Finite Group Databasebeta

← #15683716

Subgroups — #15683716

Order 2944.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#13092972C211yesmaximal, characteristic, complemented
2#13092965C211yesmaximal, characteristic
3#13092770C214yesmaximal, complemented
4#13092769C211yesmaximal, characteristic, complemented
5#13092768C211yesmaximal, characteristic, complemented
6#13092763C211yesmaximal, characteristic, complemented
7#13092410C214yesmaximal, complemented
8C4×C8×D23C211yesmaximal, characteristic, complemented
9C23×#486C211yesmaximal, characteristic, complemented
10C2×#67290C2212yes—
11C23×C4⋊Q8C2211yescharacteristic
12C23×#127C2211yescharacteristic
13#10625117—21no—
14Q8×Dic23—21no—
15#10625109—21no—
16#10625109—21no—
17#10625107C2212yes—
18D4×Dic23—21no—
19D4×Dic23—21no—
20C2×C8×D23C2212yes—
21#10625068—21no—
22#10625063C2212yes—
23#10625061C2212yes—
24#10625058—21no—
25C42×D23C2211yescharacteristic
26#10625040C2211yescharacteristic
27#10625040C2211yescharacteristic
28C23×#102C2214yes—
29C4×C8×C23C2211yescharacteristic
30#10625014C2214yes—
31#10624998C2214yes—
32C8×Dic23C2212yes—
33#10624992C2214yes—
34C4×C23⋊C8C2211yescharacteristic
35C2×Q8×C23—21no—
36C2×D4×C23—21no—
37C2×D4×C23—21no—
38C2×D4×C23C2312yes—
39C2×C22⋊D23—22no—
40C22×Dic23—22no—
41#67290—28no—
42C2×C4×D23D411yescharacteristic
43C2×C4×D23D411yescharacteristic
44C2×C4×D23C2311yescharacteristic
45C2×Dic46—21no—
46C2×Dic46C2312yes—
47C2×C8×C23C2312yes—
48C4⋊C4×C23—21no—
49C4⋊C4×C23C2312yes—
50C42×C23C2311yescharacteristic
51C22⋊Dic23—22no—
52C22⋊Dic23—22no—
53(C2×D23)⋊C4—22no—
54C4⋊Dic23—21no—
55C4⋊Dic23—21no—
56C4⋊Dic23—21no—
57C4⋊Dic23—22no—
58C4⋊Dic23C2312yes—
59Dic23⋊C4—22no—
60C4×Dic23—22no—
61C4×Dic23D411yescharacteristic
62C4×Dic23D411yescharacteristic
63C4×Dic23C2311yescharacteristic
64C2×C23⋊C8C2312yes—
65C8×D23—24no—
66C23×C23—22no—
67C22×D23C2×D411yescharacteristic
68Q8×C23—42no—
69D4×C23—24no—
70D4×C23—42no—
71D4×C23—42no—
72C2×C4×C23—22no—
73C2×C4×C23C2×D411yescharacteristic
74C2×C4×C23C2×D411yescharacteristic
75C2×C4×C23C2411yescharacteristic
76C22⋊D23—44no—
77C2×Dic23—22no—
78C2×Dic23—22no—
79C2×Dic23—44no—
80C2×Dic23C2×D411yescharacteristic
81C2×Dic23C2×D411yescharacteristic
82C2×Dic23C2×D411yescharacteristic
83C4×D23—22no—
84C4×D23—22no—
85C4×D23#4114yes—
86Dic46—24no—
87Dic46—42no—
88C8×C23—22no—
89C23⋊C8—22no—
90#3131—231nomaximal, Sylow
91C22×C23—42no—
92C22×C23—42no—
93C22×C23—42no—
94C22×C23C22×D411yescharacteristic
95C2×D23—21no—
96C2×D23—21no—
97C2×D23#12412yes—
98C4×C23—42no—
99C4×C23#13512yes—
100C4×C23#13512yes—
101C4×C23C2×#4112yes—
102Dic23—21no—
103Dic23—21no—
104Dic23—42no—
105Dic23—42no—
106Dic23#12412yes—
107#533—231no—
108#532—231no—
109#488—234no—
