Finite Group Databasebeta

← #23774449

Subgroups — #23774449

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#19099164C211yesmaximal, characteristic, complemented
2#19099126C211yesmaximal, characteristic, complemented
3#19098951C211yesmaximal, characteristic, complemented
4#19098938C211yesmaximal, characteristic, complemented
5#19098926C211yesmaximal, characteristic, complemented
6#19098916C211yesmaximal, characteristic, complemented
7#19098779C211yesmaximal, characteristic, complemented
8#19098778C211yesmaximal, characteristic, complemented
9#19098755C211yesmaximal, characteristic, complemented
10#19098709C211yesmaximal, characteristic, complemented
11#19098705C211yesmaximal, characteristic, complemented
12#19098698C211yesmaximal, characteristic, complemented
13#19098695C211yesmaximal, characteristic, complemented
14#19098623C211yesmaximal, characteristic, complemented
15#459×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×#11929613C2211yescharacteristic, complemented
19C2×#11929612C2211yescharacteristic, complemented
20C2×D632C2211yescharacteristic
21C2×#11929609C2211yescharacteristic
22C2×#11929609C2211yescharacteristic
23C2×#11929609C2211yescharacteristic, complemented
24#14579157C2211yescharacteristic
25#14579157C2211yescharacteristic, complemented
26#14579152C2211yescharacteristic, complemented
27#14579149C2211yescharacteristic
28#14579148C2211yescharacteristic
29#14579144—21no—
30#14579143—21no—
31#14579136C2211yescharacteristic
32#14579135—21no—
33#14579134—21no—
34#14579133—21no—
35#14579133—21no—
36#14579132C2211yescharacteristic
37#14579129—21no—
38#14579129—21no—
39C4×D316C2211yescharacteristic, complemented
40#14579118C2211yescharacteristic
41C4⋊(C79⋊C8)C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579084C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic
48(C2×D79)⋊C8C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C2×D8×C79C2211yescharacteristic
53C2×D8×C79C2211yescharacteristic, complemented
54#127×C79C2211yescharacteristic
55C4×D4×C79C2211yescharacteristic, complemented
56C4⋊C8×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929623—41no—
61#11929623—41no—
62C2×Dic158C2311yescharacteristic
63C2×D316—21no—
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—
73D4×D79—41no—
74D4×D79—41no—
75C22×Dic79—21no—
76C2×C4×D79—21no—
77C2×C4×D79C2311yescharacteristic
78#11929613—41no—
79#11929612—41no—
80D632—41no—
81#11929609—41no—
82#11929609—41no—
83#11929609—41no—
84C2×C79⋊C8C2311yescharacteristic
85C2×C79⋊C8C2311yescharacteristic
86C4⋊Dic79—21no—
87C4⋊Dic79C2311yescharacteristic
88Dic79⋊C4—21no—
89Dic79⋊C4D411yescharacteristic
90Dic79⋊C4D411yescharacteristic
91C22⋊Dic79—21no—
92C22⋊Dic79—21no—
93C22⋊Dic79—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4—21no—
98(C2×D79)⋊C4D411yescharacteristic
99(C2×D79)⋊C4D411yescharacteristic
100C4×Dic79C2311yescharacteristic
101C2×D4×C79—21no—
102C2×D4×C79—21no—
103C2×D4×C79C2311yescharacteristic
104C2×D4×C79C2311yescharacteristic
105C2×D4×C79C2311yescharacteristic
106C22×C4×C79—21no—
107D8×C79—41no—
108D8×C79—41no—
109C2×C8×C79C2311yescharacteristic
110C2×C8×C79C2311yescharacteristic
111C4⋊C4×C79C2311yescharacteristic
112C22⋊C4×C79—21no—
113C42×C79C2311yescharacteristic
114C23×C79—21no—
115C23×C79—21no—
116C23×C79—21no—
117C22×D79—21no—
118C22×D79—21no—
119C22×D79—42no—
120C22×D79—81no—
121C22×D79—81no—
122C22×D79C2×D411yescharacteristic
123D4×C79—21no—
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—21no—
128D4×C79—21no—
129D4×C79—81no—
130D4×C79—81no—
131C2×C4×C79—21no—
132C2×C4×C79—81no—
133C2×C4×C79C2×D411yescharacteristic
134C2×C4×C79C2×D411yescharacteristic
135C2×C4×C79C2411yescharacteristic
136C22⋊D79—42no—
137C22⋊D79—42no—
138C22⋊D79—81no—
139C22⋊D79—81no—
140C22⋊D79—81no—
141C22⋊D79—81no—
142C22⋊D79—81no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—42no—
146C2×Dic79C2×D411yescharacteristic
147C2×Dic79C2×D411yescharacteristic
148C2×Dic79C2×D411yescharacteristic
149D316—21no—
150D316—21no—
151D316—21no—
152D316—21no—
153D316—81no—
154C4×D79—21no—
155C4×D79—21no—
156C4×D79—81no—
157Dic158—21no—
158Dic158—21no—
159C8×C79—21no—
160C8×C79—21no—
161C79⋊C8—21no—
162C79⋊C8—21no—
163C22×C79—41no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—41no—
167C22×C79—41no—
168C22×C79—41no—
169C22×C79—41no—
170C22×C79—41no—
171C22×C79—41no—
172C22×C79C22×D411yescharacteristic
173C2×D79—21no—
174C2×D79—21no—
175C2×D79—21no—
