Finite Group Databasebeta

← C151×#12395 #50317320

Subgroups — C151×#12395 #50317320

Order 38656.

296 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 82 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#3341×C151C211yesmaximal, characteristic
2#2254×C151C211yesmaximal, characteristic, complemented
3#2224×C151C211yesmaximal, characteristic, complemented
4#1673×C151C211yesmaximal, characteristic, complemented
5#1365×C151C211yesmaximal, characteristic, complemented
6#1331×C151C211yesmaximal, characteristic, complemented
7D4⋊C16×C151C211yesmaximal, characteristic, complemented
8#555×C151—21no—
9#500×C151C2211yescharacteristic
10#500×C151C2211yescharacteristic
11#482×C151—22no—
12#476×C151—21no—
13#466×C151—21no—
14#461×C151—21no—
15C4×D8×C151C2211yescharacteristic
16C8×D4×C151C2211yescharacteristic
17#427×C151—21no—
18#367×C151—22no—
19#366×C151—21no—
20C4⋊C16×C151C2211yescharacteristic
21#357×C151—21no—
22C4×C16×C151C2211yescharacteristic
23#335×C151C2211yescharacteristic
24#332×C151—21no—
25C2×SD16×C151—41no—
26C2×D8×C151D411yescharacteristic
27C22×C8×C151—21no—
28C4⋊Q8×C151—21no—
29C4⋊Q8×C151—21no—
30#124×C151—42no—
31#121×C151—22no—
32#121×C151—41no—
33C4×D4×C151—21no—
34C4×D4×C151D411yescharacteristic
35#117×C151—22no—
36#117×C151—41no—
37C2×C16×C151—21no—
38C2×C16×C151—21no—
39#107×C151—21no—
40#107×C151—21no—
41#107×C151—21no—
42#107×C151D411yescharacteristic
43#107×C151D412yes—
44#106×C151—22no—
45C4⋊C8×C151—21no—
46C4⋊C8×C151D411yescharacteristic
47#103×C151—41no—
48#102×C151—22no—
49#102×C151—21no—
50C22⋊C8×C151—21no—
51C4×C8×C151C2311yescharacteristic
52C2×Q8×C151—41no—
53C2×Q8×C151—41no—
54C2×D4×C151—21no—
55C2×D4×C151—42no—
56C2×D4×C151D811yescharacteristic
57C22×C4×C151—21no—
58C22×C4×C151—41no—
59SD16×C151—82no—
60D8×C151—21no—
61D8×C151—21no—
62C2×C8×C151—21no—
63C2×C8×C151—41no—
64C2×C8×C151—41no—
65C2×C8×C151—41no—
66C2×C8×C151C2×D411yescharacteristic
67C2×C8×C151C2×D411yescharacteristic
68C4⋊C4×C151—21no—
69C4⋊C4×C151—22no—
70C4⋊C4×C151—41no—
71C4⋊C4×C151—41no—
72C4⋊C4×C151—41no—
73C4⋊C4×C151D811yescharacteristic
74C22⋊C4×C151—21no—
75C22⋊C4×C151—42no—
76C22⋊C4×C151—42no—
77C22⋊C4×C151—41no—
78C42×C151—42no—
79C42×C151C2×D411yescharacteristic
80C16×C151—22no—
81C16×C151—41no—
82C23×C151—21no—
83C23×C151—41no—
84Q8×C151—81no—
85Q8×C151—81no—
86Q8×C151—161no—
87D4×C151—21no—
88D4×C151—21no—
89D4×C151—41no—
90D4×C151—41no—
91D4×C151—162no—
92C2×C4×C151—21no—
93C2×C4×C151—41no—
94C2×C4×C151—41no—
95C2×C4×C151—42no—
96C2×C4×C151—41no—
97C2×C4×C151—81no—
98C2×C4×C151—81no—
99C2×C4×C151—81no—
100C2×C4×C151#12011yescharacteristic
101C2×C4×C151C2×D811yescharacteristic
102C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
103C8×C151—21no—
104C8×C151—41no—
105C8×C151—81no—
106C8×C151#13511yescharacteristic
107C8×C151#13711yescharacteristic
108C22×C151—41no—
109C22×C151—41no—
110C22×C151—41no—
111C22×C151—81no—
112C22×C151—81no—
113C22×C151—81no—
114C22×C151#44711yescharacteristic
115C4×C151—21no—
116C4×C151—41no—
117C4×C151—81no—
118C4×C151—82no—
119C4×C151—161no—
120C4×C151#45211yescharacteristic
121C4×C151#45611yescharacteristic
122C4×C151#50811yescharacteristic
123C4×C151#50911yescharacteristic
124C2×C151—81no—
125C2×C151—161no—
126C2×C151#164711yescharacteristic
127C2×C151#218611yescharacteristic
128C2×C151#219411yescharacteristic
129#12395C15111yesmaximal, characteristic, direct product factor, Sylow
