Finite Group Databasebeta

← #43252816

Subgroups — #43252816

Order 28544.

154 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 35 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#28383516C211yesmaximal, characteristic
2#28383304C211yesmaximal, characteristic
3#342×C223C211yesmaximal, characteristic
4C2×C4⋊Dic223C411yescharacteristic, complemented
5C2×Dic223⋊C4—21no—
6C2×C22⋊Dic223—21no—
7C22⋊(C223⋊C8)—21no—
8C223⋊#95C411yescharacteristic, complemented
9C2×C22⋊C4×C223—21no—
10C2×C22⋊C4×C223C2211yescharacteristic
11C22×Dic223—21no—
12C22×Dic223—21no—
13C2×C223⋊C8—41no—
14C4⋊Dic223—41no—
15Dic223⋊C4—42no—
16C22⋊Dic223—42no—
17C24×C223D411yescharacteristic
18C22×C4×C223—41no—
19C22×C4×C223C2×C411yescharacteristic
20C22×C4×C223D411yescharacteristic
21C22⋊C4×C223—22no—
22C22⋊C4×C223—41no—
23C22⋊C4×C223—41no—
24C2×Dic223—22no—
25C2×Dic223—41no—
26C2×Dic223—41no—
27C2×Dic223—41no—
28C2×Dic223—41no—
29C2×Dic223—41no—
30C223⋊C8—81no—
31C23×C223—21no—
32C23×C223—21no—
33C23×C223—41no—
34C23×C223—41no—
35C23×C223C22⋊C411yescharacteristic
36C23×C223SD1611yescharacteristic
37C23×C223Q1611yescharacteristic
38C2×C4×C223—21no—
39C2×C4×C223—21no—
40C2×C4×C223—41no—
41C2×C4×C223—41no—
42C2×C4×C223—42no—
43C2×C4×C223—81no—
44C2×C4×C223—81no—
45C22×C223—21no—
46C22×C223—21no—
47C22×C223—21no—
48C22×C223—21no—
49C22×C223—41no—
50C22×C223—41no—
51C22×C223—41no—
52C22×C223—41no—
53C22×C223—81no—
54C22×C223#9911yescharacteristic
55C22×C223#10311yescharacteristic
56C22×C223#10411yescharacteristic
57C4×C223—41no—
58C4×C223—41no—
59C4×C223—82no—
60Dic223—42no—
61Dic223—81no—
62C2×C223—21no—
63C2×C223—21no—
64C2×C223—41no—
65C2×C223—41no—
66C2×C223#32811yescharacteristic
67C2×C223#35211yescharacteristic
68C2×C223#35311yescharacteristic
69C223#135211yescharacteristic, complemented, Sylow
70#1352—2231nomaximal, Sylow
71#399—2231no—
72#342D22311yescharacteristic
73#323—2231no—
74C2×C4⋊C4—4461no—
75C2×C4⋊C4—2231no—
76C2×C22⋊C4—21no—
77C2×C22⋊C4—4461no—
78C2×C22⋊C4C2×D22311yescharacteristic
79C22⋊C8—4461no—
80#95—2231no—
81C24C22⋊D22311yescharacteristic
82C22×C4—41no—
83C22×C4—4461no—
84C22×C4—4461no—
85C22×C4C4×D22311yescharacteristic
86C22×C4D89211yescharacteristic
87C2×C8—8921no—
88C4⋊C4—8921no—
89C4⋊C4—8922no—
90C22⋊C4—22no—
91C22⋊C4—41no—
92C22⋊C4—41no—
93C22⋊C4—8922no—
94C23—21no—
95C23—21no—
96C23—41no—
97C23—41no—
98C23(C2×D223)⋊C411yescharacteristic
99C23#1681315811yescharacteristic
100C23#1681316011yescharacteristic
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—42no—
106C2×C4—81no—
107C2×C4—81no—
108C2×C4—8921no—
109C2×C4—8921no—
110C2×C4—8921no—
111C2×C4—8921no—
112C2×C4—8921no—
113C2×C4—4462no—
114C8—17841no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—21no—
119C22—41no—
120C22—41no—
121C22—41no—
122C22—41no—
123C22—81no—
124C22#2029721811yescharacteristic
125C22#2029722711yescharacteristic
126C22#2029723211yescharacteristic
127C4—41no—
128C4—41no—
129C4—82no—
130C4—8922no—
131C4—17841no—
132C2—21no—
133C2—21no—
134C2—41no—
135C2—41no—
136C2#2838331611yescharacteristic
137C2#2838336911yescharacteristic
138C2#2838337211yescharacteristic
subgroupG/H
centerC22#20297218
commutatorC22×C4×C223C2×C4
FrattiniC2×C22⋊C4C2×D223
Fitting#342×C223C2
socleC22×C223#99
prime radicalC24×C223D4
cosocleC2×C22⋊C4×C223C22
hypercenter#342D223
hypocenterC223#1352
LCSG ▷ C22×C4×C223 ▷ C23×C223 ▷ C2×C223 ▷ C223
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #342

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊Dic223C4semidirect
8. C223⋊#95C4semidirect
69. C223#1352semidirect

Maximal subgroups

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

subgroupindex
#283835162
#283833042
#342×C2232
#1352223