Finite Group Databasebeta

← C151×#13510 #50318435

Subgroups — C151×#13510 #50318435

Order 38656.

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

normal subgroups only

This group has 270 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×#365×C151C212yesmaximal
2#1944×C151C211yesmaximal, characteristic
3#1849×C151C211yesmaximal, characteristic
4#1387×C151C212yesmaximal
5#1377×C151C211yesmaximal, characteristic
6C2×M32×C151C2212yes—
7C2×#108×C151—21no—
8C2×#108×C151C2212yes—
9C2×#107×C151C2211yescharacteristic
10C2×#106×C151C2211yescharacteristic
11#423×C151—21no—
12C2×#97×C151C2211yescharacteristic
13#389×C151—21no—
14#365×C151—24no—
15#340×C151—21no—
16C2×M16×C151—22no—
17C22×C8×C151D411yescharacteristic
18C22×C8×C151C2311yescharacteristic
19C2×C4⋊C4×C151—21no—
20C2×C4⋊C4×C151—21no—
21C2×C4⋊C4×C151—41no—
22C2×C42×C151D411yescharacteristic
23M32×C151—22no—
24M32×C151Q814yes—
25C2×C16×C151—22no—
26#108×C151—22no—
27#108×C151—22no—
28#108×C151—42no—
29#107×C151—22no—
30#106×C151—21no—
31#106×C151D412yes—
32C4⋊C8×C151—42no—
33#97×C151—22no—
34#95×C151—41no—
35C22×C4×C151—41no—
36C22×C4×C151—41no—
37C22×C4×C151SD1611yescharacteristic
38C22×C4×C151SD1611yescharacteristic
39C22×C4×C151C2×D411yescharacteristic
40M16×C151—42no—
41M16×C151—42no—
42C2×C8×C151—21no—
43C2×C8×C151—21no—
44C2×C8×C151—42no—
45C2×C8×C151SD1612yes—
46C2×C8×C151C2×D411yescharacteristic
47C2×C8×C151C2×Q812yes—
48C2×C8×C151#4112yes—
49C2×C8×C151#4111yescharacteristic
50C4⋊C4×C151—22no—
51C4⋊C4×C151—41no—
52C4⋊C4×C151—41no—
53C4⋊C4×C151—41no—
54C4⋊C4×C151—82no—
55C42×C151—21no—
56C42×C151—21no—
57C16×C151—24no—
58C23×C151C2×SD1611yescharacteristic
59C2×C4×C151—21no—
60C2×C4×C151—21no—
61C2×C4×C151—41no—
62C2×C4×C151—41no—
63C2×C4×C151—42no—
64C2×C4×C151—81no—
65C2×C4×C151—81no—
66C2×C4×C151—81no—
67C2×C4×C151—81no—
68C2×C4×C151—81no—
69C2×C4×C151#12111yescharacteristic
70C2×C4×C151#12311yescharacteristic
71C2×C4×C151C4⋊Q811yescharacteristic
72C2×C4×C151C2×SD1611yescharacteristic
73C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
74C2×C4×C151#13711yescharacteristic
75C8×C151—22no—
76C8×C151—82no—
77C8×C151C22⋊Q812yes—
78C8×C151#12512yes—
79C22×C151—21no—
80C22×C151—21no—
81C22×C151#46111yescharacteristic
82C22×C151#48111yescharacteristic
83C22×C151#49811yescharacteristic
84C4×C151—41no—
85C4×C151—41no—
86C4×C151—82no—
87C4×C151—161no—
88C4×C151#39811yescharacteristic
89C4×C151#46011yescharacteristic
90C4×C151#48311yescharacteristic
91C4×C151#50111yescharacteristic
92C2×C151—21no—
93C2×C151—21no—
94C2×C151#208411yescharacteristic
95C2×C151#223811yescharacteristic
96C2×C151#223911yescharacteristic
97#13510C15111yesmaximal, characteristic, direct product factor, Sylow
98C151#1351011yescharacteristic, direct product factor, Sylow
99C2×#365C2×C15112yes—
100#1944C2×C15111yescharacteristic
101#1849C2×C15111yescharacteristic
102#1387C2×C15112yes—
103#1377C2×C15111yescharacteristic
104C2×M32C22×C15112yes—
105C2×#108—21no—
106C2×#108C22×C15112yes—
107C2×#107C22×C15111yescharacteristic
108C2×#106C22×C15111yescharacteristic
109#423—21no—
110C2×#97C22×C15111yescharacteristic
111#389—21no—
112#365—24no—
113#340—21no—
114C2×M16—22no—
115C22×C8D4×C15111yescharacteristic
116C22×C8C23×C15111yescharacteristic
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—41no—
120C2×C42D4×C15111yescharacteristic
121M32—22no—
122M32Q8×C15114yes—
123C2×C16—22no—
124#108—22no—
125#108—22no—
126#108—42no—
127#107—22no—
128#106—21no—
129#106D4×C15112yes—
130C4⋊C8—42no—
131#97—22no—
132#95—41no—
133C22×C4—41no—
134C22×C4—41no—
135C22×C4SD16×C15111yescharacteristic
136C22×C4SD16×C15111yescharacteristic
137C22×C4C2×D4×C15111yescharacteristic
138M16—42no—
139M16—42no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—42no—
143C2×C8SD16×C15112yes—
144C2×C8C2×D4×C15111yescharacteristic
145C2×C8C2×Q8×C15112yes—
146C2×C8#41×C15112yes—
147C2×C8#41×C15111yescharacteristic
148C4⋊C4—22no—
149C4⋊C4—41no—
150C4⋊C4—41no—
151C4⋊C4—41no—
152C4⋊C4—82no—
153C42—21no—
154C42—21no—
155C16—24no—
156C23C2×SD16×C15111yescharacteristic
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—42no—
162C2×C4—81no—
163C2×C4—81no—
164C2×C4—81no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4#121×C15111yescharacteristic
168C2×C4#123×C15111yescharacteristic
169C2×C4C4⋊Q8×C15111yescharacteristic
170C2×C4C2×SD16×C15111yescharacteristic
171C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
172C2×C4#137×C15111yescharacteristic
173C8—22no—
174C8—82no—
175C8C22⋊Q8×C15112yes—
176C8#125×C15112yes—
177C22—21no—
178C22—21no—
179C22#461×C15111yescharacteristic
180C22#481×C15111yescharacteristic
181C22#498×C15111yescharacteristic
182C4—41no—
183C4—41no—
184C4—82no—
185C4—161no—
186C4#398×C15111yescharacteristic
187C4#460×C15111yescharacteristic
188C4#483×C15111yescharacteristic
189C4#501×C15111yescharacteristic
190C2—21no—
191C2—21no—
192C2#2084×C15111yescharacteristic
193C2#2238×C15111yescharacteristic
194C2#2239×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#481
commutator, Frattini, cosocleC22×C8C23×C151
prime radicalC23×C151C2×SD16
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×#97×C151 ◁ G

Complements

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

NH ≅ G/Ntype
97. #13510C151direct (N × H)
98. C151#13510direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#365×C1512
#1944×C1512
#1849×C1512
#1387×C1512
#1377×C1512
#13510151