130C151#1239511yescharacteristic, direct product factor, Sylow
131#3341C2×C15111yescharacteristic
132#2254C2×C15111yescharacteristic, complemented
133#2224C2×C15111yescharacteristic, complemented
134#1673C2×C15111yescharacteristic, complemented
135#1365C2×C15111yescharacteristic, complemented
136#1331C2×C15111yescharacteristic, complemented
137D4⋊C16C2×C15111yescharacteristic, complemented
138#555—21no—
139#500C22×C15111yescharacteristic
140#500C22×C15111yescharacteristic
141#482—22no—
142#476—21no—
143#466—21no—
144#461—21no—
145C4×D8C22×C15111yescharacteristic
146C8×D4C22×C15111yescharacteristic
147#427—21no—
148#367—22no—
149#366—21no—
150C4⋊C16C22×C15111yescharacteristic
151#357—21no—
152C4×C16C22×C15111yescharacteristic
153#335C22×C15111yescharacteristic
154#332—21no—
155C2×SD16—41no—
156C2×D8D4×C15111yescharacteristic
157C22×C8—21no—
158C4⋊Q8—21no—
159C4⋊Q8—21no—
160#124—42no—
161#121—22no—
162#121—41no—
163C4×D4—21no—
164C4×D4D4×C15111yescharacteristic
165#117—22no—
166#117—41no—
167C2×C16—21no—
168C2×C16—21no—
169#107—21no—
170#107—21no—
171#107—21no—
172#107D4×C15111yescharacteristic
173#107D4×C15112yes—
174#106—22no—
175C4⋊C8—21no—
176C4⋊C8D4×C15111yescharacteristic
177#103—41no—
178#102—22no—
179#102—21no—
180C22⋊C8—21no—
181C4×C8C23×C15111yescharacteristic
182C2×Q8—41no—
183C2×Q8—41no—
184C2×D4—21no—
185C2×D4—42no—
186C2×D4D8×C15111yescharacteristic
187C22×C4—21no—
188C22×C4—41no—
189SD16—82no—
190D8—21no—
191D8—21no—
192C2×C8—21no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8C2×D4×C15111yescharacteristic
197C2×C8C2×D4×C15111yescharacteristic
198C4⋊C4—21no—
199C4⋊C4—22no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4D8×C15111yescharacteristic
204C22⋊C4—21no—
205C22⋊C4—42no—
206C22⋊C4—42no—
207C22⋊C4—41no—
208C42—42no—
209C42C2×D4×C15111yescharacteristic
210C16—22no—
211C16—41no—
212C23—21no—
213C23—41no—
214Q8—81no—
215Q8—81no—
216Q8—161no—
217D4—21no—
218D4—21no—
219D4—41no—
220D4—41no—
221D4—162no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—81no—
228C2×C4—81no—
229C2×C4—81no—
230C2×C4#120×C15111yescharacteristic
231C2×C4C2×D8×C15111yescharacteristic
232C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
233C8—21no—
234C8—41no—
235C8—81no—
236C8#135×C15111yescharacteristic
237C8#137×C15111yescharacteristic
238C22—41no—
239C22—41no—
240C22—41no—
241C22—81no—
242C22—81no—
243C22—81no—
244C22#447×C15111yescharacteristic
245C4—21no—
246C4—41no—
247C4—81no—
248C4—82no—
249C4—161no—
250C4#452×C15111yescharacteristic
251C4#456×C15111yescharacteristic
252C4#508×C15111yescharacteristic
253C4#509×C15111yescharacteristic
254C2—81no—
255C2—161no—
256C2#1647×C15111yescharacteristic
257C2#2186×C15111yescharacteristic
258C2#2194×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#447
commutator, Frattini, cosocleC4×C8C23×C151
prime radical#3341×C151C2
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ C8×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2254×C151C2semidirect
3. #2224×C151C2semidirect
4. #1673×C151C2semidirect
5. #1365×C151C2semidirect
6. #1331×C151C2semidirect
7. D4⋊C16×C151C2semidirect
129. #12395C151direct (N × H)
130. C151#12395direct (N × H)
132. #2254C2×C151semidirect
133. #2224C2×C151semidirect
134. #1673C2×C151semidirect
135. #1365C2×C151semidirect
136. #1331C2×C151semidirect
137. D4⋊C16C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3341×C1512
#2254×C1512
#2224×C1512
#1673×C1512
#1365×C1512
#1331×C1512
D4⋊C16×C1512
#12395151