Finite Group Databasebeta

← #15671523

Subgroups — #15671523

Order 2944.

172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C2×#10625018C211yesmaximal, characteristic
2#13092324C211yesmaximal, characteristic
3C2×C23×#101C211yesmaximal, characteristic
4C22×Q8×C23C2211yescharacteristic
5C2×M16×C23—21no—
6C2×C4⋊Dic23C411yescharacteristic
7C2×C4×Dic23C411yescharacteristic
8C2×#67267—21no—
9C23×#101—21no—
10C23×#101C412yescomplemented
11#10625018—21no—
12#10625018C412yescomplemented
13C23⋊#95—21no—
14C23⋊#95—21no—
15C2×Q8×C23—41no—
16C2×Q8×C23—41no—
17C2×Q8×C23C2×C411yescharacteristic
18C2×Q8×C23C2×C411yescharacteristic
19C2×Q8×C23D411yescharacteristic
20C2×Q8×C23Q811yescharacteristic
21C22×C4×C23C2×C411yescharacteristic
22C22×C4×C23D411yescharacteristic
23C22×C4×C23D411yescharacteristic
24C22×Dic23—21no—
25C22×Dic23—21no—
26M16×C23—22no—
27M16×C23—41no—
28C2×C8×C23—41no—
29C4⋊Dic23—41no—
30C4×Dic23—41no—
31#67267—22no—
32#67267—41no—
33C2×C23⋊C8—41no—
34C23×C23C22⋊C411yescharacteristic
35Q8×C23—41no—
36Q8×C23—41no—
37Q8×C23—41no—
38Q8×C23—41no—
39C2×C4×C23—21no—
40C2×C4×C23—21no—
41C2×C4×C23—21no—
42C2×C4×C23—21no—
43C2×C4×C23—21no—
44C2×C4×C23—21no—
45C2×C4×C23C4211yescharacteristic
46C2×C4×C23C22⋊C411yescharacteristic
47C2×C4×C23C22⋊C411yescharacteristic
48C2×C4×C23C4⋊C411yescharacteristic
49C2×C4×C23C4⋊C411yescharacteristic
50C2×C4×C23C4⋊C411yescharacteristic
51C2×Dic23—22no—
52C2×Dic23—41no—
53C2×Dic23—41no—
54C2×Dic23—42no—
55C2×Dic23—41no—
56C8×C23—42no—
57C23⋊C8—42no—
58#1394—231nomaximal, Sylow
59C22×C23—21no—
60C22×C23—21no—
61C22×C23#9511yescharacteristic
62C22×C23#9911yescharacteristic
63C22×C23#9911yescharacteristic
64C4×C23—21no—
65C4×C23—21no—
66C4×C23—21no—
67C4×C23—21no—
68C4×C23—21no—
69C4×C23—21no—
70Dic23—42no—
71Dic23—81no—
72C2×#101—231no—
73C2×#101D2311yescharacteristic
74#391—231no—
75C2×C23—21no—
76C2×C23—21no—
77C2×C23#34211yescharacteristic
78C2×C23#35511yescharacteristic
79C2×C23#35611yescharacteristic
80C22×Q8C2×D2311yescharacteristic
81C2×M16—21no—
82C2×M16—461no—
83C2×C4⋊C4—231no—
84C2×C42—231no—
85#101—21no—
86#101—232no—
87#101—461no—
88#101Dic2312yescomplemented
89#95—461no—
90#95—461no—
91C23#139411yescharacteristic, complemented, Sylow
92C2×Q8—41no—
93C2×Q8—41no—
94C2×Q8Dic4611yescharacteristic
95C2×Q8C4×D2311yescharacteristic
96C2×Q8C2×Dic2311yescharacteristic
97C2×Q8C22⋊D2311yescharacteristic
98C22×C4—461no—
99C22×C4—461no—
100C22×C4C4×D2311yescharacteristic
101C22×C4D9211yescharacteristic
102C22×C4C22⋊D2311yescharacteristic
103M16—22no—
104M16—41no—
105M16—462no—
106M16—921no—
107C2×C8—41no—
108C2×C8—921no—
109C4⋊C4—921no—
110C42—921no—
111C23(C2×D23)⋊C411yescharacteristic
112Q8—41no—
113Q8—41no—
114Q8—41no—
115Q8—41no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—21no—
119C2×C4—21no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—462no—
123C2×C4—921no—
124C2×C4—921no—
125C2×C4—922no—
126C2×C4—921no—
127C2×C4C4×Dic2311yescharacteristic
128C2×C4Dic23⋊C411yescharacteristic
129C2×C4Dic23⋊C411yescharacteristic
130C2×C4C4⋊Dic2311yescharacteristic
131C2×C4(C2×D23)⋊C411yescharacteristic
132C2×C4C22⋊Dic2311yescharacteristic
133C8—42no—
134C8—922no—
135C22—21no—
136C22—21no—
137C22#1062498811yescharacteristic
138C22#1062498811yescharacteristic
139C22C23⋊#9511yescharacteristic
140C4—21no—
141C4—21no—
142C4—21no—
143C4—21no—
144C4—21no—
145C4—21no—
146C4—922no—
147C4—1841no—
148C2—21no—
149C2—21no—
150C2#1309218311yescharacteristic
151C2#1309221311yescharacteristic
152C2#1309221511yescharacteristic
subgroupG/H
centerC22#10624988
commutatorC2×C4×C23C42
FrattiniC22×Q8C2×D23
FittingC2×C23×#101C2
socleC22×C23#99
prime radicalC23×C23C22⋊C4
cosocleC22×Q8×C23C22
hypercenterC2×#101D23
hypocenterC23#1394
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
10. C23×#101C4semidirect
12. #10625018C4semidirect
88. #101Dic23semidirect
91. C23#1394semidirect

Maximal subgroups

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

subgroupindex
C2×#106250182
#130923242
C2×C23×#1012
#139423