Finite Group Databasebeta

← #15672673

Subgroups — #15672673

Order 2944.

194 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 55 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#13093145C211yesmaximal, characteristic
2#13092813C211yesmaximal, characteristic
3#13092624C211yesmaximal, characteristic
4#13092164C211yesmaximal, characteristic
5Q8⋊(C23⋊C8)C211yesmaximal, characteristic
6#13092147C211yesmaximal, characteristic
7C23×#475C211yesmaximal, characteristic
8C23×C4⋊Q8C2211yescharacteristic
9C4×Q8×C23C2211yescharacteristic
10#10625115—21no—
11C2×#67275—21no—
12#10625060—22no—
13#10625058—21no—
14#10625041—21no—
15#10625040C2211yescharacteristic
16C4×Dic46—21no—
17C4×Dic46C2211yescharacteristic
18C23×#106—21no—
19C23×C4⋊C8C2211yescharacteristic
20C23×#103—21no—
21#10625017—21no—
22#10624990—22no—
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4×C23⋊C8C2211yescharacteristic
25C2×Q8×C23—21no—
26C2×Q8×C23D411yescharacteristic
27C2×Dic46—21no—
28C2×Dic46D411yescharacteristic
29C2×C8×C23—21no—
30C4⋊C4×C23—21no—
31C4⋊C4×C23—21no—
32C4⋊C4×C23—21no—
33C4⋊C4×C23D411yescharacteristic
34C42×C23—21no—
35C42×C23C2311yescharacteristic
36#67275—42no—
37C4⋊Dic23—21no—
38C4⋊Dic23D411yescharacteristic
39C4⋊Dic23D412yes—
40Dic23⋊C4—22no—
41Dic23⋊C4—22no—
42Dic23⋊C4—22no—
43Dic23⋊C4—21no—
44C4×Dic23—22no—
45C4×Dic23—21no—
46C2×C23⋊C8—21no—
47C2×C23⋊C8—21no—
48Q8×C23—21no—
49Q8×C23—21no—
50Q8×C23—41no—
51Q8×C23—41no—
52C2×C4×C23—21no—
53C2×C4×C23—21no—
54C2×C4×C23—41no—
55C2×C4×C23C2×D411yescharacteristic
56C2×C4×C23C2×D411yescharacteristic
57C2×C4×C23C2×D411yescharacteristic
58C2×Dic23—21no—
59C2×Dic23—21no—
60C2×Dic23—22no—
61Dic46—21no—
62Dic46—41no—
63Dic46—41no—
64Dic46SD1612yes—
65C8×C23—41no—
66C23⋊C8—22no—
67C23⋊C8—41no—
68#1653—231nomaximal, Sylow
69C22×C23#12011yescharacteristic
70C4×C23—21no—
71C4×C23—41no—
72C4×C23—41no—
73C4×C23—81no—
74C4×C23C2×SD1611yescharacteristic
75C4×C23#13511yescharacteristic
76C4×C23#13711yescharacteristic
77C4×C23#13711yescharacteristic
78Dic23—22no—
79Dic23—42no—
80Dic23—41no—
81#557—231no—
82#498—231no—
83#475D2311yescharacteristic
84#462—231no—
85#332—231no—
86Q8⋊C8—231no—
87Q8⋊C8—231no—
88C2×C23#44811yescharacteristic
89C2×C23#45211yescharacteristic
90C2×C23#45611yescharacteristic
91C2×Q16—461no—
92C4⋊Q8—231no—
93C4⋊Q8—461no—
94C4⋊Q8C2×D2311yescharacteristic
95#125—461no—
96#125—462no—
97C4×Q8—231no—
98C4×Q8—461no—
99C4×Q8—461no—
100C4×Q8C2×D2311yescharacteristic
101#106—21no—
102#106—462no—
103C4⋊C8—231no—
104C4⋊C8C2×D2311yescharacteristic
105#103—21no—
106#103—461no—
107C4×C8—231no—
108C23#165311yescharacteristic, complemented, Sylow
109C2×Q8—21no—
110C2×Q8—231no—
111C2×Q8—461no—
112C2×Q8C22⋊D2311yescharacteristic
113Q16—922no—
114C2×C8—21no—
115C2×C8—461no—
116C2×C8—461no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—231no—
121C4⋊C4—232no—
122C4⋊C4—462no—
123C4⋊C4—462no—
124C4⋊C4—462no—
125C4⋊C4—461no—
126C4⋊C4—461no—
127C4⋊C4C22⋊D2311yescharacteristic
128C42—21no—
129C42—462no—
130C42—461no—
131C42C22×D2311yescharacteristic
132Q8—21no—
133Q8—21no—
134Q8—41no—
135Q8—41no—
136Q8—232no—
137Q8—461no—
138Q8—921no—
139Q8—921no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—461no—
144C2×C4—461no—
145C2×C4—462no—
146C2×C4D4×D2311yescharacteristic
147C2×C4D4×D2311yescharacteristic
148C2×C4C2×C22⋊D2311yescharacteristic
149C8—41no—
150C8—462no—
151C8—921no—
152C22#1062510811yescharacteristic
153C4—21no—
154C4—41no—
155C4—41no—
156C4—81no—
157C4—462no—
158C4—922no—
159C4—921no—
160C4SD16×D2311yescharacteristic
161C4#1062508611yescharacteristic
162C4#1062511311yescharacteristic
163C4#1062512111yescharacteristic
164C2#1309255411yescharacteristic
165C2#1309257711yescharacteristic
166C2#1309259811yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#475C2
socle, prime radicalC22×C23#120
hypercenter#475D23
hypocenterC23#1653
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
108. C23#1653semidirect

Maximal subgroups

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

subgroupindex
#130931452
#130928132
#130926242
#130921642
Q8⋊(C23⋊C8)2
#130921472
C23×#4752
#165323