Finite Group Databasebeta

← #442×D151 #34077899

Subgroups — #442×D151 #34077899

Order 19328.

608 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 183 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×D8×D151C211yesmaximal, characteristic
2C4×D4×D151C212yesmaximal, complemented
3#23752325C211yesmaximal, characteristic, complemented
4#23752324C211yesmaximal, characteristic, complemented
5#23752323C211yesmaximal, characteristic, complemented
6#23752322C212yesmaximal, complemented
7#23752321C212yesmaximal, complemented
8#106×D151C211yesmaximal, characteristic, complemented
9#102×D151C212yesmaximal, complemented
10#97×D151C211yesmaximal, characteristic, complemented
11#442×C151C211yesmaximal, characteristic, complemented
12C2×D4×D151C2212yes—
13C22×C4×D151—22no—
14C2×D1208C2211yescharacteristic
15C2×#14558989C2212yes—
16D8×D151C418yescomplemented
17C2×C8×D151C2211yescharacteristic
18C2×C8×D151C2211yescharacteristic
19C4×D604C2212yescomplemented
20D4×Dic151C2212yescomplemented
21#18012701C2212yescomplemented
22C4×C22⋊D151—22no—
23(C22⋊D151)⋊C4—22no—
24C4⋊C4×D151C2212yes—
25C22⋊C4×D151—22no—
26C42×D151C2211yescharacteristic
27#18012671C2211yescharacteristic, complemented
28#18012670C2212yescomplemented
29#18012661C2212yescomplemented
30#18012660C2212yescomplemented
31#18012659C2212yescomplemented
32#18012650C2211yescharacteristic, complemented
33#18012649C2211yescharacteristic, complemented
34#18012649C2211yescharacteristic, complemented
35C2×D8×C151C2211yescharacteristic
36C4×D4×C151C2212yescomplemented
37#106×C151C2211yescharacteristic, complemented
38#102×C151C2212yescomplemented
39#97×C151C2211yescharacteristic, complemented
40C23×D151—22no—
41C2×D604C2312yes—
42C2×C22⋊D151—22no—
43D4×D151—24no—
44D4×D151C2×C418yescomplemented
45C22×Dic151—22no—
46C2×C4×D151—22no—
47C2×C4×D151—22no—
48C2×C4×D151—22no—
49C2×C4×D151—48no—
50C2×C4×D151D412yes—
51C2×C4×D151C2311yescharacteristic
52D1208C2×C414yescomplemented
53#14558989C2×C418yescomplemented
54C2×C151⋊C8C2311yescharacteristic
55C2×C151⋊C8C2311yescharacteristic
56C8×D151—22no—
57C8×D151C2×C414yescomplemented
58C4⋊Dic151C2312yes—
59Dic151⋊C4—22no—
60C22⋊Dic151—22no—
61(C2×D151)⋊C4—22no—
62(C2×D151)⋊C4—22no—
63C4×Dic151D412yes—
64C4×Dic151C2311yescharacteristic
65C2×D4×C151C2312yes—
66C22×C4×C151—22no—
67D8×C151C2×C414yescomplemented
68C2×C8×C151C2311yescharacteristic
69C2×C8×C151C2311yescharacteristic
70C4⋊C4×C151C2312yes—
71C22⋊C4×C151—22no—
72C42×C151C2311yescharacteristic
73C22×D151—22no—
74C22×D151—28no—
75C22×D151—44no—
76C22×D151—44no—
77C22×D151C2×D411yescharacteristic
78D604—22no—
79D604C22×C414yescomplemented
80C22⋊D151—28no—
81C2×Dic151—22no—
82C2×Dic151—44no—
83C2×Dic151C2×D412yes—
84C2×Dic151C2×D411yescharacteristic
85C4×D151—24no—
86C4×D151—44no—
87C4×D151—44no—
88C4×D151—44no—
89C4×D151C22×C412yes—
90C4×D151#4112yes—
91C151⋊C8—21no—
92C151⋊C8C22×C412yescomplemented
93C23×C151—22no—
94D4×C151—22no—
95D4×C151C22×C414yescomplemented
96C2×C4×C151—22no—
97C2×C4×C151—44no—
98C2×C4×C151C2×D412yes—
99C2×C4×C151C2411yescharacteristic
100C8×C151—21no—
101C8×C151C22×C412yescomplemented
102C22×C151—24no—
103C22×C151—42no—
104C22×C151—42no—
105C22×C151C22×D411yescharacteristic
106C2×D151—24no—
107C2×D151—42no—
108C2×D151—42no—
109C2×D151—416no—
110C2×D151C4×D412yes—
111C2×D151AGL(1,ℤ/8)14yes—
112C4×C151—22no—
113C4×C151—42no—
114C4×C151C23×C411yescharacteristic
115C4×C151C2×#4111yescharacteristic
116Dic151—22no—
117Dic151—42no—
118Dic151C4×D412yes—
119C2×C151—44no—
120C2×C151C2×C4×D411yescharacteristic
121C2×C151C2×AGL(1,ℤ/8)12yes—
122D151—44no—
123D151#44214yesdirect product factor
124C151C2×#44211yescharacteristic, complemented, Sylow
125C2×#442—1511nomaximal, Sylow
126C22×D8—1511no—
127C2×C4×D4—1512no—
128#442—1511no—
129#442—1512no—
130#442—1511no—
131#442—1512no—
132#442—1511no—
133#442D15111yescharacteristic, direct product factor
