Finite Group Databasebeta

← #23775230

Subgroups — #23775230

Order 10112.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099247C211yesmaximal, characteristic, complemented
2#19099210C211yesmaximal, characteristic
3#19098916C211yesmaximal, characteristic, complemented
4#19098895C211yesmaximal, characteristic, complemented
5#19098884C211yesmaximal, characteristic, complemented
6#19098862C211yesmaximal, characteristic, complemented
7#19098803C211yesmaximal, characteristic, complemented
8#19098783C211yesmaximal, characteristic, complemented
9#19098723C211yesmaximal, characteristic, complemented
10#19098712C211yesmaximal, characteristic, complemented
11#19098648C211yesmaximal, characteristic, complemented
12C8×C22⋊D79C211yesmaximal, characteristic, complemented
13#19098560C211yesmaximal, characteristic, complemented
14#102×D79C211yesmaximal, characteristic, complemented
15#465×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×#11929614C2211yescharacteristic, complemented
19C2×#11929611C2211yescharacteristic
20C2×C8×D79C2211yescharacteristic
21#14579154—21no—
22#14579152C2211yescharacteristic, complemented
23#14579151—21no—
24#14579148C2211yescharacteristic
25#14579143—21no—
26#14579143—21no—
27#14579141C2211yescharacteristic
28#14579137C2211yescharacteristic
29#14579132—21no—
30#14579129—21no—
31Q8×Dic79C2211yescharacteristic, complemented
32#14579123C2211yescharacteristic
33C4×C22⋊D79C2211yescharacteristic
34#14579120C2211yescharacteristic, complemented
35#14579119—21no—
36C4⋊C4×D79C2211yescharacteristic
37C22⋊C4×D79—21no—
38#14579094C2211yescharacteristic, complemented
39#14579092C2211yescharacteristic, complemented
40Dic79⋊C8C2211yescharacteristic, complemented
41#14579086C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579084C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579081C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic
51C8×Dic79C2211yescharacteristic, complemented
52C2×SD16×C79C2211yescharacteristic
53C22×C8×C79C2211yescharacteristic, complemented
54C22⋊Q8×C79C2211yescharacteristic, complemented
55#121×C79C2211yescharacteristic
56#106×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic
59C23×D79—21no—
60#11929624—22no—
61#11929624—41no—
62C2×Dic158C2311yescharacteristic
63C2×D316C2311yescharacteristic
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C2×C22⋊D79D411yescharacteristic
67D4×D79—22no—
68D4×D79—41no—
69C2×C4×D79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79C2311yescharacteristic
73#11929614—41no—
74#11929611—22no—
75C2×C79⋊C8C2311yescharacteristic
76C2×C79⋊C8C2311yescharacteristic
77C8×D79—41no—
78C4⋊Dic79—21no—
79C4⋊Dic79—21no—
80C4⋊Dic79—21no—
81C4⋊Dic79C2311yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4D411yescharacteristic
87C22⋊Dic79—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79D411yescharacteristic
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4D411yescharacteristic
95C4×Dic79—21no—
96C4×Dic79—21no—
97C4×Dic79C2311yescharacteristic
98C2×Q8×C79C2311yescharacteristic
99C2×D4×C79—21no—
100C2×D4×C79C2311yescharacteristic
101C22×C4×C79C2311yescharacteristic
102SD16×C79—41no—
103C2×C8×C79—41no—
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79—21no—
107C4⋊C4×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C22⋊C4×C79—21no—
110C22⋊C4×C79—21no—
111C23×C79—21no—
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114C22×D79—42no—
115C22×D79—42no—
116C22×D79—81no—
117C22×D79C2×D411yescharacteristic
118Q8×C79—21no—
119Q8×C79—21no—
120D4×C79—21no—
121D4×C79—21no—
122D4×C79—81no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2411yescharacteristic
130C22⋊D79—22no—
131C22⋊D79—42no—
132C22⋊D79—42no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138C2×Dic79C2×D411yescharacteristic
139D316—21no—
140D316#4112yes—
141C4×D79—21no—
142C4×D79—21no—
143C4×D79—42no—
144C4×D79—42no—
145C4×D79—81no—
146Dic158—21no—
147Dic158—21no—
148C8×C79—21no—
149C8×C79—21no—
150C79⋊C8—21no—
151C79⋊C8—21no—
152C22×C79—21no—
153C22×C79—21no—
154C22×C79—21no—
155C22×C79—41no—
156C22×C79—41no—
157C22×C79—41no—
158C22×C79C22×D411yescharacteristic
159C2×D79—21no—
160C2×D79—21no—
161C2×D79—22no—
162C2×D79—41no—
163C2×D79—41no—
164C2×D79—84no—
165C2×D79#13512yes—
166C4×C79—21no—
167C4×C79—41no—
168C4×C79—41no—
169C4×C79—41no—
170C4×C79C2×#4111yescharacteristic
171C4×C79H(5,𝔽2)11yescharacteristic
172Dic79—21no—
173Dic79—21no—
174Dic79—21no—
175Dic79—41no—
176Dic79—41no—
177Dic79—41no—
178C2×C79—41no—
179C2×C79—81no—
180C2×C79#54611yescharacteristic
181C2×C79C2×#13511yescharacteristic
