Finite Group Databasebeta

← #15671947

Subgroups — #15671947

Order 2944.

208 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 69 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#13092974C211yesmaximal, characteristic
2#13092474C211yesmaximal, characteristic
3#13092153C214yesmaximal
4C23×#383C211yesmaximal, characteristic
5C2×C42×C23C2211yescharacteristic
6#10625097—21no—
7#10625095—21no—
8#10625095C2212yes—
9#10625041—21no—
10#10625040C411yescharacteristic, complemented
11#10625040C411yescharacteristic, complemented
12C4×Dic46—21no—
13C4×Dic46C412yescomplemented
14C23×#95—21no—
15C23×#95—21no—
16C23×#95C2212yes—
17C22⋊(C23⋊C8)C2212yes—
18C4⋊(C23⋊C8)—21no—
19#10624985—21no—
20C22×C4×C23—22no—
21C22×C4×C23D411yescharacteristic
22C22×C4×C23D411yescharacteristic
23C22×C4×C23C2311yescharacteristic
24C2×Dic46—21no—
25C2×Dic46C2×C412yes—
26C42×C23C2×C411yescharacteristic
27C42×C23C2×C411yescharacteristic
28C42×C23D411yescharacteristic
29C42×C23D411yescharacteristic
30C22⋊Dic23—22no—
31C4⋊Dic23—21no—
32C4⋊Dic23—21no—
33C4⋊Dic23—21no—
34C4⋊Dic23C2×C412yes—
35Dic23⋊C4—22no—
36Dic23⋊C4—22no—
37C4×Dic23—22no—
38C2×C23⋊C8—22no—
39C23×C23C2×D411yescharacteristic
40C2×C4×C23—22no—
41C2×C4×C23—41no—
42C2×C4×C23—41no—
43C2×C4×C23—42no—
44C2×C4×C23—42no—
45C2×C4×C23—42no—
46C2×C4×C23C22⋊C411yescharacteristic
47C2×C4×C23C22⋊C411yescharacteristic
48C2×C4×C23C22⋊C411yescharacteristic
49C2×C4×C23C22⋊C411yescharacteristic
50C2×C4×C23C22×C411yescharacteristic
51C2×C4×C23C2×D411yescharacteristic
52C2×Dic23—22no—
53C2×Dic23—22no—
54Dic46—42no—
55Dic46—42no—
56C23⋊C8—42no—
57#1515—231nomaximal, Sylow
58C22×C23—21no—
59C22×C23—21no—
60C22×C23C2×C22⋊C411yescharacteristic
61C22×C23#13712yes—
62C4×C23—21no—
63C4×C23—21no—
64C4×C23—21no—
65C4×C23—21no—
66C4×C23—21no—
67C4×C23—21no—
68C4×C23—82no—
69Dic23—42no—
70Dic23—42no—
71#533—231no—
72#432—231no—
73#383D2311yescharacteristic
74#328—234no—
75C2×C23—22no—
76C2×C23#41011yescharacteristic
77C2×C23#41911yescharacteristic
78C2×C23#42111yescharacteristic
79C4⋊Q8—231no—
80C4⋊Q8—231no—
81#125—461no—
82C22⋊Q8—232no—
83C22⋊Q8—461no—
84C4×Q8—232no—
85C4×Q8—461no—
86#117—461no—
87C2×C42C2×D2311yescharacteristic
88C4⋊C8—461no—
89C22⋊C8—232no—
90#97—461no—
91#95—21no—
92#95—21no—
93#95C2×D2312yes—
94C23#151511yescharacteristic, complemented, Sylow
95C2×Q8—232no—
96C2×Q8—461no—
97C22×C4—22no—
98C22×C4C22⋊D2311yescharacteristic
99C22×C4C22⋊D2311yescharacteristic
100C22×C4C22×D2311yescharacteristic
101C2×C8—462no—
102C4⋊C4—232no—
103C4⋊C4—461no—
104C4⋊C4—461no—
105C4⋊C4—462no—
106C4⋊C4—461no—
107C4⋊C4—462no—
108C22⋊C4—462no—
109C42—462no—
110C42C4×D2311yescharacteristic
111C42C4×D2311yescharacteristic
112C42D9211yescharacteristic
113C42D9211yescharacteristic
114C23C2×C22⋊D2311yescharacteristic
115Q8—922no—
116Q8—922no—
117C2×C4—22no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—42no—
122C2×C4—42no—
123C2×C4—462no—
124C2×C4—462no—
125C2×C4(C2×D23)⋊C411yescharacteristic
126C2×C4(C2×D23)⋊C411yescharacteristic
127C2×C4(C2×D23)⋊C411yescharacteristic
128C2×C4(C2×D23)⋊C411yescharacteristic
129C2×C4C2×C4×D2311yescharacteristic
130C2×C4C2×D9211yescharacteristic
131C8—922no—
132C22—21no—
133C22—21no—
134C22C2×(C2×D23)⋊C411yescharacteristic
135C22#1062512212yes—
136C4—21no—
137C4—21no—
138C4—21no—
139C4—21no—
140C4—21no—
141C4—21no—
142C4—82no—
143C4—922no—
144C4—922no—
145C2—22no—
146C2#1309239011yescharacteristic
147C2#1309242511yescharacteristic
148C2#1309243511yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#383C2
socleC22×C23C2×C22⋊C4
prime radicalC23×C23C2×D4
cosocleC22×C4×C23C23
hypercenter#383D23
hypocenterC23#1515
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
10. #10625040C4semidirect
11. #10625040C4semidirect
13. C4×Dic46C4semidirect
94. C23#1515semidirect

Maximal subgroups

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

subgroupindex
#130929742
#130924742
#130921532
C23×#3832
#151523