Finite Group Databasebeta

← #23773335

Subgroups — #23773335

Order 10112.

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

normal subgroups only

This group has 462 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#121×D79C211yesmaximal, characteristic
2C2×#14579119C211yesmaximal, characteristic, complemented
3#19098890C212yesmaximal, complemented
4#19098886C212yesmaximal, complemented
5#19098882C211yesmaximal, characteristic, complemented
6#19098879C211yesmaximal, characteristic, complemented
7#19098876C211yesmaximal, characteristic, complemented
8#19098604C212yesmaximal, complemented
9#19098566C212yesmaximal, complemented
10#19098525C211yesmaximal, characteristic, complemented
11#480×C79C211yesmaximal, characteristic, complemented
12C2×D4×D79—21no—
13C2×D4×D79C2211yescharacteristic
14C22×C4×D79C2211yescharacteristic
15C2×#11929607C2212yes—
16#14579136C2211yescharacteristic
17#14579135C2211yescharacteristic
18#14579134—21no—
19#14579133—21no—
20#14579132C2211yescharacteristic
21#14579119—21no—
22#14579119—21no—
23#14579119C2212yes—
24#14579119C2212yescomplemented
25C2×C4⋊Dic79C2211yescharacteristic, complemented
26C4⋊C4×D79C2211yescharacteristic
27C2×(C2×D79)⋊C4—21no—
28C22⋊C4×D79—21no—
29C2×C4×Dic79—21no—
30#14579094C2212yescomplemented
31#14579093C2212yescomplemented
32#14579092C2212yescomplemented
33#14579083C2212yescomplemented
34#14579082C2212yescomplemented
35#14579081C2212yescomplemented
36C22⋊(C79⋊C8)C2211yescharacteristic, complemented
37(C2×D79)⋊C8C2212yescomplemented
38#121×C79C2211yescharacteristic
39C2×C4⋊C4×C79C2211yescharacteristic, complemented
40#107×C79C2212yescomplemented
41#102×C79C2212yescomplemented
42C22⋊C8×C79C2211yescharacteristic, complemented
43C23×D79—21no—
44C23×D79D411yescharacteristic
45C2×D316—21no—
46C2×D316C2311yescharacteristic
47C2×C22⋊D79—21no—
48C2×C22⋊D79—21no—
49C2×C22⋊D79—21no—
50D4×D79—24no—
51D4×D79—44no—
52C22×Dic79—21no—
53C22×Dic79D411yescharacteristic
54C2×C4×D79—24no—
55C2×C4×D79—21no—
56C2×C4×D79D411yescharacteristic
57C2×C4×D79D411yescharacteristic
58C2×C4×D79C2311yescharacteristic
59C2×C4×D79C2311yescharacteristic
60#11929607—24no—
61C2×C79⋊C8C2312yes—
62C4⋊Dic79—21no—
63C4⋊Dic79C2312yes—
64C4⋊Dic79C2311yescharacteristic
65Dic79⋊C4—21no—
66C22⋊Dic79—21no—
67(C2×D79)⋊C4—21no—
68(C2×D79)⋊C4—22no—
69(C2×D79)⋊C4—22no—
70(C2×D79)⋊C4—21no—
71C4×Dic79—22no—
72C4×Dic79—22no—
73C2×D4×C79—21no—
74C2×D4×C79C2311yescharacteristic
75C22×C4×C79—21no—
76C22×C4×C79C2311yescharacteristic
77C2×C8×C79C2312yes—
78C4⋊C4×C79—21no—
79C4⋊C4×C79C2312yes—
80C4⋊C4×C79C2311yescharacteristic
81C22⋊C4×C79—21no—
82C23×C79—21no—
83C23×C79C2×D411yescharacteristic
84C22×D79—22no—
85C22×D79—22no—
86C22×D79—21no—
87C22×D79—41no—
88C22×D79—42no—
89C22×D79—42no—
90C22×D79—42no—
91C22×D79C2×D411yescharacteristic
92C22×D79C2×D411yescharacteristic
93D4×C79—22no—
94D4×C79—42no—
95C2×C4×C79—22no—
96C2×C4×C79—22no—
97C2×C4×C79—21no—
98C2×C4×C79—42no—
99C2×C4×C79C2×D411yescharacteristic
100C2×C4×C79C2411yescharacteristic
101C22⋊D79—42no—
102C22⋊D79—42no—
103C22⋊D79—42no—
104C2×Dic79—22no—
105C2×Dic79—22no—
106C2×Dic79—21no—
107C2×Dic79—42no—
108C2×Dic79C2×D411yescharacteristic
109C2×Dic79C2×D411yescharacteristic
110D316—22no—
111D316—42no—
112C4×D79—22no—
113C4×D79—22no—
114C4×D79—22no—
115C4×D79—42no—
116C4×D79#4114yes—
117C8×C79—22no—
118C79⋊C8—22no—
119C22×C79—21no—
120C22×C79—21no—
121C22×C79—41no—
122C22×C79—41no—
123C22×C79—41no—
124C22×C79AGL(1,ℤ/8)12yes—
125C22×C79C22×D411yescharacteristic
126C2×D79—21no—
127C2×D79—21no—
128C2×D79—21no—
129C2×D79—21no—
130C2×D79—21no—
131C2×D79—44no—
132C2×D79—41no—
133C2×D79—41no—
134C2×D79—41no—
135C2×D79—84no—
136C2×D79#12312yes—
137C4×C79—21no—
138C4×C79—42no—
139C4×C79—41no—
140C4×C79C2×#4112yes—
141Dic79—21no—
142Dic79—41no—
143Dic79—42no—
144Dic79#12312yes—
145C2×C79—22no—
146C2×C79—81no—
147C2×C79C2×#12311yescharacteristic