110#487—231no—
111#487—231no—
112#486—231no—
113#486D2311yescharacteristic, complemented
114#416—234no—
115C2×C4×C8—231no—
116C2×C23—82no—
117C2×C23C2×#12411yescharacteristic
118C2×C23C2×#13511yescharacteristic
119C2×C23C2×#13511yescharacteristic
120D23—22no—
121C2×#41—232no—
122C22×C8—232no—
123C4⋊Q8—231no—
124C4⋊Q8—231no—
125C4⋊Q8C2×D2311yescharacteristic
126#127C2×D2311yescharacteristic
127#125—232no—
128#124—232no—
129C22⋊Q8—461no—
130C22⋊Q8—461no—
131#121—461no—
132#121—461no—
133C4×Q8—461no—
134C4×Q8—461no—
135C4×D4—461no—
136C4×D4—461no—
137#117—232no—
138C2×C42—231no—
139#103—234no—
140#103—234no—
141#102—234no—
142#102C2×D2314yes—
143C4×C8—232no—
144C4×C8—231no—
145C4×C8C2×D2311yescharacteristic
146C23#313111yescharacteristic, complemented, Sylow
147#41—468no—
148C2×Q8—21no—
149C2×Q8—232no—
150C2×Q8—461no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4—462no—
154C2×D4C22×D2312yes—
155C22×C4—231no—
156C22×C4—231no—
157C22×C4—231no—
158C22×C4—462no—
159C2×C8—232no—
160C2×C8—464no—
161C2×C8C22×D2312yes—
162C4⋊C4—21no—
163C4⋊C4—232no—
164C4⋊C4—462no—
165C4⋊C4—462no—
166C4⋊C4—461no—
167C4⋊C4—461no—
168C4⋊C4—461no—
169C4⋊C4C22×D2312yes—
170C22⋊C4—462no—
171C22⋊C4—462no—
172C22⋊C4—462no—
173C42—231no—
174C42—231no—
175C42—231no—
176C42—462no—
177C42C22×D2311yescharacteristic
178C23—22no—
179C23—231no—
180Q8—42no—
181Q8—464no—
182Q8—922no—
183D4—24no—
184D4—42no—
185D4—42no—
186D4—924no—
187C2×C4—22no—
188C2×C4—231no—
189C2×C4—234no—
190C2×C4—231no—
191C2×C4—231no—
192C2×C4—462no—
193C2×C4—462no—
194C2×C4—462no—
195C2×C4—462no—
196C2×C4—924no—
197C2×C4D4×D2311yescharacteristic
198C2×C4D4×D2311yescharacteristic
199C2×C4C23×D2311yescharacteristic
200C8—22no—
201C8—462no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—232no—
206C22—461no—
207C22—461no—
208C22C2×D4×D2311yescharacteristic
209C4—42no—
210C4—232no—
211C4—461no—
212C4—461no—
213C4—922no—
214C4—922no—
215C4#1062508312yes—
216C4#1062508712yes—
217C4#41×D2312yes—
218C2—82no—
219C2—462no—
220C2#124×D2311yescharacteristic
221C2C2×#1062508311yescharacteristic
222C2C2×#1062508711yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#486C2
socleC22×C23C22×D4
prime radical#13092965C2
hypercenter#486D23
hypocenterC23#3131
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #13092972C2semidirect
3. #13092770C2semidirect
4. #13092769C2semidirect
5. #13092768C2semidirect
6. #13092763C2semidirect
7. #13092410C2semidirect
8. C4×C8×D23C2semidirect
9. C23×#486C2semidirect
113. #486D23semidirect
146. C23#3131semidirect

Maximal subgroups

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

subgroupindex
#130929722
#130929652
#130927702
#130927692
#130927682
#130927632
#130924102
C4×C8×D232
C23×#4862
#313123