Finite Group Databasebeta

← #23774262

Subgroups — #23774262

Order 10112.

442 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 109 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#19099129C212yesmaximal, complemented
2#19098889C212yesmaximal, complemented
3#19098886C212yesmaximal, complemented
4#19098816C211yesmaximal, characteristic, complemented
5#19098797C212yesmaximal, complemented
6#19098698C212yesmaximal, complemented
7#19098695C212yesmaximal, complemented
8#19098531C211yesmaximal, characteristic, complemented
9#469×C79C211yesmaximal, characteristic, complemented
10C2×#11929624C2211yescharacteristic
11C2×D4×D79C2212yescomplemented
12C2×D632C2211yescharacteristic
13C2×#11929609C2212yes—
14C22×C79⋊C8C2211yescharacteristic, complemented
15#14579157—22no—
16#14579147—22no—
17#14579136C2212yes—
18#14579135C2212yescomplemented
19#14579132C2212yes—
20#14579131—22no—
21#14579129—22no—
22#14579119C2212yescomplemented
23#14579094C2212yescomplemented
24#14579093C2211yescharacteristic, complemented
25#14579083C2212yescomplemented
26#14579082C2212yescomplemented
27#14579081C2212yescomplemented
28(C2×D79)⋊C8C2212yescomplemented
29(C2×D79)⋊C8C2212yescomplemented
30C2×D8×C79C2211yescharacteristic
31C2×M16×C79C2211yescharacteristic, complemented
32#121×C79C2212yescomplemented
33#106×C79C2211yescharacteristic, complemented
34#102×C79C2212yescomplemented
35C23×D79—22no—
36#11929624—41no—
37#11929624—41no—
38C2×Dic158D411yescharacteristic
39C2×D316—22no—
40C2×D316D411yescharacteristic
41C2×D316C2312yes—
42C2×C22⋊D79—22no—
43C2×C22⋊D79—22no—
44C2×C22⋊D79—22no—
45C2×C22⋊D79D412yes—
46D4×D79—42no—
47D4×D79—42no—
48C2×C4×D79C2312yes—
49D632—41no—
50#11929609—42no—
51C2×C79⋊C8—41no—
52C2×C79⋊C8C2312yes—
53C4⋊Dic79C2312yes—
54C22⋊Dic79—22no—
55(C2×D79)⋊C4—22no—
56(C2×D79)⋊C4—22no—
57(C2×D79)⋊C4—22no—
58C4×Dic79—22no—
59C2×D4×C79—22no—
60C2×D4×C79C2312yes—
61C22×C4×C79C2311yescharacteristic
62D8×C79—41no—
63M16×C79—41no—
64C2×C8×C79C2311yescharacteristic
65C2×C8×C79C2311yescharacteristic
66C4⋊C4×C79C2312yes—
67C22⋊C4×C79—22no—
68C23×C79—22no—
69C23×C79C2×D411yescharacteristic
70C22×D79—22no—
71C22×D79—44no—
72C22×D79—82no—
73C22×D79—82no—
74C22×D79C2×D412yes—
75D4×C79—22no—
76D4×C79—22no—
77D4×C79—82no—
78C2×C4×C79—21no—
79C2×C4×C79—21no—
80C2×C4×C79—22no—
81C2×C4×C79C2×D411yescharacteristic
82C2×C4×C79C2411yescharacteristic
83C22⋊D79—42no—
84C22⋊D79—44no—
85C22⋊D79—82no—
86C22⋊D79—82no—
87C2×Dic79—22no—
88C2×Dic79C2×D412yes—
89D316—22no—
90D316—22no—
91D316—41no—
92D316—82no—
93C4×D79—22no—
94C4×D79—22no—
95Dic158—41no—
96C8×C79—21no—
97C8×C79—21no—
98C79⋊C8—22no—
99C22×C79—21no—
100C22×C79—22no—
101C22×C79—42no—
102C22×C79—42no—
103C22×C79—42no—
104C22×C79C22×D411yescharacteristic
105C2×D79—22no—
106C2×D79—22no—
107C2×D79—22no—
108C2×D79—42no—
109C2×D79—42no—
110C2×D79—42no—
111C2×D79—88no—
112C4×C79—21no—
113C4×C79—42no—
114C4×C79H(5,𝔽2)11yescharacteristic
115C4×C79H(5,𝔽2)11yescharacteristic
116Dic79—22no—
117Dic79—42no—
118C2×C79—41no—
119C2×C79—82no—
120C2×C79#53411yescharacteristic
121C2×C79#57612yes—
122D79—42no—
123D79—82no—
124#3199—791nomaximal, Sylow
125C79#319911yescharacteristic, complemented, Sylow
