Finite Group Databasebeta

← C151×#11858 #50316783

Subgroups — C151×#11858 #50316783

Order 38656.

358 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 114 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#3169×C151C211yesmaximal, characteristic
2#2163×C151C211yesmaximal, characteristic, complemented
3#1835×C151C211yesmaximal, characteristic, complemented
4#1347×C151C214yesmaximal, complemented
5#532×C151—21no—
6#500×C151C411yescharacteristic, complemented
7#493×C151C411yescharacteristic, complemented
8#486×C151—21no—
9#466×C151—21no—
10#466×C151C2212yes—
11C4×D8×C151—21no—
12C4×D8×C151C412yescomplemented
13C2×C4×C8×C151C2211yescharacteristic
14#382×C151—21no—
15C4⋊C16×C151—21no—
16C22⋊C16×C151C2212yes—
17#346×C151—21no—
18#340×C151—21no—
19#340×C151C2212yes—
20C2×#41×C151—41no—
21C2×D8×C151—21no—
22C2×D8×C151C2×C412yes—
23C22×C8×C151D411yescharacteristic
24C22×C8×C151C2311yescharacteristic
25C4⋊Q8×C151—21no—
26#127×C151—21no—
27#124×C151—41no—
28#121×C151—22no—
29#121×C151—41no—
30C4×D4×C151—22no—
31C4×D4×C151—41no—
32C2×C4⋊C4×C151—22no—
33C2×C42×C151D411yescharacteristic
34C2×C16×C151—22no—
35#107×C151—21no—
36#107×C151C2×C412yes—
37#102×C151—22no—
38#102×C151—22no—
39C4×C8×C151C2×C411yescharacteristic
40C4×C8×C151C2×C411yescharacteristic
41C4×C8×C151D411yescharacteristic
42C4×C8×C151D411yescharacteristic
43#95×C151—41no—
44#95×C151—41no—
45#41×C151—84no—
46C2×Q8×C151—41no—
47C2×D4×C151—22no—
48C2×D4×C151—42no—
49C2×D4×C151—41no—
50C2×D4×C151—41no—
51C22×C4×C151—42no—
52C22×C4×C151—42no—
53C22×C4×C151D811yescharacteristic
54C22×C4×C151D811yescharacteristic
55C22×C4×C151C2×D411yescharacteristic
56D8×C151—42no—
57D8×C151—42no—
58C2×C8×C151—41no—
59C2×C8×C151—41no—
60C2×C8×C151C22⋊C411yescharacteristic
61C2×C8×C151C22⋊C411yescharacteristic
62C2×C8×C151C22×C411yescharacteristic
63C2×C8×C151C2×D411yescharacteristic
64C4⋊C4×C151—22no—
65C4⋊C4×C151—42no—
66C4⋊C4×C151—42no—
67C4⋊C4×C151—41no—
68C22⋊C4×C151—42no—
69C22⋊C4×C151—42no—
70C42×C151C22⋊C411yescharacteristic
71C42×C151C22⋊C411yescharacteristic
72C42×C151SD1611yescharacteristic
73C42×C151SD1611yescharacteristic
74C16×C151—42no—
75C23×C151—42no—
76C23×C151C2×D811yescharacteristic
77Q8×C151—82no—
78D4×C151—42no—
79D4×C151—42no—
80D4×C151—82no—
81D4×C151—82no—
82D4×C151—84no—
83C2×C4×C151—22no—
84C2×C4×C151—21no—
85C2×C4×C151—21no—
86C2×C4×C151—41no—
87C2×C4×C151—42no—
88C2×C4×C151—84no—
89C2×C4×C151—82no—
90C2×C4×C151—82no—
91C2×C4×C151—82no—
92C2×C4×C151#10211yescharacteristic
93C2×C4×C151#10211yescharacteristic
94C2×C4×C151#10211yescharacteristic
95C2×C4×C151#10211yescharacteristic
96C2×C4×C151C2×C22⋊C411yescharacteristic
97C2×C4×C151C2×SD1611yescharacteristic
98C8×C151—21no—
99C8×C151—21no—
100C8×C151—21no—
101C8×C151—21no—
102C22×C151—21no—
103C22×C151—21no—
104C22×C151—82no—
105C22×C151—82no—
106C22×C151—82no—
107C22×C151C2×#10211yescharacteristic
108C22×C151#50912yes—
109C4×C151—21no—
110C4×C151—21no—
111C4×C151—21no—
112C4×C151—21no—
113C4×C151—21no—
114C4×C151—82no—
115C4×C151—162no—
116C4×C151#41011yescharacteristic
117C4×C151#42111yescharacteristic
118C2×C151—22no—
119C2×C151—162no—
120C2×C151#151711yescharacteristic
121C2×C151#214011yescharacteristic
122C2×C151#214511yescharacteristic
123#11858C15111yesmaximal, characteristic, direct product factor, Sylow
124C151#1185811yescharacteristic, direct product factor, Sylow
125#3169C2×C15111yescharacteristic
