Finite Group Databasebeta

← #23773638

Subgroups — #23773638

Order 10112.

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

normal subgroups only

This group has 418 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#19099037C211yesmaximal, characteristic, complemented
2#19098884C212yesmaximal, complemented
3#19098860C212yesmaximal, complemented
4#19098755C212yesmaximal, complemented
5#19098696C212yesmaximal, complemented
6#19098673C212yesmaximal, complemented
7C4×#11929609C212yesmaximal, complemented
8#19098624C211yesmaximal, characteristic, complemented
9#540×C79C211yesmaximal, characteristic, complemented
10C22×D316C2211yescharacteristic
11C2×#11929609C2212yes—
12C2×#11929609C2212yes—
13C4×D316C2212yes—
14C4×D316C2212yes—
15#14579123—22no—
16#14579120C2211yescharacteristic
17C22⋊C4×D79—22no—
18#14579094C2212yescomplemented
19#14579092C2212yescomplemented
20C4⋊(C79⋊C8)C2212yescomplemented
21#14579082C2212yescomplemented
22#14579082C2212yescomplemented
23#14579081C2212yes—
24#14579081C2212yes—
25C22⋊(C79⋊C8)C2212yes—
26#14579072C2211yescharacteristic, complemented
27C4×C79⋊C8C2211yescharacteristic, complemented
28#127×C79C2211yescharacteristic, complemented
29#125×C79C2211yescharacteristic, complemented
30#123×C79—22no—
31#121×C79—22no—
32#121×C79C2212yes—
33C4×D4×C79C2212yescomplemented
34#117×C79C2211yescharacteristic
35C23×D79—21no—
36C2×D316—24no—
37C2×D316—21no—
38C2×D316C2312yes—
39C2×C4×D79—22no—
40C2×C4×D79—22no—
41#11929609—24no—
42#11929609—24no—
43C2×C79⋊C8C2312yes—
44C2×C79⋊C8C2312yes—
45C4⋊Dic79C2312yes—
46C22⋊Dic79—21no—
47(C2×D79)⋊C4—22no—
48(C2×D79)⋊C4—22no—
49C4×Dic79—21no—
50C2×D4×C79—22no—
51C2×D4×C79—22no—
52C2×D4×C79C2312yes—
53C22×C4×C79—22no—
54C22×C4×C79C2311yescharacteristic
55C4⋊C4×C79—22no—
56C4⋊C4×C79D412yes—
57C4⋊C4×C79C2312yes—
58C22⋊C4×C79—22no—
59C22⋊C4×C79—22no—
60C22⋊C4×C79D412yes—
61C42×C79C2311yescharacteristic
62C42×C79C2311yescharacteristic
63C23×C79—22no—
64C23×C79C2×D411yescharacteristic
65C22×D79—22no—
66C22×D79—24no—
67C22×D79—82no—
68D4×C79—22no—
69D4×C79—22no—
70D4×C79—82no—
71D4×C79—82no—
72C2×C4×C79—22no—
73C2×C4×C79—22no—
74C2×C4×C79—82no—
75C2×C4×C79C2×D411yescharacteristic
76C2×C4×C79C2×D412yes—
77C2×C4×C79C2×D412yes—
78C2×C4×C79C2411yescharacteristic
79C2×Dic79—22no—
80D316—24no—
81D316—22no—
82D316#4114yes—
83C4×D79—82no—
84C4×D79—82no—
85C79⋊C8—22no—
86C79⋊C8—22no—
87C22×C79—21no—
88C22×C79—22no—
89C22×C79—42no—
90C22×C79—42no—
91C22×C79—42no—
92C22×C79C22×D411yescharacteristic
93C2×D79—24no—
94C2×D79—42no—
95C2×D79—42no—
96C2×D79—84no—
97C4×C79—21no—
98C4×C79—22no—
99C4×C79—22no—
100C4×C79—42no—
101C4×C79C2×#4112yes—
102Dic79—42no—
103C2×C79—41no—
104C2×C79—82no—
105C2×C79#52511yescharacteristic
106C2×C79#57612yes—
107D79—44no—
108#3122—791nomaximal, Sylow
