Finite Group Databasebeta

← #509×D79 #23776520

Subgroups — #509×D79 #23776520

Order 10112.

400 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 115 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#135×D79C211yesmaximal, characteristic, complemented
2C2×D8×D79C211yesmaximal, characteristic, complemented
3#19099001C211yesmaximal, characteristic, complemented
4#19099000C212yesmaximal, complemented
5#19098999C211yesmaximal, characteristic, complemented
6#19098998C211yesmaximal, characteristic, complemented
7#19098997C212yesmaximal, complemented
8SD32×D79C212yesmaximal, complemented
9D16×D79C212yesmaximal, complemented
10M32×D79C211yesmaximal, characteristic, complemented
11#509×C79C211yesmaximal, characteristic, complemented
12#41×D79—21no—
13C2×D4×D79—21no—
14#14579184C2211yescharacteristic, complemented
15#14579183C2211yescharacteristic, complemented
16#14579182—21no—
17#14579181—21no—
18#14579180C2211yescharacteristic, complemented
19Q16×D79C2211yescharacteristic, complemented
20SD16×D79—21no—
21C2×D632C2211yescharacteristic, complemented
22C2×#11929609—21no—
23D8×D79—21no—
24D8×D79—21no—
25D8×D79C2212yes—
26D8×D79C2212yescomplemented
27D8×D79C2211yescharacteristic, complemented
28C2×C8×D79C2211yescharacteristic
29#14579106C2212yescomplemented
30#14579105C2212yescomplemented
31#14579104C2212yescomplemented
32D1264C2212yescomplemented
33#14579102C2212yescomplemented
34#14579102C2212yescomplemented
35#14579101C2211yescharacteristic, complemented
36#14579100C2212yescomplemented
37C16×D79C2212yescomplemented
38#135×C79C2211yescharacteristic, complemented
39C2×D8×C79C2211yescharacteristic, complemented
40SD32×C79C2212yescomplemented
41D16×C79C2212yescomplemented
42M32×C79C2211yescharacteristic, complemented
43C23×D79—41no—
44#11929625—21no—
45#11929624—21no—
46#11929624—41no—
47#11929623—21no—
48#11929623—41no—
49Q8×D79—21no—
50C2×D316—21no—
51C2×C22⋊D79—41no—
52D4×D79—21no—
53D4×D79—22no—
54D4×D79—22no—
55D4×D79—41no—
56D4×D79—41no—
57D4×D79—41no—
58C2×C4×D79—41no—
59C2×C4×D79D411yescharacteristic
60Dic316C2311yescharacteristic, complemented
61#11929614—21no—
62#11929613—21no—
63#11929612—21no—
64#11929611—21no—
65D632—21no—
66D632C2312yes—
67D632C2311yescharacteristic, complemented
68#11929609—22no—
69#11929609—22no—
70#11929609—21no—
71C2×C79⋊C8D411yescharacteristic
72C8×D79D411yescharacteristic
73C8×D79D411yescharacteristic
74C8×D79C2311yescharacteristic
75C8×D79C2311yescharacteristic
76C79⋊C16C2312yescomplemented
77#41×C79—21no—
78C2×D4×C79—21no—
79Q16×C79C2311yescharacteristic, complemented
80SD16×C79—21no—
81D8×C79—21no—
82D8×C79C2312yes—
83D8×C79C2311yescharacteristic, complemented
84C2×C8×C79C2311yescharacteristic
85C16×C79C2312yescomplemented
86C23×C79—41no—
87C22×D79—41no—
88C22×D79—41no—
