Finite Group Databasebeta

← #34080876

Subgroups — #34080876

Order 19328.

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

normal subgroups only

This group has 464 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#23753018C212yesmaximal, complemented
2#23753013C212yesmaximal, complemented
3#23752479C212yesmaximal, complemented
4#23752472C212yesmaximal, complemented
5#23752389C211yesmaximal, characteristic, complemented
6#23752384C211yesmaximal, characteristic, complemented
7#23752379C212yesmaximal, complemented
8#23752335C212yesmaximal, complemented
9#496×C151C211yesmaximal, characteristic, complemented
10#18012787C2211yescharacteristic, complemented
11#18012784C2211yescharacteristic
12#18012784C2212yescomplemented
13#18012770C2212yescomplemented
14#18012768—22no—
15#18012766—22no—
16#18012765C2212yes—
17#18012765C2212yescomplemented
18#18012765C2212yescomplemented
19#18012763—22no—
20#18012763—22no—
21#18012761C2212yes—
22#18012760—22no—
23#18012758—22no—
24SD16×D151—22no—
25D8×D151—22no—
26#18012745C2212yescomplemented
27#18012745C2212yescomplemented
28#18012675C2212yescomplemented
29#18012667C2212yescomplemented
30#18012667C2212yescomplemented
31#18012658C2211yescharacteristic, complemented
32#18012656C2212yescomplemented
33#18012656C2211yescharacteristic, complemented
34C2×SD16×C151C2212yescomplemented
35C2×D8×C151C2212yescomplemented
36#127×C151C2211yescharacteristic, complemented
37#124×C151C2211yescharacteristic, complemented
38#97×C151C2211yescharacteristic, complemented
39#14559005—22no—
40#14559004—41no—
41#14559004C2312yes—
42#14559004C2312yes—
43#14559003—22no—
44#14559003—22no—
45#14559003—22no—
46Q8×D151—22no—
47C2×C22⋊D151—41no—
48C2×C22⋊D151—42no—
49D4×D151—22no—
50D4×D151—22no—
51D4×D151—22no—
52Dic604D412yescomplemented
53#14558994—22no—
54#14558993D412yescomplemented
55#14558993D412yescomplemented
56#14558992—22no—
57#14558992—22no—
58#14558992—22no—
59#14558991—22no—
60D1208D412yescomplemented
61#14558989—22no—
62#14558989—22no—
63#14558989—22no—
64#14558988C2312yes—
65#14558988C2312yes—
66#14558987—22no—
67#14558987—22no—
68C8×D151—22no—
69C8×D151—22no—
70C2×Q8×C151C2311yescharacteristic
71C2×D4×C151—41no—
72C2×D4×C151C2312yes—
73C2×D4×C151C2311yescharacteristic
74SD16×C151—22no—
75SD16×C151—22no—
76D8×C151—22no—
77D8×C151—22no—
78C2×C8×C151C2312yes—
79C22⋊C4×C151—41no—
80C42×C151C2311yescharacteristic
81C22×D151—42no—
82C22×D151—41no—
83Dic302—41no—
84Dic302C2×D412yes—
85Dic302C2×D412yes—
86D604—41no—
87D604C2×D412yes—
88D604C2×D412yes—
89C22⋊D151—22no—
90C22⋊D151—22no—
91C22⋊D151—42no—
92C22⋊D151—42no—
93C22⋊D151—42no—
94C2×Dic151—42no—
95C2×Dic151—41no—
96C4×D151—22no—
97C4×D151—22no—
98C4×D151—42no—
99C151⋊C8—22no—
100C151⋊C8—22no—
101C23×C151—21no—
102C23×C151—22no—
103Q8×C151—22no—
104D4×C151—22no—
105D4×C151—22no—
106D4×C151—22no—
107D4×C151—82no—
108C2×C4×C151—21no—
109C2×C4×C151—21no—
110C2×C4×C151C2411yescharacteristic
111C8×C151C2×D412yes—
112C8×C151C2×D412yes—
113C22×C151—41no—
114C22×C151—42no—
115C22×C151—82no—
116C22×C151—81no—
117C22×C151H(5,𝔽2)11yescharacteristic
118C2×D151—22no—
119C2×D151—22no—
120C2×D151—162no—
121C2×D151—161no—
122C4×C151—41no—
123C4×C151—41no—
124C4×C151C22×D412yes—
125Dic151—22no—
126Dic151—22no—
127C2×C151—21no—
128C2×C151—82no—
129C2×C151—81no—
130C2×C151D4211yescharacteristic
131D151—42no—
132D151—42no—
133C151#328811yescharacteristic, complemented, Sylow
134#3288—1511nomaximal, Sylow
135#577—1512no—
136#576—1512no—
137#496D15111yescharacteristic, complemented
138#472—1512no—
139#471—1512no—
140#455—1511no—
