Finite Group Databasebeta

← #34080905

Subgroups — #34080905

Order 19328.

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

normal subgroups only

This group has 460 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#23753023C212yesmaximal, complemented
2#23753022C212yesmaximal, complemented
3#23752584C211yesmaximal, characteristic, complemented
4#23752474C212yesmaximal, complemented
5#23752473C212yesmaximal, complemented
6#23752396C212yesmaximal, complemented
7#23752379C211yesmaximal, characteristic, complemented
8#23752326C212yesmaximal, complemented
9#453×C151C211yesmaximal, characteristic, complemented
10#18012786C2212yes—
11#18012784C2211yescharacteristic, complemented
12#18012772C2212yescomplemented
13#18012769—22no—
14#18012769C2212yescomplemented
15#18012768—22no—
16#18012765—22no—
17#18012765C2212yes—
18#18012763—22no—
19#18012759—22no—
20#18012759C2212yes—
21#18012758—22no—
22C2×#14558992—22no—
23C2×#14558992C2212yescomplemented
24C2×#14558992C2212yescomplemented
25SD16×D151—22no—
26#18012747C2212yescomplemented
27#18012746C2212yescomplemented
28#18012739C2211yescharacteristic, complemented
29#18012674C2212yescomplemented
30#18012667C2212yescomplemented
31#18012657C2212yescomplemented
32#18012656C2211yescharacteristic, complemented
33C4×C151⋊C8C2211yescharacteristic, complemented
34H(5,𝔽2)×C151C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C151C2212yes—
36#127×C151C2211yescharacteristic
37#104×C151C2212yescomplemented
38#100×C151C2211yescharacteristic, complemented
39#14559004—22no—
40#14559004C2312yes—
41#14559003—22no—
42#14559003—22no—
43#14559003—42no—
44C2×Dic302—22no—
45C2×Dic302C2312yes—
46Q8×D151—22no—
47C2×C22⋊D151—41no—
48D4×D151—22no—
49Dic604—22no—
50#14558994—22no—
51#14558994D412yescomplemented
52#14558993—22no—
53#14558992—22no—
54#14558992—22no—
55#14558992—22no—
56#14558992—22no—
57#14558992—22no—
58#14558992—22no—
59#14558992D412yescomplemented
60#14558991D412yescomplemented
61#14558989—22no—
62#14558989D412yescomplemented
63#14558988—22no—
64#14558988C2312yes—
65#14558987—22no—
66C2×C151⋊C8—22no—
67C2×C151⋊C8C2312yes—
68C8×D151—22no—
69C4⋊Dic151—41no—
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—41no—
82Dic302—22no—
83Dic302—22no—
84Dic302—42no—
85Dic302C2×D412yes—
86D604C2×D412yes—
87C22⋊D151—22no—
88C22⋊D151—42no—
89C22⋊D151—42no—
90C2×Dic151—22no—
91C2×Dic151—41no—
92C2×Dic151—42no—
93C4×D151—22no—
94C4×D151—42no—
95C151⋊C8—22no—
96C151⋊C8C2×D412yes—
97C151⋊C8C2×D412yes—
98C23×C151—21no—
99C23×C151—21no—
100C23×C151—41no—
101Q8×C151C2×D412yes—
102D4×C151—22no—
103D4×C151—22no—
104D4×C151—22no—
105D4×C151—42no—
106D4×C151—82no—
107D4×C151C2×D412yes—
108C2×C4×C151—21no—
109C2×C4×C151—22no—
110C2×C4×C151—41no—
111C2×C4×C151C2411yescharacteristic
112C8×C151—22no—
113C22×C151—22no—
114C22×C151—41no—
115C22×C151—41no—
116C22×C151—81no—
117C22×C151—81no—
118C22×C151—161no—
119C22×C151H(5,𝔽2)11yescharacteristic
120C2×D151—22no—
121C2×D151—161no—
122C4×C151—22no—
123C4×C151—22no—
124C4×C151C22×D412yes—
125Dic151—22no—
126Dic151—42no—
127C2×C151—21no—
128C2×C151—42no—
129C2×C151—81no—
130C2×C151—81no—
131C2×C151D4211yescharacteristic
132D151—42no—
133C151#329111yescharacteristic, complemented, Sylow
134#3291—1511nomaximal, Sylow
135#577—1512no—
136#577—1512no—
137#492—1511no—
138#471—1512no—
139#471—1512no—
140#456—1512no—
141#453—1511no—
142#453D15111yescharacteristic, complemented
