Finite Group Databasebeta

← #23774889

Subgroups — #23774889

Order 10112.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D79C211yesmaximal, characteristic, complemented
2#19099220C211yesmaximal, characteristic, complemented
3D4×C22⋊D79C211yesmaximal, characteristic, complemented
4#19098951C211yesmaximal, characteristic, complemented
5#19098809C211yesmaximal, characteristic, complemented
6#19098796C211yesmaximal, characteristic, complemented
7#19098776C211yesmaximal, characteristic, complemented
8#19098761C211yesmaximal, characteristic, complemented
9#19098714C211yesmaximal, characteristic, complemented
10#19098708C211yesmaximal, characteristic, complemented
11#19098700C211yesmaximal, characteristic, complemented
12#19098695C211yesmaximal, characteristic, complemented
13#19098664C211yesmaximal, characteristic, complemented
14#19098632C211yesmaximal, characteristic, complemented
15C2×AGL(1,ℤ/8)×C79C211yesmaximal, characteristic, complemented
16C2×Q8×D79C2211yescharacteristic, complemented
17C22×C22⋊D79—21no—
18C2×D4×D79C2211yescharacteristic
19C2×#11929613C2211yescharacteristic, complemented
20C2×#11929612C2211yescharacteristic
21C2×#11929612C2211yescharacteristic, complemented
22C2×#11929611C2211yescharacteristic, complemented
23SD16×D79—24no—
24C2×#11929609C2211yescharacteristic, complemented
25C2×C8×D79C2211yescharacteristic, complemented
26#14579157C2211yescharacteristic
27#14579148—21no—
28#14579148C2211yescharacteristic, complemented
29#14579140—21no—
30#14579140C2211yescharacteristic, complemented
31#14579135C2211yescharacteristic
32#14579133—21no—
33#14579132—21no—
34#14579132C2211yescharacteristic
35#14579132C2211yescharacteristic, complemented
36#14579130—21no—
37#14579129—21no—
38Q8×Dic79C2211yescharacteristic, complemented
39D4×Dic79C2211yescharacteristic
40C4×C22⋊D79—21no—
41C4×C22⋊D79C2211yescharacteristic
42#14579095C2211yescharacteristic, complemented
43Dic79⋊C8C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579085C2211yescharacteristic, complemented
46#14579083C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic, complemented
49#14579082C2211yescharacteristic, complemented
50C22⋊(C79⋊C8)C2211yescharacteristic, complemented
51(C2×D79)⋊C8C2211yescharacteristic, complemented
52#14579071C2211yescharacteristic, complemented
53C2×#41×C79C2211yescharacteristic, complemented
54C22×D4×C79C2211yescharacteristic
55AGL(1,ℤ/8)×C79—24no—
56C2×SD16×C79C2211yescharacteristic
57C2×SD16×C79C2211yescharacteristic, complemented
58C2×D8×C79C2211yescharacteristic
59C2×D8×C79C2211yescharacteristic, complemented
60C2×M16×C79C2211yescharacteristic, complemented
61C23×D79—21no—
62C2×Dic158—21no—
63C2×Dic158C2311yescharacteristic
64Q8×D79—22no—
65Q8×D79—41no—
66C2×D316C2311yescharacteristic
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72C2×C22⋊D79—21no—
