Finite Group Databasebeta

← #44483280

Subgroups — #44483280

Order 30592.

254 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 67 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#29505320C211yesmaximal, characteristic
2#29504794C212yesmaximal, complemented
3#29504520C212yesmaximal, complemented
4#29504516C211yesmaximal, characteristic, complemented
5#331×C239C211yesmaximal, characteristic, complemented
6C2×#16838547C412yes—
7C2×#16838531—22no—
8#21439960C2211yescharacteristic
9#21439947C412yes—
10#21439931—22no—
11D4×Dic239—22no—
12C42×D239C2211yescharacteristic
13C4⋊(C239⋊C8)C2212yes—
14Dic239⋊C8—22no—
15#127×C239C2211yescharacteristic
16C4⋊C8×C239C2212yes—
17#16838547—44no—
18C2×Dic478C2×C412yes—
19C2×C22⋊D239—22no—
20C22×Dic239—22no—
21C2×C4×D239C2×C411yescharacteristic
22C2×C4×D239D412yes—
23#16838531—44no—
24C2×C239⋊C8—22no—
25C4⋊Dic239—22no—
26C22⋊Dic239—24no—
27C4×Dic239C2×C411yescharacteristic
28C4×Dic239D412yes—
29C2×D4×C239—22no—
30C2×D4×C239C2×C412yes—
31C2×C8×C239—22no—
32C42×C239C2311yescharacteristic
33C22×D239C22⋊C411yescharacteristic
34Dic478—42no—
35C22⋊D239—44no—
36C2×Dic239—22no—
37C2×Dic239—44no—
38C2×Dic239C22⋊C412yes—
39C2×Dic239C22⋊C411yescharacteristic
40C4×D239—22no—
41C4×D239—22no—
42C4×D239—22no—
43C239⋊C8—42no—
44C23×C239—22no—
45D4×C239—42no—
46D4×C239—42no—
47D4×C239—42no—
48C2×C4×C239C22×C411yescharacteristic
49C2×C4×C239C2×D412yes—
50C8×C239—42no—
51C22×C239—42no—
52C22×C239—44no—
53C22×C239C2×C22⋊C411yescharacteristic
54C2×D239—21no—
55C2×D239—22no—
56C4×C239—21no—
57C4×C239AGL(1,ℤ/8)12yes—
58C4×C239#13712yes—
59Dic239—22no—
60Dic239—42no—
61Dic239#10012yes—
62C2×C239—82no—
63C2×C239C2×#10011yescharacteristic
64C2×C239#41712yes—
65D239—41no—
66C239#156011yescharacteristic, complemented, Sylow
67#1560—2391nomaximal, Sylow
68#532—2391no—
69#423—2392no—
70#333—2392no—
71#331—2391no—
72#331D23911yescharacteristic, complemented
73C2×#41—2392no—
74C2×M16—4782no—
75C4⋊Q8—2391no—
76#127C2×D23911yescharacteristic
77#124—2392no—
78#121—4782no—
79C4×D4—4782no—
80C2×C42—2391no—
81C4⋊C8—4782no—
82C4⋊C8—2392no—
83C4⋊C8C2×D23912yes—
84#41—9564no—
85C2×Q8—2392no—
86C2×D4—22no—
87C2×D4—4782no—
88C2×D4C4×D23912yes—
89C22×C4—4782no—
90C22×C4—2391no—
91C22×C4—2392no—
92M16—9564no—
93C2×C8—22no—
94C2×C8—4782no—
95C4⋊C4—4782no—
96C22⋊C4—4784no—
97C42—2391no—
98C42—2392no—
99C42C22×D23911yescharacteristic
100C23—22no—
101C23—2391no—
102Q8—9562no—
103D4—42no—
104D4—42no—
105D4—42no—
106D4—9564no—
107C2×C4—9564no—
108C2×C4—4782no—
109C2×C4—4782no—
110C2×C4—4782no—
111C2×C4—4782no—
112C2×C4—2392no—
113C2×C4—2391no—
114C2×C4C2×C4×D23911yescharacteristic
115C2×C4D4×D23912yes—
116C8—42no—
117C8—9562no—
118C22—44no—
119C22—42no—
120C22—4782no—
121C22—4781no—
122C22C22⋊C4×D23911yescharacteristic
123C4—21no—
124C4—9562no—
125C4—4782no—
126C4—2392no—
127C4#2143998412yes—
128C4#2143998912yes—
129C2—82no—
130C2—9561no—
131C2#100×D23911yescharacteristic
132C2#2950477012yes—
subgroupG/H
centerC22C22⋊C4×D239
commutatorC2×C4×C239C22×C4
FrattiniC42C22×D239
Fitting#331×C239C2
socleC22×C239C2×C22⋊C4
prime radical#29505320C2
cosocleC42×C239C23
hypercenter#331D239
hypocenterC239#1560
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #29504794C2semidirect
3. #29504520C2semidirect
4. #29504516C2semidirect
5. #331×C239C2semidirect
66. C239#1560semidirect
72. #331D239semidirect

Maximal subgroups

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

subgroupindex
#295053202
#295047942
#295045202
#295045162
#331×C2392
#1560239