Finite Group Databasebeta

← #23766856

Subgroups — #23766856

Order 10112.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579144C211yesmaximal, characteristic, complemented
2C2×#14579129C211yesmaximal, characteristic
3C22×(C2×D79)⋊C4C211yesmaximal, characteristic, complemented
4#19098498C211yesmaximal, characteristic, complemented
5#19098489C211yesmaximal, characteristic, complemented
6#19098478C211yesmaximal, characteristic, complemented
7#19098478C211yesmaximal, characteristic, complemented
8#19098454C211yesmaximal, characteristic, complemented
9#19098454C211yesmaximal, characteristic, complemented
10#19098443C211yesmaximal, characteristic, complemented
11#19098442C211yesmaximal, characteristic, complemented
12#19098436C211yesmaximal, characteristic, complemented
13#19098421C211yesmaximal, characteristic, complemented
14#19098418C211yesmaximal, characteristic, complemented
15C2×C4×D4×C79C211yesmaximal, characteristic, complemented
16C24×D79C2211yescharacteristic
17C22×C22⋊D79C2211yescharacteristic
18C22×C22⋊D79C2211yescharacteristic
19C23×Dic79C2211yescharacteristic
20#14579144—24no—
21#14579129—24no—
22C2×Dic79⋊C4C2211yescharacteristic, complemented
23C2×Dic79⋊C4C2211yescharacteristic, complemented
24C2×Dic79⋊C4C2211yescharacteristic, complemented
25C2×Dic79⋊C4C2211yescharacteristic, complemented
26C2×C22⋊Dic79C2211yescharacteristic
27C2×C22⋊Dic79C2211yescharacteristic
28C2×C22⋊Dic79C2211yescharacteristic, complemented
29C2×C22⋊Dic79C2211yescharacteristic, complemented
30C2×(C2×D79)⋊C4—24no—
31C2×(C2×D79)⋊C4C2211yescharacteristic
32C2×(C2×D79)⋊C4C2211yescharacteristic
33C2×(C2×D79)⋊C4C2211yescharacteristic
34C2×(C2×D79)⋊C4C2211yescharacteristic
35C2×(C2×D79)⋊C4C2211yescharacteristic
36C2×(C2×D79)⋊C4C2211yescharacteristic
37C2×(C2×D79)⋊C4C2211yescharacteristic
38C2×(C2×D79)⋊C4C2211yescharacteristic
39C2×(C2×D79)⋊C4C2211yescharacteristic
40C2×(C2×D79)⋊C4C2211yescharacteristic
41C79⋊#95C2211yescharacteristic, complemented
42C79⋊#95C2211yescharacteristic, complemented
43C79⋊#95C2211yescharacteristic, complemented
44C79⋊#95C2211yescharacteristic, complemented
45C79⋊#95C2211yescharacteristic, complemented
46C79⋊#95C2211yescharacteristic, complemented
47C22×D4×C79C2211yescharacteristic
48C23×C4×C79C2211yescharacteristic
49C23×C4×C79C2211yescharacteristic, complemented
50C4×D4×C79—24no—
51C2×C4⋊C4×C79C2211yescharacteristic, complemented
52C2×C22⋊C4×C79C2211yescharacteristic
53C2×C22⋊C4×C79C2211yescharacteristic, complemented
54C2×C42×C79C2211yescharacteristic, complemented
55C23×D79—22no—
56C23×D79—22no—
57C23×D79—22no—
58C23×D79—22no—
59C23×D79—22no—
60C23×D79—41no—
61C23×D79—41no—
62C23×D79C2311yescharacteristic
63C23×D79C2311yescharacteristic
64C2×C22⋊D79—22no—
65C2×C22⋊D79—22no—
66C2×C22⋊D79—22no—
67C2×C22⋊D79—22no—
68C2×C22⋊D79—41no—
69C2×C22⋊D79—41no—
70C22×Dic79—22no—
71C22×Dic79—22no—
72C22×Dic79—41no—
73C22×Dic79C2311yescharacteristic
74C22×Dic79C2311yescharacteristic
75C22×Dic79C2311yescharacteristic
76C22×Dic79C2311yescharacteristic
77C22×Dic79C2311yescharacteristic
