Finite Group Databasebeta

← #3531×D79 #35195166

Subgroups — #3531×D79 #35195166

Order 20224.

6554 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777548C211yesmaximal, characteristic, complemented
2#23777547C215yesmaximal, complemented
3#23777546C2110yesmaximal, complemented
4#23777545C2110yesmaximal, complemented
5#23777544C215yesmaximal, complemented
6#564×D79C211yesmaximal, characteristic, complemented
7#563×D79C2110yesmaximal, complemented
8#562×D79C215yesmaximal, complemented
9#533×D79C215yesmaximal, complemented
10#529×D79C2110yesmaximal, complemented
11C79×#3531C211yesmaximal, characteristic, complemented
12C79⋊#564C2215yescomplemented
13C79⋊#564C22110yescomplemented
14#19099317C22110yescomplemented
15#19099317C22110yescomplemented
16#19099316C22120yescomplemented
17#19099315C22120yescomplemented
18#19099315C22120yescomplemented
19#19099314C22120yescomplemented
20#19099314C22120yescomplemented
21#19099313C22110yescomplemented
22#19099312C22120yescomplemented
23#19099311C2215yescomplemented
24#19099310C22120yescomplemented
25#19099309C22120yescomplemented
26#19099308C22120yescomplemented
27#19099307C22110yescomplemented
28#19099120C2215yescomplemented
29#19099119C2215yescomplemented
30#19099119C2215yescomplemented
31#19099118C22110yescomplemented
32#19099117C22120yescomplemented
33#19099116C22110yescomplemented
34#19099115C22120yescomplemented
35C4⋊Q8×D79C22110yes—
36#19099100C22110yescomplemented
37#19099099C22110yescomplemented
38#19099098C22110yescomplemented
39#19099097C22110yescomplemented
40#19099096C22120yescomplemented
41#19099095C22110yescomplemented
42#19099094C22110yescomplemented
43#19099093C22120yescomplemented
44#19099092C22110yescomplemented
45#19099091C22120yescomplemented
46#19099090C22120yescomplemented
47#126×D79C22120yes—
48#125×D79C22110yes—
49#125×D79C2215yes—
50#125×D79C2215yes—
51#124×D79C22110yes—
52#123×D79C22120yes—
53C22⋊Q8×D79C22110yes—
54C22⋊Q8×D79C22120yes—
55#121×D79C22110yes—
56C4×Q8×D79C22110yes—
57C4×D4×D79C22110yes—
58#117×D79C22110yes—
59C2×C42×D79C2215yes—
60#564×C79C2211yescharacteristic, complemented
61#563×C79C22110yescomplemented
62#562×C79C2215yescomplemented
63#533×C79C2215yescomplemented
64#529×C79C22110yescomplemented
65C2×Q8×D79C23110yes—
66C2×D4×D79C23110yes—
67C22×C4×D79C2315yes—
68C22×C4×D79C23110yes—
69#14579161C23110yes—
70#14579160C23110yes—
71#14579160C23120yes—
72#14579160C23110yes—
73#14579159C23120yes—
74#14579156C23120yes—
75#14579156C23120yes—
76#14579156C23120yes—
77#14579155C23120yes—
78#14579154C23120yes—
79#14579154C23120yes—
80#14579154C23120yes—
81#14579153C2315yes—
82#14579153C2315yes—
83#14579153C23110yes—
84#14579152C23110yes—
85#14579152C23110yes—
86#14579152C23110yes—
87#14579152C23110yes—
88#14579151C23120yes—
89#14579151C23120yes—
