Finite Group Databasebeta

← #23774887

Subgroups — #23774887

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×#14579189C211yesmaximal, characteristic, complemented
2C2×D8×D79C211yesmaximal, characteristic, complemented
3#19099210C211yesmaximal, characteristic, complemented
4#19099197C211yesmaximal, characteristic, complemented
5#19098951C211yesmaximal, characteristic, complemented
6#19098793C211yesmaximal, characteristic, complemented
7#19098777C211yesmaximal, characteristic, complemented
8#19098757C211yesmaximal, characteristic, complemented
9#19098715C211yesmaximal, characteristic, complemented
10#19098706C211yesmaximal, characteristic, complemented
11#19098698C211yesmaximal, characteristic, complemented
12#19098696C211yesmaximal, characteristic, complemented
13#19098674C211yesmaximal, characteristic, complemented
14#19098632C211yesmaximal, characteristic, complemented
15#469×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic, complemented
17C22×D316C2211yescharacteristic, complemented
18C2×D4×D79—21no—
19C2×D4×D79C2211yescharacteristic
20C2×D4×D79C2211yescharacteristic, complemented
21#14579189—24no—
22C2×#11929613C2211yescharacteristic, complemented
23C2×#11929613C2211yescharacteristic, complemented
24C2×#11929612C2211yescharacteristic, complemented
25C2×D632C2211yescharacteristic
26C2×D632C2211yescharacteristic, complemented
27C2×#11929609C2211yescharacteristic
28C2×#11929609C2211yescharacteristic, complemented
29C2×#11929609C2211yescharacteristic, complemented
30D8×D79—24no—
31C2×C8×D79C2211yescharacteristic, complemented
32#14579157C2211yescharacteristic, complemented
33#14579148C2211yescharacteristic, complemented
34#14579143—21no—
35#14579141C2211yescharacteristic, complemented
36#14579136C2211yescharacteristic
37#14579134—21no—
38#14579132—21no—
39#14579131—21no—
40#14579129—21no—
41#14579129—21no—
42#14579123C2211yescharacteristic, complemented
43#14579123C2211yescharacteristic, complemented
44C4×C22⋊D79C2211yescharacteristic
45C22⋊C4×D79—21no—
46Dic79⋊C8C2211yescharacteristic, complemented
47#14579084C2211yescharacteristic, complemented
48#14579081C2211yescharacteristic, complemented
49#14579081C2211yescharacteristic, complemented
50#14579081C2211yescharacteristic, complemented
51C22⋊(C79⋊C8)C2211yescharacteristic, complemented
52(C2×D79)⋊C8C2211yescharacteristic, complemented
53#14579071C2211yescharacteristic, complemented
54C2×D8×C79C2211yescharacteristic, complemented
55C2×M16×C79C2211yescharacteristic, complemented
56#121×C79C2211yescharacteristic, complemented
57#121×C79C2211yescharacteristic, complemented
58#106×C79C2211yescharacteristic, complemented
59#102×C79C2211yescharacteristic, complemented
60#102×C79C2211yescharacteristic, complemented
61C23×D79—21no—
62C23×D79—21no—
63C23×D79—21no—
64#11929624—22no—
65#11929624—41no—
66C2×Dic158C2311yescharacteristic
67C2×D316—21no—
68C2×D316—22no—
69C2×D316—21no—
70C2×D316—41no—
71C2×D316C2311yescharacteristic
72C2×D316C2311yescharacteristic
73C2×D316C2311yescharacteristic
74C2×C22⋊D79—21no—
75C2×C22⋊D79—21no—
76C2×C22⋊D79—21no—
77C2×C22⋊D79—21no—
78C2×C22⋊D79—21no—
79C2×C22⋊D79D411yescharacteristic
80D4×D79—22no—
81D4×D79—22no—
82D4×D79—44no—
83D4×D79—41no—
84D4×D79—41no—
85C2×C4×D79—21no—
86C2×C4×D79—21no—
87C2×C4×D79—21no—
88C2×C4×D79C2311yescharacteristic
89#11929613—22no—
90#11929613—22no—
91#11929612—41no—
92D632—22no—
93D632D414yescomplemented
94#11929609—22no—
95#11929609—22no—
96#11929609—41no—
97C2×C79⋊C8C2311yescharacteristic
98C2×C79⋊C8C2311yescharacteristic
99C8×D79—22no—
100C4⋊Dic79—21no—
101Dic79⋊C4D411yescharacteristic
102C22⋊Dic79—21no—
103C22⋊Dic79—21no—
