Finite Group Databasebeta

← #34060083

Subgroups — #34060083

Order 19072.

228 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 60 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#23750647C211yesmaximal, characteristic
2#23750561C211yesmaximal, characteristic
3#23750478C214yesmaximal
4#23750180C211yesmaximal, characteristic
5C2×C4×#10597010—21no—
6C4⋊#11924753—21no—
7#18011968C2212yes—
8#18011966—21no—
9(C2×#10597010)⋊C4—21no—
10(C2×#10597010)⋊C4C2212yes—
11#18011911C411yescharacteristic, complemented
12#18011902—21no—
13#18011891C2212yes—
14#18011887—21no—
15Q8×Dic149—21no—
16#18011876C412yescomplemented
17#18011869—21no—
18C42×D149C2211yescharacteristic
19C4⋊Q8×C149C411yescharacteristic, complemented
20C22×#10597010—22no—
21C2×#11924753—22no—
22C4×#10597010—24no—
23C2×Dic298C2×C412yes—
24C2×C4×D149D411yescharacteristic
25C2×C4×D149D411yescharacteristic
26C2×C4×D149C2311yescharacteristic
27C4⋊Dic149—22no—
28C4⋊Dic149—21no—
29C4⋊Dic149—21no—
30#14558715—22no—
31#14558713—22no—
32C4×Dic149—22no—
33C4×Dic149C2×C411yescharacteristic
34C4×Dic149D411yescharacteristic
35C4×Dic149D411yescharacteristic
36C2×Q8×C149—21no—
37C4⋊C4×C149—21no—
38C4⋊C4×C149C2×C412yes—
39C42×C149C2×C411yescharacteristic
40C2×#10597010—24no—
41C2×#10597010—42no—
42C2×#10597010—42no—
43#11924753—42no—
44C22×D149C2×D411yescharacteristic
45Dic298—42no—
46C2×Dic149—22no—
47C2×Dic149C22⋊C411yescharacteristic
48C2×Dic149C22⋊C411yescharacteristic
49C2×Dic149C2×D411yescharacteristic
50C4×D149—22no—
51C4×D149—22no—
52C4×D149—41no—
53Q8×C149—42no—
54C2×C4×C149—22no—
55C2×C4×C149C22⋊C411yescharacteristic
56C2×C4×C149C22⋊C411yescharacteristic
57C2×C4×C149C22×C411yescharacteristic
58C22×C149C2×C22⋊C411yescharacteristic
59C2×D149—21no—
60C2×D149—21no—
61C2×D149#13712yes—
62#10597010—44no—
63C4×C149—21no—
64C4×C149—21no—
65C4×C149—42no—
66C4×C149#10412yes—
67Dic149—21no—
68Dic149—21no—
69Dic149—21no—
70Dic149—42no—
71C2×C149#41011yescharacteristic
72C2×C149#41911yescharacteristic
73C2×C149C2×#10411yescharacteristic
74D149—22no—
75C149#150611yescharacteristic, complemented, Sylow
76#1506—1491nomaximal, Sylow
77#533—1491no—
78#432—1491no—
79#376—1491no—
80#328—1494no—
81C4⋊Q8—1491no—
82C4⋊Q8#1059701011yescharacteristic, complemented
83#125—2981no—
84C22⋊Q8—2981no—
85C22⋊Q8—1492no—
86C4×Q8—2981no—
87C4×Q8—1492no—
88#117—2981no—
89C2×C42—2981no—
90C2×C42—1491no—
91C4⋊C8—2981no—
92C22⋊C8—1492no—
93#97—2981no—
94#95—2981no—
95#95—1492no—
96C2×Q8—21no—
97C2×Q8—1492no—
98C22×C4—2982no—
99C22×C4—1491no—
100C22×C4—1491no—
101C22×C4—1491no—
102C2×C8—2982no—
103C4⋊C4—21no—
104C4⋊C4—2982no—
105C4⋊C4—2982no—
106C4⋊C4—2981no—
107C4⋊C4—2981no—
108C4⋊C4C2×#1059701012yes—
109C22⋊C4—2982no—
110C42—2982no—
111C42—2984no—
112C42—1491no—
113C42—1491no—
114C42—1491no—
115C42C2×#1059701011yescharacteristic
116C23—1491no—
117Q8—42no—
118Q8—5962no—
119C2×C4—22no—
120C2×C4—2982no—
121C2×C4—2982no—
122C2×C4—2984no—
123C2×C4—2982no—
124C2×C4—5961no—
125C2×C4—5962no—
126C2×C4—5962no—
127C2×C4—1491no—
128C2×C4—1491no—
129C2×C4—1491no—
130C2×C4C22⋊#1059701011yescharacteristic
131C2×C4C22⋊#1059701011yescharacteristic
132C2×C4C22×#1059701011yescharacteristic
133C8—5962no—
134C22—2981no—
135C22—2981no—
136C22—1492no—
137C22C2×C22⋊#1059701011yescharacteristic
138C4—21no—
139C4—21no—
140C4—42no—
141C4—2981no—
142C4—2981no—
143C4—2981no—
144C4—5964no—
145C4—5962no—
146C4#1801197512yes—
147C2—2982no—
148C2#2375060611yescharacteristic
149C2#2375061811yescharacteristic
150C2C2×#1801197511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C2×D4
cosocleC2×C4×D149C23
hypercenterC4⋊Q8#10597010
hypocenterC149#1506
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
11. #18011911C4semidirect
16. #18011876C4semidirect
19. C4⋊Q8×C149C4semidirect
75. C149#1506semidirect
82. C4⋊Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506472
#237505612
#237504782
#237501802
#1506149