Finite Group Databasebeta

← #23775231

Subgroups — #23775231

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#19099248C211yesmaximal, characteristic, complemented
2#19099207C211yesmaximal, characteristic
3#19098916C211yesmaximal, characteristic, complemented
4#19098893C211yesmaximal, characteristic, complemented
5#19098885C211yesmaximal, characteristic, complemented
6#19098861C211yesmaximal, characteristic, complemented
7#19098804C211yesmaximal, characteristic, complemented
8#19098791C211yesmaximal, characteristic, complemented
9#19098784C211yesmaximal, characteristic, complemented
10#19098726C211yesmaximal, characteristic, complemented
11#19098714C211yesmaximal, characteristic, complemented
12#19098654C211yesmaximal, characteristic, complemented
13C8×C22⋊D79C211yesmaximal, characteristic, complemented
14#19098556C211yesmaximal, characteristic, complemented
15C2×#102×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C2×Dic316C2211yescharacteristic, complemented
18C2×#11929612C2211yescharacteristic
19C2×#11929612C2211yescharacteristic
20C2×C8×D79C2211yescharacteristic, complemented
21#14579156—21no—
22#14579152C2211yescharacteristic, complemented
23#14579151—21no—
24#14579148C2211yescharacteristic
25#14579144—21no—
26#14579142—21no—
27#14579141C2211yescharacteristic, complemented
28#14579140C2211yescharacteristic
29#14579140C2211yescharacteristic
30#14579133—21no—
31#14579132C2211yescharacteristic
32#14579130—21no—
33#14579126C2211yescharacteristic, complemented
34D4×Dic79C2211yescharacteristic
35C4×C22⋊D79C2211yescharacteristic
36#14579120—21no—
37#14579119C2211yescharacteristic, complemented
38C2×C22⋊Dic79—21no—
39#14579095C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41#14579092C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579084C2211yescharacteristic, complemented
46#14579084C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C22×D4×C79C2211yescharacteristic
53C22×C8×C79C2211yescharacteristic
54C2×C4⋊C4×C79C2211yescharacteristic
55#102×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic
59#11929623—22no—
60#11929623—41no—
61C2×Dic158C2311yescharacteristic
62C2×Dic158C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79D411yescharacteristic
66C22×Dic79—21no—
67C22×Dic79—21no—
68C2×C4×D79C2311yescharacteristic
69Dic316—41no—
70#11929612—22no—
71#11929612—41no—
72C2×C79⋊C8C2311yescharacteristic
73C2×C79⋊C8C2311yescharacteristic
74C8×D79—41no—
75C4⋊Dic79—21no—
76C4⋊Dic79—21no—
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4D411yescharacteristic
84C22⋊Dic79—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79D411yescharacteristic
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4D411yescharacteristic
94C4×Dic79—21no—
95C4×Dic79—21no—
96C4×Dic79C2311yescharacteristic
97C24×C79—21no—
98C2×D4×C79—22no—
99C2×D4×C79—21no—
100C2×D4×C79—41no—
101C2×D4×C79C2311yescharacteristic
102C2×D4×C79C2311yescharacteristic
103C22×C4×C79—21no—
104C22×C4×C79C2311yescharacteristic
105C2×C8×C79—41no—
106C2×C8×C79C2311yescharacteristic
107C2×C8×C79C2311yescharacteristic
108C4⋊C4×C79—21no—
109C4⋊C4×C79C2311yescharacteristic
110C4⋊C4×C79C2311yescharacteristic
111C23×C79—21no—
112C23×C79—21no—
113C23×C79—42no—
114C23×C79—42no—
115C23×C79—81no—
116C23×C79C2×D411yescharacteristic
117C22×D79C2×D411yescharacteristic
118D4×C79—21no—
119D4×C79—21no—
120D4×C79—21no—
121D4×C79—42no—
122D4×C79#4112yes—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—42no—
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2411yescharacteristic
130C22⋊D79—22no—
131C22⋊D79—42no—
132C22⋊D79—81no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—42no—
138C2×Dic79—81no—
139C2×Dic79C2×D411yescharacteristic
140C2×Dic79C2×D411yescharacteristic
141C2×Dic79C2×D411yescharacteristic
142C4×D79—21no—
143C4×D79—21no—
144Dic158—21no—
145Dic158—21no—
146Dic158—21no—
147Dic158—21no—
148C8×C79—21no—
149C8×C79—21no—
150C79⋊C8—21no—
151C79⋊C8—21no—
152C22×C79—21no—
153C22×C79—21no—
154C22×C79—22no—
155C22×C79—41no—
156C22×C79—41no—
157C22×C79—41no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79—84no—
