Finite Group Databasebeta

← C151×#12383 #50317308

Subgroups — C151×#12383 #50317308

Order 38656.

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

normal subgroups only

This group has 294 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#3393×C151C211yesmaximal, characteristic
2#2241×C151C211yesmaximal, characteristic, complemented
3#2224×C151C211yesmaximal, characteristic
4#1674×C151C211yesmaximal, characteristic, complemented
5#1362×C151C211yesmaximal, characteristic, complemented
6Q8⋊C16×C151C211yesmaximal, characteristic, complemented
7#1331×C151C211yesmaximal, characteristic
8#556×C151—21no—
9#500×C151C2211yescharacteristic
10#495×C151—21no—
11#494×C151C2211yescharacteristic
12#464×C151—22no—
13#462×C151—21no—
14#461×C151—21no—
15C8×Q8×C151C2211yescharacteristic
16C4×Q16×C151—21no—
17C4×D8×C151C2211yescharacteristic
18#366×C151—21no—
19C4⋊C16×C151C2211yescharacteristic
20#358×C151—22no—
21#357×C151—21no—
22C4×C16×C151C2211yescharacteristic
23#335×C151C2211yescharacteristic
24#332×C151—21no—
25C2×Q16×C151—21no—
26C2×Q16×C151—41no—
27C2×Q16×C151D412yes—
28C2×SD16×C151—22no—
29C2×D8×C151D411yescharacteristic
30C4⋊Q8×C151—21no—
31C4⋊Q8×C151—21no—
32#126×C151—42no—
33#124×C151—22no—
34C22⋊Q8×C151—41no—
35C4×Q8×C151—22no—
36C4×Q8×C151D411yescharacteristic
37C4×D4×C151—21no—
38#117×C151—41no—
39C2×C16×C151—21no—
40C2×C16×C151—21no—
41#107×C151—21no—
42#107×C151—21no—
43#107×C151D411yescharacteristic
44C4⋊C8×C151—21no—
45C4⋊C8×C151—21no—
46C4⋊C8×C151D411yescharacteristic
47#103×C151—22no—
48#103×C151—41no—
49#102×C151—21no—
50C4×C8×C151—21no—
51C4×C8×C151C2311yescharacteristic
52C2×Q8×C151—22no—
53C2×Q8×C151—41no—
54C2×Q8×C151D811yescharacteristic
55C2×D4×C151—21no—
56C22×C4×C151—41no—
57Q16×C151—42no—
58Q16×C151—41no—
59Q16×C151—41no—
60Q16×C151—82no—
61SD16×C151—82no—
62D8×C151—21no—
63D8×C151—21no—
64C2×C8×C151—21no—
65C2×C8×C151—41no—
66C2×C8×C151C2×D411yescharacteristic
67C2×C8×C151C2×D411yescharacteristic
68C4⋊C4×C151—21no—
69C4⋊C4×C151—21no—
70C4⋊C4×C151—42no—
71C4⋊C4×C151—41no—
72C4⋊C4×C151—41no—
73C4⋊C4×C151—41no—
74C4⋊C4×C151—41no—
75C4⋊C4×C151D811yescharacteristic
76C22⋊C4×C151—42no—
77C22⋊C4×C151—42no—
78C22⋊C4×C151—41no—
79C42×C151—21no—
80C42×C151—42no—
81C42×C151C2×D411yescharacteristic
82C16×C151—41no—
83C16×C151—41no—
84C23×C151—41no—
85Q8×C151—21no—
86Q8×C151—21no—
87Q8×C151—42no—
88Q8×C151—42no—
89Q8×C151—81no—
90Q8×C151—81no—
91D4×C151—41no—
92D4×C151—41no—
93C2×C4×C151—21no—
94C2×C4×C151—21no—
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—81no—
109C22×C151—81no—
110C22×C151—81no—
111C22×C151#44711yescharacteristic
112C4×C151—21no—
113C4×C151—41no—
114C4×C151—41no—
115C4×C151—82no—
116C4×C151—81no—
117C4×C151—161no—
118C4×C151#45211yescharacteristic
119C4×C151#45511yescharacteristic
120C4×C151#50811yescharacteristic
121C4×C151#50911yescharacteristic
122C2×C151—161no—
123C2×C151#164111yescharacteristic
124C2×C151#218611yescharacteristic
125C2×C151#219511yescharacteristic
126#12383C15111yesmaximal, characteristic, direct product factor, Sylow
127C151#1238311yescharacteristic, direct product factor, Sylow
128#3393C2×C15111yescharacteristic