90#14579151C23120yes—
91#14579151C23120yes—
92#14579150C23110yes—
93#14579149C23110yes—
94#14579148C23110yes—
95#14579147C23120yes—
96#14579147C23120yes—
97#14579146C23120yes—
98#14579146C23120yes—
99#14579145C23120yes—
100#14579144C23120yes—
101#14579143C23120yes—
102#14579143C23120yes—
103#14579142C23120yes—
104#14579141C23120yes—
105#14579141C23110yes—
106#14579140C23120yes—
107#14579140C23110yes—
108#14579139C23120yes—
109#14579139C23120yes—
110#14579139C23120yes—
111#14579138C23120yes—
112#14579138C23120yes—
113#14579138C23120yes—
114#14579137C23120yes—
115#14579137C23110yes—
116#14579136C23110yes—
117#14579135C23110yes—
118#14579134C23120yes—
119#14579133C23120yes—
120#14579132C23110yes—
121Q8×Dic79C23110yes—
122C4×Dic158C23120yes—
123C4×Dic158C23110yes—
124#14579126C23120yes—
125#14579126C23110yes—
126C4×D316C23110yes—
127D4×Dic79C23110yes—
128#14579123C23110yes—
129C4×C22⋊D79C23120yes—
130(C22⋊D79)⋊C4C23120yes—
131#14579120C23110yes—
132#14579119C23110yes—
133#14579119C23110yes—
134#14579118C23120yes—
135#14579117C23120yes—
136C4⋊C4×D79C23110yes—
137C4⋊C4×D79C23110yes—
138C4⋊C4×D79C23110yes—
139C4⋊C4×D79C23110yes—
140C4⋊C4×D79C23120yes—
141C22⋊C4×D79C23120yes—
142C22⋊C4×D79C23120yes—
143C2×C4×Dic79C23110yes—
144C2×C4×Dic79C2315yes—
145C42×D79C23110yes—
146C42×D79C2315yes—
147C42×D79C2315yes—
148C42×D79C23110yes—
149C42×D79C2315yes—
150C42×D79C2315yes—
151C4⋊Q8×C79C23110yes—
152#126×C79C23120yes—
153#125×C79C23110yes—
154#125×C79C2315yes—
155#125×C79C2315yes—
156#124×C79C23110yes—
157#123×C79C23120yes—
158C22⋊Q8×C79C23110yes—
159C22⋊Q8×C79C23120yes—
160#121×C79C23110yes—
161C4×Q8×C79C23110yes—
162C4×D4×C79C23110yes—
163#117×C79C23110yes—
164C2×C42×C79C2315yes—
165C23×D79C2415yes—
166C2×Dic158C24120yes—
167C2×Dic158C24110yes—
168Q8×D79—420no—
169C2×D316C24110yes—
170C2×C22⋊D79C24120yes—
171D4×D79—420no—
172C22×Dic79C2415yes—
173C22×Dic79C24110yes—
174C2×C4×D79—220no—
175C2×C4×D79—420no—
176C2×C4×D79C24110yes—
177C2×C4×D79C24110yes—
178C2×C4×D79C2415yes—
179C2×C4×D79C2415yes—
180C2×C4×D79C2415yes—
181C2×C4×D79C24110yes—
182C2×C4×D79C24110yes—
183C2×C4×D79C2411yescharacteristic
184C4⋊Dic79C24110yes—
185C4⋊Dic79C24110yes—
186C4⋊Dic79C24110yes—
187C4⋊Dic79C24110yes—
188C4⋊Dic79C24120yes—
189Dic79⋊C4C24120yes—
190Dic79⋊C4C24120yes—
191Dic79⋊C4C24120yes—
192Dic79⋊C4C24120yes—
193Dic79⋊C4C24120yes—
194Dic79⋊C4C24120yes—
195C22⋊Dic79C24120yes—
196C22⋊Dic79C24120yes—
197(C2×D79)⋊C4C24120yes—
198(C2×D79)⋊C4C24120yes—
199(C2×D79)⋊C4C24120yes—
200(C2×D79)⋊C4C24120yes—
201C4×Dic79C24110yes—
202C4×Dic79C24110yes—
203C4×Dic79C24110yes—
204C4×Dic79C2415yes—
205C4×Dic79C24110yes—
206C4×Dic79C24110yes—
207C4×Dic79C2415yes—
208C2×Q8×C79C24110yes—
209C2×D4×C79C24110yes—
210C22×C4×C79C2415yes—
211C22×C4×C79C24110yes—
