Finite Group Databasebeta

← #34082250

Subgroups — #34082250

Order 19328.

370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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#23753014C211yesmaximal, characteristic, complemented
2#23753013C211yesmaximal, characteristic, complemented
3#23752650C211yesmaximal, characteristic, complemented
4#23752649C212yesmaximal, complemented
5#23752646C212yesmaximal, complemented
6#23752643C212yesmaximal, complemented
7#23752642C211yesmaximal, characteristic, complemented
8C2×#18012680C211yesmaximal, characteristic, complemented
9D16×D151C212yesmaximal, complemented
10#23752630C211yesmaximal, characteristic, complemented
11#509×C151C211yesmaximal, characteristic, complemented
12#18012785—21no—
13#18012784—21no—
14#18012766—22no—
15#18012765—21no—
16#18012764—21no—
17#18012763—22no—
18#18012762C2212yescomplemented
19#18012761C2211yescharacteristic, complemented
20#18012758C2212yescomplemented
21C2×D1208C2211yescharacteristic, complemented
22D8×D151C2212yescomplemented
23D8×D151C2212yescomplemented
24#18012745C2211yescharacteristic
25#18012685C2211yescharacteristic, complemented
26#18012684C2212yescomplemented
27#18012683C2211yescharacteristic, complemented
28#18012682C2211yescharacteristic, complemented
29D2416C2212yescomplemented
30#18012680C2211yescharacteristic, complemented
31#18012680C2212yescomplemented
32#18012680C2212yescomplemented
33#18012678C2212yescomplemented
34C2×C151⋊C16C2211yescharacteristic, complemented
35C16×D151C2212yescomplemented
36#135×C151C2211yescharacteristic, complemented
37C2×D8×C151C2211yescharacteristic, complemented
38SD32×C151C2212yescomplemented
39D16×C151C2212yescomplemented
40M32×C151C2211yescharacteristic, complemented
41#14559005—22no—
42#14559004—21no—
43#14559004—41no—
44#14559004D411yescharacteristic
45#14559003—22no—
46#14559003—41no—
47C2×D604—21no—
48C2×D604—41no—
49C2×C22⋊D151—42no—
50D4×D151—22no—
51D4×D151—22no—
52D4×D151—41no—
53D4×D151—42no—
54Dic604C2311yescharacteristic
55#14558993—21no—
56#14558992—22no—
57#14558991—22no—
58D1208—21no—
59D1208C2312yes—
60D1208C2311yescharacteristic
61#14558989—22no—
62#14558989—22no—
63#14558988D411yescharacteristic
64#14558987D412yes—
65C8×D151C2312yes—
66C151⋊C16C2311yescharacteristic
67C151⋊C16C2311yescharacteristic
68#41×C151—21no—
69C2×D4×C151—21no—
70Q16×C151C2311yescharacteristic
71SD16×C151—21no—
72D8×C151—21no—
73D8×C151C2312yes—
74D8×C151C2311yescharacteristic
75C2×C8×C151C2311yescharacteristic
76C16×C151C2312yes—
77C22×D151—41no—
78C22×D151—42no—
79C22×D151—42no—
80Dic302—21no—
81Dic302D811yescharacteristic
82D604—21no—
83D604—22no—
84D604—42no—
85D604—41no—
86D604D811yescharacteristic
87C22⋊D151—41no—
88C22⋊D151—42no—
89C22⋊D151—42no—
90C22⋊D151—42no—
91C22⋊D151D812yes—
92C2×Dic151—42no—
93C4×D151—41no—
94C4×D151—42no—
95C4×D151C2×D412yes—
96C151⋊C8C2×D412yes—
97C23×C151—41no—
98Q8×C151—21no—
99D4×C151—21no—
100D4×C151—22no—
101D4×C151—41no—
102D4×C151—41no—
103C2×C4×C151—41no—
104C2×C4×C151C2×D411yescharacteristic
105C8×C151C2×D411yescharacteristic
106C8×C151C2411yescharacteristic
107C22×C151—41no—
108C22×C151—42no—
109C22×C151—161no—
110C22×C151C2×D811yescharacteristic
111C2×D151—41no—
112C2×D151—42no—
113C2×D151—162no—
114C2×D151—162no—
115C2×D151—161no—
116C2×D151C2×D812yes—
117C4×C151—41no—
118C4×C151C2×D811yescharacteristic
119C4×C151C22×D411yescharacteristic
120Dic151—41no—
121Dic151C2×D812yes—
122C2×C151—21no—
123C2×C151—81no—
124C2×C151—82no—
125C2×C151C22×D811yescharacteristic
126D151—22no—
127D151—81no—
128D151—82no—
129C151#341511yescharacteristic, complemented, Sylow
130#3415—1511nomaximal, Sylow
131#576—1511no—
132#576—1511no—
133#509—1512no—
134#509—1512no—
