Finite Group Databasebeta

← #23773773

Subgroups — #23773773

Order 10112.

484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 121 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#19099119C211yesmaximal, characteristic, complemented
2#127×D79C211yesmaximal, characteristic
3#19098929C211yesmaximal, characteristic, complemented
4#19098928C211yesmaximal, characteristic, complemented
5#19098927C211yesmaximal, characteristic, complemented
6#19098908C214yesmaximal, complemented
7#19098566C214yesmaximal, complemented
8#19098515C211yesmaximal, characteristic, complemented
9#490×C79C211yesmaximal, characteristic, complemented
10C2×D4×D79—22no—
11C2×D4×D79C2212yes—
12C2×#11929607C2212yes—
13#14579160C2212yescomplemented
14#14579158C2211yescharacteristic
15#14579157—22no—
16#14579157C2212yes—
17#14579153C2211yescharacteristic, complemented
18#14579139—22no—
19#14579126—22no—
20#14579119C2212yes—
21C42×D79C2211yescharacteristic
22#14579083C2214yescomplemented
23#14579082C2214yescomplemented
24#14579081C2214yescomplemented
25#14579072C2211yescharacteristic, complemented
26C8×Dic79C2212yescomplemented
27#127×C79C2211yescharacteristic
28#125×C79C2211yescharacteristic, complemented
29#102×C79C2214yescomplemented
30#97×C79C2211yescharacteristic, complemented
31C23×D79—22no—
32C2×Dic158—22no—
33C2×D316—22no—
34C2×D316C2312yes—
35C2×C22⋊D79—22no—
36C2×C22⋊D79—24no—
37D4×D79—28no—
38D4×D79—48no—
39C2×C4×D79D412yes—
40C2×C4×D79C2311yescharacteristic
41#11929607—24no—
42C2×C79⋊C8C2312yes—
43C4⋊Dic79C2312yes—
44Dic79⋊C4—22no—
45Dic79⋊C4—22no—
46(C2×D79)⋊C4—22no—
47C4×Dic79—22no—
48C4×Dic79D412yes—
49C4×Dic79C2311yescharacteristic
50C2×D4×C79—22no—
51C2×D4×C79C2312yes—
52C2×C8×C79C2312yes—
53C4⋊C4×C79—22no—
54C4⋊C4×C79C2312yes—
55C42×C79C2311yescharacteristic
56C23×C79—22no—
57C22×D79—22no—
58C22×D79—48no—
59C22×D79—44no—
60C22×D79C2×D411yescharacteristic
61D4×C79—24no—
62D4×C79—44no—
63C2×C4×C79—22no—
64C2×C4×C79C2×D412yes—
65C2×C4×C79C2411yescharacteristic
66C22⋊D79—44no—
67C22⋊D79—48no—
68C2×Dic79—22no—
69C2×Dic79C2×D411yescharacteristic
70C2×Dic79C2×D412yes—
71D316—24no—
72D316—44no—
73C4×D79—24no—
74C4×D79#4114yes—
75Dic158—44no—
76C8×C79—22no—
77C79⋊C8—22no—
78C22×C79—42no—
79C22×C79—44no—
80C22×C79C22×D411yescharacteristic
81C2×D79—22no—
82C2×D79—42no—
83C2×D79—44no—
84C2×D79—88no—
85C2×D79#12412yes—
86C4×C79—22no—
87C4×C79—42no—
88C4×C79C2×#4112yes—
89Dic79—42no—
90Dic79#12412yes—
91Dic79AGL(1,ℤ/8)14yes—
92C2×C79—82no—
93C2×C79C2×#12411yescharacteristic
94C2×C79C2×AGL(1,ℤ/8)12yes—
95D79—22no—
96D79—82no—
97#3138—791nomaximal, Sylow
98C79#313811yescharacteristic, complemented, Sylow
99#533—791no—
100C2×#127—791no—
101#490—791no—
102#490—791no—
103#490—791no—
104#490D7911yescharacteristic, complemented
105#486—794no—
106#418—794no—
107C4×M16—791no—
108C22×D4—792no—
109C22×D4—1582no—
110C2×M16—792no—
111C4⋊Q8—792no—
112#127—792no—
113#127—791no—
114#127—1582no—
115#127C2×D7911yescharacteristic
116#125—791no—
117#125C2×D7911yescharacteristic, complemented
118C22⋊Q8—1582no—
119C4×Q8—1582no—
120#117—792no—
121C2×C42—791no—
122#102—794no—
123#102—794no—
124#102—794no—
125#102C2×D7914yescomplemented
126#97—791no—
127#97C2×D7911yescharacteristic, complemented
128C4×C8—792no—
129C24—1582no—
130C2×Q8—1582no—
131C2×D4—22no—
132C2×D4—3168no—
133C2×D4—792no—
134C2×D4—1588no—
135C2×D4—1584no—
136C2×D4—1582no—
137C2×D4—1582no—
138C2×D4C22×D7912yes—
139C22×C4—791no—
140C22×C4—792no—
141M16—1584no—
142C2×C8—792no—
143C2×C8C22×D7912yes—
144C4⋊C4—22no—
145C4⋊C4—792no—
146C4⋊C4—1582no—
147C4⋊C4—1582no—
148C4⋊C4C22×D7912yes—
149C22⋊C4—1582no—
150C42—792no—
151C42—791no—
152C42—1582no—
153C42C22×D7911yescharacteristic
154C23—22no—
155C23—3164no—
156C23—3168no—
157C23—791no—
158C23—1582no—
159Q8—3164no—
160D4—24no—
161D4—44no—
162D4—3164no—
163D4—3168no—
164D4—3164no—
165D4—1584no—
166C2×C4—22no—
167C2×C4—791no—
168C2×C4—792no—
169C2×C4—794no—
170C2×C4—1584no—
171C2×C4—1582no—
172C2×C4D4×D7912yes—
173C2×C4C23×D7911yescharacteristic
174C8—22no—
175C8—1582no—
176C22—42no—
177C22—44no—
178C22—3162no—
179C22—3164no—
180C22—792no—
181C22—6328no—
182C22—1582no—
183C22C2×D4×D7911yescharacteristic
184C4—22no—
185C4—42no—
186C4—3162no—
187C4—792no—
188C4—794no—
189C4#41×D7912yes—
190C2—82no—
191C2—6322no—
192C2—1582no—
193C2#124×D7911yescharacteristic
194C2AGL(1,ℤ/8)×D7912yes—
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#490×C79C2
socleC22×C79C22×D4
prime radical#127×D79C2
hypercenter#490D79
hypocenterC79#3138
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #19099119C2semidirect
3. #19098929C2semidirect
4. #19098928C2semidirect
5. #19098927C2semidirect
6. #19098908C2semidirect
7. #19098566C2semidirect
8. #19098515C2semidirect
9. #490×C79C2semidirect
13. #14579160C22semidirect
17. #14579153C22semidirect
22. #14579083C22semidirect
23. #14579082C22semidirect
24. #14579081C22semidirect
25. #14579072C22semidirect
26. C8×Dic79C22semidirect
28. #125×C79C22semidirect
29. #102×C79C22semidirect
30. #97×C79C22semidirect
98. C79#3138semidirect
104. #490D79semidirect
117. #125C2×D79semidirect
125. #102C2×D79semidirect
127. #97C2×D79semidirect