Finite Group Databasebeta

← #23775418

Subgroups — #23775418

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
2D4×D316C211yesmaximal, characteristic
3#19098929C211yesmaximal, characteristic, complemented
4#19098889C211yesmaximal, characteristic, complemented
5#19098878C211yesmaximal, characteristic, complemented
6#19098810C211yesmaximal, characteristic, complemented
7#19098793C211yesmaximal, characteristic, complemented
8#19098764C211yesmaximal, characteristic, complemented
9#19098715C211yesmaximal, characteristic, complemented
10#19098715C211yesmaximal, characteristic, complemented
11#19098663C211yesmaximal, characteristic, complemented
12#19098633C211yesmaximal, characteristic, complemented
13#19098566C211yesmaximal, characteristic, complemented
14#102×D79C211yesmaximal, characteristic, complemented
15#478×C79C211yesmaximal, characteristic, complemented
16C22×D316—21no—
17C2×D4×D79C2211yescharacteristic
18C2×D4×D79C2211yescharacteristic
19C2×#11929613C2211yescharacteristic, complemented
20C2×#11929613C2211yescharacteristic, complemented
21C2×#11929612C2211yescharacteristic
22C2×#11929607C2211yescharacteristic, complemented
23C2×C8×D79C2211yescharacteristic, complemented
24#14579158C2211yescharacteristic
25#14579156—21no—
26#14579152—21no—
27#14579146—21no—
28#14579141C2211yescharacteristic, complemented
29#14579141C2211yescharacteristic, complemented
30#14579136C2211yescharacteristic
31#14579136C2211yescharacteristic
32#14579135—21no—
33#14579131—21no—
34#14579131—21no—
35C4×Dic158C2211yescharacteristic, complemented
36C4×D316C2211yescharacteristic
37#14579119—21no—
38#14579119C2211yescharacteristic, complemented
39C4⋊C4×D79C2211yescharacteristic, complemented
40#14579094C2211yescharacteristic, complemented
41#14579084C2211yescharacteristic, complemented
42#14579083C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic, complemented
44#14579082C2211yescharacteristic
45#14579081C2211yescharacteristic, complemented
46#14579081C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic, complemented
48#14579081C2211yescharacteristic, complemented
49(C2×D79)⋊C8C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51#14579072C2211yescharacteristic, complemented
52#125×C79C2211yescharacteristic, complemented
53C4×D4×C79C2211yescharacteristic
54#107×C79C2211yescharacteristic, complemented
55#106×C79C2211yescharacteristic, complemented
56C4⋊C8×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic
59C23×D79—21no—
60C23×D79—21no—
61C2×Dic158C2311yescharacteristic
62C2×D316—21no—
63C2×D316—21no—
64C2×D316—21no—
65C2×D316—21no—
66C2×D316—44no—
67C2×D316D411yescharacteristic
68C2×D316C2311yescharacteristic
69C2×D316C2311yescharacteristic
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72D4×D79—22no—
73D4×D79—22no—
74D4×D79—41no—
75D4×D79—41no—
76C2×C4×D79—21no—
77C2×C4×D79C2311yescharacteristic
78C2×C4×D79C2311yescharacteristic
79#11929613—41no—
80#11929613—41no—
81#11929612—22no—
82#11929607—41no—
83C2×C79⋊C8C2311yescharacteristic
84C2×C79⋊C8C2311yescharacteristic
85C8×D79—41no—
86C4⋊Dic79—21no—
87C4⋊Dic79—21no—
88C4⋊Dic79D411yescharacteristic
89C4⋊Dic79C2311yescharacteristic
90Dic79⋊C4—21no—
91Dic79⋊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—
97(C2×D79)⋊C4D411yescharacteristic
98(C2×D79)⋊C4D411yescharacteristic
99C4×Dic79—21no—
100C4×Dic79—21no—
101C2×D4×C79C2311yescharacteristic
102C22×C4×C79—21no—
103C2×C8×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C4⋊C4×C79—21no—
106C4⋊C4×C79—21no—
107C4⋊C4×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C42×C79C2311yescharacteristic
112C23×C79—21no—
113C22×D79—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#4112yes—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—42no—
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2×D411yescharacteristic
131C2×C4×C79C2411yescharacteristic
132C22⋊D79—42no—
133C22⋊D79—42no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138D316—22no—
139D316—21no—
140D316—21no—
141D316—21no—
142D316—21no—
143D316—42no—
144D316—42no—
145D316—42no—
146D316—81no—
147C4×D79—21no—
148C4×D79—21no—
149C4×D79—21no—
150C4×D79—21no—
151C4×D79—42no—
152Dic158—21no—
153Dic158—21no—
154C8×C79—21no—
155C8×C79—21no—
156C79⋊C8—21no—
157C79⋊C8—21no—
158C22×C79—22no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79C22×D411yescharacteristic
162C2×D79—21no—
163C2×D79—21no—
164C2×D79—21no—
165C2×D79—21no—
