Finite Group Databasebeta

← #34043829

Subgroups — #34043829

Order 19072.

206 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 57 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#23750355C211yesmaximal, characteristic
2#23749917C212yesmaximal
3#23749374C211yesmaximal, characteristic
4#23749357C212yesmaximal
5#494×C149C211yesmaximal, characteristic
6#18011910—22no—
7#18011909—22no—
8C4×Dic298C2212yes—
9#18011876—22no—
10#18011844—22no—
11C4⋊#11924746C2212yes—
12#18011834—22no—
13C2×Q16×C149—22no—
14C4⋊Q8×C149C2211yescharacteristic
15C4⋊Q8×C149C2211yescharacteristic
16C4×C8×C149C2211yescharacteristic
17C2×Dic298—22no—
18C2×Dic298D412yes—
19C2×#11924746—22no—
20C4⋊Dic149D412yes—
21#14558715—24no—
22#14558715—22no—
23C4×Dic149—22no—
24C4×Dic149—22no—
25C2×Q8×C149—21no—
26C2×Q8×C149D412yes—
27Q16×C149—44no—
28C2×C8×C149—21no—
29C4⋊C4×C149—22no—
30C4⋊C4×C149—22no—
31C42×C149C2311yescharacteristic
32Dic298—22no—
33Dic298—82no—
34Dic298Q1614yescomplemented
35C2×Dic149—22no—
36C2×Dic149—22no—
37#11924746—42no—
38Q8×C149—42no—
39Q8×C149—42no—
40C2×C4×C149—22no—
41C2×C4×C149—41no—
42C2×C4×C149C2×D412yes—
43C2×C4×C149C2×D411yescharacteristic
44C8×C149—22no—
45C22×C149#12011yescharacteristic
46C4×C149—21no—
47C4×C149—42no—
48C4×C149—81no—
49C4×C149C2×Q1612yes—
50C4×C149#13712yes—
51Dic149—24no—
52Dic149—42no—
53C2×C149#45112yes—
54C2×C149#45311yescharacteristic
55C149#163311yescharacteristic, complemented, Sylow
56#1633—1491nomaximal, Sylow
57Q82—1491no—
58#494D14911yescharacteristic
59#477—1492no—
60#333—1491no—
61Q8⋊C8—1492no—
62C2×Q16—22no—
63C4⋊Q8—2982no—
64C4⋊Q8—2982no—
65C4⋊Q8C2×D14911yescharacteristic
66C4⋊Q8C2×D14911yescharacteristic
67C4×Q8—2982no—
68C4×Q8—1492no—
69#107—2982no—
70C4⋊C8—1492no—
71#103—2982no—
72C4×C8C2×D14911yescharacteristic
73C2×Q8—21no—
74C2×Q8—2982no—
75C2×Q8—1492no—
76C2×Q8C22⋊D14912yes—
77Q16—44no—
78C2×C8—21no—
79C2×C8—2982no—
80C4⋊C4—22no—
81C4⋊C4—22no—
82C4⋊C4—2984no—
83C4⋊C4—2982no—
84C4⋊C4—1492no—
85C42—2982no—
86C42—2982no—
87C42C22×D14911yescharacteristic
88Q8—42no—
89Q8—42no—
90Q8—2982no—
91Q8—1494no—
92Q8—11922no—
93C2×C4—22no—
94C2×C4—41no—
95C2×C4—2982no—
96C2×C4—2982no—
97C2×C4D4×D14912yes—
98C2×C4C2×C22⋊D14911yescharacteristic
99C8—22no—
100C8—5962no—
101C22#1801187911yescharacteristic
102C4—21no—
103C4—42no—
104C4—81no—
105C4—2984no—
106C4—5962no—
107C4Q16×D14912yes—
108C4#1801194312yes—
109C2#2374977912yes—
110C2#2374979211yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#494×C149C2
socle, prime radicalC22×C149#120
hypercenter#494D149
hypocenterC149#1633
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
34. Dic298Q16semidirect
55. C149#1633semidirect

Maximal subgroups

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

subgroupindex
#237503552
#237499172
#237493742
#237493572
#494×C1492
#1633149