Finite Group Databasebeta

← #15682670

Subgroups — #15682670

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×#10625155C211yesmaximal, characteristic
2C2×#10625113C211yesmaximal, characteristic, complemented
3#13092991C211yesmaximal, characteristic, complemented
4#13092576C214yesmaximal, complemented
5#13092566C214yesmaximal, complemented
6#13092422C211yesmaximal, characteristic, complemented
7#13092414C211yesmaximal, characteristic, complemented
8#13092383C211yesmaximal, characteristic, complemented
9C22×SD16×C23C211yesmaximal, characteristic, complemented
10C22×Q8×C23C2211yescharacteristic, complemented
11C22×D4×C23C2211yescharacteristic
12C22×C22⋊D23—22no—
13#10625155—24no—
14#10625155—24no—
15C2×#67290—21no—
16C2×#67290C2212yes—
17C2×D4×D23—21no—
18C2×D4×D23C2212yes—
19C2×#67288C2211yescharacteristic
20C2×#67288C2211yescharacteristic
21C2×SD16×C23—24no—
22C2×SD16×C23C2214yescomplemented
23C22×C8×C23C2211yescharacteristic, complemented
24#10625118—21no—
25#10625117C2214yescomplemented
26#10625115—21no—
27C2×#67275C2212yescomplemented
28#10625113—24no—
29C2×#67274C2212yescomplemented
30#10625100—22no—
31#10625097C2211yescharacteristic, complemented
32C2×#67267C2211yescharacteristic, complemented
33#10625014C2214yescomplemented
34#10625003C2212yescomplemented
35(C2×D23)⋊C8C2214yescomplemented
36#10624998C2212yescomplemented
37C24×C23—21no—
38C23×D23—22no—
39C2×Q8×C23—21no—
40C2×Q8×C23—22no—
41C2×Q8×C23—22no—
42C2×Q8×C23C2312yes—
43C2×D4×C23—21no—
44C2×D4×C23—22no—
45C2×D4×C23D414yes—
46C2×D4×C23C2312yes—
47C22×C4×C23—21no—
48C22×C4×C23C2311yescharacteristic
49C2×C22⋊D23—216no—
50C2×C22⋊D23—21no—
51C2×C22⋊D23—22no—
52C2×C22⋊D23—22no—
53C2×C22⋊D23D412yes—
54C22×Dic23—22no—
55#67290—28no—
56#67290—24no—
57#67290—24no—
58D4×D23—28no—
59D4×D23—24no—
60D4×D23—24no—
61#67288—22no—
62#67288—22no—
63#67288—22no—
64#67288D414yes—
65C2×D92D411yescharacteristic
66C2×D92C2311yescharacteristic
67C2×C4×D23—21no—
68C2×C4×D23C2312yes—
69C2×Dic46D411yescharacteristic
70C2×Dic46C2311yescharacteristic
71SD16×C23—28no—
72C2×C8×C23—22no—
73C2×C8×C23C2312yes—
74C22⋊Dic23—21no—
75#67275—24no—
76#67274—24no—
77(C2×D23)⋊C4—24no—
78C4⋊Dic23C2312yes—
79Dic23⋊C4—24no—
80C4×Dic23—21no—
81#67267—22no—
82C2×C23⋊C8C2312yes—
83C23×C23—22no—
84C23×C23—24no—
85C23×C23—82no—
86C23×C23C2×D411yescharacteristic
87C22×D23—21no—
88C22×D23—28no—
89C22×D23—84no—
90C22×D23C2×D412yes—
91Q8×C23—22no—
92Q8×C23—22no—
93Q8×C23—42no—
94D4×C23—24no—
95D4×C23—22no—
96D4×C23C2×D414yes—
97C2×C4×C23—22no—
98C2×C4×C23—42no—
99C2×C4×C23C2×D411yescharacteristic
100C2×C4×C23C2×D412yes—
101C2×C4×C23C2×D412yes—
102C2×C4×C23C2411yescharacteristic
103C22⋊D23—28no—
104C22⋊D23—28no—
105C22⋊D23—24no—
106C22⋊D23—24no—
107C2×Dic23—28no—
108C2×Dic23—21no—
109C2×Dic23—22no—
110C2×Dic23C2×D412yes—
111D92—22no—
112D92—21no—
113D92C2×D412yes—
114C4×D23—24no—
115C4×D23—22no—
116C4×D23—22no—
117Dic46—22no—
118Dic46—21no—
119Dic46C2×D412yes—
120C8×C23—22no—
121C23⋊C8—22no—
122#3009—231nomaximal, Sylow
123C22×C23—22no—
124C22×C23—24no—
125C22×C23—44no—
126C22×C23—84no—
127C22×C23#12012yes—
128C22×C23C22×D411yescharacteristic
129C2×D23—22no—
130C2×D23—22no—
131C2×D23—24no—
132C2×D23—42no—
133C2×D23—88no—
134C4×C23—42no—
135C4×C23#12012yes—
136C4×C23C22×D411yescharacteristic
137C4×C23C22×D411yescharacteristic
138Dic23—22no—
139Dic23—22no—
140Dic23—42no—
141C2×H(5,𝔽2)—231no—
142C2×#137—231no—
143C22×SD16D2311yescharacteristic, complemented
144#536—231no—
145#452—234no—
146#450—234no—
147#418—231no—
148#416—231no—
149#408—231no—