182C2×C79#57711yescharacteristic
183D79—22no—
184D79—42no—
185#3296—791nomaximal, Sylow
186C79#329611yescharacteristic, complemented, Sylow
187#552—791no—
188#546—791no—
189#488—791no—
190#483—791no—
191#482—791no—
192#478—791no—
193#467—791no—
194#465D7911yescharacteristic, complemented
195#464—791no—
196#452—791no—
197#450—791no—
198C4×SD16—791no—
199C8×D4—791no—
200#416—791no—
201C2×#102—791no—
202C2×#41—791no—
203C22×D4—791no—
204C2×Q16—791no—
205C2×SD16—791no—
206C2×SD16C2×D7911yescharacteristic
207C22×C8—791no—
208C22×C8C2×D7911yescharacteristic, complemented
209#126—1581no—
210#125—791no—
211#125—1581no—
212#124—791no—
213#123—1581no—
214#123—1581no—
215C22⋊Q8—791no—
216C22⋊Q8—791no—
217C22⋊Q8C2×D7911yescharacteristic, complemented
218#121—1581no—
219#121C2×D7911yescharacteristic
220#120—1581no—
221C4×Q8—791no—
222C4×D4—791no—
223C4×D4—791no—
224#117—791no—
225#117—1581no—
226C2×C4⋊C4—791no—
227C2×C22⋊C4—1581no—
228#107—791no—
229#106—791no—
230#106C2×D7911yescharacteristic, complemented
231C4⋊C8—791no—
232#103—791no—
233#103—791no—
234#103—791no—
235#103C2×D7911yescharacteristic, complemented
236#102—791no—
237#102—791no—
238#102—791no—
239#102—791no—
240#102—791no—
241#102C2×D7911yescharacteristic
242C22⋊C8—791no—
243C22⋊C8—791no—
244C4×C8—791no—
245C24—1581no—
246#41—3161no—
247#41—1582no—
248C2×Q8—791no—
249C2×Q8C22×D7911yescharacteristic
250C2×D4—21no—
251C2×D4—3161no—
252C2×D4—791no—
253C2×D4—791no—
254C2×D4—1581no—
255C2×D4—1582no—
256C2×D4—1581no—
257C2×D4C22×D7911yescharacteristic
258C22×C4—791no—
259C22×C4—1581no—
260C22×C4—1581no—
261C22×C4—1581no—
262C22×C4C22×D7911yescharacteristic
263Q16—3161no—
264SD16—41no—
265SD16—1582no—
266C2×C8—41no—
267C2×C8—3161no—
268C2×C8—791no—
269C2×C8—791no—
270C2×C8C22×D7911yescharacteristic
271C2×C8C22×D7911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—791no—
274C4⋊C4—791no—
275C4⋊C4—791no—
276C4⋊C4—1581no—
277C4⋊C4—1581no—
278C4⋊C4—1581no—
279C4⋊C4—1581no—
280C4⋊C4—1581no—
281C4⋊C4—1581no—
282C4⋊C4C22×D7911yescharacteristic
283C4⋊C4C22×D7911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—791no—
287C22⋊C4—791no—
288C22⋊C4—1581no—
289C22⋊C4—1581no—
290C22⋊C4—1581no—
291C22⋊C4—1581no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C42—791no—
295C42—1581no—
296C42—1581no—
297C23—21no—
298C23—3162no—
299C23—3162no—
300C23—791no—
301C23—6321no—
302C23—1581no—
303C23D4×D7911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1581no—
307Q8—1581no—
308D4—21no—
309D4—21no—
310D4—81no—
311D4—3162no—
312D4—3162no—
313D4—792no—
314D4—1582no—
315D4—1581no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—3162no—
322C2×C4—3162no—
323C2×C4—791no—
324C2×C4—791no—
325C2×C4—791no—
326C2×C4—6321no—
327C2×C4—1581no—
328C2×C4—1581no—
329C2×C4—1581no—
330C2×C4—1581no—
331C2×C4—1581no—
332C2×C4D4×D7911yescharacteristic
333C2×C4C23×D7911yescharacteristic
334C8—21no—
335C8—21no—
336C8—1581no—
337C8—1581no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—3161no—
345C22—3161no—
346C22—792no—
347C22—6324no—
348C22—1582no—
349C22—1581no—
350C22—1581no—
351C22C2×D4×D7911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—3161no—
357C4—3161no—
358C4—3161no—
359C4—1581no—
360C4—1581no—
361C4—1581no—
362C4#41×D7911yescharacteristic
363C4#1457920611yescharacteristic
364C2—41no—
365C2—81no—
366C2—3162no—
367C2—1582no—
368C2#1909920211yescharacteristic
369C2#135×D7911yescharacteristic
370C2#1909936911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#465×C79C2
socleC22×C79C22×D4
prime radical#19099210C2
hypercenter#465D79
hypocenterC79#3296
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #19099247C2semidirect
3. #19098916C2semidirect
4. #19098895C2semidirect
5. #19098884C2semidirect
6. #19098862C2semidirect
7. #19098803C2semidirect
8. #19098783C2semidirect
9. #19098723C2semidirect
10. #19098712C2semidirect
11. #19098648C2semidirect
12. C8×C22⋊D79C2semidirect
13. #19098560C2semidirect
14. #102×D79C2semidirect
15. #465×C79C2semidirect
18. C2×#11929614C22semidirect
22. #14579152C22semidirect
31. Q8×Dic79C22semidirect
34. #14579120C22semidirect
38. #14579094C22semidirect
39. #14579092C22semidirect
40. Dic79⋊C8C22semidirect
41. #14579086C22semidirect
42. #14579086C22semidirect
43. #14579084C22semidirect
49. C22⋊(C79⋊C8)C22semidirect
51. C8×Dic79C22semidirect
53. C22×C8×C79C22semidirect
54. C22⋊Q8×C79C22semidirect
56. #106×C79C22semidirect
57. #103×C79C22semidirect
186. C79#3296semidirect
194. #465D79semidirect
208. C22×C8C2×D79semidirect
217. C22⋊Q8C2×D79semidirect
230. #106C2×D79semidirect
235. #103C2×D79semidirect