Finite Group Databasebeta

← #15685193

Subgroups — #15685193

Order 2944.

476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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#13093221C212yesmaximal, complemented
2#13093220C212yesmaximal, complemented
3#13092793C211yesmaximal, characteristic, complemented
4#13092686C212yesmaximal, complemented
5#13092685C212yesmaximal, complemented
6#13092586C212yesmaximal, complemented
7#13092584C211yesmaximal, characteristic, complemented
8#13092531C212yesmaximal, complemented
9C23×#453C211yesmaximal, characteristic, complemented
10C23×H(5,𝔽2)C2211yescharacteristic, complemented
11#10625160C2212yescomplemented
12#10625155C2211yescharacteristic, complemented
13C23×AGL(1,ℤ/8)C2212yescomplemented
14C23×#127C2211yescharacteristic, complemented
15#10625121—22no—
16#10625121C2212yes—
17#10625120—22no—
18#10625120C2212yescomplemented
19#10625119C2212yescomplemented
20#10625103—22no—
21#10625103C2212yescomplemented
22C2×#67272—22no—
23C2×#67272C2212yescomplemented
24C2×#67272C2212yescomplemented
25#10625087—22no—
26#10625085—22no—
27#10625082—22no—
28D8×D23—22no—
29#10625079C2212yescomplemented
30#10625078C2212yescomplemented
31#10625045C2211yescharacteristic, complemented
32C23×#104C2212yescomplemented
33C23×#100C2211yescharacteristic, complemented
34#10625015C2211yescharacteristic, complemented
35#10625005C2212yescomplemented
36#10625004C2212yescomplemented
37#10624987C2212yescomplemented
38C4×C23⋊C8C2211yescharacteristic, complemented
39#41×C23—22no—
40#41×C23C2312yes—
41C2×D4×C23—22no—
42C2×D4×C23—41no—
43C2×D4×C23—41no—
44C2×D4×C23C2311yescharacteristic
45C2×D4×C23C2311yescharacteristic
46C2×C22⋊D23—41no—
47#67292—22no—
48#67290—22no—
49D4×D23—22no—
50D4×D23—22no—
51D4×D23—42no—
52#67288—22no—
53#67288C2312yes—
54C2×D92—22no—
55C2×D92—41no—
56C2×D92C2312yes—
57SD16×C23—22no—
58D8×C23—22no—
59M16×C23C2312yes—
60C42×C23C2311yescharacteristic
61#67275D412yescomplemented
62#67274—22no—
63#67274D412yescomplemented
64#67273—22no—
65#67273D412yescomplemented
66#67272—22no—
67#67272—22no—
68#67272—22no—
69#67272—22no—
70#67272—22no—
71#67272—22no—
72#67272D412yescomplemented
73#67267—22no—
74#67267C2312yes—
75C2×C23⋊C8—22no—
76C2×C23⋊C8C2312yes—
77D184—22no—
78#67263—22no—
79#67262—22no—
80C8×D23—22no—
81C23×C23—21no—
82C23×C23—21no—
83C23×C23—41no—
84C22×D23—22no—
85C22×D23—41no—
86C22×D23—42no—
87Q8×C23C2×D412yes—
88D4×C23—22no—
89D4×C23—22no—
90D4×C23—22no—
91D4×C23—42no—
92D4×C23—82no—
93D4×C23C2×D412yes—
94C2×C4×C23—21no—
95C2×C4×C23—22no—
96C2×C4×C23—41no—
97C2×C4×C23C2411yescharacteristic
98C22⋊D23—22no—
99C22⋊D23—42no—
100C22⋊D23—42no—
101C2×Dic23—41no—
102D92—22no—
103D92—22no—
104D92—42no—
105D92—82no—
106D92C2×D412yes—
107C4×D23—22no—
108C4×D23—42no—
109Dic46C2×D412yes—
110C8×C23—22no—
111C23⋊C8—22no—
112C23⋊C8C2×D412yes—
113C23⋊C8C2×D412yes—
114#3292—231nomaximal, Sylow
115C22×C23—22no—
116C22×C23—41no—
117C22×C23—41no—
118C22×C23—81no—
119C22×C23—81no—
120C22×C23—161no—
121C22×C23H(5,𝔽2)11yescharacteristic
122C2×D23—22no—
123C2×D23—42no—
124C2×D23—82no—
125C2×D23—161no—
126C2×D23—162no—
127C4×C23—22no—
128C4×C23—22no—
129C4×C23C22×D412yes—
130Dic23—22no—
131#576—232no—
132#576—232no—
133#493—231no—
134#472—232no—
135#472—232no—
136#453—231no—
137#453—232no—
138#453D2311yescharacteristic, complemented
139#443—232no—
140C2×C23—21no—
141C2×C23—42no—
142C2×C23—81no—
143C2×C23—81no—
144C2×C23D4211yescharacteristic
145D23—42no—
146D23—82no—
147H(5,𝔽2)—232no—
148H(5,𝔽2)—231no—
149H(5,𝔽2)C2×D2311yescharacteristic, complemented
