Finite Group Databasebeta

← #34080154

Subgroups — #34080154

Order 19328.

420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 420 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#23752781C211yesmaximal, characteristic, complemented
2#23752599C211yesmaximal, characteristic, complemented
3#23752588C211yesmaximal, characteristic, complemented
4#23752578C211yesmaximal, characteristic, complemented
5#23752569C211yesmaximal, characteristic, complemented
6#23752427C212yesmaximal, complemented
7#23752407C212yesmaximal, complemented
8#23752355C212yesmaximal, complemented
9#23752345C212yesmaximal, complemented
10#23752273C211yesmaximal, characteristic, complemented
11#540×C151C211yesmaximal, characteristic, complemented
12C2×#14559004C2211yescharacteristic
13C22×D604C2211yescharacteristic
14C2×#14558992C2212yescomplemented
15C2×#14558989C2212yes—
16C2×#14558989C2212yes—
17C2×#14558989C2212yescomplemented
18#18012736C2211yescharacteristic
19#18012736C2211yescharacteristic
20#18012727C2211yescharacteristic
21#18012727C2211yescharacteristic
22#18012714—22no—
23#18012709—22no—
24C4⋊(C151⋊C8)C2212yescomplemented
25#18012662C2212yescomplemented
26#18012659C2212yes—
27#18012659C2212yes—
28#18012659C2212yescomplemented
29C22⋊(C151⋊C8)C2212yes—
30#18012650C2211yescharacteristic, complemented
31C4×C151⋊C8C2211yescharacteristic, complemented
32#127×C151C2211yescharacteristic, complemented
33#125×C151C2211yescharacteristic, complemented
34#123×C151—22no—
35#121×C151—22no—
36#121×C151C2212yes—
37C4×D4×C151C2212yescomplemented
38#117×C151C2211yescharacteristic
39C23×D151—21no—
40#14559004—42no—
41C2×Dic302C2311yescharacteristic
42C2×D604—21no—
43C2×D604—22no—
44C2×D604—22no—
45C2×D604—42no—
46C2×D604C2311yescharacteristic
47C2×D604C2311yescharacteristic
48C2×D604C2311yescharacteristic
49C2×C22⋊D151—21no—
50C2×C4×D151—21no—
51#14558992—42no—
52#14558989—42no—
53#14558989—42no—
54#14558989—42no—
55C2×C151⋊C8C2312yes—
56C2×C151⋊C8C2312yes—
57(C2×D151)⋊C4—22no—
58(C2×D151)⋊C4—22no—
59C2×D4×C151—22no—
60C2×D4×C151—22no—
61C2×D4×C151C2312yes—
62C22×C4×C151—22no—
63C22×C4×C151C2311yescharacteristic
64C4⋊C4×C151—22no—
65C4⋊C4×C151D412yes—
66C4⋊C4×C151C2312yes—
67C22⋊C4×C151—22no—
68C22⋊C4×C151—22no—
69C22⋊C4×C151D412yes—
70C42×C151C2311yescharacteristic
71C42×C151C2311yescharacteristic
72C22×D151—21no—
73C22×D151—21no—
74C22×D151—21no—
75C22×D151—42no—
76C22×D151—82no—
77Dic302—22no—
78D604—22no—
79D604—22no—
80D604—22no—
81D604—42no—
82D604—82no—
83D604—82no—
84C22⋊D151—42no—
85C2×Dic151—21no—
86C4×D151—42no—
87C151⋊C8—22no—
88C151⋊C8—22no—
89C23×C151—22no—
90C23×C151C2×D411yescharacteristic
91D4×C151—22no—
92D4×C151—22no—
93D4×C151—82no—
94D4×C151—82no—
95C2×C4×C151—22no—
96C2×C4×C151—22no—
97C2×C4×C151—82no—
98C2×C4×C151C2×D412yes—
99C2×C4×C151C2×D412yes—
100C2×C4×C151C2×D411yescharacteristic
101C2×C4×C151C2411yescharacteristic
102C22×C151—21no—
103C22×C151—22no—
104C22×C151—42no—
105C22×C151—42no—
106C22×C151—42no—
107C22×C151C22×D411yescharacteristic
108C2×D151—41no—
109C2×D151—41no—
110C2×D151—41no—
111C2×D151—42no—
112C2×D151—42no—
113C2×D151—42no—
114C2×D151—84no—
115C4×C151—21no—
116C4×C151—22no—
117C4×C151—22no—
118C4×C151—42no—
119C4×C151H(5,𝔽2)12yes—
120Dic151—41no—
121C2×C151—41no—
122C2×C151—82no—
123C2×C151#53511yescharacteristic
124C2×C151#57612yes—
125D151—81no—
126D151—81no—
127D151—81no—
128C151#322011yescharacteristic, complemented, Sylow
