Finite Group Databasebeta

← #23775421

Subgroups — #23775421

Order 10112.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099253C211yesmaximal, characteristic, complemented
2#19098927C211yesmaximal, characteristic, complemented
3#19098884C211yesmaximal, characteristic, complemented
4#19098874C211yesmaximal, characteristic, complemented
5#19098863C211yesmaximal, characteristic, complemented
6#19098807C211yesmaximal, characteristic, complemented
7#19098790C211yesmaximal, characteristic, complemented
8#19098760C211yesmaximal, characteristic, complemented
9#19098714C211yesmaximal, characteristic, complemented
10#19098714C211yesmaximal, characteristic, complemented
11#19098663C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098568C211yesmaximal, characteristic, complemented
14C2×#14579082C211yesmaximal, characteristic, complemented
15D42×C79C211yesmaximal, characteristic
16C2×#11929612C2211yescharacteristic
17C2×#11929612C2211yescharacteristic, complemented
18C2×#11929612C2211yescharacteristic, complemented
19C2×#11929608C2211yescharacteristic, complemented
20C22×C79⋊C8C2211yescharacteristic, complemented
21#14579154—21no—
22#14579153C2211yescharacteristic, complemented
23#14579151—21no—
24#14579142—21no—
25#14579140C2211yescharacteristic, complemented
26#14579140C2211yescharacteristic, complemented
27C4×Dic158C2211yescharacteristic, complemented
28#14579120C2211yescharacteristic, complemented
29#14579117—21no—
30C2×C4⋊Dic79C2211yescharacteristic, complemented
31#14579094C2211yescharacteristic, complemented
32#14579094C2211yescharacteristic, complemented
33#14579092C2211yescharacteristic, complemented
34C4⋊(C79⋊C8)C2211yescharacteristic, complemented
35#14579084C2211yescharacteristic, complemented
36#14579082C2211yescharacteristic
37#14579082C2211yescharacteristic
38#14579082C2211yescharacteristic
39#14579082C2211yescharacteristic, complemented
40#14579082C2211yescharacteristic, complemented
41#14579082C2211yescharacteristic, complemented
42#14579082C2211yescharacteristic, complemented
43#14579082C2211yescharacteristic, complemented
44#14579082C2211yescharacteristic, complemented
45C22⋊(C79⋊C8)C2211yescharacteristic, complemented
46C22⋊(C79⋊C8)C2211yescharacteristic, complemented
47#14579072C2211yescharacteristic, complemented
48C22×D4×C79—21no—
49C22×D4×C79C2211yescharacteristic
50C22×D4×C79C2211yescharacteristic
51#127×C79C2211yescharacteristic
52#121×C79—21no—
53#121×C79C2211yescharacteristic
54#121×C79C2211yescharacteristic
55#120×C79—21no—
56#120×C79—21no—
57C4×D4×C79C2211yescharacteristic
58C4×D4×C79C2211yescharacteristic
59C2×Dic158C2311yescharacteristic
60C22×Dic79—21no—
61#11929612—22no—
62#11929612—41no—
63#11929612—41no—
64#11929608—41no—
65C2×C79⋊C8—41no—
66C2×C79⋊C8C2311yescharacteristic
67C2×C79⋊C8C2311yescharacteristic
68C2×C79⋊C8C2311yescharacteristic
69C2×C79⋊C8C2311yescharacteristic
70C4⋊Dic79—21no—
71C4⋊Dic79C2311yescharacteristic
72C4⋊Dic79C2311yescharacteristic
73C4⋊Dic79C2311yescharacteristic
74Dic79⋊C4—21no—
75Dic79⋊C4—21no—
76Dic79⋊C4—21no—
77Dic79⋊C4—21no—
78Dic79⋊C4—21no—
79C22⋊Dic79—21no—
80C22⋊Dic79—21no—
81C22⋊Dic79—21no—
82C4×Dic79—21no—
83C4×Dic79—21no—
