Finite Group Databasebeta

← #43252722

Subgroups — #43252722

Order 28544.

150 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 37 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#28383441C211yesmaximal, characteristic
2#28383304C211yesmaximal, characteristic
3#323×C223C211yesmaximal, characteristic
4C23×Dic223C411yescharacteristic
5C2×C22⋊Dic223C411yescharacteristic
6C22⋊(C223⋊C8)—21no—
7C223⋊#95—21no—
8C223⋊#95—21no—
9C2×C22⋊C4×C223C2211yescharacteristic
10C22⋊C8×C223—21no—
11C22×Dic223—21no—
12C22×Dic223—21no—
13C22×Dic223—21no—
14C22×Dic223—41no—
15C22×Dic223—41no—
16C22×Dic223C812yescomplemented
17C2×C223⋊C8—41no—
18C22⋊Dic223—41no—
19C24×C223C2×C411yescharacteristic
20C22×C4×C223D411yescharacteristic
21C22×C4×C223D411yescharacteristic
22C2×C8×C223—41no—
23C22⋊C4×C223—41no—
24C2×Dic223—22no—
25C2×Dic223—42no—
26C2×Dic223—41no—
27C2×Dic223—41no—
28C2×Dic223—42no—
29C2×Dic223—41no—
30C2×Dic223—41no—
31C2×Dic223—41no—
32C223⋊C8—81no—
33C23×C223—21no—
34C23×C223—21no—
35C23×C223—41no—
36C23×C223—41no—
37C23×C223C22⋊C411yescharacteristic
38C23×C223C2×C811yescharacteristic
39C23×C223M1611yescharacteristic
40C2×C4×C223—21no—
41C2×C4×C223—21no—
42C2×C4×C223—41no—
43C2×C4×C223—41no—
44C8×C223—81no—
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#10011yescharacteristic
57C4×C223—41no—
58C4×C223—41no—
59Dic223—42no—
60Dic223—81no—
61C2×C223—21no—
62C2×C223—21no—
63C2×C223—41no—
64C2×C223—41no—
65C2×C223#32311yescharacteristic
66C2×C223#35211yescharacteristic
67C2×C223#35211yescharacteristic
68C223#131711yescharacteristic, complemented, Sylow
69#1317—2231nomaximal, Sylow
70#381—2231no—
71#323—2231no—
72#323D22311yescharacteristic
73C23×C4—2231no—
74C2×C22⋊C4—2231no—
75C2×C22⋊C4C2×D22311yescharacteristic
76C22⋊C8—21no—
77C22⋊C8—4461no—
78#95—4461no—
79#95—4461no—
80C24C4×D22311yescharacteristic
81C22×C4—8921no—
82C22×C4—8921no—
83C22×C4—4461no—
84C22×C4—4461no—
85C22×C4—4461no—
86C22×C4—2232no—
87C22×C4C22⋊D22311yescharacteristic
88C22×C4D89211yescharacteristic
89C2×C8—41no—
90C2×C8—8921no—
91C22⋊C4—41no—
92C22⋊C4—8921no—
93C23—21no—
94C23—21no—
95C23—41no—
96C23—41no—
97C23(C2×D223)⋊C411yescharacteristic
98C23C8×D22311yescharacteristic
99C23#1681315311yescharacteristic
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—8922no—
105C2×C4—8921no—
106C2×C4—8921no—
107C2×C4—8922no—
108C2×C4—8921no—
109C2×C4—8921no—
110C2×C4—8921no—
111C2×C4—4462no—
112C8—81no—
113C8—17841no—
114C22—21no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—41no—
119C22—41no—
120C22—42no—
121C22—41no—
122C22—41no—
123C22(C2×D223)⋊C811yescharacteristic
124C22#2029721811yescharacteristic
125C22#2029722011yescharacteristic
126C4—41no—
127C4—41no—
128C4—8922no—
129C4—17841no—
130C2—21no—
131C2—21no—
132C2—41no—
133C2—41no—
134C2#2838330311yescharacteristic
135C2#2838336911yescharacteristic
136C2#2838337111yescharacteristic
subgroupG/H
centerC22#20297218
commutatorC23×C223C2×C8
FrattiniC2×C22⋊C4C2×D223
Fitting#323×C223C2
socleC22×C223#99
prime radicalC24×C223C2×C4
cosocleC2×C22⋊C4×C223C22
hypercenter#323D223
hypocenterC223#1317
LCSG ▷ C23×C223 ▷ C22×C223 ▷ C2×C223 ▷ C223
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #323

Complements

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

NH ≅ G/Ntype
16. C22×Dic223C8semidirect
68. C223#1317semidirect

Maximal subgroups

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

subgroupindex
#283834412
#283833042
#323×C2232
#1317223