Finite Group Databasebeta

← #34080878

Subgroups — #34080878

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#23753020C212yesmaximal, complemented
2#23753016C212yesmaximal, complemented
3#23752602C211yesmaximal, characteristic, complemented
4#23752480C212yesmaximal, complemented
5#23752478C212yesmaximal, complemented
6#23752389C211yesmaximal, characteristic, complemented
7#23752381C212yesmaximal, complemented
8#23752331C212yesmaximal, complemented
9#454×C151C211yesmaximal, characteristic, complemented
10#18012785C2212yescomplemented
11#18012784C2211yescharacteristic
12#18012770—22no—
13#18012770C2212yescomplemented
14#18012767C2212yes—
15#18012766—22no—
16#18012764—22no—
17#18012764C2212yescomplemented
18#18012763—22no—
19#18012760—22no—
20#18012759—22no—
21#18012759C2212yes—
22C2×#14558991—22no—
23C2×#14558991C2212yescomplemented
24C2×#14558989C2212yescomplemented
25D8×D151—22no—
26#18012747C2212yescomplemented
27#18012746C2212yescomplemented
28#18012736C2211yescharacteristic, complemented
29#18012674C2212yescomplemented
30#18012667C2212yescomplemented
31#18012656C2211yescharacteristic, complemented
32#18012655C2212yescomplemented
33#18012650C2211yescharacteristic, complemented
342−1+4×C151C2211yescharacteristic, complemented
35AGL(1,ℤ/8)×C151C2212yescomplemented
36#124×C151C2211yescharacteristic, complemented
37#104×C151C2212yescomplemented
38#101×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#14558994—22no—
51#14558994D412yescomplemented
52#14558993—22no—
53#14558992D412yescomplemented
54#14558991—22no—
55#14558991—22no—
56#14558991—22no—
57#14558991—22no—
58#14558991D412yescomplemented
59D1208—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×C151—41no—
72#41×C151C2312yes—
73C2×Q8×C151—22no—
74C2×Q8×C151C2311yescharacteristic
75C2×D4×C151C2311yescharacteristic
76SD16×C151—22no—
77D8×C151—22no—
78M16×C151C2312yes—
79C22⋊C4×C151—41no—
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—
100Q8×C151—22no—
101Q8×C151—41no—
102Q8×C151C2×D412yes—
103D4×C151—22no—
104D4×C151—22no—
105D4×C151—41no—
106D4×C151C2×D412yes—
107C2×C4×C151—22no—
108C2×C4×C151—21no—
109C2×C4×C151—21no—
110C2×C4×C151—42no—
111C2×C4×C151C2411yescharacteristic
112C8×C151—22no—
113C22×C151—22no—
114C22×C151—41no—
115C22×C151—81no—
116C22×C151H(5,𝔽2)11yescharacteristic
117C2×D151—22no—
118C2×D151—42no—
119C2×D151—82no—
120C2×D151—161no—
121C2×D151—162no—
122C4×C151—22no—
123C4×C151—41no—
124C4×C151—41no—
125C4×C151C22×D412yes—
126Dic151—22no—
127C2×C151—21no—
128C2×C151—42no—
129C2×C151—81no—
130C2×C151D4211yescharacteristic
131D151—42no—
132D151—82no—
133C151#328811yescharacteristic, complemented, Sylow
134#3288—1511nomaximal, Sylow
135#577—1512no—
136#576—1512no—
137#496—1511no—
138#472—1512no—
139#471—1512no—
140#455—1511no—
141#454D15111yescharacteristic, complemented
142#453—1512no—
143#444—1512no—
1442−1+4C2×D15111yescharacteristic, complemented
145H(5,𝔽2)—1512no—
146H(5,𝔽2)—1511no—
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)C2×D15112yescomplemented
155#135—3022no—
156#135—3022no—
157#135—1512no—
158C2×SD16—3022no—
159C2×SD16—1512no—
160C2×D8—3022no—
161C2×D8—1512no—
162#131—1512no—
