Finite Group Databasebeta

← #23774875

Subgroups — #23774875

Order 10112.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579185C211yesmaximal, characteristic, complemented
2C2×D8×D79C211yesmaximal, characteristic, complemented
3#19099208C211yesmaximal, characteristic, complemented
4#19099198C211yesmaximal, characteristic, complemented
5#19098950C211yesmaximal, characteristic, complemented
6#19098815C211yesmaximal, characteristic, complemented
7#19098791C211yesmaximal, characteristic, complemented
8#19098779C211yesmaximal, characteristic, complemented
9#19098715C211yesmaximal, characteristic, complemented
10#19098705C211yesmaximal, characteristic, complemented
11#19098698C211yesmaximal, characteristic, complemented
12#19098695C211yesmaximal, characteristic, complemented
13#19098673C211yesmaximal, characteristic, complemented
14#19098633C211yesmaximal, characteristic, complemented
15#459×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic, complemented
17C2×D4×D79—21no—
18C2×D4×D79C2211yescharacteristic
19C2×D4×D79C2211yescharacteristic, complemented
20C2×D4×D79C2211yescharacteristic, complemented
21#14579185—24no—
22C2×#11929613C2211yescharacteristic, complemented
23C2×#11929612C2211yescharacteristic, complemented
24C2×#11929612C2211yescharacteristic, complemented
25C2×D632C2211yescharacteristic
26C2×#11929609C2211yescharacteristic
27C2×#11929609C2211yescharacteristic, complemented
28C2×#11929609C2211yescharacteristic, complemented
29D8×D79—24no—
30C2×#11929607C2211yescharacteristic, complemented
31C2×C8×D79C2211yescharacteristic, complemented
32#14579149C2211yescharacteristic, complemented
33#14579145—21no—
34#14579141C2211yescharacteristic, complemented
35#14579136C2211yescharacteristic, complemented
36#14579135—21no—
37#14579132—21no—
38#14579132C2211yescharacteristic
39#14579132C2211yescharacteristic, complemented
40#14579131—21no—
41#14579129—21no—
42#14579129—21no—
43C4×D316C2211yescharacteristic
44C4×D316C2211yescharacteristic, complemented
45C2×(C2×D79)⋊C4—21no—
46#14579092C2211yescharacteristic, complemented
47#14579086C2211yescharacteristic, complemented
48#14579083C2211yescharacteristic, complemented
49#14579082C2211yescharacteristic, complemented
50#14579081C2211yescharacteristic, complemented
51(C2×D79)⋊C8C2211yescharacteristic, complemented
52(C2×D79)⋊C8C2211yescharacteristic, complemented
53#14579072C2211yescharacteristic, complemented
54C2×D8×C79C2211yescharacteristic, complemented
55C2×D8×C79C2211yescharacteristic, complemented
56#127×C79C2211yescharacteristic, complemented
57C4×D4×C79C2211yescharacteristic, complemented
58C4⋊C8×C79C2211yescharacteristic, complemented
59#102×C79C2211yescharacteristic, complemented
60#102×C79C2211yescharacteristic, complemented
61C23×D79—21no—
62C23×D79—21no—
63C23×D79—21no—
64#11929623—22no—
65#11929623—41no—
66C2×Dic158C2311yescharacteristic
67C2×D316—21no—
68C2×D316D411yescharacteristic
69C2×D316C2311yescharacteristic
70C2×D316C2311yescharacteristic
71C2×C22⋊D79—21no—
