Finite Group Databasebeta

← #15682667

Subgroups — #15682667

Order 2944.

784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10625160C211yesmaximal, characteristic, complemented
2C2×#10625079C211yesmaximal, characteristic, complemented
3C22×D184C211yesmaximal, characteristic, complemented
4#13092981C211yesmaximal, characteristic, complemented
5#13092564C214yesmaximal, complemented
6#13092553C214yesmaximal, complemented
7#13092423C211yesmaximal, characteristic, complemented
8#13092414C211yesmaximal, characteristic, complemented
9C23×#408C211yesmaximal, characteristic, complemented
10C2×#41×C23C2211yescharacteristic
11#10625160—24no—
12#10625160—24no—
13C2×#67292—21no—
14C2×D4×D23—21no—
15C2×D4×D23—22no—
16C2×#67288C2211yescharacteristic
17C2×#67288C2212yescomplemented
18C22×D92C2211yescharacteristic
19C22×D92C2211yescharacteristic, complemented
20C22×D92C2212yescomplemented
21C2×M16×C23C2211yescharacteristic, complemented
22C22×C8×C23C2211yescharacteristic, complemented
23#10625118—21no—
24#10625111—21no—
25#10625108—22no—
26#10625101C2214yescomplemented
27#10625097C2211yescharacteristic, complemented
28#10625079—24no—
29C2×D184—24no—
30C2×D184C2214yescomplemented
31C2×D184C2212yescomplemented
32C2×#67263C2212yescomplemented
33C23×C22⋊C8C2214yescomplemented
34#10625003C2212yescomplemented
35#10625003C2214yescomplemented
36#10624998C2212yescomplemented
37C23×D23—21no—
38C23×D23—22no—
39C23×D23—21no—
40#41×C23—22no—
41#41×C23—22no—
42C2×Q8×C23D411yescharacteristic
43C2×D4×C23D412yes—
44C2×D4×C23D411yescharacteristic
45C22×C4×C23C2312yes—
46C22×C4×C23C2311yescharacteristic
47C2×C22⋊D23—21no—
48C2×C22⋊D23—22no—
49C2×C22⋊D23—24no—
50#67292—28no—
51D4×D23—216no—
52D4×D23—28no—
53#67288—22no—
54#67288—24no—
55#67288—24no—
56#67288D414yescomplemented
57C2×D92—21no—
58C2×D92—22no—
59C2×D92—22no—
60C2×D92—24no—
61C2×D92—24no—
62C2×D92—22no—
63C2×D92—22no—
64C2×D92—21no—
65C2×D92D414yescomplemented
66C2×D92C2312yes—
67C2×D92C2312yes—
68C2×D92C2311yescharacteristic
69C2×C4×D23—21no—
70C2×C4×D23—22no—
71C2×Dic46C2311yescharacteristic
72M16×C23—22no—
73C2×C8×C23—22no—
74C2×C8×C23C2312yes—
75C2×C8×C23C2312yes—
76C22⋊Dic23—21no—
77(C2×D23)⋊C4—24no—
78C4⋊Dic23C2312yes—
79C4×Dic23—21no—
80D184—28no—
81D184—24no—
82#67263—24no—
83C23×C23C2×D412yes—
84C23×C23C2×D411yescharacteristic
85C22×D23—21no—
86C22×D23—22no—
87C22×D23—28no—
88C22×D23—24no—
89C22×D23—22no—
90C22×D23—42no—
91C22×D23—82no—
92C22×D23—84no—
93C22×D23—82no—
94Q8×C23—22no—
95D4×C23—24no—
96D4×C23—22no—
97C2×C4×C23—22no—
98C2×C4×C23—22no—
99C2×C4×C23C2×D412yes—
100C2×C4×C23C2×D411yescharacteristic
101C2×C4×C23C2×D412yes—
102C2×C4×C23C2×D412yes—
103C2×C4×C23C2411yescharacteristic
104C22⋊D23—28no—
105C22⋊D23—24no—
106C22⋊D23—84no—
107C2×Dic23—21no—
108C2×Dic23—22no—
109D92—28no—
110D92—24no—
111D92—21no—
112D92—22no—
113D92—22no—
114D92—22no—
115D92—42no—
116D92C2×D412yes—
117D92C2×D414yes—
118C4×D23—28no—
119C4×D23—24no—
120Dic46—21no—
121Dic46C2×D412yes—
122C8×C23—22no—
123C8×C23—22no—
124#3008—231nomaximal, Sylow
125C22×C23—22no—
126C22×C23—22no—
127C22×C23—24no—
128C22×C23#12012yes—
129C22×C23C22×D411yescharacteristic
130C2×D23—24no—
131C2×D23—22no—
132C2×D23—44no—
133C2×D23—42no—
134C2×D23—42no—
135C2×D23—44no—
136C2×D23—84no—
137C2×D23—88no—
138C2×D23—84no—
139C4×C23—22no—
140C4×C23#12012yes—
141C4×C23C22×D411yescharacteristic
142C4×C23C22×D411yescharacteristic
143Dic23—22no—
144Dic23—42no—
145C2×H(5,𝔽2)—231no—
146C2×AGL(1,ℤ/8)—231no—
147C22×D8—231no—
148#535—231no—
149#449—234no—
150#447—234no—
151#418—231no—
152#416—231no—
153#408D2311yescharacteristic, complemented
154C2×C23—22no—
155C2×C23—42no—
156C2×C23C2×#12011yescharacteristic
157C2×C23#57612yes—
158D23—44no—
