Finite Group Databasebeta

← #15683959

Subgroups — #15683959

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#13092968C211yesmaximal, characteristic
3#13092813C211yesmaximal, characteristic, complemented
4#13092791C211yesmaximal, characteristic, complemented
5#13092764C211yesmaximal, characteristic, complemented
6#13092649C214yesmaximal, complemented
7#13092502C214yesmaximal, complemented
8C4×C8×D23C211yesmaximal, characteristic, complemented
9C23×#487C211yesmaximal, characteristic, complemented
10C2×#67292—21no—
11C23×C4⋊Q8C2211yescharacteristic
12C23×C4⋊Q8C2211yescharacteristic
13#10625118—21no—
14#10625117C2212yes—
15Q8×Dic23C2212yes—
16C2×#67274C2214yes—
17C2×C8×D23C2212yes—
18#10625068—21no—
19#10625066—21no—
20#10625066C2212yes—
21#10625064—21no—
22#10625064C2212yes—
23#10625063—21no—
24#10625061—21no—
25#10625058—21no—
26#10625045C2211yescharacteristic
27C42×D23C2211yescharacteristic
28#10625040C2211yescharacteristic
29C23×#103C2214yes—
30C4×C8×C23C2211yescharacteristic
31#10625003C2214yes—
32C8×Dic23C2212yes—
33#10624990C2214yes—
34C4×C23⋊C8C2211yescharacteristic
35C2×Q8×C23—21no—
36C2×Q8×C23C2312yes—
37#67292—44no—
38C2×D92—22no—
39C2×D92—21no—
40C2×D92—21no—
41C2×D92C2312yes—
42C2×C4×D23—22no—
43C2×C4×D23D411yescharacteristic
44C2×C4×D23D411yescharacteristic
45C2×C4×D23C2311yescharacteristic
46C2×Dic46—21no—
47C2×C8×C23C2312yes—
48C4⋊C4×C23—21no—
49C4⋊C4×C23—21no—
50C4⋊C4×C23—21no—
51C4⋊C4×C23C2312yes—
52C42×C23C2311yescharacteristic
53#67274—28no—
54(C2×D23)⋊C4—22no—
55(C2×D23)⋊C4—22no—
56(C2×D23)⋊C4—22no—
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—
67C22×D23—22no—
68C22×D23C2×D411yescharacteristic
69Q8×C23—24no—
70Q8×C23—42no—
71C2×C4×C23—22no—
72C2×C4×C23—22no—
73C2×C4×C23C2×D411yescharacteristic
74C2×C4×C23C2×D411yescharacteristic
75C2×C4×C23C2411yescharacteristic
76C2×Dic23—22no—
77C2×Dic23C2×D411yescharacteristic
78C2×Dic23C2×D411yescharacteristic
79C2×Dic23C2×D411yescharacteristic
80D92—24no—
81D92—44no—
82D92—42no—
83D92—42no—
84C4×D23—22no—
85C4×D23—22no—
86C4×D23—44no—
87C4×D23SD1614yescomplemented
88Dic46—42no—
89C8×C23—22no—
90C23⋊C8#4114yescomplemented
91#3167—231nomaximal, Sylow
92C22×C23C22×D411yescharacteristic
93C2×D23—21no—
94C2×D23—21no—
95C2×D23—42no—
96C2×D23—42no—
97C2×D23—42no—
98C2×D23C2×SD1612yes—
99C4×C23—42no—
100C4×C23—42no—
101C4×C23C2×SD1612yes—
102C4×C23#13512yes—
103C4×C23C2×#4112yes—
104Dic23—21no—
105Dic23—21no—
106Dic23—42no—
107Dic23C2×SD1612yes—
108#533—231no—
109#532—231no—
110#498—231no—
111#492—231no—
112#487D2311yescharacteristic, complemented
113#486—231no—
114#465—234no—
115C4×SD16—234no—
116C2×C4×C8—231no—
117C2×C23#53211yescharacteristic
118C2×C23C22×SD1611yescharacteristic
119C2×C23C2×#13511yescharacteristic
120D23—22no—
121D23—82no—
122C2×#41—461no—
123C2×SD16—234no—
124C22×C8—232no—
125C4⋊Q8—231no—
126C4⋊Q8C2×D2311yescharacteristic
127C4⋊Q8C2×D2311yescharacteristic
128#127—231no—
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#103C2×D2314yes—
143#102—234no—
144C4×C8—232no—
145C4×C8—231no—
146C4×C8C2×D2311yescharacteristic
147C23#316711yescharacteristic, complemented, Sylow
148#41—924no—
149C2×Q8—21no—
150C2×Q8—461no—
151C2×Q8C22×D2312yes—
152C2×D4—232no—
153C2×D4—462no—
154C2×D4—461no—
155C2×D4—461no—
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—21no—
166C4⋊C4—21no—
167C4⋊C4—232no—
168C4⋊C4—462no—
169C4⋊C4—462no—
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—231no—
181C23—462no—
182Q8—24no—
183Q8—42no—
184Q8—922no—
185D4—464no—
186D4—924no—
187D4—922no—
188D4—922no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—231no—
192C2×C4—234no—
193C2×C4—231no—
194C2×C4—231no—
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—232no—
205C22—461no—
206C22—461no—
207C22—922no—
208C22—922no—
209C22—922no—
210C22C2×D4×D2311yescharacteristic
211C4—42no—
212C4—42no—
213C4—232no—
214C4—461no—
215C4—461no—
216C4—922no—
217C4SD16×D2312yes—
218C4#1062509012yes—
219C4#41×D2312yes—
220C2—462no—
221C2—1842no—
222C2#1309296611yescharacteristic
223C2C2×SD16×D2311yescharacteristic
224C2C2×#1062509011yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#487C2
socleC22×C23C22×D4
prime radical#13092968C2
hypercenter#487D23
hypocenterC23#3167
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #13092972C2semidirect
3. #13092813C2semidirect
4. #13092791C2semidirect
5. #13092764C2semidirect
6. #13092649C2semidirect
7. #13092502C2semidirect
8. C4×C8×D23C2semidirect
9. C23×#487C2semidirect
87. C4×D23SD16semidirect
90. C23⋊C8#41semidirect
112. #487D23semidirect
147. C23#3167semidirect

Maximal subgroups

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

subgroupindex
#130929722
#130929682
#130928132
#130927912
#130927642
#130926492
#130925022
C4×C8×D232
C23×#4872
#316723