Finite Group Databasebeta

← #15683955

Subgroups — #15683955

Order 2944.

412 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 129 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#13092813C211yesmaximal, characteristic, complemented
4#13092789C211yesmaximal, characteristic, complemented
5#13092768C211yesmaximal, characteristic, complemented
6#13092645C214yesmaximal, complemented
7#13092508C214yesmaximal, complemented
8C4×C8×D23C211yesmaximal, characteristic, complemented
9C23×#486C211yesmaximal, characteristic, complemented
10C2×#67290—21no—
11C23×C4⋊Q8C2211yescharacteristic
12C23×#127C2211yescharacteristic
13#10625117—21no—
14Q8×Dic23—21no—
15#10625109—21no—
16#10625109C2212yes—
17#10625107—21no—
18D4×Dic23—21no—
19D4×Dic23C2212yes—
20C2×#67273C2214yes—
21C2×C8×D23C2212yes—
22#10625068C2212yes—
23#10625063—21no—
24#10625061—21no—
25#10625058C2212yes—
26C42×D23C2211yescharacteristic
27#10625040C2211yescharacteristic
28#10625040C2211yescharacteristic
29C23×#102C2214yes—
30C4×C8×C23C2211yescharacteristic
31#10624998C2214yes—
32C8×Dic23C2212yes—
33#10624990C2214yes—
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—44no—
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#67273—28no—
54(C2×D23)⋊C4—22no—
55C4⋊Dic23—21no—
56C4⋊Dic23—21no—
57C4⋊Dic23—21no—
58C4⋊Dic23—22no—
59C4⋊Dic23C2312yes—
60Dic23⋊C4—22no—
61C4×Dic23—22no—
62C4×Dic23D411yescharacteristic
63C4×Dic23D411yescharacteristic
64C4×Dic23C2311yescharacteristic
65C2×C23⋊C8C2312yes—
66C8×D23—24no—
67C23×C23—22no—
68C22×D23C2×D411yescharacteristic
69Q8×C23—42no—
70D4×C23—24no—
71D4×C23—42no—
72D4×C23—42no—
73C2×C4×C23—22no—
74C2×C4×C23C2×D411yescharacteristic
75C2×C4×C23C2×D411yescharacteristic
76C2×C4×C23C2411yescharacteristic
77C22⋊D23—44no—
78C2×Dic23—22no—
79C2×Dic23—22no—
80C2×Dic23—44no—
81C2×Dic23C2×D411yescharacteristic
82C2×Dic23C2×D411yescharacteristic
83C2×Dic23C2×D411yescharacteristic
84C4×D23—22no—
85C4×D23—22no—
86C4×D23SD1614yescomplemented
87Dic46—24no—
88Dic46—42no—
89C8×C23—22no—
90C23⋊C8#4114yescomplemented
91#3167—231nomaximal, Sylow
92C22×C23—42no—
93C22×C23—42no—
94C22×C23—42no—
95C22×C23C22×D411yescharacteristic
96C2×D23—21no—
97C2×D23—21no—
98C2×D23C2×SD1612yes—
99C4×C23—42no—
100C4×C23C2×SD1612yes—
101C4×C23#13512yes—
102C4×C23C2×#4112yes—
103Dic23—21no—
104Dic23—21no—
105Dic23—42no—
106Dic23—42no—
107Dic23C2×SD1612yes—
108#533—231no—
109#532—231no—
110#498—231no—
111#492—231no—
112#487—231no—
113#486D2311yescharacteristic, complemented
114#465—234no—
115C4×SD16—234no—
116C2×C4×C8—231no—
117C2×C23—82no—
118C2×C23#53211yescharacteristic
119C2×C23C22×SD1611yescharacteristic
120C2×C23C2×#13511yescharacteristic
121D23—22no—
122C2×#41—461no—
123C2×SD16—234no—
124C22×C8—232no—
125C4⋊Q8—231no—
126C4⋊Q8—231no—
127C4⋊Q8C2×D2311yescharacteristic
128#127C2×D2311yescharacteristic
129#125—461no—
130#124—461no—
131C22⋊Q8—232no—
132C22⋊Q8—461no—
133#121—232no—
134#121—461no—
135C4×Q8—232no—
136C4×Q8—461no—
137C4×D4—232no—
138C4×D4—461no—
139#117—461no—
140C2×C42—231no—
141#106—234no—
142#103—234no—
143#102C2×D2314yes—
144C4×C8—232no—
145C4×C8—231no—
146C4×C8C2×D2311yescharacteristic
147C23#316711yescharacteristic, complemented, Sylow
148#41—924no—
149C2×Q8—21no—
150C2×Q8—232no—
151C2×Q8—461no—
152C2×D4—21no—
153C2×D4—21no—
154C2×D4—462no—
155C2×D4C22×D2312yes—
156C22×C4—231no—
157C22×C4—231no—
158C22×C4—231no—
159C22×C4—462no—
160SD16—468no—
161C2×C8—232no—
162C2×C8—464no—
163C2×C8C22×D2312yes—
164C4⋊C4—21no—
165C4⋊C4—232no—
166C4⋊C4—462no—
167C4⋊C4—462no—
168C4⋊C4—461no—
169C4⋊C4—461no—
170C4⋊C4—461no—
171C4⋊C4C22×D2312yes—
172C22⋊C4—462no—
173C22⋊C4—462no—
174C22⋊C4—462no—
175C42—231no—
176C42—231no—
177C42—231no—
178C42—462no—
179C42C22×D2311yescharacteristic
180C23—22no—
181C23—231no—
182Q8—42no—
183Q8—464no—
184Q8—922no—
185D4—24no—
186D4—42no—
187D4—42no—
188D4—924no—
189C2×C4—22no—
190C2×C4—231no—
191C2×C4—234no—
192C2×C4—231no—
193C2×C4—231no—
194C2×C4—462no—
195C2×C4—462no—
196C2×C4—462no—
197C2×C4—462no—
198C2×C4—924no—
199C2×C4D4×D2311yescharacteristic
200C2×C4D4×D2311yescharacteristic
201C2×C4C23×D2311yescharacteristic
202C8—22no—
203C8—234no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—232no—
208C22—461no—
209C22—461no—
210C22C2×D4×D2311yescharacteristic
211C4—42no—
212C4—232no—
213C4—461no—
214C4—461no—
215C4—922no—
216C4—922no—
217C4#1062508312yes—
218C4SD16×D2312yes—
219C4#41×D2312yes—
220C2—82no—
221C2—462no—
222C2#1309296611yescharacteristic
223C2C2×SD16×D2311yescharacteristic
224C2C2×#1062508311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#486C2
socleC22×C23C22×D4
prime radical#13092965C2
hypercenter#486D23
hypocenterC23#3167
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. #13092813C2semidirect
4. #13092789C2semidirect
5. #13092768C2semidirect
6. #13092645C2semidirect
7. #13092508C2semidirect
8. C4×C8×D23C2semidirect
9. C23×#486C2semidirect
86. C4×D23SD16semidirect
90. C23⋊C8#41semidirect
113. #486D23semidirect
147. C23#3167semidirect

Maximal subgroups

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

subgroupindex
#130929722
#130929652
#130928132
#130927892
#130927682
#130926452
#130925082
C4×C8×D232
C23×#4862
#316723