Finite Group Databasebeta

← #23775420

Subgroups — #23775420

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#19099251C211yesmaximal, characteristic, complemented
2#19099198C211yesmaximal, characteristic
3#19098885C211yesmaximal, characteristic, complemented
4#19098875C211yesmaximal, characteristic, complemented
5#19098860C211yesmaximal, characteristic, complemented
6#19098808C211yesmaximal, characteristic, complemented
7#19098791C211yesmaximal, characteristic, complemented
8#19098760C211yesmaximal, characteristic, complemented
9#19098715C211yesmaximal, characteristic, complemented
10#19098715C211yesmaximal, characteristic, complemented
11#19098665C211yesmaximal, characteristic, complemented
12#19098636C211yesmaximal, characteristic, complemented
13#19098566C211yesmaximal, characteristic, complemented
14#102×D79C211yesmaximal, characteristic, complemented
15#490×C79C211yesmaximal, characteristic, complemented
16C2×D4×D79—21no—
17C2×D4×D79C2211yescharacteristic
18C2×D4×D79C2211yescharacteristic
19C2×#11929613C2211yescharacteristic
20C2×#11929612C2211yescharacteristic, complemented
21C2×#11929612C2211yescharacteristic, complemented
22C2×#11929607C2211yescharacteristic, complemented
23C2×C8×D79C2211yescharacteristic, complemented
24#14579156—21no—
25#14579152—21no—
26#14579146—21no—
27#14579141C2211yescharacteristic, complemented
28#14579141C2211yescharacteristic, complemented
29#14579132—21no—
30#14579132C2211yescharacteristic
31#14579132C2211yescharacteristic
32#14579129—21no—
33#14579129—21no—
34C4×Dic158C2211yescharacteristic, complemented
35C4×D316C2211yescharacteristic
36C4×D316C2211yescharacteristic
37#14579119—21no—
38#14579119C2211yescharacteristic, complemented
39C4⋊C4×D79C2211yescharacteristic, complemented
40#14579095C2211yescharacteristic, complemented
41#14579094C2211yescharacteristic, complemented
42#14579092C2211yescharacteristic, complemented
43C4⋊(C79⋊C8)C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic
46#14579082C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic, complemented
48#14579081C2211yescharacteristic
49#14579081C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51(C2×D79)⋊C8C2211yescharacteristic, complemented
52#127×C79C2211yescharacteristic
53#125×C79C2211yescharacteristic, complemented
54#102×C79C2211yescharacteristic, complemented
55#102×C79C2211yescharacteristic, complemented
56#102×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic, complemented
58#97×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C23×D79—21no—
61C2×Dic158C2311yescharacteristic
62C2×D316D411yescharacteristic
63C2×D316C2311yescharacteristic
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68D4×D79—22no—
69D4×D79—22no—
70D4×D79—41no—
71D4×D79—41no—
72D4×D79—44no—
73C2×C4×D79—21no—
74C2×C4×D79—21no—
75C2×C4×D79C2311yescharacteristic
76C2×C4×D79C2311yescharacteristic
77#11929613—22no—
78#11929612—41no—
79#11929612—41no—
80#11929607—41no—
81C2×C79⋊C8C2311yescharacteristic
82C2×C79⋊C8C2311yescharacteristic
83C8×D79—41no—
84C4⋊Dic79—21no—
85C4⋊Dic79—21no—
86C4⋊Dic79D411yescharacteristic
87C4⋊Dic79C2311yescharacteristic
88C4⋊Dic79C2311yescharacteristic
89Dic79⋊C4—21no—
90Dic79⋊C4—21no—
91C22⋊Dic79—21no—
92C22⋊Dic79—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4D411yescharacteristic
