Finite Group Databasebeta

← #34080900

Subgroups — #34080900

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#23753021C212yesmaximal, complemented
2#23753020C212yesmaximal, complemented
3#23752586C211yesmaximal, characteristic, complemented
4#23752478C212yesmaximal, complemented
5#23752477C212yesmaximal, complemented
6#23752394C211yesmaximal, characteristic, complemented
7#23752381C212yesmaximal, complemented
8#23752326C212yesmaximal, complemented
9#456×C151C211yesmaximal, characteristic, complemented
10#18012787C2211yescharacteristic
11#18012785C2212yescomplemented
12#18012771—22no—
13#18012770—22no—
14#18012770C2212yescomplemented
15#18012767C2212yes—
16#18012766—22no—
17#18012764—22no—
18#18012764C2212yes—
19#18012762—22no—
20#18012759—22no—
21#18012759C2212yes—
22C2×#14558991—22no—
23C2×#14558991C2212yescomplemented
24C2×#14558991C2212yescomplemented
25SD16×D151—22no—
26#18012747C2212yescomplemented
27#18012746C2212yescomplemented
28#18012736C2211yescharacteristic
29#18012674C2212yescomplemented
30#18012667C2212yescomplemented
31#18012658C2211yescharacteristic, complemented
32#18012655C2212yescomplemented
33C4×C151⋊C8C2211yescharacteristic, complemented
342−1+4×C151C2211yescharacteristic
35#137×C151C2212yescomplemented
36C4⋊Q8×C151C2211yescharacteristic, complemented
37#104×C151C2212yescomplemented
38#101×C151C2211yescharacteristic, complemented
39#14559005—22no—
40#14559005—22no—
41#14559004—22no—
42#14559004—41no—
43#14559004C2312yes—
44Q8×D151—22no—
45C2×D604—22no—
46C2×D604—41no—
47C2×D604C2312yes—
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#14558991—22no—
59#14558991—22no—
60#14558991D412yescomplemented
61D1208—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×Q8×C151C2311yescharacteristic
76Q16×C151—22no—
77SD16×C151—22no—
78M16×C151C2312yes—
79C4⋊C4×C151—41no—
80C42×C151C2311yescharacteristic
81C22×D151—22no—
82C22×D151—42no—
83Dic302—41no—
84Dic302C2×D412yes—
85D604—22no—
86D604—22no—
87D604—42no—
88D604—41no—
89D604—82no—
90D604C2×D412yes—
91C22⋊D151—22no—
92C22⋊D151—42no—
93C4×D151—22no—
94C4×D151—42no—
95C4×D151—42no—
96C151⋊C8—22no—
97C151⋊C8C2×D412yes—
98C151⋊C8C2×D412yes—
99Q8×C151—22no—
100Q8×C151—22no—
101Q8×C151—41no—
102Q8×C151C2×D412yes—
103D4×C151—22no—
104D4×C151—41no—
105D4×C151C2×D412yes—
106C2×C4×C151—21no—
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×C151H(5,𝔽2)11yescharacteristic
115C2×D151—22no—
116C2×D151—42no—
117C2×D151—82no—
118C2×D151—162no—
119C4×C151—22no—
120C4×C151—22no—
121C4×C151—41no—
122C4×C151—41no—
123C4×C151C22×D412yes—
124Dic151—22no—
125C2×C151—21no—
126C2×C151—42no—
127C2×C151D4211yescharacteristic
128D151—42no—
129D151—82no—
130C151#329111yescharacteristic, complemented, Sylow
131#3291—1511nomaximal, Sylow
132#577—1512no—
133#577—1512no—
134#492—1511no—
135#471—1512no—
136#471—1512no—
137#456—1511no—
138#456D15111yescharacteristic, complemented
139#453—1512no—
140#443—1512no—
1412−1+4—1511no—
1422−1+4C2×D15111yescharacteristic
143H(5,𝔽2)—1512no—
144#137—3022no—
145#137—3022no—
146#137—1512no—
147#137C2×D15112yescomplemented
148AGL(1,ℤ/8)—3022no—
149AGL(1,ℤ/8)—3022no—
