Finite Group Databasebeta

← #23773452

Subgroups — #23773452

Order 10112.

454 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099098C211yesmaximal, characteristic, complemented
2C4×D4×D79C211yesmaximal, characteristic, complemented
3#19098900C211yesmaximal, characteristic, complemented
4#19098883C211yesmaximal, characteristic, complemented
5#19098860C211yesmaximal, characteristic, complemented
6#19098779C211yesmaximal, characteristic, complemented
7#19098778C211yesmaximal, characteristic, complemented
8#19098715C211yesmaximal, characteristic, complemented
9#19098698C211yesmaximal, characteristic
10#19098654C211yesmaximal, characteristic, complemented
11#19098650C211yesmaximal, characteristic, complemented
12#19098645C211yesmaximal, characteristic, complemented
13#19098643C211yesmaximal, characteristic, complemented
14#19098615C211yesmaximal, characteristic, complemented
15#478×C79C211yesmaximal, characteristic, complemented
16C2×D4×D79C2211yescharacteristic
17C22×C4×D79—21no—
18C2×#11929613C2211yescharacteristic
19C2×#11929612C2211yescharacteristic
20C2×D632C2211yescharacteristic
21C2×#11929609C2211yescharacteristic
22#14579156—21no—
23#14579149C2211yescharacteristic, complemented
24#14579146—21no—
25#14579141C2211yescharacteristic
26#14579136C2211yescharacteristic
27#14579126C2211yescharacteristic, complemented
28C4×D316C2211yescharacteristic
29D4×Dic79C2211yescharacteristic
30#14579123—21no—
31#14579123C2211yescharacteristic
32#14579123C2211yescharacteristic, complemented
33C4×C22⋊D79—21no—
34(C22⋊D79)⋊C4—21no—
35#14579119—21no—
36C4⋊C4×D79C2211yescharacteristic
37C22⋊C4×D79—21no—
38C42×D79C2211yescharacteristic
39#14579094C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41C4⋊(C79⋊C8)C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579084C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic, complemented
45#14579081C2211yescharacteristic
46#14579081C2211yescharacteristic
47#14579081C2211yescharacteristic, complemented
48(C2×D79)⋊C8C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50C8×Dic79C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, 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—
60C2×Dic158C2311yescharacteristic
61C2×D316—21no—
62C2×D316C2311yescharacteristic
63C2×D316C2311yescharacteristic
64C2×C22⋊D79—21no—
65D4×D79—22no—
66D4×D79—22no—
67C22×Dic79—21no—
68C2×C4×D79—21no—
69C2×C4×D79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79—44no—
73C2×C4×D79D411yescharacteristic
74C2×C4×D79D411yescharacteristic
75C2×C4×D79C2311yescharacteristic
76#11929613—22no—
77#11929612—22no—
78D632—22no—
79#11929609—22no—
80C2×C79⋊C8C2311yescharacteristic
81C2×C79⋊C8C2311yescharacteristic
82C4⋊Dic79—21no—
83C4⋊Dic79C2311yescharacteristic
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86C22⋊Dic79—21no—
87(C2×D79)⋊C4—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94C4×Dic79—21no—
95C4×Dic79D411yescharacteristic
96C4×Dic79D411yescharacteristic
97C4×Dic79C2311yescharacteristic
98C2×D4×C79C2311yescharacteristic
99C22×C4×C79—21no—
100C2×C8×C79C2311yescharacteristic
