Finite Group Databasebeta

← #23775361

Subgroups — #23775361

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#19099217C211yesmaximal, characteristic, complemented
2#19098922C211yesmaximal, characteristic, complemented
3#19098891C211yesmaximal, characteristic, complemented
4#19098879C211yesmaximal, characteristic, complemented
5#19098853C211yesmaximal, characteristic, complemented
6#19098814C211yesmaximal, characteristic, complemented
7#19098794C211yesmaximal, characteristic, complemented
8#19098775C211yesmaximal, characteristic, complemented
9#19098708C211yesmaximal, characteristic, complemented
10#19098697C211yesmaximal, characteristic, complemented
11#19098673C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098564C211yesmaximal, characteristic, complemented
14C2×#14579082C211yesmaximal, characteristic, complemented
15#546×C79C211yesmaximal, characteristic, complemented
16C2×#11929623—21no—
17C2×#11929611C2211yescharacteristic, complemented
18C2×#11929609C2211yescharacteristic
19C2×#11929609C2211yescharacteristic
20C2×#11929608C2211yescharacteristic, complemented
21C22×C79⋊C8C2211yescharacteristic
22#14579161C2211yescharacteristic, complemented
23#14579145—21no—
24#14579145—21no—
25#14579141—21no—
26#14579135C2211yescharacteristic
27#14579135C2211yescharacteristic, complemented
28C4×D316C2211yescharacteristic, complemented
29C2×C4⋊Dic79C2211yescharacteristic
30C2×C4⋊Dic79C2211yescharacteristic, complemented
31#14579092C2211yescharacteristic, complemented
32#14579092C2211yescharacteristic, complemented
33#14579092C2211yescharacteristic, complemented
34C4⋊(C79⋊C8)C2211yescharacteristic, complemented
35#14579085C2211yescharacteristic, complemented
36#14579085C2211yescharacteristic, complemented
37#14579085C2211yescharacteristic, complemented
38#14579082C2211yescharacteristic
39#14579082C2211yescharacteristic
40#14579082C2211yescharacteristic
41#14579082C2211yescharacteristic
42#14579082C2211yescharacteristic
43#14579082C2211yescharacteristic
44#14579081C2211yescharacteristic, complemented
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic, complemented
47#14579072C2211yescharacteristic, complemented
48C2×#41×C79C2211yescharacteristic
49C22×D4×C79C2211yescharacteristic
50#124×C79C2211yescharacteristic
51#123×C79—21no—
52C22⋊Q8×C79C2211yescharacteristic
53#121×C79—21no—
54#121×C79C2211yescharacteristic
55#120×C79—21no—
56C4×D4×C79C2211yescharacteristic
57C4×D4×C79C2211yescharacteristic
58C2×C22⋊C4×C79—21no—
59#11929623—44no—
60C2×Dic158—21no—
61C2×D316C2311yescharacteristic
62C2×C22⋊D79—21no—
63C2×C22⋊D79—21no—
64C22×Dic79—21no—
65C22×Dic79—21no—
66C2×C4×D79—21no—
67#11929611—41no—
68#11929609—22no—
69#11929609—41no—
70#11929608—41no—
71C2×C79⋊C8—41no—
72C2×C79⋊C8C2311yescharacteristic
73C2×C79⋊C8C2311yescharacteristic
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C4⋊Dic79—21no—
77C4⋊Dic79—21no—
78C4⋊Dic79—21no—
79C4⋊Dic79C2311yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81C4⋊Dic79C2311yescharacteristic
82(C2×D79)⋊C4—21no—
83(C2×D79)⋊C4—21no—
84(C2×D79)⋊C4—21no—
85C24×C79—21no—
86#41×C79—22no—
87#41×C79—41no—
88C2×Q8×C79C2311yescharacteristic
89C2×D4×C79—22no—
90C2×D4×C79—21no—
91C2×D4×C79—21no—
92C2×D4×C79—21no—
93C2×D4×C79—41no—