212C4⋊C4×C79C24110yes—
213C4⋊C4×C79C24110yes—
214C4⋊C4×C79C24110yes—
215C4⋊C4×C79C24110yes—
216C4⋊C4×C79C24120yes—
217C22⋊C4×C79C24120yes—
218C22⋊C4×C79C24120yes—
219C42×C79C24110yes—
220C42×C79C2415yes—
221C42×C79C2415yes—
222C23×C79C2515yes—
223C22×D79—210no—
224C22×D79—220no—
225C22×D79C2515yes—
226C22×D79C2511yescharacteristic
227Q8×C79—410no—
228D4×C79—410no—
229C2×C4×C79—210no—
230C2×C4×C79—410no—
231C2×C4×C79C2515yes—
232C2×C4×C79C25110yes—
233C2×C4×C79C25110yes—
234C2×C4×C79C2511yescharacteristic
235C22⋊D79—420no—
236C2×Dic79—210no—
237C2×Dic79—410no—
238C2×Dic79C2515yes—
239C2×Dic79C25110yes—
240C2×Dic79C25110yes—
241C2×Dic79C2511yescharacteristic
242D316—410no—
243C4×D79—210no—
244C4×D79—220no—
245C4×D79—220no—
246C4×D79—210no—
247C4×D79—210no—
248C4×D79—410no—
249C4×D79—410no—
250C4×D792−1+414yes—
251Dic158—420no—
252Dic158—410no—
253C22×C79—25no—
254C22×C79—210no—
255C22×C79C2611yescharacteristic
256C2×D79—25no—
257C2×D79—210no—
258C2×D79—420no—
259C2×D79C2×2−1+412yes—
260C2×D79#58514yes—
261C4×C79—25no—
262C4×C79—210no—
263C4×C79—210no—
264C4×C79C2×2−1+412yes—
265Dic79—25no—
266Dic79—210no—
267Dic79—210no—
268Dic79C2×2−1+412yes—
269C2×#3531—791nomaximal, Sylow
270C2×C79—45no—
271C2×C79C22×2−1+411yescharacteristic
272C2×C79C2×#58512yes—
273D79—45no—
274D79#353114yesdirect product factor
275#3531—791no—
276#3531—7910no—
277#3531—795no—
278#3531—795no—
279#3531—7910no—
280#3531D7911yescharacteristic, direct product factor
281C2×#564—791no—
282C2×#563—7910no—
283C2×#562—795no—
284C2×#533—795no—
285C2×#529—7910no—
286C79C2×#353111yescharacteristic, complemented, Sylow
287#564—7910no—
288#564—795no—
289#564C2×D7911yescharacteristic, complemented
290#563—7920no—
291#563—7920no—
292#563—7920no—
293#563—7910no—
294#563—7910no—
295#563—7910no—
296#563—7920no—
297#563—7920no—
298#563—7920no—
299#563C2×D79110yescomplemented
300#562—795no—
301#562—7910no—
302#562—7920no—
303#562—7920no—
304#562—7920no—
305#562C2×D7915yescomplemented
306#533—7910no—
307#533—795no—
308#533—795no—
309#533—7920no—
310#533—7920no—
311#533—7910no—
312#533—795no—
313#533C2×D7915yescomplemented
314C2×C4⋊Q8—7910no—
315#529—7920no—
316#529—7910no—
317#529—7910no—
318#529—7920no—
319#529—7910no—
320#529—7910no—
321#529—7910no—
322#529—7920no—
323#529—7910no—
324#529—7920no—
325#529—7910no—
326#529C2×D79110yescomplemented
327C2×#126—7920no—
328C2×#125—7910no—
329C2×#125—795no—
330C2×#125—795no—
331C2×#124—7910no—
332C2×#123—7920no—
333C2×C22⋊Q8—7910no—
334C2×C22⋊Q8—7920no—
335C2×#121—7910no—
336C2×C4×Q8—7910no—
337C2×C4×D4—7910no—
338C2×#117—7910no—
339C22×C42—795no—
340C22×Q8—7910no—
341C22×D4—7910no—
342C23×C4—7910no—
343C23×C4—795no—
344C4⋊Q8—7920no—
345C4⋊Q8—7920no—
346C4⋊Q8—7910no—
347C4⋊Q8—7910no—
348C4⋊Q8—7910no—
349C4⋊Q8C22×D79110yes—
