Finite Group Databasebeta

← #15673919

Subgroups — #15673919

Order 2944.

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

normal subgroups only

This group has 312 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#13092988C211yesmaximal, characteristic
2#13092427C212yesmaximal, complemented
3#13092391C211yesmaximal, characteristic
4#13092174C212yesmaximal, complemented
5C23×#568C211yesmaximal, characteristic
6C2×#41×C23C2211yescharacteristic
7C22×Dic46C2211yescharacteristic
8C23×#131—24no—
9C2×M16×C23—22no—
10C2×M16×C23C2212yes—
11#10625115C412yescomplemented
12#10625107C412yescomplemented
13#10625106—22no—
14#10625097C2212yes—
15#10625097C2211yescharacteristic
16#10625095—22no—
17#10625016—22no—
18#10624998—24no—
19#41×C23—22no—
20#41×C23—22no—
21C2×Q8×C23C2×C411yescharacteristic
22C2×D4×C23C2×C411yescharacteristic
23C2×D4×C23D412yes—
24C22×C4×C23D412yes—
25C22×C4×C23C2311yescharacteristic
26C22×Dic23—21no—
27C2×Dic46—22no—
28C2×Dic46—22no—
29C2×Dic46—21no—
30C2×Dic46C2×C412yes—
31M16×C23—24no—
32M16×C23—22no—
33M16×C23—22no—
34C2×C8×C23—24no—
35C2×C8×C23D414yes—
36C22⋊Dic23—24no—
37C22⋊Dic23—21no—
38C22⋊Dic23—22no—
39C4⋊Dic23—21no—
40C4⋊Dic23—22no—
41Dic23⋊C4—24no—
42C4×Dic23—22no—
43C4×Dic23C2×C412yes—
44C23×C23C22⋊C412yes—
45C23×C23C2×D411yescharacteristic
46Q8×C23—22no—
47D4×C23—24no—
48D4×C23—22no—
49C2×C4×C23—22no—
50C2×C4×C23—22no—
51C2×C4×C23C22⋊C412yes—
52C2×C4×C23C22×C411yescharacteristic
53C2×C4×C23C2×D412yes—
54C2×C4×C23C2×D411yescharacteristic
55C2×C4×C23#4112yes—
56C2×Dic23—22no—
57C2×Dic23—22no—
58C2×Dic23—42no—
59C2×Dic23—42no—
60Dic46—24no—
61Dic46—41no—
62Dic46—41no—
63C8×C23—24no—
64#1909—231nomaximal, Sylow
65C22×C23—22no—
66C22×C23—41no—
67C22×C23—42no—
68C22×C23C2×C22⋊C411yescharacteristic
69C22×C23#12112yes—
70C4×C23—22no—
71C4×C23C4×D412yes—
72C4×C23#12011yescharacteristic
73C4×C23#12311yescharacteristic
74Dic23—42no—
75Dic23—42no—
76Dic23—82no—
77#568D2311yescharacteristic
78#536—231no—
79#419—232no—
80#410—231no—
81H(3,ℤ/4)—232no—
82C2×C23—21no—
83C2×C23—22no—
84C2×C23—42no—
85C2×C23#38611yescharacteristic
86C2×#41C2×D2311yescharacteristic
87C22×Q8—231no—
88#131—24no—
89C2×M16—22no—
90C2×M16C2×D2312yes—
91C4⋊Q8—232no—
92#124—232no—
93#123—462no—
94C22⋊Q8—462no—
95#117—231no—
96#117—232no—
97#103—464no—
98#99—462no—
99C23#190911yescharacteristic, complemented, Sylow
100#41—22no—
101#41—22no—
102C2×Q8—232no—
103C2×Q8—461no—
104C2×Q8—462no—
105C2×Q8—462no—
106C2×Q8C4×D2311yescharacteristic
107C2×D4C4×D2311yescharacteristic
108C2×D4D9212yes—
109C22×C4—461no—
110C22×C4C22⋊D2312yes—
111C22×C4C22×D2311yescharacteristic
112M16—24no—
113M16—22no—
114M16—22no—
115C2×C8—24no—
116C2×C8C22⋊D2314yes—
117C4⋊C4—464no—
118C4⋊C4—461no—
119C4⋊C4—462no—
120C22⋊C4—464no—
121C22⋊C4—461no—
122C22⋊C4—462no—
123C42—232no—
124C42—462no—
125C23(C2×D23)⋊C412yes—
126C23C2×D9211yescharacteristic
127Q8—22no—
128Q8—464no—
129Q8—921no—
130Q8—921no—
131D4—24no—
132D4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—462no—
136C2×C4—462no—
137C2×C4—922no—
138C2×C4—922no—
139C2×C4(C2×D23)⋊C412yes—
140C2×C4C2×C4×D2311yescharacteristic
141C2×C4#6728812yes—
142C2×C4C2×C22⋊D2312yes—
143C2×C4C2×C22⋊D2311yescharacteristic
144C8—24no—
145C22—22no—
146C22—41no—
147C22—42no—
148C22C2×(C2×D23)⋊C411yescharacteristic
149C22#1062510112yes—
150C4—22no—
151C4—922no—
152C4—922no—
153C4—1842no—
154C4C4×C22⋊D2312yes—
155C4#1062510011yescharacteristic
156C4#1062512411yescharacteristic
157C2—21no—
158C2—22no—
159C2—42no—
160C2#1309229611yescharacteristic
subgroupG/H
centerC2#13092296
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#568C2
socleC2×C23#386
prime radicalC2×#41×C23C22
cosocleC22×C4×C23C23
hypercenter#568D23
hypocenterC23#1909
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. #13092427C2semidirect
4. #13092174C2semidirect
11. #10625115C4semidirect
12. #10625107C4semidirect
99. C23#1909semidirect

Maximal subgroups

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

subgroupindex
#130929882
#130924272
#130923912
#130921742
C23×#5682
#190923