143#443—1512no—
1442−1+4—1512no—
145H(5,𝔽2)—1511no—
146H(5,𝔽2)C2×D15111yescharacteristic, complemented
147#137—3022no—
148#137—3022no—
149#137—1512no—
150#137—1512no—
151AGL(1,ℤ/8)—3022no—
152AGL(1,ℤ/8)—3022no—
153AGL(1,ℤ/8)—1512no—
154AGL(1,ℤ/8)C2×D15112yes—
155#135—3022no—
156#135—3022no—
157#135—1512no—
158C2×SD16—3022no—
159C2×SD16—3022no—
160C2×SD16—1512no—
161C2×SD16—1512no—
162#131—1512no—
163#131—1512no—
164C4⋊Q8—1511no—
165#127C2×D15111yescharacteristic
166#108—1512no—
167#104—1512no—
168#104C2×D15112yescomplemented
169#101—1512no—
170#100—1511no—
171#100C2×D15111yescharacteristic, complemented
172C4×C8—1511no—
173#41—22no—
174#41—3022no—
175#41—3022no—
176#41—3022no—
177#41—6042no—
178#41—1512no—
179#41C22×D15112yes—
180C2×Q8—3022no—
181C2×Q8—3022no—
182C2×Q8—1512no—
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C2×D4—3022no—
187C2×D4—6041no—
188C2×D4C22×D15111yescharacteristic
189C2×D4C22×D15111yescharacteristic
190Q16—3022no—
191Q16—3022no—
192Q16—1512no—
193SD16—22no—
194SD16—3022no—
195SD16—3022no—
196SD16—3022no—
197SD16—3022no—
198SD16—3022no—
199SD16—3022no—
200SD16—3022no—
201SD16—1512no—
202SD16—1512no—
203D8—22no—
204D8—3022no—
205D8—1512no—
206M16—3022no—
207M16—3022no—
208M16—1512no—
209M16C22×D15112yes—
210C2×C8—3022no—
211C2×C8—3022no—
212C2×C8—1512no—
213C4⋊C4—6041no—
214C42C22×D15111yescharacteristic
215C23—21no—
216C23—21no—
217C23—41no—
218C23—6041no—
219Q8—3022no—
220Q8—3022no—
221Q8—6042no—
222Q8—1512no—
223Q8D4×D15112yes—
224D4—22no—
225D4—22no—
226D4—22no—
227D4—42no—
228D4—82no—
229D4—3022no—
230D4—6042no—
231D4—6042no—
232D4—1512no—
233D4D4×D15112yes—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—3022no—
238C2×C4—3022no—
239C2×C4—6042no—
240C2×C4—6041no—
241C2×C4—6042no—
242C2×C4C23×D15111yescharacteristic
243C8—22no—
244C8—3022no—
245C8—1512no—
246C8—1512no—
247C22—22no—
248C22—41no—
249C22—41no—
250C22—81no—
251C22—81no—
252C22—161no—
253C22—3022no—
254C22—24161no—
255C22#1801278411yescharacteristic
256C4—22no—
257C4—22no—
258C4—3022no—
259C4—6042no—
260C4C2×D4×D15112yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—81no—
265C2—6042no—
266C2#2375284411yescharacteristic
subgroupG/H
centerC2#23752844
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#453×C151C2
socleC2×C151D42
hypercenter#453D151
hypocenterC151#3291
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. #23753023C2semidirect
2. #23753022C2semidirect
3. #23752584C2semidirect
4. #23752474C2semidirect
5. #23752473C2semidirect
6. #23752396C2semidirect
7. #23752379C2semidirect
8. #23752326C2semidirect
9. #453×C151C2semidirect
11. #18012784C22semidirect
12. #18012772C22semidirect
14. #18012769C22semidirect
23. C2×#14558992C22semidirect
24. C2×#14558992C22semidirect
26. #18012747C22semidirect
27. #18012746C22semidirect
28. #18012739C22semidirect
29. #18012674C22semidirect
30. #18012667C22semidirect
31. #18012657C22semidirect
32. #18012656C22semidirect
33. C4×C151⋊C8C22semidirect
34. H(5,𝔽2)×C151C22semidirect
37. #104×C151C22semidirect
38. #100×C151C22semidirect
51. #14558994D4semidirect
59. #14558992D4semidirect
60. #14558991D4semidirect
62. #14558989D4semidirect
133. C151#3291semidirect
142. #453D151semidirect
146. H(5,𝔽2)C2×D151semidirect
168. #104C2×D151semidirect
171. #100C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530232
#237530222
#237525842
#237524742
#237524732
#237523962
#237523792
#237523262
#453×C1512
#3291151