Finite Group Databasebeta

← C151×#13713 #50318638

Subgroups — C151×#13713 #50318638

Order 38656.

178 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 70 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#2215×C151C211yesmaximal, characteristic
2#2158×C151C211yesmaximal, characteristic, complemented
3#1424×C151C211yesmaximal, characteristic, complemented
4#1423×C151C211yesmaximal, characteristic, complemented
5#1415×C151C211yesmaximal, characteristic, complemented
6#1415×C151C211yesmaximal, characteristic, complemented
7C22⋊C32×C151C211yesmaximal, characteristic, complemented
8C2×D16×C151C2211yescharacteristic
9C22×C16×C151C2211yescharacteristic
10#466×C151—21no—
11#427×C151—21no—
12C2×C32×C151C2211yescharacteristic
13C2×C32×C151C2211yescharacteristic
14#367×C151—21no—
15#366×C151C2211yescharacteristic
16#366×C151C2211yescharacteristic
17#366×C151C2211yescharacteristic
18#357×C151—21no—
19C2×D8×C151—21no—
20C22×C8×C151D411yescharacteristic
21#121×C151—41no—
22#117×C151—41no—
23D16×C151—21no—
24D16×C151—21no—
25C2×C16×C151—21no—
26C2×C16×C151—21no—
27C2×C16×C151D411yescharacteristic
28C2×C16×C151C2311yescharacteristic
29#107×C151—21no—
30#107×C151—21no—
31#107×C151—21no—
32#106×C151—41no—
33#102×C151—41no—
34C32×C151—21no—
35C32×C151—21no—
36C2×D4×C151—41no—
37C2×D4×C151—81no—
38C22×C4×C151D811yescharacteristic
39D8×C151—41no—
40D8×C151—41no—
41C2×C8×C151—21no—
42C2×C8×C151—21no—
43C2×C8×C151D811yescharacteristic
44C2×C8×C151C2×D411yescharacteristic
45C4⋊C4×C151—41no—
46C4⋊C4×C151—41no—
47C4⋊C4×C151—41no—
48C22⋊C4×C151—81no—
49C22⋊C4×C151—81no—
50C42×C151—81no—
51C16×C151—21no—
52C16×C151#4111yescharacteristic
53C16×C151#4111yescharacteristic
54C23×C151—81no—
55C23×C151D1611yescharacteristic
56D4×C151—81no—
57D4×C151—81no—
58D4×C151—162no—
59C2×C4×C151—21no—
60C2×C4×C151—21no—
61C2×C4×C151—81no—
62C2×C4×C151—81no—
63C2×C4×C151—81no—
64C2×C4×C151D1611yescharacteristic
65C2×C4×C151C2×D811yescharacteristic
66C8×C151—21no—
67C8×C151#12311yescharacteristic
68C8×C151#13711yescharacteristic
69C22×C151—21no—
70C22×C151—21no—
71C22×C151—21no—
72C22×C151—161no—
73C22×C151—161no—
74C22×C151—161no—
75C22×C151C2×D1611yescharacteristic
76C4×C151—21no—
77C4×C151—161no—
78C4×C151—161no—
79C4×C151—161no—
80C4×C151#48011yescharacteristic
81C4×C151#51011yescharacteristic
82C2×C151—41no—
83C2×C151—321no—
84C2×C151#223211yescharacteristic
85C2×C151#226211yescharacteristic
86C2×C151#226311yescharacteristic
87#13713C15111yesmaximal, characteristic, direct product factor, Sylow
88C151#1371311yescharacteristic, direct product factor, Sylow
89#2215C2×C15111yescharacteristic
90#2158C2×C15111yescharacteristic, complemented
91#1424C2×C15111yescharacteristic, complemented
92#1423C2×C15111yescharacteristic, complemented
93#1415C2×C15111yescharacteristic, complemented
94#1415C2×C15111yescharacteristic, complemented
95C22⋊C32C2×C15111yescharacteristic, complemented
96C2×D16C22×C15111yescharacteristic
97C22×C16C22×C15111yescharacteristic
98#466—21no—
99#427—21no—
100C2×C32C22×C15111yescharacteristic
101C2×C32C22×C15111yescharacteristic
102#367—21no—
103#366C22×C15111yescharacteristic
104#366C22×C15111yescharacteristic
105#366C22×C15111yescharacteristic
106#357—21no—
107C2×D8—21no—
108C22×C8D4×C15111yescharacteristic
109#121—41no—
110#117—41no—
111D16—21no—
112D16—21no—
113C2×C16—21no—
114C2×C16—21no—
115C2×C16D4×C15111yescharacteristic
116C2×C16C23×C15111yescharacteristic
117#107—21no—
118#107—21no—
119#107—21no—
120#106—41no—
121#102—41no—
122C32—21no—
123C32—21no—
124C2×D4—41no—
125C2×D4—81no—
126C22×C4D8×C15111yescharacteristic
127D8—41no—
128D8—41no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8D8×C15111yescharacteristic
132C2×C8C2×D4×C15111yescharacteristic
133C4⋊C4—41no—
134C4⋊C4—41no—
135C4⋊C4—41no—
136C22⋊C4—81no—
137C22⋊C4—81no—
138C42—81no—
139C16—21no—
140C16#41×C15111yescharacteristic
141C16#41×C15111yescharacteristic
142C23—81no—
143C23D16×C15111yescharacteristic
144D4—81no—
145D4—81no—
146D4—162no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—81no—
150C2×C4—81no—
151C2×C4—81no—
152C2×C4D16×C15111yescharacteristic
153C2×C4C2×D8×C15111yescharacteristic
154C8—21no—
155C8#123×C15111yescharacteristic
156C8#137×C15111yescharacteristic
157C22—21no—
158C22—21no—
159C22—21no—
160C22—161no—
161C22—161no—
162C22—161no—
163C22C2×D16×C15111yescharacteristic
164C4—21no—
165C4—161no—
166C4—161no—
167C4—161no—
168C4#480×C15111yescharacteristic
169C4#510×C15111yescharacteristic
170C2—41no—
171C2—321no—
172C2#2232×C15111yescharacteristic
173C2#2262×C15111yescharacteristic
174C2#2263×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×D16
commutator, Frattini, cosocleC2×C16C23×C151
prime radical#2215×C151C2
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C22×C8×C151 ◁ C22×C16×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2158×C151C2semidirect
3. #1424×C151C2semidirect
4. #1423×C151C2semidirect
5. #1415×C151C2semidirect
6. #1415×C151C2semidirect
7. C22⋊C32×C151C2semidirect
87. #13713C151direct (N × H)
88. C151#13713direct (N × H)
90. #2158C2×C151semidirect
91. #1424C2×C151semidirect
92. #1423C2×C151semidirect
93. #1415C2×C151semidirect
94. #1415C2×C151semidirect
95. C22⋊C32C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2215×C1512
#2158×C1512
#1424×C1512
#1423×C1512
#1415×C1512
C22⋊C32×C1512
#13713151