141#454—1511no—
142#453—1512no—
143#444—1512no—
1442−1+4—1511no—
145H(5,𝔽2)—1511no—
146H(5,𝔽2)—1512no—
147#137—3022no—
148#137—1512no—
149AGL(1,ℤ/8)—3022no—
150AGL(1,ℤ/8)—3022no—
151AGL(1,ℤ/8)—3022no—
152AGL(1,ℤ/8)—1512no—
153AGL(1,ℤ/8)—1512no—
154AGL(1,ℤ/8)—1512no—
155#135—3022no—
156#135—3022no—
157#135—1512no—
158C2×SD16—3022no—
159C2×SD16C2×D15112yescomplemented
160C2×D8—3022no—
161C2×D8C2×D15112yescomplemented
162#131—1512no—
163#131—1512no—
164#127C2×D15111yescharacteristic, complemented
165#124C2×D15111yescharacteristic, complemented
166#108—1512no—
167#104—1512no—
168#104—1512no—
169#101—1511no—
170#100—1512no—
171#100—1511no—
172#97C2×D15111yescharacteristic, complemented
173#41—3022no—
174#41—3022no—
175#41—3022no—
176#41—3022no—
177#41—6041no—
178#41—1512no—
179#41—1512no—
180C2×Q8—3022no—
181C2×Q8C22×D15111yescharacteristic
182C2×D4—41no—
183C2×D4—3022no—
184C2×D4—3022no—
185C2×D4—3022no—
186C2×D4—6041no—
187C2×D4—6042no—
188C2×D4C22×D15111yescharacteristic
189C2×D4C22×D15112yes—
190Q16—3022no—
191Q16—1512no—
192SD16—22no—
193SD16—22no—
194SD16—3022no—
195SD16—3022no—
196SD16—3022no—
197SD16—3022no—
198SD16—1512no—
199SD16—1512no—
200D8—22no—
201D8—22no—
202D8—3022no—
203D8—3022no—
204D8—3022no—
205D8—1512no—
206M16—3022no—
207M16—3022no—
208M16—1512no—
209M16—1512no—
210C2×C8—3022no—
211C2×C8—3022no—
212C2×C8C22×D15112yes—
213C22⋊C4—41no—
214C42C22×D15111yescharacteristic
215C23—21no—
216C23—22no—
217C23—6042no—
218C23—6041no—
219Q8—22no—
220Q8—6041no—
221Q8—1512no—
222Q8—1512no—
223D4—22no—
224D4—22no—
225D4—22no—
226D4—82no—
227D4—3022no—
228D4—3022no—
229D4—6041no—
230D4—6042no—
231D4—6042no—
232D4—6042no—
233D4—1512no—
234D4—1512no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—3022no—
238C2×C4—3022no—
239C2×C4—6042no—
240C2×C4—6041no—
241C2×C4—6042no—
242C2×C4C23×D15111yescharacteristic
243C8—3022no—
244C8—3022no—
245C8D4×D15112yes—
246C8D4×D15112yes—
247C22—41no—
248C22—42no—
249C22—82no—
250C22—81no—
251C22—3022no—
252C22—3022no—
253C22—24161no—
254C22—24162no—
255C22#1801278411yescharacteristic
256C4—41no—
257C4—41no—
258C4—3022no—
259C4—3022no—
260C4C2×D4×D15112yes—
261C2—21no—
262C2—82no—
263C2—81no—
264C2—6042no—
265C2—6042no—
266C2#2375284711yescharacteristic
subgroupG/H
centerC2#23752847
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#496×C151C2
socleC2×C151D42
hypercenter#496D151
hypocenterC151#3288
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #23753018C2semidirect
2. #23753013C2semidirect
3. #23752479C2semidirect
4. #23752472C2semidirect
5. #23752389C2semidirect
6. #23752384C2semidirect
7. #23752379C2semidirect
8. #23752335C2semidirect
9. #496×C151C2semidirect
10. #18012787C22semidirect
12. #18012784C22semidirect
13. #18012770C22semidirect
17. #18012765C22semidirect
18. #18012765C22semidirect
26. #18012745C22semidirect
27. #18012745C22semidirect
28. #18012675C22semidirect
29. #18012667C22semidirect
30. #18012667C22semidirect
31. #18012658C22semidirect
32. #18012656C22semidirect
33. #18012656C22semidirect
34. C2×SD16×C151C22semidirect
35. C2×D8×C151C22semidirect
36. #127×C151C22semidirect
37. #124×C151C22semidirect
38. #97×C151C22semidirect
52. Dic604D4semidirect
54. #14558993D4semidirect
55. #14558993D4semidirect
60. D1208D4semidirect
133. C151#3288semidirect
137. #496D151semidirect
159. C2×SD16C2×D151semidirect
161. C2×D8C2×D151semidirect
164. #127C2×D151semidirect
165. #124C2×D151semidirect
172. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530182
#237530132
#237524792
#237524722
#237523892
#237523842
#237523792
#237523352
#496×C1512
#3288151