Finite Group Databasebeta

← #34082253

Subgroups — #34082253

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#23753026C211yesmaximal, characteristic, complemented
2#23753014C211yesmaximal, characteristic, complemented
3#23752654C212yesmaximal, complemented
4#23752652C211yesmaximal, characteristic, complemented
5#23752647C211yesmaximal, characteristic, complemented
6#23752646C212yesmaximal, complemented
7#23752643C212yesmaximal, complemented
8C2×#18012684C211yesmaximal, characteristic, complemented
9SD32×D151C212yesmaximal, complemented
10#23752628C211yesmaximal, characteristic, complemented
11#508×C151C211yesmaximal, characteristic, complemented
12#18012786—21no—
13#18012785—21no—
14#18012769—21no—
15#18012768—22no—
16#18012766—22no—
17#18012764—21no—
18#18012762C2212yes—
19#18012758C2212yescomplemented
20C2×Dic604C2211yescharacteristic, complemented
21Q16×D151C2212yescomplemented
22C2×D1208C2211yescharacteristic
23D8×D151C2212yes—
24#18012745C2211yescharacteristic
25#18012685C2212yescomplemented
26#18012684C2212yescomplemented
27#18012684C2212yescomplemented
28#18012683C2212yescomplemented
29#18012682C2212yescomplemented
30#18012680C2212yescomplemented
31#18012679C2211yescharacteristic, complemented
32#18012678C2212yescomplemented
33C16×D151C2212yescomplemented
34#135×C151C2211yescharacteristic
35#135×C151C2211yescharacteristic, complemented
36Q32×C151C2211yescharacteristic, complemented
37SD32×C151C2211yescharacteristic, complemented
38SD32×C151C2211yescharacteristic, complemented
39D16×C151C2211yescharacteristic, complemented
40C2×C16×C151C2211yescharacteristic, complemented
41#14559005—22no—
42#14559004—41no—
43#14559004—41no—
44#14559004D411yescharacteristic
45#14559003—22no—
46#14559003—42no—
47C2×Dic302—21no—
48C2×Dic302—41no—
49Q8×D151—22no—
50C2×D604—21no—
51C2×D604—41no—
52D4×D151—22no—
53D4×D151—42no—
54Dic604—21no—
55Dic604C2312yes—
56#14558994—22no—
57#14558992—22no—
58#14558991—22no—
59D1208—21no—
60D1208C2312yes—
61#14558989—22no—
62#14558988D411yescharacteristic
63#14558987D412yes—
64C8×D151C2312yes—
65C151⋊C16C2312yes—
66#41×C151—21no—
67#41×C151—21no—
68Q16×C151C2311yescharacteristic
69Q16×C151C2311yescharacteristic
70SD16×C151—21no—
71SD16×C151—21no—
72D8×C151C2311yescharacteristic
73D8×C151C2311yescharacteristic
74C2×C8×C151C2311yescharacteristic
75C16×C151C2311yescharacteristic
76C16×C151C2311yescharacteristic
77C22×D151—41no—
78C22×D151—42no—
79Dic302—22no—
80Dic302—41no—
81Dic302—42no—
82Dic302D811yescharacteristic
83D604—22no—
84D604—42no—
85D604—41no—
86D604D811yescharacteristic
87C22⋊D151—42no—
88C22⋊D151—42no—
89C22⋊D151D812yes—
90C2×Dic151—41no—
91C2×Dic151—42no—
92C4×D151—42no—
93C4×D151—42no—
94C4×D151C2×D412yes—
95C151⋊C8C2×D412yes—
96Q8×C151—21no—
97Q8×C151—21no—
98D4×C151—21no—
99D4×C151—21no—
100D4×C151—41no—
101D4×C151—41no—
102C2×C4×C151—41no—
103C2×C4×C151—41no—
104C2×C4×C151C2×D411yescharacteristic
105C8×C151C2×D411yescharacteristic
106C8×C151C2411yescharacteristic
107C22×C151—41no—
108C22×C151—41no—
109C22×C151C2×D811yescharacteristic
110C2×D151—42no—
111C2×D151—162no—
112C2×D151—161no—
113C2×D151C2×D812yes—
114C4×C151—41no—
115C4×C151—41no—
116C4×C151C2×D811yescharacteristic
117C4×C151C22×D411yescharacteristic
118Dic151—42no—
119Dic151C2×D812yes—
120C2×C151—21no—
121C2×C151—81no—
122C2×C151—81no—
123C2×C151C22×D811yescharacteristic
124D151—22no—
125D151—82no—
126C151#341611yescharacteristic, complemented, Sylow
127#3416—1511nomaximal, Sylow
128#578—1511no—
129#576—1511no—
130#510—1511no—
131#510—1512no—
132#509—1511no—
133#509—1512no—
134#508—1512no—
135#508D15111yescharacteristic, complemented
136C2×SD32—1512no—
137C2×SD32—1511no—
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#135C2×D15111yescharacteristic
148#135C2×D15111yescharacteristic, complemented
149C2×Q16—1512no—
150C2×Q16—1511no—
151C2×D8—1512no—
152C2×D8—1511no—
153#131—1511no—
154Q32—1512no—
155Q32C2×D15111yescharacteristic, complemented
156SD32—1512no—
157SD32—1512no—
158SD32—1512no—
159SD32—1512no—
160SD32C2×D15111yescharacteristic, complemented
161SD32C2×D15111yescharacteristic, complemented
162D16—1512no—
163D16C2×D15111yescharacteristic, complemented
164M32—1511no—
165M32—1512no—
166C2×C16—1512no—
167C2×C16C2×D15111yescharacteristic, complemented
168#41—21no—
169#41—21no—
170#41—3022no—
171#41—3022no—
172#41—6041no—
173#41—6041no—
174#41—6042no—
175#41—1511no—
176C2×Q8—3022no—
177C2×Q8—3021no—
178C2×Q8—6041no—
179C2×D4—3022no—
180C2×D4—3021no—
181C2×D4—6041no—
182C2×D4—6042no—
183Q16—3022no—
184Q16—3021no—
185Q16—1512no—
186Q16C22×D15111yescharacteristic
187Q16C22×D15111yescharacteristic
188SD16—21no—
189SD16—21no—
190SD16—3022no—
191SD16—3022no—
192D8—3022no—
193D8—3021no—
194D8—1512no—
195D8C22×D15111yescharacteristic
196D8C22×D15111yescharacteristic
197M16—1511no—
198M16—1512no—
199C2×C8—1512no—
200C2×C8C22×D15111yescharacteristic
201C16—1512no—
202C16C22×D15111yescharacteristic
203C16C22×D15111yescharacteristic
204C23—6042no—
205C23—6041no—
206Q8—21no—
207Q8—21no—
208Q8—3022no—
209Q8—6042no—
210Q8—6041no—
211Q8—1511no—
212D4—21no—
213D4—21no—
214D4—41no—
215D4—41no—
216D4—3022no—
217D4—6042no—
218D4—6042no—
219D4—6042no—
220D4—6041no—
221D4—1512no—
222D4—1511no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—6042no—
226C2×C4—6042no—
227C2×C4—6041no—
228C2×C4—6042no—
229C2×C4—1512no—
230C2×C4D4×D15111yescharacteristic
231C8—1512no—
232C8D4×D15111yescharacteristic
233C8C23×D15111yescharacteristic
234C22—41no—
235C22—41no—
236C22—6042no—
237C22—24161no—
238C22—24162no—
239C22—1512no—
240C22D8×D15111yescharacteristic
241C4—41no—
242C4—41no—
243C4—6042no—
244C4—1512no—
245C4D8×D15111yescharacteristic
246C4C2×D4×D15111yescharacteristic
247C2—21no—
248C2—81no—
249C2—81no—
250C2—3022no—
251C2—12082no—
252C2C2×D8×D15111yescharacteristic
subgroupG/H
centerC2C2×D8×D151
commutator, cosocleC8×C151C24
FrattiniC8C23×D151
Fitting#508×C151C2
socleC2×C151C22×D8
hypercenter#508D151
hypocenterC151#3416
LCSG ▷ C8×C151 ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #508

