Finite Group Databasebeta

← #15675413

Subgroups — #15675413

Order 2944.

248 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 41 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#13093159C211yesmaximal, characteristic, complemented
2#13092590C212yesmaximal, complemented
3#13092214C211yesmaximal, characteristic, complemented
4#13092213C212yesmaximal, complemented
5C23×#454C211yesmaximal, characteristic, complemented
6C23×2−1+4C2211yescharacteristic, complemented
7C23×AGL(1,ℤ/8)—21no—
8C23×#124C2211yescharacteristic
9#10625120—22no—
10#10625118C2212yes—
11#10625108—21no—
12#10625056—22no—
13#10625053—22no—
14#10625046—21no—
15C23×#104—21no—
16C23×#101C2211yescharacteristic, complemented
17#10625019—22no—
18#10625018C2212yescomplemented
19C23×D23—21no—
20#41×C23—21no—
21#41×C23—22no—
22#41×C23—41no—
23C2×Q8×C23—41no—
24C2×Q8×C23C2311yescharacteristic
25C2×D4×C23D411yescharacteristic
26C2×C22⋊D23—22no—
27C2×D92—21no—
28C2×D92D412yes—
29C2×Dic46—21no—
30SD16×C23—41no—
31D8×C23—41no—
32M16×C23—21no—
33C22⋊C4×C23—22no—
34C42×C23D411yescharacteristic
35C22⋊Dic23—21no—
36#67274—42no—
37#67272—42no—
38(C2×D23)⋊C4—22no—
39(C2×D23)⋊C4—22no—
40(C2×D23)⋊C4—22no—
41C4×Dic23D412yes—
42#67267—22no—
43C23×C23—21no—
44C22×D23—22no—
45C22×D23—82no—
46C22×D23—81no—
47Q8×C23—22no—
48Q8×C23—21no—
49Q8×C23—41no—
50D4×C23—22no—
51D4×C23—21no—
52D4×C23—41no—
53D4×C23—41no—
54C2×C4×C23—21no—
55C2×C4×C23—42no—
56C2×C4×C23—41no—
57C2×C4×C23C2×D412yes—
58C2×C4×C23C2×D411yescharacteristic
59C22⋊D23—82no—
60C2×Dic23—22no—
61D92—42no—
62D92—81no—
63Dic46—81no—
64C8×C23—41no—
65C23⋊C8—42no—
66#2202—231nomaximal, Sylow
67C22×C23—42no—
68C22×C23—41no—
69C22×C23—41no—
70C22×C23#12011yescharacteristic
71C2×D23—42no—
72C2×D23—42no—
73C2×D23—42no—
74C2×D23—84no—
75C4×C23—22no—
76C4×C23—21no—
77C4×C23—41no—
78C4×C23—41no—
79Dic23—42no—
80H(3,𝔽4)—231no—
81#454—232no—
82#454D2311yescharacteristic, complemented
83#355—231no—
84#355—232no—
85C2×C23—21no—
86C2×C23—81no—
87C2×C23—81no—
88C2×C23B(4,𝔽2)11yescharacteristic
89D23—82no—
902−1+4C2×D2311yescharacteristic, complemented
91AGL(1,ℤ/8)—21no—
92AGL(1,ℤ/8)—462no—
93#124—232no—
94#124—462no—
95#124—461no—
96#124C2×D2311yescharacteristic
97#120—462no—
98#120—461no—
99#104—21no—
100#104—462no—
101#101—232no—
102#101C2×D2311yescharacteristic, complemented
103C23#220211yescharacteristic, complemented, Sylow
104C24—461no—
105#41—22no—
106#41—21no—
107#41—41no—
108C2×Q8—41no—
109C2×Q8—461no—
110C2×Q8C22×D2311yescharacteristic
111C2×D4—232no—
112C2×D4—461no—
113C2×D4—462no—
114C2×D4C22⋊D2311yescharacteristic
115SD16—41no—
116SD16—922no—
117D8—41no—
118D8—922no—
119M16—21no—
120M16—462no—
121C22⋊C4—22no—
122C22⋊C4—462no—
123C22⋊C4—461no—
124C22⋊C4—462no—
125C22⋊C4—462no—
126C42—232no—
127C42C22⋊D2311yescharacteristic
128C23—21no—
129C23—462no—
130C23—1842no—
131C23—1841no—
132Q8—21no—
133Q8—22no—
134Q8—41no—
135Q8—1841no—
136D4—21no—
137D4—22no—
138D4—41no—
139D4—41no—
140D4—922no—
141D4—1841no—
142D4—1842no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—42no—
146C2×C4—462no—
147C2×C4D4×D2312yes—
148C2×C4C2×C22⋊D2311yescharacteristic
149C8—41no—
150C8—922no—
151C22—42no—
152C22—41no—
153C22—41no—
154C22—922no—
155C22—922no—
156C22—922no—
157C22—1844no—
158C22#1062510811yescharacteristic
159C4—21no—
160C4—22no—
161C4—41no—
162C4—41no—
163C4—922no—
164C2—21no—
165C2—81no—
166C2—81no—
167C2—1842no—
168C2#1309260311yescharacteristic
subgroupG/H
centerC2#13092603
commutator, cosocleC2×Q8×C23C23
FrattiniC2×Q8C22×D23
FittingC23×#454C2
socleC2×C23B(4,𝔽2)
hypercenter#454D23
hypocenterC23#2202
LCSG ▷ C2×Q8×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #13093159C2semidirect
2. #13092590C2semidirect
3. #13092214C2semidirect
4. #13092213C2semidirect
5. C23×#454C2semidirect
6. C23×2−1+4C22semidirect
16. C23×#101C22semidirect
18. #10625018C22semidirect
82. #454D23semidirect
90. 2−1+4C2×D23semidirect
102. #101C2×D23semidirect
103. C23#2202semidirect

Maximal subgroups

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

subgroupindex
#130931592
#130925902
#130922142
#130922132
C23×#4542
#220223