Finite Group Databasebeta

← #23773587

Subgroups — #23773587

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#19099037C211yesmaximal, characteristic, complemented
3#19098887C211yesmaximal, characteristic, complemented
4#19098852C211yesmaximal, characteristic, complemented
5#19098842C211yesmaximal, characteristic, complemented
6#19098781C211yesmaximal, characteristic, complemented
7#19098781C211yesmaximal, characteristic, complemented
8#19098713C211yesmaximal, characteristic, complemented
9#19098699C211yesmaximal, characteristic
10#19098674C211yesmaximal, characteristic, complemented
11#19098666C211yesmaximal, characteristic, complemented
12#19098648C211yesmaximal, characteristic, complemented
13#19098645C211yesmaximal, characteristic, complemented
14#19098621C211yesmaximal, characteristic, complemented
15#485×C79C211yesmaximal, characteristic, complemented
16C22×D316C2211yescharacteristic
17C2×#11929611C2211yescharacteristic
18C2×#11929611C2211yescharacteristic
19C2×D632C2211yescharacteristic
20C2×D632C2211yescharacteristic
21#14579160C2211yescharacteristic, complemented
22#14579156—21no—
23#14579150C2211yescharacteristic, complemented
24#14579147—21no—
25#14579143—21no—
26#14579141—21no—
27#14579135C2211yescharacteristic
28Q8×Dic79C2211yescharacteristic, complemented
29C4×D316—21no—
30C4×D316—21no—
31#14579123C2211yescharacteristic
32#14579123C2211yescharacteristic
33#14579123C2211yescharacteristic
34#14579123C2211yescharacteristic
35#14579123C2211yescharacteristic, complemented
36#14579120C2211yescharacteristic
37C22⋊C4×D79—21no—
38C22⋊C4×D79—21no—
39#14579094C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic
44#14579083C2211yescharacteristic
45#14579081C2211yescharacteristic
46#14579081C2211yescharacteristic
47#14579081C2211yescharacteristic, complemented
48#14579081C2211yescharacteristic, complemented
49C22⋊(C79⋊C8)C2211yescharacteristic
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C22⋊Q8×C79C2211yescharacteristic
53#117×C79C2211yescharacteristic
54#107×C79C2211yescharacteristic, complemented
55#106×C79C2211yescharacteristic, complemented
56#103×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58C22⋊C8×C79C2211yescharacteristic
59C23×D79—21no—
60C2×Dic158—21no—
61C2×D316—22no—
62C2×D316—22no—
63C2×D316—21no—
64C2×D316C2311yescharacteristic
65C2×D316C2311yescharacteristic
66C2×D316C2311yescharacteristic
67C2×C22⋊D79—21no—
68C2×C4×D79—21no—
69C2×C4×D79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73#11929611—22no—
74#11929611—22no—
75D632—22no—
76D632—22no—
77C2×C79⋊C8C2311yescharacteristic
78C2×C79⋊C8C2311yescharacteristic
79C4⋊Dic79—21no—
80C4⋊Dic79D411yescharacteristic
81C4⋊Dic79D411yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83Dic79⋊C4—21no—
84C22⋊Dic79D411yescharacteristic
85C22⋊Dic79D411yescharacteristic
86(C2×D79)⋊C4—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×Dic79C2311yescharacteristic
96C4×Dic79C2311yescharacteristic
97C2×Q8×C79C2311yescharacteristic
98C22×C4×C79C2311yescharacteristic
99C2×C8×C79C2311yescharacteristic
100C2×C8×C79C2311yescharacteristic
101C4⋊C4×C79—21no—
102C4⋊C4×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C42×C79—21no—
108C23×C79C2×D411yescharacteristic
109C22×D79—21no—
110C22×D79—21no—
111C22×D79—24no—
112C22×D79—21no—
113C22×D79—81no—
114C22×D79—81no—
115Q8×C79—21no—
116Q8×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79C2×D411yescharacteristic
124C2×C4×C79C2411yescharacteristic
125C22⋊D79—81no—
126C2×Dic79—21no—
127C2×Dic79C2×D411yescharacteristic
128C2×Dic79C2×D411yescharacteristic
129C2×Dic79C2×D411yescharacteristic
130C2×Dic79C2×D411yescharacteristic
131D316—24no—
132D316—21no—
133D316—21no—
134D316—21no—
135D316—21no—
136D316#4112yes—
137D316#4112yes—
138C4×D79—81no—
139C4×D79—81no—
140C4×D79—81no—
141C4×D79—81no—
142C4×D79—81no—
143Dic158—81no—
144C8×C79—21no—
145C8×C79—21no—
146C79⋊C8—21no—
147C79⋊C8—21no—
148C22×C79—21no—
149C22×C79—21no—
150C22×C79—21no—
151C22×C79C22×D411yescharacteristic
152C2×D79—22no—
153C2×D79—22no—
154C2×D79—41no—
155C2×D79—41no—
156C2×D79—41no—
157C2×D79—41no—
158C2×D79—41no—
159C2×D79—41no—
160C2×D79—41no—
161C2×D79—84no—
162C4×C79—21no—
163C4×C79—41no—
164C4×C79—41no—
165C4×C79—41no—