73C2×C22⋊D79—44no—
74C2×C22⋊D79D411yescharacteristic
75D4×D79—22no—
76D4×D79—41no—
77C22×Dic79—21no—
78C2×C4×D79—21no—
79C2×C4×D79C2311yescharacteristic
80#11929613—22no—
81#11929612—22no—
82#11929612—41no—
83#11929611—22no—
84#11929609—41no—
85C2×C79⋊C8C2311yescharacteristic
86C2×C79⋊C8C2311yescharacteristic
87C8×D79—22no—
88C4⋊Dic79—21no—
89C4⋊Dic79C2311yescharacteristic
90C4⋊Dic79C2311yescharacteristic
91Dic79⋊C4—21no—
92Dic79⋊C4D411yescharacteristic
93C22⋊Dic79—21no—
94C22⋊Dic79—21no—
95C22⋊Dic79—21no—
96C22⋊Dic79—21no—
97C22⋊Dic79—21no—
98C22⋊Dic79—21no—
99C22⋊Dic79D411yescharacteristic
100(C2×D79)⋊C4—21no—
101(C2×D79)⋊C4D411yescharacteristic
102C4×Dic79—21no—
103C4×Dic79C2311yescharacteristic
104C24×C79—21no—
105#41×C79—22no—
106#41×C79—41no—
107C2×Q8×C79C2311yescharacteristic
108C2×D4×C79—22no—
109C2×D4×C79—21no—
110C2×D4×C79—21no—
111C2×D4×C79—41no—
112C2×D4×C79C2311yescharacteristic
113C2×D4×C79C2311yescharacteristic
114C2×D4×C79C2311yescharacteristic
115C22×C4×C79—21no—
116C22×C4×C79C2311yescharacteristic
117SD16×C79—22no—
118SD16×C79D414yescomplemented
119D8×C79—22no—
120D8×C79—22no—
121M16×C79—22no—
122C2×C8×C79C2311yescharacteristic
123C2×C8×C79C2311yescharacteristic
124C23×C79—21no—
125C23×C79—21no—
126C23×C79—21no—
127C23×C79—42no—
128C23×C79—42no—
129C23×C79—81no—
130C23×C79C2×D411yescharacteristic
131C22×D79—21no—
132C22×D79—42no—
133C22×D79—42no—
134C22×D79—81no—
135C22×D79C2×D411yescharacteristic
136Q8×C79—21no—
137Q8×C79C2×D412yescomplemented
138D4×C79—21no—
139D4×C79—21no—
140D4×C79—21no—
141D4×C79—21no—
142D4×C79—21no—
143D4×C79—42no—
144D4×C79—42no—
145D4×C79C2×D412yes—
146C2×C4×C79—21no—
147C2×C4×C79—21no—
148C2×C4×C79—21no—
149C2×C4×C79—42no—
150C2×C4×C79C2×D411yescharacteristic
151C2×C4×C79C2411yescharacteristic
152C22⋊D79—22no—
153C22⋊D79—42no—
154C22⋊D79—42no—
155C22⋊D79—42no—
156C22⋊D79—42no—
157C22⋊D79—42no—
158C22⋊D79—81no—
159C2×Dic79—21no—
160C2×Dic79—21no—
161C2×Dic79—21no—
162C2×Dic79—42no—
163C2×Dic79C2×D411yescharacteristic
164C2×Dic79C2×D411yescharacteristic
165C2×Dic79C2×D411yescharacteristic
166D316—21no—
167D316—21no—
168C4×D79—21no—
169C4×D79—21no—
170C4×D79—42no—
171Dic158—21no—
172Dic158—21no—
173Dic158—42no—
174C8×C79—21no—
175C8×C79C2×D412yescomplemented
176C79⋊C8—21no—
177C79⋊C8—21no—
178C22×C79—22no—
179C22×C79—21no—
180C22×C79—21no—
181C22×C79—21no—
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×C79—84no—
191C22×C79C22×D411yescharacteristic
192C2×D79—21no—
193C2×D79—21no—
194C2×D79—41no—
195C2×D79—41no—
196C2×D79—41no—
197C2×D79—84no—
198C2×D79AGL(1,ℤ/8)12yescomplemented
199C4×C79—21no—
200C4×C79—22no—
201C4×C79C22×D411yescharacteristic
202C4×C79H(5,𝔽2)11yescharacteristic
203Dic79—21no—
204Dic79—21no—
205Dic79—21no—
206Dic79—41no—
207Dic79—41no—
208Dic79—41no—
209C2×C79—42no—
210C2×C79—41no—
211C2×C79—81no—