104C22⋊Dic79D411yescharacteristic
105(C2×D79)⋊C4—21no—
106(C2×D79)⋊C4—21no—
107(C2×D79)⋊C4—21no—
108(C2×D79)⋊C4—21no—
109(C2×D79)⋊C4D411yescharacteristic
110C4×Dic79C2311yescharacteristic
111C2×D4×C79—21no—
112C2×D4×C79—21no—
113C2×D4×C79C2311yescharacteristic
114C2×D4×C79C2311yescharacteristic
115C22×C4×C79C2311yescharacteristic
116D8×C79—22no—
117M16×C79—22no—
118C2×C8×C79C2311yescharacteristic
119C2×C8×C79C2311yescharacteristic
120C4⋊C4×C79C2311yescharacteristic
121C4⋊C4×C79C2311yescharacteristic
122C22⋊C4×C79—21no—
123C22⋊C4×C79—21no—
124C23×C79—21no—
125C23×C79—21no—
126C23×C79C2×D411yescharacteristic
127C22×D79—21no—
128C22×D79—21no—
129C22×D79—21no—
130C22×D79—42no—
131C22×D79—42no—
132C22×D79—42no—
133C22×D79—42no—
134C22×D79—42no—
135C22×D79—42no—
136C22×D79—81no—
137C22×D79—81no—
138C22×D79—81no—
139C22×D79C2×D411yescharacteristic
140D4×C79—21no—
141D4×C79—21no—
142D4×C79—21no—
143D4×C79—21no—
144D4×C79—42no—
145D4×C79—81no—
146C2×C4×C79—21no—
147C2×C4×C79—21no—
148C2×C4×C79—21no—
149C2×C4×C79—21no—
150C2×C4×C79C2×D411yescharacteristic
151C2×C4×C79C2411yescharacteristic
152C22⋊D79—22no—
153C22⋊D79—42no—
154C22⋊D79—42no—
155C22⋊D79—42no—
156C22⋊D79—42no—
157C22⋊D79—81no—
158C2×Dic79—21no—
159C2×Dic79C2×D411yescharacteristic
160C2×Dic79C2×D411yescharacteristic
161C2×Dic79C2×D411yescharacteristic
162D316—21no—
163D316—21no—
164D316—21no—
165D316—21no—
166D316—42no—
167D316—42no—
168D316C2×D412yes—
169D316C2×D412yescomplemented
170C4×D79—21no—
171C4×D79—21no—
172C4×D79—42no—
173C4×D79—42no—
174C4×D79—81no—
175Dic158—21no—
176Dic158—21no—
177C8×C79—21no—
178C8×C79C2×D412yescomplemented
179C79⋊C8—21no—
180C79⋊C8—21no—
181C22×C79—21no—
182C22×C79—21no—
183C22×C79—21no—
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—22no—
195C2×D79—41no—
196C2×D79—41no—
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—41no—
208C4×C79—41no—
209C4×C79C22×D411yescharacteristic
210C4×C79H(5,𝔽2)11yescharacteristic
211Dic79—21no—
212Dic79—21no—
213Dic79—21no—
214Dic79—41no—
215C2×C79—41no—
216C2×C79—81no—
217C2×C79—81no—
218C2×C79D4211yescharacteristic
219C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
220C2×C79#57611yescharacteristic
221D79—22no—
222D79—42no—
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#469D7911yescharacteristic, complemented
233#465—791no—
234#463—791no—
235#459—791no—
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—791no—
256C2×D8—1584no—
257C2×D8C2×D7911yescharacteristic, complemented
258C2×M16C2×D7911yescharacteristic, complemented
259C22×C8—791no—
260#127—791no—
261#124—791no—
262#123—1581no—
263C22⋊Q8—791no—
264#121—791no—
265#121—1581no—
266#121—1581no—
267#121C2×D7911yescharacteristic, complemented
268#121C2×D7911yescharacteristic, complemented
269#120—1581no—
270#120—1581no—
271#120—1581no—
272C4×D4—791no—
273C4×D4—791no—
274C4×D4—791no—
275C2×C22⋊C4—1581no—
276#106C2×D7911yescharacteristic, complemented
277C4⋊C8—791no—
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—3161no—
296C2×D4—3164no—
297C2×D4—3161no—
298C2×D4—3161no—
299C2×D4—791no—
300C2×D4—791no—
301C2×D4—791no—
302C2×D4—791no—
303C2×D4—1581no—
304C2×D4—1582no—
305C2×D4—1581no—
306C2×D4—1581no—
307C2×D4—1581no—
308C2×D4—1581no—
309C2×D4—1582no—
310C2×D4—1582no—
311C2×D4—1581no—
312C2×D4—1581no—
313C2×D4C22×D7911yescharacteristic
314C2×D4C22×D7911yescharacteristic
315C22×C4—791no—
316C22×C4—1581no—
317C22×C4—1581no—
318C22×C4—1581no—
319C22×C4C22×D7911yescharacteristic
320SD16—3161no—
321SD16—1582no—
322SD16—1582no—
323D8—22no—
324D8—3161no—
325D8—794no—
326D8—1582no—
327D8—1582no—
328D8—1582no—
329M16—22no—
330C2×C8—791no—
331C2×C8—791no—
332C2×C8—1582no—