89C22×D79—42no—
90C22×D79—42no—
91C22×D79—84no—
92C22×D79D811yescharacteristic
93Q8×C79—21no—
94D4×C79—22no—
95D4×C79—21no—
96D4×C79—41no—
97D4×C79—41no—
98C2×C4×C79—41no—
99C2×C4×C79C2×D411yescharacteristic
100C22⋊D79—41no—
101C22⋊D79—41no—
102C22⋊D79—42no—
103C22⋊D79—42no—
104C22⋊D79—41no—
105C2×Dic79—41no—
106C2×Dic79D811yescharacteristic
107D316—22no—
108D316—21no—
109D316—41no—
110D316—41no—
111C4×D79—41no—
112C4×D79—41no—
113C4×D79—41no—
114C4×D79D811yescharacteristic
115C4×D79D811yescharacteristic
116C4×D79C2×D411yescharacteristic
117C4×D79C2×D411yescharacteristic
118Dic158—21no—
119Dic158—41no—
120C8×C79C2×D411yescharacteristic
121C8×C79C2411yescharacteristic
122C79⋊C8C2×D411yescharacteristic
123C79⋊C8C2×D411yescharacteristic
124C22×C79—41no—
125C22×C79—42no—
126C22×C79—82no—
127C22×C79C2×D811yescharacteristic
128C2×D79—22no—
129C2×D79—42no—
130C2×D79—41no—
131C2×D79—84no—
132C2×D79—82no—
133C2×D79—82no—
134C2×D79—84no—
135C2×D79C2×D811yescharacteristic
136C2×D79C2×D811yescharacteristic
137C4×C79—41no—
138C4×C79C2×D811yescharacteristic
139C4×C79C22×D411yescharacteristic
140Dic79—41no—
141Dic79C2×D811yescharacteristic
142Dic79C2×D811yescharacteristic
143C2×C79—21no—
144C2×C79—82no—
145C2×C79—81no—
146C2×C79C22×D811yescharacteristic
147D79—21no—
148D79—81no—
149D79—82no—
150D79#50912yesdirect product factor
151C2×#509—791nomaximal, Sylow
152C79C2×#50911yescharacteristic, complemented, Sylow
153C2×#135—791no—
154C22×D8—791no—
155#509—791no—
156#509—791no—
157#509—792no—
158#509—792no—
159#509—791no—
160#509D7911yescharacteristic, direct product factor
161C2×SD32—792no—
162C2×D16—792no—
163C2×M32—791no—
164C2×#41—1581no—
165C22×D4—1581no—
166#135—791no—
167#135—791no—
168#135—791no—
169#135—1581no—
170#135—1581no—
171#135C2×D7911yescharacteristic, complemented
172C2×Q16—791no—
173C2×SD16—1581no—
174C2×D8—792no—
175C2×D8—792no—
176C2×D8—791no—
177C2×D8—791no—
178C2×D8—1581no—
179C2×D8—1581no—
180C2×D8—1581no—
181C2×D8C2×D7911yescharacteristic, complemented
182C22×C8—791no—
183SD32—792no—
184SD32—792no—
185SD32—792no—
186SD32C2×D7912yescomplemented
187D16—792no—
188D16—792no—
189D16—792no—
190D16C2×D7912yescomplemented
191M32—791no—
192M32—792no—
193M32C2×D7911yescharacteristic, complemented
194C2×C16—792no—
195C24—3161no—
196#41—21no—
197#41—3161no—
198#41—3161no—
199#41—1581no—
200#41—1581no—
201#41—1581no—
202C2×Q8—1581no—
203C2×D4—21no—
204C2×D4—3161no—
205C2×D4—3161no—
206C2×D4—3161no—
207C2×D4—3161no—
208C2×D4—1582no—
209C2×D4—1582no—
210C2×D4—1581no—
211C2×D4—1581no—
212C22×C4—3161no—
213C22×C4—791no—
214Q16—791no—
215Q16—1581no—
216Q16C22×D7911yescharacteristic, complemented
217SD16—21no—
218SD16—1581no—
219SD16—1581no—
220SD16—1581no—
221D8—21no—
222D8—792no—
223D8—791no—
224D8—1582no—
225D8—1582no—
