Finite Group Databasebeta

← #15683341

Subgroups — #15683341

Order 2944.

410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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×#10625097C211yesmaximal, characteristic
2#13092755C214yesmaximal, complemented
3#13092750C212yesmaximal, complemented
4#13092745C212yesmaximal, complemented
5#13092457C212yesmaximal, complemented
6#13092426C212yesmaximal, complemented
7#13092381C211yesmaximal, characteristic
8C2×C23×C22⋊Q8C211yesmaximal, characteristic
9C22×Q8×C23C2211yescharacteristic
10C23×C4×C23C2211yescharacteristic
11C23×C22⋊Q8—21no—
12C23×C22⋊Q8—21no—
13C23×C22⋊Q8C2212yes—
14C23×C22⋊Q8C2212yes—
15C2×C4⋊C4×C23—21no—
16C2×C4⋊C4×C23C2211yescharacteristic
17C2×C22⋊C4×C23—21no—
18C2×C22⋊Dic23—21no—
19#10625097—21no—
20#10625097—21no—
21#10625097C2212yes—
22#10625097C2212yes—
23C2×C4⋊Dic23C2211yescharacteristic
24C2×C4⋊Dic23C2211yescharacteristic
25C2×C4×Dic23—21no—
26C2×#67267C2212yes—
27#10625017C2214yescomplemented
28#10625017C2214yescomplemented
29C22⋊(C23⋊C8)C2212yes—
30C22⋊(C23⋊C8)C2212yes—
31#10624990C2214yescomplemented
32#10624989C2214yescomplemented
33C24×C23D411yescharacteristic
34C2×Q8×C23—21no—
35C2×Q8×C23—24no—
36C2×Q8×C23C2312yes—
37C22×C4×C23—24no—
38C22×C4×C23—21no—
39C22×C4×C23—21no—
40C22×C4×C23D411yescharacteristic
41C22×C4×C23D411yescharacteristic
42C22×C4×C23D411yescharacteristic
43C22×C4×C23C2311yescharacteristic
44C22×C4×C23C2311yescharacteristic
45C22×C4×C23C2311yescharacteristic
46C22×Dic23—21no—
47C22×Dic23—21no—
48C4⋊C4×C23—22no—
49C4⋊C4×C23—22no—
50C4⋊C4×C23—21no—
51C4⋊C4×C23C2312yes—
52C22⋊C4×C23—22no—
53C22⋊C4×C23—22no—
54C22⋊Dic23—22no—
55C22⋊Dic23—22no—
56C4⋊Dic23—21no—
57C4⋊Dic23—21no—
58C4⋊Dic23C2312yes—
59C4⋊Dic23C2312yes—
60C4×Dic23—22no—
61C4×Dic23—22no—
62#67267—24no—
63C2×C23⋊C8C2314yes—
64C23×C23—22no—
65C23×C23—22no—
66C23×C23—41no—
67C23×C23C2×D411yescharacteristic
68C23×C23C2×D411yescharacteristic
69C23×C23C2×D411yescharacteristic
70Q8×C23—24no—
71Q8×C23—42no—
72C2×C4×C23—22no—
73C2×C4×C23—22no—
74C2×C4×C23—22no—
75C2×C4×C23—22no—
76C2×C4×C23—22no—
77C2×C4×C23—22no—
78C2×C4×C23—22no—
79C2×C4×C23—42no—
80C2×C4×C23—42no—
81C2×C4×C23C2×D411yescharacteristic
82C2×C4×C23C2×D411yescharacteristic
83C2×C4×C23C2×D411yescharacteristic
84C2×C4×C23#4114yes—
85C2×C4×C23C2411yescharacteristic
86C2×Dic23—22no—
87C2×Dic23—22no—
88C2×Dic23—42no—
89C2×Dic23—42no—
90C23⋊C8—24no—
91#3095—231nomaximal, Sylow
92C22×C23—21no—
93C22×C23—21no—
94C22×C23—21no—
95C22×C23—21no—
96C22×C23—21no—
97C22×C23—21no—
98C22×C23—21no—
99C22×C23—44no—
100C22×C23#12312yes—
101C22×C23#13712yes—
102C22×C23C22×D411yescharacteristic
103C4×C23—21no—
104C4×C23—21no—
105C4×C23—42no—
106C4×C23—42no—
107C4×C23#12312yes—
108C4×C23C2×#4112yes—
109Dic23—42no—
110Dic23—42no—
111C2×C22⋊Q8D2311yescharacteristic
112C2×#117—231no—
113#485—234no—
114#484—232no—
115#483—232no—