350#126—7920no—
351#126—7920no—
352#126—7920no—
353#126—7920no—
354#126—7920no—
355#126—7920no—
356#126—7920no—
357#126C22×D79120yes—
358#125—7920no—
359#125—7920no—
360#125—7910no—
361#125—7910no—
362#125—7920no—
363#125—7910no—
364#125—7920no—
365#125—7910no—
366#125—7910no—
367#125—795no—
368#125—795no—
369#125C22×D79110yes—
370#125C22×D7915yes—
371#125C22×D7915yes—
372#124—7910no—
373#124—7910no—
374#124—7920no—
375#124—7920no—
376#124—7910no—
377#124C22×D79110yes—
378#123—7920no—
379#123—7920no—
380#123—7920no—
381#123—7920no—
382#123—7920no—
383#123—7920no—
384#123—7920no—
385#123C22×D79120yes—
386C22⋊Q8—7910no—
387C22⋊Q8—7920no—
388C22⋊Q8—7910no—
389C22⋊Q8—7920no—
390C22⋊Q8—7920no—
391C22⋊Q8—7910no—
392C22⋊Q8—7920no—
393C22⋊Q8—7920no—
394C22⋊Q8—7920no—
395C22⋊Q8—7920no—
396C22⋊Q8—7920no—
397C22⋊Q8—7920no—
398C22⋊Q8C22×D79110yes—
399C22⋊Q8C22×D79120yes—
400#121—7910no—
401#121—7920no—
402#121—7910no—
403#121—7910no—
404#121—7920no—
405#121C22×D79110yes—
406C4×Q8—7910no—
407C4×Q8—7920no—
408C4×Q8—7910no—
409C4×Q8—7920no—
410C4×Q8—7910no—
411C4×Q8C22×D79110yes—
412C4×D4—7910no—
413C4×D4—7920no—
414C4×D4—7910no—
415C4×D4—7920no—
416C4×D4—7910no—
417C4×D4C22×D79110yes—
418#117—7910no—
419#117—7910no—
420#117—7910no—
421#117—7920no—
422#117—7920no—
423#117C22×D79110yes—
424C2×C4⋊C4—7910no—
425C2×C4⋊C4—7910no—
426C2×C4⋊C4—7910no—
427C2×C4⋊C4—7910no—
428C2×C4⋊C4—7920no—
429C2×C22⋊C4—7920no—
430C2×C22⋊C4—7920no—
431C2×C42—7910no—
432C2×C42—795no—
433C2×C42—7910no—
434C2×C42—795no—
435C2×C42—795no—
436C2×C42—795no—
437C2×C42—795no—
438C2×C42—7910no—
439C2×C42C22×D7915yes—
440C24—795no—
441C2×Q8—31620no—
442C2×Q8—7910no—
443C2×Q8—7920no—
444C2×Q8C23×D79110yes—
445C2×D4—31620no—
446C2×D4—7920no—
447C2×D4—7910no—
448C2×D4C23×D79110yes—
449C22×C4—31620no—
450C22×C4—7910no—
451C22×C4—7910no—
452C22×C4—7910no—
453C22×C4—791no—
454C22×C4—795no—
455C22×C4—795no—
456C22×C4—7910no—
457C22×C4—7910no—
458C22×C4—795no—
459C22×C4—795no—
460C22×C4—15820no—
461C22×C4C23×D7915yes—
462C22×C4C23×D79110yes—
463C4⋊C4—7920no—
464C4⋊C4—7920no—
465C4⋊C4—7920no—
466C4⋊C4—7920no—
467C4⋊C4—7920no—
468C4⋊C4—7920no—
469C4⋊C4—7910no—
470C4⋊C4—7910no—
471C4⋊C4—7910no—
472C4⋊C4—7910no—
473C4⋊C4—7920no—
474C4⋊C4C23×D79110yes—
475C4⋊C4C23×D79110yes—
476C4⋊C4C23×D79110yes—
477C4⋊C4C23×D79110yes—
478C4⋊C4C23×D79120yes—
479C22⋊C4—7920no—
480C22⋊C4—7920no—
481C22⋊C4—7920no—
482C22⋊C4—7920no—
483C22⋊C4—7920no—
484C22⋊C4—7920no—
485C22⋊C4C23×D79120yes—
486C22⋊C4C23×D79120yes—
487C42—7910no—
488C42—7910no—
489C42—7910no—
490C42—795no—
491C42—7910no—
492C42—795no—
493C42—7910no—
494C42C23×D7915yes—
495C42C23×D7915yes—
496C42C23×D79110yes—
497C23—791no—
498C23—795no—
499C23—15820no—
500C23—15810no—
501C23C24×D7915yes—
502Q8—410no—
503Q8—31610no—
504Q8—31620no—
