Finite Group Databasebeta

← #489×D151 #34079436

Subgroups — #489×D151 #34079436

Order 19328.

436 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C4⋊Q8×D151C211yesmaximal, characteristic, complemented
2#124×D151C211yesmaximal, characteristic
3#23752574C211yesmaximal, characteristic, complemented
4#23752573C212yesmaximal, complemented
5#23752572C211yesmaximal, characteristic, complemented
6#23752571C211yesmaximal, characteristic, complemented
7#23752570C212yesmaximal, complemented
8#103×D151C212yesmaximal, complemented
9#102×D151C212yesmaximal
10#97×D151C211yesmaximal, characteristic, complemented
11#489×C151C211yesmaximal, characteristic, complemented
12C2×Q8×D151—21no—
13C2×Q8×D151C2211yescharacteristic
14C2×D4×D151C2211yescharacteristic
15C2×C8×D151C2212yes—
16#18012739C2211yescharacteristic, complemented
17#18012738—21no—
18#18012738C2212yescomplemented
19#18012737—21no—
20#18012728C2211yescharacteristic
21#18012727C2211yescharacteristic
22#18012726C2211yescharacteristic
23#18012725—21no—
24#18012725—21no—
25C4⋊C4×D151—21no—
26C4⋊C4×D151C2212yes—
27C22⋊C4×D151—21no—
28C22⋊C4×D151—21no—
29C42×D151C2211yescharacteristic
30#18012664C2212yescomplemented
31#18012663C2212yescomplemented
32#18012662C2212yescomplemented
33#18012661C2212yes—
34#18012660C2212yes—
35#18012659C2212yes—
36#18012650C2211yescharacteristic, complemented
37#18012649C2212yescomplemented
38C4⋊Q8×C151C2211yescharacteristic, complemented
39#124×C151C2211yescharacteristic
40#103×C151C2212yescomplemented
41#102×C151C2212yes—
42#97×C151C2211yescharacteristic, complemented
43C23×D151—21no—
44C2×Dic302—21no—
45C2×Dic302—22no—
46C2×Dic302—21no—
47C2×Dic302C2311yescharacteristic
48Q8×D151—24no—
49Q8×D151—44no—
50C2×D604C2311yescharacteristic
51C2×C22⋊D151—21no—
52D4×D151—24no—
53C2×C4×D151—21no—
54C2×C4×D151—22no—
55C2×C4×D151D411yescharacteristic
56C2×C4×D151D411yescharacteristic
57C2×C4×D151C2311yescharacteristic
58C2×C151⋊C8C2312yes—
59C8×D151—24no—
60C4⋊Dic151—21no—
61C4⋊Dic151C2312yes—
62Dic151⋊C4—22no—
63Dic151⋊C4—22no—
64C22⋊Dic151—21no—
65C22⋊Dic151—21no—
66(C2×D151)⋊C4—21no—
67(C2×D151)⋊C4—21no—
68(C2×D151)⋊C4—21no—
69(C2×D151)⋊C4—21no—
70C4×Dic151D411yescharacteristic
71C4×Dic151D411yescharacteristic
72C4×Dic151C2311yescharacteristic
73C2×Q8×C151—21no—
74C2×Q8×C151C2311yescharacteristic
75C2×D4×C151C2311yescharacteristic
76C2×C8×C151C2312yes—
77C4⋊C4×C151—21no—
78C4⋊C4×C151C2312yes—
79C22⋊C4×C151—21no—
80C22⋊C4×C151—21no—
81C42×C151C2311yescharacteristic
82C22×D151—21no—
83C22×D151—42no—
84C22×D151—42no—
85C22×D151—42no—
86C22×D151C2×D411yescharacteristic
87Dic302—22no—
88Dic302—44no—
89Dic302—42no—
90Dic302—42no—
91D604—22no—
92C22⋊D151—42no—
93C2×Dic151—21no—
94C2×Dic151—22no—
95C2×Dic151C2×D411yescharacteristic
96C2×Dic151C2×D411yescharacteristic
97C2×Dic151C2×D411yescharacteristic
98C4×D151—22no—
99C4×D151—22no—
100C4×D151—42no—
101C4×D151—44no—
102C4×D151#4114yes—
103C151⋊C8—22no—
104C23×C151—21no—
105Q8×C151—22no—
106Q8×C151—42no—
107D4×C151—22no—
108C2×C4×C151—22no—
109C2×C4×C151—21no—
110C2×C4×C151C2×D411yescharacteristic
111C2×C4×C151C2×D411yescharacteristic
112C2×C4×C151C2411yescharacteristic
113C8×C151—22no—
114C22×C151—41no—
115C22×C151—41no—
116C22×C151—41no—
117C22×C151C22×D411yescharacteristic
118C2×D151—41no—
119C2×D151—41no—
120C2×D151—41no—
121C2×D151—84no—
122C2×D151#12412yes—
123C2×D151AGL(1,ℤ/8)12yes—
124C2×D151#13712yes—
125C4×C151—21no—
126C4×C151—21no—
127C4×C151—41no—
128C4×C151—42no—
129C4×C151C2×#4112yes—
130Dic151—21no—
131Dic151—21no—
132Dic151—41no—
133Dic151—42no—
134Dic151#12412yes—
135C2×C151—81no—
136C2×C151C2×#12411yescharacteristic
137C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C151C2×#13711yescharacteristic
139D151—81no—