72C2×C22⋊D79—21no—
73C2×C22⋊D79—21no—
74C2×C22⋊D79—21no—
75C2×C22⋊D79—21no—
76C2×C22⋊D79—21no—
77D4×D79—22no—
78D4×D79—22no—
79D4×D79—22no—
80D4×D79—41no—
81D4×D79—41no—
82D4×D79—41no—
83D4×D79—44no—
84C22×Dic79—21no—
85C2×C4×D79—21no—
86C2×C4×D79C2311yescharacteristic
87C2×C4×D79C2311yescharacteristic
88#11929613—22no—
89#11929612—22no—
90#11929612—41no—
91D632—22no—
92#11929609—22no—
93#11929609—41no—
94#11929609D414yescomplemented
95#11929607—22no—
96C2×C79⋊C8C2311yescharacteristic
97C2×C79⋊C8C2311yescharacteristic
98C8×D79—22no—
99C4⋊Dic79—21no—
100C4⋊Dic79D411yescharacteristic
101C4⋊Dic79C2311yescharacteristic
102C22⋊Dic79—21no—
103C22⋊Dic79—21no—
104(C2×D79)⋊C4—21no—
105(C2×D79)⋊C4—21no—
106(C2×D79)⋊C4—21no—
107(C2×D79)⋊C4—21no—
108(C2×D79)⋊C4—21no—
109(C2×D79)⋊C4D411yescharacteristic
110(C2×D79)⋊C4D411yescharacteristic
111C2×D4×C79—21no—
112C2×D4×C79—21no—
113C2×D4×C79C2311yescharacteristic
114C2×D4×C79C2311yescharacteristic
115C2×D4×C79C2311yescharacteristic
116C22×C4×C79—21no—
117D8×C79—22no—
118D8×C79—22no—
119C2×C8×C79C2311yescharacteristic
120C2×C8×C79C2311yescharacteristic
121C4⋊C4×C79C2311yescharacteristic
122C22⋊C4×C79—21no—
123C42×C79C2311yescharacteristic
124C23×C79—21no—
125C23×C79—21no—
126C23×C79—21no—
127C22×D79—21no—
128C22×D79—21no—
129C22×D79—42no—
130C22×D79—42no—
131C22×D79—42no—
132C22×D79—42no—
133C22×D79—42no—
134C22×D79—42no—
135C22×D79—81no—
136C22×D79—81no—
137C22×D79—81no—
138C22×D79C2×D411yescharacteristic
139C22×D79C2×D411yescharacteristic
140D4×C79—21no—
141D4×C79—21no—
142D4×C79—21no—
143D4×C79—21no—
144D4×C79—21no—
145D4×C79—42no—
146D4×C79—81no—
147D4×C79C2×D412yescomplemented
148C2×C4×C79—21no—
149C2×C4×C79—81no—
150C2×C4×C79C2×D411yescharacteristic
151C2×C4×C79C2×D411yescharacteristic
152C2×C4×C79C2411yescharacteristic
153C22⋊D79—42no—
154C22⋊D79—42no—
155C22⋊D79—42no—
156C22⋊D79—42no—
157C22⋊D79—42no—
158C22⋊D79—42no—
159C2×Dic79—21no—
160C2×Dic79—21no—
161C2×Dic79—42no—
162C2×Dic79C2×D411yescharacteristic
163C2×Dic79C2×D411yescharacteristic
164D316—22no—
165D316—21no—
166D316—21no—
167D316—21no—
168D316—81no—
169D316C2×D412yes—
170C4×D79—21no—
171C4×D79—21no—
172C4×D79—21no—
173C4×D79—21no—
174C4×D79—42no—
175Dic158—21no—
176Dic158—21no—
177C8×C79—21no—
178C8×C79—21no—
179C79⋊C8—21no—
180C79⋊C8C2×D412yescomplemented
181C22×C79—22no—
182C22×C79—41no—
183C22×C79—41no—
184C22×C79—41no—
185C22×C79—41no—
186C22×C79—41no—
187C22×C79—41no—
188C22×C79—41no—
189C22×C79—41no—
190C22×C79C22×D411yescharacteristic
191C2×D79—21no—
192C2×D79—21no—
193C2×D79—22no—
194C2×D79—21no—
195C2×D79—21no—
196C2×D79—21no—
197C2×D79—41no—
198C2×D79—41no—
199C2×D79—41no—
200C2×D79—41no—
201C2×D79—41no—
202C2×D79—84no—
203C2×D79—84no—
204C2×D79—84no—
205C2×D79AGL(1,ℤ/8)12yescomplemented
206C4×C79—21no—
207C4×C79—21no—
208C4×C79—41no—
209C4×C79C22×D411yescharacteristic
210C4×C79H(5,𝔽2)11yescharacteristic
211Dic79—21no—
212Dic79—21no—
213Dic79—41no—
214Dic79—41no—
215C2×C79—42no—
216C2×C79—81no—
217C2×C79—81no—