126#535—792no—
127#482—792no—
128#482—792no—
129#469—791no—
130#469D7911yescharacteristic, complemented
131#466—792no—
132#447—792no—
133#447—792no—
134#408—791no—
135C2×#41—791no—
136C22×D4—792no—
137C2×D8—792no—
138C2×D8—791no—
139C2×D8C2×D7911yescharacteristic
140C2×M16C2×D7911yescharacteristic, complemented
141C22×C8—791no—
142#127—1582no—
143#124—1582no—
144#121—792no—
145#121—792no—
146#121—792no—
147#121C2×D7912yescomplemented
148#120—1582no—
149#120—1582no—
150#117—792no—
151#107—792no—
152#106—791no—
153#106C2×D7911yescharacteristic, complemented
154#102—792no—
155#102—792no—
156#102—792no—
157#102C2×D7912yescomplemented
158C22⋊C8—792no—
159C22⋊C8—792no—
160C24—1582no—
161#41—3161no—
162#41—3161no—
163C2×Q8—791no—
164C2×D4—22no—
165C2×D4—3162no—
166C2×D4—3162no—
167C2×D4—792no—
168C2×D4—791no—
169C2×D4—792no—
170C2×D4—1582no—
171C2×D4—1582no—
172C2×D4—1582no—
173C2×D4—1582no—
174C2×D4C22×D7912yes—
175C22×C4—792no—
176C22×C4C22×D7911yescharacteristic
177D8—41no—
178D8—3161no—
179D8—3162no—
180M16—41no—
181C2×C8—3161no—
182C2×C8—792no—
183C2×C8C22×D7911yescharacteristic
184C2×C8C22×D7911yescharacteristic
185C4⋊C4—792no—
186C4⋊C4C22×D7912yes—
187C22⋊C4—22no—
188C22⋊C4—1582no—
189C22⋊C4—1582no—
190C22⋊C4—1582no—
191C22⋊C4—1582no—
192C42—1582no—
193C23—22no—
194C23—3164no—
195C23—792no—
196C23—6322no—
197C23—6322no—
198C23—1582no—
199C23D4×D7911yescharacteristic
200Q8—3161no—
201D4—22no—
202D4—22no—
203D4—82no—
204D4—3161no—
205D4—3162no—
206D4—3164no—
207D4—6322no—
208D4—6322no—
209D4—6322no—
210D4—1582no—
211D4—1582no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—792no—
216C2×C4—1582no—
217C2×C4—1582no—
218C2×C4—1582no—
219C2×C4D4×D7911yescharacteristic
220C2×C4C23×D7911yescharacteristic
221C8—21no—
222C8—21no—
223C8—1582no—
224C22—22no—
225C22—21no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—3162no—
230C22—3162no—
231C22—3162no—
232C22—6328no—
233C22—1582no—
234C22—1582no—
235C22—1582no—
236C22C2×D4×D7911yescharacteristic
237C4—21no—
238C4—42no—
239C4—3162no—
240C4—1582no—
241C4#1457920611yescharacteristic
242C4#1457920711yescharacteristic
243C2—41no—
244C2—82no—
245C2—3162no—
246C2—6322no—
247C2#1909912111yescharacteristic
248C2#1909936712yes—
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#469×C79C2
socleC22×C79C22×D4
hypercenter#469D79
hypocenterC79#3199
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #19099129C2semidirect
2. #19098889C2semidirect
3. #19098886C2semidirect
4. #19098816C2semidirect
5. #19098797C2semidirect
6. #19098698C2semidirect
7. #19098695C2semidirect
8. #19098531C2semidirect
9. #469×C79C2semidirect
11. C2×D4×D79C22semidirect
14. C22×C79⋊C8C22semidirect
18. #14579135C22semidirect
22. #14579119C22semidirect
23. #14579094C22semidirect
24. #14579093C22semidirect
25. #14579083C22semidirect
26. #14579082C22semidirect
27. #14579081C22semidirect
28. (C2×D79)⋊C8C22semidirect
29. (C2×D79)⋊C8C22semidirect
31. C2×M16×C79C22semidirect
32. #121×C79C22semidirect
33. #106×C79C22semidirect
34. #102×C79C22semidirect
125. C79#3199semidirect
130. #469D79semidirect
140. C2×M16C2×D79semidirect
147. #121C2×D79semidirect
153. #106C2×D79semidirect
157. #102C2×D79semidirect