Finite Group Databasebeta

← #23774448

Subgroups — #23774448

Order 10112.

420 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099166C211yesmaximal, characteristic, complemented
2#19099127C211yesmaximal, characteristic, complemented
3#19098949C211yesmaximal, characteristic, complemented
4#19098938C211yesmaximal, characteristic, complemented
5#19098926C211yesmaximal, characteristic, complemented
6#19098919C211yesmaximal, characteristic, complemented
7#19098781C211yesmaximal, characteristic, complemented
8#19098780C211yesmaximal, characteristic, complemented
9#19098757C211yesmaximal, characteristic, complemented
10#19098756C211yesmaximal, characteristic, complemented
11#19098708C211yesmaximal, characteristic, complemented
12#19098699C211yesmaximal, characteristic, complemented
13#19098696C211yesmaximal, characteristic, complemented
14#19098621C211yesmaximal, characteristic, complemented
15#449×C79C211yesmaximal, characteristic, complemented
16C22×D316C2211yescharacteristic
17C2×#11929611C2211yescharacteristic, complemented
18C2×D632C2211yescharacteristic
19C2×D632C2211yescharacteristic
20C2×#11929609C2211yescharacteristic
21C2×#11929609C2211yescharacteristic
22C2×#11929609C2211yescharacteristic, complemented
23#14579157C2211yescharacteristic
24#14579157C2211yescharacteristic
25#14579157C2211yescharacteristic, complemented
26#14579152C2211yescharacteristic, complemented
27#14579150C2211yescharacteristic
28#14579150C2211yescharacteristic
29#14579145—21no—
30#14579143—21no—
31#14579135—21no—
32#14579135—21no—
33#14579135C2211yescharacteristic
34#14579133—21no—
35#14579132—21no—
36#14579129—21no—
37#14579129—21no—
38D4×Dic79C2211yescharacteristic, complemented
39#14579123C2211yescharacteristic, complemented
40#14579120C2211yescharacteristic
41Dic79⋊C8C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579085C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579082C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C2×#41×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic, complemented
54C2×D8×C79C2211yescharacteristic, complemented
55#121×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic, complemented
58C22⋊C8×C79C2211yescharacteristic
59C23×D79—21no—
60C2×D316—21no—
61C2×D316—41no—
62C2×D316—41no—
63C2×D316C2311yescharacteristic
64C2×D316C2311yescharacteristic
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72C2×C22⋊D79—21no—
73C22×Dic79—21no—
74C2×C4×D79—21no—
75#11929611—41no—
76D632—41no—
77D632—41no—
78#11929609—41no—
79#11929609—41no—
80#11929609—41no—
81C2×C79⋊C8C2311yescharacteristic
82C2×C79⋊C8C2311yescharacteristic
83C4⋊Dic79—21no—
84C4⋊Dic79D411yescharacteristic
85C4⋊Dic79D411yescharacteristic
86C4⋊Dic79C2311yescharacteristic
87Dic79⋊C4—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79D411yescharacteristic
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)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97C4×Dic79C2311yescharacteristic
98C4×Dic79C2311yescharacteristic
99#41×C79—41no—
100#41×C79—41no—
101C2×Q8×C79C2311yescharacteristic
102C2×D4×C79—21no—
103C2×D4×C79—21no—
104C2×D4×C79C2311yescharacteristic
105C2×D4×C79C2311yescharacteristic
106C22×C4×C79—21no—
107C22×C4×C79C2311yescharacteristic
108SD16×C79—41no—