150AGL(1,ℤ/8)—1512no—
151AGL(1,ℤ/8)—1512no—
152#135—3022no—
153#135—3022no—
154#135—1512no—
155C2×SD16—3022no—
156C2×SD16—3022no—
157C2×SD16—1512no—
158C2×SD16—1512no—
159#131—1512no—
160#131—1512no—
161C4⋊Q8C2×D15111yescharacteristic, complemented
162#127—1511no—
163#108—1512no—
164#104—1512no—
165#104C2×D15112yescomplemented
166#101—1511no—
167#101C2×D15111yescharacteristic, complemented
168#100—1512no—
169C4×C8—1511no—
170#41—22no—
171#41—41no—
172#41—3022no—
173#41—3022no—
174#41—3022no—
175#41—6041no—
176#41—1512no—
177#41C22×D15112yes—
178C2×Q8—22no—
179C2×Q8—3022no—
180C2×Q8C22×D15111yescharacteristic
181C2×Q8C22×D15111yescharacteristic
182C2×D4—3022no—
183C2×D4—3022no—
184C2×D4—6041no—
185C2×D4—6042no—
186C2×D4—1512no—
187Q16—22no—
188Q16—3022no—
189Q16—1512no—
190SD16—22no—
191SD16—3022no—
192SD16—3022no—
193SD16—3022no—
194SD16—3022no—
195SD16—3022no—
196SD16—3022no—
197SD16—3022no—
198SD16—1512no—
199SD16—1512no—
200D8—3022no—
201D8—3022no—
202D8—1512no—
203M16—3022no—
204M16—3022no—
205M16—1512no—
206M16C22×D15112yes—
207C2×C8—3022no—
208C2×C8—3022no—
209C2×C8—1512no—
210C4⋊C4—41no—
211C42C22×D15111yescharacteristic
212C23—3022no—
213C23—6042no—
214Q8—22no—
215Q8—22no—
216Q8—41no—
217Q8—6041no—
218Q8—1512no—
219Q8D4×D15112yes—
220D4—22no—
221D4—41no—
222D4—3022no—
223D4—3022no—
224D4—3022no—
225D4—6042no—
226D4—6041no—
227D4—6042no—
228D4—1512no—
229D4—12082no—
230D4D4×D15112yes—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—3022no—
237C2×C4—6042no—
238C2×C4—6042no—
239C2×C4C23×D15111yescharacteristic
240C8—22no—
241C8—3022no—
242C8—1512no—
243C8—1512no—
244C22—22no—
245C22—3022no—
246C22—6042no—
247C22—24162no—
248C22—12082no—
249C22#1801278411yescharacteristic
250C4—22no—
251C4—22no—
252C4—41no—
253C4—41no—
254C4—3022no—
255C4C2×D4×D15112yes—
256C2—21no—
257C2—42no—
258C2—6042no—
259C2—12082no—
260C2#2375284411yescharacteristic
subgroupG/H
centerC2#23752844
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#456×C151C2
socleC2×C151D42
hypercenter#456D151
hypocenterC151#3291
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #23753021C2semidirect
2. #23753020C2semidirect
3. #23752586C2semidirect
4. #23752478C2semidirect
5. #23752477C2semidirect
6. #23752394C2semidirect
7. #23752381C2semidirect
8. #23752326C2semidirect
9. #456×C151C2semidirect
11. #18012785C22semidirect
14. #18012770C22semidirect
23. C2×#14558991C22semidirect
24. C2×#14558991C22semidirect
26. #18012747C22semidirect
27. #18012746C22semidirect
29. #18012674C22semidirect
30. #18012667C22semidirect
31. #18012658C22semidirect
32. #18012655C22semidirect
33. C4×C151⋊C8C22semidirect
35. #137×C151C22semidirect
36. C4⋊Q8×C151C22semidirect
37. #104×C151C22semidirect
38. #101×C151C22semidirect
51. #14558994D4semidirect
53. #14558992D4semidirect
60. #14558991D4semidirect
63. #14558989D4semidirect
130. C151#3291semidirect
138. #456D151semidirect
147. #137C2×D151semidirect
161. C4⋊Q8C2×D151semidirect
165. #104C2×D151semidirect
167. #101C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530212
#237530202
#237525862
#237524782
#237524772
#237523942
#237523812
#237523262
#456×C1512
#3291151