Finite Group Databasebeta

← #15682676

Subgroups — #15682676

Order 2944.

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

normal subgroups only

This group has 752 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
2C2×#10625080C211yesmaximal, characteristic, complemented
3C22×#67263C211yesmaximal, characteristic, complemented
4#13092988C211yesmaximal, characteristic, complemented
5#13092581C214yesmaximal, complemented
6#13092570C214yesmaximal, 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—22no—
15C2×D4×D23—21no—
16C2×#67288C2212yes—
17C2×#67288C2211yescharacteristic
18C22×D92C2212yes—
19C22×D92C2211yescharacteristic
20C22×Dic46C2211yescharacteristic, complemented
21C2×M16×C23C2211yescharacteristic, complemented
22C22×C8×C23C2211yescharacteristic, complemented
23#10625115—21no—
24#10625107—21no—
25#10625106—22no—
26#10625097C2211yescharacteristic, complemented
27#10625095C2214yescomplemented
28#10625080—24no—
29C2×Dic92C2212yescomplemented
30C2×#67263—24no—
31C2×#67263C2214yescomplemented
32C2×#67263C2212yescomplemented
33C23×C22⋊C8C2214yescomplemented
34#10625003C2212yescomplemented
35#10625003C2214yescomplemented
36#10624998C2212yescomplemented
37C23×D23—22no—
38C23×D23—21no—
39#41×C23—22no—
40#41×C23—22no—
41C2×Q8×C23D411yescharacteristic
42C2×D4×C23D412yes—
43C2×D4×C23D411yescharacteristic
44C22×C4×C23C2312yes—
45C22×C4×C23C2311yescharacteristic
46C2×C22⋊D23—22no—
47C2×C22⋊D23—21no—
48C22×Dic23—21no—
49#67292—28no—
50D4×D23—216no—
51D4×D23—28no—
52#67288—22no—
53#67288—24no—
54#67288—24no—
55#67288D414yes—
56C2×D92—22no—
57C2×D92—21no—
58C2×D92—22no—
59C2×D92—24no—
60C2×D92—24no—
61C2×D92D414yes—
62C2×D92C2311yescharacteristic
63C2×D92C2312yes—
64C2×C4×D23—22no—
65C2×C4×D23—21no—
66C2×Dic46—22no—
67C2×Dic46—22no—
68C2×Dic46—21no—
69C2×Dic46C2312yes—
70C2×Dic46C2311yescharacteristic
71M16×C23—22no—
72C2×C8×C23—22no—
73C2×C8×C23C2312yes—
74C2×C8×C23C2312yes—
75C22⋊Dic23—24no—
76C22⋊Dic23—21no—
77C4⋊Dic23C2312yes—
78Dic23⋊C4—24no—
79C4×Dic23—21no—
80Dic92—24no—
81#67263—28no—
82#67263—24no—
83C23×C23C2×D412yes—
84C23×C23C2×D411yescharacteristic
85C22×D23—22no—
86C22×D23—21no—
87C22×D23—28no—
88C22×D23—24no—
89C22×D23—82no—
90C22×D23—84no—
91Q8×C23—22no—
92D4×C23—24no—
93D4×C23—22no—
94C2×C4×C23—22no—
95C2×C4×C23—22no—
96C2×C4×C23C2×D412yes—
97C2×C4×C23C2×D411yescharacteristic
98C2×C4×C23C2×D412yes—
99C2×C4×C23C2×D412yes—
100C2×C4×C23C2411yescharacteristic
101C22⋊D23—28no—
102C22⋊D23—24no—
103C2×Dic23—21no—
104C2×Dic23—22no—
105C2×Dic23—22no—
106C2×Dic23—42no—
107D92—28no—
108D92—24no—
109D92—21no—
110D92—22no—
111D92C2×D412yes—
112D92C2×D414yes—
113C4×D23—28no—
114C4×D23—24no—
115Dic46—21no—
116Dic46—22no—
117Dic46—22no—
118Dic46—42no—
119Dic46C2×D412yes—
120C8×C23—22no—
121C8×C23—22no—
122#3009—231nomaximal, Sylow
123C22×C23—22no—
124C22×C23—22no—
125C22×C23—24no—
126C22×C23#12012yes—
127C22×C23C22×D411yescharacteristic
128C2×D23—24no—
129C2×D23—22no—
130C2×D23—44no—
131C2×D23—42no—
132C2×D23—84no—
133C2×D23—88no—
134C4×C23—22no—
135C4×C23#12012yes—
136C4×C23C22×D411yescharacteristic
137C4×C23C22×D411yescharacteristic
138Dic23—22no—
139Dic23—42no—
140Dic23—42no—
141C2×H(5,𝔽2)—231no—
142C2×#137—231no—
143C22×SD16—231no—
144#536—231no—
145#452—234no—
146#450—234no—
147#418—231no—
148#416—231no—
149#408D2311yescharacteristic, complemented
150C2×C23—22no—
151C2×C23—42no—
152C2×C23C2×#12011yescharacteristic
153C2×C23#57712yes—
154D23—44no—
155D23—42no—
156H(5,𝔽2)—464no—
157H(5,𝔽2)—464no—