109D8×C79—41no—
110C2×C8×C79C2311yescharacteristic
111C2×C8×C79C2311yescharacteristic
112C4⋊C4×C79C2311yescharacteristic
113C22⋊C4×C79—21no—
114C23×C79—21no—
115C23×C79—21no—
116C23×C79C2×D411yescharacteristic
117C22×D79—21no—
118C22×D79—21no—
119C22×D79—21no—
120C22×D79—42no—
121C22×D79—81no—
122C22×D79—81no—
123Q8×C79—21no—
124Q8×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—21no—
128D4×C79—21no—
129D4×C79—42no—
130D4×C79—81no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79—42no—
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2411yescharacteristic
138C22⋊D79—81no—
139C22⋊D79—81no—
140C22⋊D79—81no—
141C22⋊D79—81no—
142C22⋊D79—81no—
143C22⋊D79—81no—
144C22⋊D79—81no—
145C2×Dic79—21no—
146C2×Dic79—81no—
147C2×Dic79C2×D411yescharacteristic
148C2×Dic79C2×D411yescharacteristic
149C2×Dic79C2×D411yescharacteristic
150C2×Dic79C2×D411yescharacteristic
151D316—21no—
152D316—21no—
153D316—21no—
154D316—21no—
155D316—21no—
156D316—21no—
157D316—42no—
158C4×D79—81no—
159C8×C79—21no—
160C8×C79—21no—
161C79⋊C8—21no—
162C79⋊C8—21no—
163C22×C79—21no—
164C22×C79—21no—
165C22×C79—21no—
166C22×C79—41no—
167C22×C79—41no—
168C22×C79—41no—
169C22×C79—41no—
170C22×C79—41no—
171C22×C79—41no—
172C22×C79C22×D411yescharacteristic
173C2×D79—41no—
174C2×D79—41no—
175C2×D79—41no—
176C2×D79—41no—
177C2×D79—41no—
178C2×D79—41no—
179C2×D79—41no—
180C2×D79—41no—
181C2×D79—41no—
182C2×D79—84no—
183C4×C79—21no—
184C4×C79—41no—
185C4×C79—41no—
186C4×C79H(5,𝔽2)11yescharacteristic
187C4×C79H(5,𝔽2)11yescharacteristic
188Dic79—21no—
189Dic79—21no—
190Dic79—21no—
191Dic79—21no—
192Dic79—41no—
193C2×C79—41no—
194C2×C79—81no—
195C2×C79—81no—
196C2×C79#53511yescharacteristic
197C2×C79#57611yescharacteristic
198C2×C79#57611yescharacteristic
199D79—81no—
200D79—81no—
201D79—81no—
202#3220—791nomaximal, Sylow
203C79#322011yescharacteristic, complemented, Sylow
204#540—791no—
205#535—791no—
206#496—791no—
207#493—791no—
208#490—791no—
209#488—791no—
210#463—791no—
211#463—791no—
212#459—791no—
213#459—791no—
214#449—791no—
215#449D7911yescharacteristic, complemented
216#447—791no—
217#447—791no—
218#433—791no—
219C2×#41C2×D7911yescharacteristic
220C22×D4—791no—
221C2×SD16—791no—
222C2×SD16C2×D7911yescharacteristic, complemented
223C2×D8—791no—
224C2×D8—791no—
225C2×D8—791no—
226C2×D8—791no—
227C2×D8—791no—
228C2×D8C2×D7911yescharacteristic, complemented
229#127—791no—
230#127—791no—
231#127—791no—
232#125—791no—
233#124—791no—
234#124—791no—
235#123—1581no—
236#123—1581no—
237#121—791no—
238#121—1581no—
239#121—1581no—
240#121—1581no—
241#121—1581no—
242#121C2×D7911yescharacteristic
243#120—1581no—
244#120—1581no—
245C4×D4—791no—
246C4×D4—791no—
247#117—791no—
248C4⋊C8—791no—
249C4⋊C8—791no—
250#103—791no—
251#103C2×D7911yescharacteristic, complemented
252#102—791no—
253#102—791no—
254#102—791no—
255#102—791no—
256#102—791no—
257#102C2×D7911yescharacteristic, complemented
258C22⋊C8—791no—
259C22⋊C8C2×D7911yescharacteristic
260#97—791no—
261C4×C8—791no—
262C24—1581no—
263#41—41no—
264#41—41no—
265C2×Q8C22×D7911yescharacteristic
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—3161no—
269C2×D4—3161no—
270C2×D4—791no—
271C2×D4—791no—
272C2×D4—791no—
273C2×D4—1581no—
