Finite Group Databasebeta

← #34046038

Subgroups — #34046038

Order 19072.

230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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#23749668C212yesmaximal
2#23749490C211yesmaximal, characteristic
3#23749394C211yesmaximal, characteristic
4#23749384C212yesmaximal
5#544×C149C211yesmaximal, characteristic
6C2×#14558720C2212yes—
7C2×C4⋊Dic149C2211yescharacteristic
8C2×C4×Dic149C2211yescharacteristic
9#18011844—22no—
10#18011842—22no—
11#18011818—22no—
12C4⋊Q8×C149—22no—
13#125×C149—22no—
14C22⋊Q8×C149—22no—
15#117×C149C2212yes—
16C2×C4⋊C4×C149C2211yescharacteristic
17C22×Dic149—21no—
18C22×Dic149—21no—
19#14558720—22no—
20#14558720Q814yescomplemented
21C2×#11924746—22no—
22C4⋊Dic149—22no—
23C4×Dic149—21no—
24C4×Dic149Q812yescomplemented
25C2×Q8×C149—22no—
26C22×C4×C149D412yes—
27C22×C4×C149C2311yescharacteristic
28C4⋊C4×C149—22no—
29C4⋊C4×C149—24no—
30C4⋊C4×C149—22no—
31C4⋊C4×C149D412yes—
32C4⋊C4×C149D412yes—
33C22⋊C4×C149—22no—
34C42×C149—22no—
35C2×Dic149—22no—
36C2×Dic149—41no—
37C2×Dic149—41no—
38C2×Dic149—42no—
39C2×Dic149—41no—
40#11924746—24no—
41C23×C149C2×D411yescharacteristic
42Q8×C149—82no—
43C2×C4×C149—22no—
44C2×C4×C149—22no—
45C2×C4×C149—22no—
46C2×C4×C149—42no—
47C2×C4×C149C2×D412yes—
48C2×C4×C149C2×Q812yes—
49C2×C4×C149C2×Q811yescharacteristic
50C2×C4×C149#4111yescharacteristic
51C22×C149—21no—
52C22×C149—21no—
53C22×C149#12011yescharacteristic
54C22×C149C22⋊Q811yescharacteristic
55C22×C149C4⋊Q811yescharacteristic
56C4×C149—42no—
57C4×C149—42no—
58C4×C149—42no—
59C4×C149C22⋊Q812yes—
60C4×C149C4⋊Q812yes—
61Dic149—42no—
62Dic149—81no—
63C2×C149—21no—
64C2×C149—21no—
65C2×C149#39511yescharacteristic
66C2×C149#45411yescharacteristic
67C2×C149#45511yescharacteristic
68C149#206111yescharacteristic, complemented, Sylow
69#2061—1491nomaximal, Sylow
70#544D14911yescharacteristic
71#428—1492no—
72#382—1491no—
73#343—1491no—
74#339—1492no—
75C2×M16—1492no—
76C4⋊Q8—22no—
77#125—22no—
78C22⋊Q8—22no—
79#117C2×D14912yes—
80C2×C4⋊C4—1491no—
81C2×C4⋊C4C2×D14911yescharacteristic
82C2×C42—1491no—
83#107—2982no—
84#106—2982no—
85#95—2982no—
86C2×Q8—22no—
87C22×C4—2981no—
88C22×C4—2981no—
89C22×C4C22⋊D14912yes—
90C22×C4C22×D14911yescharacteristic
91M16—2982no—
92M16—1494no—
93C2×C8—2982no—
94C4⋊C4—22no—
95C4⋊C4—24no—
96C4⋊C4—22no—
97C4⋊C4—2982no—
98C4⋊C4C22⋊D14912yes—
99C4⋊C4C22⋊D14912yes—
100C22⋊C4—22no—
101C42—22no—
102C42—2981no—
103C42—1492no—
104C23C2×C22⋊D14911yescharacteristic
105Q8—82no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—42no—
110C2×C4—2982no—
111C2×C4—5961no—
112C2×C4—5961no—
113C2×C4—5962no—
114C2×C4—5961no—
115C2×C4C2×C22⋊D14912yes—
116C2×C4Q8×D14911yescharacteristic
117C2×C4Q8×D14912yes—
118C2×C4#1455873711yescharacteristic
119C8—2984no—
120C22—21no—
121C22—21no—
122C22#1801188011yescharacteristic
123C22#1801188711yescharacteristic
124C22#1801190911yescharacteristic
125C4—42no—
126C4—42no—
127C4—42no—
128C4—5962no—
129C4—11921no—
130C4#1801188712yes—
131C4#1801190912yes—
132C2—21no—
133C2—21no—
134C2#2374954411yescharacteristic
135C2#2374979811yescharacteristic
136C2#2374980311yescharacteristic
subgroupG/H
centerC22#18011880
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#544×C149C2
socleC22×C149#120
prime radicalC23×C149C2×D4
hypercenter#544D149
hypocenterC149#2061
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
20. #14558720Q8semidirect
24. C4×Dic149Q8semidirect
68. C149#2061semidirect

Maximal subgroups

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

subgroupindex
#237496682
#237494902
#237493942
#237493842
#544×C1492
#2061149