Finite Group Databasebeta

← C151×#13413 #50318338

Subgroups — C151×#13413 #50318338

Order 38656.

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

normal subgroups only

This group has 540 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
1C2×#493×C151C211yesmaximal, characteristic
2C2×#361×C151C212yesmaximal, complemented
3#2140×C151C212yesmaximal, complemented
4#1945×C151C211yesmaximal, characteristic, complemented
5#1376×C151C211yesmaximal, characteristic, complemented
6C22×D8×C151—21no—
7C22×D8×C151C2212yes—
8C2×#127×C151—21no—
9C2×M32×C151C2212yes—
10#493×C151—24no—
11C2×#108×C151C2211yescharacteristic
12#427×C151C2211yescharacteristic
13#424×C151—21no—
14C2×C4×C8×C151C2211yescharacteristic
15#361×C151—24no—
16#357×C151—24no—
17#339×C151—21no—
18C22×D4×C151—22no—
19C22×D4×C151—42no—
20C2×D8×C151—24no—
21C2×D8×C151—22no—
22C2×D8×C151—22no—
23C2×D8×C151—22no—
24C2×D8×C151—22no—
25C2×D8×C151—22no—
26C2×D8×C151—42no—
27C2×D8×C151—42no—
28C2×D8×C151D414yes—
29C2×M16×C151—21no—
30C22×C8×C151D411yescharacteristic
31C22×C8×C151C2311yescharacteristic
32#127×C151—24no—
33#127×C151—42no—
34#117×C151—21no—
35C2×C42×C151D411yescharacteristic
36M32×C151—22no—
37M32×C151—22no—
38C2×C16×C151—22no—
39#108×C151—22no—
40#107×C151D412yescomplemented
41#106×C151—21no—
42C4⋊C8×C151—42no—
43C4×C8×C151—22no—
44C24×C151—42no—
45C2×D4×C151—24no—
46C2×D4×C151—48no—
47C2×D4×C151—42no—
48C2×D4×C151—42no—
49C2×D4×C151—42no—
50C2×D4×C151—42no—
51C2×D4×C151—42no—
52C2×D4×C151—88no—
53C22×C4×C151—21no—
54C22×C4×C151C2×D411yescharacteristic
55D8×C151—24no—
56D8×C151—24no—
57D8×C151—48no—
58D8×C151—42no—
59D8×C151—42no—
60M16×C151—41no—
61M16×C151—41no—
62C2×C8×C151—21no—
63C2×C8×C151—21no—
64C2×C8×C151—41no—
65C2×C8×C151D812yes—
66C2×C8×C151C2×D411yescharacteristic
67C2×C8×C151C2×D412yes—
68C2×C8×C151#4112yes—
69C2×C8×C151#4111yescharacteristic
70C4⋊C4×C151—22no—
71C22⋊C4×C151—41no—
72C42×C151—21no—
73C42×C151—41no—
74C42×C151SD1612yes—
75C16×C151—42no—
76C23×C151—44no—
77C23×C151—88no—
78C23×C151—82no—
79C23×C151—82no—
80C23×C151AGL(1,ℤ/8)11yescharacteristic
81D4×C151—44no—
82D4×C151—44no—
83D4×C151—816no—
84D4×C151—82no—
85D4×C151—82no—
86C2×C4×C151—24no—
87C2×C4×C151—22no—
88C2×C4×C151—42no—
89C2×C4×C151#12011yescharacteristic
90C2×C4×C151#12111yescharacteristic
91C2×C4×C151#12411yescharacteristic
92C2×C4×C151C2×D811yescharacteristic
93C2×C4×C151C2×SD1611yescharacteristic
94C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
95C8×C151—22no—
96C8×C151—81no—
97C8×C151#12112yes—
98C8×C151#12312yes—
99C22×C151—22no—
100C22×C151—88no—
101C22×C151—84no—
102C22×C151—164no—
103C22×C151—164no—
104C22×C151#45011yescharacteristic
105C22×C151#45911yescharacteristic
106C22×C151#49011yescharacteristic
107C4×C151—24no—
108C4×C151—82no—
109C4×C151#39411yescharacteristic
110C4×C151#44711yescharacteristic
111C4×C151#46011yescharacteristic
112C4×C151#48611yescharacteristic
113C2×C151—21no—
114C2×C151—21no—
115C2×C151—164no—
116C2×C151#204111yescharacteristic
117C2×C151#221312yes—
118#13413C15111yesmaximal, characteristic, direct product factor, Sylow
119C151#1341311yescharacteristic, direct product factor, Sylow
