Finite Group Databasebeta

← #34053600

Subgroups — #34053600

Order 19072.

458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 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#23749746C214yesmaximal, complemented
4#23749741C214yesmaximal, complemented
5C2×#18011837C212yesmaximal, complemented
6M16×Dic149C211yesmaximal, characteristic, complemented
7#430×C149C211yesmaximal, characteristic, complemented
8C2×#14558736C2212yes—
9#18011944C414yescomplemented
10#18011939C414yescomplemented
11#18011933C2214yes—
12#18011919C2218yescomplemented
13#18011917—24no—
14C2×#14558720C2211yescharacteristic
15M16×D149—24no—
16C2×C4×Dic149C2211yescharacteristic
17#18011837C2214yescomplemented
18#18011837C2214yescomplemented
19#18011821C2212yescomplemented
20C8×Dic149C2212yescomplemented
21C2×M16×C149C2212yes—
22C2×M16×C149C2211yescharacteristic
23#108×C149C2214yescomplemented
24#14558736—22no—
25#14558736—22no—
26#14558736C2×C414yes—
27#14558736C2314yes—
28C2×Dic298C2×C412yes—
29C2×D596C2×C412yes—
30C2×C22⋊D149—22no—
31C22×Dic149—21no—
32C2×C4×D149—22no—
33Dic596C2×C414yescomplemented
34#14558725C2×C418yescomplemented
35D1192C2×C414yescomplemented
36#14558720D414yes—
37#14558719—28no—
38C2×#11924746C2312yes—
39C8×D149—28no—
40C4×Dic149—21no—
41C4×Dic149C2311yescharacteristic
42C4×Dic149C2311yescharacteristic
43C22×C4×C149C2311yescharacteristic
44M16×C149—22no—
45M16×C149C2×C414yes—
46M16×C149C2314yes—
47C2×C8×C149—22no—
48C2×C8×C149C2312yes—
49C22×D149—22no—
50Dic298—22no—
51Dic298C22×C414yes—
52D596—22no—
53D596C22×C414yes—
54C22⋊D149—24no—
55C22⋊D149—24no—
56C2×Dic149—22no—
57C2×Dic149—21no—
58C2×Dic149—21no—
59C2×Dic149—42no—
60C4×D149—24no—
61C4×D149—24no—
62#11924746C2×D414yes—
63C23×C149#4111yescharacteristic
64C2×C4×C149C22×C412yes—
65C2×C4×C149C2×D412yes—
66C2×C4×C149#4111yescharacteristic
67C2×C4×C149C2411yescharacteristic
68C8×C149—24no—
69C8×C149C22×C414yes—
70C22×C149—41no—
71C22×C149C4×D412yes—
72C22×C149C2×#4111yescharacteristic
73C2×D149—24no—
74C2×D149—82no—
75C4×C149C4×D412yes—
76C4×C149C23×C411yescharacteristic
77C4×C149C22×D411yescharacteristic
78Dic149—22no—
79Dic149—24no—
80Dic149—41no—
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#430D14911yescharacteristic, complemented
92C2×#104—1492no—
93C4×M16—1491no—
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—1491no—
102C2×M16C2×D14912yes—
103C2×M16C2×D14911yescharacteristic
104C2×C42—1491no—
105#108C2×D14914yescomplemented
106#104—1494no—
107#104—1494no—
108#97—1492no—
109C4×C8—1492no—
110#41—2982no—
111#41—2982no—
112#41—1494no—
113#41—1494no—
114C2×Q8—1492no—
115C2×D4—2982no—
116C2×D4—1492no—
117C22×C4—2982no—
118C22×C4—2981no—
119C22×C4C22×D14911yescharacteristic
120Q16—1494no—
121SD16—1498no—
122D8—1494no—
123M16—22no—
124M16—2988no—
125M16—1494no—
126M16C4×D14914yes—
127M16C22×D14914yes—
128C2×C8—22no—
129C2×C8—2988no—
130C2×C8—1492no—
131C2×C8C22×D14912yes—
132C42—2981no—
133C42—1491no—
134C42—1491no—
135C23—2982no—
136C23#1455873711yescharacteristic
137Q8—2982no—
138Q8—1494no—
139D4—2984no—
140D4—2984no—
141D4—2982no—
142D4—1494no—
143C2×C4—2981no—
144C2×C4—2982no—
145C2×C4—2984no—
146C2×C4—2984no—
147C2×C4—2981no—
148C2×C4—5962no—
149C2×C4C2×C4×D14912yes—
150C2×C4D4×D14912yes—
151C2×C4#1455873711yescharacteristic
152C2×C4C23×D14911yescharacteristic
153C8—24no—
154C8—1494no—
155C8C2×C4×D14914yes—
156C22—41no—
157C22—2984no—
158C22—11922no—
159C22#1801187312yes—
160C22C2×#1455873711yescharacteristic
161C4—2982no—
162C4—2984no—
163C4—5961no—
164C4#1801187312yes—
165C4C22×C4×D14911yescharacteristic
166C4C2×D4×D14911yescharacteristic
167C2—21no—
168C2—22no—
169C2—5964no—
170C2C2×#1801187311yescharacteristic
subgroupG/H
centerC4C2×D4×D149
commutatorC4×C149C23×C4
FrattiniC2×C4C23×D149
Fitting#430×C149C2
socleC2×C149C2×C4×D4
prime radical#23750425C2
cosocleC2×C4×C149C24
hypercenter#430D149
hypocenterC149#2956
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C22×C4 ◁ #430

Complements

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

NH ≅ G/Ntype
2. #23750391C2semidirect
3. #23749746C2semidirect
4. #23749741C2semidirect
5. C2×#18011837C2semidirect
6. M16×Dic149C2semidirect
7. #430×C149C2semidirect
9. #18011944C4semidirect
10. #18011939C4semidirect
12. #18011919C22semidirect
17. #18011837C22semidirect
18. #18011837C22semidirect
19. #18011821C22semidirect
20. C8×Dic149C22semidirect
23. #108×C149C22semidirect
33. Dic596C2×C4semidirect
34. #14558725C2×C4semidirect
35. D1192C2×C4semidirect
85. C149#2956semidirect
91. #430D149semidirect
105. #108C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237504252
#237503912
#237497462
#237497412
C2×#180118372
M16×Dic1492
#430×C1492
#2956149