Finite Group Databasebeta

← #23775543

Subgroups — #23775543

Order 10112.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099259C211yesmaximal, characteristic, complemented
2D4×D316C211yesmaximal, characteristic, complemented
3#19098928C211yesmaximal, characteristic, complemented
4#19098888C211yesmaximal, characteristic, complemented
5#19098882C211yesmaximal, characteristic, complemented
6#19098864C211yesmaximal, characteristic, complemented
7#19098816C211yesmaximal, characteristic, complemented
8#19098799C211yesmaximal, characteristic, complemented
9#19098759C211yesmaximal, characteristic, complemented
10#19098699C211yesmaximal, characteristic, complemented
11#19098699C211yesmaximal, characteristic, complemented
12#19098676C211yesmaximal, characteristic, complemented
13#19098569C211yesmaximal, characteristic, complemented
14C2×#14579083C211yesmaximal, characteristic, complemented
15#435×C79C211yesmaximal, characteristic, complemented
16C22×D316C2211yescharacteristic
17C22×D316C2211yescharacteristic
18C2×D4×D79—21no—
19C2×D632C2211yescharacteristic
20C2×D632C2211yescharacteristic, complemented
21C2×D632C2211yescharacteristic, complemented
22#14579158C2211yescharacteristic
23#14579156—21no—
24#14579153C2211yescharacteristic, complemented
25#14579143—21no—
26#14579136—21no—
27#14579135C2211yescharacteristic
28#14579135C2211yescharacteristic
29#14579135C2211yescharacteristic, complemented
30#14579135C2211yescharacteristic, complemented
31#14579133—21no—
32#14579131—21no—
33#14579131—21no—
34C4×D316C2211yescharacteristic
35C4×D316C2211yescharacteristic, complemented
36(C22⋊D79)⋊C4—21no—
37#14579120C2211yescharacteristic, complemented
38C2×C4⋊Dic79C2211yescharacteristic, complemented
39#14579095C2211yescharacteristic, complemented
40#14579093C2211yescharacteristic, complemented
41#14579093C2211yescharacteristic, complemented
42#14579083C2211yescharacteristic
43#14579083C2211yescharacteristic
44#14579083C2211yescharacteristic
45#14579083C2211yescharacteristic, complemented
46#14579083C2211yescharacteristic, complemented
47#14579083C2211yescharacteristic, complemented
48#14579083C2211yescharacteristic, complemented
49#14579083C2211yescharacteristic, complemented
50#14579083C2211yescharacteristic, complemented
51#14579083C2211yescharacteristic, complemented
52C2×M16×C79C2211yescharacteristic, complemented
53C22×C8×C79C2211yescharacteristic, complemented
54C4×D4×C79C2211yescharacteristic
55C4⋊C8×C79C2211yescharacteristic, complemented
56C22⋊C8×C79C2211yescharacteristic, complemented
57C22⋊C8×C79C2211yescharacteristic, complemented
58#97×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C23×D79—21no—
61C2×D316—22no—
62C2×D316—22no—
63C2×D316—21no—
64C2×D316—21no—
65C2×D316—21no—
66C2×D316—21no—
67C2×D316—41no—
68C2×D316—41no—
69C2×D316C2311yescharacteristic
70C2×D316C2311yescharacteristic
71C2×D316C2311yescharacteristic
72C2×D316C2311yescharacteristic
73C2×C22⋊D79—21no—
74C2×C22⋊D79—21no—
75C2×C22⋊D79—21no—
76C2×C22⋊D79—21no—
77D4×D79—44no—
78C22×Dic79—21no—
79C2×C4×D79—21no—
80C2×C4×D79—21no—
81D632—22no—
82D632—41no—
83D632—41no—
84C4⋊Dic79—21no—
85C4⋊Dic79C2311yescharacteristic
86C4⋊Dic79C2311yescharacteristic
87C4⋊Dic79C2311yescharacteristic
88C4⋊Dic79C2311yescharacteristic
89Dic79⋊C4—21no—
90Dic79⋊C4—21no—
91C22⋊Dic79—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4—21no—
98C4×Dic79—21no—
99C2×D4×C79D411yescharacteristic
100C22×C4×C79C2311yescharacteristic
101C22×C4×C79C2311yescharacteristic
102M16×C79—41no—
103C2×C8×C79—41no—