84C24×C79—21no—
85C24×C79—21no—
86C2×D4×C79—22no—
87C2×D4×C79—22no—
88C2×D4×C79—21no—
89C2×D4×C79—21no—
90C2×D4×C79—21no—
91C2×D4×C79—21no—
92C2×D4×C79—21no—
93C2×D4×C79—21no—
94C2×D4×C79—41no—
95C2×D4×C79—41no—
96C2×D4×C79—44no—
97C2×D4×C79D411yescharacteristic
98C2×D4×C79C2311yescharacteristic
99C2×D4×C79C2311yescharacteristic
100C2×D4×C79C2311yescharacteristic
101C22×C4×C79—21no—
102C22×C4×C79C2311yescharacteristic
103C22×C4×C79C2311yescharacteristic
104C4⋊C4×C79D411yescharacteristic
105C4⋊C4×C79C2311yescharacteristic
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—21no—
115C23×C79—42no—
116C23×C79—42no—
117C23×C79—42no—
118C23×C79—42no—
119C23×C79—81no—
120C23×C79—81no—
121C23×C79C2×D411yescharacteristic
122C23×C79C2×D411yescharacteristic
123D4×C79—22no—
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—21no—
128D4×C79—21no—
129D4×C79—42no—
130D4×C79—42no—
131D4×C79—42no—
132D4×C79—42no—
133D4×C79—42no—
134D4×C79—81no—
135D4×C79#4112yes—
136C2×C4×C79—21no—
137C2×C4×C79—21no—
138C2×C4×C79—21no—
139C2×C4×C79—21no—
140C2×C4×C79—21no—
141C2×C4×C79—42no—
142C2×C4×C79C2×D411yescharacteristic
143C2×C4×C79C2×D411yescharacteristic
144C2×C4×C79C2×D411yescharacteristic
145C2×C4×C79C2×D411yescharacteristic
146C2×C4×C79C2411yescharacteristic
147C2×Dic79—21no—
148C2×Dic79—21no—
149C2×Dic79—21no—
150C2×Dic79—21no—
151C2×Dic79—42no—
152Dic158—21no—
153Dic158—21no—
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—41no—
170C22×C79—41no—
171C22×C79—41no—
172C22×C79—84no—
173C22×C79—84no—
174C22×C79AGL(1,ℤ/8)12yes—
175C22×C79C22×D411yescharacteristic
176C4×C79—21no—
177C4×C79—21no—
178C4×C79—21no—
179C4×C79—21no—
180C4×C79—41no—
181C4×C79C2×#4111yescharacteristic
182C4×C79H(5,𝔽2)11yescharacteristic
183Dic79—41no—
184Dic79—41no—
185Dic79—41no—
186Dic79—41no—
187C2×C79—22no—
188C2×C79—41no—
189C2×C79—42no—
190C2×C79—81no—
191C2×C79—81no—
192C2×C79#54611yescharacteristic
193C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
194C2×C79#57711yescharacteristic
195#3310—791nomaximal, Sylow
196C79#331011yescharacteristic, complemented, Sylow
197#552—791no—
198D42D7911yescharacteristic
199#490—791no—
200#482—791no—
201#480—791no—
202#478—791no—
203#468—791no—
204#465—791no—
205#460—791no—
206#450—791no—
207#450—791no—
208#440—791no—
209#435—791no—
210#418—791no—
211C2×#102—791no—
212C22×D4—21no—
213C22×D4C2×D7911yescharacteristic
214C22×D4C2×D7911yescharacteristic
215C2×SD16—791no—
216C2×SD16—791no—
217C2×SD16—791no—
218C2×M16—791no—
219C22×C8—791no—
220#127C2×D7911yescharacteristic
221#126—1581no—
222#125—791no—
223#125—1581no—
224#123—1581no—
225C22⋊Q8—791no—
226C22⋊Q8—791no—
227#121—21no—
228#121C2×D7911yescharacteristic
229#121C2×D7911yescharacteristic
230#120—21no—
231#120—21no—
232C4×Q8—791no—
233C4×D4C2×D7911yescharacteristic
234C4×D4C2×D7911yescharacteristic
235#117—791no—
236#117—1581no—
237C2×C4⋊C4—791no—
238#107—791no—
239#107—791no—
240#106—791no—
241C4⋊C8—791no—
242#103—791no—
243#102—791no—
244#102—791no—
245#102—791no—
246#102—791no—
247#102—791no—
248#102—791no—
249#102—791no—
250#102—791no—
251#102—791no—
252C22⋊C8—791no—
253C22⋊C8—791no—
254#97—791no—
255C24—21no—
256C24—21no—