126#2163C2×C15111yescharacteristic, complemented
127#1835C2×C15111yescharacteristic, complemented
128#1347C2×C15114yescomplemented
129#532—21no—
130#500C4×C15111yescharacteristic, complemented
131#493C4×C15111yescharacteristic, complemented
132#486—21no—
133#466—21no—
134#466C22×C15112yes—
135C4×D8—21no—
136C4×D8C4×C15112yescomplemented
137C2×C4×C8C22×C15111yescharacteristic
138#382—21no—
139C4⋊C16—21no—
140C22⋊C16C22×C15112yes—
141#346—21no—
142#340—21no—
143#340C22×C15112yes—
144C2×#41—41no—
145C2×D8—21no—
146C2×D8C2×C4×C15112yes—
147C22×C8D4×C15111yescharacteristic
148C22×C8C23×C15111yescharacteristic
149C4⋊Q8—21no—
150#127—21no—
151#124—41no—
152#121—22no—
153#121—41no—
154C4×D4—22no—
155C4×D4—41no—
156C2×C4⋊C4—22no—
157C2×C42D4×C15111yescharacteristic
158C2×C16—22no—
159#107—21no—
160#107C2×C4×C15112yes—
161#102—22no—
162#102—22no—
163C4×C8C2×C4×C15111yescharacteristic
164C4×C8C2×C4×C15111yescharacteristic
165C4×C8D4×C15111yescharacteristic
166C4×C8D4×C15111yescharacteristic
167#95—41no—
168#95—41no—
169#41—84no—
170C2×Q8—41no—
171C2×D4—22no—
172C2×D4—42no—
173C2×D4—41no—
174C2×D4—41no—
175C22×C4—42no—
176C22×C4—42no—
177C22×C4D8×C15111yescharacteristic
178C22×C4D8×C15111yescharacteristic
179C22×C4C2×D4×C15111yescharacteristic
180D8—42no—
181D8—42no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8C22⋊C4×C15111yescharacteristic
185C2×C8C22⋊C4×C15111yescharacteristic
186C2×C8C22×C4×C15111yescharacteristic
187C2×C8C2×D4×C15111yescharacteristic
188C4⋊C4—22no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—41no—
192C22⋊C4—42no—
193C22⋊C4—42no—
194C42C22⋊C4×C15111yescharacteristic
195C42C22⋊C4×C15111yescharacteristic
196C42SD16×C15111yescharacteristic
197C42SD16×C15111yescharacteristic
198C16—42no—
199C23—42no—
200C23C2×D8×C15111yescharacteristic
201Q8—82no—
202D4—42no—
203D4—42no—
204D4—82no—
205D4—82no—
206D4—84no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—84no—
213C2×C4—82no—
214C2×C4—82no—
215C2×C4—82no—
216C2×C4#102×C15111yescharacteristic
217C2×C4#102×C15111yescharacteristic
218C2×C4#102×C15111yescharacteristic
219C2×C4#102×C15111yescharacteristic
220C2×C4C2×C22⋊C4×C15111yescharacteristic
221C2×C4C2×SD16×C15111yescharacteristic
222C8—21no—
223C8—21no—
224C8—21no—
225C8—21no—
226C22—21no—
227C22—21no—
228C22—82no—
229C22—82no—
230C22—82no—
231C22C2×#102×C15111yescharacteristic
232C22#509×C15112yes—
233C4—21no—
234C4—21no—
235C4—21no—
236C4—21no—
237C4—21no—
238C4—82no—
239C4—162no—
240C4#410×C15111yescharacteristic
241C4#421×C15111yescharacteristic
242C2—22no—
243C2—162no—
244C2#1517×C15111yescharacteristic
245C2#2140×C15111yescharacteristic
246C2#2145×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#102
commutatorC2×C8C22×C4×C151
Frattini, cosocleC22×C8C23×C151
prime radical#3169×C151C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ C2×C4×C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2163×C151C2semidirect
3. #1835×C151C2semidirect
4. #1347×C151C2semidirect
6. #500×C151C4semidirect
7. #493×C151C4semidirect
12. C4×D8×C151C4semidirect
123. #11858C151direct (N × H)
124. C151#11858direct (N × H)
126. #2163C2×C151semidirect
127. #1835C2×C151semidirect
128. #1347C2×C151semidirect
130. #500C4×C151semidirect
131. #493C4×C151semidirect
136. C4×D8C4×C151semidirect

Maximal subgroups

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

subgroupindex
#3169×C1512
#2163×C1512
#1835×C1512
#1347×C1512
#11858151