161C22×C79#13512yes—
162C22×C79C22×D411yescharacteristic
163C2×D79—21no—
164C2×D79—21no—
165C2×D79—21no—
166C4×C79—21no—
167C4×C79—41no—
168C4×C79—41no—
169C4×C79C2×#4111yescharacteristic
170C4×C79H(5,𝔽2)11yescharacteristic
171Dic79—21no—
172Dic79—21no—
173Dic79—21no—
174Dic79—41no—
175Dic79—41no—
176Dic79—41no—
177Dic79—41no—
178C2×C79—22no—
179C2×C79—42no—
180C2×C79—81no—
181C2×C79#54611yescharacteristic
182C2×C79C2×#13511yescharacteristic
183C2×C79#57711yescharacteristic
184D79—41no—
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#465—791no—
195#464—791no—
196#452—791no—
197#450—791no—
198C4×SD16—791no—
199C8×D4—791no—
200#416—791no—
201C2×#102D7911yescharacteristic, complemented
202C2×#41—791no—
203C22×D4C2×D7911yescharacteristic
204C2×Q16—791no—
205C2×SD16—791no—
206C2×SD16—791no—
207C22×C8—791no—
208C22×C8C2×D7911yescharacteristic
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⋊Q8—791no—
218#121—791no—
219#121—1581no—
220#120—1581no—
221C4×Q8—791no—
222C4×D4—791no—
223C4×D4—791no—
224#117—791no—
225#117—1581no—
226C2×C4⋊C4C2×D7911yescharacteristic
227C2×C22⋊C4—1581no—
228#107—791no—
229#106—791no—
230#106—791no—
231C4⋊C8—791no—
232#103—791no—
233#103—791no—
234#103—791no—
235#103—791no—
236#102—791no—
237#102—791no—
238#102C2×D7911yescharacteristic
239#102C2×D7911yescharacteristic
240#102C2×D7911yescharacteristic
241#102C2×D7911yescharacteristic
242C22⋊C8—791no—
243C22⋊C8—791no—
244C4×C8—791no—
245C24—21no—
246#41—3161no—
247#41—1582no—
248C2×Q8—791no—
249C2×Q8—791no—
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—791no—
254C2×D4—1581no—
255C2×D4—1581no—
256C2×D4C22×D7911yescharacteristic
257C2×D4C22×D7911yescharacteristic
258C22×C4—21no—
259C22×C4—791no—
260C22×C4—1581no—
261C22×C4—1581no—
262C22×C4C22×D7911yescharacteristic
263Q16—3161no—
264SD16—3161no—
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—791no—
285C22⋊C4—791no—
286C22⋊C4—1581no—
287C22⋊C4—1581no—
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—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—791no—
303C23D4×D7911yescharacteristic
304Q8—1581no—
305Q8—1581no—
306Q8—1581no—
307Q8—1581no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—3162no—
313D4—6321no—
314D4—1582no—
315D4#1192962412yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—42no—
321C2×C4—3162no—
322C2×C4—791no—
323C2×C4—791no—
324C2×C4—791no—
325C2×C4—6321no—
326C2×C4—1581no—
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—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—84no—
347C22—1581no—
348C22—1581no—
349C22—1581no—
350C22#1457918012yes—
351C22C2×D4×D7911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—3161no—
356C4—3161no—
357C4—3161no—
358C4—3161no—
359C4—1581no—
360C4—1581no—
361C4—1581no—
362C4C2×#1192962411yescharacteristic
363C4#1457920611yescharacteristic
364C2—22no—
365C2—42no—
366C2—81no—
367C2—3161no—
368C2#1909920311yescharacteristic
369C2C2×#1457918011yescharacteristic
370C2#1909936911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC2×#102×C79C2
socleC22×C79C22×D4
prime radical#19099207C2
hypercenterC2×#102D79
hypocenterC79#3296
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #19099248C2semidirect
3. #19098916C2semidirect
4. #19098893C2semidirect
5. #19098885C2semidirect
6. #19098861C2semidirect
7. #19098804C2semidirect
8. #19098791C2semidirect
9. #19098784C2semidirect
10. #19098726C2semidirect
11. #19098714C2semidirect
12. #19098654C2semidirect
13. C8×C22⋊D79C2semidirect
14. #19098556C2semidirect
15. C2×#102×C79C2semidirect
17. C2×Dic316C22semidirect
20. C2×C8×D79C22semidirect
22. #14579152C22semidirect
27. #14579141C22semidirect
33. #14579126C22semidirect
37. #14579119C22semidirect
39. #14579095C22semidirect
40. #14579092C22semidirect
41. #14579092C22semidirect
42. Dic79⋊C8C22semidirect
43. #14579086C22semidirect
44. #14579086C22semidirect
45. #14579084C22semidirect
46. #14579084C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. C8×Dic79C22semidirect
186. C79#3296semidirect
201. C2×#102D79semidirect