Finite Group Databasebeta

← #15683332

Subgroups — #15683332

Order 2944.

462 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 121 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#121×D23C211yesmaximal, characteristic
2C2×#10625063C211yesmaximal, characteristic, complemented
3#13092744C212yesmaximal, complemented
4#13092740C212yesmaximal, complemented
5#13092736C211yesmaximal, characteristic, complemented
6#13092733C211yesmaximal, characteristic, complemented
7#13092730C211yesmaximal, characteristic, complemented
8#13092458C212yesmaximal, complemented
9#13092420C212yesmaximal, complemented
10#13092379C211yesmaximal, characteristic, complemented
11C23×#480C211yesmaximal, characteristic, complemented
12C2×D4×D23—21no—
13C2×D4×D23C2211yescharacteristic
14C22×C4×D23C2211yescharacteristic
15C23×#121C2211yescharacteristic
16C2×C4⋊C4×C23C2211yescharacteristic, complemented
17#10625110—21no—
18#10625109C2211yescharacteristic
19#10625101C2211yescharacteristic
20C2×(C2×D23)⋊C4—21no—
21C2×C4⋊Dic23C2211yescharacteristic, complemented
22C2×C4×Dic23—21no—
23C2×#67262C2212yes—
24#10625066C2211yescharacteristic
25#10625063—21no—
26#10625063—21no—
27#10625063C2212yes—
28#10625063C2212yescomplemented
29C4⋊C4×D23C2211yescharacteristic
30#10625055—21no—
31C22⋊C4×D23—21no—
32C23×#107C2212yescomplemented
33C23×#102C2212yescomplemented
34C23×C22⋊C8C2211yescharacteristic, complemented
35#10625014C2212yescomplemented
36C22⋊(C23⋊C8)C2211yescharacteristic, complemented
37#10625003C2212yescomplemented
38(C2×D23)⋊C8C2212yescomplemented
39#10624999C2212yescomplemented
40#10624991C2212yescomplemented
41#10624990C2212yescomplemented
42#10624989C2212yescomplemented
43C23×D23—21no—
44C23×D23D411yescharacteristic
45C2×D4×C23—21no—
46C2×D4×C23C2311yescharacteristic
47C22×C4×C23—21no—
48C22×C4×C23C2311yescharacteristic
49C2×C22⋊D23—21no—
50C2×C22⋊D23—21no—
51C2×C22⋊D23—21no—
52C22×Dic23—21no—
53C22×Dic23D411yescharacteristic
54D4×D23—24no—
55D4×D23—44no—
56C2×D92—21no—
57C2×D92C2311yescharacteristic
58C2×C4×D23—24no—
59C2×C4×D23—21no—
60C2×C4×D23D411yescharacteristic
61C2×C4×D23D411yescharacteristic
62C2×C4×D23C2311yescharacteristic
63C2×C4×D23C2311yescharacteristic
64C2×C8×C23C2312yes—
65C4⋊C4×C23—21no—
66C4⋊C4×C23C2312yes—
67C4⋊C4×C23C2311yescharacteristic
68C22⋊C4×C23—21no—
69C22⋊Dic23—21no—
70(C2×D23)⋊C4—22no—
71(C2×D23)⋊C4—22no—
72(C2×D23)⋊C4—21no—
73(C2×D23)⋊C4—21no—
74C4⋊Dic23—21no—
75C4⋊Dic23C2311yescharacteristic
76C4⋊Dic23C2312yes—
77Dic23⋊C4—21no—
78C4×Dic23—22no—
79C4×Dic23—22no—
80C2×C23⋊C8C2312yes—
81#67262—24no—
82C23×C23—21no—
83C23×C23C2×D411yescharacteristic
84C22×D23—22no—
85C22×D23—22no—
86C22×D23—21no—
87C22×D23—41no—
88C22×D23—42no—
89C22×D23—42no—
90C22×D23—42no—
91C22×D23C2×D411yescharacteristic
92C22×D23C2×D411yescharacteristic
93D4×C23—22no—
94D4×C23—42no—
95C2×C4×C23—22no—
96C2×C4×C23—22no—
97C2×C4×C23—21no—
98C2×C4×C23—42no—
99C2×C4×C23C2×D411yescharacteristic
100C2×C4×C23C2411yescharacteristic
101C22⋊D23—42no—
102C22⋊D23—42no—
103C22⋊D23—42no—
104C2×Dic23—22no—
105C2×Dic23—22no—
106C2×Dic23—21no—
107C2×Dic23—42no—
108C2×Dic23C2×D411yescharacteristic
109C2×Dic23C2×D411yescharacteristic
110D92—22no—
111D92—42no—
112C4×D23—22no—
113C4×D23—22no—
114C4×D23—22no—
115C4×D23—42no—
116C4×D23#4114yes—
117C8×C23—22no—
118C23⋊C8—22no—
119#3094—231nomaximal, Sylow
120C22×C23—21no—
121C22×C23—21no—
122C22×C23—41no—
123C22×C23—41no—
124C22×C23—41no—
125C22×C23AGL(1,ℤ/8)12yes—
126C22×C23C22×D411yescharacteristic
127C2×D23—21no—
128C2×D23—21no—
129C2×D23—21no—
130C2×D23—21no—
131C2×D23—21no—
132C2×D23—44no—
133C2×D23—41no—
134C2×D23—41no—
135C2×D23—41no—
136C2×D23—84no—
137C2×D23#12312yes—
138C4×C23—21no—
139C4×C23—41no—
140C4×C23—42no—
141C4×C23C2×#4112yes—
142Dic23—21no—
143Dic23—41no—
144Dic23—42no—
145Dic23#12312yes—
146C2×#121—231no—
147C2×#117—231no—
148#482—232no—
149#482—232no—
150#481—231no—
151#481—231no—
152#480—231no—
153#480D2311yescharacteristic, complemented
