Finite Group Databasebeta

← #15683788

Subgroups — #15683788

Order 2944.

424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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#13092963C211yesmaximal, characteristic
2C2×#10625059C211yesmaximal, characteristic, complemented
3#13092778C212yesmaximal, complemented
4#13092775C212yesmaximal, complemented
5#13092766C212yesmaximal, complemented
6#13092762C212yesmaximal, complemented
7#13092419C211yesmaximal, characteristic, complemented
8#13092418C211yesmaximal, characteristic, complemented
9#13092416C211yesmaximal, characteristic, complemented
10M16×Dic23C211yesmaximal, characteristic, complemented
11C23×#417C211yesmaximal, characteristic, complemented
12C2×#41×C23C2211yescharacteristic
13C2×#67288C2211yescharacteristic
14C22×Dic46—21no—
15C2×M16×C23C2211yescharacteristic
16C2×C4⋊C4×C23C2211yescharacteristic
17#10625118C2211yescharacteristic
18#10625115C2211yescharacteristic
19#10625111C2211yescharacteristic
20#10625110—21no—
21#10625110—21no—
22#10625107C2211yescharacteristic
23C4×C22⋊D23—21no—
24C4×C22⋊D23—21no—
25C2×C4⋊Dic23C2211yescharacteristic
26C2×Dic23⋊C4—21no—
27C2×C4×Dic23C2211yescharacteristic
28C2×#67267C2211yescharacteristic
29#10625059—21no—
30#10625059—21no—
31#10625059C2212yes—
32#10625059C2212yes—
33C23×#103C2212yes—
34C23×#102C2212yes—
35#10625017C2212yes—
36#10625014C2212yes—
37#10625003C2212yes—
38#10624998C2212yes—
39#10624997C2212yes—
40C8×Dic23C2212yes—
41#10624992C2212yes—
42#10624991C2212yes—
43#41×C23—22no—
44#41×C23—22no—
45C2×Q8×C23C2311yescharacteristic
46C2×D4×C23—21no—
47C2×D4×C23C2311yescharacteristic
48C22×C4×C23—21no—
49C22×C4×C23—21no—
50C22×C4×C23C2311yescharacteristic
51C2×C22⋊D23—21no—
52C2×C22⋊D23—21no—
53C2×C22⋊D23—21no—
54C22×Dic23—21no—
55C22×Dic23D411yescharacteristic
56C22×Dic23D411yescharacteristic
57#67288—22no—
58#67288—22no—
59C2×D92C2311yescharacteristic
60C2×C4×D23—21no—
61C2×Dic46—22no—
62C2×Dic46—22no—
63C2×Dic46—44no—
64C2×Dic46C2311yescharacteristic
65M16×C23—22no—
66C2×C8×C23C2312yes—
67C4⋊C4×C23—21no—
68C4⋊C4×C23C2312yes—
69C22⋊Dic23—21no—
70C22⋊Dic23—21no—
71(C2×D23)⋊C4—21no—
72(C2×D23)⋊C4—21no—
73C4⋊Dic23—21no—
74C4⋊Dic23C2312yes—
75Dic23⋊C4—22no—
76Dic23⋊C4—22no—
77Dic23⋊C4—21no—
78Dic23⋊C4—21no—
79C4×Dic23D411yescharacteristic
80C4×Dic23D411yescharacteristic
81C4×Dic23C2311yescharacteristic
82C4×Dic23C2311yescharacteristic
83#67267—22no—
84C2×C23⋊C8C2312yes—
85C23×C23—21no—
86C23×C23C2×D411yescharacteristic
87C22×D23—21no—
88Q8×C23—21no—
89Q8×C23—21no—
90D4×C23—21no—
91D4×C23—21no—
92D4×C23—42no—
93C2×C4×C23—21no—
94C2×C4×C23—22no—
95C2×C4×C23—42no—
96C2×C4×C23—42no—
97C2×C4×C23C2×D411yescharacteristic
98C2×C4×C23#4112yes—
99C2×C4×C23#4112yes—
100C2×C4×C23C2411yescharacteristic
101C22⋊D23—42no—
102C22⋊D23—42no—
103C22⋊D23—42no—
104C2×Dic23—22no—
105C2×Dic23—22no—
106C2×Dic23—22no—
107C2×Dic23—21no—
108C2×Dic23—42no—
109C2×Dic23C2×D411yescharacteristic
110C2×Dic23C2×D411yescharacteristic
111C2×Dic23C2×D411yescharacteristic
112C2×Dic23C2×D411yescharacteristic
113D92—21no—
114D92—21no—
115C4×D23—42no—
116Dic46—21no—
117Dic46—21no—
118Dic46—44no—
119Dic46—44no—
120C8×C23—22no—
121C23⋊C8—22no—
122#3141—231nomaximal, Sylow
123C22×C23—21no—
124C22×C23—21no—
125C22×C23—41no—
126C22×C23—41no—
127C22×C23—41no—
128C22×C23#12412yes—
129C22×C23C22×D411yescharacteristic
130C2×D23—41no—
131C2×D23—41no—
132C2×D23—41no—
133C4×C23—41no—
134C4×C23—42no—
135C4×C23#12412yes—
136C4×C23C2×#4111yescharacteristic
137C4×C23C2×#4111yescharacteristic
138Dic23—21no—
139Dic23—21no—
140Dic23—41no—
