Finite Group Databasebeta

← C151×#10688 #50315613

Subgroups — C151×#10688 #50315613

Order 38656.

264 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 106 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#1940×C151C211yesmaximal, characteristic
2#1849×C151C211yesmaximal, characteristic
3#1303×C151C212yesmaximal
4#1301×C151C212yesmaximal
5#1275×C151C211yesmaximal, characteristic
6#431×C151C2212yes—
7C2×#108×C151—21no—
8C2×#108×C151—21no—
9#423×C151C2212yes—
10C2×C4⋊C8×C151—21no—
11C2×C4⋊C8×C151C2211yescharacteristic
12C2×#97×C151C2211yescharacteristic
13C4×C4⋊C4×C151C2211yescharacteristic
14#336×C151—21no—
15C2×M16×C151—22no—
16C22×C8×C151—21no—
17C22×C8×C151D411yescharacteristic
18C22×C8×C151D411yescharacteristic
19C2×C4⋊C4×C151—21no—
20C2×C42×C151—21no—
21C2×C42×C151C2311yescharacteristic
22#108×C151—42no—
23#108×C151—42no—
24C4⋊C8×C151—22no—
25C4⋊C8×C151—24no—
26C4⋊C8×C151—22no—
27C4⋊C8×C151—42no—
28C22⋊C8×C151—22no—
29#97×C151—22no—
30C4×C8×C151—22no—
31#95×C151Q811yescharacteristic
32#95×C151Q811yescharacteristic
33C22×C4×C151—21no—
34C22×C4×C151—21no—
35C22×C4×C151C2×D411yescharacteristic
36C22×C4×C151C2×Q811yescharacteristic
37C22×C4×C151#4111yescharacteristic
38M16×C151—42no—
39M16×C151—42no—
40C2×C8×C151—21no—
41C2×C8×C151—21no—
42C2×C8×C151—21no—
43C2×C8×C151—21no—
44C2×C8×C151—41no—
45C2×C8×C151—42no—
46C2×C8×C151—42no—
47C2×C8×C151—41no—
48C2×C8×C151—41no—
49C2×C8×C151SD1612yes—
50C2×C8×C151Q1612yes—
51C4⋊C4×C151—42no—
52C42×C151—41no—
53C42×C151—41no—
54C42×C151#4112yes—
55C42×C151#4112yes—
56C23×C151C22⋊Q811yescharacteristic
57C2×C4×C151—22no—
58C2×C4×C151—41no—
59C2×C4×C151—41no—
60C2×C4×C151—41no—
61C2×C4×C151—41no—
62C2×C4×C151—41no—
63C2×C4×C151—41no—
64C2×C4×C151—41no—
65C2×C4×C151#12311yescharacteristic
66C2×C4×C151#12411yescharacteristic
67C2×C4×C151#12512yes—
68C2×C4×C151#12612yes—
69C2×C4×C151C2×SD1611yescharacteristic
70C2×C4×C151C2×Q1611yescharacteristic
71C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
72C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
73C8×C151—22no—
74C8×C151—22no—
75C8×C151—82no—
76C8×C151—81no—
77C8×C151—82no—
78C22×C151—21no—
79C22×C151—21no—
80C22×C151#40011yescharacteristic
81C22×C151#47611yescharacteristic
82C22×C151#47711yescharacteristic
83C4×C151—22no—
84C4×C151—22no—
85C4×C151—42no—
86C4×C151—81no—
87C4×C151#48111yescharacteristic
88C4×C151#48411yescharacteristic
89C4×C151#48711yescharacteristic
90C4×C151#49011yescharacteristic
91C2×C151—21no—
92C2×C151—21no—
93C2×C151#210011yescharacteristic
94C2×C151#210211yescharacteristic
95C2×C151#210311yescharacteristic
96#10688C15111yesmaximal, characteristic, direct product factor, Sylow
97C151#1068811yescharacteristic, direct product factor, Sylow
98#1940C2×C15111yescharacteristic
99#1849C2×C15111yescharacteristic
100#1303C2×C15112yes—
101#1301C2×C15112yes—
102#1275C2×C15111yescharacteristic
103#431C22×C15112yes—
104C2×#108—21no—
105C2×#108—21no—
106#423C22×C15112yes—
107C2×C4⋊C8—21no—
108C2×C4⋊C8C22×C15111yescharacteristic
109C2×#97C22×C15111yescharacteristic
110C4×C4⋊C4C22×C15111yescharacteristic
111#336—21no—
112C2×M16—22no—
113C22×C8—21no—
114C22×C8D4×C15111yescharacteristic
115C22×C8D4×C15111yescharacteristic
116C2×C4⋊C4—21no—
117C2×C42—21no—
118C2×C42C23×C15111yescharacteristic
119#108—42no—
120#108—42no—
121C4⋊C8—22no—
122C4⋊C8—24no—
123C4⋊C8—22no—
124C4⋊C8—42no—
125C22⋊C8—22no—
126#97—22no—
127C4×C8—22no—
128#95Q8×C15111yescharacteristic
129#95Q8×C15111yescharacteristic
130C22×C4—21no—
131C22×C4—21no—
132C22×C4C2×D4×C15111yescharacteristic
133C22×C4C2×Q8×C15111yescharacteristic
134C22×C4#41×C15111yescharacteristic
135M16—42no—
136M16—42no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—41no—
142C2×C8—42no—
143C2×C8—42no—
144C2×C8—41no—
145C2×C8—41no—
146C2×C8SD16×C15112yes—
147C2×C8Q16×C15112yes—
148C4⋊C4—42no—
149C42—41no—
150C42—41no—
151C42#41×C15112yes—
152C42#41×C15112yes—
153C23C22⋊Q8×C15111yescharacteristic
154C2×C4—22no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4#123×C15111yescharacteristic
163C2×C4#124×C15111yescharacteristic
164C2×C4#125×C15112yes—
165C2×C4#126×C15112yes—
166C2×C4C2×SD16×C15111yescharacteristic
167C2×C4C2×Q16×C15111yescharacteristic
168C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
169C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
170C8—22no—
171C8—22no—
172C8—82no—
173C8—81no—
174C8—82no—
175C22—21no—
176C22—21no—
177C22#400×C15111yescharacteristic
178C22#476×C15111yescharacteristic
179C22#477×C15111yescharacteristic
180C4—22no—
181C4—22no—
182C4—42no—
183C4—81no—
184C4#481×C15111yescharacteristic
185C4#484×C15111yescharacteristic
186C4#487×C15111yescharacteristic
187C4#490×C15111yescharacteristic
188C2—21no—
189C2—21no—
190C2#2100×C15111yescharacteristic
191C2#2102×C15111yescharacteristic
192C2#2103×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151#124
commutator, Frattini, cosocleC2×C42C23×C151
socleC22×C151#400
prime radicalC23×C151C22⋊Q8
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
96. #10688C151direct (N × H)
97. C151#10688direct (N × H)

Maximal subgroups

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

subgroupindex
#1940×C1512
#1849×C1512
#1303×C1512
#1301×C1512
#1275×C1512
#10688151