Finite Group Databasebeta

← #15682666

Subgroups — #15682666

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×#10625155C211yesmaximal, characteristic, complemented
2C2×#10625079C211yesmaximal, characteristic, complemented
3C22×#67272C211yesmaximal, characteristic, complemented
4#13092986C211yesmaximal, characteristic, complemented
5#13092563C214yesmaximal, complemented
6#13092552C214yesmaximal, complemented
7#13092411C211yesmaximal, characteristic, complemented
8#13092385C211yesmaximal, characteristic, complemented
9C23×#418C211yesmaximal, characteristic, complemented
10C22×D4×C23C2211yescharacteristic
11C22×C22⋊D23—22no—
12#10625155—24no—
13#10625155—24no—
14C2×#67290—21no—
15C2×#67290C2212yescomplemented
16C2×D4×D23—21no—
17C2×D4×D23C2212yescomplemented
18C2×#67288C2211yescharacteristic
19C2×#67288C2211yescharacteristic
20C22×D92C2211yescharacteristic, complemented
21C2×M16×C23C2211yescharacteristic, complemented
22C23×#117C2211yescharacteristic, complemented
23C2×#67272—24no—
24C2×#67272C2214yescomplemented
25C22×C23⋊C8C2211yescharacteristic, complemented
26#10625079—24no—
27C2×D184C2212yescomplemented
28C2×#67263C2212yescomplemented
29#10625066C2214yescomplemented
30#10625053—22no—
31#10625046—21no—
32#10625045—21no—
33C23×#102C2214yescomplemented
34(C2×D23)⋊C8C2214yescomplemented
35#10624992C2212yescomplemented
36#10624991C2212yescomplemented
37C24×C23—21no—
38C23×D23—22no—
39C23×D23—21no—
40C2×D4×C23—21no—
41C2×D4×C23—22no—
42C2×D4×C23D414yescomplemented
43C2×D4×C23C2312yes—
44C22×C4×C23C2311yescharacteristic
45C2×C22⋊D23—216no—
46C2×C22⋊D23—21no—
47C2×C22⋊D23—22no—
48C2×C22⋊D23—22no—
49C2×C22⋊D23D412yes—
50C22×Dic23—22no—
51#67290—28no—
52#67290—24no—
53#67290—24no—
54D4×D23—28no—
55D4×D23—24no—
56D4×D23—24no—
57#67288—22no—
58#67288—22no—
59#67288—22no—
60#67288D414yescomplemented
61C2×D92—22no—
62C2×D92—22no—
63C2×D92—21no—
64C2×D92—24no—
65C2×D92D411yescharacteristic
66C2×D92C2312yes—
67C2×D92C2311yescharacteristic
68C2×C4×D23—21no—
69C2×C4×D23C2312yes—
70C2×Dic46D411yescharacteristic
71C2×Dic46C2311yescharacteristic
72M16×C23—22no—
73C2×C8×C23C2312yes—
74C4⋊C4×C23C2312yes—
75C22⋊C4×C23—21no—
76C42×C23—21no—
77#67272—28no—
78(C2×D23)⋊C4—24no—
79C2×C23⋊C8—22no—
80C2×C23⋊C8C2312yes—
81D184—24no—
82#67263—24no—
83C23×C23—22no—
84C23×C23—24no—
85C23×C23—82no—
86C23×C23C2×D411yescharacteristic
87C22×D23—21no—
88C22×D23—28no—
89C22×D23—22no—
90C22×D23—42no—
91C22×D23—84no—
92C22×D23—82no—
93C22×D23C2×D412yes—
94D4×C23—24no—
95D4×C23—22no—
96D4×C23C2×D414yes—
97C2×C4×C23—22no—
98C2×C4×C23C2×D412yes—
99C2×C4×C23C2×D411yescharacteristic
100C2×C4×C23C2×D412yes—
101C2×C4×C23C2411yescharacteristic
102C22⋊D23—28no—
103C22⋊D23—28no—
104C22⋊D23—24no—
105C22⋊D23—24no—
106C2×Dic23—28no—
107C2×Dic23—21no—
108C2×Dic23C2×D412yes—
109D92—22no—
110D92—21no—
111D92—22no—
112D92—22no—
113D92—42no—
114D92—84no—
115D92C2×D412yes—
116C4×D23—24no—
117C4×D23—22no—
118C4×D23—22no—
119Dic46—22no—
120Dic46—21no—
121Dic46C2×D412yes—
122C8×C23—22no—
123C23⋊C8—22no—
124#3008—231nomaximal, Sylow
125C22×C23—22no—
126C22×C23—24no—
127C22×C23—44no—
128C22×C23—84no—
129C22×C23#12012yes—
130C22×C23C22×D411yescharacteristic
131C2×D23—22no—
132C2×D23—22no—
133C2×D23—24no—
134C2×D23—42no—
135C2×D23—42no—
136C2×D23—44no—
137C2×D23—88no—
138C2×D23—84no—
139C4×C23—42no—
140C4×C23#12012yes—
141C4×C23C22×D411yescharacteristic
142C4×C23C22×D411yescharacteristic
143Dic23—22no—
144Dic23—22no—
145C2×H(5,𝔽2)—231no—
146C2×AGL(1,ℤ/8)—231no—
147C22×D8—231no—
148#535—231no—
149#449—234no—
150#447—234no—
151#418D2311yescharacteristic, complemented
152#416—231no—
153#408—231no—
154C2×C23—22no—
155C2×C23—44no—
156C2×C23C2×#12011yescharacteristic
