Finite Group Databasebeta

← C151×#13671 #50318596

Subgroups — C151×#13671 #50318596

Order 38656.

284 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 74 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#3415×C151C211yesmaximal, characteristic
2#2264×C151C211yesmaximal, characteristic, complemented
3C2×SD64×C151C211yesmaximal, characteristic, complemented
4#2222×C151C211yesmaximal, characteristic, complemented
5#1419×C151C211yesmaximal, characteristic, complemented
6#1417×C151C211yesmaximal, characteristic, complemented
7#1401×C151C211yesmaximal, characteristic, complemented
8#576×C151—21no—
9#509×C151—22no—
10#509×C151—21no—
11#508×C151—21no—
12#508×C151C2211yescharacteristic
13C2×Q32×C151C2211yescharacteristic, complemented
14C2×D16×C151—21no—
15C2×D16×C151C2211yescharacteristic
16#504×C151C2211yescharacteristic
17#473×C151—21no—
18Q64×C151—21no—
19SD64×C151—22no—
20SD64×C151—21no—
21M64×C151C2211yescharacteristic, complemented
22C2×C32×C151C2211yescharacteristic, complemented
23#368×C151C2211yescharacteristic, complemented
24#362×C151—21no—
25H(5,𝔽2)×C151—41no—
26#137×C151—41no—
27AGL(1,ℤ/8)×C151—42no—
28AGL(1,ℤ/8)×C151—41no—
29#135×C151—22no—
30#135×C151—21no—
31C2×Q16×C151—21no—
32C2×D8×C151—22no—
33C2×D8×C151—21no—
34#131×C151D411yescharacteristic
35Q32×C151—21no—
36Q32×C151—21no—
37Q32×C151D411yescharacteristic
38SD32×C151—22no—
39SD32×C151—21no—
40D16×C151—22no—
41D16×C151—21no—
42D16×C151D411yescharacteristic
43D16×C151D412yes—
44M32×C151—21no—
45M32×C151D411yescharacteristic
46C2×C16×C151—21no—
47C2×C16×C151C2311yescharacteristic
48#108×C151—21no—
49#101×C151—41no—
50C32×C151—21no—
51C32×C151—21no—
52#41×C151—42no—
53#41×C151—41no—
54#41×C151—81no—
55#41×C151D811yescharacteristic
56C2×Q8×C151—41no—
57C2×D4×C151—42no—
58C2×D4×C151—41no—
59C2×D4×C151—82no—
60C2×D4×C151—81no—
61Q16×C151—21no—
62Q16×C151—41no—
63Q16×C151—41no—
64Q16×C151—81no—
65SD16×C151—42no—
66SD16×C151—41no—
67SD16×C151—81no—
68D8×C151—21no—
69D8×C151—22no—
70D8×C151—42no—
71D8×C151—41no—
72M16×C151—21no—
73M16×C151—41no—
74M16×C151D811yescharacteristic
75C2×C8×C151—21no—
76C2×C8×C151C2×D411yescharacteristic
77C16×C151—21no—
78C16×C151C2×D411yescharacteristic
79C16×C151C2×D411yescharacteristic
80C23×C151—82no—
81C23×C151—81no—
82Q8×C151—41no—
83Q8×C151—81no—
84Q8×C151—81no—
85Q8×C151D1611yescharacteristic
86D4×C151—21no—
87D4×C151—42no—
88D4×C151—41no—
89D4×C151—82no—
90D4×C151—82no—
91D4×C151—81no—
92D4×C151—81no—
93D4×C151D1611yescharacteristic
94C2×C4×C151—21no—
95C2×C4×C151—82no—
96C2×C4×C151—81no—
97C2×C4×C151—81no—
98C2×C4×C151C2×D811yescharacteristic
99C8×C151—21no—
100C8×C151—81no—
101C8×C151#12011yescharacteristic
102C8×C151AGL(1,ℤ/8)11yescharacteristic
103C22×C151—21no—
104C22×C151—82no—
105C22×C151—81no—
106C22×C151—321no—
107C22×C151—322no—
108C22×C151#50911yescharacteristic
109C4×C151—21no—
110C4×C151—81no—
111C4×C151—161no—
112C4×C151#44711yescharacteristic
113C4×C151C2×D1611yescharacteristic
114C2×C151—21no—
115C2×C151—41no—
116C2×C151—162no—
117C2×C151—161no—
118C2×C151#218411yescharacteristic
119#13671C15111yesmaximal, characteristic, direct product factor, Sylow
120C151#1367111yescharacteristic, direct product factor, Sylow
121#3415C2×C15111yescharacteristic
122#2264C2×C15111yescharacteristic, complemented
123C2×SD64C2×C15111yescharacteristic, complemented