166C2×D79—21no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
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×C79—41no—
181C4×C79C2×#4111yescharacteristic
182C4×C79H(5,𝔽2)11yescharacteristic
183Dic79—21no—
184Dic79—21no—
185Dic79—41no—
186Dic79—41no—
187C2×C79—42no—
188C2×C79#54611yescharacteristic
189C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C79#57711yescharacteristic
191D79—22no—
192D79—41no—
193D79—81no—
194D79—81no—
195#3310—791nomaximal, Sylow
196C79#331011yescharacteristic, complemented, Sylow
197#552—791no—
198D42—791no—
199#490—791no—
200#482—791no—
201#480—791no—
202#478D7911yescharacteristic, complemented
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#127—791no—
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×D4C2×D7911yescharacteristic
235#117—791no—
236#117—1581no—
237C2×C4⋊C4—791no—
238#107—791no—
239#107C2×D7911yescharacteristic, complemented
240#106C2×D7911yescharacteristic, complemented
241C4⋊C8C2×D7911yescharacteristic, complemented
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#102C2×D7911yescharacteristic
251#102C2×D7911yescharacteristic
252C22⋊C8—791no—
253C22⋊C8—791no—
254#97—791no—
255C24—1581no—
256C24—1581no—
257C2×Q8—791no—
258C2×D4—3164no—
259C2×D4—3161no—
260C2×D4—3161no—
261C2×D4—791no—
262C2×D4—791no—
263C2×D4—791no—
264C2×D4—1581no—
265C2×D4—1581no—
266C2×D4—1581no—
267C2×D4—1581no—
268C2×D4—1582no—
269C2×D4—1582no—
270C2×D4—1581no—
271C2×D4—1581no—
272C2×D4C22×D7911yescharacteristic
273C22×C4—21no—
274C22×C4—791no—
275C22×C4—791no—
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—1581no—
291C4⋊C4—1581no—
292C4⋊C4—1581no—
293C4⋊C4—1581no—
294C4⋊C4C22×D7911yescharacteristic
295C4⋊C4C22×D7911yescharacteristic
296C4⋊C4C22×D7911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—791no—
299C22⋊C4—791no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C42—1581no—
306C42—1581no—
307C42C22×D7911yescharacteristic
308C23—21no—
309C23—3162no—
310C23—3162no—
311C23—3162no—
312C23—3162no—
313C23—791no—
314C23—791no—
315C23—6321no—
316C23—6321no—
317C23—1581no—
318C23—1581no—
319Q8—1581no—
320Q8—1581no—
321D4—21no—
322D4—3162no—
323D4—3162no—
324D4—3162no—
325D4—3162no—
326D4—3162no—
327D4—6321no—
328D4—1582no—
329D4—1581no—
330D4—1581no—
331D4—1581no—
332D4—1581no—
333D4#1192962512yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—3162no—
339C2×C4—791no—
340C2×C4—791no—
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—22no—
355C22—41no—
356C22—41no—
357C22—3161no—
358C22—3161no—
359C22—3161no—
360C22—3161no—
361C22—3161no—
362C22—3161no—
363C22—792no—
364C22—6324no—
365C22—6324no—
366C22—1581no—
367C22—1581no—
368C22—1581no—
369C22—1581no—
370C22—1581no—
371C22C2×D4×D7911yescharacteristic
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—3161no—
378C4—3161no—
379C4—1581no—
380C4—1581no—
381C4C2×#1192962511yescharacteristic
382C4#1457920711yescharacteristic
383C2—42no—
384C2—3161no—
385C2—6321no—
386C2—6321no—
387C2—1582no—
388C2#1909920411yescharacteristic
389C2AGL(1,ℤ/8)×D7911yescharacteristic
390C2#1909937011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#478×C79C2
socleC22×C79C22×D4
prime radicalD4×D316C2
hypercenter#478D79
hypocenterC79#3310
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #19099251C2semidirect
3. #19098929C2semidirect
4. #19098889C2semidirect
5. #19098878C2semidirect
6. #19098810C2semidirect
7. #19098793C2semidirect
8. #19098764C2semidirect
9. #19098715C2semidirect
10. #19098715C2semidirect
11. #19098663C2semidirect
12. #19098633C2semidirect
13. #19098566C2semidirect
14. #102×D79C2semidirect
15. #478×C79C2semidirect
19. C2×#11929613C22semidirect
20. C2×#11929613C22semidirect
22. C2×#11929607C22semidirect
23. C2×C8×D79C22semidirect
28. #14579141C22semidirect
29. #14579141C22semidirect
35. C4×Dic158C22semidirect
38. #14579119C22semidirect
39. C4⋊C4×D79C22semidirect
40. #14579094C22semidirect
41. #14579084C22semidirect
42. #14579083C22semidirect
43. #14579083C22semidirect
45. #14579081C22semidirect
46. #14579081C22semidirect
47. #14579081C22semidirect
48. #14579081C22semidirect
49. (C2×D79)⋊C8C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. #14579072C22semidirect
52. #125×C79C22semidirect
54. #107×C79C22semidirect
55. #106×C79C22semidirect
56. C4⋊C8×C79C22semidirect
196. C79#3310semidirect
202. #478D79semidirect
223. #125C2×D79semidirect
239. #107C2×D79semidirect
240. #106C2×D79semidirect
241. C4⋊C8C2×D79semidirect