212C2×C79—81no—
213C2×C79D4211yescharacteristic
214C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
215C2×C79#57711yescharacteristic
216D79—22no—
217D79—81no—
218#3265—791nomaximal, Sylow
219C79#326511yescharacteristic, complemented, Sylow
220C2×AGL(1,ℤ/8)D7911yescharacteristic, complemented
221C22×SD16—791no—
222#548—791no—
223D42—791no—
224#496—791no—
225#468—791no—
226#466—791no—
227#463—791no—
228#460—791no—
229#450—791no—
230#449—791no—
231#448—791no—
232#447—791no—
233#440—791no—
234#435—791no—
235C2×#41C2×D7911yescharacteristic, complemented
236C22×Q8—791no—
237C22×D4—791no—
238C22×D4—1581no—
239C22×D4C2×D7911yescharacteristic
240AGL(1,ℤ/8)—24no—
241C2×SD16—791no—
242C2×SD16—791no—
243C2×SD16—791no—
244C2×SD16—791no—
245C2×SD16—1584no—
246C2×SD16C2×D7911yescharacteristic
247C2×SD16C2×D7911yescharacteristic, complemented
248C2×D8—791no—
249C2×D8C2×D7911yescharacteristic
250C2×D8C2×D7911yescharacteristic, complemented
251C2×M16C2×D7911yescharacteristic, complemented
252C22×C8—791no—
253#127—791no—
254#124—791no—
255#124—1581no—
256C22⋊Q8—791no—
257C22⋊Q8—1581no—
258#121—791no—
259#121—791no—
260#121—791no—
261#121—1581no—
262#121—1581no—
263#120—1581no—
264#120—1581no—
265C4×Q8—791no—
266C4×D4—791no—
267C4×D4—791no—
268C4×D4—1581no—
269#107—791no—
270C4⋊C8—791no—
271#103—791no—
272#103—791no—
273#102—791no—
274#102—791no—
275#102—791no—
276#102—791no—
277C22⋊C8—791no—
278C22⋊C8—791no—
279#97—791no—
280C24—21no—
281C24—1581no—
282#41—22no—
283#41—41no—
284C2×Q8—3161no—
285C2×Q8—791no—
286C2×Q8—1581no—
287C2×Q8—1582no—
288C2×Q8C22×D7911yescharacteristic
289C2×D4—22no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—41no—
293C2×D4—3164no—
294C2×D4—3161no—
295C2×D4—791no—
296C2×D4—791no—
297C2×D4—1581no—
298C2×D4—1581no—
299C2×D4—1581no—
300C2×D4—1581no—
301C2×D4—1581no—
302C2×D4—1581no—
303C2×D4—1582no—
304C2×D4C22×D7911yescharacteristic
305C2×D4C22×D7911yescharacteristic
306C2×D4C22×D7911yescharacteristic
307C22×C4—21no—
308C22×C4—791no—
309C22×C4—1581no—
310C22×C4—1581no—
311C22×C4C22×D7911yescharacteristic
312SD16—22no—
313SD16—3161no—
314SD16—1582no—
315SD16—1582no—
316SD16—1582no—
317SD16C22⋊D7914yescomplemented
318D8—22no—
319D8—22no—
320D8—3161no—
321M16—22no—
322C2×C8—791no—
323C2×C8—791no—
324C2×C8—1582no—
325C2×C8C22×D7911yescharacteristic
326C2×C8C22×D7911yescharacteristic
327C4⋊C4—791no—
328C4⋊C4—791no—
329C4⋊C4—791no—
330C4⋊C4—1581no—
331C4⋊C4—1581no—
332C22⋊C4—791no—
333C22⋊C4—791no—
334C22⋊C4—1581no—
335C22⋊C4—1581no—
336C22⋊C4—1581no—
337C22⋊C4—1581no—
338C22⋊C4—1581no—
339C22⋊C4—1581no—
340C22⋊C4—1581no—
341C42—791no—
342C42—1581no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—81no—
349C23—3162no—
350C23—3162no—
351C23—791no—
352C23—6321no—
353C23—1581no—
354C23D4×D7911yescharacteristic
355Q8—21no—
356Q8—3162no—
357Q8—1581no—
358Q8—1581no—
