Finite Group Databasebeta

← #15671720

Subgroups — #15671720

Order 2944.

248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×C4×Dic46C211yesmaximal, characteristic
2#13092470C211yesmaximal, characteristic
3#13092142C214yesmaximal
4C23×#431C211yesmaximal, characteristic
5C22×Dic46C411yescharacteristic
6C2×C42×C23C2211yescharacteristic
7C2×C4⋊Dic23C411yescharacteristic
8C2×Dic23⋊C4C2212yes—
9C2×C4×Dic23C412yes—
10C4×Dic46—21no—
11C4×Dic46—21no—
12C4×Dic46—21no—
13C4×Dic46—21no—
14C23×C4⋊C8—21no—
15C23×C22⋊C8C2212yes—
16C4×C8×C23—21no—
17C22⋊(C23⋊C8)C2212yes—
18C4⋊(C23⋊C8)—21no—
19C4×C23⋊C8—21no—
20C22×C4×C23C2×C411yescharacteristic
21C22×C4×C23C2×C411yescharacteristic
22C22×C4×C23C2311yescharacteristic
23C22×Dic23C2×C412yes—
24C22×Dic23C2×C412yes—
25C2×Dic46—21no—
26C2×Dic46—21no—
27C2×Dic46—22no—
28C2×Dic46C814yescomplemented
29C2×C8×C23—22no—
30C42×C23D411yescharacteristic
31C42×C23D411yescharacteristic
32C42×C23D411yescharacteristic
33C42×C23D411yescharacteristic
34C4⋊Dic23—21no—
35C4⋊Dic23—21no—
36Dic23⋊C4—22no—
37Dic23⋊C4—22no—
38C4×Dic23—22no—
39C4×Dic23—22no—
40C2×C23⋊C8—22no—
41C23×C23C22×C411yescharacteristic
42C2×C4×C23—22no—
43C2×C4×C23—41no—
44C2×C4×C23C22⋊C411yescharacteristic
45C2×C4×C23C22⋊C411yescharacteristic
46C2×C4×C23C22⋊C411yescharacteristic
47C2×C4×C23C22⋊C411yescharacteristic
48C2×C4×C23C2×C812yes—
49C2×C4×C23M1612yes—
50C2×C4×C23C2×D411yescharacteristic
51C2×C4×C23C2×D411yescharacteristic
52C2×Dic23—22no—
53C2×Dic23—22no—
54C2×Dic23—22no—
55C2×Dic23—42no—
56C2×Dic23C2×C814yes—
57Dic46—24no—
58Dic46—24no—
59C8×C23—42no—
60C23⋊C8—42no—
61#1461—231nomaximal, Sylow
62C22×C23—21no—
63C22×C23—21no—
64C22×C23C2×C22⋊C411yescharacteristic
65C22×C23C22×C811yescharacteristic
66C22×C23C2×M1611yescharacteristic
67C4×C23—21no—
68C4×C23—21no—
69C4×C23—21no—
70C4×C23C22⋊C812yes—
71C4×C23C22⋊C812yes—
72C4×C23#10112yes—
73Dic23—24no—
74Dic23—42no—
75C2×C4×Q8—231no—
76#431—231no—
77#431D2311yescharacteristic
78#324—234no—
79C2×C23—21no—
80C2×C23—21no—
81C2×C23C2×C22⋊C811yescharacteristic
82C2×C23#41011yescharacteristic
83C2×C23C2×#10111yescharacteristic
84C22×Q8—231no—
85C4×Q8—461no—
86C4×Q8—461no—
87C4×Q8—461no—
88C4×Q8—461no—
89C2×C4⋊C4—231no—
90C2×C4⋊C4—232no—
91C2×C42—232no—
92C2×C42C2×D2311yescharacteristic
93C4⋊C8—21no—
94C4⋊C8—461no—
95C22⋊C8—232no—
96C22⋊C8C2×D2312yes—
97C4×C8—21no—
98C4×C8—461no—
99C23#146111yescharacteristic, complemented, Sylow
100C2×Q8—234no—
101C2×Q8—462no—
102C2×Q8—461no—
103C2×Q8—461no—
104C22×C4—232no—
105C22×C4—232no—
106C22×C4C4×D2311yescharacteristic
107C22×C4C4×D2311yescharacteristic
108C22×C4C22×D2311yescharacteristic
109C2×C8—22no—
110C2×C8—462no—
111C4⋊C4—461no—
112C4⋊C4—461no—
113C4⋊C4—462no—
114C4⋊C4—462no—
115C42—462no—
116C42—462no—
117C42D9211yescharacteristic
118C42D9211yescharacteristic
119C42C22⋊D2311yescharacteristic
120C42C22⋊D2311yescharacteristic
121C23C2×C4×D2311yescharacteristic
122Q8—464no—
123Q8—464no—
124C2×C4—22no—
125C2×C4—41no—
126C2×C4—234no—
127C2×C4—462no—
128C2×C4—462no—
129C2×C4—462no—
130C2×C4—922no—
131C2×C4C8×D2312yes—
132C2×C4#6726212yes—
133C2×C4(C2×D23)⋊C411yescharacteristic
134C2×C4(C2×D23)⋊C411yescharacteristic
135C2×C4(C2×D23)⋊C411yescharacteristic
136C2×C4(C2×D23)⋊C411yescharacteristic
137C2×C4C2×D9211yescharacteristic
138C2×C4C2×C22⋊D2311yescharacteristic
139C8—42no—
140C8—922no—
141C22—21no—
142C22—21no—
143C22C2×C8×D2311yescharacteristic
144C22C2×#6726211yescharacteristic
145C22C2×(C2×D23)⋊C411yescharacteristic
146C4—21no—
147C4—21no—
148C4—21no—
149C4—464no—
150C4—922no—
151C4(C2×D23)⋊C812yes—
152C4(C2×D23)⋊C812yes—
153C4#1062500612yes—
154C2—21no—
155C2—21no—
156C2C2×(C2×D23)⋊C811yescharacteristic
157C2#1309239011yescharacteristic
158C2C2×#1062500611yescharacteristic
subgroupG/H
centerC2×C4(C2×D23)⋊C4
commutatorC22×C23C22×C8
FrattiniC22×C4C22×D23
FittingC23×#431C2
socleC22×C23C2×C22⋊C4
prime radicalC23×C23C22×C4
cosocleC22×C4×C23C23
hypercenter#431D23
hypocenterC23#1461
LCSG ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
28. C2×Dic46C8semidirect
99. C23#1461semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic462
#130924702
#130921422
C23×#4312
#146123