Finite Group Databasebeta

← #23773585

Subgroups — #23773585

Order 10112.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099186C211yesmaximal, characteristic, complemented
2#19099038C211yesmaximal, characteristic, complemented
3#19098901C211yesmaximal, characteristic, complemented
4#19098888C211yesmaximal, characteristic, complemented
5#19098851C211yesmaximal, characteristic, complemented
6#19098841C211yesmaximal, characteristic, complemented
7#19098780C211yesmaximal, characteristic, complemented
8#19098780C211yesmaximal, characteristic, complemented
9#19098697C211yesmaximal, characteristic
10#19098672C211yesmaximal, characteristic, complemented
11#19098664C211yesmaximal, characteristic, complemented
12SD16×Dic79C211yesmaximal, characteristic, complemented
13#19098643C211yesmaximal, characteristic, complemented
14#19098621C211yesmaximal, characteristic, complemented
15#450×C79C211yesmaximal, characteristic, complemented
16C2×#11929609C2211yescharacteristic
17C2×#11929609C2211yescharacteristic
18#14579160C2211yescharacteristic, complemented
19#14579156—21no—
20#14579150C2211yescharacteristic, complemented
21#14579147—21no—
22#14579143—21no—
23#14579141—21no—
24#14579135C2211yescharacteristic
25Q8×Dic79C2211yescharacteristic, complemented
26D4×Dic79—21no—
27D4×Dic79—21no—
28D4×Dic79C2211yescharacteristic
29D4×Dic79C2211yescharacteristic
30D4×Dic79C2211yescharacteristic
31D4×Dic79C2211yescharacteristic
32#14579123C2211yescharacteristic, complemented
33#14579120C2211yescharacteristic
34#14579120C2211yescharacteristic
35C2×C22⋊Dic79—21no—
36C2×C22⋊Dic79—21no—
37#14579095C2211yescharacteristic, complemented
38#14579094C2211yescharacteristic, complemented
39#14579093C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579085C2211yescharacteristic, complemented
44#14579085C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic, complemented
46#14579083C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C22×D4×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic
54C2×SD16×C79C2211yescharacteristic
55C22⋊Q8×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59C2×Dic158—21no—
60C2×D316C2311yescharacteristic
61C2×C22⋊D79—21no—
62C22×Dic79—21no—
63C22×Dic79—21no—
64C22×Dic79—21no—
65C22×Dic79—21no—
66C2×C4×D79—21no—
67#11929609—22no—
68#11929609—22no—
69C2×C79⋊C8C2311yescharacteristic
70C2×C79⋊C8C2311yescharacteristic
71C4⋊Dic79—21no—
72C4⋊Dic79D411yescharacteristic
73C4⋊Dic79D411yescharacteristic
74C4⋊Dic79C2311yescharacteristic
75C4⋊Dic79C2311yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77Dic79⋊C4—21no—
78C22⋊Dic79—21no—
79C22⋊Dic79—21no—
80C22⋊Dic79—21no—
81C22⋊Dic79—21no—
82C22⋊Dic79—21no—
83C22⋊Dic79D411yescharacteristic
84C22⋊Dic79D411yescharacteristic
85(C2×D79)⋊C4—21no—
86(C2×D79)⋊C4—21no—
87(C2×D79)⋊C4—21no—
88(C2×D79)⋊C4—21no—
89C4×Dic79—21no—
90C4×Dic79—21no—
91C4×Dic79C2311yescharacteristic
92C4×Dic79C2311yescharacteristic
93C24×C79—21no—
94C2×Q8×C79C2311yescharacteristic
95C2×D4×C79—22no—
96C2×D4×C79—22no—
97C2×D4×C79—21no—
98C2×D4×C79C2311yescharacteristic
99C2×D4×C79C2311yescharacteristic
100C22×C4×C79C2311yescharacteristic
101SD16×C79—22no—
102SD16×C79—22no—
103C2×C8×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C4⋊C4×C79—21no—
106C4⋊C4×C79C2311yescharacteristic
107C22⋊C4×C79—21no—
108C23×C79—24no—
109C23×C79—21no—
110C23×C79—21no—
111C23×C79—81no—
112C23×C79—81no—
113C23×C79C2×D411yescharacteristic
114C22×D79—21no—
115Q8×C79—21no—
116Q8×C79—21no—
117D4×C79—24no—
118D4×C79—21no—
119D4×C79—21no—
120D4×C79#4112yes—
121D4×C79#4112yes—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2411yescharacteristic
128C22⋊D79—81no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—81no—
133C2×Dic79—81no—
134C2×Dic79—81no—
135C2×Dic79—81no—
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138C2×Dic79C2×D411yescharacteristic
139C2×Dic79C2×D411yescharacteristic
140D316—21no—
141D316—21no—
142C4×D79—81no—
143Dic158—81no—
144C8×C79—21no—
145C8×C79—21no—
146C79⋊C8—21no—
147C79⋊C8—21no—
148C22×C79—21no—
149C22×C79—22no—
150C22×C79—22no—
151C22×C79—21no—
152C22×C79—21no—
153C22×C79—41no—
154C22×C79—41no—
155C22×C79—41no—
156C22×C79—41no—
157C22×C79—84no—
158C22×C79C22×D411yescharacteristic
159C2×D79—41no—
160C2×D79—41no—
161C2×D79—41no—
162C4×C79—21no—
163C4×C79—41no—
164C4×C79—41no—
165C4×C79C2×#4111yescharacteristic
166C4×C79C2×#4111yescharacteristic
