Finite Group Databasebeta

← #34082255

Subgroups — #34082255

Order 19328.

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

normal subgroups only

This group has 360 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#23753025C211yesmaximal, characteristic, complemented
2#23753014C211yesmaximal, characteristic, complemented
3#23752654C212yesmaximal, complemented
4#23752650C211yesmaximal, characteristic, complemented
5#23752649C212yesmaximal, complemented
6#23752645C212yesmaximal, complemented
7#23752642C211yesmaximal, characteristic, complemented
8C2×#18012682C211yesmaximal, characteristic, complemented
9SD32×D151C212yesmaximal, complemented
10#23752630C211yesmaximal, characteristic, complemented
11#510×C151C211yesmaximal, characteristic, complemented
12#18012787—21no—
13#18012785—21no—
14#18012771—22no—
15#18012770—21no—
16#18012766—22no—
17#18012764—21no—
18#18012762C2212yes—
19#18012762C2212yescomplemented
20#18012761C2211yescharacteristic, complemented
21Q16×D151C2212yescomplemented
22C2×D1208C2211yescharacteristic
23D8×D151C2212yes—
24#18012745C2211yescharacteristic
25#18012685C2211yescharacteristic, complemented
26#18012684C2212yescomplemented
27#18012683C2211yescharacteristic, complemented
28#18012682C2212yescomplemented
29#18012682C2212yescomplemented
30#18012682C2211yescharacteristic, complemented
31D2416C2212yescomplemented
32#18012680C2211yescharacteristic, complemented
33#18012678C2212yescomplemented
34C2×C151⋊C16C2211yescharacteristic, complemented
35C16×D151C2212yescomplemented
36#135×C151C2211yescharacteristic
37C2×Q16×C151C2211yescharacteristic, complemented
38Q32×C151C2212yescomplemented
39SD32×C151C2212yescomplemented
40M32×C151C2211yescharacteristic, complemented
41#14559005—22no—
42#14559005—22no—
43#14559005—41no—
44#14559004—21no—
45#14559004—41no—
46#14559004—42no—
47#14559004D411yescharacteristic
48Q8×D151—22no—
49Q8×D151—41no—
50C2×D604—21no—
51C2×D604—41no—
52D4×D151—22no—
53D4×D151—42no—
54Dic604C2311yescharacteristic
55#14558994—22no—
56#14558993—21no—
57#14558991—22no—
58#14558991—22no—
59D1208—21no—
60D1208C2311yescharacteristic
61D1208C2312yes—
62#14558989—22no—
63#14558988D411yescharacteristic
64#14558987D412yes—
65C8×D151C2312yes—
66C151⋊C16C2311yescharacteristic
67C151⋊C16C2311yescharacteristic
68#41×C151—21no—
69C2×Q8×C151—21no—
70Q16×C151—21no—
71Q16×C151C2312yes—
72Q16×C151C2311yescharacteristic
73SD16×C151—21no—
74D8×C151C2311yescharacteristic
75C2×C8×C151C2311yescharacteristic
76C16×C151C2312yes—
77C22×D151—41no—
78C22×D151—42no—
79Dic302—21no—
80Dic302—42no—
81Dic302D811yescharacteristic
82D604—22no—
83D604—21no—
84D604—42no—
85D604—42no—
86D604—41no—
87D604D811yescharacteristic
88C22⋊D151—41no—
89C22⋊D151—42no—
90C22⋊D151D812yes—
91C4×D151—42no—
92C4×D151—41no—
93C4×D151—42no—
94C4×D151—42no—
95C4×D151C2×D412yes—
96C151⋊C8C2×D412yes—
97Q8×C151—22no—
98Q8×C151—21no—
99Q8×C151—41no—
100D4×C151—21no—
101D4×C151—41no—
102C2×C4×C151—41no—
103C2×C4×C151—41no—
104C2×C4×C151C2×D411yescharacteristic
105C8×C151C2×D411yescharacteristic
106C8×C151C2411yescharacteristic
107C22×C151—41no—
108C22×C151C2×D811yescharacteristic
109C2×D151—41no—
110C2×D151—42no—
111C2×D151—162no—
112C2×D151—161no—
113C2×D151C2×D812yes—
114C4×C151—41no—
115C4×C151—42no—
116C4×C151C2×D811yescharacteristic
117C4×C151C22×D411yescharacteristic
118Dic151—41no—
119Dic151C2×D812yes—
120C2×C151—21no—
121C2×C151—81no—
122C2×C151C22×D811yescharacteristic
123D151—22no—
124D151—81no—
125D151—82no—
126C151#341611yescharacteristic, complemented, Sylow
127#3416—1511nomaximal, Sylow
128#578—1511no—