116#428—232no—
117#419—232no—
118#407—231no—
119C2×C23—22no—
120C2×C23—22no—
121C2×C23—41no—
122C2×C23C2×#12311yescharacteristic
123C2×C23C2×#13711yescharacteristic
124C2×C23#57511yescharacteristic
125C22×Q8C2×D2311yescharacteristic
126C23×C4C2×D2311yescharacteristic
127C2×M16—232no—
128C22⋊Q8—21no—
129C22⋊Q8—21no—
130C22⋊Q8C2×D2312yes—
131C22⋊Q8C2×D2312yes—
132#117—232no—
133#117—232no—
134#117—461no—
135#117—461no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—231no—
138C2×C4⋊C4—231no—
139C2×C4⋊C4C2×D2311yescharacteristic
140C2×C22⋊C4—21no—
141C2×C22⋊C4—461no—
142C2×C42—461no—
143#107—234no—
144#106—234no—
145#103—234no—
146#103—234no—
147C22⋊C8—232no—
148C22⋊C8—232no—
149C23#309511yescharacteristic, complemented, Sylow
150C24C22⋊D2311yescharacteristic
151C2×Q8—21no—
152C2×Q8—24no—
153C2×Q8C22×D2312yes—
154C22×C4—24no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—461no—
158C22×C4—461no—
159C22×C4C22⋊D2311yescharacteristic
160C22×C4C22⋊D2311yescharacteristic
161C22×C4C22⋊D2311yescharacteristic
162C22×C4C22×D2311yescharacteristic
163C22×C4C22×D2311yescharacteristic
164C22×C4C22×D2311yescharacteristic
165M16—464no—
166C2×C8—234no—
167C4⋊C4—22no—
168C4⋊C4—22no—
169C4⋊C4—21no—
170C4⋊C4—232no—
171C4⋊C4—232no—
172C4⋊C4—461no—
173C4⋊C4—461no—
174C4⋊C4C22×D2312yes—
175C22⋊C4—22no—
176C22⋊C4—22no—
177C22⋊C4—462no—
178C22⋊C4—462no—
179C42—462no—
180C42—462no—
181C23—22no—
182C23—22no—
183C23—41no—
184C23C2×C22⋊D2311yescharacteristic
185C23C2×C22⋊D2311yescharacteristic
186C23C2×C22⋊D2311yescharacteristic
187Q8—24no—
188Q8—42no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—462no—
199C2×C4—462no—
200C2×C4—922no—
201C2×C4—922no—
202C2×C4#6729014yes—
203C2×C4C2×C22⋊D2311yescharacteristic
204C2×C4C2×C22⋊D2311yescharacteristic
205C2×C4C2×C22⋊D2311yescharacteristic
206C2×C4C23×D2311yescharacteristic
207C8—464no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—44no—
216C22#1062510612yes—
217C22#1062511312yes—
218C22C22×C22⋊D2311yescharacteristic
219C4—21no—
220C4—21no—
221C4—42no—
222C4—42no—
223C4—922no—
224C4—922no—
225C4#1062510612yes—
226C4C2×#6729012yes—
227C2—22no—
228C2—22no—
229C2—41no—
230C2C2×#1062510611yescharacteristic
231C2C2×#1062511311yescharacteristic
232C2#1309321511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×C22⋊Q8C2
socleC22×C23C22×D4
prime radicalC24×C23D4
hypercenterC2×C22⋊Q8D23
hypocenterC23#3095
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13092755C2semidirect
3. #13092750C2semidirect
4. #13092745C2semidirect
5. #13092457C2semidirect
6. #13092426C2semidirect
27. #10625017C22semidirect
28. #10625017C22semidirect
31. #10624990C22semidirect
32. #10624989C22semidirect
149. C23#3095semidirect

Maximal subgroups

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

subgroupindex
C2×#106250972
#130927552
#130927502
#130927452
#130924572
#130924262
#130923812
C2×C23×C22⋊Q82
#309523