135#509—1511no—
136#509D15111yescharacteristic, complemented
137#508—1511no—
138#508—1512no—
139C2×D16—1511no—
140C2×D16—1512no—
141#504—1511no—
142H(5,𝔽2)—3021no—
143H(5,𝔽2)—3021no—
144AGL(1,ℤ/8)—3022no—
145AGL(1,ℤ/8)—3022no—
146AGL(1,ℤ/8)—3021no—
147AGL(1,ℤ/8)—3021no—
148#135—1512no—
149#135—1512no—
150#135—1511no—
151#135C2×D15111yescharacteristic, complemented
152C2×D8—1512no—
153C2×D8—1512no—
154C2×D8—1511no—
155C2×D8C2×D15111yescharacteristic, complemented
156#131—1511no—
157Q32—1511no—
158SD32—1511no—
159SD32—1511no—
160SD32—1512no—
161SD32C2×D15112yescomplemented
162D16—1512no—
163D16—1511no—
164D16—1512no—
165D16—1512no—
166D16C2×D15112yescomplemented
167M32—1512no—
168M32C2×D15111yescharacteristic, complemented
169C2×C16—1511no—
170C2×C16—1512no—
171#41—21no—
172#41—3022no—
173#41—3022no—
174#41—3021no—
175#41—6041no—
176#41—6041no—
177#41—1511no—
178C2×D4—21no—
179C2×D4—3022no—
180C2×D4—3022no—
181C2×D4—3021no—
182C2×D4—6041no—
183C2×D4—6042no—
184C2×D4—6041no—
185C2×D4—6042no—
186Q16—1511no—
187Q16C22×D15111yescharacteristic
188SD16—21no—
189SD16—3022no—
190SD16—3022no—
191SD16—3021no—
192D8—21no—
193D8—3022no—
194D8—3022no—
195D8—3021no—
196D8—1512no—
197D8—1511no—
198D8C22×D15112yes—
199D8C22×D15111yescharacteristic
200M16—1511no—
201M16—1512no—
202C2×C8—1512no—
203C2×C8C22×D15111yescharacteristic
204C16—1511no—
205C16—1511no—
206C16C22×D15112yes—
207C23—41no—
208C23—6042no—
209C23—6042no—
210C23—6041no—
211Q8—21no—
212Q8—3021no—
213Q8—1511no—
214D4—22no—
215D4—21no—
216D4—41no—
217D4—41no—
218D4—3021no—
219D4—3022no—
220D4—6042no—
221D4—6042no—
222D4—6041no—
223D4—6042no—
224D4—6042no—
225D4—6041no—
226D4—1512no—
227D4—1511no—
228C2×C4—41no—
229C2×C4—6042no—
230C2×C4—6042no—
231C2×C4—6041no—
232C2×C4—1512no—
233C2×C4D4×D15111yescharacteristic
234C8—1512no—
235C8D4×D15111yescharacteristic
236C8C23×D15111yescharacteristic
237C22—41no—
238C22—42no—
239C22—161no—
240C22—6042no—
241C22—6041no—
242C22—24161no—
243C22—24162no—
244C22—24162no—
245C22—1512no—
246C22D8×D15111yescharacteristic
247C4—41no—
248C4—6041no—
249C4—1512no—
250C4D8×D15111yescharacteristic
251C4C2×D4×D15111yescharacteristic
252C2—21no—
253C2—82no—
254C2—81no—
255C2—3022no—
256C2—12082no—
257C2—12081no—
258C2C2×D8×D15111yescharacteristic
subgroupG/H
centerC2C2×D8×D151
commutator, cosocleC8×C151C24
FrattiniC8C23×D151
Fitting#509×C151C2
socleC2×C151C22×D8
hypercenter#509D151
hypocenterC151#3415
LCSG ▷ C8×C151 ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #23753014C2semidirect
2. #23753013C2semidirect
3. #23752650C2semidirect
4. #23752649C2semidirect
5. #23752646C2semidirect
6. #23752643C2semidirect
7. #23752642C2semidirect
8. C2×#18012680C2semidirect
9. D16×D151C2semidirect
10. #23752630C2semidirect
11. #509×C151C2semidirect
18. #18012762C22semidirect
19. #18012761C22semidirect
20. #18012758C22semidirect
21. C2×D1208C22semidirect
22. D8×D151C22semidirect
23. D8×D151C22semidirect
25. #18012685C22semidirect
26. #18012684C22semidirect
27. #18012683C22semidirect
28. #18012682C22semidirect
29. D2416C22semidirect
30. #18012680C22semidirect
31. #18012680C22semidirect
32. #18012680C22semidirect
33. #18012678C22semidirect
34. C2×C151⋊C16C22semidirect
35. C16×D151C22semidirect
36. #135×C151C22semidirect
37. C2×D8×C151C22semidirect
38. SD32×C151C22semidirect
39. D16×C151C22semidirect
40. M32×C151C22semidirect
129. C151#3415semidirect
136. #509D151semidirect
151. #135C2×D151semidirect
155. C2×D8C2×D151semidirect
161. SD32C2×D151semidirect
166. D16C2×D151semidirect
168. M32C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530142
#237530132
#237526502
#237526492
#237526462
#237526432
#237526422
C2×#180126802
D16×D1512
#237526302
#509×C1512
#3415151