Finite Group Databasebeta

← #37565435

Subgroups — #37565435

Order 24256.

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#27131376C211yesmaximal, characteristic
2#27131315C212yesmaximal, complemented
3#27131312C211yesmaximal, characteristic, complemented
4#27131245C212yesmaximal, complemented
5#99×C379C211yesmaximal, characteristic, complemented
6#20258606—21no—
7#20258605—22no—
8C2×C22⋊D379—21no—
9C2×C22⋊D379C2212yes—
10D4×D379—22no—
11C22×Dic379C2211yescharacteristic, complemented
12C4⋊Dic379—22no—
13Dic379⋊C4—21no—
14C22⋊Dic379—21no—
15C22⋊Dic379C2211yescharacteristic, complemented
16(C2×D379)⋊C4—22no—
17C2×D4×C379C2211yescharacteristic
18C22⋊C4×C379C2212yescomplemented
19C22×D379—21no—
20C22×D379D412yes—
21Dic758—21no—
22D1516—21no—
23C22⋊D379—22no—
24C22⋊D379—22no—
25C22⋊D379—22no—
26C2×Dic379—21no—
27C2×Dic379—22no—
28C2×Dic379—21no—
29C2×Dic379—21no—
30C2×Dic379D412yes—
31C4×D379—22no—
32C23×C379D411yescharacteristic
33C23×C379C2311yescharacteristic
34D4×C379—22no—
35C2×C4×C379—22no—
36C2×C4×C379D411yescharacteristic
37C22×C379—21no—
38C22×C379—41no—
39C22×C379—41no—
40C22×C379C2×D412yes—
41C22×C379C2×D411yescharacteristic
42C2×D379—22no—
43C2×D379—42no—
44C2×D379—81no—
45C4×C379—21no—
46C4×C379—42no—
47Dic379—22no—
48Dic379—41no—
49Dic379—41no—
50C2×C379—21no—
51C2×C379—22no—
52C2×C379—41no—
53C2×C379#12011yescharacteristic
54D379—42no—
55C379#45811yescharacteristic, complemented, Sylow
56#458—3791nomaximal, Sylow
57H(5,𝔽2)—3791no—
58#123—3791no—
59#123—3792no—
60#99—3792no—
61#99D37911yescharacteristic, complemented
62#41—7582no—
63#41—7581no—
64C2×D4—3792no—
65C2×D4—7582no—
66C2×D4—7581no—
67C2×D4C2×D37911yescharacteristic
68C22×C4—3791no—
69C4⋊C4—7582no—
70C4⋊C4—7581no—
71C22⋊C4—3791no—
72C22⋊C4—7582no—
73C22⋊C4—7581no—
74C22⋊C4C2×D37912yescomplemented
75C23—3792no—
76C23—7581no—
77C23D151611yescharacteristic
78C23C22×D37911yescharacteristic
79Q8—7581no—
80D4—22no—
81D4—7581no—
82D4—7582no—
83D4—7582no—
84D4—7582no—
85C2×C4—22no—
86C2×C4—3792no—
87C2×C4—7582no—
88C2×C4—7582no—
89C2×C4—7581no—
90C2×C4—7581no—
91C2×C4—7581no—
92C2×C4D151611yescharacteristic
93C22—21no—
94C22—41no—
95C22—41no—
96C22—30321no—
97C22—15162no—
98C22—7582no—
99C22D4×D37912yes—
100C22C2×D151611yescharacteristic
101C4—21no—
102C4—42no—
103C4—15161no—
104C4—15161no—
105C4—7582no—
106C2—22no—
107C2—21no—
108C2—41no—
109C2—15162no—
110C2#2713130111yescharacteristic
subgroupG/H
centerC2#27131301
commutator, cosocleC23×C379C23
FrattiniC23C22×D379
Fitting#99×C379C2
socleC2×C379#120
prime radical#27131376C2
hypercenter#99D379
hypocenterC379#458
LCSG ▷ C23×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #27131315C2semidirect
3. #27131312C2semidirect
4. #27131245C2semidirect
5. #99×C379C2semidirect
11. C22×Dic379C22semidirect
15. C22⋊Dic379C22semidirect
18. C22⋊C4×C379C22semidirect
55. C379#458semidirect
61. #99D379semidirect
74. C22⋊C4C2×D379semidirect

Maximal subgroups

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

subgroupindex
#271313762
#271313152
#271313122
#271312452
#99×C3792
#458379