Finite Group Databasebeta

← C151×#13077 #50318002

Subgroups — C151×#13077 #50318002

Order 38656.

470 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 146 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#3407×C151C211yesmaximal, characteristic, complemented
2#3060×C151C211yesmaximal, characteristic
3#2145×C151C212yesmaximal, complemented
4#1812×C151C211yesmaximal, characteristic, complemented
5#1386×C151C212yesmaximal, complemented
6C2×#135×C151C2211yescharacteristic
7C2×#131×C151C2211yescharacteristic
8#537×C151—21no—
9#504×C151—24no—
10C2×M32×C151—22no—
11C2×M32×C151C2212yes—
12#470×C151C412yescomplemented
13#469×C151C412yescomplemented
14#465×C151—22no—
15#427×C151C2212yes—
16C2×#106×C151C2211yescharacteristic
17#417×C151—21no—
18#410×C151—21no—
19#360×C151—24no—
20H(3,ℤ/4)×C151—21no—
21C2×#41×C151—21no—
22C2×#41×C151D411yescharacteristic
23#135×C151—22no—
24#135×C151—22no—
25C2×Q16×C151C2×C411yescharacteristic
26C2×SD16×C151—21no—
27C2×D8×C151C2×C411yescharacteristic
28#131×C151—22no—
29#131×C151—22no—
30C2×M16×C151C2×C412yes—
31C2×M16×C151D411yescharacteristic
32C22×C8×C151D412yes—
33C22×C8×C151C2311yescharacteristic
34C22⋊Q8×C151—22no—
35C22⋊Q8×C151—41no—
36#121×C151—22no—
37#121×C151—42no—
38#121×C151—41no—
39#117×C151—22no—
40C2×C4⋊C4×C151—21no—
41M32×C151—24no—
42M32×C151—22no—
43M32×C151D414yescomplemented
44C2×C16×C151—24no—
45C2×C16×C151—22no—
46#107×C151—22no—
47#106×C151—21no—
48#106×C151—22no—
49#106×C151C2×C412yes—
50#103×C151—22no—
51#102×C151—22no—
52#99×C151—42no—
53#41×C151—22no—
54#41×C151—22no—
55#41×C151—42no—
56#41×C151—42no—
57C2×Q8×C151—21no—
58C2×Q8×C151SD1611yescharacteristic
59C2×D4×C151—21no—
60C2×D4×C151—41no—
61C2×D4×C151—42no—
62C2×D4×C151D812yes—
63C2×D4×C151SD1611yescharacteristic
64C22×C4×C151—41no—
65C22×C4×C151—41no—
66C22×C4×C151C22⋊C412yes—
67C22×C4×C151C2×D411yescharacteristic
68Q16×C151—22no—
69SD16×C151—41no—
70SD16×C151—41no—
71D8×C151—22no—
72M16×C151—22no—
73M16×C151—24no—
74C2×C8×C151—22no—
75C2×C8×C151—22no—
76C2×C8×C151C22⋊C412yes—
77C2×C8×C151C22×C411yescharacteristic
78C2×C8×C151C2×D412yes—
79C2×C8×C151C2×D411yescharacteristic
80C2×C8×C151#4112yes—
81C4⋊C4×C151—22no—
82C4⋊C4×C151—42no—
83C4⋊C4×C151—41no—
84C4⋊C4×C151—42no—
85C22⋊C4×C151—42no—
86C22⋊C4×C151—42no—
87C22⋊C4×C151—42no—
88C42×C151—42no—
89C16×C151—24no—
90C23×C151—41no—
91C23×C151#10212yes—
92C23×C151C2×D811yescharacteristic
93Q8×C151—22no—
94Q8×C151—41no—
95Q8×C151—41no—
96D4×C151—24no—
97D4×C151—22no—
98D4×C151—41no—
99D4×C151—41no—
100D4×C151—82no—
101D4×C151—162no—
102C2×C4×C151—22no—
103C2×C4×C151—22no—
104C2×C4×C151—41no—
105C2×C4×C151—42no—
106C2×C4×C151—82no—
107C2×C4×C151—82no—
108C2×C4×C151—161no—
109C2×C4×C151#10212yes—
110C2×C4×C151C2×C22⋊C411yescharacteristic
111C2×C4×C151#12112yes—
112C2×C4×C151C2×SD1611yescharacteristic
113C2×C4×C151#13512yes—
114C8×C151—22no—
115C8×C151C4×D412yes—
116C8×C151#12011yescharacteristic
117C8×C151#12311yescharacteristic
118C22×C151—22no—
119C22×C151—41no—
120C22×C151—42no—
121C22×C151—81no—
122C22×C151—81no—
123C22×C151—81no—
124C22×C151C2×#10211yescharacteristic
125C22×C151#46612yes—
126C4×C151—22no—
127C4×C151—82no—
128C4×C151—81no—
129C4×C151—162no—
130C4×C151#38611yescharacteristic
131C4×C151#41611yescharacteristic
132C4×C151#46512yes—
133C2×C151—21no—
134C2×C151—22no—
135C2×C151—42no—
136C2×C151—161no—
137C2×C151#189311yescharacteristic
138#13077C15111yesmaximal, characteristic, direct product factor, Sylow
139C151#1307711yescharacteristic, direct product factor, Sylow