94C2×D4×C79D411yescharacteristic
95C2×D4×C79C2311yescharacteristic
96C2×D4×C79C2311yescharacteristic
97C22×C4×C79—21no—
98C22×C4×C79—21no—
99C22×C4×C79C2311yescharacteristic
100C22×C4×C79C2311yescharacteristic
101C4⋊C4×C79—21no—
102C4⋊C4×C79D411yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C22⋊C4×C79—21no—
108C22⋊C4×C79—21no—
109C22⋊C4×C79D411yescharacteristic
110C22⋊C4×C79D411yescharacteristic
111C42×C79C2311yescharacteristic
112C23×C79—21no—
113C23×C79—21no—
114C23×C79—42no—
115C23×C79—42no—
116C23×C79—81no—
117C23×C79C2×D411yescharacteristic
118C23×C79C2×D411yescharacteristic
119C22×D79—21no—
120Q8×C79—21no—
121Q8×C79—21no—
122D4×C79—22no—
123D4×C79—21no—
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—42no—
127D4×C79—42no—
128D4×C79—81no—
129D4×C79#4112yescomplemented
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79—21no—
136C2×C4×C79—42no—
137C2×C4×C79—81no—
138C2×C4×C79C2×D411yescharacteristic
139C2×C4×C79C2×D411yescharacteristic
140C2×C4×C79C2×D411yescharacteristic
141C2×C4×C79C2×D411yescharacteristic
142C2×C4×C79C2411yescharacteristic
143C22⋊D79—42no—
144C22⋊D79—42no—
145C2×Dic79—21no—
146C2×Dic79—21no—
147C2×Dic79—21no—
148C2×Dic79—42no—
149C2×Dic79—42no—
150D316—21no—
151D316—21no—
152C4×D79—42no—
153Dic158—42no—
154C79⋊C8—21no—
155C79⋊C8—21no—
156C79⋊C8—21no—
157C79⋊C8—21no—
158C22×C79—21no—
159C22×C79—21no—
160C22×C79—21no—
161C22×C79—22no—
162C22×C79—21no—
163C22×C79—21no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—41no—
167C22×C79—41no—
168C22×C79—41no—
169C22×C79—84no—
170C22×C79AGL(1,ℤ/8)12yes—
171C22×C79C22×D411yescharacteristic
172C2×D79—41no—
173C2×D79—41no—
174C2×D79—41no—
175C4×C79—21no—
176C4×C79—21no—
177C4×C79—21no—
178C4×C79—21no—
179C4×C79—41no—
180C4×C79—41no—
181C4×C79C2×#4111yescharacteristic
182C4×C79H(5,𝔽2)11yescharacteristic
183Dic79—41no—
184Dic79—41no—
185Dic79—41no—
186C2×C79—22no—
187C2×C79—41no—
188C2×C79—42no—
189C2×C79—81no—
190C2×C79#54611yescharacteristic
191C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C79#57711yescharacteristic
193D79—81no—
194#3306—791nomaximal, Sylow
195C79#330611yescharacteristic, complemented, Sylow
196#547—791no—
197#546D7911yescharacteristic, complemented
198#489—791no—
199#483—791no—
200#481—791no—
201#476—791no—
202#469—791no—
203#465—791no—
204#463—791no—
205#449—791no—
206#447—791no—
207#442—791no—
208#435—791no—
209#417—791no—
210C2×#102—791no—
211C2×#41—1581no—
212C2×#41C2×D7911yescharacteristic
213C22×D4C2×D7911yescharacteristic
214C2×SD16—791no—
215C2×D8—791no—
216C2×D8—791no—
217C2×M16—791no—
218C22×C8—791no—
219C4⋊Q8—791no—
220#124C2×D7911yescharacteristic
221#123—21no—
222#123—1581no—
223#123—1581no—
224C22⋊Q8—1581no—
225C22⋊Q8C2×D7911yescharacteristic
226#121—21no—
227#121—791no—
228#121—791no—
229#121C2×D7911yescharacteristic
230#120—21no—
231C4×D4—791no—
232C4×D4C2×D7911yescharacteristic
233C4×D4C2×D7911yescharacteristic
234C2×C4⋊C4—791no—
235C2×C4⋊C4—791no—
236C2×C22⋊C4—21no—
237#106—791no—
238#106—791no—
239#106—791no—
240C4⋊C8—791no—
241#103—791no—
242#103—791no—
243#103—791no—
244#102—791no—
245#102—791no—
246#102—791no—
247#102—791no—
248#102—791no—
249#102—791no—
250#102—791no—
251C22⋊C8—791no—
252C22⋊C8—791no—
253#97—791no—
254C24—21no—
255#41—22no—
256#41—41no—