154#428—232no—
155#418—232no—
156#407—231no—
157C2×C23—22no—
158C2×C23—81no—
159C2×C23C2×#12311yescharacteristic
160C2×C23C2×AGL(1,ℤ/8)11yescharacteristic
161C2×C23#57511yescharacteristic
162D23—22no—
163D23—41no—
164D23—81no—
165C22×D4—231no—
166C22×D4—461no—
167C23×C4—231no—
168C2×M16—232no—
169#121—231no—
170#121—231no—
171#121—231no—
172#121—461no—
173#121—461no—
174#121C2×D2311yescharacteristic
175#117—232no—
176#117—232no—
177#117—461no—
178#117—461no—
179C2×C4⋊C4—231no—
180C2×C4⋊C4—231no—
181C2×C4⋊C4C2×D2311yescharacteristic, complemented
182C2×C22⋊C4—461no—
183C2×C22⋊C4—461no—
184C2×C42—461no—
185#107—232no—
186#107C2×D2312yescomplemented
187#106—232no—
188#106—232no—
189#102—232no—
190#102—232no—
191#102—232no—
192#102C2×D2312yescomplemented
193C22⋊C8—231no—
194C22⋊C8—232no—
195C22⋊C8C2×D2311yescharacteristic, complemented
196C23#309411yescharacteristic, complemented, Sylow
197C24—231no—
198C24—461no—
199C2×D4—21no—
200C2×D4—231no—
201C2×D4—461no—
202C2×D4—464no—
203C2×D4—461no—
204C2×D4—461no—
205C2×D4—461no—
206C2×D4—924no—
207C2×D4C22×D2311yescharacteristic
208C22×C4—21no—
209C22×C4—231no—
210C22×C4—231no—
211C22×C4—231no—
212C22×C4—231no—
213C22×C4—231no—
214C22×C4—464no—
215C22×C4—461no—
216C22×C4—461no—
217C22×C4C22×D2311yescharacteristic
218M16—464no—
219C2×C8—232no—
220C2×C8C22×D2312yes—
221C4⋊C4—21no—
222C4⋊C4—232no—
223C4⋊C4—231no—
224C4⋊C4—461no—
225C4⋊C4—461no—
226C4⋊C4C22×D2312yes—
227C4⋊C4C22×D2311yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—461no—
230C22⋊C4—462no—
231C22⋊C4—462no—
232C22⋊C4—461no—
233C22⋊C4—461no—
234C42—462no—
235C42—462no—
236C23—21no—
237C23—231no—
238C23—231no—
239C23—462no—
240C23—462no—
241C23—461no—
242C23—921no—
243C23—922no—
244C23—922no—
245C23—922no—
246C23D4×D2311yescharacteristic
247D4—22no—
248D4—42no—
249D4—462no—
250D4—922no—
251D4—922no—
252D4—922no—
253D4—922no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—231no—
259C2×C4—234no—
260C2×C4—231no—
261C2×C4—462no—
262C2×C4—462no—
263C2×C4—462no—
264C2×C4—462no—
265C2×C4—462no—
266C2×C4—461no—
267C2×C4—922no—
268C2×C4—922no—
269C2×C4D4×D2311yescharacteristic
270C2×C4C23×D2311yescharacteristic
271C8—22no—
272C8—462no—
273C22—21no—
274C22—21no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—232no—
279C22—461no—
280C22—461no—
281C22—461no—
282C22—461no—
283C22—461no—
284C22—924no—
285C22—921no—
286C22—921no—
287C22—921no—
288C22—1844no—
289C22#1062508212yes—
290C22C2×D4×D2311yescharacteristic
291C4—21no—
292C4—42no—
293C4—41no—
294C4—232no—
295C4—461no—
296C4—921no—
297C4—922no—
298C4#41×D2312yes—
299C2—22no—
300C2—81no—
301C2—462no—
302C2—921no—
303C2—1841no—
304C2#123×D2311yescharacteristic
305C2C2×#1062508211yescharacteristic
306C2#1309321611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#480C2
socleC22×C23C22×D4
prime radical#121×D23C2
hypercenter#480D23
hypocenterC23#3094
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#10625063C2semidirect
3. #13092744C2semidirect
4. #13092740C2semidirect
5. #13092736C2semidirect
6. #13092733C2semidirect
7. #13092730C2semidirect
8. #13092458C2semidirect
9. #13092420C2semidirect
10. #13092379C2semidirect
11. C23×#480C2semidirect
16. C2×C4⋊C4×C23C22semidirect
21. C2×C4⋊Dic23C22semidirect
28. #10625063C22semidirect
32. C23×#107C22semidirect
33. C23×#102C22semidirect
34. C23×C22⋊C8C22semidirect
35. #10625014C22semidirect
36. C22⋊(C23⋊C8)C22semidirect
37. #10625003C22semidirect
38. (C2×D23)⋊C8C22semidirect
39. #10624999C22semidirect
40. #10624991C22semidirect
41. #10624990C22semidirect
42. #10624989C22semidirect
153. #480D23semidirect
181. C2×C4⋊C4C2×D23semidirect
186. #107C2×D23semidirect
192. #102C2×D23semidirect
195. C22⋊C8C2×D23semidirect
196. C23#3094semidirect

Maximal subgroups

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

subgroupindex
#121×D232
C2×#106250632
#130927442
#130927402
#130927362
#130927332
#130927302
#130924582
#130924202
#130923792
C23×#4802
#309423