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C2×C8×C79C2311yescharacteristic
108C4⋊C4×C79D411yescharacteristic
109C22⋊C4×C79D411yescharacteristic
110C22⋊C4×C79D411yescharacteristic
111C42×C79C2311yescharacteristic
112C23×C79C2×D411yescharacteristic
113C23×C79C2×D411yescharacteristic
114C22×D79—21no—
115C22×D79—21no—
116C22×D79—21no—
117C22×D79—21no—
118C22×D79—42no—
119C22×D79—42no—
120C22×D79—42no—
121C22×D79—42no—
122C22×D79—81no—
123C22×D79—81no—
124D4×C79—22no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2×D411yescharacteristic
131C2×C4×C79C2×D411yescharacteristic
132C2×C4×C79C2×D411yescharacteristic
133C2×C4×C79C2411yescharacteristic
134C22⋊D79—42no—
135C22⋊D79—42no—
136C22⋊D79—42no—
137C22⋊D79—81no—
138C2×Dic79—21no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142C2×Dic79—81no—
143D316—21no—
144D316—21no—
145D316—21no—
146D316—21no—
147D316—21no—
148D316—21no—
149D316—21no—
150D316—42no—
151D316—42no—
152D316—42no—
153D316—81no—
154D316#4112yes—
155C4×D79—42no—
156C4×D79—81no—
157C8×C79—21no—
158C8×C79—21no—
159C8×C79—21no—
160C8×C79—21no—
161C22×C79—21no—
162C22×C79—21no—
163C22×C79—21no—
164C22×C79—21no—
165C22×C79—21no—
166C22×C79AGL(1,ℤ/8)12yes—
167C22×C79C22×D411yescharacteristic
168C2×D79—22no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—41no—
172C2×D79—41no—
173C2×D79—41no—
174C2×D79—41no—
175C2×D79—41no—
176C2×D79—41no—
177C2×D79—41no—
178C2×D79—41no—
179C2×D79—41no—
180C2×D79—84no—
181C2×D79—84no—
182C4×C79—21no—
183C4×C79—21no—
184C4×C79—21no—
185C4×C79—21no—
186C4×C79C2×#4111yescharacteristic
187C4×C79H(5,𝔽2)11yescharacteristic
188Dic79—41no—
189Dic79—41no—
190Dic79—41no—
191Dic79—41no—
192C2×C79—22no—
193C2×C79—41no—
194C2×C79#54611yescharacteristic
195C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
196C2×C79#57611yescharacteristic
197D79—42no—
198D79—81no—
199D79—81no—
200D79—81no—
201#3318—791nomaximal, Sylow
202C79#331811yescharacteristic, complemented, Sylow
203#553—791no—
204D42—791no—
205#490—791no—
206#482—791no—
207#481—791no—
208#478—791no—
209#469—791no—
210#466—791no—
211#459—791no—
212#447—791no—
213#447—791no—
214#442—791no—
215#435D7911yescharacteristic, complemented
216#418—791no—
217C2×#102—791no—
218C22×D4—791no—
219C22×D4—791no—
220C22×D4—1581no—
221C2×D8—791no—
222C2×D8—791no—
223C2×D8—791no—
224C2×M16C2×D7911yescharacteristic, complemented
225C22×C8C2×D7911yescharacteristic, complemented
226#127—791no—
227#126—1581no—
228#125—791no—
229#123—1581no—
230#121—791no—
231#121—791no—
232#121—791no—
233#121—791no—
234#121—1581no—
235#121—1581no—
236#120—1581no—
237#120—1581no—
238C4×D4—791no—
239C4×D4—791no—
240C4×D4—1581no—
241C4×D4C2×D7911yescharacteristic
242#117—791no—
243C2×C4⋊C4—791no—
244#107—791no—
245#106—791no—
246#106—791no—
247C4⋊C8C2×D7911yescharacteristic, complemented
248#102—791no—
249#102—791no—
250#102—791no—
251#102—791no—
252#102—791no—
253#102—791no—
254#102—791no—
255#102—791no—
256#102—791no—
257#102—791no—
258C22⋊C8C2×D7911yescharacteristic, complemented
259C22⋊C8C2×D7911yescharacteristic, complemented
260#97C2×D7911yescharacteristic, complemented
261C24—1581no—
262C24—1581no—
263C2×D4—3161no—
264C2×D4—3161no—
265C2×D4—3164no—
266C2×D4—791no—
267C2×D4—791no—
268C2×D4—791no—
269C2×D4—791no—
270C2×D4—1582no—
271C2×D4—1582no—
272C2×D4—1581no—
273C2×D4—1581no—
274C2×D4—1581no—
275C2×D4—1581no—
276C2×D4—1581no—
277C2×D4—1581no—
278C2×D4—1581no—
279C2×D4—1581no—
280C2×D4D31611yescharacteristic
281C22×C4—1581no—
282C22×C4—1581no—
283C22×C4—1581no—
284C22×C4C22×D7911yescharacteristic
