⋊C4×C307C2212yescomplemented
19C22×D307—21no—
20C22×D307D412yes—
21Dic614—21no—
22D1228—21no—
23C22⋊D307—22no—
24C22⋊D307—22no—
25C22⋊D307—22no—
26C2×Dic307—21no—
27C2×Dic307—22no—
28C2×Dic307—21no—
29C2×Dic307—21no—
30C2×Dic307D412yes—
31C4×D307—22no—
32C23×C307D411yescharacteristic
33C23×C307C2311yescharacteristic
34D4×C307—22no—
35C2×C4×C307—22no—
36C2×C4×C307D411yescharacteristic
37C22×C307—21no—
38C22×C307—41no—
39C22×C307—41no—
40C22×C307C2×D412yes—
41C22×C307C2×D411yescharacteristic
42C2×D307—22no—
43C2×D307—42no—
44C2×D307—81no—
45C4×C307—21no—
46C4×C307—42no—
47Dic307—22no—
48Dic307—41no—
49Dic307—41no—
50C2×C307—21no—
51C2×C307—22no—
52C2×C307—41no—
53C2×C307#12011yescharacteristic
54D307—42no—
55C307#45811yescharacteristic, complemented, Sylow
56#458—3071nomaximal, Sylow
57H(5,𝔽2)—3071no—
58#123—3071no—
59#123—3072no—
60#99—3072no—
61#99D30711yescharacteristic, complemented
62#41—6142no—
63#41—6141no—
64C2×D4—3072no—
65C2×D4—6142no—
66C2×D4—6141no—
67C2×D4C2×D30711yescharacteristic
68C22×C4—3071no—
69C4⋊C4—6142no—
70C4⋊C4—6141no—
71C22⋊C4—3071no—
72C22⋊C4—6142no—
73C22⋊C4—6141no—
74C22⋊C4C2×D30712yescomplemented
75C23—3072no—
76C23—6141no—
77C23D122811yescharacteristic
78C23C22×D30711yescharacteristic
79Q8—6141no—
80D4—22no—
81D4—6141no—
82D4—6142no—
83D4—6142no—
84D4—6142no—
85C2×C4—22no—
86C2×C4—3072no—
87C2×C4—6142no—
88C2×C4—6141no—
89C2×C4—6142no—
90C2×C4—6141no—
91C2×C4—6141no—
92C2×C4D122811yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—6142no—
97C22—24561no—
98C22—12282no—
99C22D4×D30712yes—
100C22C2×D122811yescharacteristic
101C4—21no—
102C4—42no—
103C4—6142no—
104C4—12281no—
105C4—12281no—
106C2—22no—
107C2—21no—
108C2—41no—
109C2—12282no—
110C2#2375423011yescharacteristic
subgroupG/H
centerC2#23754230
commutator, cosocleC23×C307C23
FrattiniC23C22×D307
Fitting#99×C307C2
socleC2×C307#120
prime radical#23754305C2
hypercenter#99D307
hypocenterC307#458
LCSG ▷ C23×C307 ▷ C2×C307 ▷ C307
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #23754244C2semidirect
3. #23754241C2semidirect
4. #23754174C2semidirect
5. #99×C307C2semidirect
11. C22×Dic307C22semidirect
15. C22⋊Dic307C22semidirect
18. C22⋊C4×C307C22semidirect
55. C307#458semidirect
61. #99D307semidirect
74. C22⋊C4C2×D307semidirect

Maximal subgroups

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

subgroupindex
#237543052
#237542442
#237542412
#237541742
#99×C3072
#458307