78C22×Dic79C2311yescharacteristic
79Dic79⋊C4—22no—
80Dic79⋊C4—22no—
81Dic79⋊C4—41no—
82Dic79⋊C4—41no—
83C22⋊Dic79—22no—
84C22⋊Dic79—22no—
85C22⋊Dic79—22no—
86C22⋊Dic79—41no—
87(C2×D79)⋊C4—22no—
88(C2×D79)⋊C4—22no—
89(C2×D79)⋊C4—22no—
90(C2×D79)⋊C4—22no—
91(C2×D79)⋊C4—22no—
92(C2×D79)⋊C4—22no—
93(C2×D79)⋊C4—22no—
94(C2×D79)⋊C4—41no—
95(C2×D79)⋊C4—41no—
96(C2×D79)⋊C4D414yescomplemented
97C24×C79C2311yescharacteristic
98C24×C79C2311yescharacteristic
99C2×D4×C79—22no—
100C2×D4×C79—22no—
101C2×D4×C79D414yes—
102C22×C4×C79—22no—
103C22×C4×C79—22no—
104C22×C4×C79—22no—
105C22×C4×C79—22no—
106C22×C4×C79—41no—
107C22×C4×C79—41no—
108C22×C4×C79C2311yescharacteristic
109C22×C4×C79C2311yescharacteristic
110C22×C4×C79C2311yescharacteristic
111C22×C4×C79C2311yescharacteristic
112C22×C4×C79C2311yescharacteristic
113C4⋊C4×C79—22no—
114C22⋊C4×C79—22no—
115C22⋊C4×C79—22no—
116C42×C79—22no—
117C23×C79—21no—
118C23×C79—21no—
119C23×C79—21no—
120C23×C79—21no—
121C23×C79—21no—
122C23×C79—21no—
123C23×C79—21no—
124C23×C79—21no—
125C23×C79—21no—
126C23×C79—21no—
127C23×C79C2×D412yes—
128C23×C79C2×D412yes—
129C23×C79#4112yes—
130C23×C79#4112yes—
131C23×C79C2411yescharacteristic
132C22×D79—28no—
133C22×D79—21no—
134C22×D79—21no—
135C22×D79—21no—
136C22×D79—21no—
137C22×D79—21no—
138C22×D79—21no—
139C22×D79—21no—
140C22×D79—21no—
141C22×D79—21no—
142C22×D79—21no—
143C22×D79—21no—
144C22×D79—21no—
145C22×D79—44no—
146C22×D79—44no—
147C22×D79—44no—
148C22×D79—44no—
149C22×D79—44no—
150C22×D79—44no—
151C22×D79C2×D412yes—
152C22×D79#4112yes—
153D4×C79—28no—
154C2×C4×C79—21no—
155C2×C4×C79—21no—
156C2×C4×C79—21no—
157C2×C4×C79—21no—
158C2×C4×C79—21no—
159C2×C4×C79—21no—
160C2×C4×C79—21no—
161C2×C4×C79—21no—
162C2×C4×C79—21no—
163C2×C4×C79—21no—
164C2×C4×C79—21no—
165C2×C4×C79—21no—
166C2×C4×C79—21no—
167C2×C4×C79—44no—
168C2×C4×C79—44no—
169C2×C4×C79C2×D412yes—
170C2×C4×C79C2×D412yes—
171C22⋊D79—44no—
172C22⋊D79—44no—
173C2×Dic79—21no—
174C2×Dic79—21no—
175C2×Dic79—21no—
176C2×Dic79—21no—
177C2×Dic79—21no—
178C2×Dic79—21no—
179C2×Dic79—21no—
180C2×Dic79—21no—
181C2×Dic79—21no—
182C2×Dic79—21no—
183C2×Dic79—21no—
184C2×Dic79—21no—
185C2×Dic79—21no—
186C2×Dic79—21no—
187C2×Dic79—21no—
188C2×Dic79—21no—
189C2×Dic79—21no—
190C2×Dic79—44no—
191C2×Dic79C2×D412yes—
192C22×C79—22no—
193C22×C79—22no—
194C22×C79—22no—
195C22×C79—22no—
196C22×C79—22no—
197C22×C79—22no—
198C22×C79—22no—
199C22×C79—22no—
200C22×C79—22no—
201C22×C79—41no—
202C22×C79—41no—
203C22×C79—41no—
204C22×C79—41no—
205C22×C79#12314yescomplemented
206C22×C79C22×D411yescharacteristic
207C22×C79C22×D411yescharacteristic
208C22×C79C2×#4111yescharacteristic
209C22×C79C2×#4111yescharacteristic
210C22×C79C2×#4111yescharacteristic
211C22×C79H(5,𝔽2)11yescharacteristic
212C22×C79H(5,𝔽2)11yescharacteristic
213C2×D79—22no—
214C2×D79—22no—
215C2×D79—22no—
216C2×D79—22no—
217C2×D79—22no—
218C2×D79—22no—
219C2×D79—416no—
220C2×D79—41no—
221C2×D79—41no—
222C2×D79—41no—
223C2×D79—41no—
224C2×D79—41no—
225C2×D79—41no—
226C2×D79—41no—
