Finite Group Databasebeta

← #469×D79 #23772992

Subgroups — #469×D79 #23772992

Order 10112.

596 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C2×D8×D79C211yesmaximal, characteristic, complemented
2C2×M16×D79C211yesmaximal, characteristic, complemented
3#121×D79C212yesmaximal, complemented
4#19098817C211yesmaximal, characteristic, complemented
5#19098816C211yesmaximal, characteristic, complemented
6#19098815C212yesmaximal, complemented
7#19098814C212yesmaximal, complemented
8#19098813C211yesmaximal, characteristic, complemented
9#106×D79C211yesmaximal, characteristic, complemented
10#102×D79C212yesmaximal, complemented
11#469×C79C211yesmaximal, characteristic, complemented
12C2×D4×D79—22no—
13C2×D4×D79C2212yes—
14C22×C4×D79C2211yescharacteristic
15C2×D632C2211yescharacteristic, complemented
16C2×#11929609C2212yescomplemented
17D8×D79—24no—
18C2×#11929608C2211yescharacteristic, complemented
19C2×#11929607C2211yescharacteristic, complemented
20C2×#11929607C2211yescharacteristic, complemented
21M16×D79—24no—
22C2×C8×D79C2211yescharacteristic
23C2×C8×D79C2211yescharacteristic
24#14579136C2212yescomplemented
25#14579135C2212yescomplemented
26#14579134—22no—
27#14579133—22no—
28#14579132C2212yescomplemented
29C4⋊C4×D79C2212yes—
30C22⋊C4×D79—22no—
31#14579093C2211yescharacteristic, complemented
32#14579092C2212yescomplemented
33#14579083C2212yescomplemented
34#14579082C2212yescomplemented
35#14579081C2212yescomplemented
36C2×D8×C79C2211yescharacteristic, complemented
37C2×M16×C79C2211yescharacteristic, complemented
38#121×C79C2212yescomplemented
39#106×C79C2211yescharacteristic, complemented
40#102×C79C2212yescomplemented
41C23×D79—22no—
42C23×D79D411yescharacteristic
43C2×D316—22no—
44C2×D316C2312yes—
45C2×C22⋊D79—22no—
46C2×C22⋊D79—22no—
47C2×C22⋊D79—22no—
48D4×D79—24no—
49D4×D79—24no—
50D4×D79—48no—
51C22×Dic79D411yescharacteristic
52C2×C4×D79—22no—
53C2×C4×D79—22no—
54C2×C4×D79—22no—
55C2×C4×D79D411yescharacteristic
56C2×C4×D79D411yescharacteristic
57C2×C4×D79C2311yescharacteristic
58C2×C4×D79C2311yescharacteristic
59D632—22no—
60#11929609—24no—
61#11929608—22no—
62#11929607—22no—
63#11929607—22no—
64C2×C79⋊C8C2311yescharacteristic
65C2×C79⋊C8C2311yescharacteristic
66C8×D79—22no—
67C8×D79D414yescomplemented
68C4⋊Dic79C2312yes—
69Dic79⋊C4—22no—
70C22⋊Dic79—22no—
71(C2×D79)⋊C4—22no—
72(C2×D79)⋊C4—22no—
73C2×D4×C79—22no—
74C2×D4×C79C2312yes—
75C22×C4×C79C2311yescharacteristic
76D8×C79—22no—
77M16×C79—22no—
78C2×C8×C79C2311yescharacteristic
79C2×C8×C79C2311yescharacteristic
80C4⋊C4×C79C2312yes—
81C22⋊C4×C79—22no—
82C23×C79—22no—
83C23×C79C2×D411yescharacteristic
84C22×D79—22no—
85C22×D79—24no—
86C22×D79—22no—