129#3220—1511nomaximal, Sylow
130#540D15111yescharacteristic, complemented
131#535—1511no—
132#496—1511no—
133#493—1511no—
134#490—1511no—
135#488—1511no—
136#463—1512no—
137#459—1512no—
138#449—1512no—
139#447—1512no—
140#433—1511no—
141C2×#41—1511no—
142C22×D4—1511no—
143C2×SD16—1512no—
144C2×D8—1512no—
145C2×D8—1512no—
146C2×D8—1512no—
147#127—1511no—
148#127—1511no—
149#127C2×D15111yescharacteristic, complemented
150#125C2×D15111yescharacteristic, complemented
151#124—1511no—
152#124—1511no—
153#123—22no—
154#121—22no—
155#121—3022no—
156#121C2×D15112yes—
157#120—3022no—
158C4×D4C2×D15112yescomplemented
159#117C2×D15111yescharacteristic
160C4⋊C8—1512no—
161#103—1512no—
162#102—1512no—
163#102—1512no—
164#102—1512no—
165C22⋊C8—1512no—
166#97—1511no—
167C4×C8—1511no—
168C24—3021no—
169#41—6042no—
170C2×Q8—1511no—
171C2×D4—22no—
172C2×D4—22no—
173C2×D4—3021no—
174C2×D4—3021no—
175C2×D4—3022no—
176C2×D4—3022no—
177C2×D4—6042no—
178C2×D4—1511no—
179C2×D4—1511no—
180C2×D4—1511no—
181C2×D4C22×D15112yes—
182C22×C4—22no—
183C22×C4—3021no—
184C22×C4C22×D15111yescharacteristic
185SD16—6042no—
186D8—6042no—
187D8—6042no—
188D8—6042no—
189C2×C8—1512no—
190C2×C8—1512no—
191C4⋊C4—22no—
192C4⋊C4C22⋊D15112yes—
193C4⋊C4C22×D15112yes—
194C22⋊C4—22no—
195C22⋊C4—22no—
196C22⋊C4—3022no—
197C22⋊C4—3022no—
198C22⋊C4C22⋊D15112yes—
199C42C22×D15111yescharacteristic
200C42C22×D15111yescharacteristic
201C23—22no—
202C23—3021no—
203C23—3021no—
204C23—3021no—
205C23—6042no—
206C23—12082no—
207C23C2×C22⋊D15111yescharacteristic
208Q8—3022no—
209D4—22no—
210D4—22no—
211D4—82no—
212D4—82no—
213D4—3022no—
214D4—3022no—
215D4—3022no—
216D4—6042no—
217D4—6042no—
218D4—12082no—
219D4—12082no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—82no—
223C2×C4—3021no—
224C2×C4—6042no—
225C2×C4C2×C22⋊D15112yes—
226C2×C4C2×C22⋊D15112yes—
227C2×C4C2×C22⋊D15111yescharacteristic
228C2×C4C23×D15111yescharacteristic
229C8—3022no—
230C8—3022no—
231C22—22no—
232C22—21no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—6042no—
237C22—6042no—
238C22—6042no—
239C22—6041no—
240C22—6041no—
241C22—6041no—
242C22—12084no—
243C22C22×C22⋊D15111yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—42no—
248C4—6041no—
249C4#1801278512yes—
250C2—41no—
251C2—82no—
252C2—12081no—
253C2—12081no—
254C2—12081no—
255C2#2375277611yescharacteristic
256C2#2375301512yes—
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#540×C151C2
socleC22×C151C22×D4
hypercenter#540D151
hypocenterC151#3220
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #23752781C2semidirect
2. #23752599C2semidirect
3. #23752588C2semidirect
4. #23752578C2semidirect
5. #23752569C2semidirect
6. #23752427C2semidirect
7. #23752407C2semidirect
8. #23752355C2semidirect
9. #23752345C2semidirect
10. #23752273C2semidirect
11. #540×C151C2semidirect
14. C2×#14558992C22semidirect
17. C2×#14558989C22semidirect
24. C4⋊(C151⋊C8)C22semidirect
25. #18012662C22semidirect
28. #18012659C22semidirect
30. #18012650C22semidirect
31. C4×C151⋊C8C22semidirect
32. #127×C151C22semidirect
33. #125×C151C22semidirect
37. C4×D4×C151C22semidirect
128. C151#3220semidirect
130. #540D151semidirect
149. #127C2×D151semidirect
150. #125C2×D151semidirect
158. C4×D4C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237527812
#237525992
#237525882
#237525782
#237525692
#237524272
#237524072
#237523552
#237523452
#237522732
#540×C1512
#3220151