505D4—410no—
506D4—31610no—
507D4—31620no—
508C2×C4—210no—
509C2×C4—410no—
510C2×C4—31610no—
511C2×C4—31610no—
512C2×C4—31610no—
513C2×C4—791no—
514C2×C4—794no—
515C2×C4—795no—
516C2×C4—7910no—
517C2×C4—7910no—
518C2×C4—15810no—
519C2×C4—15820no—
520C2×C4—15820no—
521C2×C4—15810no—
522C2×C4—15810no—
523C2×C4—15810no—
524C2×C4C24×D7915yes—
525C2×C4C24×D79110yes—
526C2×C4C24×D79110yes—
527C2×C4C24×D7911yescharacteristic
528C22—25no—
529C22—210no—
530C22—31620no—
531C22—792no—
532C22—794no—
533C22—1585no—
534C22—15810no—
535C22C25×D7911yescharacteristic
536C4—25no—
537C4—210no—
538C4—210no—
539C4—792no—
540C4—1585no—
541C4—15810no—
542C4—15810no—
543C42−1+4×D7912yes—
544C2—45no—
545C2—3165no—
546C2—794no—
547C2C2×2−1+4×D7911yescharacteristic
548C2#585×D7912yes—
subgroupG/H
centerC2×C4C24×D79
commutator, socle, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC79×#3531C2
hypercenter#3531D79
hypocenterC79C2×#3531
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ #3531

Complements

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

NH ≅ G/Ntype
1. #23777548C2semidirect
2. #23777547C2semidirect
3. #23777546C2semidirect
4. #23777545C2semidirect
5. #23777544C2semidirect
6. #564×D79C2semidirect
7. #563×D79C2semidirect
8. #562×D79C2semidirect
9. #533×D79C2semidirect
10. #529×D79C2semidirect
11. C79×#3531C2semidirect
12. C79⋊#564C22semidirect
13. C79⋊#564C22semidirect
14. #19099317C22semidirect
15. #19099317C22semidirect
16. #19099316C22semidirect
17. #19099315C22semidirect
18. #19099315C22semidirect
19. #19099314C22semidirect
20. #19099314C22semidirect
21. #19099313C22semidirect
22. #19099312C22semidirect
23. #19099311C22semidirect
24. #19099310C22semidirect
25. #19099309C22semidirect
26. #19099308C22semidirect
27. #19099307C22semidirect
28. #19099120C22semidirect
29. #19099119C22semidirect
30. #19099119C22semidirect
31. #19099118C22semidirect
32. #19099117C22semidirect
33. #19099116C22semidirect
34. #19099115C22semidirect
36. #19099100C22semidirect
37. #19099099C22semidirect
38. #19099098C22semidirect
39. #19099097C22semidirect
40. #19099096C22semidirect
41. #19099095C22semidirect
42. #19099094C22semidirect
43. #19099093C22semidirect
44. #19099092C22semidirect
45. #19099091C22semidirect
46. #19099090C22semidirect
60. #564×C79C22semidirect
61. #563×C79C22semidirect
62. #562×C79C22semidirect
63. #533×C79C22semidirect
64. #529×C79C22semidirect
274. D79#3531direct (N × H)
280. #3531D79direct (N × H)
286. C79C2×#3531semidirect
289. #564C2×D79semidirect
299. #563C2×D79semidirect
305. #562C2×D79semidirect
313. #533C2×D79semidirect
326. #529C2×D79semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237775482
#237775472
#237775462
#237775452
#237775442
#564×D792
#563×D792
#562×D792
#533×D792
#529×D792
C79×#35312
C2×#353179