87C22×D79—44no—
88C22×D79—44no—
89C22×D79—44no—
90C22×D79C2×D411yescharacteristic
91C22×D79C2×D411yescharacteristic
92D4×C79—22no—
93D4×C79—22no—
94D4×C79—44no—
95C2×C4×C79—21no—
96C2×C4×C79—21no—
97C2×C4×C79—22no—
98C2×C4×C79C2×D411yescharacteristic
99C2×C4×C79C2411yescharacteristic
100C22⋊D79—44no—
101C22⋊D79—44no—
102C22⋊D79—44no—
103C2×Dic79—22no—
104C2×Dic79—22no—
105C2×Dic79C2×D411yescharacteristic
106C2×Dic79C2×D411yescharacteristic
107D316—22no—
108D316—22no—
109D316—44no—
110C4×D79—22no—
111C4×D79—21no—
112C4×D79—21no—
113C4×D79—22no—
114C4×D79—44no—
115C4×D79C2×D412yes—
116C4×D79#4112yes—
117C8×C79—21no—
118C8×C79C2×D412yescomplemented
119C79⋊C8—21no—
120C79⋊C8C2×D412yescomplemented
121C22×C79—21no—
122C22×C79—22no—
123C22×C79—42no—
124C22×C79—42no—
125C22×C79—42no—
126C22×C79C22×D411yescharacteristic
127C2×D79—21no—
128C2×D79—22no—
129C2×D79—44no—
130C2×D79—42no—
131C2×D79—42no—
132C2×D79—42no—
133C2×D79—88no—
134C2×D79#12112yes—
135C2×D79AGL(1,ℤ/8)14yes—
136C4×C79—21no—
137C4×C79—42no—
138C4×C79C22×D411yescharacteristic
139C4×C79C2×#4111yescharacteristic
140Dic79—21no—
141Dic79—42no—
142Dic79#12112yes—
143C2×C79—41no—
144C2×C79—82no—
145C2×C79C2×#12111yescharacteristic
146C2×C79C2×AGL(1,ℤ/8)12yes—
147D79—41no—
148D79—82no—
149D79#46914yesdirect product factor
150C2×#469—791nomaximal, Sylow
151C79C2×#46911yescharacteristic, complemented, Sylow
152C22×D8—791no—
153C22×M16—791no—
154C2×#121—792no—
155#469—791no—
156#469—791no—
157#469—792no—
158#469—791no—
159#469—792no—
160#469D7911yescharacteristic, direct product factor
161C2×#106—791no—
162C2×#102—792no—
163C22×D4—792no—
164C22×D4—1582no—
165C23×C4—791no—
166C2×D8—792no—
167C2×D8—791no—
168C2×D8—1584no—
169C2×D8C2×D7911yescharacteristic, complemented
170C2×M16—791no—
171C2×M16—791no—
172C2×M16—791no—
173C2×M16—1584no—
174C2×M16C2×D7911yescharacteristic, complemented
175C22×C8—791no—
176C22×C8—791no—
177#121—792no—
178#121—792no—
179#121—792no—
180#121—1582no—
181#121—1582no—
182#121C2×D7912yescomplemented
183C2×C4⋊C4—792no—
184C2×C22⋊C4—1582no—
185#106—791no—
186#106—792no—
187#106C2×D7911yescharacteristic, complemented
188#102—792no—
189#102—792no—
190#102—792no—
191#102C2×D7912yescomplemented
192C24—791no—
193C24—1582no—
194C2×D4—22no—
195C2×D4—3168no—
196C2×D4—792no—
197C2×D4—1582no—
198C2×D4—1584no—
199C2×D4—1584no—
200C2×D4—1582no—
201C2×D4—1582no—
202C2×D4—1582no—
203C2×D4C22×D7912yes—
204C22×C4—791no—
205C22×C4—791no—
206C22×C4—791no—
207C22×C4—791no—
208C22×C4—791no—
209C22×C4—1582no—
210C22×C4—1582no—
211C22×C4—1582no—
212C22×C4C22×D7911yescharacteristic
213D8—22no—
214D8—1584no—
215D8—1582no—
216M16—22no—
217M16—1582no—
218M16—1582no—
219M16—1582no—