218C2×C79D4211yescharacteristic
219C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
220C2×C79#57611yescharacteristic
221D79—22no—
222D79—41no—
223D79—42no—
224D79—81no—
225#3264—791nomaximal, Sylow
226C79#326411yescharacteristic, complemented, Sylow
227C2×AGL(1,ℤ/8)—791no—
228C22×D8—791no—
229#546—791no—
230D42—791no—
231#496—791no—
232#469—791no—
233#465—791no—
234#463—791no—
235#459D7911yescharacteristic, complemented
236#450—791no—
237#449—791no—
238#447—791no—
239#447—791no—
240#442—791no—
241#435—791no—
242C2×#41—791no—
243C22×D4—791no—
244C22×D4—791no—
245C22×D4—791no—
246C22×D4—1581no—
247AGL(1,ℤ/8)—1584no—
248C2×SD16—791no—
249C2×SD16—791no—
250C2×SD16—791no—
251C2×D8—791no—
252C2×D8—791no—
253C2×D8—791no—
254C2×D8—791no—
255C2×D8—1584no—
256C2×D8C2×D7911yescharacteristic, complemented
257C2×D8C2×D7911yescharacteristic, complemented
258C2×M16—791no—
259C22×C8—791no—
260#127C2×D7911yescharacteristic, complemented
261#124—791no—
262#123—1581no—
263C22⋊Q8—791no—
264#121—791no—
265#121—791no—
266#121—791no—
267#121—1581no—
268#121—1581no—
269#120—1581no—
270#120—1581no—
271#120—1581no—
272C4×D4—791no—
273C4×D4—791no—
274C4×D4C2×D7911yescharacteristic, complemented
275C2×C22⋊C4—1581no—
276#106—791no—
277C4⋊C8C2×D7911yescharacteristic, complemented
278#103—791no—
279#102—791no—
280#102—791no—
281#102—791no—
282#102C2×D7911yescharacteristic, complemented
283#102C2×D7911yescharacteristic, complemented
284C22⋊C8—791no—
285C22⋊C8—791no—
286#97—791no—
287C24—1581no—
288C24—1581no—
289C24—1581no—
290#41—3161no—
291#41—1582no—
292C2×Q8—791no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—3164no—
296C2×D4—3161no—
297C2×D4—3161no—
298C2×D4—3161no—
299C2×D4—791no—
300C2×D4—791no—
301C2×D4—791no—
302C2×D4—1581no—
303C2×D4—1581no—
304C2×D4—1581no—
305C2×D4—1581no—
306C2×D4—1582no—
307C2×D4—1582no—
308C2×D4—1581no—
309C2×D4—1581no—
310C2×D4—1581no—
311C2×D4—1582no—
312C2×D4C22×D7911yescharacteristic
313C2×D4C22×D7911yescharacteristic
314C2×D4C22×D7911yescharacteristic
315C22×C4—21no—
316C22×C4—791no—
317C22×C4—791no—
318C22×C4—1581no—
319C22×C4—1581no—
320SD16—3161no—
321SD16—1582no—
322SD16—1582no—
323D8—22no—
324D8—22no—
325D8—3161no—
326D8—794no—
327D8—1582no—
328D8—1582no—
329M16—1582no—
330C2×C8—791no—
331C2×C8—791no—
332C2×C8—1582no—
333C2×C8C22×D7911yescharacteristic
334C2×C8C22×D7911yescharacteristic
335C4⋊C4—791no—
336C4⋊C4—791no—
337C4⋊C4—1581no—
338C4⋊C4C22×D7911yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—791no—
341C22⋊C4—791no—
342C22⋊C4—1581no—
343C22⋊C4—1581no—
344C22⋊C4—1581no—
345C22⋊C4—1581no—
346C22⋊C4—1581no—
347C22⋊C4—1581no—
348C22⋊C4—1581no—
349C42C22×D7911yescharacteristic
350C23—21no—
351C23—21no—
352C23—21no—
353C23—3162no—
354C23—3162no—
355C23—3162no—
356C23—3162no—
357C23—3162no—
358C23—3162no—
359C23—791no—
360C23—791no—
361C23—6321no—
362C23—6321no—
363C23—6321no—
364C23—1581no—
365C23—1581no—
366Q8—1581no—
367Q8—1581no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—21no—
