Finite Group Databasebeta

← C151×#13716 #50318641

Subgroups — C151×#13716 #50318641

Order 38656.

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

normal subgroups only

This group has 168 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#2216×C151C211yesmaximal, characteristic
2#2158×C151C211yesmaximal, characteristic
3#1424×C151C211yesmaximal, characteristic, complemented
4#1423×C151C211yesmaximal, characteristic, complemented
5#1416×C151C211yesmaximal, characteristic, complemented
6#1416×C151C211yesmaximal, characteristic, complemented
7C22⋊C32×C151C211yesmaximal, characteristic
8C2×Q32×C151C2211yescharacteristic
9C22×C16×C151C2211yescharacteristic
10#467×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#358×C151—21no—
19C2×Q16×C151—21no—
20C22×C8×C151D411yescharacteristic
21C22⋊Q8×C151—41no—
22#117×C151—41no—
23Q32×C151—21no—
24Q32×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#103×C151—41no—
34C32×C151—21no—
35C32×C151—21no—
36C2×Q8×C151—41no—
37C22×C4×C151D811yescharacteristic
38Q16×C151—41no—
39Q16×C151—41no—
40C2×C8×C151—21no—
41C2×C8×C151—21no—
42C2×C8×C151D811yescharacteristic
43C2×C8×C151C2×D411yescharacteristic
44C4⋊C4×C151—41no—
45C4⋊C4×C151—41no—
46C4⋊C4×C151—41no—
47C4⋊C4×C151—81no—
48C22⋊C4×C151—81no—
49C22⋊C4×C151—81no—
50C42×C151—81no—
51C16×C151—21no—
52C16×C151#4111yescharacteristic
53C16×C151#4111yescharacteristic
54C23×C151D1611yescharacteristic
55Q8×C151—81no—
56Q8×C151—81no—
57C2×C4×C151—21no—
58C2×C4×C151—21no—
59C2×C4×C151—81no—
60C2×C4×C151—81no—
61C2×C4×C151—81no—
62C2×C4×C151—81no—
63C2×C4×C151D1611yescharacteristic
64C2×C4×C151C2×D811yescharacteristic
65C8×C151—21no—
66C8×C151#12311yescharacteristic
67C8×C151#13711yescharacteristic
68C22×C151—21no—
69C22×C151—21no—
70C22×C151—21no—
71C22×C151C2×D1611yescharacteristic
72C4×C151—21no—
73C4×C151—161no—
74C4×C151—161no—
75C4×C151—161no—
76C4×C151—161no—
77C4×C151#48011yescharacteristic
78C4×C151#51011yescharacteristic
79C2×C151—41no—
80C2×C151#223211yescharacteristic
81C2×C151#226211yescharacteristic
82C2×C151#226411yescharacteristic
83#13716C15111yesmaximal, characteristic, direct product factor, Sylow
84C151#1371611yescharacteristic, direct product factor, Sylow
85#2216C2×C15111yescharacteristic
86#2158C2×C15111yescharacteristic
87#1424C2×C15111yescharacteristic, complemented
88#1423C2×C15111yescharacteristic, complemented
89#1416C2×C15111yescharacteristic, complemented
90#1416C2×C15111yescharacteristic, complemented
91C22⋊C32C2×C15111yescharacteristic
92C2×Q32C22×C15111yescharacteristic
93C22×C16C22×C15111yescharacteristic
94#467—21no—
95#427—21no—
96C2×C32C22×C15111yescharacteristic
97C2×C32C22×C15111yescharacteristic
98#367—21no—
99#366C22×C15111yescharacteristic
100#366C22×C15111yescharacteristic
101#366C22×C15111yescharacteristic
102#358—21no—
103C2×Q16—21no—
104C22×C8D4×C15111yescharacteristic
105C22⋊Q8—41no—
106#117—41no—
107Q32—21no—
108Q32—21no—
109C2×C16—21no—
110C2×C16—21no—
111C2×C16D4×C15111yescharacteristic
112C2×C16C23×C15111yescharacteristic
113#107—21no—
114#107—21no—
115#107—21no—
116#106—41no—
117#103—41no—
118C32—21no—
119C32—21no—
120C2×Q8—41no—
121C22×C4D8×C15111yescharacteristic
122Q16—41no—
123Q16—41no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8D8×C15111yescharacteristic
127C2×C8C2×D4×C15111yescharacteristic
128C4⋊C4—41no—
129C4⋊C4—41no—
130C4⋊C4—41no—
131C4⋊C4—81no—
132C22⋊C4—81no—
133C22⋊C4—81no—
134C42—81no—
135C16—21no—
136C16#41×C15111yescharacteristic
137C16#41×C15111yescharacteristic
138C23D16×C15111yescharacteristic
139Q8—81no—
140Q8—81no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—81no—
144C2×C4—81no—
145C2×C4—81no—
146C2×C4—81no—
147C2×C4D16×C15111yescharacteristic
148C2×C4C2×D8×C15111yescharacteristic
149C8—21no—
150C8#123×C15111yescharacteristic
151C8#137×C15111yescharacteristic
152C22—21no—
153C22—21no—
154C22—21no—
155C22C2×D16×C15111yescharacteristic
156C4—21no—
157C4—161no—
158C4—161no—
159C4—161no—
160C4—161no—
161C4#480×C15111yescharacteristic
162C4#510×C15111yescharacteristic
163C2—41no—
164C2#2232×C15111yescharacteristic
165C2#2262×C15111yescharacteristic
166C2#2264×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×D16
commutator, Frattini, cosocleC2×C16C23×C151
prime radicalC23×C151D16
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
3. #1424×C151C2semidirect
4. #1423×C151C2semidirect
5. #1416×C151C2semidirect
6. #1416×C151C2semidirect
83. #13716C151direct (N × H)
84. C151#13716direct (N × H)
87. #1424C2×C151semidirect
88. #1423C2×C151semidirect
89. #1416C2×C151semidirect
90. #1416C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2216×C1512
#2158×C1512
#1424×C1512
#1423×C1512
#1416×C1512
C22⋊C32×C1512
#13716151