Finite Group Databasebeta

← #458×D151 #34078496

Subgroups — #458×D151 #34078496

Order 19328.

794 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 794 conjugacy classes of subgroups — too many to draw. Only its 135 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
1H(5,𝔽2)×D151C211yesmaximal, characteristic
2#123×D151C213yesmaximal, complemented
3#23752403C213yesmaximal, complemented
4#23752402C211yesmaximal, characteristic, complemented
5#23752401C213yesmaximal, complemented
6#99×D151C213yesmaximal, complemented
7#458×C151C211yesmaximal, characteristic, complemented
8#18012785—23no—
9#18012784—23no—
10#18012784C2213yes—
11#41×D151—23no—
12C2×D4×D151—23no—
13C2×D4×D151C2213yes—
14C22×C4×D151C2211yescharacteristic, complemented
15#18012724—23no—
16#18012723C2213yescomplemented
17#18012722C2213yescomplemented
18#18012721—23no—
19#18012720C2213yescomplemented
20C4⋊C4×D151—23no—
21C22⋊C4×D151—23no—
22C22⋊C4×D151C2213yescomplemented
23#18012654C2213yescomplemented
24#18012653C2216yescomplemented
25H(5,𝔽2)×C151C2211yescharacteristic
26#123×C151C2213yescomplemented
27#99×C151C2213yescomplemented
28C23×D151—21no—
29C23×D151D413yes—
30C23×D151C2311yescharacteristic
31#14559005—23no—
32#14559004—26no—
33#14559004—23no—
34#14559003—23no—
35#14559003—26no—
36Q8×D151—21no—
37C2×D604—23no—
38C2×D604D413yes—
39C2×C22⋊D151—23no—
40C2×C22⋊D151—23no—
41C2×C22⋊D151D413yes—
42C2×C22⋊D151C2313yes—
43D4×D151—23no—
44D4×D151—26no—
45D4×D151—26no—
46D4×D151—26no—
47D4×D151—26no—
48C22×Dic151C2311yescharacteristic, complemented
49C2×C4×D151—23no—
50C2×C4×D151—23no—
51C2×C4×D151—23no—
52C2×C4×D151—23no—
53C2×C4×D151D413yes—
54C4⋊Dic151—23no—
55Dic151⋊C4—23no—
56Dic151⋊C4—23no—
57C22⋊Dic151—23no—
58C22⋊Dic151C2313yescomplemented
59(C2×D151)⋊C4—23no—
60(C2×D151)⋊C4—23no—
61(C2×D151)⋊C4—23no—
62#41×C151—23no—
63C2×D4×C151—23no—
64C2×D4×C151C2313yes—
65C22×C4×C151C2311yescharacteristic, complemented
66C4⋊C4×C151—23no—
67C22⋊C4×C151—23no—
68C22⋊C4×C151C2313yescomplemented
69C22×D151—23no—
70C22×D151—23no—
71C22×D151—23no—
72C22×D151—42no—
73C22×D151—46no—
74C22×D151—82no—
75C22×D151C2×D413yes—
76C22×D151C2×D413yes—
77C22×D151C2×D413yes—
78Dic302—23no—
79D604—23no—
80D604—26no—
81C22⋊D151—26no—
82C22⋊D151—26no—
83C22⋊D151—26no—
84C2×Dic151—23no—
85C2×Dic151—23no—
86C2×Dic151—23no—
87C2×Dic151C2×D413yes—
88C4×D151—26no—
89C4×D151—23no—
90C4×D151—23no—
91C4×D151—46no—
92C4×D151—43no—
93C4×D151—41no—
94C23×C151—21no—
95C23×C151C2×D413yes—
96C23×C151C2411yescharacteristic
97Q8×C151—21no—
98D4×C151—23no—
99D4×C151—26no—
100C2×C4×C151—23no—
101C2×C4×C151—23no—
102C2×C4×C151—23no—
103C2×C4×C151C2×D413yes—
104C22×C151—23no—
105C22×C151—41no—
106C22×C151—43no—
107C22×C151—81no—
108C22×C151C22×D413yes—
109C2×D151—26no—
110C2×D151—23no—
111C2×D151—43no—
112C2×D151—46no—
113C2×D151—43no—
114C2×D151—83no—
115C2×D151—83no—
116C2×D151#12013yes—
117C2×D151#12011yescharacteristic
118C4×C151—23no—
119C4×C151—43no—
120C4×C151—41no—
121Dic151—23no—
122Dic151—43no—
123Dic151—41no—
124C2×C151—23no—
125C2×C151—43no—
126C2×C151C2×#12011yescharacteristic
127D151—23no—
128D151—43no—
129D151#45812yesdirect product factor
130C151C2×#45811yescharacteristic, complemented, Sylow
131C2×#458—1511nomaximal, Sylow
132C2×H(5,𝔽2)—1511no—
133C2×#123—1513no—
134#458—1511no—
135#458—1513no—
136#458—1513no—
137#458D15111yescharacteristic, direct product factor
