Finite Group Databasebeta

← #15683338

Subgroups — #15683338

Order 2944.

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

normal subgroups only

This group has 462 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×#10625101C211yesmaximal, characteristic
2C2×#10625097C211yesmaximal, characteristic, complemented
3#13092742C214yesmaximal, complemented
4#13092736C212yesmaximal, complemented
5#13092731C212yesmaximal, complemented
6#13092459C212yesmaximal, complemented
7#13092423C212yesmaximal, complemented
8C23×#407C211yesmaximal, characteristic, complemented
9C23×C4×C23C2211yescharacteristic
10C22×C22⋊D23—21no—
11C22×D92C2211yescharacteristic
12C2×M16×C23C2212yes—
13C2×C22⋊Dic23—21no—
14#10625101—21no—
15#10625101—21no—
16#10625101C2212yes—
17#10625101C2212yes—
18C2×(C2×D23)⋊C4—21no—
19#10625097—21no—
20#10625097—21no—
21#10625097C2212yes—
22#10625097C2212yescomplemented
23C2×C4⋊Dic23C2211yescharacteristic
24C2×C4⋊Dic23C2211yescharacteristic, complemented
25C2×C4⋊Dic23C2211yescharacteristic, complemented
26C2×C4×Dic23—21no—
27C23×C22⋊C8C2212yescomplemented
28C23×C22⋊C8C2212yescomplemented
29#10625003C2214yescomplemented
30#10625003C2214yescomplemented
31#10625000C2214yescomplemented
32#10624999C2214yescomplemented
33C24×C23D411yescharacteristic
34C23×D23—21no—
35C22×C4×C23—24no—
36C22×C4×C23D411yescharacteristic
37C22×C4×C23D411yescharacteristic
38C22×C4×C23D411yescharacteristic
39C22×C4×C23C2311yescharacteristic
40C22×C4×C23C2311yescharacteristic
41C22×C4×C23C2311yescharacteristic
42C2×C22⋊D23—22no—
43C2×C22⋊D23—22no—
44C2×C22⋊D23—44no—
45C22×Dic23—21no—
46C22×Dic23—21no—
47C22×Dic23—21no—
48C2×D92—24no—
49C2×D92—21no—
50C2×D92C2312yes—
51M16×C23—24no—
52C2×C8×C23C2314yes—
53C22⋊Dic23—22no—
54C22⋊Dic23—22no—
55(C2×D23)⋊C4—22no—
56(C2×D23)⋊C4—22no—
57C4⋊Dic23—21no—
58C4⋊Dic23—21no—
59C4⋊Dic23—21no—
60C4⋊Dic23C2312yes—
61C4⋊Dic23C2312yes—
62C4⋊Dic23C2312yes—
63C4×Dic23—22no—
64C4×Dic23—22no—
65C23×C23—22no—
66C23×C23—22no—
67C23×C23—41no—
68C23×C23C2×D411yescharacteristic
69C23×C23C2×D411yescharacteristic
70C23×C23C2×D411yescharacteristic
71C22×D23—22no—
72C22×D23—42no—
73C22×D23—42no—
74C22×D23—42no—
75C2×C4×C23—22no—
76C2×C4×C23—22no—
77C2×C4×C23—22no—
78C2×C4×C23—22no—
79C2×C4×C23—22no—
80C2×C4×C23C2×D411yescharacteristic
81C2×C4×C23C2×D411yescharacteristic
82C2×C4×C23C2×D411yescharacteristic
83C2×C4×C23#4114yes—
84C2×C4×C23C2411yescharacteristic
85C22⋊D23—44no—
86C22⋊D23—44no—
87C2×Dic23—22no—
88C2×Dic23—22no—
89C2×Dic23—22no—
90C2×Dic23—42no—
91C2×Dic23—42no—
92C2×Dic23—42no—
93D92—24no—
94D92—42no—
95C8×C23—24no—
96#3094—231nomaximal, Sylow
97C22×C23—21no—
98C22×C23—21no—
99C22×C23—21no—
100C22×C23—21no—
101C22×C23—21no—
102C22×C23—21no—
103C22×C23—21no—
104C22×C23—44no—
105C22×C23#12312yes—
106C22×C23AGL(1,ℤ/8)12yes—
107C22×C23C22×D411yescharacteristic
108C2×D23—42no—
109C2×D23—42no—
110C2×D23—42no—
111C2×D23—84no—
112C4×C23—21no—
113C4×C23—21no—
114C4×C23#12312yes—
115C4×C23C2×#4112yes—
116Dic23—42no—
117Dic23—42no—
118Dic23—42no—
119C2×#121—231no—
120C2×#117—231no—
121#482—234no—
122#481—232no—
123#480—232no—
124#428—232no—
125#418—232no—
126#407D2311yescharacteristic, complemented
127C2×C23—22no—
128C2×C23—22no—
129C2×C23—41no—
