Finite Group Databasebeta

← #23763841

Subgroups — #23763841

Order 10112.

442 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 97 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#19099074C211yesmaximal, characteristic
2C22×C4×Dic79C211yesmaximal, characteristic, complemented
3C2×#14579087C212yesmaximal, complemented
4#19098324C212yesmaximal, complemented
5#407×C79C211yesmaximal, characteristic, complemented
6C2×#11929624C2211yescharacteristic
7C23×Dic79—21no—
8#14579144—21no—
9#14579140C412yescomplemented
10#14579135C412yescomplemented
11#14579130—21no—
12C4×C22⋊D79—22no—
13#14579120C2211yescharacteristic
14C2×C4×Dic79—21no—
15C2×C4×Dic79—24no—
16C2×C4×Dic79C2212yes—
17#14579087—24no—
18C23×C4×C79C2211yescharacteristic
19C2×M16×C79C2212yes—
20C22⋊C8×C79—22no—
21#11929624—22no—
22#11929624—22no—
23C2×Dic158C2×C411yescharacteristic, complemented
24C2×D316C2×C411yescharacteristic, complemented
25C2×C22⋊D79—22no—
26C2×C22⋊D79—21no—
27C22×Dic79—24no—
28C22×Dic79—28no—
29C22×Dic79—22no—
30C2×C4×D79—21no—
31C4⋊Dic79C2×C412yescomplemented
32Dic79⋊C4—22no—
33C22⋊Dic79—22no—
34C22⋊Dic79—21no—
35(C2×D79)⋊C4—22no—
36C4×Dic79—24no—
37C4×Dic79—22no—
38C4×Dic79—21no—
39C4×Dic79D414yescomplemented
40C24×C79D411yescharacteristic
41C22×C4×C79—22no—
42C22×C4×C79—22no—
43C22×C4×C79C2×C412yes—
44C22×C4×C79D411yescharacteristic
45C22×C4×C79D412yes—
46C22×C4×C79C2311yescharacteristic
47M16×C79—22no—
48M16×C79—22no—
49C2×C8×C79—22no—
50C23×C79—24no—
51C23×C79—21no—
52C23×C79—21no—
53C23×C79C22⋊C412yes—
54C23×C79C2×D411yescharacteristic
55C22×D79—21no—
56C2×C4×C79—21no—
57C2×C4×C79—21no—
58C2×C4×C79—24no—
59C2×C4×C79—24no—
60C2×C4×C79C22⋊C412yes—
61C2×C4×C79C22×C411yescharacteristic
62C2×C4×C79C2×D412yes—
63C2×C4×C79C2×D411yescharacteristic
64C2×C4×C79#4112yes—
65C22⋊D79—44no—
66C22⋊D79—41no—
67C22⋊D79—41no—
68C2×Dic79—216no—
69C2×Dic79—28no—
70C2×Dic79—24no—
71C2×Dic79—22no—
72C2×Dic79—21no—
73D316—22no—
74C4×D79—42no—
75Dic158—22no—
76C8×C79—42no—
77C22×C79—24no—
78C22×C79—24no—
79C22×C79—22no—
80C22×C79—22no—
81C22×C79—22no—
82C22×C79#10414yescomplemented
83C22×C79C2×C22⋊C411yescharacteristic
84C22×C79#12011yescharacteristic
85C22×C79#12311yescharacteristic
86C2×D79—41no—
87C2×D79—42no—
88C4×C79—22no—
89C4×C79C4×D412yes—
90C4×C79#12112yes—
91Dic79—28no—
92Dic79—41no—
93Dic79—42no—
94C2×C79—21no—
95C2×C79—24no—
96C2×C79—21no—
97C2×C79#38611yescharacteristic
98C2×C79C2×#10412yes—
99D79—81no—
100#1896—791nomaximal, Sylow
101C79#189611yescharacteristic, complemented, Sylow
102#525—791no—
103C22×C42—791no—
104C2×#104—792no—
105#407D7911yescharacteristic, complemented
106#339—792no—
107C2×#41—791no—
108C23×C4—1581no—
109C23×C4C2×D7911yescharacteristic
110C2×M16C2×D7912yes—
111#123—1581no—
112C22⋊Q8—792no—
113#121—792no—
114#120—1581no—
115C4×D4—1582no—
116#117—791no—
117C2×C42—792no—
118C2×C42—1584no—
119C2×C42—1581no—
120#104—1584no—
121C22⋊C8—22no—
122C24D31611yescharacteristic
123#41—1582no—
124#41—1582no—
125C2×Q8—791no—
126C2×D4—791no—
127C2×D4—1582no—
128C2×D4—1581no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—1581no—
132C22×C4—1584no—
133C22×C4—1588no—
134C22×C4—1582no—
135C22×C4C4×D7912yes—
136C22×C4D31611yescharacteristic
137C22×C4C22⋊D7912yes—
138C22×C4C22×D7911yescharacteristic
139M16—22no—
140M16—22no—
141C2×C8—22no—
142C4⋊C4—792no—
143C4⋊C4—1582no—
144C22⋊C4—1582no—
145C22⋊C4—1581no—
146C22⋊C4—1582no—
147C42—794no—
148C42—1584no—
149C42—1582no—
150C42—1581no—
151C23—24no—
152C23—21no—
153C23—21no—
154C23—1581no—
155C23(C2×D79)⋊C412yes—
156C23C2×D31611yescharacteristic
157Q8—1582no—
158D4—3164no—
159D4—3161no—
160D4—3161no—
161D4—1582no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—24no—
165C2×C4—24no—
166C2×C4—3162no—
167C2×C4—1582no—
168C2×C4—1581no—
169C2×C4—15816no—
170C2×C4—1588no—
171C2×C4—1584no—
172C2×C4(C2×D79)⋊C412yes—
173C2×C4C2×C4×D7911yescharacteristic
174C2×C4D4×D7912yes—
175C2×C4C2×C22⋊D7911yescharacteristic
176C2×C4#1192962312yes—
177C8—42no—
178C22—24no—
179C22—24no—
180C22—22no—
181C22—22no—
182C22—22no—
183C22—3161no—
184C22—3162no—
185C22#1457908714yescomplemented
186C22C2×(C2×D79)⋊C411yescharacteristic
187C22#1457913111yescharacteristic
188C22#1457914511yescharacteristic
189C4—22no—
190C4—3161no—
191C4—3162no—
192C4—1588no—
193C4(C22⋊D79)⋊C412yes—
194C4#1457913312yes—
195C2—21no—
196C2—24no—
197C2—21no—
198C2—6321no—
199C2#1909844011yescharacteristic
200C2C2×#1457908712yes—
subgroupG/H
centerC2×C4C2×C22⋊D79
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#407×C79C2
socleC22×C79C2×C22⋊C4
prime radical#19099074C2
cosocleC22×C4×C79C23
hypercenter#407D79
hypocenterC79#1896
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic79C2semidirect
3. C2×#14579087C2semidirect
4. #19098324C2semidirect
5. #407×C79C2semidirect
9. #14579140C4semidirect
10. #14579135C4semidirect
23. C2×Dic158C2×C4semidirect
24. C2×D316C2×C4semidirect
31. C4⋊Dic79C2×C4semidirect
39. C4×Dic79D4semidirect
82. C22×C79#104semidirect
101. C79#1896semidirect
105. #407D79semidirect
185. C22#14579087semidirect