373D4—42no—
374D4—81no—
375D4—3162no—
376D4—3162no—
377D4—3162no—
378D4—3162no—
379D4—3162no—
380D4—3162no—
381D4—792no—
382D4—6321no—
383D4—1582no—
384D4—1581no—
385D4—1581no—
386D4—1581no—
387D4D4×D7912yescomplemented
388C2×C4—21no—
389C2×C4—81no—
390C2×C4—3162no—
391C2×C4—3162no—
392C2×C4—791no—
393C2×C4—791no—
394C2×C4—1581no—
395C2×C4—1581no—
396C2×C4—1581no—
397C2×C4—1581no—
398C2×C4—1581no—
399C2×C4—1581no—
400C2×C4D4×D7911yescharacteristic
401C2×C4D4×D7911yescharacteristic
402C2×C4C23×D7911yescharacteristic
403C8—21no—
404C8—21no—
405C8—792no—
406C8—1581no—
407C22—22no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—3161no—
417C22—3161no—
418C22—3161no—
419C22—3161no—
420C22—3161no—
421C22—792no—
422C22—6324no—
423C22—6324no—
424C22—6324no—
425C22—1581no—
426C22—1582no—
427C22—1581no—
428C22—1581no—
429C22—1581no—
430C22—1581no—
431C22C2×D4×D7911yescharacteristic
432C4—21no—
433C4—21no—
434C4—41no—
435C4—3161no—
436C4—3161no—
437C4—1581no—
438C4—1581no—
439C4C2×D4×D7911yescharacteristic
440C4#1457920711yescharacteristic
441C2—42no—
442C2—81no—
443C2—81no—
444C2—3162no—
445C2—3161no—
446C2—6321no—
447C2—1582no—
448C2#1909919711yescharacteristic
449C2AGL(1,ℤ/8)×D7911yescharacteristic
450C2#1909936411yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#459×C79C2
socleC22×C79C22×D4
hypercenter#459D79
hypocenterC79#3264
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#14579185C2semidirect
2. C2×D8×D79C2semidirect
3. #19099208C2semidirect
4. #19099198C2semidirect
5. #19098950C2semidirect
6. #19098815C2semidirect
7. #19098791C2semidirect
8. #19098779C2semidirect
9. #19098715C2semidirect
10. #19098705C2semidirect
11. #19098698C2semidirect
12. #19098695C2semidirect
13. #19098673C2semidirect
14. #19098633C2semidirect
15. #459×C79C2semidirect
16. C2×#11929623C22semidirect
19. C2×D4×D79C22semidirect
20. C2×D4×D79C22semidirect
22. C2×#11929613C22semidirect
23. C2×#11929612C22semidirect
24. C2×#11929612C22semidirect
27. C2×#11929609C22semidirect
28. C2×#11929609C22semidirect
30. C2×#11929607C22semidirect
31. C2×C8×D79C22semidirect
32. #14579149C22semidirect
34. #14579141C22semidirect
35. #14579136C22semidirect
39. #14579132C22semidirect
44. C4×D316C22semidirect
46. #14579092C22semidirect
47. #14579086C22semidirect
48. #14579083C22semidirect
49. #14579082C22semidirect
50. #14579081C22semidirect
51. (C2×D79)⋊C8C22semidirect
52. (C2×D79)⋊C8C22semidirect
53. #14579072C22semidirect
54. C2×D8×C79C22semidirect
55. C2×D8×C79C22semidirect
56. #127×C79C22semidirect
57. C4×D4×C79C22semidirect
58. C4⋊C8×C79C22semidirect
59. #102×C79C22semidirect
60. #102×C79C22semidirect
94. #11929609D4semidirect
147. D4×C79C2×D4semidirect
180. C79⋊C8C2×D4semidirect
205. C2×D79AGL(1,ℤ/8)semidirect
226. C79#3264semidirect
235. #459D79semidirect
256. C2×D8C2×D79semidirect
257. C2×D8C2×D79semidirect
260. #127C2×D79semidirect
274. C4×D4C2×D79semidirect
277. C4⋊C8C2×D79semidirect
282. #102C2×D79semidirect
283. #102C2×D79semidirect
387. D4D4×D79semidirect