Finite Group Databasebeta

← #15683339

Subgroups — #15683339

Order 2944.

462 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 127 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×#10625066C211yesmaximal, characteristic
2#117×D23C211yesmaximal, characteristic, complemented
3#13092744C212yesmaximal, complemented
4#13092743C212yesmaximal, complemented
5#13092737C212yesmaximal, complemented
6#13092732C212yesmaximal, complemented
7#13092457C211yesmaximal, characteristic, complemented
8#13092423C211yesmaximal, characteristic, complemented
9#13092421C211yesmaximal, characteristic, complemented
10#13092380C211yesmaximal, characteristic, complemented
11C23×#428C211yesmaximal, characteristic, complemented
12C22×D92—21no—
13C22×D92C2211yescharacteristic
14C22×C4×D23C2211yescharacteristic
15C2×M16×C23C2211yescharacteristic
16C23×#117C2211yescharacteristic
17C2×C4⋊C4×C23C2211yescharacteristic
18C2×(C2×D23)⋊C4—21no—
19#10625097C2211yescharacteristic
20C2×#67267C2211yescharacteristic
21#10625066—21no—
22#10625066—21no—
23#10625066C2212yes—
24#10625066C2212yes—
25#10625063C2211yescharacteristic, complemented
26#10625063C2211yescharacteristic, complemented
27C4⋊C4×D23C2211yescharacteristic, complemented
28C4⋊C4×D23C2211yescharacteristic, complemented
29C22⋊C4×D23—21no—
30#10625048—21no—
31#10625043—21no—
32C42×D23—21no—
33C23×#107C2212yescomplemented
34C23×#106C2212yescomplemented
35#10625003C2212yescomplemented
36#10625003C2212yescomplemented
37(C2×D23)⋊C8C2212yescomplemented
38(C2×D23)⋊C8C2212yescomplemented
39#10624991C2212yescomplemented
40#10624991C2212yescomplemented
41#10624990C2212yescomplemented
42#10624989C2212yescomplemented
43C23×D23—21no—
44C23×D23D411yescharacteristic
45C22×C4×C23—21no—
46C22×C4×C23C2311yescharacteristic
47C22×Dic23D411yescharacteristic
48C2×D92—22no—
49C2×D92—22no—
50C2×D92—22no—
51C2×D92—22no—
52C2×D92—21no—
53C2×D92—44no—
54C2×D92C2312yes—
55C2×C4×D23—22no—
56C2×C4×D23—22no—
57C2×C4×D23—21no—
58C2×C4×D23—21no—
59C2×C4×D23D411yescharacteristic
60C2×C4×D23D411yescharacteristic
61C2×C4×D23C2311yescharacteristic
62C2×C4×D23C2311yescharacteristic
63M16×C23—22no—
64C2×C8×C23C2312yes—
65C4⋊C4×C23—21no—
66C4⋊C4×C23C2311yescharacteristic
67C4⋊C4×C23C2312yes—
68C4⋊C4×C23C2311yescharacteristic
69C22⋊C4×C23—21no—
70C42×C23—21no—
71C22⋊Dic23—21no—
72(C2×D23)⋊C4—21no—
73(C2×D23)⋊C4—21no—
74(C2×D23)⋊C4—22no—
75(C2×D23)⋊C4—22no—
76C4⋊Dic23C2311yescharacteristic
77C4⋊Dic23C2311yescharacteristic
78Dic23⋊C4—21no—
79Dic23⋊C4—21no—
80C4×Dic23—21no—
81C4×Dic23—21no—
82C4×Dic23—21no—
83#67267—22no—
84C2×C23⋊C8C2312yes—
85C23×C23C2×D411yescharacteristic
86C22×D23—22no—
87C22×D23—22no—
88C22×D23—22no—
89C22×D23—41no—
90C22×D23—42no—
91C22×D23—42no—
92C22×D23—42no—
93C22×D23C2×D411yescharacteristic
94C22×D23C2×D411yescharacteristic
95C2×C4×C23—21no—
96C2×C4×C23—21no—
97C2×C4×C23—22no—
98C2×C4×C23—42no—
99C2×C4×C23C2×D411yescharacteristic
100C2×C4×C23#4112yes—
101C2×C4×C23#4112yes—
102C2×C4×C23C2411yescharacteristic
103C2×Dic23—22no—
104C2×Dic23—21no—
105C2×Dic23—21no—
106C2×Dic23C2×D411yescharacteristic
107C2×Dic23C2×D411yescharacteristic
108D92—22no—
109D92—22no—
110D92—44no—
111D92—44no—
112D92—42no—
113C4×D23—22no—
114C4×D23—22no—
115C4×D23—21no—
116C4×D23—21no—
117C4×D23—21no—
118C4×D23—21no—
119C4×D23—42no—
120C4×D23—42no—
121C8×C23—22no—
122C23⋊C8—22no—
123#3094—231nomaximal, Sylow
124C22×C23—21no—
125C22×C23—21no—
126C22×C23#12312yes—
127C22×C23C22×D411yescharacteristic
128C2×D23—21no—
129C2×D23—21no—
130C2×D23—21no—
131C2×D23—21no—
132C2×D23—21no—
133C2×D23—44no—
134C2×D23—42no—
135C2×D23—42no—
136C2×D23—42no—
137C2×D23—84no—
138C2×D23AGL(1,ℤ/8)12yes—
139C4×C23—41no—
140C4×C23—42no—
141C4×C23—41no—
142C4×C23#12312yes—
143C4×C23C2×#4111yescharacteristic
144C4×C23C2×#4111yescharacteristic
145Dic23—21no—
146Dic23—21no—
147Dic23—41no—
148Dic23—41no—
149C2×#121—231no—
150C2×#117—231no—
151#482—232no—
152#482—232no—
153#481—232no—
154#480—232no—
155#428—231no—