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—21no—
185C4×C79—41no—
186C4×C79H(5,𝔽2)11yescharacteristic
187C4×C79H(5,𝔽2)11yescharacteristic
188Dic79—21no—
189Dic79—21no—
190Dic79—21no—
191Dic79—41no—
192Dic79—41no—
193C2×C79—81no—
194C2×C79—81no—
195C2×C79—81no—
196C2×C79#53511yescharacteristic
197C2×C79#57611yescharacteristic
198C2×C79#57611yescharacteristic
199D79—41no—
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#459D7911yescharacteristic, complemented
214#449—791no—
215#449—791no—
216#447—791no—
217#447—791no—
218#433—791no—
219C2×#41—791no—
220C22×D4—791no—
221C2×SD16—791no—
222C2×SD16—791no—
223C2×D8—791no—
224C2×D8—791no—
225C2×D8—791no—
226C2×D8—791no—
227C2×D8C2×D7911yescharacteristic
228C2×D8C2×D7911yescharacteristic, complemented
229#127—791no—
230#127—791no—
231#127C2×D7911yescharacteristic
232#125—791no—
233#124—791no—
234#124—791no—
235#123—1581no—
236#123—1581no—
237#121—791no—
238#121—791no—
239#121—1581no—
240#121—1581no—
241#121—1581no—
242#121—1581no—
243#120—1581no—
244#120—1581no—
245C4×D4—791no—
246C4×D4C2×D7911yescharacteristic, complemented
247#117—791no—
248C4⋊C8—791no—
249C4⋊C8C2×D7911yescharacteristic, complemented
250#103—791no—
251#103—791no—
252#102—791no—
253#102—791no—
254#102—791no—
255#102—791no—
256#102C2×D7911yescharacteristic
257#102C2×D7911yescharacteristic, complemented
258C22⋊C8—791no—
259C22⋊C8—791no—
260#97—791no—
261C4×C8—791no—
262C24—1581no—
263#41—3161no—
264#41—3161no—
265C2×Q8—791no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—3161no—
269C2×D4—3161no—
270C2×D4—791no—
271C2×D4—791no—
272C2×D4—1581no—
273C2×D4—1581no—
274C2×D4—1581no—
275C2×D4—1581no—
276C2×D4—1581no—
277C2×D4—1581no—
278C2×D4—1581no—
279C2×D4—1581no—
280C2×D4C22×D7911yescharacteristic
281C2×D4C22×D7911yescharacteristic
282C2×D4C22×D7911yescharacteristic
283C22×C4—21no—
284C22×C4—791no—
285C22×C4—1581no—
286C22×C4—1581no—
287SD16—3161no—
288SD16—3161no—
289D8—41no—
290D8—41no—
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—
316C42C22×D7911yescharacteristic
317C23—21no—
318C23—21no—
319C23—21no—
320C23—3162no—
321C23—791no—
322C23—6321no—
323C23—6321no—
324C23—1581no—
325C23—1581no—
326Q8—1581no—
327Q8—1581no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—81no—
335D4—81no—
336D4—3162no—
337D4—3162no—
338D4—6321no—
339D4—6321no—
340D4—6321no—
341D4—6321no—
342D4—6321no—
343D4—6321no—
344D4—1581no—
345D4—1581no—
346D4—1581no—
347D4—1581no—
348C2×C4—21no—
349C2×C4—81no—
350C2×C4—3162no—
351C2×C4—791no—
352C2×C4—791no—
353C2×C4—791no—
354C2×C4—6321no—
355C2×C4—1581no—
356C2×C4—1581no—
357C2×C4—1581no—
358C2×C4—1581no—
359C2×C4D4×D7911yescharacteristic
360C2×C4D4×D7911yescharacteristic
361C2×C4C23×D7911yescharacteristic
362C8—21no—
363C8—21no—
364C8—1581no—
365C8—1581no—
366C22—41no—
367C22—41no—
368C22—41no—
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—6324no—
382C22—1581no—
383C22—1581no—
384C22—1581no—
385C22C2×D4×D7911yescharacteristic
386C4—21no—
387C4—21no—
388C4—41no—
389C4—3161no—
390C4—3161no—
391C4—1581no—
392C4—1581no—
393C4—1581no—
394C4#1457920611yescharacteristic
395C4#1457920711yescharacteristic
396C2—81no—
397C2—81no—
398C2—81no—
399C2—3161no—
400C2—6321no—
401C2—6321no—
402C2#1909912911yescharacteristic
403C2#1909936411yescharacteristic
404C2#1909936711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#459×C79C2
socleC22×C79C22×D4
hypercenter#459D79
hypocenterC79#3220
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #19099164C2semidirect
2. #19099126C2semidirect
3. #19098951C2semidirect
4. #19098938C2semidirect
5. #19098926C2semidirect
6. #19098916C2semidirect
7. #19098779C2semidirect
8. #19098778C2semidirect
9. #19098755C2semidirect
10. #19098709C2semidirect
11. #19098705C2semidirect
12. #19098698C2semidirect
13. #19098695C2semidirect
14. #19098623C2semidirect
15. #459×C79C2semidirect
18. C2×#11929613C22semidirect
19. C2×#11929612C22semidirect
23. C2×#11929609C22semidirect
25. #14579157C22semidirect
26. #14579152C22semidirect
39. C4×D316C22semidirect
41. C4⋊(C79⋊C8)C22semidirect
42. #14579086C22semidirect
43. #14579084C22semidirect
46. #14579082C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
53. C2×D8×C79C22semidirect
55. C4×D4×C79C22semidirect
56. C4⋊C8×C79C22semidirect
58. #102×C79C22semidirect
203. C79#3220semidirect
213. #459D79semidirect
228. C2×D8C2×D79semidirect
246. C4×D4C2×D79semidirect
249. C4⋊C8C2×D79semidirect
257. #102C2×D79semidirect