98(C2×D79)⋊C4D411yescharacteristic
99C4×Dic79—21no—
100C4×Dic79—21no—
101C2×D4×C79—21no—
102C2×D4×C79—21no—
103C2×D4×C79C2311yescharacteristic
104C2×D4×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79—21no—
108C4⋊C4×C79—21no—
109C4⋊C4×C79C2311yescharacteristic
110C4⋊C4×C79C2311yescharacteristic
111C42×C79C2311yescharacteristic
112C23×C79—21no—
113C23×C79—21no—
114C22×D79—21no—
115C22×D79—42no—
116C22×D79—42no—
117C22×D79—42no—
118C22×D79—42no—
119C22×D79—81no—
120C22×D79—81no—
121C22×D79C2×D411yescharacteristic
122C22×D79C2×D411yescharacteristic
123D4×C79—21no—
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—42no—
128D4×C79—81no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79C2×D411yescharacteristic
132C2×C4×C79C2×D411yescharacteristic
133C2×C4×C79C2411yescharacteristic
134C22⋊D79—42no—
135C22⋊D79—42no—
136C22⋊D79—42no—
137C22⋊D79—42no—
138C2×Dic79—21no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141C2×Dic79C2×D411yescharacteristic
142C2×Dic79C2×D411yescharacteristic
143D316—22no—
144D316—21no—
145D316#4112yes—
146C4×D79—21no—
147C4×D79—21no—
148C4×D79—21no—
149C4×D79—21no—
150C4×D79—42no—
151C4×D79—42no—
152Dic158—21no—
153Dic158—21no—
154C8×C79—21no—
155C8×C79—21no—
156C79⋊C8—21no—
157C79⋊C8—21no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79C22×D411yescharacteristic
165C2×D79—21no—
166C2×D79—21no—
167C2×D79—22no—
168C2×D79—21no—
169C2×D79—21no—
170C2×D79—21no—
171C2×D79—41no—
172C2×D79—41no—
173C2×D79—84no—
174C2×D79—84no—
175C2×D79AGL(1,ℤ/8)12yes—
176C4×C79—21no—
177C4×C79—21no—
178C4×C79—41no—
179C4×C79—41no—
180C4×C79C2×#4111yescharacteristic
181C4×C79H(5,𝔽2)11yescharacteristic
182Dic79—21no—
183Dic79—21no—
184Dic79—41no—
185Dic79—41no—
186Dic79—41no—
187C2×C79—81no—
188C2×C79—81no—
189C2×C79#54611yescharacteristic
190C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C79#57711yescharacteristic
192D79—22no—
193D79—41no—
194D79—42no—
195#3310—791nomaximal, Sylow
196C79#331011yescharacteristic, complemented, Sylow
197#552—791no—
198D42—791no—
199#490D7911yescharacteristic, complemented
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—791no—
213C22×D4—791no—
214C22×D4—1581no—
215C2×SD16—791no—
216C2×SD16—791no—
217C2×SD16—791no—
218C2×M16—791no—
219C22×C8—791no—
220#127C2×D7911yescharacteristic
221#126—1581no—
222#125—1581no—
223#125C2×D7911yescharacteristic, complemented
224#123—1581no—
225C22⋊Q8—791no—
226C22⋊Q8—791no—
227#121—791no—
228#121—791no—
229#121—1581no—
230#120—1581no—
231#120—1581no—
232C4×Q8—791no—
233C4×D4—791no—
234C4×D4—791no—
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#102C2×D7911yescharacteristic, complemented
249#102C2×D7911yescharacteristic, complemented
250#102C2×D7911yescharacteristic, complemented
251#102C2×D7911yescharacteristic, complemented
252C22⋊C8—791no—
253C22⋊C8—791no—
254#97C2×D7911yescharacteristic, complemented
255C24—1581no—
256C24—1581no—
257C2×Q8—791no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—3164no—
261C2×D4—3161no—
262C2×D4—3161no—
263C2×D4—791no—
264C2×D4—791no—
265C2×D4—1581no—
266C2×D4—1581no—
267C2×D4—1582no—
268C2×D4—1582no—
269C2×D4—1581no—
270C2×D4—1581no—
271C2×D4C22×D7911yescharacteristic
272C2×D4C22×D7911yescharacteristic
273C22×C4—791no—
274C22×C4—791no—
275C22×C4—1581no—
276C22×C4—1581no—
277SD16—3161no—
