Finite Group Databasebeta

← #23762968

Subgroups — #23762968

Order 10112.

162 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 53 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#19098910C211yesmaximal, characteristic
2#19098773C211yesmaximal, characteristic, complemented
3#19098763C211yesmaximal, characteristic
4#19098314C211yesmaximal, characteristic, complemented
5#19098308C211yesmaximal, characteristic, complemented
6#19098306C211yesmaximal, characteristic
7#446×C79C211yesmaximal, characteristic, complemented
8C2×#11929614—21no—
9C2×#11929611—21no—
10#14579161C2211yescharacteristic
11#14579158C2211yescharacteristic
12C4⋊(C79⋊C8)C2211yescharacteristic
13C4⋊(C79⋊C8)C2211yescharacteristic
14#14579084—21no—
15#14579083—21no—
16#14579083—21no—
17#14579081—21no—
18C4×Q8×C79C2211yescharacteristic
19C4⋊C8×C79—21no—
20C4⋊C8×C79C2211yescharacteristic
21#97×C79—21no—
22C4×C8×C79C2211yescharacteristic
23C2×Dic158—21no—
24C2×D316—21no—
25C2×D316—21no—
26C2×D316—21no—
27#11929614—42no—
28#11929611—42no—
29C2×C79⋊C8—21no—
30C2×C79⋊C8—21no—
31C4⋊Dic79—21no—
32C4⋊Dic79—21no—
33C2×Q8×C79D411yescharacteristic
34C2×C8×C79—21no—
35C2×C8×C79D411yescharacteristic
36C2×C8×C79D411yescharacteristic
37C4⋊C4×C79—21no—
38C4⋊C4×C79D411yescharacteristic
39C42×C79—21no—
40C42×C79C2311yescharacteristic
41C22×D79—41no—
42Q8×C79—21no—
43Q8×C79—21no—
44C2×C4×C79—21no—
45C2×C4×C79—21no—
46C2×C4×C79C2×D411yescharacteristic
47C2×C4×C79C2×D411yescharacteristic
48C2×C4×C79#4111yescharacteristic
49C2×Dic79—41no—
50D316—41no—
51D316—41no—
52D316—41no—
53D316—41no—
54D316—81no—
55Dic158—41no—
56Dic158—41no—
57C8×C79—21no—
58C8×C79—21no—
59C8×C79—41no—
60C79⋊C8—41no—
61C79⋊C8—41no—
62C22×C79#12111yescharacteristic
63C2×D79—81no—
64C2×D79—81no—
65C2×D79—81no—
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#46411yescharacteristic
75C2×C79#46911yescharacteristic
76C2×C79#47111yescharacteristic
77D79—161no—
78#1702—791nomaximal, Sylow
79C79#170211yescharacteristic, complemented, Sylow
80#486—791no—
81#462—791no—
82#460—791no—
83#446D7911yescharacteristic, complemented
84#334—791no—
85#332—791no—
86#331—791no—
87C2×Q16—1581no—
88C2×SD16—1581no—
89C4⋊Q8—791no—
90#127—791no—
91C4×Q8C2×D7911yescharacteristic
92C4⋊C8—21no—
93C4⋊C8—791no—
94C4⋊C8—791no—
95C4⋊C8C2×D7911yescharacteristic
96#103—1581no—
97#102—1581no—
98#102—1581no—
99#102—1581no—
100#97—21no—
101C4×C8C2×D7911yescharacteristic
102C2×Q8—1581no—
103C2×Q8D31611yescharacteristic
104C2×D4—1581no—
105C2×D4—1581no—
106C2×D4—1581no—
107Q16—3162no—
108SD16—3162no—
109C2×C8—21no—
110C2×C8—1581no—
111C2×C8—1581no—
112C2×C8C22⋊D7911yescharacteristic
113C2×C8C22⋊D7911yescharacteristic
114C4⋊C4—21no—
115C4⋊C4—1581no—
116C4⋊C4—1581no—
117C4⋊C4D31611yescharacteristic
118C42—21no—
119C42C22×D7911yescharacteristic
120C23—3161no—
121Q8—21no—
122Q8—21no—
123Q8—3161no—
124Q8—3161no—
125D4—3161no—
126D4—3161no—
127D4—3161no—
128D4—3161no—
129D4—6321no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—3161no—
133C2×C4C2×C22⋊D7911yescharacteristic
134C2×C4C2×D31611yescharacteristic
135C2×C4#1192962411yescharacteristic
136C8—21no—
137C8—21no—
138C8—41no—
139C8—3161no—
140C8—3161no—
141C22—6321no—
142C22—6321no—
143C22—6321no—
144C22#1457913511yescharacteristic
145C4—21no—
146C4—41no—
147C4—41no—
148C4—6321no—
149C4#1457918111yescharacteristic
150C4#1457918911yescharacteristic
151C4#1457918911yescharacteristic
152C4#1457919211yescharacteristic
153C2—12641no—
154C2#1909878511yescharacteristic
155C2#1909881611yescharacteristic
156C2#1909882611yescharacteristic
subgroupG/H
centerC22#14579135
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
Fitting#446×C79C2
socleC22×C79#121
prime radical#14579158C22
hypercenter#446D79
hypocenterC79#1702
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #446

Complements

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

NH ≅ G/Ntype
2. #19098773C2semidirect
4. #19098314C2semidirect
5. #19098308C2semidirect
7. #446×C79C2semidirect
79. C79#1702semidirect
83. #446D79semidirect