Finite Group Databasebeta

← #23775354

Subgroups — #23775354

Order 10112.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099213C211yesmaximal, characteristic, complemented
2#19099201C211yesmaximal, characteristic, complemented
3#19098924C211yesmaximal, characteristic, complemented
4#19098892C211yesmaximal, characteristic, complemented
5#19098882C211yesmaximal, characteristic, complemented
6#19098851C211yesmaximal, characteristic, complemented
7#19098814C211yesmaximal, characteristic, complemented
8#19098789C211yesmaximal, characteristic, complemented
9#19098780C211yesmaximal, characteristic, complemented
10#19098695C211yesmaximal, characteristic, complemented
11#19098675C211yesmaximal, characteristic, complemented
12#19098637C211yesmaximal, characteristic, complemented
13#19098564C211yesmaximal, characteristic, complemented
14#102×D79C211yesmaximal, characteristic, complemented
15#449×C79C211yesmaximal, characteristic, complemented
16C2×#11929623—21no—
17C2×D4×D79C2211yescharacteristic
18C2×#11929609C2211yescharacteristic
19C2×#11929608C2211yescharacteristic, complemented
20C2×C8×D79C2211yescharacteristic
21#14579160C2211yescharacteristic, complemented
22#14579150C2211yescharacteristic
23#14579144—21no—
24#14579143—21no—
25#14579142—21no—
26#14579138—21no—
27#14579137C2211yescharacteristic
28#14579135C2211yescharacteristic
29#14579133—21no—
30#14579132C2211yescharacteristic
31#14579129—21no—
32D4×Dic79C2211yescharacteristic
33D4×Dic79C2211yescharacteristic, complemented
34C4×C22⋊D79C2211yescharacteristic
35C2×C4⋊Dic79C2211yescharacteristic, complemented
36C4⋊C4×D79C2211yescharacteristic
37C2×(C2×D79)⋊C4—21no—
38#14579093C2211yescharacteristic, complemented
39#14579093C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42#14579085C2211yescharacteristic, complemented
43#14579085C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic, complemented
49#14579081C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51#14579071C2211yescharacteristic, complemented
52C2×#41×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic, complemented
54C2×D8×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic, complemented
56#103×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929623—44no—
61C2×Dic158—21no—
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C2×C22⋊D79D411yescharacteristic
67D4×D79—22no—
68D4×D79—41no—
69C22×Dic79—21no—
70C22×Dic79—21no—
71C22×Dic79—21no—
72C2×C4×D79—21no—
73C2×C4×D79C2311yescharacteristic
74#11929609—41no—
75#11929608—41no—
76C2×C79⋊C8C2311yescharacteristic
77C2×C79⋊C8C2311yescharacteristic
78C8×D79—41no—
79C4⋊Dic79—21no—
80C4⋊Dic79C2311yescharacteristic
81C4⋊Dic79C2311yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4D411yescharacteristic
87C22⋊Dic79—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79D411yescharacteristic
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4D411yescharacteristic
96C4×Dic79C2311yescharacteristic
97#41×C79—22no—
98#41×C79—41no—
99C2×Q8×C79C2311yescharacteristic
100C2×D4×C79—21no—
101C2×D4×C79—21no—
102C2×D4×C79C2311yescharacteristic
103C2×D4×C79C2311yescharacteristic
104C22×C4×C79—21no—
105C22×C4×C79C2311yescharacteristic
106SD16×C79—41no—