129#576—1511no—
130#510—1512no—
131#510D15111yescharacteristic, complemented
132#509—1512no—
133#509—1511no—
134#508—1511no—
135#508—1512no—
136C2×SD32—1511no—
137C2×SD32—1512no—
138#504—1511no—
1392−1+4—3021no—
140H(5,𝔽2)—3021no—
141#137—3022no—
142#137—3021no—
143AGL(1,ℤ/8)—3022no—
144AGL(1,ℤ/8)—3021no—
145#135—1512no—
146#135—1512no—
147#135—1511no—
148#135C2×D15111yescharacteristic
149C2×Q16—1512no—
150C2×Q16C2×D15111yescharacteristic, complemented
151C2×D8—1512no—
152C2×D8—1511no—
153#131—1511no—
154Q32—1511no—
155Q32C2×D15112yescomplemented
156SD32—1512no—
157SD32—1512no—
158SD32—1511no—
159SD32—1511no—
160SD32—1512no—
161SD32C2×D15112yescomplemented
162D16—1511no—
163D16—1512no—
164M32—1512no—
165M32C2×D15111yescharacteristic, complemented
166C2×C16—1511no—
167C2×C16—1512no—
168#41—21no—
169#41—3022no—
170#41—3022no—
171#41—3021no—
172#41—6041no—
173#41—6042no—
174#41—6041no—
175#41—1511no—
176C2×Q8—21no—
177C2×Q8—3022no—
178C2×Q8—6041no—
179C2×D4—3022no—
180C2×D4—3021no—
181C2×D4—6041no—
182C2×D4—6042no—
183Q16—21no—
184Q16—3022no—
185Q16—1511no—
186Q16C22×D15112yes—
187Q16C22×D15111yescharacteristic
188SD16—21no—
189SD16—3022no—
190SD16—3022no—
191SD16—3021no—
192D8—3022no—
193D8—3021no—
194D8—1511no—
195D8—1512no—
196D8C22×D15111yescharacteristic
197M16—1511no—
198M16—1512no—
199C2×C8—1512no—
200C2×C8C22×D15111yescharacteristic
201C16—1511no—
202C16—1511no—
203C16C22×D15112yes—
204C23—6042no—
205C23—6041no—
206Q8—21no—
207Q8—22no—
208Q8—41no—
209Q8—3021no—
210Q8—6042no—
211Q8—1511no—
212D4—21no—
213D4—41no—
214D4—3022no—
215D4—3021no—
216D4—6042no—
217D4—6042no—
218D4—6041no—
219D4—6042no—
220D4—6041no—
221D4—1512no—
222D4—1511no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—6042no—
226C2×C4—6042no—
227C2×C4—6042no—
228C2×C4—6041no—
229C2×C4—1512no—
230C2×C4D4×D15111yescharacteristic
231C8—1512no—
232C8D4×D15111yescharacteristic
233C8C23×D15111yescharacteristic
234C22—41no—
235C22—6041no—
236C22—6042no—
237C22—24161no—
238C22—24162no—
239C22—1512no—
240C22D8×D15111yescharacteristic
241C4—41no—
242C4—42no—
243C4—6041no—
244C4—1512no—
245C4D8×D15111yescharacteristic
246C4C2×D4×D15111yescharacteristic
247C2—21no—
248C2—81no—
249C2—3022no—
250C2—12082no—
251C2—12081no—
252C2C2×D8×D15111yescharacteristic
subgroupG/H
centerC2C2×D8×D151
commutator, cosocleC8×C151C24
FrattiniC8C23×D151
Fitting#510×C151C2
socleC2×C151C22×D8
hypercenter#510D151
hypocenterC151#3416
LCSG ▷ C8×C151 ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
1. #23753025C2semidirect
2. #23753014C2semidirect
3. #23752654C2semidirect
4. #23752650C2semidirect
5. #23752649C2semidirect
6. #23752645C2semidirect
7. #23752642C2semidirect
8. C2×#18012682C2semidirect
9. SD32×D151C2semidirect
10. #23752630C2semidirect
11. #510×C151C2semidirect
19. #18012762C22semidirect
20. #18012761C22semidirect
21. Q16×D151C22semidirect
25. #18012685C22semidirect
26. #18012684C22semidirect
27. #18012683C22semidirect
28. #18012682C22semidirect
29. #18012682C22semidirect
30. #18012682C22semidirect
31. D2416C22semidirect
32. #18012680C22semidirect
33. #18012678C22semidirect
34. C2×C151⋊C16C22semidirect
35. C16×D151C22semidirect
37. C2×Q16×C151C22semidirect
38. Q32×C151C22semidirect
39. SD32×C151C22semidirect
40. M32×C151C22semidirect
126. C151#3416semidirect
131. #510D151semidirect
150. C2×Q16C2×D151semidirect
155. Q32C2×D151semidirect
161. SD32C2×D151semidirect
165. M32C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530252
#237530142
#237526542
#237526502
#237526492
#237526452
#237526422
C2×#180126822
SD32×D1512
#237526302
#510×C1512
#3416151