Finite Group Databasebeta

← #23762966

Subgroups — #23762966

Order 10112.

162 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 51 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#19098909C211yesmaximal, characteristic
2#19098773C211yesmaximal, characteristic, complemented
3#19098694C211yesmaximal, characteristic, complemented
4#19098313C211yesmaximal, characteristic, complemented
5#19098310C211yesmaximal, characteristic, complemented
6#19098307C211yesmaximal, characteristic
7#460×C79C211yesmaximal, characteristic
8C2×#11929614—21no—
9#14579161C2211yescharacteristic
10C4⋊(C79⋊C8)—21no—
11C4⋊(C79⋊C8)C2211yescharacteristic
12C4⋊(C79⋊C8)C2211yescharacteristic
13#14579084—21no—
14#14579082—21no—
15#14579082—21no—
16#14579072—21no—
17C4×C79⋊C8C2211yescharacteristic
18C2×SD16×C79—21no—
19#127×C79C2211yescharacteristic
20C4×Q8×C79C2211yescharacteristic
21C4⋊C8×C79C2211yescharacteristic
22#102×C79—21no—
23C2×Dic158—21no—
24#11929614—42no—
25C2×C79⋊C8—21no—
26C2×C79⋊C8—21no—
27C2×C79⋊C8D411yescharacteristic
28C2×C79⋊C8D411yescharacteristic
29C4⋊Dic79—21no—
30C4⋊Dic79—21no—
31C2×Q8×C79D411yescharacteristic
32C2×D4×C79—21no—
33C2×D4×C79—21no—
34C2×D4×C79—21no—
35SD16×C79—42no—
36C2×C8×C79—21no—
37C4⋊C4×C79—21no—
38C4⋊C4×C79D411yescharacteristic
39C42×C79—21no—
40C42×C79C2311yescharacteristic
41C23×C79—41no—
42Q8×C79—21no—
43Q8×C79—21no—
44D4×C79—41no—
45D4×C79—41no—
46D4×C79—41no—
47D4×C79—41no—
48D4×C79—81no—
49C2×C4×C79—21no—
50C2×C4×C79—21no—
51C2×C4×C79C2×D411yescharacteristic
52C2×C4×C79C2×D411yescharacteristic
53C2×C4×C79#4111yescharacteristic
54C2×Dic79—41no—
55Dic158—41no—
56Dic158—41no—
57C8×C79—41no—
58C79⋊C8—21no—
59C79⋊C8—21no—
60C79⋊C8—41no—
61C79⋊C8—41no—
62C22×C79—81no—
63C22×C79—81no—
64C22×C79—81no—
65C22×C79#12111yescharacteristic
66C4×C79—21no—
67C4×C79—41no—
68C4×C79—41no—
69C4×C79#13511yescharacteristic
70C4×C79AGL(1,ℤ/8)11yescharacteristic
71C4×C79AGL(1,ℤ/8)11yescharacteristic
72C4×C79#13711yescharacteristic
73Dic79—81no—
74C2×C79—161no—
75C2×C79#46411yescharacteristic
76C2×C79#46911yescharacteristic
77C2×C79#47111yescharacteristic
78#1702—791nomaximal, Sylow
79C79#170211yescharacteristic, complemented, Sylow
80#486—791no—
81#462—791no—
82#460D7911yescharacteristic
83#446—791no—
84#334—791no—
85#332—791no—
86#331—791no—
87C2×Q16—1581no—
88C2×SD16—21no—
89C4⋊Q8—791no—
90#127C2×D7911yescharacteristic
91C4×Q8C2×D7911yescharacteristic
92C4⋊C8—791no—
93C4⋊C8—791no—
94C4⋊C8—1581no—
95C4⋊C8C2×D7911yescharacteristic
96#103—1581no—
97#102—21no—
98#102—1581no—
99#102—1581no—
100#97—1581no—
101C4×C8—791no—
102C2×Q8—1581no—
103C2×Q8C22⋊D7911yescharacteristic
104C2×D4—21no—
105C2×D4—21no—
106C2×D4—21no—
107Q16—3162no—
108SD16—42no—
109C2×C8—21no—
110C2×C8—791no—
111C2×C8—791no—
112C2×C8—1581no—
113C2×C8—1581no—
114C4⋊C4—21no—
115C4⋊C4—1581no—
116C4⋊C4—1581no—
117C4⋊C4C22⋊D7911yescharacteristic
118C42—21no—
119C42C22×D7911yescharacteristic
120C23—41no—
121Q8—21no—
122Q8—21no—
123Q8—3161no—
124Q8—3161no—
125D4—41no—
126D4—41no—
127D4—41no—
128D4—41no—
129D4—81no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—3161no—
133C2×C4D4×D7911yescharacteristic
134C2×C4C2×C22⋊D7911yescharacteristic
135C2×C4#1192962311yescharacteristic
136C8—41no—
137C8—3161no—
138C8—3161no—
139C8—1581no—
140C8—1581no—
141C22—81no—
142C22—81no—
143C22—81no—
144C22#1457913311yescharacteristic
145C4—21no—
146C4—41no—
147C4—41no—
148C4—6321no—
149C4#1457918211yescharacteristic
150C4#1457918611yescharacteristic
151C4#1457918711yescharacteristic
152C4#1457919011yescharacteristic
153C2—161no—
154C2#1909878311yescharacteristic
155C2#1909881411yescharacteristic
156C2#1909882411yescharacteristic
subgroupG/H
centerC22#14579133
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
Fitting#460×C79C2
socleC22×C79#121
prime radical#127×C79C22
hypercenter#460D79
hypocenterC79#1702
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #19098773C2semidirect
3. #19098694C2semidirect
4. #19098313C2semidirect
5. #19098310C2semidirect
79. C79#1702semidirect