Finite Group Databasebeta

← #44484180

Subgroups — #44484180

Order 30592.

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

normal subgroups only

This group has 176 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#29505168C211yesmaximal, characteristic
2#29505168C211yesmaximal, characteristic
3#29505151C211yesmaximal, characteristic
4#29505123C211yesmaximal, characteristic
5#29505122C211yesmaximal, characteristic
6#29504494C211yesmaximal, characteristic
7#498×C239C211yesmaximal, characteristic
8C2×#16838538—22no—
9#21439960C2211yescharacteristic
10#21439960C2211yescharacteristic
11#21439891—22no—
12#21439891—22no—
13#21439885—22no—
14#21439884—22no—
15C4×C239⋊C8C2211yescharacteristic
16C4×C239⋊C8C2211yescharacteristic
17C4⋊Q8×C239C2211yescharacteristic
18C4⋊Q8×C239C2211yescharacteristic
19#106×C239—22no—
20C4×C8×C239C2211yescharacteristic
21C2×Dic478—21no—
22C2×Dic478—21no—
23#16838538—44no—
24C2×C239⋊C8D412yes—
25C2×C239⋊C8D412yes—
26C4⋊Dic239—21no—
27C4⋊Dic239—21no—
28C4⋊Dic239—21no—
29C4⋊Dic239—21no—
30C2×Q8×C239—21no—
31C2×Q8×C239—21no—
32C2×C8×C239D412yes—
33C4⋊C4×C239—21no—
34C4⋊C4×C239—21no—
35C4⋊C4×C239—21no—
36C4⋊C4×C239—21no—
37C42×C239C2311yescharacteristic
38Dic478—42no—
39Dic478—42no—
40C2×Dic239—41no—
41C2×Dic239—41no—
42C239⋊C8—22no—
43C239⋊C8SD1614yes—
44Q8×C239—42no—
45Q8×C239—42no—
46C2×C4×C239—41no—
47C2×C4×C239—41no—
48C2×C4×C239C2×D411yescharacteristic
49C2×C4×C239C2×D411yescharacteristic
50C2×C4×C239C2×D411yescharacteristic
51C8×C239—22no—
52C22×C239#12711yescharacteristic
53C4×C239—81no—
54C4×C239—81no—
55C4×C239C2×SD1612yes—
56C4×C239#13712yes—
57C4×C239#13712yes—
58Dic239—81no—
59Dic239—81no—
60C2×C239#49211yescharacteristic
61C2×C239#49711yescharacteristic
62C2×C239#49711yescharacteristic
63C239#171611yescharacteristic, complemented, Sylow
64#1716—2391nomaximal, Sylow
65#498—2391no—
66#498—2391no—
67#498D23911yescharacteristic
68#494—2391no—
69#487—2391no—
70#487—2391no—
71#322—2391no—
72C2×Q16—4782no—
73C4⋊Q8—2391no—
74C4⋊Q8—2391no—
75C4⋊Q8C2×D23911yescharacteristic
76C4⋊Q8C2×D23911yescharacteristic
77#106—22no—
78#106—4782no—
79#106—4782no—
80#103—4782no—
81#103—4782no—
82C4×C8—2391no—
83C4×C8—2391no—
84C4×C8C2×D23911yescharacteristic
85C2×Q8—21no—
86C2×Q8—21no—
87C2×Q8—4781no—
88C2×Q8—4781no—
89Q16—9564no—
90C2×C8—2392no—
91C2×C8—2392no—
92C2×C8C22⋊D23912yes—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—21no—
97C4⋊C4—4781no—
98C4⋊C4—4781no—
99C4⋊C4—4781no—
100C4⋊C4—4781no—
101C42C22×D23911yescharacteristic
102Q8—42no—
103Q8—42no—
104Q8—9562no—
105Q8—9562no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—9561no—
109C2×C4—9561no—
110C2×C4D4×D23911yescharacteristic
111C2×C4D4×D23911yescharacteristic
112C2×C4C2×C22⋊D23911yescharacteristic
113C8—22no—
114C8—4782no—
115C8—2394no—
116C22#2143995611yescharacteristic
117C4—81no—
118C4—81no—
119C4—19121no—
120C4—19121no—
121C4SD16×D23912yes—
122C4#2143998912yes—
123C4#2143999112yes—
124C2#2950514311yescharacteristic
125C2#2950516311yescharacteristic
126C2#2950516411yescharacteristic
subgroupG/H
centerC22#21439956
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#498×C239C2
socle, prime radicalC22×C239#127
hypercenter#498D239
hypocenterC239#1716
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
63. C239#1716semidirect

Maximal subgroups

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

subgroupindex
#295051682
#295051512
#295051232
#295051222
#295044942
#498×C2392
#1716239