Finite Group Databasebeta

← #15671399

Subgroups — #15671399

Order 2944.

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

normal subgroups only

This group has 168 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#13092334C211yesmaximal, characteristic
2#13092143C211yesmaximal, characteristic, complemented
3C23×#343C211yesmaximal, characteristic, complemented
4C22×D92C411yescharacteristic
5C2×M16×C23—21no—
6C2×C4⋊C4×C23C2211yescharacteristic
7C2×(C2×D23)⋊C4—21no—
8C2×(C2×D23)⋊C4—21no—
9C23⋊#95C411yescharacteristic
10C22⋊(C23⋊C8)—21no—
11C23×D23—21no—
12C22×C4×C23C2×C411yescharacteristic
13C22×C4×C23D411yescharacteristic
14C22×C4×C23D411yescharacteristic
15C22×Dic23—21no—
16C2×D92—41no—
17C2×D92—42no—
18M16×C23—22no—
19M16×C23—41no—
20C2×C8×C23—41no—
21C4⋊C4×C23—41no—
22(C2×D23)⋊C4—42no—
23(C2×D23)⋊C4—41no—
24(C2×D23)⋊C4—41no—
25C2×C23⋊C8—41no—
26C23×C23C22⋊C411yescharacteristic
27C22×D23—22no—
28C22×D23—41no—
29C22×D23—41no—
30C22×D23—41no—
31C22×D23—41no—
32C22×D23—41no—
33C22×D23—41no—
34C2×C4×C23—21no—
35C2×C4×C23—21no—
36C2×C4×C23—21no—
37C2×C4×C23—21no—
38C2×C4×C23—41no—
39C2×C4×C23—41no—
40C2×C4×C23D811yescharacteristic
41C2×C4×C23SD1611yescharacteristic
42C2×Dic23—41no—
43C2×Dic23—41no—
44C2×Dic23—41no—
45D92—42no—
46D92—42no—
47C8×C23—42no—
48C23⋊C8—81no—
49#1345—231nomaximal, Sylow
50C22×C23—21no—
51C22×C23—21no—
52C22×C23#9911yescharacteristic
53C22×C23#10211yescharacteristic
54C22×C23#10411yescharacteristic
55C2×D23—42no—
56C2×D23—42no—
57C2×D23—42no—
58C2×D23—81no—
59C2×D23—81no—
60C2×D23—81no—
61C2×D23—81no—
62C4×C23—21no—
63C4×C23—21no—
64C4×C23—41no—
65C4×C23—41no—
66Dic23—81no—
67#394—231no—
68#343D2311yescharacteristic, complemented
69#324—231no—
70C2×C23—21no—
71C2×C23—21no—
72C2×C23#32711yescharacteristic
73C2×C23AΣL(1,𝔽16)11yescharacteristic
74C2×C23#35511yescharacteristic
75D23—82no—
76C22×D4—231no—
77C2×M16—21no—
78C2×C4⋊C4C2×D2311yescharacteristic
79C2×C22⋊C4—461no—
80C2×C22⋊C4—461no—
81C22⋊C8—461no—
82#95—231no—
83C23#134511yescharacteristic, complemented, Sylow
84C24—461no—
85C2×D4—921no—
86C2×D4—922no—
87C22×C4—461no—
88C22×C4C4×D2311yescharacteristic
89C22×C4D9211yescharacteristic
90C22×C4C22⋊D2311yescharacteristic
91M16—22no—
92M16—41no—
93C2×C8—41no—
94C2×C8—921no—
95C4⋊C4—41no—
96C22⋊C4—922no—
97C22⋊C4—921no—
98C22⋊C4—921no—
99C23—462no—
100C23—921no—
101C23—921no—
102C23—921no—
103C23—921no—
104C23—921no—
105C23—921no—
106C23(C2×D23)⋊C411yescharacteristic
107D4—922no—
108D4—922no—
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4—921no—
116C2×C4—921no—
117C2×C4—921no—
118C2×C4#6727211yescharacteristic
119C2×C4#6727411yescharacteristic
120C8—42no—
121C8—1841no—
122C22—21no—
123C22—21no—
124C22—922no—
125C22—922no—
126C22—922no—
127C22—1841no—
128C22—1841no—
129C22—1841no—
130C22—1841no—
131C22#1062498711yescharacteristic
132C22#1062498811yescharacteristic
133C22#1062499111yescharacteristic
134C4—21no—
135C4—21no—
136C4—41no—
137C4—41no—
138C4—1841no—
139C2—21no—
140C2—21no—
141C2—1842no—
142C2#1309215011yescharacteristic
143C2#1309220511yescharacteristic
144C2#1309221311yescharacteristic
subgroupG/H
centerC22#10624988
commutatorC22×C4×C23C2×C4
FrattiniC2×C4⋊C4C2×D23
FittingC23×#343C2
socleC22×C23#99
prime radicalC22×D92C4
cosocleC2×C4⋊C4×C23C22
hypercenter#343D23
hypocenterC23#1345
LCSG ▷ C22×C4×C23 ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #343

Complements

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

NH ≅ G/Ntype
2. #13092143C2semidirect
3. C23×#343C2semidirect
68. #343D23semidirect
83. C23#1345semidirect

Maximal subgroups

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

subgroupindex
#130923342
#130921432
C23×#3432
#134523