159D23—42no—
160D23—82no—
161H(5,𝔽2)—464no—
162H(5,𝔽2)—464no—
163C2×#41—231no—
164C2×#41—232no—
165C2×#41—461no—
166C2×#41C2×D2311yescharacteristic
167C22×D4—231no—
168C22×D4—231no—
169C22×D4—232no—
170C22×D4—462no—
171C22×D4—461no—
172AGL(1,ℤ/8)—464no—
173C2×SD16—232no—
174C2×D8—234no—
175C2×D8—232no—
176C2×D8—464no—
177C2×M16C2×D2311yescharacteristic, complemented
178C22×C8C2×D2311yescharacteristic, complemented
179#127—461no—
180#124—461no—
181#121—234no—
182#120—462no—
183#117—231no—
184#103—232no—
185#102—232no—
186#102—234no—
187C22⋊C8C2×D2314yescomplemented
188C23#300811yescharacteristic, complemented, Sylow
189C24—462no—
190C24—461no—
191C24—461no—
192#41—22no—
193#41—22no—
194#41—234no—
195#41—464no—
196#41—464no—
197#41—468no—
198#41—462no—
199C2×Q8—231no—
200C2×Q8D9211yescharacteristic
201C2×D4—234no—
202C2×D4—232no—
203C2×D4—231no—
204C2×D4—232no—
205C2×D4—464no—
206C2×D4—464no—
207C2×D4—4616no—
208C2×D4—468no—
209C2×D4—462no—
210C2×D4—461no—
211C2×D4—464no—
212C2×D4—462no—
213C2×D4—461no—
214C2×D4—461no—
215C2×D4—462no—
216C2×D4—462no—
217C2×D4—462no—
218C2×D4D9212yes—
219C2×D4D9211yescharacteristic
220C22×C4—462no—
221C22×C4—461no—
222C22×C4C22×D2312yes—
223C22×C4C22×D2311yescharacteristic
224SD16—464no—
225D8—468no—
226D8—464no—
227M16—22no—
228C2×C8—22no—
229C2×C8C22×D2312yes—
230C2×C8C22×D2312yes—
231C4⋊C4—232no—
232C22⋊C4—461no—
233C22⋊C4—464no—
234C42—461no—
235C23—468no—
236C23—462no—
237C23—461no—
238C23—464no—
239C23—462no—
240C23—922no—
241C23—1842no—
242C23—1842no—
243C23—1844no—
244C23C2×D9212yes—
245C23C2×D9211yescharacteristic
246Q8—22no—
247Q8—232no—
248Q8—461no—
249D4—24no—
250D4—22no—
251D4—234no—
252D4—232no—
253D4—468no—
254D4—468no—
255D4—464no—
256D4—464no—
257D4—461no—
258D4—462no—
259D4—462no—
260D4—462no—
261D4—922no—
262D4—1844no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—468no—
266C2×C4—461no—
267C2×C4—464no—
268C2×C4—462no—
269C2×C4C2×D9212yes—
270C2×C4C2×D9211yescharacteristic
271C2×C4D4×D2312yes—
272C2×C4D4×D2312yes—
273C2×C4C23×D2311yescharacteristic
274C8—22no—
275C8—22no—
276C22—22no—
277C22—22no—
278C22—24no—
279C22—464no—
280C22—462no—
281C22—924no—
282C22—922no—
283C22—922no—
284C22—924no—
285C22—1844no—
286C22—1844no—
287C22—1848no—
288C22#1062505312yes—
289C22C22×D9211yescharacteristic
290C4—22no—
291C4—462no—
292C4—922no—
293C4#1062505312yes—
294C4C2×D4×D2311yescharacteristic
295C4C2×D4×D2311yescharacteristic
296C2—22no—
297C2—42no—
298C2—924no—
299C2—922no—
300C2—1842no—
301C2C2×#1062505311yescharacteristic
302C2#1309322212yes—
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#408C2
socleC22×C23C22×D4
hypercenter#408D23
hypocenterC23#3008
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. C2×#10625160C2semidirect
2. C2×#10625079C2semidirect
3. C22×D184C2semidirect
4. #13092981C2semidirect
5. #13092564C2semidirect
6. #13092553C2semidirect
7. #13092423C2semidirect
8. #13092414C2semidirect
9. C23×#408C2semidirect
17. C2×#67288C22semidirect
19. C22×D92C22semidirect
20. C22×D92C22semidirect
21. C2×M16×C23C22semidirect
22. C22×C8×C23C22semidirect
26. #10625101C22semidirect
27. #10625097C22semidirect
30. C2×D184C22semidirect
31. C2×D184C22semidirect
32. C2×#67263C22semidirect
33. C23×C22⋊C8C22semidirect
34. #10625003C22semidirect
35. #10625003C22semidirect
36. #10624998C22semidirect
56. #67288D4semidirect
65. C2×D92D4semidirect
153. #408D23semidirect
177. C2×M16C2×D23semidirect
178. C22×C8C2×D23semidirect
187. C22⋊C8C2×D23semidirect
188. C23#3008semidirect

Maximal subgroups

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

subgroupindex
C2×#106251602
C2×#106250792
C22×D1842
#130929812
#130925642
#130925532
#130924232
#130924142
C23×#4082
#300823