285C22×C4C22×D7911yescharacteristic
286D8—3161no—
287D8—3161no—
288D8—1582no—
289M16—41no—
290C2×C8—41no—
291C2×C8C22×D7911yescharacteristic
292C2×C8C22×D7911yescharacteristic
293C2×C8C22×D7911yescharacteristic
294C2×C8C22×D7911yescharacteristic
295C4⋊C4—791no—
296C4⋊C4—791no—
297C4⋊C4—791no—
298C4⋊C4—791no—
299C4⋊C4—1581no—
300C4⋊C4—1581no—
301C4⋊C4—1581no—
302C4⋊C4D31611yescharacteristic
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C22⋊C4—1581no—
306C22⋊C4—1581no—
307C22⋊C4—1581no—
308C22⋊C4—1581no—
309C22⋊C4—1581no—
310C22⋊C4D31611yescharacteristic
311C22⋊C4D31611yescharacteristic
312C42—1581no—
313C42C22×D7911yescharacteristic
314C23—3162no—
315C23—3162no—
316C23—3162no—
317C23—3162no—
318C23—6321no—
319C23—6321no—
320C23—1581no—
321C23—1581no—
322C23—1581no—
323C23—1581no—
324C23C2×D31611yescharacteristic
325C23C2×D31611yescharacteristic
326D4—22no—
327D4—3162no—
328D4—3162no—
329D4—3162no—
330D4—3162no—
331D4—3162no—
332D4—3162no—
333D4—792no—
334D4—6321no—
335D4—6321no—
336D4—1581no—
337D4—1581no—
338D4—1581no—
339D4—1581no—
340D4—1581no—
341D4—1581no—
342D4—1581no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—3162no—
348C2×C4—6321no—
349C2×C4—6321no—
350C2×C4—1581no—
351C2×C4—1581no—
352C2×C4—1581no—
353C2×C4—1581no—
354C2×C4C2×D31611yescharacteristic
355C2×C4C2×D31611yescharacteristic
356C2×C4C2×D31611yescharacteristic
357C2×C4C2×D31611yescharacteristic
358C2×C4C23×D7911yescharacteristic
359C8—21no—
360C8—21no—
361C8—21no—
362C8—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—3161no—
369C22—3161no—
370C22—3161no—
371C22—3161no—
372C22—3161no—
373C22—3161no—
374C22—3161no—
375C22—3161no—
376C22—3161no—
377C22—3161no—
378C22—3161no—
379C22—6324no—
380C22—6324no—
381C22—1582no—
382C22#1457918912yes—
383C22C22×D31611yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—3161no—
389C4—3161no—
390C4—3161no—
391C4—3161no—
392C4#41×D7911yescharacteristic
393C4#1457920611yescharacteristic
394C2—22no—
395C2—41no—
396C2—3162no—
397C2—6321no—
398C2—6321no—
399C2—6321no—
400C2#1909920811yescharacteristic
401C2C2×#1457918911yescharacteristic
402C2#1909936811yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#435×C79C2
socleC22×C79C22×D4
hypercenter#435D79
hypocenterC79#3318
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #19099259C2semidirect
2. D4×D316C2semidirect
3. #19098928C2semidirect
4. #19098888C2semidirect
5. #19098882C2semidirect
6. #19098864C2semidirect
7. #19098816C2semidirect
8. #19098799C2semidirect
9. #19098759C2semidirect
10. #19098699C2semidirect
11. #19098699C2semidirect
12. #19098676C2semidirect
13. #19098569C2semidirect
14. C2×#14579083C2semidirect
15. #435×C79C2semidirect
20. C2×D632C22semidirect
21. C2×D632C22semidirect
24. #14579153C22semidirect
29. #14579135C22semidirect
30. #14579135C22semidirect
35. C4×D316C22semidirect
37. #14579120C22semidirect
38. C2×C4⋊Dic79C22semidirect
39. #14579095C22semidirect
40. #14579093C22semidirect
41. #14579093C22semidirect
45. #14579083C22semidirect
46. #14579083C22semidirect
47. #14579083C22semidirect
48. #14579083C22semidirect
49. #14579083C22semidirect
50. #14579083C22semidirect
51. #14579083C22semidirect
52. C2×M16×C79C22semidirect
53. C22×C8×C79C22semidirect
55. C4⋊C8×C79C22semidirect
56. C22⋊C8×C79C22semidirect
57. C22⋊C8×C79C22semidirect
58. #97×C79C22semidirect
202. C79#3318semidirect
215. #435D79semidirect
224. C2×M16C2×D79semidirect
225. C22×C8C2×D79semidirect
247. C4⋊C8C2×D79semidirect
258. C22⋊C8C2×D79semidirect
259. C22⋊C8C2×D79semidirect
260. #97C2×D79semidirect