141Dic23—42no—
142Dic23AGL(1,ℤ/8)12yes—
143Dic23#13712yes—
144#532—231no—
145C2×C4⋊Q8—231no—
146#489—232no—
147#489—232no—
148#487—232no—
149#486—232no—
150#417—231no—
151#417—231no—
152#417—231no—
153#417D2311yescharacteristic, complemented
154C4×M16—231no—
155C2×C23—22no—
156C2×C23—81no—
157C2×C23C2×#12411yescharacteristic
158C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
159C2×C23C2×#13711yescharacteristic
160D23—81no—
161C2×#41—231no—
162C2×#41C2×D2311yescharacteristic
163C22×Q8—461no—
164C2×M16—231no—
165C2×M16C2×D2311yescharacteristic
166C4⋊Q8—232no—
167C4⋊Q8—232no—
168C4⋊Q8—231no—
169C4⋊Q8—461no—
170C4⋊Q8—461no—
171#127—231no—
172#124—231no—
173#124—231no—
174#121—461no—
175#121—461no—
176C4×D4—461no—
177C4×D4—461no—
178C2×C4⋊C4—231no—
179C2×C4⋊C4—461no—
180C2×C4⋊C4C2×D2311yescharacteristic
181C2×C42—231no—
182#103—232no—
183#103—232no—
184#103—232no—
185#103C2×D2312yes—
186#102—232no—
187#102—232no—
188#102—232no—
189#102C2×D2312yes—
190#97—232no—
191C4×C8—232no—
192C23#314111yescharacteristic, complemented, Sylow
193#41—22no—
194#41—22no—
195#41—462no—
196#41—462no—
197C2×Q8—231no—
198C2×Q8—462no—
199C2×Q8—462no—
200C2×Q8—924no—
201C2×Q8C22×D2311yescharacteristic
202C2×D4—21no—
203C2×D4—231no—
204C2×D4—461no—
205C2×D4—461no—
206C2×D4—461no—
207C2×D4C22×D2311yescharacteristic
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—231no—
211C22×C4—231no—
212C22×C4—461no—
213C22×C4—461no—
214C22×C4C22×D2311yescharacteristic
215M16—22no—
216M16—462no—
217C2×C8—232no—
218C2×C8C22×D2312yes—
219C4⋊C4—21no—
220C4⋊C4—232no—
221C4⋊C4—462no—
222C4⋊C4—462no—
223C4⋊C4—461no—
224C4⋊C4—461no—
225C4⋊C4—461no—
226C4⋊C4C22×D2312yes—
227C22⋊C4—461no—
228C22⋊C4—461no—
229C22⋊C4—461no—
230C22⋊C4—461no—
231C42—231no—
232C42—231no—
233C42—231no—
234C42—231no—
235C23—21no—
236C23—461no—
237C23D4×D2311yescharacteristic
238Q8—21no—
239Q8—21no—
240Q8—461no—
241Q8—461no—
242Q8—924no—
243Q8—924no—
244D4—21no—
245D4—21no—
246D4—42no—
247D4—461no—
248D4—461no—
249D4—922no—
250D4—922no—
251D4—922no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—231no—
257C2×C4—231no—
258C2×C4—231no—
259C2×C4—231no—
260C2×C4—462no—
261C2×C4—462no—
262C2×C4—461no—
263C2×C4—462no—
264C2×C4—922no—
265C2×C4—922no—
266C2×C4#6728812yes—
267C2×C4D4×D2311yescharacteristic
268C2×C4#6729012yes—
269C2×C4C23×D2311yescharacteristic
270C8—22no—
271C8—462no—
272C22—21no—
273C22—21no—
274C22—41no—
275C22—41no—
276C22—41no—
277C22—921no—
278C22—921no—
279C22—921no—
280C22#1062505612yes—
281C22C2×D4×D2311yescharacteristic
282C4—41no—
283C4—42no—
284C4—232no—
285C4—232no—
286C4—461no—
287C4—461no—
288C4—921no—
289C4—922no—
290C4#1062505612yes—
291C4C2×#6728811yescharacteristic
292C4C2×#6729011yescharacteristic
293C2—22no—
294C2—81no—
295C2—1841no—
296C2C2×#1062505611yescharacteristic
297C2AGL(1,ℤ/8)×D2311yescharacteristic
298C2#137×D2311yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#417C2
socleC22×C23C22×D4
prime radical#13092963C2
hypercenter#417D23
hypocenterC23#3141
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#10625059C2semidirect
3. #13092778C2semidirect
4. #13092775C2semidirect
5. #13092766C2semidirect
6. #13092762C2semidirect
7. #13092419C2semidirect
8. #13092418C2semidirect
9. #13092416C2semidirect
10. M16×Dic23C2semidirect
11. C23×#417C2semidirect
153. #417D23semidirect
192. C23#3141semidirect

Maximal subgroups

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

subgroupindex
#130929632
C2×#106250592
#130927782
#130927752
#130927662
#130927622
#130924192
#130924182
#130924162
M16×Dic232
C23×#4172
#314123