124#2222C2×C15111yescharacteristic, complemented
125#1419C2×C15111yescharacteristic, complemented
126#1417C2×C15111yescharacteristic, complemented
127#1401C2×C15111yescharacteristic, complemented
128#576—21no—
129#509—22no—
130#509—21no—
131#508—21no—
132#508C22×C15111yescharacteristic
133C2×Q32C22×C15111yescharacteristic, complemented
134C2×D16—21no—
135C2×D16C22×C15111yescharacteristic
136#504C22×C15111yescharacteristic
137#473—21no—
138Q64—21no—
139SD64—22no—
140SD64—21no—
141M64C22×C15111yescharacteristic, complemented
142C2×C32C22×C15111yescharacteristic, complemented
143#368C22×C15111yescharacteristic, complemented
144#362—21no—
145H(5,𝔽2)—41no—
146#137—41no—
147AGL(1,ℤ/8)—42no—
148AGL(1,ℤ/8)—41no—
149#135—22no—
150#135—21no—
151C2×Q16—21no—
152C2×D8—22no—
153C2×D8—21no—
154#131D4×C15111yescharacteristic
155Q32—21no—
156Q32—21no—
157Q32D4×C15111yescharacteristic
158SD32—22no—
159SD32—21no—
160D16—22no—
161D16—21no—
162D16D4×C15111yescharacteristic
163D16D4×C15112yes—
164M32—21no—
165M32D4×C15111yescharacteristic
166C2×C16—21no—
167C2×C16C23×C15111yescharacteristic
168#108—21no—
169#101—41no—
170C32—21no—
171C32—21no—
172#41—42no—
173#41—41no—
174#41—81no—
175#41D8×C15111yescharacteristic
176C2×Q8—41no—
177C2×D4—42no—
178C2×D4—41no—
179C2×D4—82no—
180C2×D4—81no—
181Q16—21no—
182Q16—41no—
183Q16—41no—
184Q16—81no—
185SD16—42no—
186SD16—41no—
187SD16—81no—
188D8—21no—
189D8—22no—
190D8—42no—
191D8—41no—
192M16—21no—
193M16—41no—
194M16D8×C15111yescharacteristic
195C2×C8—21no—
196C2×C8C2×D4×C15111yescharacteristic
197C16—21no—
198C16C2×D4×C15111yescharacteristic
199C16C2×D4×C15111yescharacteristic
200C23—82no—
201C23—81no—
202Q8—41no—
203Q8—81no—
204Q8—81no—
205Q8D16×C15111yescharacteristic
206D4—21no—
207D4—41no—
208D4—42no—
209D4—82no—
210D4—82no—
211D4—81no—
212D4—81no—
213D4D16×C15111yescharacteristic
214C2×C4—21no—
215C2×C4—82no—
216C2×C4—81no—
217C2×C4—81no—
218C2×C4C2×D8×C15111yescharacteristic
219C8—21no—
220C8—81no—
221C8#120×C15111yescharacteristic
222C8AGL(1,ℤ/8)×C15111yescharacteristic
223C22—21no—
224C22—82no—
225C22—81no—
226C22—321no—
227C22—322no—
228C22#509×C15111yescharacteristic
229C4—21no—
230C4—81no—
231C4—161no—
232C4#447×C15111yescharacteristic
233C4C2×D16×C15111yescharacteristic
234C2—21no—
235C2—41no—
236C2—162no—
237C2—161no—
238C2#2184×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#2184
commutator, Frattini, cosocleC2×C16C23×C151
prime radical#3415×C151C2
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C2×C4×C151 ◁ #131×C151 ◁ #504×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2264×C151C2semidirect
3. C2×SD64×C151C2semidirect
4. #2222×C151C2semidirect
5. #1419×C151C2semidirect
6. #1417×C151C2semidirect
7. #1401×C151C2semidirect
13. C2×Q32×C151C22semidirect
21. M64×C151C22semidirect
22. C2×C32×C151C22semidirect
23. #368×C151C22semidirect
119. #13671C151direct (N × H)
120. C151#13671direct (N × H)
122. #2264C2×C151semidirect
123. C2×SD64C2×C151semidirect
124. #2222C2×C151semidirect
125. #1419C2×C151semidirect
126. #1417C2×C151semidirect
127. #1401C2×C151semidirect
133. C2×Q32C22×C151semidirect
141. M64C22×C151semidirect
142. C2×C32C22×C151semidirect
143. #368C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3415×C1512
#2264×C1512
C2×SD64×C1512
#2222×C1512
#1419×C1512
#1417×C1512
#1401×C1512
#13671151