Finite Group Databasebeta

← #43252738

Subgroups — #43252738

Order 28544.

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

normal subgroups only

This group has 134 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#28383449C211yesmaximal, characteristic
2#28383306C211yesmaximal, characteristic
3#324×C223C211yesmaximal, characteristic
4C2×C4⋊Dic223C411yescharacteristic
5C2×Dic223⋊C4—21no—
6C2×Dic223⋊C4—21no—
7C2×C4×Dic223C411yescharacteristic
8C22⋊(C223⋊C8)—21no—
9C2×C4⋊C4×C223C2211yescharacteristic
10C22⋊C8×C223—21no—
11C22×Dic223—21no—
12C22×Dic223—21no—
13C2×C223⋊C8—41no—
14C4⋊Dic223—41no—
15Dic223⋊C4—42no—
16Dic223⋊C4—42no—
17C4×Dic223—21no—
18C4×Dic223C812yescomplemented
19C22×C4×C223C2×C411yescharacteristic
20C22×C4×C223D411yescharacteristic
21C22×C4×C223D411yescharacteristic
22C2×C8×C223—41no—
23C4⋊C4×C223—41no—
24C2×Dic223—22no—
25C2×Dic223—22no—
26C2×Dic223—22no—
27C2×Dic223—41no—
28C2×Dic223—41no—
29C2×Dic223—41no—
30C223⋊C8—81no—
31C23×C223C22⋊C411yescharacteristic
32C2×C4×C223—21no—
33C2×C4×C223—21no—
34C2×C4×C223—21no—
35C2×C4×C223—21no—
36C2×C4×C223—41no—
37C2×C4×C223—41no—
38C2×C4×C223C2×C811yescharacteristic
39C2×C4×C223M1611yescharacteristic
40C8×C223—81no—
41C22×C223—21no—
42C22×C223—21no—
43C22×C223C22⋊C811yescharacteristic
44C22×C223#9911yescharacteristic
45C22×C223#10111yescharacteristic
46C4×C223—21no—
47C4×C223—21no—
48C4×C223—41no—
49C4×C223—41no—
50Dic223—24no—
51Dic223—81no—
52C2×C223—21no—
53C2×C223—21no—
54C2×C223#32411yescharacteristic
55C2×C223#35311yescharacteristic
56C2×C223#35611yescharacteristic
57C223#132511yescharacteristic, complemented, Sylow
58#1325—2231nomaximal, Sylow
59#384—2231no—
60#324—2231no—
61#324D22311yescharacteristic
62C2×C4⋊C4—4461no—
63C2×C4⋊C4—4461no—
64C2×C4⋊C4—2231no—
65C2×C4⋊C4C2×D22311yescharacteristic
66C2×C42—2231no—
67C22⋊C8—21no—
68C22⋊C8—4461no—
69C22×C4—4461no—
70C22×C4—4461no—
71C22×C4C4×D22311yescharacteristic
72C22×C4C22⋊D22311yescharacteristic
73C22×C4D89211yescharacteristic
74C2×C8—41no—
75C2×C8—8921no—
76C4⋊C4—41no—
77C4⋊C4—8921no—
78C4⋊C4—8922no—
79C4⋊C4—8922no—
80C42—4461no—
81C42—2232no—
82C23(C2×D223)⋊C411yescharacteristic
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—41no—
88C2×C4—41no—
89C2×C4—8921no—
90C2×C4—8921no—
91C2×C4—8921no—
92C2×C4—4462no—
93C2×C4—4462no—
94C2×C4—4462no—
95C2×C4C8×D22311yescharacteristic
96C2×C4#1681315311yescharacteristic
97C8—81no—
98C8—17841no—
99C22—21no—
100C22—21no—
101C22(C2×D223)⋊C811yescharacteristic
102C22#2029721811yescharacteristic
103C22#2029722211yescharacteristic
104C4—21no—
105C4—21no—
106C4—41no—
107C4—41no—
108C4—4464no—
109C4—17841no—
110C2—21no—
111C2—21no—
112C2#2838330511yescharacteristic
113C2#2838337211yescharacteristic
114C2#2838337811yescharacteristic
subgroupG/H
centerC22#20297218
commutatorC2×C4×C223C2×C8
FrattiniC2×C4⋊C4C2×D223
Fitting#324×C223C2
socleC22×C223#99
prime radicalC23×C223C22⋊C4
cosocleC2×C4⋊C4×C223C22
hypercenter#324D223
hypocenterC223#1325
LCSG ▷ C2×C4×C223 ▷ C22×C223 ▷ C2×C223 ▷ C223
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
18. C4×Dic223C8semidirect
57. C223#1325semidirect

Maximal subgroups

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

subgroupindex
#283834492
#283833062
#324×C2232
#1325223