130C2×C23C2×#12311yescharacteristic
131C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
132C2×C23#57511yescharacteristic
133D23—82no—
134C22×D4—231no—
135C22×D4—461no—
136C23×C4C2×D2311yescharacteristic
137C2×M16C2×D2312yes—
138#121—232no—
139#121—232no—
140#121—461no—
141#121—461no—
142#117—232no—
143#117—232no—
144#117—461no—
145#117—461no—
146C2×C4⋊C4—231no—
147C2×C4⋊C4—231no—
148C2×C4⋊C4—231no—
149C2×C22⋊C4—461no—
150C2×C22⋊C4—461no—
151C2×C42—461no—
152#107—234no—
153#106—234no—
154#102—234no—
155#102—234no—
156C22⋊C8C2×D2312yescomplemented
157C22⋊C8C2×D2312yescomplemented
158C23#309411yescharacteristic, complemented, Sylow
159C24—461no—
160C24D9211yescharacteristic
161C2×D4—232no—
162C2×D4—462no—
163C2×D4—462no—
164C2×D4—461no—
165C2×D4—464no—
166C2×D4—924no—
167C22×C4—24no—
168C22×C4—461no—
169C22×C4—461no—
170C22×C4—461no—
171C22×C4D9211yescharacteristic
172C22×C4D9211yescharacteristic
173C22×C4D9211yescharacteristic
174C22×C4C22×D2311yescharacteristic
175C22×C4C22×D2311yescharacteristic
176C22×C4C22×D2311yescharacteristic
177M16—24no—
178C2×C8C22×D2314yes—
179C4⋊C4—232no—
180C4⋊C4—232no—
181C4⋊C4—232no—
182C4⋊C4—461no—
183C4⋊C4—461no—
184C4⋊C4—461no—
185C22⋊C4—462no—
186C22⋊C4—462no—
187C22⋊C4—462no—
188C22⋊C4—462no—
189C42—462no—
190C42—462no—
191C23—22no—
192C23—22no—
193C23—41no—
194C23—462no—
195C23—922no—
196C23—922no—
197C23—922no—
198C23C2×D9211yescharacteristic
199C23C2×D9211yescharacteristic
200C23C2×D9211yescharacteristic
201D4—464no—
202D4—924no—
203D4—924no—
204D4—922no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—462no—
211C2×C4—462no—
212C2×C4—462no—
213C2×C4—922no—
214C2×C4—922no—
215C2×C4—922no—
216C2×C4C2×D9211yescharacteristic
217C2×C4C2×D9211yescharacteristic
218C2×C4C2×D9211yescharacteristic
219C2×C4#6729014yes—
220C2×C4C23×D2311yescharacteristic
221C8—24no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—44no—
230C22—922no—
231C22—922no—
232C22—922no—
233C22—1844no—
234C22#1062505712yes—
235C22#1062507912yes—
236C22C22×D9211yescharacteristic
237C4—21no—
238C4—21no—
239C4—922no—
240C4—922no—
241C4—922no—
242C4#1062505712yes—
243C4C2×#6729012yes—
244C2—22no—
245C2—22no—
246C2—41no—
247C2—1842no—
248C2C2×#1062505711yescharacteristic
249C2C2×#1062507911yescharacteristic
250C2#1309321711yescharacteristic
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#407C2
socleC22×C23C22×D4
prime radicalC2×#10625101C2
hypercenter#407D23
hypocenterC23#3094
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#10625097C2semidirect
3. #13092742C2semidirect
4. #13092736C2semidirect
5. #13092731C2semidirect
6. #13092459C2semidirect
7. #13092423C2semidirect
8. C23×#407C2semidirect
22. #10625097C22semidirect
24. C2×C4⋊Dic23C22semidirect
25. C2×C4⋊Dic23C22semidirect
27. C23×C22⋊C8C22semidirect
28. C23×C22⋊C8C22semidirect
29. #10625003C22semidirect
30. #10625003C22semidirect
31. #10625000C22semidirect
32. #10624999C22semidirect
126. #407D23semidirect
156. C22⋊C8C2×D23semidirect
157. C22⋊C8C2×D23semidirect
158. C23#3094semidirect

Maximal subgroups

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

subgroupindex
C2×#106251012
C2×#106250972
#130927422
#130927362
#130927312
#130924592
#130924232
C23×#4072
#309423