109C79#312211yescharacteristic, complemented, Sylow
110#540D7911yescharacteristic, complemented
111#518—791no—
112#482—792no—
113#478—792no—
114#459—792no—
115#447—792no—
116#442—792no—
117C4×D8—792no—
118#433—791no—
119C22×D4—791no—
120C2×D8—792no—
121C2×D8—792no—
122#127C2×D7911yescharacteristic, complemented
123#125C2×D7911yescharacteristic, complemented
124#123—22no—
125#121—22no—
126#121C2×D7912yes—
127C4×D4—792no—
128C4×D4—792no—
129C4×D4—1582no—
130C4×D4C2×D7912yescomplemented
131#117—791no—
132#117C2×D7911yescharacteristic
133C2×C22⋊C4—1582no—
134#107—792no—
135#106—792no—
136C4⋊C8—792no—
137#102—792no—
138#102—792no—
139#102—792no—
140#102—792no—
141C22⋊C8—792no—
142#97—791no—
143C4×C8—791no—
144C24—1581no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—792no—
148C2×D4—1584no—
149C2×D4—1581no—
150C2×D4C22×D7912yes—
151C22×C4—22no—
152C22×C4—1582no—
153C22×C4—1582no—
154C22×C4C22×D7911yescharacteristic
155D8—1584no—
156D8—1584no—
157C2×C8—792no—
158C2×C8—792no—
159C4⋊C4—22no—
160C4⋊C4—792no—
161C4⋊C4C22⋊D7912yes—
162C4⋊C4C22×D7912yes—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—1581no—
166C22⋊C4—1582no—
167C22⋊C4—1582no—
168C22⋊C4C22⋊D7912yes—
169C42—1581no—
170C42C22×D7911yescharacteristic
171C42C22×D7911yescharacteristic
172C23—22no—
173C23—6322no—
174C23—1584no—
175C23—1582no—
176C23C2×C22⋊D7911yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—82no—
181D4—794no—
182D4—1584no—
183D4—1582no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—6322no—
188C2×C4—6322no—
189C2×C4—1582no—
190C2×C4C2×C22⋊D7911yescharacteristic
191C2×C4C2×C22⋊D7912yes—
192C2×C4C2×C22⋊D7912yes—
193C2×C4C23×D7911yescharacteristic
194C8—1582no—
195C8—1582no—
196C22—21no—
197C22—22no—
198C22—42no—
199C22—42no—
200C22—42no—
201C22—3162no—
202C22—3162no—
203C22—6324no—
204C22—1584no—
205C22C22×C22⋊D7911yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—3162no—
211C4#41×D7912yes—
212C2—41no—
213C2—82no—
214C2—3164no—
215C2#1909907011yescharacteristic
216C2#1909936612yes—
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#540×C79C2
socleC22×C79C22×D4
hypercenter#540D79
hypocenterC79#3122
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #19099037C2semidirect
2. #19098884C2semidirect
3. #19098860C2semidirect
4. #19098755C2semidirect
5. #19098696C2semidirect
6. #19098673C2semidirect
7. C4×#11929609C2semidirect
8. #19098624C2semidirect
9. #540×C79C2semidirect
18. #14579094C22semidirect
19. #14579092C22semidirect
20. C4⋊(C79⋊C8)C22semidirect
21. #14579082C22semidirect
22. #14579082C22semidirect
26. #14579072C22semidirect
27. C4×C79⋊C8C22semidirect
28. #127×C79C22semidirect
29. #125×C79C22semidirect
33. C4×D4×C79C22semidirect
109. C79#3122semidirect
110. #540D79semidirect
122. #127C2×D79semidirect
123. #125C2×D79semidirect
130. C4×D4C2×D79semidirect