156#428D2311yescharacteristic, complemented
157#418—231no—
158#418—231no—
159#407—231no—
160C2×C23—22no—
161C2×C23C2×#12311yescharacteristic
162C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
163C2×C23#57511yescharacteristic
164D23—22no—
165D23—41no—
166D23—82no—
167C22×D4—231no—
168C22×D4—461no—
169C23×C4—231no—
170C2×M16—231no—
171C2×M16C2×D2311yescharacteristic
172#121—232no—
173#121—232no—
174#121—461no—
175#121—461no—
176#117—231no—
177#117—231no—
178#117—231no—
179#117—461no—
180#117—461no—
181#117C2×D2311yescharacteristic
182C2×C4⋊C4—231no—
183C2×C4⋊C4—231no—
184C2×C4⋊C4C2×D2311yescharacteristic
185C2×C22⋊C4—461no—
186C2×C22⋊C4—461no—
187C2×C42—461no—
188#107—232no—
189#107C2×D2312yescomplemented
190#106—232no—
191#106C2×D2312yescomplemented
192#102—232no—
193#102—232no—
194#102—232no—
195#102—232no—
196C22⋊C8—232no—
197C22⋊C8—232no—
198C23#309411yescharacteristic, complemented, Sylow
199C24—231no—
200C24—461no—
201C2×D4—232no—
202C2×D4—462no—
203C2×D4—462no—
204C2×D4—462no—
205C2×D4—461no—
206C2×D4—462no—
207C2×D4—924no—
208C22×C4—21no—
209C22×C4—231no—
210C22×C4—231no—
211C22×C4—231no—
212C22×C4—231no—
213C22×C4—231no—
214C22×C4—461no—
215C22×C4—461no—
216C22×C4—462no—
217C22×C4—462no—
218C22×C4C22×D2311yescharacteristic
219M16—22no—
220M16—462no—
221C2×C8—232no—
222C2×C8C22×D2312yes—
223C4⋊C4—21no—
224C4⋊C4—231no—
225C4⋊C4—231no—
226C4⋊C4—461no—
227C4⋊C4—461no—
228C4⋊C4C22×D2311yescharacteristic
229C4⋊C4C22×D2311yescharacteristic
230C4⋊C4C22×D2312yes—
231C22⋊C4—21no—
232C22⋊C4—462no—
233C22⋊C4—462no—
234C22⋊C4—461no—
235C22⋊C4—461no—
236C22⋊C4—461no—
237C42—21no—
238C42—461no—
239C42—461no—
240C42—461no—
241C23—231no—
242C23—231no—
243C23—462no—
244C23—462no—
245C23—462no—
246C23—921no—
247C23—922no—
248C23—922no—
249C23—922no—
250C23D4×D2311yescharacteristic
251D4—462no—
252D4—462no—
253D4—924no—
254D4—924no—
255D4—922no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—42no—
260C2×C4—231no—
261C2×C4—231no—
262C2×C4—462no—
263C2×C4—462no—
264C2×C4—462no—
265C2×C4—461no—
266C2×C4—461no—
267C2×C4—461no—
268C2×C4—461no—
269C2×C4—461no—
270C2×C4—461no—
271C2×C4—922no—
272C2×C4—922no—
273C2×C4#6728812yes—
274C2×C4D4×D2311yescharacteristic
275C2×C4#6729212yes—
276C2×C4C23×D2311yescharacteristic
277C8—22no—
278C8—462no—
279C22—21no—
280C22—21no—
281C22—232no—
282C22—461no—
283C22—461no—
284C22—461no—
285C22—461no—
286C22—461no—
287C22—924no—
288C22—922no—
289C22—922no—
290C22—922no—
291C22—1844no—
292C22#1062506512yes—
293C22C2×D4×D2311yescharacteristic
294C4—42no—
295C4—41no—
296C4—41no—
297C4—461no—
298C4—461no—
299C4—921no—
300C4—921no—
301C4#1062506512yes—
302C4C2×#6728811yescharacteristic
303C4C2×#6729211yescharacteristic
304C2—22no—
305C2—462no—
306C2—921no—
307C2—1842no—
308C2C2×#1062506511yescharacteristic
309C2AGL(1,ℤ/8)×D2311yescharacteristic
310C2#1309321611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#428C2
socleC22×C23C22×D4
prime radicalC2×#10625066C2
hypercenter#428D23
hypocenterC23#3094
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #117×D23C2semidirect
3. #13092744C2semidirect
4. #13092743C2semidirect
5. #13092737C2semidirect
6. #13092732C2semidirect
7. #13092457C2semidirect
8. #13092423C2semidirect
9. #13092421C2semidirect
10. #13092380C2semidirect
11. C23×#428C2semidirect
25. #10625063C22semidirect
26. #10625063C22semidirect
27. C4⋊C4×D23C22semidirect
28. C4⋊C4×D23C22semidirect
33. C23×#107C22semidirect
34. C23×#106C22semidirect
35. #10625003C22semidirect
36. #10625003C22semidirect
37. (C2×D23)⋊C8C22semidirect
38. (C2×D23)⋊C8C22semidirect
39. #10624991C22semidirect
40. #10624991C22semidirect
41. #10624990C22semidirect
42. #10624989C22semidirect
156. #428D23semidirect
189. #107C2×D23semidirect
191. #106C2×D23semidirect
198. C23#3094semidirect

Maximal subgroups

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

subgroupindex
C2×#106250662
#117×D232
#130927442
#130927432
#130927372
#130927322
#130924572
#130924232
#130924212
#130923802
C23×#4282
#309423