167Dic79—21no—
168Dic79—21no—
169Dic79—21no—
170Dic79—21no—
171Dic79—41no—
172Dic79—41no—
173Dic79—41no—
174C2×C79—41no—
175C2×C79—42no—
176C2×C79—42no—
177C2×C79#52511yescharacteristic
178C2×C79#57611yescharacteristic
179C2×C79#57711yescharacteristic
180D79—81no—
181#3118—791nomaximal, Sylow
182C79#311811yescharacteristic, complemented, Sylow
183#542—791no—
184#518—791no—
185#485—791no—
186#482—791no—
187#476—791no—
188#474—791no—
189#463—791no—
190#463—791no—
191#450D7911yescharacteristic, complemented
192#447—791no—
193#442—791no—
194#440—791no—
195C4×SD16—791no—
196C4×D8—791no—
197#433—791no—
198C22×D4C2×D7911yescharacteristic
199C2×SD16C2×D7911yescharacteristic
200C2×SD16C2×D7911yescharacteristic
201C2×D8—791no—
202C2×D8—791no—
203C4⋊Q8—791no—
204#126—1581no—
205#124—791no—
206#124—1581no—
207#123—1581no—
208C22⋊Q8—1581no—
209C22⋊Q8C2×D7911yescharacteristic
210#121—791no—
211C4×Q8—791no—
212C4×D4—791no—
213C4×D4—791no—
214C4×D4—791no—
215C4×D4—791no—
216C4×D4—791no—
217C4×D4—1581no—
218C4×D4—1581no—
219#117—791no—
220#117—791no—
221C2×C22⋊C4—1581no—
222C2×C22⋊C4—1581no—
223#107—791no—
224#107—791no—
225#106—791no—
226#106—791no—
227C4⋊C8—791no—
228C4⋊C8—791no—
229#103—791no—
230#103—791no—
231#102—791no—
232#102—791no—
233#102—791no—
234#102—791no—
235#102C2×D7911yescharacteristic
236#102C2×D7911yescharacteristic
237C22⋊C8—791no—
238C22⋊C8C2×D7911yescharacteristic
239#97—791no—
240C4×C8—791no—
241C24—21no—
242C2×Q8—1581no—
243C2×Q8C22×D7911yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—791no—
248C2×D4—1581no—
249C2×D4C22×D7911yescharacteristic
250C2×D4C22×D7911yescharacteristic
251C22×C4—1581no—
252C22×C4—1581no—
253C22×C4—1581no—
254C22×C4—1581no—
255C22×C4—1581no—
256C22×C4C22×D7911yescharacteristic
257SD16—22no—
258SD16—22no—
259D8—1582no—
260D8—1582no—
261C2×C8—791no—
262C2×C8—791no—
263C2×C8C22×D7911yescharacteristic
264C2×C8C22×D7911yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—791no—
267C4⋊C4—791no—
268C4⋊C4—791no—
269C4⋊C4—791no—
270C4⋊C4—791no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4C22×D7911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—791no—
276C22⋊C4—791no—
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C42—791no—
287C42—791no—
288C42—1581no—
289C42—1581no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—1581no—
296C23D4×D7911yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—6321no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—6321no—
304D4—1581no—
305D4—1581no—
306D4#1192962312yes—
307D4#1192962312yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—791no—
313C2×C4—791no—
314C2×C4—791no—
315C2×C4—791no—
316C2×C4—6321no—
317C2×C4—6321no—
318C2×C4—6321no—
319C2×C4—6321no—
320C2×C4—6321no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4—1581no—
324C2×C4D4×D7911yescharacteristic
325C2×C4C23×D7911yescharacteristic
326C8—21no—
327C8—21no—
328C8—1581no—
329C8—1581no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—3161no—
341C22—3161no—
342C22—3161no—
343C22C2×D4×D7911yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—3161no—
348C4—3161no—
349C4—3161no—
350C4—1581no—
351C4—1581no—
352C4—1581no—
353C4—1581no—
354C4C2×#1192962311yescharacteristic
355C4C2×#1192962311yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—6321no—
360C2#1909906911yescharacteristic
361C2#1909936711yescharacteristic
362C2#1909936911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#450×C79C2
socleC22×C79C22×D4
prime radical#19098697C2
hypercenter#450D79
hypocenterC79#3118
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #19099186C2semidirect
2. #19099038C2semidirect
3. #19098901C2semidirect
4. #19098888C2semidirect
5. #19098851C2semidirect
6. #19098841C2semidirect
7. #19098780C2semidirect
8. #19098780C2semidirect
10. #19098672C2semidirect
11. #19098664C2semidirect
12. SD16×Dic79C2semidirect
13. #19098643C2semidirect
14. #19098621C2semidirect
15. #450×C79C2semidirect
18. #14579160C22semidirect
20. #14579150C22semidirect
25. Q8×Dic79C22semidirect
32. #14579123C22semidirect
37. #14579095C22semidirect
38. #14579094C22semidirect
39. #14579093C22semidirect
40. #14579092C22semidirect
41. Dic79⋊C8C22semidirect
42. Dic79⋊C8C22semidirect
43. #14579085C22semidirect
44. #14579085C22semidirect
45. #14579083C22semidirect
46. #14579083C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
182. C79#3118semidirect
191. #450D79semidirect