227C2×D79—41no—
228C4×C79—22no—
229C4×C79—22no—
230C4×C79—41no—
231C4×C79—41no—
232C4×C79—41no—
233Dic79—22no—
234Dic79—41no—
235Dic79—41no—
236Dic79—41no—
237Dic79—41no—
238Dic79—41no—
239C2×C79—24no—
240C2×C79—42no—
241C2×C79C2×#12311yescharacteristic
242C2×C79#52511yescharacteristic
243C2×C79#53811yescharacteristic
244C2×C79D4211yescharacteristic
245C2×C79#54611yescharacteristic
246C2×C79#54611yescharacteristic
247C2×C79#55111yescharacteristic
248D79—42no—
249D79—42no—
250#2418—791nomaximal, Sylow
251C79#241811yescharacteristic, complemented, Sylow
252C2×#123—791no—
253C2×#120—791no—
254C2×C4×D4D7911yescharacteristic, complemented
255C22×C22⋊C4—791no—
256#399—791no—
257#397—791no—
258#394—791no—
259#394—791no—
260#388—791no—
261#388—791no—
262#386—791no—
263#386—791no—
264#385—791no—
265#380—791no—
266#379—791no—
267C25—791no—
268C22×D4—791no—
269C22×D4—791no—
270C22×D4C2×D7911yescharacteristic
271C23×C4—791no—
272C23×C4C2×D7911yescharacteristic
273C23×C4C2×D7911yescharacteristic, complemented
274#123—1584no—
275#120—1584no—
276C4×D4—24no—
277C2×C4⋊C4—791no—
278C2×C4⋊C4—791no—
279C2×C4⋊C4—791no—
280C2×C4⋊C4—791no—
281C2×C4⋊C4C2×D7911yescharacteristic, complemented
282C2×C22⋊C4—791no—
283C2×C22⋊C4—791no—
284C2×C22⋊C4—791no—
285C2×C22⋊C4—791no—
286C2×C22⋊C4—791no—
287C2×C22⋊C4—791no—
288C2×C22⋊C4—791no—
289C2×C22⋊C4—791no—
290C2×C22⋊C4—791no—
291C2×C22⋊C4—791no—
292C2×C22⋊C4—791no—
293C2×C22⋊C4—791no—
294C2×C22⋊C4—791no—
295C2×C22⋊C4—791no—
296C2×C22⋊C4—1584no—
297C2×C22⋊C4C2×D7911yescharacteristic
298C2×C22⋊C4C2×D7911yescharacteristic, complemented
299C2×C42C2×D7911yescharacteristic, complemented
300#95—791no—
301#95—791no—
302#95—791no—
303#95—791no—
304#95—791no—
305#95—791no—
306C24—3161no—
307C24—3161no—
308C24—791no—
309C24—791no—
310C24—1582no—
311C24—1582no—
312C24—1582no—
313C24—1582no—
314C24—1582no—
315C24C22×D7911yescharacteristic
316C24C22×D7911yescharacteristic
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—3161no—
320C2×D4—3161no—
321C2×D4—1582no—
322C2×D4—1582no—
323C2×D4—1582no—
324C2×D4—1582no—
325C2×D4C22⋊D7914yes—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—3161no—
333C22×C4—791no—
334C22×C4—791no—
335C22×C4—791no—
336C22×C4—791no—
337C22×C4—791no—
338C22×C4—791no—
339C22×C4—1582no—
340C22×C4—1582no—
341C22×C4C22×D7911yescharacteristic
342C22×C4C22×D7911yescharacteristic
343C22×C4C22×D7911yescharacteristic
344C22×C4C22×D7911yescharacteristic
345C22×C4C22×D7911yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—3161no—
348C4⋊C4—3161no—
349C4⋊C4—1582no—
350C4⋊C4—1582no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—3161no—
354C22⋊C4—3161no—
355C22⋊C4—3161no—
356C22⋊C4—794no—
357C22⋊C4—1582no—
358C22⋊C4—1582no—
359C22⋊C4—1582no—
360C22⋊C4—1582no—
361C22⋊C4—1582no—
362C22⋊C4—1582no—
363C22⋊C4—1582no—
364C22⋊C4—1582no—
365C22⋊C4—1582no—
366C22⋊C4—1582no—
367C42—22no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—3164no—
379C23—3164no—
380C23—3164no—
381C23—3164no—
382C23—3164no—
383C23—3164no—
384C23—792no—
385C23—792no—