148C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
149C2×C79#57511yescharacteristic
150D79—22no—
151D79—41no—
152D79—81no—
153#3094—791nomaximal, Sylow
154C79#309411yescharacteristic, complemented, Sylow
155C2×#121—791no—
156C2×#117—791no—
157#482—792no—
158#482—792no—
159#481—791no—
160#481—791no—
161#480—791no—
162#480D7911yescharacteristic, complemented
163#428—792no—
164#418—792no—
165#407—791no—
166C22×D4—791no—
167C22×D4—1581no—
168C23×C4—791no—
169C2×M16—792no—
170#121—791no—
171#121—791no—
172#121—791no—
173#121—1581no—
174#121—1581no—
175#121C2×D7911yescharacteristic
176#117—792no—
177#117—792no—
178#117—1581no—
179#117—1581no—
180C2×C4⋊C4—791no—
181C2×C4⋊C4—791no—
182C2×C4⋊C4C2×D7911yescharacteristic, complemented
183C2×C22⋊C4—1581no—
184C2×C22⋊C4—1581no—
185C2×C42—1581no—
186#107—792no—
187#107C2×D7912yescomplemented
188#106—792no—
189#106—792no—
190#102—792no—
191#102—792no—
192#102—792no—
193#102C2×D7912yescomplemented
194C22⋊C8—791no—
195C22⋊C8—792no—
196C22⋊C8C2×D7911yescharacteristic, complemented
197C24—791no—
198C24—1581no—
199C2×D4—21no—
200C2×D4—3164no—
201C2×D4—791no—
202C2×D4—1581no—
203C2×D4—1584no—
204C2×D4—1581no—
205C2×D4—1581no—
206C2×D4—1581no—
207C2×D4C22×D7911yescharacteristic
208C22×C4—21no—
209C22×C4—791no—
210C22×C4—791no—
211C22×C4—791no—
212C22×C4—791no—
213C22×C4—791no—
214C22×C4—1581no—
215C22×C4—1584no—
216C22×C4—1581no—
217C22×C4C22×D7911yescharacteristic
218M16—1584no—
219C2×C8—792no—
220C2×C8C22×D7912yes—
221C4⋊C4—21no—
222C4⋊C4—792no—
223C4⋊C4—791no—
224C4⋊C4—1581no—
225C4⋊C4—1581no—
226C4⋊C4C22×D7912yes—
227C4⋊C4C22×D7911yescharacteristic
228C22⋊C4—21no—
229C22⋊C4—1581no—
230C22⋊C4—1582no—
231C22⋊C4—1582no—
232C22⋊C4—1581no—
233C22⋊C4—1581no—
234C42—1582no—
235C42—1582no—
236C23—21no—
237C23—3161no—
238C23—3162no—
239C23—3162no—
240C23—3162no—
241C23—791no—
242C23—791no—
243C23—1582no—
244C23—1581no—
245C23—1582no—
246C23D4×D7911yescharacteristic
247D4—22no—
248D4—42no—
249D4—3162no—
250D4—3162no—
251D4—3162no—
252D4—3162no—
253D4—1582no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—3162no—
259C2×C4—3162no—
260C2×C4—791no—
261C2×C4—794no—
262C2×C4—791no—
263C2×C4—1582no—
264C2×C4—1582no—
265C2×C4—1582no—
266C2×C4—1581no—
267C2×C4—1582no—
268C2×C4—1582no—
269C2×C4D4×D7911yescharacteristic
270C2×C4C23×D7911yescharacteristic
271C8—22no—
272C8—1582no—
273C22—21no—
274C22—21no—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—3164no—
279C22—3161no—
280C22—3161no—
281C22—3161no—
282C22—792no—
283C22—6324no—
284C22—1581no—
285C22—1581no—
286C22—1581no—
287C22—1581no—
288C22—1581no—
289C22#1457918512yes—
290C22C2×D4×D7911yescharacteristic
291C4—21no—
292C4—42no—
293C4—41no—
294C4—3161no—
295C4—3162no—
296C4—792no—
297C4—1581no—
298C4#41×D7912yes—
299C2—22no—
300C2—81no—
301C2—3161no—
302C2—6321no—
303C2—1582no—
304C2#123×D7911yescharacteristic
305C2C2×#1457918511yescharacteristic
306C2#1909936211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#480×C79C2
socleC22×C79C22×D4
prime radical#121×D79C2
hypercenter#480D79
hypocenterC79#3094
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#14579119C2semidirect
3. #19098890C2semidirect
4. #19098886C2semidirect
5. #19098882C2semidirect
6. #19098879C2semidirect
7. #19098876C2semidirect
8. #19098604C2semidirect
9. #19098566C2semidirect
10. #19098525C2semidirect
11. #480×C79C2semidirect
24. #14579119C22semidirect
25. C2×C4⋊Dic79C22semidirect
30. #14579094C22semidirect
31. #14579093C22semidirect
32. #14579092C22semidirect
33. #14579083C22semidirect
34. #14579082C22semidirect
35. #14579081C22semidirect
36. C22⋊(C79⋊C8)C22semidirect
37. (C2×D79)⋊C8C22semidirect
39. C2×C4⋊C4×C79C22semidirect
40. #107×C79C22semidirect
41. #102×C79C22semidirect
42. C22⋊C8×C79C22semidirect
154. C79#3094semidirect
162. #480D79semidirect
182. C2×C4⋊C4C2×D79semidirect
187. #107C2×D79semidirect
193. #102C2×D79semidirect
196. C22⋊C8C2×D79semidirect