Finite Group Databasebeta

← C151×#13707 #50318632

Subgroups — C151×#13707 #50318632

Order 38656.

170 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 74 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#2253×C151C211yesmaximal, characteristic, complemented
2C4×D16×C151C211yesmaximal, characteristic
3#1424×C151C211yesmaximal, characteristic, complemented
4#1423×C151C211yesmaximal, characteristic, complemented
5C4⋊C32×C151C211yesmaximal, characteristic, complemented
6#1415×C151C211yesmaximal, characteristic
7#1415×C151C211yesmaximal, characteristic
8C2×D16×C151C2211yescharacteristic
9#499×C151—21no—
10C4×D8×C151—21no—
11C2×C32×C151C2211yescharacteristic
12C2×C32×C151C2211yescharacteristic
13#367×C151—21no—
14#366×C151C2211yescharacteristic
15#366×C151C2211yescharacteristic
16#366×C151C2211yescharacteristic
17#357×C151—21no—
18C4×C16×C151C2211yescharacteristic
19C2×D8×C151—21no—
20#125×C151—41no—
21C4×D4×C151—41no—
22D16×C151—21no—
23D16×C151Q812yes—
24C2×C16×C151D411yescharacteristic
25C2×C16×C151C2311yescharacteristic
26#107×C151—21no—
27#107×C151—21no—
28#107×C151—21no—
29#106×C151—41no—
30#102×C151—41no—
31C4×C8×C151D411yescharacteristic
32C32×C151—21no—
33C32×C151—21no—
34C2×D4×C151—41no—
35C22×C4×C151—81no—
36D8×C151—22no—
37D8×C151—41no—
38C2×C8×C151D811yescharacteristic
39C2×C8×C151C2×D411yescharacteristic
40C4⋊C4×C151—41no—
41C4⋊C4×C151—41no—
42C4⋊C4×C151—41no—
43C4⋊C4×C151—81no—
44C4⋊C4×C151—81no—
45C22⋊C4×C151—81no—
46C42×C151D811yescharacteristic
47C16×C151—21no—
48C16×C151C2×Q811yescharacteristic
49C16×C151#4111yescharacteristic
50C23×C151—81no—
51D4×C151—42no—
52D4×C151—81no—
53C2×C4×C151—81no—
54C2×C4×C151—81no—
55C2×C4×C151—81no—
56C2×C4×C151—162no—
57C2×C4×C151D1611yescharacteristic
58C2×C4×C151D1611yescharacteristic
59C2×C4×C151C2×D811yescharacteristic
60C8×C151—21no—
61C8×C151C22⋊Q811yescharacteristic
62C8×C151#13711yescharacteristic
63C22×C151—82no—
64C22×C151—161no—
65C22×C151—161no—
66C22×C151C2×D1611yescharacteristic
67C4×C151—21no—
68C4×C151—21no—
69C4×C151—161no—
70C4×C151—161no—
71C4×C151—161no—
72C4×C151#47411yescharacteristic
73C4×C151#51011yescharacteristic
74C2×C151—162no—
75C2×C151#222411yescharacteristic
76C2×C151#226211yescharacteristic
77C2×C151#226311yescharacteristic
78#13707C15111yesmaximal, characteristic, direct product factor, Sylow
79C151#1370711yescharacteristic, direct product factor, Sylow
80#2253C2×C15111yescharacteristic, complemented
81C4×D16C2×C15111yescharacteristic
82#1424C2×C15111yescharacteristic, complemented
83#1423C2×C15111yescharacteristic, complemented
84C4⋊C32C2×C15111yescharacteristic, complemented
85#1415C2×C15111yescharacteristic
86#1415C2×C15111yescharacteristic
87C2×D16C22×C15111yescharacteristic
88#499—21no—
89C4×D8—21no—
90C2×C32C22×C15111yescharacteristic
91C2×C32C22×C15111yescharacteristic
92#367—21no—
93#366C22×C15111yescharacteristic
94#366C22×C15111yescharacteristic
95#366C22×C15111yescharacteristic
96#357—21no—
97C4×C16C22×C15111yescharacteristic
98C2×D8—21no—
99#125—41no—
100C4×D4—41no—
101D16—21no—
102D16Q8×C15112yes—
103C2×C16D4×C15111yescharacteristic
104C2×C16C23×C15111yescharacteristic
105#107—21no—
106#107—21no—
107#107—21no—
108#106—41no—
109#102—41no—
110C4×C8D4×C15111yescharacteristic
111C32—21no—
112C32—21no—
113C2×D4—41no—
114C22×C4—81no—
115D8—22no—
116D8—41no—
117C2×C8D8×C15111yescharacteristic
118C2×C8C2×D4×C15111yescharacteristic
119C4⋊C4—41no—
120C4⋊C4—41no—
121C4⋊C4—41no—
122C4⋊C4—81no—
123C4⋊C4—81no—
124C22⋊C4—81no—
125C42D8×C15111yescharacteristic
126C16—21no—
127C16C2×Q8×C15111yescharacteristic
128C16#41×C15111yescharacteristic
129C23—81no—
130D4—42no—
131D4—81no—
132C2×C4—81no—
133C2×C4—81no—
134C2×C4—81no—
135C2×C4—162no—
136C2×C4D16×C15111yescharacteristic
137C2×C4D16×C15111yescharacteristic
138C2×C4C2×D8×C15111yescharacteristic
139C8—21no—
140C8C22⋊Q8×C15111yescharacteristic
141C8#137×C15111yescharacteristic
142C22—82no—
143C22—161no—
144C22—161no—
145C22C2×D16×C15111yescharacteristic
146C4—21no—
147C4—21no—
148C4—161no—
149C4—161no—
150C4—161no—
151C4#474×C15111yescharacteristic
152C4#510×C15111yescharacteristic
153C2—162no—
154C2#2224×C15111yescharacteristic
155C2#2262×C15111yescharacteristic
156C2#2263×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×D16
commutator, Frattini, cosocleC2×C16C23×C151
prime radicalC2×D16×C151C22
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ C4×C8×C151 ◁ C4×C16×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2253×C151C2semidirect
3. #1424×C151C2semidirect
4. #1423×C151C2semidirect
5. C4⋊C32×C151C2semidirect
78. #13707C151direct (N × H)
79. C151#13707direct (N × H)
80. #2253C2×C151semidirect
82. #1424C2×C151semidirect
83. #1423C2×C151semidirect
84. C4⋊C32C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2253×C1512
C4×D16×C1512
#1424×C1512
#1423×C1512
C4⋊C32×C1512
#1415×C1512
#13707151