274C2×D4—1581no—
275C2×D4—1581no—
276C2×D4—1581no—
277C2×D4—1581no—
278C2×D4—1581no—
279C2×D4—1581no—
280C2×D4—1581no—
281C2×D4C22×D7911yescharacteristic
282C2×D4C22×D7911yescharacteristic
283C22×C4—21no—
284C22×C4—1581no—
285C22×C4—1581no—
286C22×C4C22×D7911yescharacteristic
287SD16—41no—
288SD16—3161no—
289D8—41no—
290D8—3161no—
291D8—3161no—
292D8—3161no—
293D8—3161no—
294D8—3161no—
295C2×C8—791no—
296C2×C8—791no—
297C2×C8C22×D7911yescharacteristic
298C2×C8C22×D7911yescharacteristic
299C4⋊C4—791no—
300C4⋊C4—791no—
301C4⋊C4—791no—
302C4⋊C4—1581no—
303C4⋊C4—1581no—
304C4⋊C4C22×D7911yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—791no—
307C22⋊C4—791no—
308C22⋊C4—1581no—
309C22⋊C4—1581no—
310C22⋊C4—1581no—
311C22⋊C4—1581no—
312C22⋊C4—1581no—
313C22⋊C4—1581no—
314C22⋊C4—1581no—
315C42—791no—
316C42—791no—
317C23—21no—
318C23—21no—
319C23—3162no—
320C23—6321no—
321C23—6321no—
322C23—1581no—
323C23—1581no—
324C23—1581no—
325C23D4×D7911yescharacteristic
326Q8—21no—
327Q8—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—81no—
334D4—3162no—
335D4—6321no—
336D4—6321no—
337D4—6321no—
338D4—6321no—
339D4—6321no—
340D4—6321no—
341D4—6321no—
342D4—1581no—
343D4—1581no—
344D4—1581no—
345D4—1581no—
346D4—1581no—
347D4—1581no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—791no—
354C2×C4—791no—
355C2×C4—791no—
356C2×C4—791no—
357C2×C4—6321no—
358C2×C4—6321no—
359C2×C4—1581no—
360C2×C4D4×D7911yescharacteristic
361C2×C4C23×D7911yescharacteristic
362C8—21no—
363C8—21no—
364C8—1581no—
365C8—1581no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—3161no—
376C22—3161no—
377C22—3161no—
378C22—3161no—
379C22—3161no—
380C22—3161no—
381C22—3161no—
382C22—3161no—
383C22—3161no—
384C22—6324no—
385C22C2×D4×D7911yescharacteristic
386C4—21no—
387C4—41no—
388C4—41no—
389C4—3161no—
390C4—1581no—
391C4—1581no—
392C4—1581no—
393C4—1581no—
394C4#1457920611yescharacteristic
395C4#1457920611yescharacteristic
396C2—41no—
397C2—81no—
398C2—81no—
399C2—6321no—
400C2—6321no—
401C2—6321no—
402C2#1909912811yescharacteristic
403C2#1909936511yescharacteristic
404C2#1909936711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#449×C79C2
socleC22×C79C22×D4
hypercenter#449D79
hypocenterC79#3220
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. #19099166C2semidirect
2. #19099127C2semidirect
3. #19098949C2semidirect
4. #19098938C2semidirect
5. #19098926C2semidirect
6. #19098919C2semidirect
7. #19098781C2semidirect
8. #19098780C2semidirect
9. #19098757C2semidirect
10. #19098756C2semidirect
11. #19098708C2semidirect
12. #19098699C2semidirect
13. #19098696C2semidirect
14. #19098621C2semidirect
15. #449×C79C2semidirect
17. C2×#11929611C22semidirect
22. C2×#11929609C22semidirect
25. #14579157C22semidirect
26. #14579152C22semidirect
38. D4×Dic79C22semidirect
39. #14579123C22semidirect
41. Dic79⋊C8C22semidirect
42. Dic79⋊C8C22semidirect
43. #14579085C22semidirect
46. #14579082C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
53. C2×SD16×C79C22semidirect
54. C2×D8×C79C22semidirect
56. #103×C79C22semidirect
57. #102×C79C22semidirect
203. C79#3220semidirect
215. #449D79semidirect
222. C2×SD16C2×D79semidirect
228. C2×D8C2×D79semidirect
251. #103C2×D79semidirect
257. #102C2×D79semidirect