220C2×C8—791no—
221C2×C8—794no—
222C2×C8—791no—
223C2×C8—1582no—
224C2×C8C22×D7911yescharacteristic
225C2×C8C22×D7911yescharacteristic
226C4⋊C4—792no—
227C4⋊C4—1582no—
228C4⋊C4C22×D7912yes—
229C22⋊C4—22no—
230C22⋊C4—1582no—
231C22⋊C4—1582no—
232C22⋊C4—1582no—
233C23—22no—
234C23—3164no—
235C23—3164no—
236C23—3164no—
237C23—791no—
238C23—791no—
239C23—1582no—
240C23—1584no—
241C23—1582no—
242C23D4×D7911yescharacteristic
243D4—22no—
244D4—22no—
245D4—44no—
246D4—3164no—
247D4—3164no—
248D4—3164no—
249D4—3164no—
250D4—1582no—
251D4—1582no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—3164no—
256C2×C4—791no—
257C2×C4—792no—
258C2×C4—792no—
259C2×C4—791no—
260C2×C4—1582no—
261C2×C4—1582no—
262C2×C4—1582no—
263C2×C4—1582no—
264C2×C4—1581no—
265C2×C4—1581no—
266C2×C4D4×D7911yescharacteristic
267C2×C4C23×D7911yescharacteristic
268C8—21no—
269C8—792no—
270C8—1581no—
271C8D4×D7912yescomplemented
272C22—21no—
273C22—22no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—3164no—
278C22—3162no—
279C22—3162no—
280C22—3162no—
281C22—792no—
282C22—794no—
283C22—6328no—
284C22—1581no—
285C22—1582no—
286C22C2×D4×D7911yescharacteristic
287C4—21no—
288C4—42no—
289C4—3162no—
290C4—792no—
291C4—1581no—
292C4C2×D4×D7911yescharacteristic
293C4#41×D7911yescharacteristic
294C2—41no—
295C2—82no—
296C2—3161no—
297C2—794no—
298C2—6322no—
299C2#121×D7911yescharacteristic
300C2AGL(1,ℤ/8)×D7912yes—
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#469×C79C2
socleC22×C79C22×D4
hypercenter#469D79
hypocenterC79C2×#469
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. C2×D8×D79C2semidirect
2. C2×M16×D79C2semidirect
3. #121×D79C2semidirect
4. #19098817C2semidirect
5. #19098816C2semidirect
6. #19098815C2semidirect
7. #19098814C2semidirect
8. #19098813C2semidirect
9. #106×D79C2semidirect
10. #102×D79C2semidirect
11. #469×C79C2semidirect
15. C2×D632C22semidirect
16. C2×#11929609C22semidirect
18. C2×#11929608C22semidirect
19. C2×#11929607C22semidirect
20. C2×#11929607C22semidirect
24. #14579136C22semidirect
25. #14579135C22semidirect
28. #14579132C22semidirect
31. #14579093C22semidirect
32. #14579092C22semidirect
33. #14579083C22semidirect
34. #14579082C22semidirect
35. #14579081C22semidirect
36. C2×D8×C79C22semidirect
37. C2×M16×C79C22semidirect
38. #121×C79C22semidirect
39. #106×C79C22semidirect
40. #102×C79C22semidirect
67. C8×D79D4semidirect
118. C8×C79C2×D4semidirect
120. C79⋊C8C2×D4semidirect
149. D79#469direct (N × H)
151. C79C2×#469semidirect
160. #469D79direct (N × H)
169. C2×D8C2×D79semidirect
174. C2×M16C2×D79semidirect
182. #121C2×D79semidirect
187. #106C2×D79semidirect
191. #102C2×D79semidirect
271. C8D4×D79semidirect