101C2×C8×C79C2311yescharacteristic
102C4⋊C4×C79—21no—
103C4⋊C4×C79—21no—
104C4⋊C4×C79C2311yescharacteristic
105C4⋊C4×C79C2311yescharacteristic
106C4⋊C4×C79C2311yescharacteristic
107C22⋊C4×C79—21no—
108C42×C79C2311yescharacteristic
109C23×C79—21no—
110C22×D79—24no—
111C22×D79—21no—
112C22×D79—21no—
113C22×D79—42no—
114C22×D79—42no—
115C22×D79C2×D411yescharacteristic
116D4×C79—21no—
117D4×C79#4112yes—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—42no—
122C2×C4×C79C2×D411yescharacteristic
123C2×C4×C79C2×D411yescharacteristic
124C2×C4×C79C2411yescharacteristic
125C22⋊D79—24no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—42no—
129C2×Dic79C2×D411yescharacteristic
130C2×Dic79C2×D411yescharacteristic
131C2×Dic79C2×D411yescharacteristic
132D316—21no—
133D316—21no—
134D316—21no—
135D316—42no—
136D316#4112yes—
137C4×D79—22no—
138C4×D79—21no—
139C4×D79—21no—
140C4×D79—22no—
141C4×D79—42no—
142C4×D79—42no—
143C4×D79—42no—
144C4×D79—42no—
145Dic158—21no—
146Dic158—21no—
147C8×C79—21no—
148C8×C79—21no—
149C79⋊C8—21no—
150C79⋊C8—21no—
151C22×C79—22no—
152C22×C79—41no—
153C22×C79—41no—
154C22×C79C22×D411yescharacteristic
155C2×D79—21no—
156C2×D79—21no—
157C2×D79—22no—
158C2×D79—48no—
159C2×D79—41no—
160C2×D79—41no—
161C2×D79—41no—
162C2×D79—41no—
163C2×D79—41no—
164C2×D79#13512yes—
165C4×C79—21no—
166C4×C79—21no—
167C4×C79—41no—
168C4×C79—41no—
169C4×C79—41no—
170C4×C79C2×#4111yescharacteristic
171C4×C79C2×#4111yescharacteristic
172Dic79—21no—
173Dic79—21no—
174Dic79—41no—
175Dic79—41no—
176Dic79AGL(1,ℤ/8)12yes—
177C2×C79—42no—
178C2×C79#52511yescharacteristic
179C2×C79C2×#13511yescharacteristic
180C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
181D79—22no—
182D79—42no—
183D79—81no—
184#3105—791nomaximal, Sylow
185C79#310511yescharacteristic, complemented, Sylow
186#529—791no—
187C2×C4×D4—791no—
188#484—791no—
189#481—791no—
190#478—791no—
191#478D7911yescharacteristic, complemented
192#463—791no—
193#463—791no—
194#450—791no—
195#447—791no—
196C4×SD16—791no—
197C4×SD16—791no—
198C4×D8—791no—
199C4×D8—791no—
200#431—791no—
201C22×D4—791no—
202C23×C4—1581no—
203C2×SD16—791no—
204C2×SD16—791no—
205C2×D8—791no—
206C2×D8—791no—
207#126—1581no—
208#125C2×D7911yescharacteristic, complemented
209#124—791no—
210#123—1581no—
211C22⋊Q8—791no—
212#121—791no—
213C4×Q8—791no—
214C4×D4—791no—
215C4×D4—791no—
216C4×D4—791no—
217C4×D4—791no—
218C4×D4—1581no—
219C4×D4—1581no—
220C4×D4—1581no—
221C4×D4C2×D7911yescharacteristic
222#117—1581no—
223C2×C4⋊C4—791no—
224C2×C22⋊C4—1581no—
225C2×C42—791no—
226#107—791no—
227#107C2×D7911yescharacteristic, complemented
228#106—791no—
229#106C2×D7911yescharacteristic, complemented
230C4⋊C8—791no—
231C4⋊C8C2×D7911yescharacteristic, complemented
232#103—791no—
233#103—791no—
234#102—791no—
235#102—791no—
236#102—791no—
237#102—791no—
238#102C2×D7911yescharacteristic
239#102C2×D7911yescharacteristic
240C22⋊C8—791no—
241C22⋊C8—791no—
242C4×C8—791no—
243C4×C8—791no—
244C24—1581no—
245C2×Q8—791no—
246C2×D4—791no—
247C2×D4—791no—
248C2×D4—1581no—
249C2×D4—1581no—
250C2×D4—1582no—
251C2×D4—1582no—
252C2×D4C22×D7911yescharacteristic
