Finite Group Databasebeta

← #44482573

Subgroups — #44482573

Order 30592.

154 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 35 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#29504708C211yesmaximal, characteristic
2#29504539C211yesmaximal, characteristic
3#323×C239C211yesmaximal, characteristic
4C2×C4⋊Dic239C411yescharacteristic, complemented
5C2×Dic239⋊C4—21no—
6C2×C22⋊Dic239—21no—
7C2×C22⋊Dic239—21no—
8C239⋊#95C411yescharacteristic, complemented
9C2×C22⋊C4×C239C2211yescharacteristic
10C22⋊C8×C239—21no—
11C22×Dic239—21no—
12C22×Dic239—21no—
13C22×Dic239—41no—
14C4⋊Dic239—41no—
15Dic239⋊C4—42no—
16C22⋊Dic239—22no—
17C22⋊Dic239—42no—
18C22⋊Dic239—41no—
19C24×C239D411yescharacteristic
20C22×C4×C239C2×C411yescharacteristic
21C22×C4×C239D411yescharacteristic
22C2×C8×C239—41no—
23C22⋊C4×C239—41no—
24C2×Dic239—22no—
25C2×Dic239—41no—
26C2×Dic239—41no—
27C2×Dic239—42no—
28C2×Dic239—41no—
29C2×Dic239—41no—
30C2×Dic239—41no—
31C2×Dic239—81no—
32C2×Dic239—81no—
33C23×C239—21no—
34C23×C239—21no—
35C23×C239—41no—
36C23×C239—41no—
37C23×C239C22⋊C411yescharacteristic
38C23×C239SD1611yescharacteristic
39C23×C239Q1611yescharacteristic
40C2×C4×C239—21no—
41C2×C4×C239—21no—
42C2×C4×C239—41no—
43C2×C4×C239—41no—
44C8×C239—81no—
45C22×C239—21no—
46C22×C239—21no—
47C22×C239—21no—
48C22×C239—21no—
49C22×C239—41no—
50C22×C239—41no—
51C22×C239—41no—
52C22×C239—41no—
53C22×C239—81no—
54C22×C239#9911yescharacteristic
55C22×C239#10311yescharacteristic
56C22×C239#10411yescharacteristic
57C4×C239—41no—
58C4×C239—41no—
59Dic239—42no—
60Dic239—82no—
61Dic239—81no—
62C2×C239—21no—
63C2×C239—21no—
64C2×C239—41no—
65C2×C239—41no—
66C2×C239#32811yescharacteristic
67C2×C239#35211yescharacteristic
68C2×C239#35311yescharacteristic
69C239#135211yescharacteristic, complemented, Sylow
70#1352—2391nomaximal, Sylow
71#399—2391no—
72#342—2391no—
73#323D23911yescharacteristic
74C2×C4⋊C4—4781no—
75C2×C4⋊C4—2391no—
76C2×C22⋊C4—4781no—
77C2×C22⋊C4—4781no—
78C2×C22⋊C4C2×D23911yescharacteristic
79C22⋊C8—21no—
80#95—2391no—
81C24D95611yescharacteristic
82C22×C4—9561no—
83C22×C4—4781no—
84C22×C4—4781no—
85C22×C4C4×D23911yescharacteristic
86C22×C4C22⋊D23911yescharacteristic
87C2×C8—41no—
88C4⋊C4—9561no—
89C4⋊C4—9562no—
90C22⋊C4—41no—
91C22⋊C4—9561no—
92C22⋊C4—9562no—
93C22⋊C4—4782no—
94C23—21no—
95C23—21no—
96C23—41no—
97C23—41no—
98C23(C2×D239)⋊C411yescharacteristic
99C23#1683853711yescharacteristic
100C23Dic95611yescharacteristic
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—19121no—
106C2×C4—19121no—
107C2×C4—9561no—
108C2×C4—9562no—
109C2×C4—9561no—
110C2×C4—9561no—
111C2×C4—9561no—
112C2×C4—9561no—
113C2×C4—4782no—
114C8—81no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—21no—
119C22—41no—
120C22—41no—
121C22—41no—
122C22—41no—
123C22—81no—
124C22#2143987411yescharacteristic
125C22#2143988511yescharacteristic
126C22#2143988611yescharacteristic
127C4—41no—
128C4—41no—
129C4—19122no—
130C4—19121no—
131C4—9562no—
132C2—21no—
133C2—21no—
134C2—41no—
135C2—41no—
136C2#2950451011yescharacteristic
137C2#2950456311yescharacteristic
138C2#2950456411yescharacteristic
subgroupG/H
centerC22#21439874
commutatorC22×C4×C239C2×C4
FrattiniC2×C22⋊C4C2×D239
Fitting#323×C239C2
socleC22×C239#99
prime radicalC24×C239D4
cosocleC2×C22⋊C4×C239C22
hypercenter#323D239
hypocenterC239#1352
LCSG ▷ C22×C4×C239 ▷ C23×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #323

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊Dic239C4semidirect
8. C239⋊#95C4semidirect
69. C239#1352semidirect

Maximal subgroups

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

subgroupindex
#295047082
#295045392
#323×C2392
#1352239