257C2×Q8—791no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—44no—
269C2×D4C22⋊D7911yescharacteristic
270C2×D4C22×D7911yescharacteristic
271C2×D4C22×D7911yescharacteristic
272C2×D4C22×D7911yescharacteristic
273C22×C4—21no—
274C22×C4—1581no—
275C22×C4C22×D7911yescharacteristic
276C22×C4C22×D7911yescharacteristic
277SD16—3161no—
278SD16—3161no—
279SD16—1582no—
280M16—3161no—
281C2×C8—3161no—
282C2×C8—791no—
283C2×C8—791no—
284C2×C8—791no—
285C2×C8—791no—
286C4⋊C4—791no—
287C4⋊C4—791no—
288C4⋊C4—791no—
289C4⋊C4—1581no—
290C4⋊C4—1581no—
291C4⋊C4—1581no—
292C4⋊C4—1581no—
293C4⋊C4—1581no—
294C4⋊C4—1581no—
295C4⋊C4C22⋊D7911yescharacteristic
296C4⋊C4C22×D7911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4C22⋊D7911yescharacteristic
304C22⋊C4C22⋊D7911yescharacteristic
305C42—1581no—
306C42—1581no—
307C42C22×D7911yescharacteristic
308C23—21no—
309C23—21no—
310C23—21no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23C2×C22⋊D7911yescharacteristic
318C23C2×C22⋊D7911yescharacteristic
319Q8—1581no—
320Q8—1581no—
321D4—22no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4#1192962312yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—3162no—
341C2×C4—1581no—
342C2×C4—1581no—
343C2×C4—1581no—
344C2×C4—1581no—
345C2×C4C2×C22⋊D7911yescharacteristic
346C2×C4C2×C22⋊D7911yescharacteristic
347C2×C4C2×C22⋊D7911yescharacteristic
348C2×C4C2×C22⋊D7911yescharacteristic
349C2×C4C23×D7911yescharacteristic
350C8—1581no—
351C8—1581no—
352C8—1581no—
353C8—1581no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—84no—
370C22#1457918712yes—
371C22C22×C22⋊D7911yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—3161no—
378C4—3161no—
379C4—3161no—
380C4—3161no—
381C4C2×#1192962311yescharacteristic
382C4#1457920611yescharacteristic
383C2—22no—
384C2—41no—
385C2—42no—
386C2—81no—
387C2—81no—
388C2#1909920711yescharacteristic
389C2C2×#1457918711yescharacteristic
390C2#1909937411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting, prime radicalD42×C79C2
socleC22×C79C22×D4
hypercenterD42D79
hypocenterC79#3310
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #19099253C2semidirect
2. #19098927C2semidirect
3. #19098884C2semidirect
4. #19098874C2semidirect
5. #19098863C2semidirect
6. #19098807C2semidirect
7. #19098790C2semidirect
8. #19098760C2semidirect
9. #19098714C2semidirect
10. #19098714C2semidirect
11. #19098663C2semidirect
12. #19098635C2semidirect
13. #19098568C2semidirect
14. C2×#14579082C2semidirect
17. C2×#11929612C22semidirect
18. C2×#11929612C22semidirect
19. C2×#11929608C22semidirect
20. C22×C79⋊C8C22semidirect
22. #14579153C22semidirect
25. #14579140C22semidirect
26. #14579140C22semidirect
27. C4×Dic158C22semidirect
28. #14579120C22semidirect
30. C2×C4⋊Dic79C22semidirect
31. #14579094C22semidirect
32. #14579094C22semidirect
33. #14579092C22semidirect
34. C4⋊(C79⋊C8)C22semidirect
35. #14579084C22semidirect
39. #14579082C22semidirect
40. #14579082C22semidirect
41. #14579082C22semidirect
42. #14579082C22semidirect
43. #14579082C22semidirect
44. #14579082C22semidirect
45. C22⋊(C79⋊C8)C22semidirect
46. C22⋊(C79⋊C8)C22semidirect
47. #14579072C22semidirect
196. C79#3310semidirect