Finite Group Databasebeta

← #34080906

Subgroups — #34080906

Order 19328.

476 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 117 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#23753016C212yesmaximal, complemented
2#23753015C212yesmaximal, complemented
3#23752588C211yesmaximal, characteristic, complemented
4#23752481C212yesmaximal, complemented
5#23752480C212yesmaximal, complemented
6#23752381C212yesmaximal, complemented
7#23752379C211yesmaximal, characteristic, complemented
8#23752326C212yesmaximal, complemented
9#453×C151C211yesmaximal, characteristic, complemented
10#18012785C2212yescomplemented
11#18012784C2211yescharacteristic, complemented
12#18012767C2212yescomplemented
13#18012766—22no—
14#18012765—22no—
15#18012765C2212yescomplemented
16#18012764—22no—
17#18012764C2212yescomplemented
18#18012763—22no—
19#18012760—22no—
20#18012759—22no—
21#18012759C2212yes—
22C2×#14558989—22no—
23C2×#14558989C2212yescomplemented
24C2×#14558989C2212yescomplemented
25D8×D151—22no—
26#18012747C2212yescomplemented
27#18012746C2212yescomplemented
28#18012736C2211yescharacteristic, complemented
29#18012674C2212yescomplemented
30#18012667C2212yescomplemented
31#18012656C2211yescharacteristic, complemented
32#18012655C2212yescomplemented
33C4×C151⋊C8C2211yescharacteristic, complemented
34H(5,𝔽2)×C151C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C151C2212yescomplemented
36#127×C151C2211yescharacteristic, complemented
37#104×C151C2212yescomplemented
38#100×C151C2211yescharacteristic, complemented
39#14559005—22no—
40#14559004—22no—
41#14559004C2312yes—
42#14559003—22no—
43C2×D604—22no—
44C2×D604—41no—
45C2×D604C2312yes—
46C2×C22⋊D151—41no—
47D4×D151—22no—
48D4×D151—22no—
49D4×D151—42no—
50#14558994D412yescomplemented
51#14558993—22no—
52#14558992—22no—
53#14558992D412yescomplemented
54#14558991—22no—
55#14558991D412yescomplemented
56D1208—22no—
57#14558989—22no—
58#14558989—22no—
59#14558989—22no—
60#14558989—22no—
61#14558989—22no—
62#14558989—22no—
63#14558989D412yescomplemented
64#14558988—22no—
65#14558988C2312yes—
66#14558987—22no—
67C2×C151⋊C8—22no—
68C2×C151⋊C8C2312yes—
69C8×D151—22no—
70#41×C151—22no—
71#41×C151C2312yes—
72C2×D4×C151—22no—
73C2×D4×C151—41no—
74C2×D4×C151—41no—
75C2×D4×C151C2311yescharacteristic
76C2×D4×C151C2311yescharacteristic
77SD16×C151—22no—
78D8×C151—22no—
79M16×C151C2312yes—
80C42×C151C2311yescharacteristic
81C22×D151—22no—
82C22×D151—41no—
83C22×D151—42no—
84Dic302C2×D412yes—
85D604—22no—
86D604—22no—
87D604—42no—
88D604—82no—
89D604C2×D412yes—
90C22⋊D151—22no—
91C22⋊D151—42no—
92C22⋊D151—42no—
93C2×Dic151—41no—
94C4×D151—22no—
95C4×D151—42no—
96C151⋊C8—22no—
97C151⋊C8C2×D412yes—
98C151⋊C8C2×D412yes—
99C23×C151—21no—
100C23×C151—21no—
101C23×C151—41no—
102Q8×C151C2×D412yes—
103D4×C151—22no—
104D4×C151—22no—
105D4×C151—22no—
106D4×C151—42no—
107D4×C151—82no—
108D4×C151C2×D412yes—
109C2×C4×C151—21no—
110C2×C4×C151—22no—
111C2×C4×C151—41no—
112C2×C4×C151C2411yescharacteristic
113C8×C151—22no—
114C22×C151—22no—
115C22×C151—41no—
116C22×C151—41no—
117C22×C151—81no—
118C22×C151—81no—
119C22×C151—161no—
120C22×C151H(5,𝔽2)11yescharacteristic
121C2×D151—22no—
122C2×D151—42no—
123C2×D151—82no—
124C2×D151—161no—
125C2×D151—162no—
126C4×C151—22no—
127C4×C151—22no—
128C4×C151C22×D412yes—
129Dic151—22no—
130C2×C151—21no—
131C2×C151—42no—
132C2×C151—81no—
133C2×C151—81no—
134C2×C151D4211yescharacteristic
135D151—42no—
136D151—82no—
137C151#329211yescharacteristic, complemented, Sylow
138#3292—1511nomaximal, Sylow
139#576—1512no—
140#576—1512no—
141#493—1511no—
142#472—1512no—
143#472—1512no—
144#453—1511no—
145#453—1512no—
146#453D15111yescharacteristic, complemented