150C2×C23—22no—
151C2×C23—44no—
152C2×C23C2×#12011yescharacteristic
153C2×C23#57712yes—
154D23—42no—
155D23—42no—
156H(5,𝔽2)—464no—
157H(5,𝔽2)—464no—
158C2×#41—231no—
159C2×#41—232no—
160C2×#41—231no—
161C2×#41—461no—
162C22×Q8C2×D2311yescharacteristic, complemented
163C22×D4—232no—
164C22×D4—461no—
165C22×D4—462no—
166C22×D4C2×D2311yescharacteristic
167#137—464no—
168C2×Q16—232no—
169C2×SD16—24no—
170C2×SD16—232no—
171C2×SD16C2×D2314yescomplemented
172C2×M16—231no—
173C22×C8C2×D2311yescharacteristic, complemented
174C4⋊Q8—461no—
175#124—461no—
176#123—462no—
177C22⋊Q8—234no—
178#117—231no—
179#103—232no—
180#102—234no—
181#102—232no—
182C22⋊C8—234no—
183C23#300911yescharacteristic, complemented, Sylow
184C24—21no—
185C24—462no—
186#41—234no—
187#41—464no—
188#41—468no—
189#41—464no—
190#41—462no—
191#41—462no—
192#41—462no—
193C2×Q8—21no—
194C2×Q8—22no—
195C2×Q8—22no—
196C2×Q8—231no—
197C2×Q8—231no—
198C2×Q8C22×D2312yes—
199C2×D4—21no—
200C2×D4—22no—
201C2×D4—232no—
202C2×D4—231no—
203C2×D4—231no—
204C2×D4—462no—
205C2×D4—464no—
206C2×D4—468no—
207C2×D4—462no—
208C2×D4—4616no—
209C2×D4—461no—
210C2×D4—464no—
211C2×D4C22⋊D2314yes—
212C2×D4C22×D2312yes—
213C22×C4—21no—
214C22×C4—232no—
215C22×C4—462no—
216C22×C4—461no—
217C22×C4C22×D2311yescharacteristic
218Q16—464no—
219SD16—28no—
220SD16—464no—
221M16—462no—
222C2×C8—22no—
223C2×C8—232no—
224C2×C8C22×D2312yes—
225C4⋊C4—232no—
226C4⋊C4—464no—
227C22⋊C4—464no—
228C22⋊C4—461no—
229C42—461no—
230C23—22no—
231C23—24no—
232C23—82no—
233C23—232no—
234C23—468no—
235C23—461no—
236C23—1844no—
237C23D4×D2311yescharacteristic
238Q8—22no—
239Q8—22no—
240Q8—42no—
241Q8—232no—
242Q8—462no—
243Q8—461no—
244D4—24no—
245D4—22no—
246D4—232no—
247D4—468no—
248D4—468no—
249D4—464no—
250D4—464no—
251D4—462no—
252D4—461no—
253D4C2×C22⋊D2314yes—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—232no—
257C2×C4—468no—
258C2×C4—461no—
259C2×C4—464no—
260C2×C4—462no—
261C2×C4—462no—
262C2×C4—462no—
263C2×C4D4×D2311yescharacteristic
264C2×C4D4×D2312yes—
265C2×C4C2×C22⋊D2312yes—
266C2×C4C23×D2311yescharacteristic
267C8—22no—
268C8—462no—
269C22—22no—
270C22—24no—
271C22—44no—
272C22—84no—
273C22—462no—
274C22—462no—
275C22—464no—
276C22—922no—
277C22—1848no—
278C22#1062510812yes—
279C22C2×D4×D2311yescharacteristic
280C4—42no—
281C4—462no—
282C4—462no—
283C4—922no—
284C4#1062510812yes—
285C4C2×D4×D2311yescharacteristic
286C4C22×C22⋊D2311yescharacteristic
287C2—22no—
288C2—44no—
289C2—922no—
290C2—922no—
291C2C2×#1062510811yescharacteristic
292C2#1309322312yes—
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC22×SD16×C23C2
socleC22×C23C22×D4
prime radicalC2×#10625155C2
hypercenterC22×SD16D23
hypocenterC23#3009
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#10625113C2semidirect
3. #13092991C2semidirect
4. #13092576C2semidirect
5. #13092566C2semidirect
6. #13092422C2semidirect
7. #13092414C2semidirect
8. #13092383C2semidirect
9. C22×SD16×C23C2semidirect
10. C22×Q8×C23C22semidirect
22. C2×SD16×C23C22semidirect
23. C22×C8×C23C22semidirect
25. #10625117C22semidirect
27. C2×#67275C22semidirect
29. C2×#67274C22semidirect
31. #10625097C22semidirect
32. C2×#67267C22semidirect
33. #10625014C22semidirect
34. #10625003C22semidirect
35. (C2×D23)⋊C8C22semidirect
36. #10624998C22semidirect
143. C22×SD16D23semidirect
162. C22×Q8C2×D23semidirect
171. C2×SD16C2×D23semidirect
173. 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×#106251552
C2×#106251132
#130929912
#130925762
#130925662
#130924222
#130924142
#130923832
C22×SD16×C232
#300923