Finite Group Databasebeta

← #15671962

Subgroups — #15671962

Order 2944.

220 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 85 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#13092283C211yesmaximal, characteristic
3#13092155C214yesmaximal
4C23×#431C211yesmaximal, characteristic
5C2×C42×C23C2211yescharacteristic
6#10625097—21no—
7C2×C4⋊Dic23—21no—
8#10625095—21no—
9#10625095C2212yes—
10#10625041—21no—
11#10625040C411yescharacteristic, complemented
12#10625040C411yescharacteristic, complemented
13C4×Dic46—21no—
14C4×Dic46C412yescomplemented
15C23×C4⋊C8—21no—
16C23×C22⋊C8C2212yes—
17C4×C8×C23—21no—
18C23⋊#95—21no—
19C23⋊#95C2212yes—
20C22×C4×C23D411yescharacteristic
21C22×C4×C23D411yescharacteristic
22C22×C4×C23C2311yescharacteristic
23C22×Dic23—22no—
24C2×Dic46—21no—
25C2×Dic46C2×C412yes—
26C2×C8×C23—22no—
27C42×C23C2×C411yescharacteristic
28C42×C23C2×C411yescharacteristic
29C42×C23D411yescharacteristic
30C42×C23D411yescharacteristic
31C22⋊Dic23—22no—
32C4⋊Dic23—21no—
33C4⋊Dic23—21no—
34C4⋊Dic23—21no—
35C4⋊Dic23—42no—
36C4⋊Dic23C2×C412yes—
37Dic23⋊C4—22no—
38Dic23⋊C4—22no—
39C4×Dic23—22no—
40C23×C23C2×D411yescharacteristic
41C2×C4×C23—41no—
42C2×C4×C23—41no—
43C2×C4×C23C22⋊C411yescharacteristic
44C2×C4×C23C22⋊C411yescharacteristic
45C2×C4×C23C22⋊C411yescharacteristic
46C2×C4×C23C22⋊C411yescharacteristic
47C2×C4×C23SD1612yes—
48C2×C4×C23Q1612yes—
49C2×C4×C23C22×C411yescharacteristic
50C2×C4×C23C2×D411yescharacteristic
51C2×Dic23—22no—
52C2×Dic23—22no—
53C2×Dic23—42no—
54C2×Dic23—42no—
55C2×Dic23—42no—
56Dic46—42no—
57Dic46—42no—
58C8×C23—42no—
59#1518—231nomaximal, Sylow
60C22×C23—21no—
61C22×C23—21no—
62C22×C23C2×C22⋊C411yescharacteristic
63C22×C23C2×SD1611yescharacteristic
64C22×C23C2×Q1611yescharacteristic
65C4×C23—21no—
66C4×C23—21no—
67C4×C23—21no—
68C4×C23—21no—
69C4×C23#10312yes—
70C4×C23#10312yes—
71Dic23—42no—
72Dic23—42no—
73Dic23—82no—
74#533—231no—
75#431D2311yescharacteristic
76#382—231no—
77#328—234no—
78C2×C23—21no—
79C2×C23—21no—
80C2×C23#41011yescharacteristic
81C2×C23C2×#10311yescharacteristic
82C2×C23#42111yescharacteristic
83C4⋊Q8—231no—
84C4⋊Q8—231no—
85#125—461no—
86C22⋊Q8—232no—
87C22⋊Q8—461no—
88C4×Q8—232no—
89C4×Q8—461no—
90#117—461no—
91C2×C4⋊C4—461no—
92C2×C42C2×D2311yescharacteristic
93C4⋊C8—21no—
94C22⋊C8C2×D2312yes—
95C4×C8—21no—
96#95—232no—
97#95—461no—
98C23#151811yescharacteristic, complemented, Sylow
99C2×Q8—232no—
100C2×Q8—461no—
101C22×C4—462no—
102C22×C4D9211yescharacteristic
103C22×C4D9211yescharacteristic
104C22×C4C22×D2311yescharacteristic
105C2×C8—22no—
106C4⋊C4—232no—
107C4⋊C4—461no—
108C4⋊C4—461no—
109C4⋊C4—462no—
110C4⋊C4—461no—
111C4⋊C4—462no—
112C4⋊C4—922no—
113C22⋊C4—462no—
114C42—462no—
115C42C4×D2311yescharacteristic
116C42C4×D2311yescharacteristic
117C42C22⋊D2311yescharacteristic
118C42C22⋊D2311yescharacteristic
119C23C2×D9211yescharacteristic
120Q8—922no—
121Q8—922no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—462no—
125C2×C4—462no—
126C2×C4—922no—
127C2×C4—922no—
128C2×C4—922no—
129C2×C4#6726312yes—
130C2×C4Dic9212yes—
131C2×C4(C2×D23)⋊C411yescharacteristic
132C2×C4(C2×D23)⋊C411yescharacteristic
133C2×C4(C2×D23)⋊C411yescharacteristic
134C2×C4(C2×D23)⋊C411yescharacteristic
135C2×C4C2×C4×D2311yescharacteristic
136C2×C4C2×C22⋊D2311yescharacteristic
137C8—42no—
138C22—21no—
139C22—21no—
140C22C2×#6726311yescharacteristic
141C22C2×Dic9211yescharacteristic
142C22C2×(C2×D23)⋊C411yescharacteristic
143C4—21no—
144C4—21no—
145C4—21no—
146C4—21no—
147C4—922no—
148C4—922no—
149C4—1842no—
150C4#1062499812yes—
151C4#1062499812yes—
152C2—21no—
153C2—21no—
154C2#1309239011yescharacteristic
155C2C2×#1062499811yescharacteristic
156C2#1309243311yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#431C2
socleC22×C23C2×C22⋊C4
prime radicalC23×C23C2×D4
cosocleC22×C4×C23C23
hypercenter#431D23
hypocenterC23#1518
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
11. #10625040C4semidirect
12. #10625040C4semidirect
14. C4×Dic46C4semidirect
98. C23#1518semidirect

Maximal subgroups

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

subgroupindex
#130929742
#130922832
#130921552
C23×#4312
#151823