163#131—1512no—
164#127—1511no—
165#124C2×D15111yescharacteristic, complemented
166#108—1512no—
167#104—1512no—
168#104C2×D15112yescomplemented
169#101C2×D15111yescharacteristic, complemented
170#100—1511no—
171#100—1512no—
172#97—1511no—
173#41—22no—
174#41—41no—
175#41—3022no—
176#41—3022no—
177#41—3022no—
178#41—1512no—
179#41C22×D15112yes—
180C2×Q8—22no—
181C2×Q8C22×D15111yescharacteristic
182C2×D4—3022no—
183C2×D4—3022no—
184C2×D4—3022no—
185C2×D4—6041no—
186C2×D4—6042no—
187C2×D4—6041no—
188C2×D4—1512no—
189C2×D4C22×D15111yescharacteristic
190Q16—3022no—
191Q16—1512no—
192SD16—22no—
193SD16—3022no—
194SD16—3022no—
195SD16—3022no—
196SD16—3022no—
197SD16—3022no—
198SD16—1512no—
199SD16—1512no—
200D8—22no—
201D8—3022no—
202D8—3022no—
203D8—3022no—
204D8—3022no—
205D8—1512no—
206M16—3022no—
207M16—3022no—
208M16—1512no—
209M16C22×D15112yes—
210C2×C8—3022no—
211C2×C8—3022no—
212C2×C8—1512no—
213C22⋊C4—41no—
214C42C22×D15111yescharacteristic
215C23—21no—
216C23—3022no—
217C23—6042no—
218C23—6041no—
219Q8—22no—
220Q8—41no—
221Q8—1512no—
222Q8D4×D15112yes—
223D4—22no—
224D4—22no—
225D4—41no—
226D4—3022no—
227D4—3022no—
228D4—3022no—
229D4—6042no—
230D4—6042no—
231D4—6042no—
232D4—1512no—
233D4—12082no—
234D4D4×D15112yes—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—42no—
239C2×C4—3022no—
240C2×C4—6042no—
241C2×C4—6041no—
242C2×C4C23×D15111yescharacteristic
243C8—22no—
244C8—3022no—
245C8—1512no—
246C8—1512no—
247C22—22no—
248C22—41no—
249C22—81no—
250C22—3022no—
251C22—6042no—
252C22—24162no—
253C22—24161no—
254C22—12082no—
255C22#1801278411yescharacteristic
256C4—22no—
257C4—41no—
258C4—41no—
259C4—3022no—
260C4C2×D4×D15112yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—6042no—
265C2—12082no—
266C2#2375284411yescharacteristic
subgroupG/H
centerC2#23752844
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#454×C151C2
socleC2×C151D42
hypercenter#454D151
hypocenterC151#3288
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #23753020C2semidirect
2. #23753016C2semidirect
3. #23752602C2semidirect
4. #23752480C2semidirect
5. #23752478C2semidirect
6. #23752389C2semidirect
7. #23752381C2semidirect
8. #23752331C2semidirect
9. #454×C151C2semidirect
10. #18012785C22semidirect
13. #18012770C22semidirect
17. #18012764C22semidirect
23. C2×#14558991C22semidirect
24. C2×#14558989C22semidirect
26. #18012747C22semidirect
27. #18012746C22semidirect
28. #18012736C22semidirect
29. #18012674C22semidirect
30. #18012667C22semidirect
31. #18012656C22semidirect
32. #18012655C22semidirect
33. #18012650C22semidirect
34. 2−1+4×C151C22semidirect
35. AGL(1,ℤ/8)×C151C22semidirect
36. #124×C151C22semidirect
37. #104×C151C22semidirect
38. #101×C151C22semidirect
51. #14558994D4semidirect
53. #14558992D4semidirect
58. #14558991D4semidirect
63. #14558989D4semidirect
133. C151#3288semidirect
141. #454D151semidirect
144. 2−1+4C2×D151semidirect
154. AGL(1,ℤ/8)C2×D151semidirect
165. #124C2×D151semidirect
168. #104C2×D151semidirect
169. #101C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530202
#237530162
#237526022
#237524802
#237524782
#237523892
#237523812
#237523312
#454×C1512
#3288151