158C2×#41—231no—
159C2×#41—232no—
160C2×#41—461no—
161C2×#41C2×D2311yescharacteristic
162C22×Q8—231no—
163C22×D4—231no—
164C22×D4—232no—
165C22×D4—462no—
166C22×D4—461no—
167#137—464no—
168C2×Q16—232no—
169C2×SD16—234no—
170C2×SD16—232no—
171C2×SD16—464no—
172C2×M16C2×D2311yescharacteristic, complemented
173C22×C8C2×D2311yescharacteristic, complemented
174C4⋊Q8—461no—
175#124—461no—
176#123—462no—
177C22⋊Q8—234no—
178#117—231no—
179#103—232no—
180#102—232no—
181#102—234no—
182C22⋊C8C2×D2314yescomplemented
183C23#300911yescharacteristic, complemented, Sylow
184C24—462no—
185C24—461no—
186#41—22no—
187#41—22no—
188#41—234no—
189#41—464no—
190#41—464no—
191#41—468no—
192#41—462no—
193C2×Q8—231no—
194C2×Q8—232no—
195C2×Q8—461no—
196C2×Q8—462no—
197C2×Q8—462no—
198C2×Q8D9211yescharacteristic
199C2×D4—234no—
200C2×D4—232no—
201C2×D4—231no—
202C2×D4—464no—
203C2×D4—464no—
204C2×D4—4616no—
205C2×D4—468no—
206C2×D4—462no—
207C2×D4—461no—
208C2×D4—462no—
209C2×D4—461no—
210C2×D4—462no—
211C2×D4D9212yes—
212C2×D4D9211yescharacteristic
213C22×C4—462no—
214C22×C4—461no—
215C22×C4—461no—
216C22×C4C22×D2312yes—
217C22×C4C22×D2311yescharacteristic
218Q16—464no—
219SD16—468no—
220SD16—464no—
221M16—22no—
222C2×C8—22no—
223C2×C8C22×D2312yes—
224C2×C8C22×D2312yes—
225C4⋊C4—232no—
226C4⋊C4—464no—
227C22⋊C4—461no—
228C22⋊C4—464no—
229C42—461no—
230C23—468no—
231C23—462no—
232C23—461no—
233C23—464no—
234C23—1842no—
235C23—1844no—
236C23C2×D9212yes—
237C23C2×D9211yescharacteristic
238Q8—22no—
239Q8—232no—
240Q8—461no—
241Q8—462no—
242Q8—462no—
243Q8—922no—
244D4—24no—
245D4—22no—
246D4—234no—
247D4—232no—
248D4—468no—
249D4—468no—
250D4—464no—
251D4—464no—
252D4—461no—
253D4—462no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—468no—
257C2×C4—461no—
258C2×C4—464no—
259C2×C4—462no—
260C2×C4—462no—
261C2×C4—922no—
262C2×C4C2×D9212yes—
263C2×C4C2×D9211yescharacteristic
264C2×C4D4×D2312yes—
265C2×C4D4×D2312yes—
266C2×C4C23×D2311yescharacteristic
267C8—22no—
268C8—22no—
269C22—22no—
270C22—22no—
271C22—24no—
272C22—464no—
273C22—462no—
274C22—924no—
275C22—922no—
276C22—1844no—
277C22—1848no—
278C22#1062505312yes—
279C22C22×D9211yescharacteristic
280C4—22no—
281C4—462no—
282C4—922no—
283C4—922no—
284C4#1062505312yes—
285C4C2×D4×D2311yescharacteristic
286C4C2×D4×D2311yescharacteristic
287C2—22no—
288C2—42no—
289C2—924no—
290C2—922no—
291C2C2×#1062505311yescharacteristic
292C2#1309322912yes—
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#408C2
socleC22×C23C22×D4
prime radicalC2×#10625160C2
hypercenter#408D23
hypocenterC23#3009
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
2. C2×#10625080C2semidirect
3. C22×#67263C2semidirect
4. #13092988C2semidirect
5. #13092581C2semidirect
6. #13092570C2semidirect
7. #13092423C2semidirect
8. #13092414C2semidirect
9. C23×#408C2semidirect
20. C22×Dic46C22semidirect
21. C2×M16×C23C22semidirect
22. C22×C8×C23C22semidirect
26. #10625097C22semidirect
27. #10625095C22semidirect
29. C2×Dic92C22semidirect
31. C2×#67263C22semidirect
32. C2×#67263C22semidirect
33. C23×C22⋊C8C22semidirect
34. #10625003C22semidirect
35. #10625003C22semidirect
36. #10624998C22semidirect
149. #408D23semidirect
172. C2×M16C2×D23semidirect
173. C22×C8C2×D23semidirect
182. C22⋊C8C2×D23semidirect
183. C23#3009semidirect

Maximal subgroups

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

subgroupindex
C2×#106251602
C2×#106250802
C22×#672632
#130929882
#130925812
#130925702
#130924232
#130924142
C23×#4082
#300923