Finite Group Databasebeta

← #44482578

Subgroups — #44482578

Order 30592.

140 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 37 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#29504541C211yesmaximal, characteristic
2#29504498C211yesmaximal, characteristic
3#395×C239C211yesmaximal, characteristic
4C2×#16838532—21no—
5C22⋊(C239⋊C8)—21no—
6C22×Q8×C239C411yescharacteristic
7C2×C4⋊C4×C239—21no—
8C2×C4⋊C4×C239C2211yescharacteristic
9#95×C239—21no—
10#95×C239C411yescharacteristic
11#16838532—22no—
12#16838532—41no—
13C2×C239⋊C8—41no—
14C2×C239⋊C8—41no—
15C2×Q8×C239—42no—
16C2×Q8×C239—41no—
17C22×C4×C239—21no—
18C22×C4×C239—21no—
19C22×C4×C239C2×C411yescharacteristic
20C22×C4×C239D411yescharacteristic
21C22×C4×C239D411yescharacteristic
22C4⋊C4×C239—41no—
23C4⋊C4×C239—42no—
24C239⋊C8—42no—
25C239⋊C8—81no—
26C23×C239C22⋊C411yescharacteristic
27Q8×C239—42no—
28Q8×C239—42no—
29C2×C4×C239—21no—
30C2×C4×C239—21no—
31C2×C4×C239—22no—
32C2×C4×C239—22no—
33C2×C4×C239—21no—
34C2×C4×C239—21no—
35C2×C4×C239—41no—
36C2×C4×C239—41no—
37C2×C4×C239—41no—
38C2×C4×C239—41no—
39C2×C4×C239—41no—
40C2×C4×C239—41no—
41C2×C4×C239SD1611yescharacteristic
42C2×C4×C239Q1611yescharacteristic
43C22×C239—21no—
44C22×C239—21no—
45C22×C239#9911yescharacteristic
46C22×C239#10311yescharacteristic
47C22×C239#10411yescharacteristic
48C4×C239—21no—
49C4×C239—21no—
50C4×C239—42no—
51C4×C239—42no—
52C4×C239—41no—
53C4×C239—41no—
54C2×C239—21no—
55C2×C239—21no—
56C2×C239#32811yescharacteristic
57C2×C239AΣL(1,𝔽16)11yescharacteristic
58C2×C239#35611yescharacteristic
59C239#135411yescharacteristic, complemented, Sylow
60#1354—2391nomaximal, Sylow
61#395D23911yescharacteristic
62#343—2391no—
63#324—2391no—
64C22×Q8Dic23911yescharacteristic
65C2×M16—4781no—
66C2×C4⋊C4—21no—
67C2×C4⋊C4C2×D23911yescharacteristic
68C22⋊C8—4781no—
69#95—21no—
70#95Dic23911yescharacteristic
71C2×Q8—42no—
72C2×Q8—41no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4C2×Dic23911yescharacteristic
76C22×C4C22⋊D23911yescharacteristic
77C22×C4C22⋊D23911yescharacteristic
78M16—9561no—
79M16—4782no—
80C2×C8—9561no—
81C2×C8—9561no—
82C4⋊C4—41no—
83C4⋊C4—42no—
84C23C22⋊Dic23911yescharacteristic
85Q8—42no—
86Q8—42no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—22no—
90C2×C4—22no—
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—41no—
94C2×C4—41no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—41no—
98C2×C4—41no—
99C2×C4#1683853511yescharacteristic
100C2×C4#1683853811yescharacteristic
101C8—19121no—
102C8—9562no—
103C22—21no—
104C22—21no—
105C22#2143987511yescharacteristic
106C22#2143988411yescharacteristic
107C22#2143988711yescharacteristic
108C4—21no—
109C4—21no—
110C4—42no—
111C4—41no—
112C4—42no—
113C4—41no—
114C2—21no—
115C2—21no—
116C2#2950450911yescharacteristic
117C2#2950455911yescharacteristic
118C2#2950457111yescharacteristic
subgroupG/H
centerC22#21439875
commutatorC22×C4×C239C2×C4
FrattiniC2×C4⋊C4C2×D239
Fitting#395×C239C2
socleC22×C239#99
prime radicalC23×C239C22⋊C4
cosocleC2×C4⋊C4×C239C22
hypercenter#395D239
hypocenterC239#1354
LCSG ▷ C22×C4×C239 ▷ C23×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #395

Complements

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

NH ≅ G/Ntype
59. C239#1354semidirect

Maximal subgroups

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

subgroupindex
#295045412
#295044982
#395×C2392
#1354239