138C2×#99—1513no—
139H(5,𝔽2)—3023no—
140H(5,𝔽2)—3023no—
141H(5,𝔽2)—1513no—
142H(5,𝔽2)C2×D15111yescharacteristic
143C2×#41—3023no—
144C22×D4—3023no—
145C22×D4—1513no—
146C23×C4—1511no—
147#123—3023no—
148#123—3023no—
149#123—1513no—
150#123—1513no—
151#123—1513no—
152#123C2×D15113yescomplemented
153C2×C4⋊C4—3023no—
154C2×C22⋊C4—3023no—
155C2×C22⋊C4—1513no—
156#99—1513no—
157#99—1516no—
158#99C2×D15113yescomplemented
159C24—3021no—
160C24—1513no—
161C24—1511no—
162#41—23no—
163#41—3026no—
164#41—3023no—
165#41—3023no—
166#41—3026no—
167#41—3023no—
168C2×Q8—3021no—
169C2×D4—23no—
170C2×D4—3023no—
171C2×D4—3023no—
172C2×D4—3026no—
173C2×D4—3026no—
174C2×D4—3026no—
175C2×D4—3026no—
176C2×D4—3023no—
177C2×D4—3023no—
178C2×D4—1513no—
179C2×D4—1513no—
180C2×D4—1513no—
181C2×D4C22×D15113yes—
182C22×C4—3023no—
183C22×C4—3023no—
184C22×C4—3023no—
185C22×C4—3023no—
186C22×C4—1511no—
187C22×C4—1513no—
188C22×C4C22×D15111yescharacteristic, complemented
189C4⋊C4—23no—
190C4⋊C4—3023no—
191C4⋊C4—3023no—
192C4⋊C4—3023no—
193C22⋊C4—23no—
194C22⋊C4—3023no—
195C22⋊C4—3023no—
196C22⋊C4—3023no—
197C22⋊C4—3023no—
198C22⋊C4—1513no—
199C22⋊C4C22×D15113yescomplemented
200C23—21no—
201C23—3023no—
202C23—3023no—
203C23—3023no—
204C23—6042no—
205C23—6046no—
206C23—1513no—
207C23—1513no—
208C23—1513no—
209C23—12082no—
210C23D4×D15113yes—
211C23C23×D15111yescharacteristic
212Q8—21no—
213Q8—3023no—
214D4—23no—
215D4—26no—
216D4—3023no—
217D4—3026no—
218D4—3026no—
219D4—3026no—
220D4—3026no—
221C2×C4—23no—
222C2×C4—23no—
223C2×C4—23no—
224C2×C4—3026no—
225C2×C4—3023no—
226C2×C4—3023no—
227C2×C4—3023no—
228C2×C4—3023no—
229C2×C4—3023no—
230C2×C4—6046no—
231C2×C4—6043no—
232C2×C4—6041no—
233C2×C4—1513no—
234C2×C4D4×D15113yes—
235C22—23no—
236C22—41no—
237C22—43no—
238C22—81no—
239C22—3026no—
240C22—3023no—
241C22—6043no—
242C22—6043no—
243C22—6046no—
244C22—1513no—
245C22—1511no—
246C22—12083no—
247C22—12083no—
248C22C2×D4×D15113yes—
249C4—23no—
250C4—43no—
251C4—41no—
252C4—3023no—
253C4—6043no—
254C4—6041no—
255C2—23no—
256C2—43no—
257C2—3023no—
258C2—6043no—
259C2—1512no—
260C2#120×D15111yescharacteristic
subgroupG/H
centerC2#120×D151
commutator, cosocleC23×C151C24
FrattiniC23C23×D151
Fitting#458×C151C2
socleC2×C151C2×#120
prime radicalH(5,𝔽2)×D151C2
hypercenter#458D151
hypocenterC151C2×#458
LCSG ▷ C23×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C23 ◁ #458

Complements

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

NH ≅ G/Ntype
2. #123×D151C2semidirect
3. #23752403C2semidirect
4. #23752402C2semidirect
5. #23752401C2semidirect
6. #99×D151C2semidirect
7. #458×C151C2semidirect
14. C22×C4×D151C22semidirect
16. #18012723C22semidirect
17. #18012722C22semidirect
19. #18012720C22semidirect
22. C22⋊C4×D151C22semidirect
23. #18012654C22semidirect
24. #18012653C22semidirect
26. #123×C151C22semidirect
27. #99×C151C22semidirect
48. C22×Dic151C23semidirect
58. C22⋊Dic151C23semidirect
65. C22×C4×C151C23semidirect
68. C22⋊C4×C151C23semidirect
129. D151#458direct (N × H)
130. C151C2×#458semidirect
137. #458D151direct (N × H)
152. #123C2×D151semidirect
158. #99C2×D151semidirect
188. C22×C4C22×D151semidirect
199. C22⋊C4C22×D151semidirect

Maximal subgroups

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

subgroupindex
H(5,𝔽2)×D1512
#123×D1512
#237524032
#237524022
#237524012
#99×D1512
#458×C1512
C2×#458151