Finite Group Databasebeta

← #1678×C151 #34065010

Subgroups — #1678×C151 #34065010

Order 19328.

160 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 68 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#486×C151C211yesmaximal, characteristic
2#477×C151C211yesmaximal, characteristic, complemented
3#460×C151C211yesmaximal, characteristic
4C8×Q8×C151C211yesmaximal, characteristic, complemented
5#334×C151C211yesmaximal, characteristic, complemented
6#333×C151C211yesmaximal, characteristic, complemented
7#331×C151C211yesmaximal, characteristic
8C2×SD16×C151—21no—
9C4⋊Q8×C151C2211yescharacteristic
10#127×C151C2211yescharacteristic
11C4×Q8×C151C2211yescharacteristic
12#107×C151—21no—
13C4⋊C8×C151—21no—
14C4⋊C8×C151C2211yescharacteristic
15C4⋊C8×C151C2211yescharacteristic
16C4⋊C8×C151C2211yescharacteristic
17#103×C151—21no—
18#102×C151—21no—
19#102×C151—21no—
20#102×C151—21no—
21C4×C8×C151—21no—
22C4×C8×C151C2211yescharacteristic
23C2×Q8×C151—21no—
24C2×Q8×C151D411yescharacteristic
25C2×D4×C151—21no—
26C2×D4×C151—21no—
27C2×D4×C151—21no—
28SD16×C151—42no—
29C2×C8×C151—21no—
30C2×C8×C151—21no—
31C2×C8×C151—21no—
32C2×C8×C151D411yescharacteristic
33C2×C8×C151D411yescharacteristic
34C4⋊C4×C151—21no—
35C4⋊C4×C151—21no—
36C4⋊C4×C151—21no—
37C4⋊C4×C151D411yescharacteristic
38C42×C151—21no—
39C42×C151C2311yescharacteristic
40C23×C151—41no—
41Q8×C151—21no—
42Q8×C151—81no—
43Q8×C151SD1612yes—
44D4×C151—41no—
45D4×C151—41no—
46D4×C151—41no—
47D4×C151—41no—
48D4×C151—81no—
49C2×C4×C151—21no—
50C2×C4×C151—21no—
51C2×C4×C151—41no—
52C2×C4×C151C2×D411yescharacteristic
53C2×C4×C151C2×D411yescharacteristic
54C2×C4×C151#4111yescharacteristic
55C8×C151—21no—
56C8×C151—21no—
57C8×C151—41no—
58C8×C151—41no—
59C8×C151—41no—
60C22×C151—81no—
61C22×C151—81no—
62C22×C151—81no—
63C22×C151#12111yescharacteristic
64C4×C151—22no—
65C4×C151—21no—
66C4×C151—41no—
67C4×C151—81no—
68C4×C151C2×SD1611yescharacteristic
69C4×C151#13511yescharacteristic
70C4×C151#13511yescharacteristic
71C4×C151#13711yescharacteristic
72C2×C151—161no—
73C2×C151#46411yescharacteristic
74C2×C151#46511yescharacteristic
75C2×C151#47211yescharacteristic
76C151#167811yescharacteristic, direct product factor, Sylow
77#1678C15111yesmaximal, characteristic, direct product factor, Sylow
78#486C2×C15111yescharacteristic
79#477C2×C15111yescharacteristic, complemented
80#460C2×C15111yescharacteristic
81C8×Q8C2×C15111yescharacteristic, complemented
82#334C2×C15111yescharacteristic, complemented
83#333C2×C15111yescharacteristic, complemented
84#331C2×C15111yescharacteristic
85C2×SD16—21no—
86C4⋊Q8C22×C15111yescharacteristic
87#127C22×C15111yescharacteristic
88C4×Q8C22×C15111yescharacteristic
89#107—21no—
90C4⋊C8—21no—
91C4⋊C8C22×C15111yescharacteristic
92C4⋊C8C22×C15111yescharacteristic
93C4⋊C8C22×C15111yescharacteristic
94#103—21no—
95#102—21no—
96#102—21no—
97#102—21no—
98C4×C8—21no—
99C4×C8C22×C15111yescharacteristic
100C2×Q8—21no—
101C2×Q8D4×C15111yescharacteristic
102C2×D4—21no—
103C2×D4—21no—
104C2×D4—21no—
105SD16—42no—
106C2×C8—21no—
107C2×C8—21no—
108C2×C8—21no—
109C2×C8D4×C15111yescharacteristic
110C2×C8D4×C15111yescharacteristic
111C4⋊C4—21no—
112C4⋊C4—21no—
113C4⋊C4—21no—
114C4⋊C4D4×C15111yescharacteristic
115C42—21no—
116C42C23×C15111yescharacteristic
117C23—41no—
118Q8—21no—
119Q8—81no—
120Q8SD16×C15112yes—
121D4—41no—
122D4—41no—
123D4—41no—
124D4—41no—
125D4—81no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—41no—
129C2×C4C2×D4×C15111yescharacteristic
130C2×C4C2×D4×C15111yescharacteristic
131C2×C4#41×C15111yescharacteristic
132C8—21no—
133C8—21no—
134C8—41no—
135C8—41no—
136C8—41no—
137C22—81no—
138C22—81no—
139C22—81no—
140C22#121×C15111yescharacteristic
141C4—22no—
142C4—21no—
143C4—41no—
144C4—81no—
145C4C2×SD16×C15111yescharacteristic
146C4#135×C15111yescharacteristic
147C4#135×C15111yescharacteristic
148C4#137×C15111yescharacteristic
149C2—161no—
150C2#464×C15111yescharacteristic
151C2#465×C15111yescharacteristic
152C2#472×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#121
commutator, Frattini, cosocleC42C23×C151
prime radical#127×C151C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #477×C151C2semidirect
4. C8×Q8×C151C2semidirect
5. #334×C151C2semidirect
6. #333×C151C2semidirect
76. C151#1678direct (N × H)
77. #1678C151direct (N × H)
79. #477C2×C151semidirect
81. C8×Q8C2×C151semidirect
82. #334C2×C151semidirect
83. #333C2×C151semidirect

Maximal subgroups

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

subgroupindex
#486×C1512
#477×C1512
#460×C1512
C8×Q8×C1512
#334×C1512
#333×C1512
#331×C1512
#1678151