107D8×C79—22no—
108C2×C8×C79C2311yescharacteristic
109C2×C8×C79C2311yescharacteristic
110C4⋊C4×C79C2311yescharacteristic
111C22⋊C4×C79—21no—
112C23×C79—21no—
113C23×C79—21no—
114C23×C79C2×D411yescharacteristic
115C22×D79—21no—
116C22×D79—42no—
117C22×D79—42no—
118C22×D79—81no—
119C22×D79C2×D411yescharacteristic
120Q8×C79—21no—
121Q8×C79—21no—
122D4×C79—21no—
123D4×C79—21no—
124D4×C79—21no—
125D4×C79—42no—
126D4×C79—42no—
127D4×C79#4112yescomplemented
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—42no—
133C2×C4×C79C2×D411yescharacteristic
134C2×C4×C79C2411yescharacteristic
135C22⋊D79—22no—
136C22⋊D79—42no—
137C22⋊D79—42no—
138C22⋊D79—81no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142C2×Dic79—42no—
143C2×Dic79—42no—
144C2×Dic79—81no—
145C2×Dic79C2×D411yescharacteristic
146C2×Dic79C2×D411yescharacteristic
147C2×Dic79C2×D411yescharacteristic
148D316—21no—
149D316—21no—
150C4×D79—21no—
151C4×D79—21no—
152C4×D79—42no—
153Dic158—42no—
154C8×C79—21no—
155C8×C79—21no—
156C79⋊C8—21no—
157C79⋊C8—21no—
158C22×C79—22no—
159C22×C79—21no—
160C22×C79—21no—
161C22×C79—21no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—41no—
167C22×C79C22×D411yescharacteristic
168C2×D79—21no—
169C2×D79—21no—
170C2×D79—41no—
171C2×D79—41no—
172C2×D79—41no—
173C2×D79—84no—
174C2×D79AGL(1,ℤ/8)12yes—
175C4×C79—21no—
176C4×C79—41no—
177C4×C79—41no—
178C4×C79C2×#4111yescharacteristic
179C4×C79H(5,𝔽2)11yescharacteristic
180Dic79—21no—
181Dic79—21no—
182Dic79—21no—
183Dic79—41no—
184Dic79—41no—
185Dic79—41no—
186C2×C79—42no—
187C2×C79—41no—
188C2×C79—81no—
189C2×C79#54611yescharacteristic
190C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C79#57711yescharacteristic
192D79—22no—
193D79—81no—
194#3306—791nomaximal, Sylow
195C79#330611yescharacteristic, complemented, Sylow
196#547—791no—
197#546—791no—
198#489—791no—
199#483—791no—
200#481—791no—
201#476—791no—
202#469—791no—
203#465—791no—
204#463—791no—
205#449D7911yescharacteristic, complemented
206#447—791no—
207#442—791no—
208#435—791no—
209#417—791no—
210C2×#102—791no—
211C2×#41—1581no—
212C2×#41C2×D7911yescharacteristic
213C22×D4—791no—
214C2×SD16C2×D7911yescharacteristic, complemented
215C2×D8—791no—
216C2×D8C2×D7911yescharacteristic
217C2×M16—791no—
218C22×C8—791no—
219C4⋊Q8—791no—
220#124—791no—
221#123—1581no—
222#123—1581no—
223#123—1581no—
224C22⋊Q8—791no—
225C22⋊Q8—1581no—
226#121—791no—
227#121—791no—
228#121—1581no—
229#121C2×D7911yescharacteristic, complemented
230#120—1581no—
231C4×D4—791no—
232C4×D4—791no—
233C4×D4—791no—
234C2×C4⋊C4—791no—
235C2×C4⋊C4—791no—
236C2×C22⋊C4—1581no—
237#106—791no—
238#106—791no—
239#106—791no—
240C4⋊C8—791no—
241#103—791no—
242#103—791no—
243#103C2×D7911yescharacteristic, complemented
244#102—791no—
245#102—791no—
246#102—791no—
247#102—791no—
248#102—791no—
249#102—791no—
250#102C2×D7911yescharacteristic
251C22⋊C8—791no—
252C22⋊C8C2×D7911yescharacteristic, complemented
253#97—791no—
254C24—1581no—
255#41—22no—
256#41—41no—
257#41—3164no—
258C2×Q8—1581no—
259C2×Q8C22×D7911yescharacteristic
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—3161no—
263C2×D4—791no—
264C2×D4—791no—
265C2×D4—1581no—
266C2×D4—1581no—
267C2×D4—1582no—
