Finite Group Databasebeta

← #34044003

Subgroups — #34044003

Order 19072.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#23750375C211yesmaximal, characteristic
2#23750034C212yesmaximal, complemented
3#23750020C211yesmaximal, characteristic
4#23749366C212yesmaximal, complemented
5#329×C149C211yesmaximal, characteristic
6C2×#14558726—21no—
7C2×#14558724—21no—
8#18011911C2211yescharacteristic
9#18011909—21no—
10#18011904—22no—
11#18011903C2212yes—
12#18011892—21no—
13#18011888—22no—
14#18011845—22no—
15#18011843—22no—
16#18011822C2211yescharacteristic
17#124×C149C2211yescharacteristic
18#97×C149C2212yes—
19C2×Dic298—21no—
20C2×Dic298—21no—
21C22×Dic149—21no—
22#14558726—42no—
23#14558724—42no—
24C2×#11924746—21no—
25C4⋊Dic149—22no—
26C4⋊Dic149D412yes—
27C4⋊Dic149D412yes—
28#14558715—22no—
29#14558715—22no—
30#14558715—22no—
31C22⋊Dic149—21no—
32C22⋊Dic149—22no—
33C4×Dic149—21no—
34C2×Q8×C149D411yescharacteristic
35C2×D4×C149D411yescharacteristic
36C2×C8×C149—22no—
37C22⋊C4×C149—22no—
38C42×C149C2311yescharacteristic
39Dic298—41no—
40Dic298—41no—
41Dic298—81no—
42C2×Dic149—22no—
43C2×Dic149—22no—
44C2×Dic149—41no—
45C2×Dic149—81no—
46#11924746—22no—
47C23×C149—21no—
48Q8×C149—41no—
49D4×C149—41no—
50C2×C4×C149—21no—
51C2×C4×C149C2×D412yes—
52C2×C4×C149C2×D411yescharacteristic
53C8×C149—24no—
54C22×C149—41no—
55C22×C149—42no—
56C22×C149#12011yescharacteristic
57C4×C149—21no—
58C4×C149—22no—
59C4×C149—41no—
60Dic149—42no—
61Dic149—42no—
62Dic149—81no—
63C2×C149—81no—
64C2×C149#45311yescharacteristic
65C2×C149#45612yes—
66C149#166011yescharacteristic, complemented, Sylow
67#1660—1491nomaximal, Sylow
68#563—1491no—
69#501—1492no—
70#497—1491no—
71#330—1492no—
72#329D14911yescharacteristic
73C2×Q16—2981no—
74C2×SD16—2981no—
75C4⋊Q8—2981no—
76C4⋊Q8—1491no—
77#126—2982no—
78#125—1492no—
79#124C2×D14911yescharacteristic
80#123—2981no—
81C22⋊Q8—2982no—
82#107—2982no—
83#106—2982no—
84#97—1491no—
85#97C2×D14912yes—
86C2×Q8—2981no—
87C2×Q8—2981no—
88C2×Q8D59611yescharacteristic
89C2×D4D59611yescharacteristic
90C22×C4—2981no—
91Q16—5962no—
92SD16—5962no—
93C2×C8—22no—
94C2×C8—2981no—
95C4⋊C4—2982no—
96C4⋊C4—2982no—
97C4⋊C4—2982no—
98C4⋊C4—2982no—
99C4⋊C4—1492no—
100C4⋊C4—1492no—
101C22⋊C4—22no—
102C22⋊C4—2982no—
103C22⋊C4—2981no—
104C42—2981no—
105C42C22×D14911yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—5961no—
109Q8—5961no—
110Q8—11921no—
111D4—41no—
112C2×C4—21no—
113C2×C4—2982no—
114C2×C4—2982no—
115C2×C4—5961no—
116C2×C4—11921no—
117C2×C4D4×D14912yes—
118C2×C4C2×D59611yescharacteristic
119C8—24no—
120C8—2982no—
121C22—41no—
122C22—42no—
123C22#1801188111yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—5962no—
128C4—5962no—
129C4—11921no—
130C2—81no—
131C2#2374979511yescharacteristic
132C2#2374980912yes—
subgroupG/H
centerC22#18011881
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#329×C149C2
socleC22×C149#120
prime radicalC2×D4×C149D4
hypercenter#329D149
hypocenterC149#1660
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #23750034C2semidirect
4. #23749366C2semidirect
66. C149#1660semidirect

Maximal subgroups

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

subgroupindex
#237503752
#237500342
#237500202
#237493662
#329×C1492
#1660149