Finite Group Databasebeta

← #15673924

Subgroups — #15673924

Order 2944.

344 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 89 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#13092981C211yesmaximal, characteristic
2#13092423C212yesmaximal, complemented
3#13092391C211yesmaximal, characteristic, complemented
4#13092174C212yesmaximal, complemented
5C23×#568C211yesmaximal, characteristic, complemented
6C2×#41×C23C2211yescharacteristic
7C22×D92C2211yescharacteristic
8C23×#131—24no—
9C2×M16×C23—22no—
10C2×M16×C23C2212yes—
11#10625118C412yescomplemented
12#10625111C412yescomplemented
13#10625108—22no—
14#10625101—22no—
15#10625097C2212yes—
16#10625097C2211yescharacteristic
17#10625016—22no—
18#10625003—24no—
19C23×D23—21no—
20#41×C23—22no—
21#41×C23—22no—
22C2×Q8×C23C2×C411yescharacteristic
23C2×D4×C23C2×C411yescharacteristic
24C2×D4×C23D412yes—
25C22×C4×C23D412yes—
26C22×C4×C23C2311yescharacteristic
27C2×C22⋊D23—24no—
28C2×D92—22no—
29C2×D92—22no—
30C2×D92—21no—
31C2×D92C2×C412yes—
32M16×C23—24no—
33M16×C23—22no—
34M16×C23—22no—
35C2×C8×C23—24no—
36C2×C8×C23D414yescomplemented
37C22⋊Dic23—21no—
38C22⋊Dic23—22no—
39(C2×D23)⋊C4—24no—
40C4⋊Dic23—21no—
41C4⋊Dic23—22no—
42C4×Dic23—22no—
43C4×Dic23C2×C412yes—
44C23×C23C22⋊C412yes—
45C23×C23C2×D411yescharacteristic
46C22×D23—22no—
47C22×D23—42no—
48C22×D23—82no—
49Q8×C23—22no—
50D4×C23—24no—
51D4×C23—22no—
52C2×C4×C23—22no—
53C2×C4×C23—22no—
54C2×C4×C23C22⋊C412yes—
55C2×C4×C23C22×C411yescharacteristic
56C2×C4×C23C2×D412yes—
57C2×C4×C23C2×D411yescharacteristic
58C2×C4×C23#4112yes—
59C22⋊D23—84no—
60C2×Dic23—22no—
61C2×Dic23—42no—
62D92—24no—
63D92—41no—
64D92—41no—
65C8×C23—24no—
66#1910—231nomaximal, Sylow
67C22×C23—22no—
68C22×C23—41no—
69C22×C23—42no—
70C22×C23C2×C22⋊C411yescharacteristic
71C22×C23#12112yes—
72C2×D23—44no—
73C2×D23—42no—
74C2×D23—84no—
75C4×C23—22no—
76C4×C23C4×D412yes—
77C4×C23#12011yescharacteristic
78C4×C23#12311yescharacteristic
79Dic23—42no—
80Dic23—82no—
81#568D2311yescharacteristic, complemented
82#535—231no—
83#418—232no—
84#410—231no—
85H(3,ℤ/4)—232no—
86C2×C23—21no—
87C2×C23—22no—
88C2×C23—42no—
89C2×C23#38611yescharacteristic
90D23—82no—
91C2×#41C2×D2311yescharacteristic
92C22×D4—231no—
93#131—24no—
94C2×M16—22no—
95C2×M16C2×D2312yes—
96#127—232no—
97#124—232no—
98#121—462no—
99#120—462no—
100#117—231no—
101#117—232no—
102#102—464no—
103#99—462no—
104C23#191011yescharacteristic, complemented, Sylow
105C24—461no—
106#41—22no—
107#41—22no—
108C2×Q8C4×D2311yescharacteristic
109C2×D4—232no—
110C2×D4—464no—
111C2×D4—462no—
112C2×D4—462no—
113C2×D4—461no—
114C2×D4C4×D2311yescharacteristic
115C2×D4D9212yes—
116C22×C4C22⋊D2312yes—
117C22×C4C22×D2311yescharacteristic
118M16—24no—
119M16—22no—
120M16—22no—
121C2×C8—24no—
122C2×C8C22⋊D2314yescomplemented
123C4⋊C4—461no—
124C4⋊C4—462no—
125C22⋊C4—461no—
126C22⋊C4—464no—
127C22⋊C4—462no—
128C42—232no—
129C42—462no—
130C23—462no—
131C23—922no—
132C23—1842no—
133C23(C2×D23)⋊C412yes—
134C23C2×D9211yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—464no—
139D4—921no—
140D4—921no—
141D4—1844no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—462no—
145C2×C4—922no—
146C2×C4(C2×D23)⋊C412yes—
147C2×C4C2×C4×D2311yescharacteristic
148C2×C4#6728812yes—
149C2×C4C2×C22⋊D2312yes—
150C2×C4C2×C22⋊D2311yescharacteristic
151C8—24no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—924no—
156C22—922no—
157C22—1844no—
158C22C2×(C2×D23)⋊C411yescharacteristic
159C22#1062510112yes—
160C4—22no—
161C4—922no—
162C4—1842no—
163C4C4×C22⋊D2312yes—
164C4#1062510011yescharacteristic
165C4#1062512411yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—1842no—
170C2#1309229611yescharacteristic
subgroupG/H
centerC2#13092296
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#568C2
socleC2×C23#386
prime radical#13092981C2
cosocleC22×C4×C23C23
hypercenter#568D23
hypocenterC23#1910
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #13092423C2semidirect
3. #13092391C2semidirect
4. #13092174C2semidirect
5. C23×#568C2semidirect
11. #10625118C4semidirect
12. #10625111C4semidirect
36. C2×C8×C23D4semidirect
81. #568D23semidirect
104. C23#1910semidirect
122. C2×C8C22⋊D23semidirect

Maximal subgroups

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

subgroupindex
#130929812
#130924232
#130923912
#130921742
C23×#5682
#191023