129#2241C2×C15111yescharacteristic, complemented
130#2224C2×C15111yescharacteristic
131#1674C2×C15111yescharacteristic, complemented
132#1362C2×C15111yescharacteristic, complemented
133Q8⋊C16C2×C15111yescharacteristic, complemented
134#1331C2×C15111yescharacteristic
135#556—21no—
136#500C22×C15111yescharacteristic
137#495—21no—
138#494C22×C15111yescharacteristic
139#464—22no—
140#462—21no—
141#461—21no—
142C8×Q8C22×C15111yescharacteristic
143C4×Q16—21no—
144C4×D8C22×C15111yescharacteristic
145#366—21no—
146C4⋊C16C22×C15111yescharacteristic
147#358—22no—
148#357—21no—
149C4×C16C22×C15111yescharacteristic
150#335C22×C15111yescharacteristic
151#332—21no—
152C2×Q16—21no—
153C2×Q16—41no—
154C2×Q16D4×C15112yes—
155C2×SD16—22no—
156C2×D8D4×C15111yescharacteristic
157C4⋊Q8—21no—
158C4⋊Q8—21no—
159#126—42no—
160#124—22no—
161C22⋊Q8—41no—
162C4×Q8—22no—
163C4×Q8D4×C15111yescharacteristic
164C4×D4—21no—
165#117—41no—
166C2×C16—21no—
167C2×C16—21no—
168#107—21no—
169#107—21no—
170#107D4×C15111yescharacteristic
171C4⋊C8—21no—
172C4⋊C8—21no—
173C4⋊C8D4×C15111yescharacteristic
174#103—22no—
175#103—41no—
176#102—21no—
177C4×C8—21no—
178C4×C8C23×C15111yescharacteristic
179C2×Q8—22no—
180C2×Q8—41no—
181C2×Q8D8×C15111yescharacteristic
182C2×D4—21no—
183C22×C4—41no—
184Q16—42no—
185Q16—41no—
186Q16—41no—
187Q16—82no—
188SD16—82no—
189D8—21no—
190D8—21no—
191C2×C8—21no—
192C2×C8—41no—
193C2×C8C2×D4×C15111yescharacteristic
194C2×C8C2×D4×C15111yescharacteristic
195C4⋊C4—21no—
196C4⋊C4—21no—
197C4⋊C4—42no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4D8×C15111yescharacteristic
203C22⋊C4—42no—
204C22⋊C4—42no—
205C22⋊C4—41no—
206C42—21no—
207C42—42no—
208C42C2×D4×C15111yescharacteristic
209C16—41no—
210C16—41no—
211C23—41no—
212Q8—21no—
213Q8—21no—
214Q8—42no—
215Q8—42no—
216Q8—81no—
217Q8—81no—
218D4—41no—
219D4—41no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—81no—
225C2×C4—81no—
226C2×C4—81no—
227C2×C4#120×C15111yescharacteristic
228C2×C4C2×D8×C15111yescharacteristic
229C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
230C8—21no—
231C8—41no—
232C8—81no—
233C8#135×C15111yescharacteristic
234C8#137×C15111yescharacteristic
235C22—81no—
236C22—81no—
237C22—81no—
238C22#447×C15111yescharacteristic
239C4—21no—
240C4—41no—
241C4—41no—
242C4—82no—
243C4—81no—
244C4—161no—
245C4#452×C15111yescharacteristic
246C4#455×C15111yescharacteristic
247C4#508×C15111yescharacteristic
248C4#509×C15111yescharacteristic
249C2—161no—
250C2#1641×C15111yescharacteristic
251C2#2186×C15111yescharacteristic
252C2#2195×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#447
commutator, Frattini, cosocleC4×C8C23×C151
prime radicalC2×D8×C151D4
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ C8×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2241×C151C2semidirect
4. #1674×C151C2semidirect
5. #1362×C151C2semidirect
6. Q8⋊C16×C151C2semidirect
126. #12383C151direct (N × H)
127. C151#12383direct (N × H)
129. #2241C2×C151semidirect
131. #1674C2×C151semidirect
132. #1362C2×C151semidirect
133. Q8⋊C16C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3393×C1512
#2241×C1512
#2224×C1512
#1674×C1512
#1362×C1512
Q8⋊C16×C1512
#1331×C1512
#12383151