257#41—3164no—
258C2×Q8—1581no—
259C2×Q8C22×D7911yescharacteristic
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—791no—
266C2×D4—1581no—
267C2×D4—1581no—
268C2×D4C22⋊D7911yescharacteristic
269C2×D4C22×D7911yescharacteristic
270C2×D4C22×D7911yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—1581no—
274C22×C4—1581no—
275C22×C4—1581no—
276C22×C4C22×D7911yescharacteristic
277C22×C4C22×D7911yescharacteristic
278SD16—3161no—
279D8—3161no—
280D8—1582no—
281M16—3161no—
282C2×C8—3161no—
283C2×C8—791no—
284C2×C8—791no—
285C2×C8—791no—
286C2×C8—791no—
287C4⋊C4—21no—
288C4⋊C4—791no—
289C4⋊C4—791no—
290C4⋊C4—791no—
291C4⋊C4—1581no—
292C4⋊C4—1581no—
293C4⋊C4—1581no—
294C4⋊C4C22⋊D7911yescharacteristic
295C4⋊C4C22×D7911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4C22⋊D7911yescharacteristic
305C22⋊C4C22⋊D7911yescharacteristic
306C42C22×D7911yescharacteristic
307C23—21no—
308C23—21no—
309C23—42no—
310C23—42no—
311C23—81no—
312C23—1581no—
313C23C2×C22⋊D7911yescharacteristic
314C23C2×C22⋊D7911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—3162no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—42no—
324D4—81no—
325D4—3162no—
326D4—3162no—
327D4—1581no—
328D4—1581no—
329D4#1192962312yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—81no—
338C2×C4—3162no—
339C2×C4—3162no—
340C2×C4—3162no—
341C2×C4—1581no—
342C2×C4—1581no—
343C2×C4—1581no—
344C2×C4C2×C22⋊D7911yescharacteristic
345C2×C4C2×C22⋊D7911yescharacteristic
346C2×C4C2×C22⋊D7911yescharacteristic
347C2×C4C2×C22⋊D7911yescharacteristic
348C2×C4C23×D7911yescharacteristic
349C8—1581no—
350C8—1581no—
351C8—1581no—
352C8—1581no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—22no—
357C22—21no—
358C22—21no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—3161no—
366C22—3161no—
367C22—3161no—
368C22#1457918612yes—
369C22C22×C22⋊D7911yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—3161no—
377C4—3161no—
378C4—3161no—
379C4C2×#1192962311yescharacteristic
380C4#1457920611yescharacteristic
381C2—22no—
382C2—41no—
383C2—42no—
384C2—81no—
385C2—6321no—
386C2#1909920711yescharacteristic
387C2C2×#1457918611yescharacteristic
388C2#1909937411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#546×C79C2
socleC22×C79C22×D4
hypercenter#546D79
hypocenterC79#3306
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #19099217C2semidirect
2. #19098922C2semidirect
3. #19098891C2semidirect
4. #19098879C2semidirect
5. #19098853C2semidirect
6. #19098814C2semidirect
7. #19098794C2semidirect
8. #19098775C2semidirect
9. #19098708C2semidirect
10. #19098697C2semidirect
11. #19098673C2semidirect
12. #19098635C2semidirect
13. #19098564C2semidirect
14. C2×#14579082C2semidirect
15. #546×C79C2semidirect
17. C2×#11929611C22semidirect
20. C2×#11929608C22semidirect
22. #14579161C22semidirect
27. #14579135C22semidirect
28. C4×D316C22semidirect
30. C2×C4⋊Dic79C22semidirect
31. #14579092C22semidirect
32. #14579092C22semidirect
33. #14579092C22semidirect
34. C4⋊(C79⋊C8)C22semidirect
35. #14579085C22semidirect
36. #14579085C22semidirect
37. #14579085C22semidirect
44. #14579081C22semidirect
46. C22⋊(C79⋊C8)C22semidirect
47. #14579072C22semidirect
129. D4×C79#41semidirect
195. C79#3306semidirect
197. #546D79semidirect
329. D4#11929623semidirect