134C2×#106—1511no—
135C2×#102—1512no—
136C2×#97—1511no—
137C22×D4—1512no—
138C23×C4—3022no—
139C2×D8—1512no—
140C2×D8—1518no—
141C2×D8—1511no—
142C2×D8C2×D15111yescharacteristic
143C22×C8—1511no—
144C22×C8—1511no—
145C4×D4—3022no—
146C4×D4—3022no—
147C4×D4—1512no—
148C4×D4—1512no—
149C4×D4—1512no—
150C4×D4C2×D15112yescomplemented
151C2×C4⋊C4—1512no—
152C2×C22⋊C4—3022no—
153C2×C42—1511no—
154#106—1511no—
155#106—1512no—
156#106C2×D15111yescharacteristic, complemented
157#102—1512no—
158#102—1512no—
159#102—1512no—
160#102C2×D15112yescomplemented
161#97—1511no—
162#97—1511no—
163#97—1511no—
164#97C2×D15111yescharacteristic, complemented
165C24—3022no—
166C2×D4—3024no—
167C2×D4—3022no—
168C2×D4—1518no—
169C2×D4—1512no—
170C2×D4C22×D15112yes—
171C22×C4—22no—
172C22×C4—3022no—
173C22×C4—3022no—
174C22×C4—3022no—
175C22×C4—3022no—
176C22×C4—6048no—
177C22×C4—1512no—
178C22×C4—1511no—
179D8—1518no—
180D8—1514no—
181D8C4×D15114yescomplemented
182C2×C8—3022no—
183C2×C8—1511no—
184C2×C8—1511no—
185C2×C8—1514no—
186C2×C8C22×D15111yescharacteristic
187C2×C8C22×D15111yescharacteristic
188C4⋊C4—3022no—
189C4⋊C4—1512no—
190C4⋊C4C22×D15112yes—
191C22⋊C4—22no—
192C22⋊C4—3022no—
193C22⋊C4—3022no—
194C22⋊C4—3022no—
195C42—1512no—
196C42—1511no—
197C42C22×D15111yescharacteristic
198C23—22no—
199C23—3028no—
200C23—3022no—
201C23—6044no—
202C23—6044no—
203C23—1511no—
204D4—22no—
205D4—3028no—
206D4—3022no—
207D4—1514no—
208D4C2×C4×D15114yescomplemented
209C2×C4—22no—
210C2×C4—44no—
211C2×C4—3024no—
212C2×C4—3022no—
213C2×C4—6044no—
214C2×C4—6044no—
215C2×C4—6044no—
216C2×C4—6044no—
217C2×C4—1512no—
218C2×C4—1511no—
219C2×C4—1512no—
220C2×C4—1512no—
221C2×C4D4×D15112yes—
222C2×C4C23×D15111yescharacteristic
223C8—21no—
224C8—3021no—
225C8—1512no—
226C8C2×C4×D15112yescomplemented
227C22—24no—
228C22—42no—
229C22—42no—
230C22—3024no—
231C22—60416no—
232C22—6042no—
233C22—6042no—
234C22—1514no—
235C22—1512no—
236C22C2×D4×D15111yescharacteristic
237C4—22no—
238C4—42no—
239C4—3022no—
240C4—6042no—
241C4—1512no—
242C4C22×C4×D15111yescharacteristic
243C4#41×D15111yescharacteristic
244C2—44no—
245C2—6044no—
246C2—1514no—
247C2C4×D4×D15111yescharacteristic
248C2AGL(1,ℤ/8)×D15112yes—
subgroupG/H
centerC22C2×D4×D151
commutatorC4×C151C23×C4
FrattiniC2×C4C23×D151
Fitting#442×C151C2
socleC22×C151C22×D4
prime radicalC2×D8×D151C2
cosocleC2×C4×C151C24
hypercenter#442D151
hypocenterC151C2×#442
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. C4×D4×D151C2semidirect
3. #23752325C2semidirect
4. #23752324C2semidirect
5. #23752323C2semidirect
6. #23752322C2semidirect
7. #23752321C2semidirect
8. #106×D151C2semidirect
9. #102×D151C2semidirect
10. #97×D151C2semidirect
11. #442×C151C2semidirect
16. D8×D151C4semidirect
19. C4×D604C22semidirect
20. D4×Dic151C22semidirect
21. #18012701C22semidirect
27. #18012671C22semidirect
28. #18012670C22semidirect
29. #18012661C22semidirect
30. #18012660C22semidirect
31. #18012659C22semidirect
32. #18012650C22semidirect
33. #18012649C22semidirect
34. #18012649C22semidirect
36. C4×D4×C151C22semidirect
37. #106×C151C22semidirect
38. #102×C151C22semidirect
39. #97×C151C22semidirect
44. D4×D151C2×C4semidirect
52. D1208C2×C4semidirect
53. #14558989C2×C4semidirect
57. C8×D151C2×C4semidirect
67. D8×C151C2×C4semidirect
79. D604C22×C4semidirect
92. C151⋊C8C22×C4semidirect
95. D4×C151C22×C4semidirect
101. C8×C151C22×C4semidirect
123. D151#442direct (N × H)
124. C151C2×#442semidirect
133. #442D151direct (N × H)
150. C4×D4C2×D151semidirect
156. #106C2×D151semidirect
160. #102C2×D151semidirect
164. #97C2×D151semidirect
181. D8C4×D151semidirect
208. D4C2×C4×D151semidirect
226. C8C2×C4×D151semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1512
C4×D4×D1512
#237523252
#237523242
#237523232
#237523222
#237523212
#106×D1512
#102×D1512
#97×D1512
#442×C1512
C2×#442151