Finite Group Databasebeta

← #34080903

Subgroups — #34080903

Order 19328.

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#23753018C214yesmaximal, complemented
2#23752472C214yesmaximal, complemented
3#23752394C212yesmaximal, complemented
4#23752379C212yesmaximal, complemented
5#23752330C212yesmaximal, complemented
6#492×C151C211yesmaximal, characteristic, complemented
7#18012787C2212yes—
8#18012784C2212yescomplemented
9#18012770C2214yescomplemented
10#18012768—24no—
11#18012766—24no—
12#18012765C2214yes—
13#18012761C2212yes—
14#18012760—24no—
15SD16×D151—24no—
16#18012745C2214yescomplemented
17#18012675C2212yescomplemented
18#18012667C2214yescomplemented
19#18012658C2212yescomplemented
20#18012656C2212yescomplemented
21C2×SD16×C151C2214yescomplemented
22C4⋊Q8×C151C2211yescharacteristic, complemented
23#127×C151C2211yescharacteristic
24C4×C8×C151C2211yescharacteristic, complemented
25#14559005—24no—
26#14559004—42no—
27#14559004C2314yes—
28#14559003—24no—
29Q8×D151—24no—
30C2×C22⋊D151—42no—
31D4×D151—24no—
32Dic604D412yescomplemented
33#14558994—24no—
34#14558993D414yescomplemented
35#14558992—24no—
36#14558991—24no—
37D1208D412yescomplemented
38#14558989—24no—
39#14558988C2314yes—
40#14558987—24no—
41C8×D151—24no—
42C2×Q8×C151C2312yes—
43C2×D4×C151—41no—
44C2×D4×C151C2312yes—
45SD16×C151—24no—
46SD16×C151—24no—
47C2×C8×C151C2312yes—
48C4⋊C4×C151—41no—
49C42×C151C2311yescharacteristic
50C22×D151—42no—
51Dic302—42no—
52Dic302C2×D414yes—
53D604—42no—
54D604C2×D414yes—
55C22⋊D151—24no—
56C22⋊D151—44no—
57C2×Dic151—42no—
58C4×D151—24no—
59C4×D151—44no—
60C151⋊C8—24no—
61C23×C151—22no—
62Q8×C151—24no—
63D4×C151—24no—
64D4×C151—82no—
65C2×C4×C151—21no—
66C2×C4×C151—22no—
67C2×C4×C151C2411yescharacteristic
68C8×C151C2×D412yes—
69C8×C151C2×D412yes—
70C22×C151—42no—
71C22×C151—82no—
72C22×C151H(5,𝔽2)11yescharacteristic
73C2×D151—24no—
74C2×D151—162no—
75C4×C151—22no—
76C4×C151—42no—
77C4×C151C22×D412yes—
78Dic151—24no—
79C2×C151—21no—
80C2×C151—82no—
81C2×C151D4211yescharacteristic
82D151—44no—
83C151#329111yescharacteristic, complemented, Sylow
84#3291—1511nomaximal, Sylow
85#577—1514no—
86#492D15111yescharacteristic, complemented
87#471—1514no—
88#456—1512no—
89#453—1512no—
90#443—1512no—
912−1+4—1512no—
92H(5,𝔽2)—1512no—
93#137—3024no—
94#137—1514no—
95AGL(1,ℤ/8)—3024no—
96AGL(1,ℤ/8)—1514no—
97#135—3024no—
98#135—1512no—
99C2×SD16—3024no—
100C2×SD16C2×D15114yescomplemented
101#131—1514no—
102C4⋊Q8C2×D15111yescharacteristic, complemented
103#127C2×D15111yescharacteristic
104#108—1512no—
105#104—1514no—
106#101—1512no—
107#100—1512no—
108C4×C8C2×D15111yescharacteristic, complemented
109#41—3024no—
110#41—3024no—
111#41—6042no—
112#41—1514no—
113C2×Q8—3024no—
114C2×Q8C22×D15112yes—
115C2×D4—41no—
116C2×D4—3024no—
117C2×D4—6042no—
118C2×D4C22×D15112yes—
119Q16—3024no—
120Q16—1512no—
121SD16—24no—
122SD16—24no—
123SD16—3024no—
124SD16—3024no—
125SD16—1514no—
126D8—3024no—
127D8—1512no—
128M16—3024no—
129M16—1514no—
130C2×C8—3024no—
131C2×C8C22×D15112yes—
132C4⋊C4—41no—
133C42C22×D15111yescharacteristic
134C23—22no—
135C23—6042no—
136Q8—24no—
137Q8—6042no—
138Q8—1514no—
139D4—24no—
140D4—82no—
141D4—3024no—
142D4—6042no—
143D4—6044no—
144D4—1514no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—3024no—
148C2×C4—6044no—
149C2×C4—6042no—
150C2×C4C23×D15111yescharacteristic
151C8—3024no—
152C8D4×D15112yes—
153C8D4×D15112yes—
154C22—42no—
155C22—82no—
156C22—3024no—
157C22—24162no—
158C22#1801278411yescharacteristic
159C4—22no—
160C4—42no—
161C4—3024no—
162C4C2×D4×D15112yes—
163C2—21no—
164C2—82no—
165C2—6044no—
166C2#2375284711yescharacteristic
subgroupG/H
centerC2#23752847
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#492×C151C2
socleC2×C151D42
hypercenter#492D151
hypocenterC151#3291
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #23753018C2semidirect
2. #23752472C2semidirect
3. #23752394C2semidirect
4. #23752379C2semidirect
5. #23752330C2semidirect
6. #492×C151C2semidirect
8. #18012784C22semidirect
9. #18012770C22semidirect
16. #18012745C22semidirect
17. #18012675C22semidirect
18. #18012667C22semidirect
19. #18012658C22semidirect
20. #18012656C22semidirect
21. C2×SD16×C151C22semidirect
22. C4⋊Q8×C151C22semidirect
24. C4×C8×C151C22semidirect
32. Dic604D4semidirect
34. #14558993D4semidirect
37. D1208D4semidirect
83. C151#3291semidirect
86. #492D151semidirect
100. C2×SD16C2×D151semidirect
102. C4⋊Q8C2×D151semidirect
108. C4×C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530182
#237524722
#237523942
#237523792
#237523302
#492×C1512
#3291151