140D151#48914yesdirect product factor
141C151C2×#48911yescharacteristic, complemented, Sylow
142C2×#489—1511nomaximal, Sylow
143C2×C4⋊Q8—1511no—
144C2×#124—1511no—
145#489—1511no—
146#489—1511no—
147#489—1512no—
148#489—1512no—
149#489—1511no—
150#489D15111yescharacteristic, direct product factor
151C2×#103—1512no—
152C2×#102—1512no—
153C2×#97—1511no—
154C22×Q8—3021no—
155C22×Q8—1511no—
156C22×D4—1511no—
157C22×C8—1512no—
158C4⋊Q8—3021no—
159C4⋊Q8—3021no—
160C4⋊Q8—1512no—
161C4⋊Q8—1511no—
162C4⋊Q8C2×D15111yescharacteristic, complemented
163#124—3021no—
164#124—3021no—
165#124—1511no—
166#124—1511no—
167#124—1511no—
168#124C2×D15111yescharacteristic
169C2×C4⋊C4—3021no—
170C2×C4⋊C4—1512no—
171C2×C22⋊C4—3021no—
172C2×C22⋊C4—3021no—
173C2×C42—1511no—
174#103—1512no—
175#103—1512no—
176#103—1512no—
177#103C2×D15112yescomplemented
178#102—1512no—
179#102—1512no—
180#102—1512no—
181#102C2×D15112yes—
182#97—1512no—
183#97—1511no—
184#97C2×D15111yescharacteristic, complemented
185C24—3021no—
186C2×Q8—21no—
187C2×Q8—3021no—
188C2×Q8—3022no—
189C2×Q8—3021no—
190C2×Q8—3024no—
191C2×Q8—6044no—
192C2×Q8—1511no—
193C2×Q8C22×D15111yescharacteristic
194C2×D4—3024no—
195C2×D4—3021no—
196C2×D4—1511no—
197C2×D4C22×D15111yescharacteristic
198C22×C4—3021no—
199C22×C4—3022no—
200C22×C4—1511no—
201C22×C4—1511no—
202C22×C4—1511no—
203C2×C8—3024no—
204C2×C8—1512no—
205C2×C8C22×D15112yes—
206C4⋊C4—21no—
207C4⋊C4—3022no—
208C4⋊C4—3022no—
209C4⋊C4—3021no—
210C4⋊C4—1512no—
211C4⋊C4C22×D15112yes—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—3021no—
215C22⋊C4—3021no—
216C22⋊C4—3021no—
217C22⋊C4—3021no—
218C22⋊C4—3021no—
219C22⋊C4—3021no—
220C42—1511no—
221C42—1511no—
222C42—1511no—
223C42C22×D15111yescharacteristic
224C23—21no—
225C23—3021no—
226C23—6042no—
227C23—6042no—
228C23—6042no—
229C23—1511no—
230Q8—22no—
231Q8—42no—
232Q8—3022no—
233Q8—6042no—
234Q8—6044no—
235Q8—6042no—
236D4—22no—
237D4—3022no—
238D4—6042no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—3022no—
242C2×C4—3022no—
243C2×C4—3021no—
244C2×C4—3022no—
245C2×C4—6042no—
246C2×C4—6044no—
247C2×C4—1511no—
248C2×C4—1511no—
249C2×C4—1511no—
250C2×C4—1514no—
251C2×C4D4×D15111yescharacteristic
252C2×C4D4×D15111yescharacteristic
253C2×C4C23×D15111yescharacteristic
254C8—22no—
255C8—3022no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—6041no—
260C22—6041no—
261C22—6041no—
262C22—1512no—
263C22—1512no—
264C22—1512no—
265C22—12084no—
266C22C2×D4×D15111yescharacteristic
267C4—21no—
268C4—21no—
269C4—41no—
270C4—42no—
271C4—3021no—
272C4—3021no—
273C4—6041no—
274C4—6042no—
275C4—1512no—
276C4#41×D15112yes—
277C2—81no—
278C2—1514no—
279C2—12081no—
280C2#124×D15111yescharacteristic
281C2AGL(1,ℤ/8)×D15111yescharacteristic
282C2#137×D15111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#489×C151C2
socleC22×C151C22×D4
prime radicalC2×D4×D151C22
hypercenter#489D151
hypocenterC151C2×#489
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D151C2semidirect
3. #23752574C2semidirect
4. #23752573C2semidirect
5. #23752572C2semidirect
6. #23752571C2semidirect
7. #23752570C2semidirect
8. #103×D151C2semidirect
10. #97×D151C2semidirect
11. #489×C151C2semidirect
16. #18012739C22semidirect
18. #18012738C22semidirect
30. #18012664C22semidirect
31. #18012663C22semidirect
32. #18012662C22semidirect
36. #18012650C22semidirect
37. #18012649C22semidirect
38. C4⋊Q8×C151C22semidirect
40. #103×C151C22semidirect
42. #97×C151C22semidirect
140. D151#489direct (N × H)
141. C151C2×#489semidirect
150. #489D151direct (N × H)
162. C4⋊Q8C2×D151semidirect
177. #103C2×D151semidirect
184. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D1512
#124×D1512
#237525742
#237525732
#237525722
#237525712
#237525702
#103×D1512
#102×D1512
#97×D1512
#489×C1512
C2×#489151