157C2×C23#57612yes—
158D23—42no—
159D23—42no—
160D23—82no—
161H(5,𝔽2)—464no—
162H(5,𝔽2)—464no—
163C2×#41—231no—
164C2×#41—232no—
165C2×#41—231no—
166C2×#41—461no—
167C22×D4—232no—
168C22×D4—231no—
169C22×D4—461no—
170C22×D4—462no—
171C22×D4C2×D2311yescharacteristic
172AGL(1,ℤ/8)—464no—
173C2×SD16—232no—
174C2×D8—234no—
175C2×D8—232no—
176C2×D8—464no—
177C2×M16C2×D2311yescharacteristic, complemented
178C22×C8—231no—
179#127—461no—
180#124—461no—
181#121—234no—
182#120—462no—
183#117C2×D2311yescharacteristic, complemented
184#103—232no—
185#102—232no—
186#102C2×D2314yescomplemented
187C22⋊C8—234no—
188C23#300811yescharacteristic, complemented, Sylow
189C24—21no—
190C24—462no—
191C24—461no—
192#41—234no—
193#41—464no—
194#41—468no—
195#41—464no—
196#41—462no—
197#41—462no—
198#41—462no—
199C2×Q8—231no—
200C2×Q8—231no—
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—232no—
204C2×D4—231no—
205C2×D4—231no—
206C2×D4—232no—
207C2×D4—464no—
208C2×D4—462no—
209C2×D4—464no—
210C2×D4—468no—
211C2×D4—462no—
212C2×D4—4616no—
213C2×D4—461no—
214C2×D4—464no—
215C2×D4—462no—
216C2×D4—462no—
217C2×D4—461no—
218C2×D4D9214yescomplemented
219C2×D4C22×D2312yes—
220C22×C4—232no—
221C22×C4—462no—
222C22×C4—461no—
223C22×C4C22×D2311yescharacteristic
224SD16—464no—
225D8—464no—
226D8—468no—
227M16—22no—
228C2×C8—232no—
229C2×C8—462no—
230C2×C8C22×D2312yes—
231C4⋊C4C22×D2312yes—
232C22⋊C4—21no—
233C22⋊C4—464no—
234C42—21no—
235C23—22no—
236C23—24no—
237C23—82no—
238C23—232no—
239C23—468no—
240C23—461no—
241C23—462no—
242C23—922no—
243C23—1842no—
244C23—1844no—
245C23D4×D2311yescharacteristic
246Q8—232no—
247Q8—462no—
248Q8—461no—
249D4—24no—
250D4—22no—
251D4—232no—
252D4—468no—
253D4—468no—
254D4—464no—
255D4—464no—
256D4—462no—
257D4—461no—
258D4—462no—
259D4—462no—
260D4—922no—
261D4—1844no—
262D4C2×D9214yes—
263C2×C4—22no—
264C2×C4—232no—
265C2×C4—468no—
266C2×C4—461no—
267C2×C4—464no—
268C2×C4—462no—
269C2×C4—462no—
270C2×C4C2×D9212yes—
271C2×C4D4×D2311yescharacteristic
272C2×C4D4×D2312yes—
273C2×C4C23×D2311yescharacteristic
274C8—22no—
275C8—462no—
276C22—22no—
277C22—24no—
278C22—44no—
279C22—84no—
280C22—462no—
281C22—462no—
282C22—464no—
283C22—922no—
284C22—922no—
285C22—924no—
286C22—1844no—
287C22—1848no—
288C22#1062505312yes—
289C22C2×D4×D2311yescharacteristic
290C4—42no—
291C4—462no—
292C4—462no—
293C4#1062505312yes—
294C4C22×D9211yescharacteristic
295C4C2×D4×D2311yescharacteristic
296C2—22no—
297C2—44no—
298C2—922no—
299C2—922no—
300C2—1842no—
301C2C2×#1062505311yescharacteristic
302C2#1309322112yes—
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#418C2
socleC22×C23C22×D4
hypercenter#418D23
hypocenterC23#3008
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#10625155C2semidirect
2. C2×#10625079C2semidirect
3. C22×#67272C2semidirect
4. #13092986C2semidirect
5. #13092563C2semidirect
6. #13092552C2semidirect
7. #13092411C2semidirect
8. #13092385C2semidirect
9. C23×#418C2semidirect
15. C2×#67290C22semidirect
17. C2×D4×D23C22semidirect
20. C22×D92C22semidirect
21. C2×M16×C23C22semidirect
22. C23×#117C22semidirect
24. C2×#67272C22semidirect
25. C22×C23⋊C8C22semidirect
27. C2×D184C22semidirect
28. C2×#67263C22semidirect
29. #10625066C22semidirect
33. C23×#102C22semidirect
34. (C2×D23)⋊C8C22semidirect
35. #10624992C22semidirect
36. #10624991C22semidirect
42. C2×D4×C23D4semidirect
60. #67288D4semidirect
151. #418D23semidirect
177. C2×M16C2×D23semidirect
183. #117C2×D23semidirect
186. #102C2×D23semidirect
188. C23#3008semidirect
218. C2×D4D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106251552
C2×#106250792
C22×#672722
#130929862
#130925632
#130925522
#130924112
#130923852
C23×#4182
#300823