Finite Group Databasebeta

← #2211×C151 #34065543

Subgroups — #2211×C151 #34065543

Order 19328.

158 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 64 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×Q32×C151C211yesmaximal, characteristic, complemented
2C2×SD32×C151C211yesmaximal, characteristic
3#495×C151C211yesmaximal, characteristic
4C4×Q16×C151C211yesmaximal, characteristic, complemented
5C4⋊C16×C151C211yesmaximal, characteristic, complemented
6#358×C151C211yesmaximal, characteristic, complemented
7#357×C151C211yesmaximal, characteristic
8C2×Q16×C151C2211yescharacteristic
9C2×Q16×C151C2211yescharacteristic
10C2×SD16×C151—21no—
11C2×D8×C151C2211yescharacteristic
12#124×C151—21no—
13C4×Q8×C151—21no—
14Q32×C151—22no—
15SD32×C151—22no—
16C2×C16×C151C2211yescharacteristic
17C2×C16×C151C2211yescharacteristic
18#107×C151C2211yescharacteristic
19#103×C151—21no—
20C4×C8×C151C2211yescharacteristic
21C2×Q8×C151—21no—
22C2×Q8×C151—21no—
23C2×D4×C151—21no—
24Q16×C151—21no—
25Q16×C151—21no—
26Q16×C151—21no—
27Q16×C151D412yes—
28SD16×C151—42no—
29D8×C151—21no—
30D8×C151—21no—
31C2×C8×C151D411yescharacteristic
32C2×C8×C151C2311yescharacteristic
33C4⋊C4×C151—21no—
34C4⋊C4×C151—41no—
35C22⋊C4×C151—41no—
36C22⋊C4×C151—41no—
37C42×C151—41no—
38C42×C151D411yescharacteristic
39C16×C151—21no—
40C16×C151—21no—
41C23×C151—41no—
42Q8×C151—22no—
43Q8×C151—41no—
44Q8×C151—41no—
45Q8×C151—41no—
46D4×C151—41no—
47D4×C151—41no—
48C2×C4×C151—41no—
49C2×C4×C151—41no—
50C2×C4×C151—41no—
51C2×C4×C151D811yescharacteristic
52C2×C4×C151D811yescharacteristic
53C2×C4×C151C2×D411yescharacteristic
54C8×C151—21no—
55C8×C151C2×D411yescharacteristic
56C8×C151#4111yescharacteristic
57C22×C151—81no—
58C22×C151—81no—
59C22×C151—81no—
60C22×C151C2×D811yescharacteristic
61C4×C151—21no—
62C4×C151—21no—
63C4×C151—42no—
64C4×C151—81no—
65C4×C151—81no—
66C4×C151#12111yescharacteristic
67C4×C151AGL(1,ℤ/8)11yescharacteristic
68C2×C151—161no—
69C2×C151#45911yescharacteristic
70C2×C151#50811yescharacteristic
71C2×C151#51011yescharacteristic
72C151#221111yescharacteristic, direct product factor, Sylow
73#2211C15111yesmaximal, characteristic, direct product factor, Sylow
74C2×Q32C2×C15111yescharacteristic, complemented
75C2×SD32C2×C15111yescharacteristic
76#495C2×C15111yescharacteristic
77C4×Q16C2×C15111yescharacteristic, complemented
78C4⋊C16C2×C15111yescharacteristic, complemented
79#358C2×C15111yescharacteristic, complemented
80#357C2×C15111yescharacteristic
81C2×Q16C22×C15111yescharacteristic
82C2×Q16C22×C15111yescharacteristic
83C2×SD16—21no—
84C2×D8C22×C15111yescharacteristic
85#124—21no—
86C4×Q8—21no—
87Q32—22no—
88SD32—22no—
89C2×C16C22×C15111yescharacteristic
90C2×C16C22×C15111yescharacteristic
91#107C22×C15111yescharacteristic
92#103—21no—
93C4×C8C22×C15111yescharacteristic
94C2×Q8—21no—
95C2×Q8—21no—
96C2×D4—21no—
97Q16—21no—
98Q16—21no—
99Q16—21no—
100Q16D4×C15112yes—
101SD16—42no—
102D8—21no—
103D8—21no—
104C2×C8D4×C15111yescharacteristic
105C2×C8C23×C15111yescharacteristic
106C4⋊C4—21no—
107C4⋊C4—41no—
108C22⋊C4—41no—
109C22⋊C4—41no—
110C42—41no—
111C42D4×C15111yescharacteristic
112C16—21no—
113C16—21no—
114C23—41no—
115Q8—22no—
116Q8—41no—
117Q8—41no—
118Q8—41no—
119D4—41no—
120D4—41no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4D8×C15111yescharacteristic
125C2×C4D8×C15111yescharacteristic
126C2×C4C2×D4×C15111yescharacteristic
127C8—21no—
128C8C2×D4×C15111yescharacteristic
129C8#41×C15111yescharacteristic
130C22—81no—
131C22—81no—
132C22—81no—
133C22C2×D8×C15111yescharacteristic
134C4—21no—
135C4—21no—
136C4—42no—
137C4—81no—
138C4—81no—
139C4#121×C15111yescharacteristic
140C4AGL(1,ℤ/8)×C15111yescharacteristic
141C2—161no—
142C2#459×C15111yescharacteristic
143C2#508×C15111yescharacteristic
144C2#510×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×D8
commutator, Frattini, cosocleC2×C8C23×C151
prime radicalC2×D8×C151C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ C4×C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×Q32×C151C2semidirect
4. C4×Q16×C151C2semidirect
5. C4⋊C16×C151C2semidirect
6. #358×C151C2semidirect
72. C151#2211direct (N × H)
73. #2211C151direct (N × H)
74. C2×Q32C2×C151semidirect
77. C4×Q16C2×C151semidirect
78. C4⋊C16C2×C151semidirect
79. #358C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×Q32×C1512
C2×SD32×C1512
#495×C1512
C4×Q16×C1512
C4⋊C16×C1512
#358×C1512
#357×C1512
#2211151