140#3407C2×C15111yescharacteristic, complemented
141#3060C2×C15111yescharacteristic
142#2145C2×C15112yescomplemented
143#1812C2×C15111yescharacteristic, complemented
144#1386C2×C15112yescomplemented
145C2×#135C22×C15111yescharacteristic
146C2×#131C22×C15111yescharacteristic
147#537—21no—
148#504—24no—
149C2×M32—22no—
150C2×M32C22×C15112yes—
151#470C4×C15112yescomplemented
152#469C4×C15112yescomplemented
153#465—22no—
154#427C22×C15112yes—
155C2×#106C22×C15111yescharacteristic
156#417—21no—
157#410—21no—
158#360—24no—
159H(3,ℤ/4)—21no—
160C2×#41—21no—
161C2×#41D4×C15111yescharacteristic
162#135—22no—
163#135—22no—
164C2×Q16C2×C4×C15111yescharacteristic
165C2×SD16—21no—
166C2×D8C2×C4×C15111yescharacteristic
167#131—22no—
168#131—22no—
169C2×M16C2×C4×C15112yes—
170C2×M16D4×C15111yescharacteristic
171C22×C8D4×C15112yes—
172C22×C8C23×C15111yescharacteristic
173C22⋊Q8—22no—
174C22⋊Q8—41no—
175#121—22no—
176#121—42no—
177#121—41no—
178#117—22no—
179C2×C4⋊C4—21no—
180M32—24no—
181M32—22no—
182M32D4×C15114yescomplemented
183C2×C16—24no—
184C2×C16—22no—
185#107—22no—
186#106—21no—
187#106—22no—
188#106C2×C4×C15112yes—
189#103—22no—
190#102—22no—
191#99—42no—
192#41—22no—
193#41—22no—
194#41—42no—
195#41—42no—
196C2×Q8—21no—
197C2×Q8SD16×C15111yescharacteristic
198C2×D4—21no—
199C2×D4—41no—
200C2×D4—42no—
201C2×D4D8×C15112yes—
202C2×D4SD16×C15111yescharacteristic
203C22×C4—41no—
204C22×C4—41no—
205C22×C4C22⋊C4×C15112yes—
206C22×C4C2×D4×C15111yescharacteristic
207Q16—22no—
208SD16—41no—
209SD16—41no—
210D8—22no—
211M16—22no—
212M16—24no—
213C2×C8—22no—
214C2×C8—22no—
215C2×C8C22⋊C4×C15112yes—
216C2×C8C22×C4×C15111yescharacteristic
217C2×C8C2×D4×C15112yes—
218C2×C8C2×D4×C15111yescharacteristic
219C2×C8#41×C15112yes—
220C4⋊C4—22no—
221C4⋊C4—42no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C22⋊C4—42no—
225C22⋊C4—42no—
226C22⋊C4—42no—
227C42—42no—
228C16—24no—
229C23—41no—
230C23#102×C15112yes—
231C23C2×D8×C15111yescharacteristic
232Q8—22no—
233Q8—41no—
234Q8—41no—
235D4—24no—
236D4—22no—
237D4—41no—
238D4—41no—
239D4—82no—
240D4—162no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—82no—
246C2×C4—82no—
247C2×C4—161no—
248C2×C4#102×C15112yes—
249C2×C4C2×C22⋊C4×C15111yescharacteristic
250C2×C4#121×C15112yes—
251C2×C4C2×SD16×C15111yescharacteristic
252C2×C4#135×C15112yes—
253C8—22no—
254C8C4×D4×C15112yes—
255C8#120×C15111yescharacteristic
256C8#123×C15111yescharacteristic
257C22—22no—
258C22—41no—
259C22—42no—
260C22—81no—
261C22—81no—
262C22—81no—
263C22C2×#102×C15111yescharacteristic
264C22#466×C15112yes—
265C4—22no—
266C4—82no—
267C4—81no—
268C4—162no—
269C4#386×C15111yescharacteristic
270C4#416×C15111yescharacteristic
271C4#465×C15112yes—
272C2—21no—
273C2—22no—
274C2—42no—
275C2—161no—
276C2#1893×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#1893
commutatorC2×C8C22×C4×C151
Frattini, cosocleC22×C8C23×C151
prime radical#3060×C151C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C22×C4×C151 ◁ C2×#131×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3407×C151C2semidirect
3. #2145×C151C2semidirect
4. #1812×C151C2semidirect
5. #1386×C151C2semidirect
12. #470×C151C4semidirect
13. #469×C151C4semidirect
43. M32×C151D4semidirect
138. #13077C151direct (N × H)
139. C151#13077direct (N × H)
140. #3407C2×C151semidirect
142. #2145C2×C151semidirect
143. #1812C2×C151semidirect
144. #1386C2×C151semidirect
151. #470C4×C151semidirect
152. #469C4×C151semidirect
182. M32D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3407×C1512
#3060×C1512
#2145×C1512
#1812×C1512
#1386×C1512
#13077151