Finite Group Databasebeta

← #34056484

Subgroups — #34056484

Order 19072.

460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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#23750431C214yesmaximal, complemented
2#23749885C214yesmaximal, complemented
3#23749807C212yesmaximal, complemented
4#23749792C212yesmaximal, complemented
5#23749743C212yesmaximal, complemented
6#492×C149C211yesmaximal, characteristic, complemented
7#18011959C2212yes—
8#18011956C2212yescomplemented
9#18011942C2214yescomplemented
10#18011940—24no—
11#18011938—24no—
12#18011937C2214yes—
13#18011933C2212yes—
14#18011932—24no—
15SD16×D149—24no—
16#18011917C2214yescomplemented
17#18011847C2212yescomplemented
18#18011839C2214yescomplemented
19#18011830C2212yescomplemented
20#18011828C2212yescomplemented
21C2×SD16×C149C2214yescomplemented
22C4⋊Q8×C149C2211yescharacteristic, complemented
23#127×C149C2211yescharacteristic
24C4×C8×C149C2211yescharacteristic, complemented
25#14558737—24no—
26#14558736—42no—
27#14558736C2314yes—
28#14558735—24no—
29Q8×D149—24no—
30C2×C22⋊D149—42no—
31D4×D149—24no—
32Dic596D412yescomplemented
33#14558726—24no—
34#14558725D414yescomplemented
35#14558724—24no—
36#14558723—24no—
37D1192D412yescomplemented
38#14558721—24no—
39#14558720C2314yes—
40#14558719—24no—
41C8×D149—24no—
42C2×Q8×C149C2312yes—
43C2×D4×C149—41no—
44C2×D4×C149C2312yes—
45SD16×C149—24no—
46SD16×C149—24no—
47C2×C8×C149C2312yes—
48C4⋊C4×C149—41no—
49C42×C149C2311yescharacteristic
50C22×D149—42no—
51Dic298—42no—
52Dic298C2×D414yes—
53D596—42no—
54D596C2×D414yes—
55C22⋊D149—24no—
56C22⋊D149—44no—
57C2×Dic149—42no—
58C4×D149—24no—
59C4×D149—44no—
60#11924746—24no—
61C23×C149—22no—
62Q8×C149—24no—
63D4×C149—24no—
64D4×C149—82no—
65C2×C4×C149—21no—
66C2×C4×C149—22no—
67C2×C4×C149C2411yescharacteristic
68C8×C149C2×D412yes—
69C8×C149C2×D412yes—
70C22×C149—42no—
71C22×C149—82no—
72C22×C149H(5,𝔽2)11yescharacteristic
73C2×D149—24no—
74C2×D149—162no—
75C4×C149—22no—
76C4×C149—42no—
77C4×C149C22×D412yes—
78Dic149—24no—
79C2×C149—21no—
80C2×C149—82no—
81C2×C149D4211yescharacteristic
82D149—44no—
83C149#329111yescharacteristic, complemented, Sylow
84#3291—1491nomaximal, Sylow
85#577—1494no—
86#492D14911yescharacteristic, complemented
87#471—1494no—
88#456—1492no—
89#453—1492no—
90#443—1492no—
912−1+4—1492no—
92H(5,𝔽2)—1492no—
93#137—2984no—
94#137—1494no—
95AGL(1,ℤ/8)—2984no—
96AGL(1,ℤ/8)—1494no—
97#135—2984no—
98#135—1492no—
99C2×SD16—2984no—
100C2×SD16C2×D14914yescomplemented
101#131—1494no—
102C4⋊Q8C2×D14911yescharacteristic, complemented
103#127C2×D14911yescharacteristic
104#108—1492no—
105#104—1494no—
106#101—1492no—
107#100—1492no—
108C4×C8C2×D14911yescharacteristic, complemented
109#41—2984no—
110#41—2984no—
111#41—5962no—
112#41—1494no—
113C2×Q8—2984no—
114C2×Q8C22×D14912yes—
115C2×D4—41no—
116C2×D4—2984no—
117C2×D4—5962no—
118C2×D4C22×D14912yes—
119Q16—2984no—
120Q16—1492no—
121SD16—24no—
122SD16—24no—
123SD16—2984no—
124SD16—2984no—
125SD16—1494no—
126D8—2984no—
127D8—1492no—
128M16—2984no—
129M16—1494no—
130C2×C8—2984no—
131C2×C8C22×D14912yes—
132C4⋊C4—41no—
133C42C22×D14911yescharacteristic
134C23—22no—
135C23—5962no—
136Q8—24no—
137Q8—5962no—
138Q8—1494no—
139D4—24no—
140D4—82no—
141D4—2984no—
142D4—5962no—
143D4—5964no—
144D4—1494no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—2984no—
148C2×C4—5964no—
149C2×C4—5962no—
150C2×C4C23×D14911yescharacteristic
151C8—2984no—
152C8D4×D14912yes—
153C8D4×D14912yes—
154C22—42no—
155C22—82no—
156C22—2984no—
157C22—23842no—
158C22#1801195611yescharacteristic
159C4—22no—
160C4—42no—
161C4—2984no—
162C4C2×D4×D14912yes—
163C2—21no—
164C2—82no—
165C2—5964no—
166C2#2375026011yescharacteristic
subgroupG/H
centerC2#23750260
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#492×C149C2
socleC2×C149D42
hypercenter#492D149
hypocenterC149#3291
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #23750431C2semidirect
2. #23749885C2semidirect
3. #23749807C2semidirect
4. #23749792C2semidirect
5. #23749743C2semidirect
6. #492×C149C2semidirect
8. #18011956C22semidirect
9. #18011942C22semidirect
16. #18011917C22semidirect
17. #18011847C22semidirect
18. #18011839C22semidirect
19. #18011830C22semidirect
20. #18011828C22semidirect
21. C2×SD16×C149C22semidirect
22. C4⋊Q8×C149C22semidirect
24. C4×C8×C149C22semidirect
32. Dic596D4semidirect
34. #14558725D4semidirect
37. D1192D4semidirect
83. C149#3291semidirect
86. #492D149semidirect
100. C2×SD16C2×D149semidirect
102. C4⋊Q8C2×D149semidirect
108. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237504312
#237498852
#237498072
#237497922
#237497432
#492×C1492
#3291149