333C2×C8C22×D7911yescharacteristic
334C2×C8C22×D7911yescharacteristic
335C4⋊C4—791no—
336C4⋊C4—1581no—
337C4⋊C4C22×D7911yescharacteristic
338C4⋊C4C22×D7911yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—791no—
342C22⋊C4—791no—
343C22⋊C4—1581no—
344C22⋊C4—1581no—
345C22⋊C4—1581no—
346C22⋊C4—1581no—
347C22⋊C4—1581no—
348C22⋊C4—1581no—
349C42—791no—
350C23—21no—
351C23—21no—
352C23—3162no—
353C23—3162no—
354C23—3162no—
355C23—3162no—
356C23—3162no—
357C23—3162no—
358C23—791no—
359C23—6321no—
360C23—6321no—
361C23—6321no—
362C23—1581no—
363C23—1581no—
364C23—1581no—
365C23D4×D7911yescharacteristic
366Q8—1581no—
367Q8—1581no—
368D4—21no—
369D4—21no—
370D4—21no—
371D4—21no—
372D4—42no—
373D4—81no—
374D4—3162no—
375D4—3162no—
376D4—3162no—
377D4—3162no—
378D4—3162no—
379D4—3162no—
380D4—792no—
381D4—792no—
382D4—6321no—
383D4—1582no—
384D4—1581no—
385D4—1581no—
386D4—1581no—
387D4—1581no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—3162no—
393C2×C4—3162no—
394C2×C4—791no—
395C2×C4—791no—
396C2×C4—791no—
397C2×C4—6321no—
398C2×C4—1581no—
399C2×C4—1581no—
400C2×C4—1581no—
401C2×C4D4×D7911yescharacteristic
402C2×C4C23×D7911yescharacteristic
403C8—21no—
404C8—1581no—
405C8—1581no—
406C8D4×D7912yescomplemented
407C22—21no—
408C22—21no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—3161no—
417C22—3161no—
418C22—3161no—
419C22—3161no—
420C22—3161no—
421C22—3161no—
422C22—3161no—
423C22—792no—
424C22—6324no—
425C22—6324no—
426C22—6324no—
427C22—1582no—
428C22—1582no—
429C22—1581no—
430C22—1581no—
431C22C2×D4×D7911yescharacteristic
432C4—21no—
433C4—41no—
434C4—41no—
435C4—3161no—
436C4—1581no—
437C4—1581no—
438C4—1581no—
439C4C2×D4×D7911yescharacteristic
440C4#1457920711yescharacteristic
441C2—41no—
442C2—81no—
443C2—81no—
444C2—3162no—
445C2—3162no—
446C2—6321no—
447C2—1582no—
448C2#1909919711yescharacteristic
449C2AGL(1,ℤ/8)×D7911yescharacteristic
450C2#1909936711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#469×C79C2
socleC22×C79C22×D4
hypercenter#469D79
hypocenterC79#3264
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×#14579189C2semidirect
2. C2×D8×D79C2semidirect
3. #19099210C2semidirect
4. #19099197C2semidirect
5. #19098951C2semidirect
6. #19098793C2semidirect
7. #19098777C2semidirect
8. #19098757C2semidirect
9. #19098715C2semidirect
10. #19098706C2semidirect
11. #19098698C2semidirect
12. #19098696C2semidirect
13. #19098674C2semidirect
14. #19098632C2semidirect
15. #469×C79C2semidirect
16. C2×#11929624C22semidirect
17. C22×D316C22semidirect
20. C2×D4×D79C22semidirect
22. C2×#11929613C22semidirect
23. C2×#11929613C22semidirect
24. C2×#11929612C22semidirect
26. C2×D632C22semidirect
28. C2×#11929609C22semidirect
29. C2×#11929609C22semidirect
31. C2×C8×D79C22semidirect
32. #14579157C22semidirect
33. #14579148C22semidirect
35. #14579141C22semidirect
42. #14579123C22semidirect
43. #14579123C22semidirect
46. Dic79⋊C8C22semidirect
47. #14579084C22semidirect
48. #14579081C22semidirect
49. #14579081C22semidirect
50. #14579081C22semidirect
51. C22⋊(C79⋊C8)C22semidirect
52. (C2×D79)⋊C8C22semidirect
53. #14579071C22semidirect
54. C2×D8×C79C22semidirect
55. C2×M16×C79C22semidirect
56. #121×C79C22semidirect
57. #121×C79C22semidirect
58. #106×C79C22semidirect
59. #102×C79C22semidirect
60. #102×C79C22semidirect
93. D632D4semidirect
169. D316C2×D4semidirect
178. C8×C79C2×D4semidirect
205. C2×D79AGL(1,ℤ/8)semidirect
226. C79#3264semidirect
232. #469D79semidirect
257. C2×D8C2×D79semidirect
258. C2×M16C2×D79semidirect
267. #121C2×D79semidirect
268. #121C2×D79semidirect
276. #106C2×D79semidirect
282. #102C2×D79semidirect
283. #102C2×D79semidirect
406. C8D4×D79semidirect