150AGL(1,ℤ/8)—232no—
151AGL(1,ℤ/8)—232no—
152AGL(1,ℤ/8)—232no—
153AGL(1,ℤ/8)—462no—
154AGL(1,ℤ/8)—462no—
155AGL(1,ℤ/8)—462no—
156AGL(1,ℤ/8)—462no—
157AGL(1,ℤ/8)C2×D2312yescomplemented
158#135—232no—
159#135—462no—
160#135—462no—
161C2×D8—232no—
162C2×D8—232no—
163C2×D8—462no—
164C2×D8—462no—
165#131—232no—
166#131—232no—
167#127—231no—
168#127C2×D2311yescharacteristic, complemented
169#108—232no—
170#104—232no—
171#104C2×D2312yescomplemented
172#100—231no—
173#100—232no—
174#100C2×D2311yescharacteristic, complemented
175C4×C8—231no—
176C23#329211yescharacteristic, complemented, Sylow
177#41—22no—
178#41—232no—
179#41—462no—
180#41—462no—
181#41—462no—
182#41C22×D2312yes—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—232no—
187C2×D4—462no—
188C2×D4—462no—
189C2×D4—462no—
190C2×D4—921no—
191C2×D4—922no—
192C2×D4—921no—
193C2×D4C22×D2311yescharacteristic
194C2×D4C22×D2311yescharacteristic
195Q16—232no—
196SD16—22no—
197SD16—232no—
198SD16—232no—
199SD16—462no—
200SD16—462no—
201SD16—462no—
202D8—22no—
203D8—232no—
204D8—462no—
205D8—462no—
206D8—462no—
207D8—462no—
208D8—462no—
209D8—462no—
210D8—462no—
211M16—232no—
212M16—462no—
213M16—462no—
214M16C22×D2312yes—
215C2×C8—232no—
216C2×C8—462no—
217C2×C8—462no—
218C42C22×D2311yescharacteristic
219C23—21no—
220C23—21no—
221C23—41no—
222C23—462no—
223C23—922no—
224C23—921no—
225Q8—232no—
226Q8D4×D2312yes—
227D4—22no—
228D4—22no—
229D4—22no—
230D4—42no—
231D4—82no—
232D4—232no—
233D4—462no—
234D4—462no—
235D4—462no—
236D4—922no—
237D4—922no—
238D4—922no—
239D4—1842no—
240D4D4×D2312yes—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—462no—
245C2×C4—922no—
246C2×C4—921no—
247C2×C4C23×D2311yescharacteristic
248C8—22no—
249C8—232no—
250C8—232no—
251C8—462no—
252C22—22no—
253C22—41no—
254C22—41no—
255C22—81no—
256C22—81no—
257C22—161no—
258C22—462no—
259C22—922no—
260C22—3682no—
261C22—3681no—
262C22—1842no—
263C22#1062515511yescharacteristic
264C4—22no—
265C4—22no—
266C4—462no—
267C4C2×D4×D2312yes—
268C2—21no—
269C2—42no—
270C2—81no—
271C2—81no—
272C2—922no—
273C2—1842no—
274C2#1309304911yescharacteristic
subgroupG/H
centerC2#13093049
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#453C2
socleC2×C23D42
hypercenter#453D23
hypocenterC23#3292
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #13093221C2semidirect
2. #13093220C2semidirect
3. #13092793C2semidirect
4. #13092686C2semidirect
5. #13092685C2semidirect
6. #13092586C2semidirect
7. #13092584C2semidirect
8. #13092531C2semidirect
9. C23×#453C2semidirect
10. C23×H(5,𝔽2)C22semidirect
11. #10625160C22semidirect
12. #10625155C22semidirect
13. C23×AGL(1,ℤ/8)C22semidirect
14. C23×#127C22semidirect
18. #10625120C22semidirect
19. #10625119C22semidirect
21. #10625103C22semidirect
23. C2×#67272C22semidirect
24. C2×#67272C22semidirect
29. #10625079C22semidirect
30. #10625078C22semidirect
31. #10625045C22semidirect
32. C23×#104C22semidirect
33. C23×#100C22semidirect
34. #10625015C22semidirect
35. #10625005C22semidirect
36. #10625004C22semidirect
37. #10624987C22semidirect
38. C4×C23⋊C8C22semidirect
61. #67275D4semidirect
63. #67274D4semidirect
65. #67273D4semidirect
72. #67272D4semidirect
138. #453D23semidirect
149. H(5,𝔽2)C2×D23semidirect
157. AGL(1,ℤ/8)C2×D23semidirect
168. #127C2×D23semidirect
171. #104C2×D23semidirect
174. #100C2×D23semidirect
176. C23#3292semidirect

Maximal subgroups

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

subgroupindex
#130932212
#130932202
#130927932
#130926862
#130926852
#130925862
#130925842
#130925312
C23×#4532
#329223