Finite Group Databasebeta

← #44483141

Subgroups — #44483141

Order 30592.

226 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 63 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#29505328C211yesmaximal, characteristic
2#29504724C212yesmaximal
3#29504514C211yesmaximal, characteristic, complemented
4#29504513C212yesmaximal, complemented
5#330×C239C211yesmaximal, characteristic, complemented
6C2×#16838531—22no—
7#21439959C412yes—
8#21439952C2211yescharacteristic
9#21439938—22no—
10#21439925—22no—
11#21439918C412yes—
12C42×D239C2211yescharacteristic
13#21439871C2212yes—
14C8×Dic239—22no—
15#125×C239C2211yescharacteristic
16#97×C239C2212yes—
17C2×Dic478—22no—
18C2×C4×D239C2×C411yescharacteristic
19C2×C4×D239D412yes—
20#16838531—28no—
21C2×C239⋊C8—22no—
22C4⋊Dic239C2×C412yes—
23Dic239⋊C4—22no—
24Dic239⋊C4—22no—
25(C2×D239)⋊C4—22no—
26C4×Dic239—22no—
27C4×Dic239C2×C411yescharacteristic
28C4×Dic239D412yes—
29C2×C8×C239—22no—
30C4⋊C4×C239—22no—
31C4⋊C4×C239C2×C412yes—
32C42×C239C2311yescharacteristic
33C22×D239C22⋊C411yescharacteristic
34Dic478—44no—
35C2×Dic239—22no—
36C2×Dic239C22⋊C411yescharacteristic
37C2×Dic239C22⋊C412yes—
38C4×D239—22no—
39C4×D239—24no—
40C239⋊C8—24no—
41C2×C4×C239—22no—
42C2×C4×C239C22×C411yescharacteristic
43C2×C4×C239C2×D412yes—
44C8×C239—24no—
45C22×C239C2×C22⋊C411yescharacteristic
46C2×D239—21no—
47C2×D239—22no—
48C4×C239—21no—
49C4×C239—22no—
50C4×C239—42no—
51Dic239—42no—
52Dic239#10112yes—
53Dic239#10414yes—
54C2×C239C2×#10111yescharacteristic
55C2×C239C2×#10412yes—
56D239—41no—
57C239#152611yescharacteristic, complemented, Sylow
58#1526—2391nomaximal, Sylow
59#533—2391no—
60C4×M16—2392no—
61#330—2391no—
62#330—2392no—
63#330D23911yescharacteristic, complemented
64C2×M16—4782no—
65C4⋊Q8—2392no—
66#125—2391no—
67#125C2×D23911yescharacteristic
68C22⋊Q8—4782no—
69C4×Q8—4782no—
70#117—2392no—
71C2×C42—2391no—
72#97—2392no—
73#97C2×D23912yes—
74C4×C8—4782no—
75C2×Q8—4782no—
76C22×C4—2391no—
77C22×C4—2392no—
78M16—4788no—
79C2×C8—22no—
80C2×C8—4782no—
81C4⋊C4—22no—
82C4⋊C4—4782no—
83C4⋊C4—4782no—
84C4⋊C4—2392no—
85C4⋊C4C4×D23912yes—
86C22⋊C4—4782no—
87C42—4782no—
88C42—2391no—
89C42—2392no—
90C42C22×D23911yescharacteristic
91C23—2391no—
92Q8—9564no—
93C2×C4—22no—
94C2×C4—4784no—
95C2×C4—4782no—
96C2×C4—4782no—
97C2×C4—2391no—
98C2×C4—2392no—
99C2×C4C2×C4×D23911yescharacteristic
100C2×C4D4×D23912yes—
101C8—24no—
102C8—4784no—
103C22—4782no—
104C22—4781no—
105C22C22⋊C4×D23911yescharacteristic
106C4—22no—
107C4—21no—
108C4—42no—
109C4—9562no—
110C4—2394no—
111C4—2392no—
112C2—9561no—
113C2#101×D23911yescharacteristic
114C2#104×D23912yes—
subgroupG/H
centerC22C22⋊C4×D239
commutatorC2×C4×C239C22×C4
FrattiniC42C22×D239
Fitting#330×C239C2
socleC22×C239C2×C22⋊C4
prime radicalC22×D239C22⋊C4
cosocleC42×C239C23
hypercenter#330D239
hypocenterC239#1526
LCSG ▷ C2×C4×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #29504514C2semidirect
4. #29504513C2semidirect
5. #330×C239C2semidirect
57. C239#1526semidirect
63. #330D239semidirect

Maximal subgroups

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

subgroupindex
#295053282
#295047242
#295045142
#295045132
#330×C2392
#1526239