268C2×D4—1581no—
269C2×D4C22×D7911yescharacteristic
270C2×D4C22×D7911yescharacteristic
271C22×C4—21no—
272C22×C4—791no—
273C22×C4—1581no—
274C22×C4—1581no—
275C22×C4—1581no—
276C22×C4—1581no—
277C22×C4C22×D7911yescharacteristic
278SD16—41no—
279D8—22no—
280D8—3161no—
281M16—3161no—
282C2×C8—3161no—
283C2×C8—791no—
284C2×C8—791no—
285C2×C8C22×D7911yescharacteristic
286C2×C8C22×D7911yescharacteristic
287C4⋊C4—791no—
288C4⋊C4—791no—
289C4⋊C4—791no—
290C4⋊C4—791no—
291C4⋊C4—1581no—
292C4⋊C4—1581no—
293C4⋊C4—1581no—
294C4⋊C4—1581no—
295C4⋊C4C22×D7911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—791no—
298C22⋊C4—791no—
299C22⋊C4—1581no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C22⋊C4—1581no—
306C42—791no—
307C23—21no—
308C23—21no—
309C23—3162no—
310C23—3162no—
311C23—791no—
312C23—6321no—
313C23—1581no—
314C23D4×D7911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—3162no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—3162no—
324D4—3162no—
325D4—6321no—
326D4—1582no—
327D4—1581no—
328D4—1581no—
329D4#1192962312yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—3162no—
336C2×C4—3162no—
337C2×C4—3162no—
338C2×C4—791no—
339C2×C4—791no—
340C2×C4—791no—
341C2×C4—6321no—
342C2×C4—1581no—
343C2×C4—1581no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4—1581no—
347C2×C4D4×D7911yescharacteristic
348C2×C4C23×D7911yescharacteristic
349C8—21no—
350C8—21no—
351C8—1581no—
352C8—1581no—
353C22—21no—
354C22—22no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—3161no—
363C22—3161no—
364C22—3161no—
365C22—792no—
366C22—6324no—
367C22—1581no—
368C22—1581no—
369C22C2×D4×D7911yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—3161no—
374C4—3161no—
375C4—3161no—
376C4—1581no—
377C4—1581no—
378C4—1581no—
379C4C2×#1192962311yescharacteristic
380C4#1457920611yescharacteristic
381C2—41no—
382C2—42no—
383C2—81no—
384C2—6321no—
385C2—1582no—
386C2#1909920011yescharacteristic
387C2AGL(1,ℤ/8)×D7911yescharacteristic
388C2#1909937011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#449×C79C2
socleC22×C79C22×D4
hypercenter#449D79
hypocenterC79#3306
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #19099213C2semidirect
2. #19099201C2semidirect
3. #19098924C2semidirect
4. #19098892C2semidirect
5. #19098882C2semidirect
6. #19098851C2semidirect
7. #19098814C2semidirect
8. #19098789C2semidirect
9. #19098780C2semidirect
10. #19098695C2semidirect
11. #19098675C2semidirect
12. #19098637C2semidirect
13. #19098564C2semidirect
14. #102×D79C2semidirect
15. #449×C79C2semidirect
19. C2×#11929608C22semidirect
21. #14579160C22semidirect
33. D4×Dic79C22semidirect
35. C2×C4⋊Dic79C22semidirect
38. #14579093C22semidirect
39. #14579093C22semidirect
40. #14579092C22semidirect
41. Dic79⋊C8C22semidirect
42. #14579085C22semidirect
43. #14579085C22semidirect
48. #14579082C22semidirect
51. #14579071C22semidirect
53. C2×SD16×C79C22semidirect
55. #121×C79C22semidirect
56. #103×C79C22semidirect
58. C22⋊C8×C79C22semidirect
127. D4×C79#41semidirect
195. C79#3306semidirect
205. #449D79semidirect
214. C2×SD16C2×D79semidirect
229. #121C2×D79semidirect
243. #103C2×D79semidirect
252. C22⋊C8C2×D79semidirect
329. D4#11929623semidirect