Finite Group Databasebeta

← #44483872

Subgroups — #44483872

Order 30592.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#29505520C211yesmaximal, characteristic
2#29505142C211yesmaximal, characteristic, complemented
3#29505132C212yesmaximal, complemented
4#29504511C212yesmaximal, complemented
5#330×C239C211yesmaximal, characteristic, complemented
6#21439960C2211yescharacteristic
7#21439948C2212yes—
8#21439945—22no—
9#21439938—22no—
10#21439935—22no—
11#21439885—22no—
12#21439883—22no—
13#21439882—22no—
14#21439871C2211yescharacteristic
15#125×C239C2211yescharacteristic
16#97×C239C2212yes—
17C2×Dic478—21no—
18C2×Dic478D412yes—
19C2×D956—22no—
20C2×D956D412yes—
21C2×C4×D239—22no—
22C2×C239⋊C8—21no—
23C4⋊Dic239—22no—
24Dic239⋊C4—22no—
25(C2×D239)⋊C4—22no—
26(C2×D239)⋊C4—22no—
27(C2×D239)⋊C4—22no—
28C2×C8×C239—22no—
29C4⋊C4×C239—22no—
30C4⋊C4×C239D412yes—
31C42×C239C2311yescharacteristic
32C22×D239—22no—
33Dic478—42no—
34Dic478—42no—
35D956—42no—
36D956—82no—
37C2×Dic239—22no—
38C2×Dic239—41no—
39C4×D239—82no—
40C239⋊C8—41no—
41C2×C4×C239—22no—
42C2×C4×C239C2×D412yes—
43C2×C4×C239C2×D411yescharacteristic
44C8×C239—42no—
45C22×C239#12011yescharacteristic
46C2×D239—42no—
47C2×D239—42no—
48C2×D239—42no—
49C4×C239—21no—
50C4×C239—22no—
51C4×C239—42no—
52Dic239—42no—
53Dic239—81no—
54C2×C239#45411yescharacteristic
55C2×C239#45512yes—
56D239—82no—
57C239#166211yescharacteristic, complemented, Sylow
58#1662—2391nomaximal, Sylow
59#562—2391no—
60#491—2391no—
61#489—2392no—
62#330D23911yescharacteristic, complemented
63#329—2392no—
64C4⋊Q8—2391no—
65#125C2×D23911yescharacteristic
66#124—2392no—
67#123—4782no—
68C22⋊Q8—4782no—
69#121—4782no—
70#103—4782no—
71#103—4782no—
72#102—4782no—
73#97—2391no—
74#97C2×D23912yes—
75C2×Q8—4781no—
76C2×Q8—2392no—
77C2×D4—4782no—
78C2×D4—2392no—
79C22×C4—4782no—
80C2×C8—22no—
81C2×C8—4781no—
82C4⋊C4—22no—
83C4⋊C4—4782no—
84C4⋊C4—4782no—
85C4⋊C4D95612yes—
86C22⋊C4—4782no—
87C22⋊C4—4782no—
88C22⋊C4—4782no—
89C42C22×D23911yescharacteristic
90C23—4782no—
91Q8—9562no—
92Q8—9562no—
93D4—19122no—
94D4—9562no—
95C2×C4—22no—
96C2×C4—19122no—
97C2×C4—9561no—
98C2×C4—4782no—
99C2×C4D4×D23912yes—
100C2×C4C2×D95611yescharacteristic
101C8—42no—
102C8—9561no—
103C22—9562no—
104C22—9562no—
105C22—9562no—
106C22#2143993011yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—19121no—
111C4—9562no—
112C2—19122no—
113C2#2950494711yescharacteristic
114C2#2950495112yes—
subgroupG/H
centerC22#21439930
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#330×C239C2
socleC22×C239#120
prime radical#29505520C2
hypercenter#330D239
hypocenterC239#1662
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #29505142C2semidirect
3. #29505132C2semidirect
4. #29504511C2semidirect
5. #330×C239C2semidirect
57. C239#1662semidirect
62. #330D239semidirect

Maximal subgroups

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

subgroupindex
#295055202
#295051422
#295051322
#295045112
#330×C2392
#1662239