Finite Group Databasebeta

← #37565432

Subgroups — #37565432

Order 24256.

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

normal subgroups only

This group has 198 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, complemented
2#27131301C212yesmaximal, complemented
3#27131299C211yesmaximal, characteristic, complemented
4#27131245C212yesmaximal, complemented
5#99×C379C211yesmaximal, characteristic, complemented
6C23×D379C2211yescharacteristic, complemented
7#20258606—21no—
8#20258605—22no—
9C2×D1516—22no—
10C2×C22⋊D379—21no—
11C2×C22⋊D379—21no—
12C2×C22⋊D379C2212yes—
13D4×D379—22no—
14C22⋊Dic379C2211yescharacteristic, complemented
15(C2×D379)⋊C4—22no—
16(C2×D379)⋊C4—21no—
17C2×D4×C379C2211yescharacteristic
18C22⋊C4×C379C2212yescomplemented
19C22×D379—21no—
20C22×D379—22no—
21C22×D379—21no—
22C22×D379—42no—
23C22×D379D412yescomplemented
24Dic758—21no—
25D1516—21no—
26D1516—44no—
27C22⋊D379—22no—
28C22⋊D379—22no—
29C22⋊D379—22no—
30C22⋊D379—42no—
31C2×Dic379—21no—
32C2×Dic379—21no—
33C2×Dic379D412yescomplemented
34C4×D379—22no—
35C23×C379D411yescharacteristic, complemented
36C23×C379C2311yescharacteristic
37D4×C379—22no—
38C2×C4×C379—22no—
39C2×C4×C379D411yescharacteristic, complemented
40C22×C379—21no—
41C22×C379—41no—
42C22×C379—41no—
43C22×C379C2×D412yes—
44C22×C379C2×D411yescharacteristic
45C2×D379—22no—
46C2×D379—24no—
47C2×D379—22no—
48C2×D379—41no—
49C2×D379—42no—
50C2×D379—41no—
51C2×D379—42no—
52C2×D379—81no—
53C4×C379—21no—
54C4×C379—42no—
55Dic379—22no—
56Dic379—41no—
57C2×C379—21no—
58C2×C379—22no—
59C2×C379—41no—
60C2×C379#12011yescharacteristic
61D379—42no—
62D379—42no—
63C379B(4,𝔽2)11yescharacteristic, complemented, Sylow
64B(4,𝔽2)—3791nomaximal, Sylow
65H(5,𝔽2)—3791no—
66#120—3791no—
67#120—3792no—
68#99—3792no—
69#99D37911yescharacteristic, complemented
70C24—3791no—
71#41—7582no—
72#41—7581no—
73C2×D4—3792no—
74C2×D4—7582no—
75C2×D4—7582no—
76C2×D4—7581no—
77C2×D4—7581no—
78C2×D4C2×D37911yescharacteristic
79C22⋊C4—3791no—
80C22⋊C4—7582no—
81C22⋊C4—7581no—
82C22⋊C4C2×D37912yescomplemented
83C23—3792no—
84C23—15162no—
85C23—7581no—
86C23—7582no—
87C23—7581no—
88C23D151611yescharacteristic, complemented
89C23C22×D37911yescharacteristic
90Q8—7581no—
91D4—22no—
92D4—15164no—
93D4—15162no—
94D4—7581no—
95D4—7582no—
96D4—7582no—
97D4—7582no—
98C2×C4—22no—
99C2×C4—3792no—
100C2×C4—7582no—
101C2×C4—7581no—
102C2×C4—7581no—
103C2×C4D151611yescharacteristic, complemented
104C22—21no—
105C22—41no—
106C22—41no—
107C22—30321no—
108C22—15162no—
109C22—15162no—
110C22—15161no—
111C22—15161no—
112C22—7584no—
113C22—7582no—
114C22—7582no—
115C22D4×D37912yes—
116C22C2×D151611yescharacteristic
117C4—21no—
118C4—42no—
119C4—15161no—
120C4—7582no—
121C2—22no—
122C2—21no—
123C2—41no—
124C2—15162no—
125C2—15162no—
126C2#2713130111yescharacteristic
subgroupG/H
centerC2#27131301
commutator, cosocleC23×C379C23
FrattiniC23C22×D379
Fitting#99×C379C2
socleC2×C379#120
hypercenter#99D379
hypocenterC379B(4,𝔽2)
LCSG ▷ C23×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
1. #27131376C2semidirect
2. #27131301C2semidirect
3. #27131299C2semidirect
4. #27131245C2semidirect
5. #99×C379C2semidirect
6. C23×D379C22semidirect
14. C22⋊Dic379C22semidirect
18. C22⋊C4×C379C22semidirect
23. C22×D379D4semidirect
33. C2×Dic379D4semidirect
35. C23×C379D4semidirect
39. C2×C4×C379D4semidirect
63. C379B(4,𝔽2)semidirect
69. #99D379semidirect
82. C22⋊C4C2×D379semidirect
88. C23D1516semidirect
103. C2×C4D1516semidirect

Maximal subgroups

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

subgroupindex
#271313762
#271313012
#271312992
#271312452
#99×C3792
B(4,𝔽2)379