147#443—1512no—
148H(5,𝔽2)—1512no—
149H(5,𝔽2)—1511no—
150H(5,𝔽2)C2×D15111yescharacteristic, complemented
151AGL(1,ℤ/8)—3022no—
152AGL(1,ℤ/8)—3022no—
153AGL(1,ℤ/8)—3022no—
154AGL(1,ℤ/8)—3022no—
155AGL(1,ℤ/8)—1512no—
156AGL(1,ℤ/8)—1512no—
157AGL(1,ℤ/8)—1512no—
158AGL(1,ℤ/8)C2×D15112yescomplemented
159#135—3022no—
160#135—3022no—
161#135—1512no—
162C2×D8—3022no—
163C2×D8—3022no—
164C2×D8—1512no—
165C2×D8—1512no—
166#131—1512no—
167#131—1512no—
168#127—1511no—
169#127C2×D15111yescharacteristic, complemented
170#108—1512no—
171#104—1512no—
172#104C2×D15112yescomplemented
173#100—1511no—
174#100—1512no—
175#100C2×D15111yescharacteristic, complemented
176C4×C8—1511no—
177#41—22no—
178#41—3022no—
179#41—3022no—
180#41—3022no—
181#41—1512no—
182#41C22×D15112yes—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—3022no—
187C2×D4—3022no—
188C2×D4—3022no—
189C2×D4—6041no—
190C2×D4—6042no—
191C2×D4—6041no—
192C2×D4—1512no—
193C2×D4C22×D15111yescharacteristic
194C2×D4C22×D15111yescharacteristic
195Q16—1512no—
196SD16—22no—
197SD16—3022no—
198SD16—3022no—
199SD16—3022no—
200SD16—1512no—
201SD16—1512no—
202D8—22no—
203D8—3022no—
204D8—3022no—
205D8—3022no—
206D8—3022no—
207D8—3022no—
208D8—3022no—
209D8—3022no—
210D8—1512no—
211M16—3022no—
212M16—3022no—
213M16—1512no—
214M16C22×D15112yes—
215C2×C8—3022no—
216C2×C8—3022no—
217C2×C8—1512no—
218C42C22×D15111yescharacteristic
219C23—21no—
220C23—21no—
221C23—41no—
222C23—3022no—
223C23—6042no—
224C23—6041no—
225Q8—1512no—
226Q8D4×D15112yes—
227D4—22no—
228D4—22no—
229D4—22no—
230D4—42no—
231D4—82no—
232D4—3022no—
233D4—3022no—
234D4—3022no—
235D4—6042no—
236D4—6042no—
237D4—6042no—
238D4—1512no—
239D4—12082no—
240D4D4×D15112yes—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—3022no—
245C2×C4—6042no—
246C2×C4—6041no—
247C2×C4C23×D15111yescharacteristic
248C8—22no—
249C8—3022no—
250C8—1512no—
251C8—1512no—
252C22—22no—
253C22—41no—
254C22—41no—
255C22—81no—
256C22—81no—
257C22—161no—
258C22—3022no—
259C22—6042no—
260C22—24162no—
261C22—24161no—
262C22—12082no—
263C22#1801278411yescharacteristic
264C4—22no—
265C4—22no—
266C4—3022no—
267C4C2×D4×D15112yes—
268C2—21no—
269C2—42no—
270C2—81no—
271C2—81no—
272C2—6042no—
273C2—12082no—
274C2#2375284411yescharacteristic
subgroupG/H
centerC2#23752844
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#453×C151C2
socleC2×C151D42
hypercenter#453D151
hypocenterC151#3292
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #23753016C2semidirect
2. #23753015C2semidirect
3. #23752588C2semidirect
4. #23752481C2semidirect
5. #23752480C2semidirect
6. #23752381C2semidirect
7. #23752379C2semidirect
8. #23752326C2semidirect
9. #453×C151C2semidirect
10. #18012785C22semidirect
11. #18012784C22semidirect
12. #18012767C22semidirect
15. #18012765C22semidirect
17. #18012764C22semidirect
23. C2×#14558989C22semidirect
24. C2×#14558989C22semidirect
26. #18012747C22semidirect
27. #18012746C22semidirect
28. #18012736C22semidirect
29. #18012674C22semidirect
30. #18012667C22semidirect
31. #18012656C22semidirect
32. #18012655C22semidirect
33. C4×C151⋊C8C22semidirect
34. H(5,𝔽2)×C151C22semidirect
35. AGL(1,ℤ/8)×C151C22semidirect
36. #127×C151C22semidirect
37. #104×C151C22semidirect
38. #100×C151C22semidirect
50. #14558994D4semidirect
53. #14558992D4semidirect
55. #14558991D4semidirect
63. #14558989D4semidirect
137. C151#3292semidirect
146. #453D151semidirect
150. H(5,𝔽2)C2×D151semidirect
158. AGL(1,ℤ/8)C2×D151semidirect
169. #127C2×D151semidirect
172. #104C2×D151semidirect
175. #100C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530162
#237530152
#237525882
#237524812
#237524802
#237523812
#237523792
#237523262
#453×C1512
#3292151