Complements

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

NH ≅ G/Ntype
1. #23753026C2semidirect
2. #23753014C2semidirect
3. #23752654C2semidirect
4. #23752652C2semidirect
5. #23752647C2semidirect
6. #23752646C2semidirect
7. #23752643C2semidirect
8. C2×#18012684C2semidirect
9. SD32×D151C2semidirect
10. #23752628C2semidirect
11. #508×C151C2semidirect
19. #18012758C22semidirect
20. C2×Dic604C22semidirect
21. Q16×D151C22semidirect
25. #18012685C22semidirect
26. #18012684C22semidirect
27. #18012684C22semidirect
28. #18012683C22semidirect
29. #18012682C22semidirect
30. #18012680C22semidirect
31. #18012679C22semidirect
32. #18012678C22semidirect
33. C16×D151C22semidirect
35. #135×C151C22semidirect
36. Q32×C151C22semidirect
37. SD32×C151C22semidirect
38. SD32×C151C22semidirect
39. D16×C151C22semidirect
40. C2×C16×C151C22semidirect
126. C151#3416semidirect
135. #508D151semidirect
148. #135C2×D151semidirect
155. Q32C2×D151semidirect
160. SD32C2×D151semidirect
161. SD32C2×D151semidirect
163. D16C2×D151semidirect
167. C2×C16C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530262
#237530142
#237526542
#237526522
#237526472
#237526462
#237526432
C2×#180126842
SD32×D1512
#237526282
#508×C1512
#3416151