253C22×C4—21no—
254C22×C4—3164no—
255C22×C4—791no—
256C22×C4—791no—
257C22×C4—791no—
258C22×C4—1581no—
259C22×C4—1581no—
260C22×C4—1581no—
261C22×C4—1581no—
262C22×C4—1581no—
263SD16—1582no—
264SD16—1582no—
265D8—1582no—
266D8—1582no—
267C2×C8—791no—
268C2×C8—791no—
269C2×C8C22×D7911yescharacteristic
270C2×C8C22×D7911yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—791no—
274C4⋊C4—1581no—
275C4⋊C4—1581no—
276C4⋊C4—1581no—
277C4⋊C4C22×D7911yescharacteristic
278C4⋊C4C22×D7911yescharacteristic
279C4⋊C4C22×D7911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C22⋊C4—1581no—
287C22⋊C4—1581no—
288C22⋊C4—1581no—
289C42—791no—
290C42—791no—
291C42—791no—
292C42—1581no—
293C42C22×D7911yescharacteristic
294C23—21no—
295C23—3162no—
296C23—3162no—
297C23—791no—
298C23—1584no—
299C23—1581no—
300C23—1581no—
301Q8—1581no—
302Q8—1581no—
303D4—21no—
304D4—3162no—
305D4—792no—
306D4—1584no—
307D4—1581no—
308D4—1581no—
309D4—1581no—
310D4#1192962512yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—3162no—
316C2×C4—3162no—
317C2×C4—3162no—
318C2×C4—3162no—
319C2×C4—3162no—
320C2×C4—791no—
321C2×C4—791no—
322C2×C4—791no—
323C2×C4—1582no—
324C2×C4—1582no—
325C2×C4—1581no—
326C2×C4—1581no—
327C2×C4—1581no—
328C2×C4—1581no—
329C2×C4D4×D7911yescharacteristic
330C2×C4D4×D7911yescharacteristic
331C2×C4C23×D7911yescharacteristic
332C8—21no—
333C8—21no—
334C8—1581no—
335C8—1581no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—3168no—
340C22—3161no—
341C22—3161no—
342C22—3161no—
343C22—3161no—
344C22—3161no—
345C22—792no—
346C22—1582no—
347C22—1581no—
348C22—1581no—
349C22C2×D4×D7911yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—3161no—
356C4—3161no—
357C4—792no—
358C4—1581no—
359C4—1581no—
360C4#41×D7911yescharacteristic
361C4C2×#1192962511yescharacteristic
362C2—42no—
363C2—3162no—
364C2—6321no—
365C2—1582no—
366C2#1909907611yescharacteristic
367C2#135×D7911yescharacteristic
368C2AGL(1,ℤ/8)×D7911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#478×C79C2
socleC22×C79C22×D4
prime radical#19098698C2
hypercenter#478D79
hypocenterC79#3105
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. #19099098C2semidirect
2. C4×D4×D79C2semidirect
3. #19098900C2semidirect
4. #19098883C2semidirect
5. #19098860C2semidirect
6. #19098779C2semidirect
7. #19098778C2semidirect
8. #19098715C2semidirect
10. #19098654C2semidirect
11. #19098650C2semidirect
12. #19098645C2semidirect
13. #19098643C2semidirect
14. #19098615C2semidirect
15. #478×C79C2semidirect
23. #14579149C22semidirect
27. #14579126C22semidirect
32. #14579123C22semidirect
39. #14579094C22semidirect
40. #14579092C22semidirect
41. C4⋊(C79⋊C8)C22semidirect
42. #14579086C22semidirect
43. #14579084C22semidirect
44. #14579083C22semidirect
47. #14579081C22semidirect
50. C8×Dic79C22semidirect
51. C8×Dic79C22semidirect
52. #125×C79C22semidirect
54. #107×C79C22semidirect
55. #106×C79C22semidirect
56. C4⋊C8×C79C22semidirect
185. C79#3105semidirect
191. #478D79semidirect
208. #125C2×D79semidirect
227. #107C2×D79semidirect
229. #106C2×D79semidirect
231. C4⋊C8C2×D79semidirect