Finite Group Databasebeta

← #44482710

Subgroups — #44482710

Order 30592.

120 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 23 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#29505148C211yesmaximal, characteristic
2#29504565C211yesmaximal, characteristic, complemented
3#353×C239C211yesmaximal, characteristic, complemented
4C2×#16838533—21no—
5C2×#16838533—21no—
6#21439957C411yescharacteristic, complemented
7#21439875—21no—
8C4×C239⋊C8C411yescharacteristic, complemented
9#127×C239C2211yescharacteristic
10#99×C239—21no—
11C2×D956—21no—
12C2×D956—41no—
13#16838533—42no—
14#16838533—42no—
15C2×C239⋊C8—21no—
16C22⋊Dic239—41no—
17C2×D4×C239—41no—
18C2×D4×C239D411yescharacteristic
19C2×D4×C239D411yescharacteristic
20C22⋊C4×C239—41no—
21C42×C239C2×C411yescharacteristic
22C22×D239—41no—
23D956—41no—
24D956—41no—
25D956—82no—
26C2×Dic239—81no—
27C239⋊C8—22no—
28C23×C239—21no—
29C23×C239—21no—
30D4×C239—41no—
31D4×C239—41no—
32D4×C239—82no—
33C2×C4×C239—21no—
34C2×C4×C239—81no—
35C2×C4×C239C22⋊C411yescharacteristic
36C22×C239—41no—
37C22×C239—41no—
38C22×C239—81no—
39C22×C239—81no—
40C22×C239#9911yescharacteristic
41C2×D239—82no—
42C2×D239—81no—
43C4×C239—22no—
44C4×C239—21no—
45C4×C239—161no—
46Dic239—161no—
47C2×C239—21no—
48C2×C239—81no—
49C2×C239—81no—
50C2×C239#35311yescharacteristic
51D239—161no—
52C239#140811yescharacteristic, complemented, Sylow
53#1408—2391nomaximal, Sylow
54#493—2391no—
55#353—2391no—
56#353D23911yescharacteristic, complemented
57C2×D8—4781no—
58C2×D8—4781no—
59#127—2391no—
60#127C2×D23911yescharacteristic
61#99—21no—
62#99—4781no—
63C4×C8—2391no—
64C2×D4—41no—
65C2×D4—9561no—
66C2×D4—4781no—
67C2×D4C22⋊D23911yescharacteristic
68C2×D4D95611yescharacteristic
69D8—9562no—
70D8—9562no—
71C2×C8—4781no—
72C22⋊C4—41no—
73C22⋊C4—9561no—
74C42C4×D23911yescharacteristic
75C23—21no—
76C23—21no—
77C23—9561no—
78D4—41no—
79D4—41no—
80D4—82no—
81D4—19122no—
82D4—9561no—
83D4—9561no—
84C2×C4—21no—
85C2×C4—81no—
86C2×C4—19121no—
87C2×C4(C2×D239)⋊C411yescharacteristic
88C8—4782no—
89C22—41no—
90C22—41no—
91C22—81no—
92C22—81no—
93C22—19122no—
94C22—19121no—
95C22#2143987411yescharacteristic
96C4—22no—
97C4—21no—
98C4—161no—
99C4—38241no—
100C2—21no—
101C2—81no—
102C2—81no—
103C2—38241no—
104C2#2950456411yescharacteristic
subgroupG/H
centerC2#29504564
commutatorC42×C239C2×C4
Frattini#127C2×D239
Fitting#353×C239C2
socleC2×C239#353
prime radical#29505148C2
cosocle#127×C239C22
hypercenter#353D239
hypocenterC239#1408
LCSG ▷ C42×C239 ▷ C2×C4×C239 ▷ C22×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #29504565C2semidirect
3. #353×C239C2semidirect
6. #21439957C4semidirect
8. C4×C239⋊C8C4semidirect
52. C239#1408semidirect
56. #353D239semidirect

Maximal subgroups

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

subgroupindex
#295051482
#295045652
#353×C2392
#1408239