386C23—1588no—
387C23—1581no—
388C23—1581no—
389C23—1581no—
390C23—1581no—
391C23—1581no—
392C23—1581no—
393C23—1581no—
394C23—1581no—
395C23—1581no—
396C23—1581no—
397C23—1581no—
398C23—1581no—
399C23C2×C22⋊D7912yes—
400C23C2×C22⋊D7912yes—
401C23#1192962412yes—
402C23#1192962412yes—
403C23C23×D7911yescharacteristic
404D4—28no—
405D4—3164no—
406D4—3164no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—44no—
421C2×C4—44no—
422C2×C4—3164no—
423C2×C4—792no—
424C2×C4—1581no—
425C2×C4—1581no—
426C2×C4—1581no—
427C2×C4—1581no—
428C2×C4—1581no—
429C2×C4—1581no—
430C2×C4—1581no—
431C2×C4—1581no—
432C2×C4—1581no—
433C2×C4—1581no—
434C2×C4—1581no—
435C2×C4—1581no—
436C2×C4—1581no—
437C2×C4—1581no—
438C2×C4—1581no—
439C2×C4—1581no—
440C2×C4—1581no—
441C2×C4D4×D7912yes—
442C2×C4C2×C22⋊D7912yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—31616no—
457C22—3161no—
458C22—3161no—
459C22—3161no—
460C22—3161no—
461C22—3161no—
462C22—3161no—
463C22—3161no—
464C22—3161no—
465C22—1582no—
466C22—1582no—
467C22—1582no—
468C22—1582no—
469C22—1582no—
470C22—1582no—
471C22#1457914414yescomplemented
472C22C2×D4×D7911yescharacteristic
473C22C22×C22⋊D7911yescharacteristic
474C22#41×D7911yescharacteristic
475C22C2×#1192962411yescharacteristic
476C22C2×#1192962411yescharacteristic
477C22#1457920611yescharacteristic
478C22#1457920711yescharacteristic
479C4—22no—
480C4—22no—
481C4—41no—
482C4—41no—
483C4—41no—
484C4—3161no—
485C4—3161no—
486C4—3161no—
487C4—3161no—
488C4—3161no—
489C4—1582no—
490C2—24no—
491C2—42no—
492C2—3162no—
493C2—3162no—
494C2C2×#1457914411yescharacteristic
495C2#1909907211yescharacteristic
496C2#1909914611yescharacteristic
497C2D4×C22⋊D7911yescharacteristic
498C2#1909920111yescharacteristic
499C2#1909920911yescharacteristic
500C2#1909924211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
FittingC2×C4×D4×C79C2
prime radicalC2×#14579129C2
hypercenterC2×C4×D4D79
hypocenterC79#2418
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14579144C2semidirect
3. C22×(C2×D79)⋊C4C2semidirect
4. #19098498C2semidirect
5. #19098489C2semidirect
6. #19098478C2semidirect
7. #19098478C2semidirect
8. #19098454C2semidirect
9. #19098454C2semidirect
10. #19098443C2semidirect
11. #19098442C2semidirect
12. #19098436C2semidirect
13. #19098421C2semidirect
14. #19098418C2semidirect
15. C2×C4×D4×C79C2semidirect
22. C2×Dic79⋊C4C22semidirect
23. C2×Dic79⋊C4C22semidirect
24. C2×Dic79⋊C4C22semidirect
25. C2×Dic79⋊C4C22semidirect
28. C2×C22⋊Dic79C22semidirect
29. C2×C22⋊Dic79C22semidirect
41. C79⋊#95C22semidirect
42. C79⋊#95C22semidirect
43. C79⋊#95C22semidirect
44. C79⋊#95C22semidirect
45. C79⋊#95C22semidirect
46. C79⋊#95C22semidirect
49. C23×C4×C79C22semidirect
51. C2×C4⋊C4×C79C22semidirect
53. C2×C22⋊C4×C79C22semidirect
54. C2×C42×C79C22semidirect
96. (C2×D79)⋊C4D4semidirect
205. C22×C79#123semidirect
251. C79#2418semidirect
254. C2×C4×D4D79semidirect
273. C23×C4C2×D79semidirect
281. C2×C4⋊C4C2×D79semidirect
298. C2×C22⋊C4C2×D79semidirect
299. C2×C42C2×D79semidirect
471. C22#14579144semidirect