Finite Group Databasebeta

← #23765384

Subgroups — #23765384

Order 10112.

354 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 45 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#19098749C212yesmaximal, complemented
2#19098730C211yesmaximal, characteristic, complemented
3#19098356C211yesmaximal, characteristic, complemented
4#19098350C212yesmaximal, complemented
5D42×C79C211yesmaximal, characteristic, complemented
6#14579206C2211yescharacteristic, complemented
7#14579187—21no—
8#14579130—22no—
9#14579089—21no—
10#14579078C2211yescharacteristic, complemented
11#14579076C2212yescomplemented
12#14579075—22no—
13C22×D4×C79—22no—
14#127×C79C2211yescharacteristic
15#121×C79—22no—
16#120×C79—21no—
17#120×C79C2212yes—
18C4×D4×C79—21no—
19#11929624—21no—
20#11929623—41no—
21C2×C22⋊D79—22no—
22C2×C22⋊D79—42no—
23D4×D79—41no—
24#11929612—41no—
25#11929609—41no—
26#11929608—21no—
27C22⋊Dic79—22no—
28C22⋊Dic79—42no—
29C24×C79—21no—
30C24×C79D412yescomplemented
31C2×D4×C79—21no—
32C2×D4×C79—22no—
33C2×D4×C79—22no—
34C2×D4×C79—22no—
35C2×D4×C79—48no—
36C2×D4×C79D411yescharacteristic, complemented
37C2×D4×C79C2311yescharacteristic
38C22×C4×C79—22no—
39C4⋊C4×C79—21no—
40C22⋊C4×C79—21no—
41C22⋊C4×C79—22no—
42C22⋊C4×C79D412yescomplemented
43C42×C79D411yescharacteristic, complemented
44C23×C79—22no—
45C23×C79—21no—
46C23×C79—42no—
47C23×C79—44no—
48C23×C79—44no—
49C23×C79—81no—
50C23×C79C2×D412yes—
51C22×D79—22no—
52D4×C79—24no—
53D4×C79—41no—
54D4×C79—41no—
55D4×C79—44no—
56D4×C79—44no—
57D4×C79—44no—
58C2×C4×C79—21no—
59C2×C4×C79—22no—
60C2×C4×C79—44no—
61C2×C4×C79C2×D411yescharacteristic
62C22⋊D79—42no—
63C22⋊D79—41no—
64C22⋊D79—84no—
65C2×Dic79—22no—
66C2×Dic79—42no—
67D316—21no—
68C4×D79—41no—
69Dic158—21no—
70C79⋊C8—41no—
71C22×C79—24no—
72C22×C79—22no—
73C22×C79—42no—
74C22×C79—42no—
75C22×C79—42no—
76C22×C79—44no—
77C22×C79—42no—
78C22×C79—41no—
79C22×C79—82no—
80C22×C79—84no—
81C22×C79#12011yescharacteristic
82C2×D79—41no—
83C2×D79—82no—
84C4×C79—22no—
85C4×C79—21no—
86C4×C79—42no—
87Dic79—41no—
88Dic79—82no—
89C2×C79—21no—
90C2×C79—42no—
91C2×C79—44no—
92C2×C79—81no—
93C2×C79B(4,𝔽2)11yescharacteristic
94D79—81no—
95#2196—791nomaximal, Sylow
96C79#219611yescharacteristic, complemented, Sylow
97D42D7911yescharacteristic, complemented
98B(4,𝔽2)—792no—
99#453—791no—
100#353—791no—
101AΣL(1,𝔽16)—792no—
102H(5,𝔽2)—791no—
103C22×D4—22no—
104AGL(1,ℤ/8)—1581no—
105#127C2×D7911yescharacteristic
106#121—22no—
107#120—21no—
108#120—1582no—
109#120C2×D7912yes—
110C4×D4—21no—
111#104—1581no—
112#100—791no—
113#99—792no—
114#99—1582no—
115C24—21no—
116C24C22⋊D7912yescomplemented
117#41—3161no—
118#41—1581no—
119C2×D4—21no—
120C2×D4—22no—
121C2×D4—22no—
122C2×D4—22no—
123C2×D4—48no—
124C2×D4—3161no—
125C2×D4—3162no—
126C2×D4—1582no—
127C2×D4C22⋊D7911yescharacteristic, complemented
128C2×D4C22×D7911yescharacteristic
129C22×C4—22no—
130SD16—3161no—
131D8—3161no—
132M16—1581no—
133C4⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—22no—
136C22⋊C4—3162no—
137C22⋊C4—1582no—
138C22⋊C4C22⋊D7912yescomplemented
139C42C22⋊D7911yescharacteristic, complemented
140C23—22no—
141C23—21no—
142C23—42no—
143C23—44no—
144C23—44no—
145C23—81no—
146C23—1582no—
147C23C2×C22⋊D7912yes—
148Q8—1581no—
149D4—24no—
150D4—41no—
151D4—41no—
152D4—44no—
153D4—44no—
154D4—44no—
155D4—3162no—
156D4—3161no—
157D4—6324no—
158D4—1581no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—44no—
162C2×C4—3161no—
163C2×C4—3162no—
164C2×C4—1582no—
165C2×C4C2×C22⋊D7911yescharacteristic
166C8—3161no—
167C22—24no—
168C22—22no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—44no—
173C22—42no—
174C22—41no—
175C22—82no—
176C22—84no—
177C22—3161no—
178C22—6322no—
179C22#1457913011yescharacteristic
180C4—22no—
181C4—21no—
182C4—42no—
183C4—3161no—
184C4—6322no—
185C2—21no—
186C2—42no—
187C2—44no—
188C2—81no—
189C2—6321no—
190C2#1909875011yescharacteristic
subgroupG/H
centerC2#19098750
commutator, cosocleC2×D4×C79C23
FrattiniC2×D4C22×D79
FittingD42×C79C2
socleC2×C79B(4,𝔽2)
hypercenterD42D79
hypocenterC79#2196
LCSG ▷ C2×D4×C79 ▷ C22×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #19098749C2semidirect
2. #19098730C2semidirect
3. #19098356C2semidirect
4. #19098350C2semidirect
5. D42×C79C2semidirect
6. #14579206C22semidirect
10. #14579078C22semidirect
11. #14579076C22semidirect
30. C24×C79D4semidirect
36. C2×D4×C79D4semidirect
42. C22⋊C4×C79D4semidirect
43. C42×C79D4semidirect
96. C79#2196semidirect
97. D42D79semidirect
116. C24C22⋊D79semidirect
127. C2×D4C22⋊D79semidirect
138. C22⋊C4C22⋊D79semidirect
139. C42C22⋊D79semidirect