Finite Group Databasebeta

← #34053602

Subgroups — #34053602

Order 19072.

458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 185 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#23750425C211yesmaximal, characteristic
2#23750391C212yesmaximal, complemented
3#23749748C214yesmaximal, complemented
4#23749743C214yesmaximal, complemented
5#23749674C211yesmaximal, characteristic, complemented
6C2×#18011839C212yesmaximal, complemented
7C4×M16×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2212yes—
9#18011944C414yescomplemented
10#18011939C414yescomplemented
11#18011933C2214yes—
12#18011919—24no—
13#18011917C2218yescomplemented
14C2×#14558720C2212yes—
15M16×D149—24no—
16#18011847C2214yescomplemented
17#18011839C2214yescomplemented
18#18011839C2214yescomplemented
19C2×M16×C149C2211yescharacteristic
20C2×M16×C149C2211yescharacteristic
21C2×C42×C149C2211yescharacteristic
22#97×C149C2212yescomplemented
23C4×C8×C149C2212yescomplemented
24#14558736—22no—
25#14558736—22no—
26#14558736C2×C414yes—
27#14558736C2314yes—
28C2×Dic298C2×C412yes—
29C2×D596C2×C412yes—
30C2×C22⋊D149—22no—
31C2×C4×D149—22no—
32Dic596C2×C414yescomplemented
33#14558725C2×C418yescomplemented
34D1192C2×C414yescomplemented
35#14558720—22no—
36#14558720C2314yes—
37#14558719—28no—
38C2×#11924746—22no—
39C8×D149—28no—
40C22×C4×C149—21no—
41C22×C4×C149C2311yescharacteristic
42M16×C149C2×C414yes—
43M16×C149D414yes—
44C2×C8×C149C2312yes—
45C2×C8×C149C2312yes—
46C42×C149—21no—
47C42×C149C2311yescharacteristic
48C42×C149C2311yescharacteristic
49C22×D149—22no—
50Dic298—22no—
51Dic298C22×C414yes—
52D596—22no—
53D596C22×C414yes—
54C22⋊D149—24no—
55C22⋊D149—24no—
56C2×Dic149—22no—
57C4×D149—24no—
58C4×D149—24no—
59#11924746—24no—
60C23×C149#4111yescharacteristic
61C2×C4×C149—21no—
62C2×C4×C149—21no—
63C2×C4×C149—42no—
64C2×C4×C149C22×C412yes—
65C2×C4×C149C2×D412yes—
66C2×C4×C149#4111yescharacteristic
67C2×C4×C149C2411yescharacteristic
68C8×C149C22×C414yes—
69C8×C149C2×D414yes—
70C22×C149—41no—
71C22×C149C4×D412yes—
72C22×C149C2×#4111yescharacteristic
73C2×D149—24no—
74C2×D149—82no—
75C4×C149—22no—
76C4×C149—41no—
77C4×C149C4×D412yes—
78C4×C149C23×C411yescharacteristic
79C4×C149C22×D411yescharacteristic
80Dic149—24no—
81C2×C149—21no—
82C2×C149—22no—
83C2×C149C2×C4×D411yescharacteristic
84D149—44no—
85C149#295611yescharacteristic, complemented, Sylow
86#2956—1491nomaximal, Sylow
87#575—1491no—
88#568—1492no—
89#444—1494no—
90#443—1494no—
91#430—1491no—
92C2×#104—1492no—
93C4×M16D14911yescharacteristic, complemented
94C2×#41—1492no—
95#137—1494no—
96AGL(1,ℤ/8)—1494no—
97#135—1494no—
98#131—2984no—
99#131—1498no—
100C2×M16—2984no—
101C2×M16—1492no—
102C2×M16C2×D14911yescharacteristic
103C2×M16C2×D14911yescharacteristic
104C2×C42C2×D14911yescharacteristic
105#108—1494no—
106#104—1494no—
107#104—1494no—
108#97C2×D14912yescomplemented
109C4×C8C2×D14912yescomplemented
110#41—2982no—
111#41—2982no—
112#41—1494no—
113#41—1494no—
114C2×Q8—1492no—
115C2×D4—2982no—
116C2×D4—1492no—
117C22×C4—21no—
118C22×C4—2982no—
119C22×C4C22×D14911yescharacteristic
120Q16—1494no—
121SD16—1498no—
122D8—1494no—
123M16—2982no—
124M16—2988no—
125M16—1494no—
126M16C4×D14914yes—
127M16D59614yes—
128C2×C8—2982no—
129C2×C8—2988no—
130C2×C8C22×D14912yes—
131C2×C8C22×D14912yes—
132C42—21no—
133C42C22×D14911yescharacteristic
134C42C22×D14911yescharacteristic
135C23—2982no—
136C23#1455873611yescharacteristic
137Q8—2982no—
138Q8—1494no—
139D4—2984no—
140D4—2984no—
141D4—2982no—
142D4—1494no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—42no—
146C2×C4—2982no—
147C2×C4—2984no—
148C2×C4—2984no—
149C2×C4C2×C4×D14912yes—
150C2×C4C2×D59612yes—
151C2×C4#1455873611yescharacteristic
152C2×C4C23×D14911yescharacteristic
153C8—2984no—
154C8C2×C4×D14914yes—
155C8C2×D59614yes—
156C22—41no—
157C22—2984no—
158C22—11922no—
159C22C4×D59612yes—
160C22C2×#1455873611yescharacteristic
161C4—22no—
162C4—41no—
163C4—2984no—
164C4C4×D59612yes—
165C4C22×C4×D14911yescharacteristic
166C4C22×D59611yescharacteristic
167C2—21no—
168C2—22no—
169C2—5964no—
170C2C2×C4×D59611yescharacteristic
subgroupG/H
centerC4C22×D596
commutatorC4×C149C23×C4
FrattiniC2×C4C23×D149
FittingC4×M16×C149C2
socleC2×C149C2×C4×D4
prime radical#23750425C2
cosocleC2×C4×C149C24
hypercenterC4×M16D149
hypocenterC149#2956
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C2×M16 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. #23750391C2semidirect
3. #23749748C2semidirect
4. #23749743C2semidirect
5. #23749674C2semidirect
6. C2×#18011839C2semidirect
7. C4×M16×C149C2semidirect
9. #18011944C4semidirect
10. #18011939C4semidirect
13. #18011917C22semidirect
16. #18011847C22semidirect
17. #18011839C22semidirect
18. #18011839C22semidirect
22. #97×C149C22semidirect
23. C4×C8×C149C22semidirect
32. Dic596C2×C4semidirect
33. #14558725C2×C4semidirect
34. D1192C2×C4semidirect
85. C149#2956semidirect
93. C4×M16D149semidirect
108. #97C2×D149semidirect
109. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237504252
#237503912
#237497482
#237497432
#237496742
C2×#180118392
C4×M16×C1492
#2956149