Finite Group Databasebeta

← #15674700

Subgroups — #15674700

Order 2944.

264 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 67 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#13092445C211yesmaximal, characteristic, complemented
2#13092413C212yesmaximal, complemented
3#13092391C212yesmaximal, complemented
4#13092174C211yesmaximal, characteristic, complemented
5C23×#575C211yesmaximal, characteristic
6C2×#41×C23C2212yes—
7C23×#137—22no—
8C23×AGL(1,ℤ/8)—22no—
9C23×#135—22no—
10C2×M16×C23C2211yescharacteristic
11#10625097C2212yes—
12#10625097C2211yescharacteristic
13C22×C23⋊C8C2211yescharacteristic
14#10625017—22no—
15#10625016—24no—
16#10625014—22no—
17Dic23⋊C8—22no—
18#41×C23—22no—
19#41×C23—22no—
20#41×C23—22no—
21#41×C23—22no—
22C2×Q8×C23D412yes—
23C2×D4×C23—22no—
24C2×D4×C23D412yes—
25C22×C4×C23—22no—
26C22×C4×C23C2311yescharacteristic
27Q16×C23—22no—
28SD16×C23—24no—
29D8×C23—22no—
30M16×C23—22no—
31C2×C8×C23D412yes—
32C22⋊Dic23—22no—
33C22⋊Dic23D412yes—
34C4⋊Dic23—21no—
35C4⋊Dic23—22no—
36C4×Dic23—21no—
37C4×Dic23—22no—
38C2×C23⋊C8—21no—
39C2×C23⋊C8—22no—
40C23×C23—22no—
41C23×C23C2×D411yescharacteristic
42Q8×C23—22no—
43Q8×C23—22no—
44D4×C23—22no—
45D4×C23—22no—
46D4×C23—42no—
47D4×C23—42no—
48C2×C4×C23—22no—
49C2×C4×C23—42no—
50C2×C4×C23—42no—
51C2×C4×C23C2×D412yes—
52C2×C4×C23C2×D411yescharacteristic
53C2×C4×C23#4111yescharacteristic
54C2×C4×C23#4112yes—
55C2×Dic23—22no—
56C2×Dic23—42no—
57C8×C23—22no—
58C23⋊C8—41no—
59#2053—231nomaximal, Sylow
60C22×C23—41no—
61C22×C23—42no—
62C22×C23—82no—
63C22×C23#12111yescharacteristic
64C22×C23#12112yes—
65C4×C23—42no—
66C4×C23#12011yescharacteristic
67C4×C23#12312yes—
68C4×C23#12411yescharacteristic
69Dic23—42no—
70Dic23—82no—
71#575D2311yescharacteristic
72#424—231no—
73#416—232no—
74#410—232no—
75H(3,ℤ/4)—231no—
76C2×C23—21no—
77C2×C23—22no—
78C2×C23—82no—
79C2×C23#39411yescharacteristic
80C2×#41C2×D2312yes—
81#137—22no—
82AGL(1,ℤ/8)—22no—
83#135—22no—
84C2×M16C2×D2311yescharacteristic
85C22×C8—231no—
86#117—231no—
87#117—232no—
88C4⋊C8—462no—
89#103—462no—
90#102—462no—
91#99—464no—
92C23#205311yescharacteristic, complemented, Sylow
93#41—22no—
94#41—22no—
95#41—22no—
96#41—22no—
97C2×Q8C22⋊D2312yes—
98C2×D4—22no—
99C2×D4C22⋊D2312yes—
100C22×C4—22no—
101C22×C4C22×D2311yescharacteristic
102Q16—22no—
103SD16—24no—
104D8—22no—
105M16—22no—
106C2×C8—462no—
107C2×C8—461no—
108C2×C8C22⋊D2312yes—
109C4⋊C4—461no—
110C4⋊C4—462no—
111C22⋊C4—232no—
112C22⋊C4—462no—
113C42—461no—
114C42—462no—
115C23—22no—
116C23D4×D2311yescharacteristic
117Q8—22no—
118Q8—22no—
119D4—22no—
120D4—22no—
121D4—42no—
122D4—42no—
123C2×C4—22no—
124C2×C4—42no—
125C2×C4—42no—
126C2×C4—462no—
127C2×C4—922no—
128C2×C4#6729011yescharacteristic
129C2×C4#6729012yes—
130C2×C4C2×C22⋊D2312yes—
131C2×C4C2×C22⋊D2311yescharacteristic
132C8—22no—
133C8—921no—
134C22—41no—
135C22—42no—
136C22—82no—
137C22#1062510911yescharacteristic
138C22#1062511012yes—
139C4—42no—
140C4—922no—
141C4—1842no—
142C4#1062510612yes—
143C4#1062510711yescharacteristic
144C4#1062512411yescharacteristic
145C2—21no—
146C2—22no—
147C2—82no—
148C2#1309233111yescharacteristic
subgroupG/H
centerC4#10625107
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
Fitting, prime radicalC23×#575C2
socleC2×C23#394
hypercenter#575D23
hypocenterC23#2053
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #13092445C2semidirect
2. #13092413C2semidirect
3. #13092391C2semidirect
4. #13092174C2semidirect
92. C23#2053semidirect

Maximal subgroups

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

subgroupindex
#130924452
#130924132
#130923912
#130921742
C23×#5752
#205323