Finite Group Databasebeta

← #43252741

Subgroups — #43252741

Order 28544.

158 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 41 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#28383304C211yesmaximal, characteristic
2#28383304C211yesmaximal, characteristic
3#385×C223C211yesmaximal, characteristic
4C22⋊(C223⋊C8)—21no—
5C22⋊(C223⋊C8)—21no—
6C23×C4×C223C411yescharacteristic
7C2×C4⋊C4×C223—21no—
8C2×C22⋊C4×C223C411yescharacteristic
9C2×C22⋊C4×C223C2211yescharacteristic
10#95×C223—21no—
11C2×C223⋊C8—41no—
12C2×C223⋊C8—41no—
13C24×C223C2×C411yescharacteristic
14C22×C4×C223—21no—
15C22×C4×C223—21no—
16C22×C4×C223—42no—
17C22×C4×C223—41no—
18C22×C4×C223D411yescharacteristic
19C22×C4×C223D411yescharacteristic
20C4⋊C4×C223—42no—
21C22⋊C4×C223—21no—
22C22⋊C4×C223—41no—
23C22⋊C4×C223C812yescomplemented
24C223⋊C8—81no—
25C223⋊C8—81no—
26C23×C223—21no—
27C23×C223—21no—
28C23×C223—41no—
29C23×C223—41no—
30C23×C223C22⋊C411yescharacteristic
31C23×C223C2×C811yescharacteristic
32C23×C223M1611yescharacteristic
33C2×C4×C223—22no—
34C2×C4×C223—22no—
35C2×C4×C223—21no—
36C2×C4×C223—21no—
37C2×C4×C223—41no—
38C2×C4×C223—41no—
39C2×C4×C223—41no—
40C2×C4×C223—42no—
41C2×C4×C223—41no—
42C2×C4×C223—41no—
43C2×C4×C223—41no—
44C2×C4×C223—42no—
45C22×C223—21no—
46C22×C223—21no—
47C22×C223—21no—
48C22×C223—21no—
49C22×C223—41no—
50C22×C223—41no—
51C22×C223—42no—
52C22×C223—41no—
53C22×C223—41no—
54C22×C223C22⋊C811yescharacteristic
55C22×C223#9911yescharacteristic
56C22×C223#10111yescharacteristic
57C4×C223—42no—
58C4×C223—42no—
59C4×C223—41no—
60C4×C223—41no—
61C2×C223—21no—
62C2×C223—21no—
63C2×C223—41no—
64C2×C223—41no—
65C2×C223#32411yescharacteristic
66C2×C223AΣL(1,𝔽16)11yescharacteristic
67C2×C223#35211yescharacteristic
68C223#132611yescharacteristic, complemented, Sylow
69#1326—2231nomaximal, Sylow
70#385D22311yescharacteristic
71#323—2231no—
72#323—2231no—
73C23×C4Dic22311yescharacteristic
74C2×C4⋊C4—21no—
75C2×C22⋊C4Dic22311yescharacteristic
76C2×C22⋊C4C2×D22311yescharacteristic
77C22⋊C8—4461no—
78C22⋊C8—4461no—
79#95—21no—
80C24C2×Dic22311yescharacteristic
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—42no—
84C22×C4—41no—
85C22×C4C22⋊D22311yescharacteristic
86C22×C4C22⋊D22311yescharacteristic
87C2×C8—8921no—
88C2×C8—8921no—
89C4⋊C4—42no—
90C22⋊C4—21no—
91C22⋊C4—41no—
92C22⋊C4C223⋊C812yescomplemented
93C23—21no—
94C23—21no—
95C23—41no—
96C23—41no—
97C23C22⋊Dic22311yescharacteristic
98C23C2×C223⋊C811yescharacteristic
99C23#1681315411yescharacteristic
100C2×C4—22no—
101C2×C4—22no—
102C2×C4—21no—
103C2×C4—21no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—42no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—42no—
112C8—17841no—
113C8—17841no—
114C22—21no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—41no—
119C22—41no—
120C22—42no—
121C22—41no—
122C22—41no—
123C22C22⋊(C223⋊C8)11yescharacteristic
124C22#2029721911yescharacteristic
125C22#2029722311yescharacteristic
126C4—42no—
127C4—41no—
128C4—42no—
129C4—41no—
130C2—21no—
131C2—21no—
132C2—41no—
133C2—41no—
134C2#2838330611yescharacteristic
135C2#2838336711yescharacteristic
136C2#2838337011yescharacteristic
subgroupG/H
centerC22#20297219
commutatorC23×C223C2×C8
FrattiniC2×C22⋊C4C2×D223
Fitting#385×C223C2
socleC22×C223#99
prime radicalC24×C223C2×C4
cosocleC2×C22⋊C4×C223C22
hypercenter#385D223
hypocenterC223#1326
LCSG ▷ C23×C223 ▷ C22×C223 ▷ C2×C223 ▷ C223
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #385

Complements

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

NH ≅ G/Ntype
23. C22⋊C4×C223C8semidirect
68. C223#1326semidirect
92. C22⋊C4C223⋊C8semidirect

Maximal subgroups

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

subgroupindex
#283833042
#385×C2232
#1326223