Finite Group Databasebeta

← #1351×C149 #34040264

Subgroups — #1351×C149 #34040264

Order 19072.

162 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 40 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#393×C149C211yesmaximal, characteristic
2#342×C149C211yesmaximal, characteristic
3#323×C149C211yesmaximal, characteristic
4C22×Q8×C149C411yescharacteristic, complemented
5C2×C22⋊C4×C149—21no—
6C2×C22⋊C4×C149—21no—
7C2×C22⋊C4×C149C2211yescharacteristic
8C22⋊C8×C149—21no—
9#95×C149—21no—
10#95×C149C411yescharacteristic, complemented
11C24×C149D411yescharacteristic
12C2×Q8×C149—42no—
13C2×Q8×C149—41no—
14C22×C4×C149—21no—
15C22×C4×C149—21no—
16C22×C4×C149—41no—
17C22×C4×C149C2×C411yescharacteristic
18C22×C4×C149D411yescharacteristic
19C2×C8×C149—41no—
20C22⋊C4×C149—22no—
21C22⋊C4×C149—41no—
22C22⋊C4×C149—42no—
23C22⋊C4×C149—41no—
24C23×C149—21no—
25C23×C149—21no—
26C23×C149—41no—
27C23×C149—41no—
28C23×C149C22⋊C411yescharacteristic
29C23×C149SD1611yescharacteristic
30C23×C149Q1611yescharacteristic
31Q8×C149—42no—
32Q8×C149—42no—
33C2×C4×C149—22no—
34C2×C4×C149—21no—
35C2×C4×C149—21no—
36C2×C4×C149—41no—
37C2×C4×C149—41no—
38C2×C4×C149—41no—
39C2×C4×C149—41no—
40C2×C4×C149—42no—
41C2×C4×C149—41no—
42C2×C4×C149—41no—
43C2×C4×C149—41no—
44C2×C4×C149—81no—
45C2×C4×C149—81no—
46C8×C149—81no—
47C22×C149—21no—
48C22×C149—21no—
49C22×C149—21no—
50C22×C149—21no—
51C22×C149—41no—
52C22×C149—41no—
53C22×C149—41no—
54C22×C149—41no—
55C22×C149—81no—
56C22×C149#9911yescharacteristic
57C22×C149#10311yescharacteristic
58C22×C149#10411yescharacteristic
59C4×C149—42no—
60C4×C149—41no—
61C4×C149—41no—
62C4×C149—81no—
63C4×C149—82no—
64C2×C149—21no—
65C2×C149—21no—
66C2×C149—41no—
67C2×C149—41no—
68C2×C149#32811yescharacteristic
69C2×C149AΣL(1,𝔽16)11yescharacteristic
70C2×C149#35411yescharacteristic
71C149#135111yescharacteristic, direct product factor, Sylow
72#1351C14911yesmaximal, characteristic, direct product factor, Sylow
73#393C2×C14911yescharacteristic
74#342C2×C14911yescharacteristic
75#323C2×C14911yescharacteristic
76C22×Q8C4×C14911yescharacteristic, complemented
77C2×C22⋊C4—21no—
78C2×C22⋊C4—21no—
79C2×C22⋊C4C22×C14911yescharacteristic
80C22⋊C8—21no—
81#95—21no—
82#95C4×C14911yescharacteristic, complemented
83C24D4×C14911yescharacteristic
84C2×Q8—42no—
85C2×Q8—41no—
86C22×C4—21no—
87C22×C4—21no—
88C22×C4—41no—
89C22×C4C2×C4×C14911yescharacteristic
90C22×C4D4×C14911yescharacteristic
91C2×C8—41no—
92C22⋊C4—22no—
93C22⋊C4—41no—
94C22⋊C4—42no—
95C22⋊C4—41no—
96C23—21no—
97C23—21no—
98C23—41no—
99C23—41no—
100C23C22⋊C4×C14911yescharacteristic
101C23SD16×C14911yescharacteristic
102C23Q16×C14911yescharacteristic
103Q8—42no—
104Q8—42no—
105C2×C4—22no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—42no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4—41no—
116C2×C4—81no—
117C2×C4—81no—
118C8—81no—
119C22—21no—
120C22—21no—
121C22—21no—
122C22—21no—
123C22—41no—
124C22—41no—
125C22—41no—
126C22—41no—
127C22—81no—
128C22#99×C14911yescharacteristic
129C22#103×C14911yescharacteristic
130C22#104×C14911yescharacteristic
131C4—42no—
132C4—41no—
133C4—41no—
134C4—81no—
135C4—82no—
136C2—21no—
137C2—21no—
138C2—41no—
139C2—41no—
140C2#328×C14911yescharacteristic
141C2AΣL(1,𝔽16)×C14911yescharacteristic
142C2#354×C14911yescharacteristic
subgroupG/H
center, socleC22×C149#99
commutatorC22×C4C2×C4×C149
Frattini, cosocleC2×C22⋊C4C22×C149
prime radicalC24×C149D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C149 ◁ C23×C149 ◁ C2×C22⋊C4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
4. C22×Q8×C149C4semidirect
10. #95×C149C4semidirect
71. C149#1351direct (N × H)
72. #1351C149direct (N × H)
76. C22×Q8C4×C149semidirect
82. #95C4×C149semidirect

Maximal subgroups

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

subgroupindex
#393×C1492
#342×C1492
#323×C1492
#1351149