226D8—1581no—
227D8—1581no—
228D8C22×D7912yes—
229D8C22×D7911yescharacteristic, complemented
230C2×C8—791no—
231C2×C8—791no—
232C2×C8—791no—
233C2×C8—791no—
234C2×C8—791no—
235C2×C8C22×D7911yescharacteristic
236C16—792no—
237C16C22×D7912yescomplemented
238C23—41no—
239C23—3161no—
240C23—3162no—
241C23—3162no—
242C23—3161no—
243C23—791no—
244C23—6324no—
245Q8—21no—
246Q8—3161no—
247Q8—1581no—
248D4—22no—
249D4—21no—
250D4—41no—
251D4—41no—
252D4—3161no—
253D4—3161no—
254D4—3161no—
255D4—3162no—
256D4—3162no—
257D4—3161no—
258D4—3161no—
259D4—1582no—
260D4—1581no—
261C2×C4—41no—
262C2×C4—3161no—
263C2×C4—3161no—
264C2×C4—3161no—
265C2×C4—3161no—
266C2×C4—791no—
267C2×C4—791no—
268C2×C4—791no—
269C2×C4—791no—
270C2×C4—791no—
271C2×C4D4×D7911yescharacteristic
272C8—791no—
273C8—791no—
274C8D4×D7911yescharacteristic
275C8C23×D7911yescharacteristic
276C22—41no—
277C22—42no—
278C22—82no—
279C22—3161no—
280C22—3162no—
281C22—791no—
282C22—791no—
283C22—6322no—
284C22—6324no—
285C22—6322no—
286C22—6324no—
287C22—1582no—
288C22D8×D7911yescharacteristic
289C4—41no—
290C4—3161no—
291C4—791no—
292C4—791no—
293C4D8×D7911yescharacteristic
294C4C2×D4×D7911yescharacteristic
295C2—21no—
296C2—82no—
297C2—81no—
298C2—792no—
299C2—6322no—
300C2—6321no—
301C2—1581no—
302C2C2×D8×D7911yescharacteristic
subgroupG/H
centerC2C2×D8×D79
commutator, cosocleC8×C79C24
FrattiniC8C23×D79
Fitting#509×C79C2
socleC2×C79C22×D8
hypercenter#509D79
hypocenterC79C2×#509
LCSG ▷ C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #135×D79C2semidirect
2. C2×D8×D79C2semidirect
3. #19099001C2semidirect
4. #19099000C2semidirect
5. #19098999C2semidirect
6. #19098998C2semidirect
7. #19098997C2semidirect
8. SD32×D79C2semidirect
9. D16×D79C2semidirect
10. M32×D79C2semidirect
11. #509×C79C2semidirect
14. #14579184C22semidirect
15. #14579183C22semidirect
18. #14579180C22semidirect
19. Q16×D79C22semidirect
21. C2×D632C22semidirect
26. D8×D79C22semidirect
27. D8×D79C22semidirect
29. #14579106C22semidirect
30. #14579105C22semidirect
31. #14579104C22semidirect
32. D1264C22semidirect
33. #14579102C22semidirect
34. #14579102C22semidirect
35. #14579101C22semidirect
36. #14579100C22semidirect
37. C16×D79C22semidirect
38. #135×C79C22semidirect
39. C2×D8×C79C22semidirect
40. SD32×C79C22semidirect
41. D16×C79C22semidirect
42. M32×C79C22semidirect
60. Dic316C23semidirect
67. D632C23semidirect
76. C79⋊C16C23semidirect
79. Q16×C79C23semidirect
83. D8×C79C23semidirect
85. C16×C79C23semidirect
150. D79#509direct (N × H)
152. C79C2×#509semidirect
160. #509D79direct (N × H)
171. #135C2×D79semidirect
181. C2×D8C2×D79semidirect
186. SD32C2×D79semidirect
190. D16C2×D79semidirect
193. M32C2×D79semidirect
216. Q16C22×D79semidirect
229. D8C22×D79semidirect
237. C16C22×D79semidirect