166C4×C79—41no—
167C4×C79C2×#4111yescharacteristic
168C4×C79C2×#4111yescharacteristic
169Dic79—21no—
170Dic79—21no—
171Dic79—21no—
172Dic79—21no—
173Dic79—41no—
174C2×C79—41no—
175C2×C79#52511yescharacteristic
176C2×C79#57611yescharacteristic
177C2×C79#57711yescharacteristic
178D79—42no—
179D79—42no—
180D79—81no—
181#3118—791nomaximal, Sylow
182C79#311811yescharacteristic, complemented, Sylow
183#542—791no—
184#518—791no—
185#485D7911yescharacteristic, complemented
186#482—791no—
187#476—791no—
188#474—791no—
189#463—791no—
190#463—791no—
191#450—791no—
192#447—791no—
193#442—791no—
194#440—791no—
195C4×SD16—791no—
196C4×D8—791no—
197#433—791no—
198C22×D4—791no—
199C2×SD16—791no—
200C2×SD16—791no—
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#117C2×D7911yescharacteristic
221C2×C22⋊C4—1581no—
222C2×C22⋊C4—1581no—
223#107—791no—
224#107C2×D7911yescharacteristic, complemented
225#106—791no—
226#106C2×D7911yescharacteristic, complemented
227C4⋊C8—791no—
228C4⋊C8—791no—
229#103C2×D7911yescharacteristic, complemented
230#103C2×D7911yescharacteristic, complemented
231#102—791no—
232#102—791no—
233#102—791no—
234#102—791no—
235#102—791no—
236#102—791no—
237C22⋊C8—791no—
238C22⋊C8C2×D7911yescharacteristic
239#97—791no—
240C4×C8—791no—
241C24—1581no—
242C2×Q8—1581no—
243C2×Q8C22×D7911yescharacteristic
244C2×D4—791no—
245C2×D4—791no—
246C2×D4—791no—
247C2×D4—1582no—
248C2×D4—1582no—
249C2×D4—1581no—
250C2×D4—1581no—
251C22×C4—1581no—
252C22×C4—1581no—
253C22×C4—1581no—
254C22×C4—1581no—
255C22×C4—1581no—
256C22×C4C22×D7911yescharacteristic
257SD16—1582no—
258SD16—1582no—
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—1581no—
270C4⋊C4—1581no—
271C4⋊C4C22×D7911yescharacteristic
272C4⋊C4C22×D7911yescharacteristic
273C4⋊C4C22×D7911yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—791no—
277C22⋊C4—791no—
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—21no—
287C42—791no—
288C42—791no—
289C42—1581no—
290C23—6321no—
291C23—6321no—
292C23—1584no—
293C23—1581no—
294C23—1581no—
295C23—1581no—
296C23D4×D7911yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—6321no—
300D4—792no—
301D4—792no—
302D4—6321no—
303D4—1584no—
304D4—1581no—
305D4—1581no—
306D4—1581no—
307D4—1581no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—791no—
315C2×C4—791no—
316C2×C4—791no—
317C2×C4—791no—
318C2×C4—6321no—
319C2×C4—6321no—
320C2×C4—6321no—
321C2×C4—6321no—
322C2×C4—6321no—
323C2×C4—1581no—
324C2×C4D4×D7911yescharacteristic
325C2×C4C23×D7911yescharacteristic
326C8—21no—
327C8—21no—
328C8—1581no—
329C8—1581no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—3161no—
334C22—3161no—
335C22—3161no—
336C22—3161no—
337C22—3161no—
338C22—3161no—
339C22—3161no—
340C22—6324no—
341C22—1582no—
342C22—1582no—
343C22C2×D4×D7911yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—3161no—
350C4—1581no—
351C4—1581no—
352C4—1581no—
353C4—1581no—
354C4#41×D7911yescharacteristic
355C4#41×D7911yescharacteristic
356C2—41no—
357C2—3162no—
358C2—3162no—
359C2—6321no—
360C2#1909907111yescharacteristic
361C2#1909936511yescharacteristic
362C2#1909937211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#485×C79C2
socleC22×C79C22×D4
prime radical#19098699C2
hypercenter#485D79
hypocenterC79#3118
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #19099186C2semidirect
2. #19099037C2semidirect
3. #19098887C2semidirect
4. #19098852C2semidirect
5. #19098842C2semidirect
6. #19098781C2semidirect
7. #19098781C2semidirect
8. #19098713C2semidirect
10. #19098674C2semidirect
11. #19098666C2semidirect
12. #19098648C2semidirect
13. #19098645C2semidirect
14. #19098621C2semidirect
15. #485×C79C2semidirect
21. #14579160C22semidirect
23. #14579150C22semidirect
28. Q8×Dic79C22semidirect
35. #14579123C22semidirect
39. #14579094C22semidirect
40. #14579092C22semidirect
41. Dic79⋊C8C22semidirect
42. Dic79⋊C8C22semidirect
47. #14579081C22semidirect
48. #14579081C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
54. #107×C79C22semidirect
55. #106×C79C22semidirect
56. #103×C79C22semidirect
57. #103×C79C22semidirect
182. C79#3118semidirect
185. #485D79semidirect
224. #107C2×D79semidirect
226. #106C2×D79semidirect
229. #103C2×D79semidirect
230. #103C2×D79semidirect