120C2×#493C2×C15111yescharacteristic
121C2×#361C2×C15112yescomplemented
122#2140C2×C15112yescomplemented
123#1945C2×C15111yescharacteristic, complemented
124#1376C2×C15111yescharacteristic, complemented
125C22×D8—21no—
126C22×D8C22×C15112yes—
127C2×#127—21no—
128C2×M32C22×C15112yes—
129#493—24no—
130C2×#108C22×C15111yescharacteristic
131#427C22×C15111yescharacteristic
132#424—21no—
133C2×C4×C8C22×C15111yescharacteristic
134#361—24no—
135#357—24no—
136#339—21no—
137C22×D4—22no—
138C22×D4—42no—
139C2×D8—24no—
140C2×D8—22no—
141C2×D8—22no—
142C2×D8—22no—
143C2×D8—22no—
144C2×D8—22no—
145C2×D8—42no—
146C2×D8—42no—
147C2×D8D4×C15114yes—
148C2×M16—21no—
149C22×C8D4×C15111yescharacteristic
150C22×C8C23×C15111yescharacteristic
151#127—24no—
152#127—42no—
153#117—21no—
154C2×C42D4×C15111yescharacteristic
155M32—22no—
156M32—22no—
157C2×C16—22no—
158#108—22no—
159#107D4×C15112yescomplemented
160#106—21no—
161C4⋊C8—42no—
162C4×C8—22no—
163C24—42no—
164C2×D4—24no—
165C2×D4—48no—
166C2×D4—42no—
167C2×D4—42no—
168C2×D4—42no—
169C2×D4—42no—
170C2×D4—42no—
171C2×D4—88no—
172C22×C4—21no—
173C22×C4C2×D4×C15111yescharacteristic
174D8—24no—
175D8—24no—
176D8—48no—
177D8—42no—
178D8—42no—
179M16—41no—
180M16—41no—
181C2×C8—21no—
182C2×C8—21no—
183C2×C8—41no—
184C2×C8D8×C15112yes—
185C2×C8C2×D4×C15111yescharacteristic
186C2×C8C2×D4×C15112yes—
187C2×C8#41×C15112yes—
188C2×C8#41×C15111yescharacteristic
189C4⋊C4—22no—
190C22⋊C4—41no—
191C42—21no—
192C42—41no—
193C42SD16×C15112yes—
194C16—42no—
195C23—44no—
196C23—88no—
197C23—82no—
198C23—82no—
199C23AGL(1,ℤ/8)×C15111yescharacteristic
200D4—44no—
201D4—44no—
202D4—816no—
203D4—82no—
204D4—82no—
205C2×C4—24no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4#120×C15111yescharacteristic
209C2×C4#121×C15111yescharacteristic
210C2×C4#124×C15111yescharacteristic
211C2×C4C2×D8×C15111yescharacteristic
212C2×C4C2×SD16×C15111yescharacteristic
213C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
214C8—22no—
215C8—81no—
216C8#121×C15112yes—
217C8#123×C15112yes—
218C22—22no—
219C22—88no—
220C22—84no—
221C22—164no—
222C22—164no—
223C22#450×C15111yescharacteristic
224C22#459×C15111yescharacteristic
225C22#490×C15111yescharacteristic
226C4—24no—
227C4—82no—
228C4#394×C15111yescharacteristic
229C4#447×C15111yescharacteristic
230C4#460×C15111yescharacteristic
231C4#486×C15111yescharacteristic
232C2—21no—
233C2—21no—
234C2—164no—
235C2#2041×C15111yescharacteristic
236C2#2213×C15112yes—
subgroupG/H
center, socleC22×C151#459
commutator, Frattini, cosocleC22×C8C23×C151
prime radicalC2×#493×C151C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×C4×C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#361×C151C2semidirect
3. #2140×C151C2semidirect
4. #1945×C151C2semidirect
5. #1376×C151C2semidirect
40. #107×C151D4semidirect
118. #13413C151direct (N × H)
119. C151#13413direct (N × H)
121. C2×#361C2×C151semidirect
122. #2140C2×C151semidirect
123. #1945C2×C151semidirect
124. #1376C2×C151semidirect
159. #107D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#493×C1512
C2×#361×C1512
#2140×C1512
#1945×C1512
#1376×C1512
#13413151