359Q8C2×C22⋊D7912yescomplemented
360D4—21no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—42no—
366D4—42no—
367D4—3162no—
368D4—3162no—
369D4—3162no—
370D4—3162no—
371D4—3162no—
372D4—6321no—
373D4—1582no—
374D4—1581no—
375D4—1581no—
376D4C2×C22⋊D7912yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—42no—
381C2×C4—3162no—
382C2×C4—3162no—
383C2×C4—791no—
384C2×C4—791no—
385C2×C4—791no—
386C2×C4—1581no—
387C2×C4—1581no—
388C2×C4—1581no—
389C2×C4—1581no—
390C2×C4—1581no—
391C2×C4D4×D7911yescharacteristic
392C2×C4C23×D7911yescharacteristic
393C8—21no—
394C8—1581no—
395C8—1581no—
396C8C2×C22⋊D7912yescomplemented
397C22—21no—
398C22—22no—
399C22—21no—
400C22—21no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—84no—
410C22—3161no—
411C22—3161no—
412C22—3161no—
413C22—792no—
414C22—6324no—
415C22—1581no—
416C22—1581no—
417C22C2×D4×D7911yescharacteristic
418C4—21no—
419C4—22no—
420C4—3161no—
421C4—3161no—
422C4—3161no—
423C4—1581no—
424C4—1581no—
425C4—1581no—
426C4C22×C22⋊D7911yescharacteristic
427C4#1457920611yescharacteristic
428C2—41no—
429C2—42no—
430C2—81no—
431C2—81no—
432C2—6321no—
433C2—1582no—
434C2D4×C22⋊D7911yescharacteristic
435C2AGL(1,ℤ/8)×D7911yescharacteristic
436C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC2×AGL(1,ℤ/8)×C79C2
socleC22×C79C22×D4
hypercenterC2×AGL(1,ℤ/8)D79
hypocenterC79#3265
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D79C2semidirect
2. #19099220C2semidirect
3. D4×C22⋊D79C2semidirect
4. #19098951C2semidirect
5. #19098809C2semidirect
6. #19098796C2semidirect
7. #19098776C2semidirect
8. #19098761C2semidirect
9. #19098714C2semidirect
10. #19098708C2semidirect
11. #19098700C2semidirect
12. #19098695C2semidirect
13. #19098664C2semidirect
14. #19098632C2semidirect
15. C2×AGL(1,ℤ/8)×C79C2semidirect
16. C2×Q8×D79C22semidirect
19. C2×#11929613C22semidirect
21. C2×#11929612C22semidirect
22. C2×#11929611C22semidirect
24. C2×#11929609C22semidirect
25. C2×C8×D79C22semidirect
28. #14579148C22semidirect
30. #14579140C22semidirect
35. #14579132C22semidirect
38. Q8×Dic79C22semidirect
42. #14579095C22semidirect
43. Dic79⋊C8C22semidirect
44. #14579086C22semidirect
45. #14579085C22semidirect
46. #14579083C22semidirect
48. #14579082C22semidirect
49. #14579082C22semidirect
50. C22⋊(C79⋊C8)C22semidirect
51. (C2×D79)⋊C8C22semidirect
52. #14579071C22semidirect
53. C2×#41×C79C22semidirect
57. C2×SD16×C79C22semidirect
59. C2×D8×C79C22semidirect
60. C2×M16×C79C22semidirect
118. SD16×C79D4semidirect
137. Q8×C79C2×D4semidirect
175. C8×C79C2×D4semidirect
198. C2×D79AGL(1,ℤ/8)semidirect
219. C79#3265semidirect
220. C2×AGL(1,ℤ/8)D79semidirect
235. C2×#41C2×D79semidirect
247. C2×SD16C2×D79semidirect
250. C2×D8C2×D79semidirect
251. C2×M16C2×D79semidirect
317. SD16C22⋊D79semidirect
359. Q8C2×C22⋊D79semidirect
396. C8C2×C22⋊D79semidirect