278SD16—3161no—
279SD16—1582no—
280M16—3161no—
281C2×C8—3161no—
282C2×C8—791no—
283C2×C8—791no—
284C2×C8C22×D7911yescharacteristic
285C2×C8C22×D7911yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—791no—
289C4⋊C4—791no—
290C4⋊C4—791no—
291C4⋊C4—1581no—
292C4⋊C4—1581no—
293C4⋊C4—1581no—
294C4⋊C4—1581no—
295C4⋊C4C22×D7911yescharacteristic
296C4⋊C4C22×D7911yescharacteristic
297C22⋊C4—791no—
298C22⋊C4—791no—
299C22⋊C4—1581no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C42—1581no—
306C42—1581no—
307C42C22×D7911yescharacteristic
308C23—21no—
309C23—21no—
310C23—3162no—
311C23—3162no—
312C23—3162no—
313C23—3162no—
314C23—791no—
315C23—791no—
316C23—6321no—
317C23—6321no—
318C23—1581no—
319Q8—1581no—
320Q8—1581no—
321D4—21no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—42no—
326D4—81no—
327D4—3162no—
328D4—3162no—
329D4—3162no—
330D4—3162no—
331D4—792no—
332D4—1582no—
333D4—1581no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—3162no—
337C2×C4—3162no—
338C2×C4—791no—
339C2×C4—791no—
340C2×C4—1581no—
341C2×C4—1581no—
342C2×C4—1581no—
343C2×C4—1581no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4—1581no—
347C2×C4D4×D7911yescharacteristic
348C2×C4D4×D7911yescharacteristic
349C2×C4C23×D7911yescharacteristic
350C8—21no—
351C8—21no—
352C8—1581no—
353C8—1581no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—3161no—
361C22—3161no—
362C22—792no—
363C22—6324no—
364C22—6324no—
365C22—1581no—
366C22—1582no—
367C22—1581no—
368C22—1581no—
369C22—1581no—
370C22—1581no—
371C22C2×D4×D7911yescharacteristic
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—3161no—
377C4—3161no—
378C4—3161no—
379C4—1581no—
380C4—1581no—
381C4#41×D7911yescharacteristic
382C4#1457920711yescharacteristic
383C2—81no—
384C2—81no—
385C2—3162no—
386C2—3161no—
387C2—1582no—
388C2#1909920611yescharacteristic
389C2AGL(1,ℤ/8)×D7911yescharacteristic
390C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#490×C79C2
socleC22×C79C22×D4
prime radical#19099198C2
hypercenter#490D79
hypocenterC79#3310
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #19099251C2semidirect
3. #19098885C2semidirect
4. #19098875C2semidirect
5. #19098860C2semidirect
6. #19098808C2semidirect
7. #19098791C2semidirect
8. #19098760C2semidirect
9. #19098715C2semidirect
10. #19098715C2semidirect
11. #19098665C2semidirect
12. #19098636C2semidirect
13. #19098566C2semidirect
14. #102×D79C2semidirect
15. #490×C79C2semidirect
20. C2×#11929612C22semidirect
21. C2×#11929612C22semidirect
22. C2×#11929607C22semidirect
23. C2×C8×D79C22semidirect
27. #14579141C22semidirect
28. #14579141C22semidirect
34. C4×Dic158C22semidirect
38. #14579119C22semidirect
39. C4⋊C4×D79C22semidirect
40. #14579095C22semidirect
41. #14579094C22semidirect
42. #14579092C22semidirect
43. C4⋊(C79⋊C8)C22semidirect
44. #14579086C22semidirect
46. #14579082C22semidirect
47. #14579082C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. (C2×D79)⋊C8C22semidirect
53. #125×C79C22semidirect
54. #102×C79C22semidirect
55. #102×C79C22semidirect
56. #102×C79C22semidirect
57. #102×C79C22semidirect
58. #97×C79C22semidirect
196. C79#3310semidirect
199. #490D79semidirect
223. #125C2×D79semidirect
248. #102C2×D79semidirect
249. #102C2×D79semidirect
250. #102C2×D79semidirect
251. #102C2×D79semidirect
254. #97C2×D79semidirect