Finite Group Databasebeta

← C61×#19016 #29522449

Subgroups — C61×#19016 #29522449

Order 15616.

1008 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3559C211yesmaximal, characteristic, complemented
2C61×#3217C211yesmaximal, characteristic, complemented
3C61×#3151C211yesmaximal, characteristic, complemented
4C2×C61×#490C211yesmaximal, characteristic, complemented
5C61×#1657C214yesmaximal, complemented
6C61×#1656C214yesmaximal, complemented
7C61×#1530C211yesmaximal, characteristic, complemented
8C61×#1528C211yesmaximal, characteristic, complemented
9C61×#1524C211yesmaximal, characteristic, complemented
10C2×AGL(1,ℤ/8)×C61—22no—
11C61×#563C2212yescomplemented
12C61×#562C2212yescomplemented
13C61×#554—21no—
14C61×#553—21no—
15C61×#553—21no—
16C61×#547—22no—
17C61×#547—21no—
18C61×#544—21no—
19C61×#540—21no—
20C61×#539—22no—
21C61×#539—21no—
22C61×#537—21no—
23C61×#532C2211yescharacteristic
24C2×#127×C61C2211yescharacteristic
25C61×#529C2211yescharacteristic
26C2×#125×C61C2211yescharacteristic
27C61×#496C2214yes—
28C61×#496C2212yes—
29C61×#493—21no—
30C61×#492—21no—
31C61×#490—22no—
32C61×#490C2214yes—
33C61×#490C2212yes—
34C61×#460—21no—
35C61×#459—21no—
36C61×#450—21no—
37C61×#447—21no—
38C61×#432C2211yescharacteristic
39C2×#102×C61—21no—
40C2×#102×C61—21no—
41C4×M16×C61C2211yescharacteristic
42C2×#97×C61C2211yescharacteristic
43C61×#330C2212yescomplemented
44C61×#330C2214yescomplemented
45C61×#329C2212yescomplemented
46C61×#329C2214yescomplemented
47C2×#41×C61—22no—
48C2×#41×C61D412yes—
49C22×D4×C61—21no—
50C22×D4×C61—21no—
51C22×D4×C61—21no—
52AGL(1,ℤ/8)×C61—48no—
53C2×SD16×C61—24no—
54C2×SD16×C61—22no—
55C2×D8×C61—24no—
56C2×D8×C61—22no—
57C2×M16×C61—21no—
58C22×C8×C61—21no—
59C4⋊Q8×C61—21no—
60C4⋊Q8×C61—22no—
61C4⋊Q8×C61D411yescharacteristic
62#127×C61—21no—
63#127×C61—21no—
64#127×C61—21no—
65#127×C61D411yescharacteristic
66#127×C61C2312yes—
67#126×C61—22no—
68#126×C61—22no—
69#126×C61—21no—
70#125×C61—22no—
71#125×C61—21no—
72#125×C61—21no—
73#125×C61—21no—
74#125×C61D412yes—
75#125×C61C2312yes—
76#125×C61C2311yescharacteristic
77#124×C61C2312yes—
78#124×C61C2311yescharacteristic
79#123×C61—22no—
80#123×C61—22no—
81#123×C61—22no—
82#123×C61—22no—
83#123×C61—21no—
84#123×C61—22no—
85#123×C61—22no—
86C22⋊Q8×C61—22no—
87C22⋊Q8×C61—22no—
88C22⋊Q8×C61—22no—
89C22⋊Q8×C61—22no—
90C22⋊Q8×C61—22no—
91C22⋊Q8×C61—22no—
92C22⋊Q8×C61D411yescharacteristic
93#121×C61—22no—
94#121×C61—22no—
95#121×C61—21no—
96#121×C61—21no—
97#121×C61—22no—
98#121×C61—22no—
99#121×C61—21no—
100#121×C61—21no—
101#121×C61D411yescharacteristic
102C4×Q8×C61D411yescharacteristic
103C4×D4×C61—22no—
104C4×D4×C61—22no—
105C4×D4×C61—21no—
106C4×D4×C61—21no—
107C4×D4×C61—21no—
108C4×D4×C61—21no—
109C4×D4×C61—21no—
110C4×D4×C61D411yescharacteristic
111#117×C61—21no—
112#117×C61—21no—
113C2×C4⋊C4×C61—22no—
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61D411yescharacteristic
118C2×C4⋊C4×C61D411yescharacteristic
119C2×C42×C61C2311yescharacteristic
120C4⋊C8×C61—21no—
121#102×C61—24no—
122#102×C61—24no—
123#102×C61—22no—
124#102×C61—22no—
125C22⋊C8×C61—21no—
126#97×C61—21no—
127#97×C61C2312yes—
128#97×C61C2312yes—
129#97×C61C2312yes—
130C4×C8×C61—21no—
131C24×C61—41no—
132#41×C61—44no—
133#41×C61—84no—
134C2×Q8×C61—22no—
135C2×Q8×C61C2×D411yescharacteristic
136C2×Q8×C61C2×D412yes—
137C2×D4×C61—22no—
138C2×D4×C61—21no—
139C2×D4×C61—22no—
140C2×D4×C61—22no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C2×D4×C61—22no—
146C2×D4×C61—44no—
147C2×D4×C61—44no—
148C2×D4×C61—41no—
149C2×D4×C61—41no—
150C2×D4×C61—41no—
151C2×D4×C61—82no—
152C2×D4×C61C2×D411yescharacteristic
153C2×D4×C61C2×D412yes—
154C22×C4×C61—21no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—22no—
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164SD16×C61—48no—
165SD16×C61—82no—
166D8×C61—48no—
167D8×C61—82no—
168M16×C61—24no—
169C2×C8×C61—22no—
170C2×C8×C61—22no—
171C2×C8×C61—22no—
172C2×C8×C61—42no—
173C4⋊C4×C61—22no—
174C4⋊C4×C61—22no—
175C4⋊C4×C61—22no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61—22no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—22no—
186C4⋊C4×C61—22no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61C2×D412yes—
190C4⋊C4×C61C2×D412yes—
191C4⋊C4×C61C2×D411yescharacteristic
192C4⋊C4×C61C2×D411yescharacteristic
193C22⋊C4×C61—22no—
194C22⋊C4×C61—22no—
195C22⋊C4×C61—22no—
196C22⋊C4×C61—22no—
197C22⋊C4×C61—22no—
198C22⋊C4×C61—21no—
199C22⋊C4×C61—21no—
200C22⋊C4×C61—21no—
201C22⋊C4×C61—21no—
202C22⋊C4×C61—22no—
203C22⋊C4×C61—22no—
204C22⋊C4×C61—21no—
205C42×C61—22no—
206C42×C61—21no—
207C42×C61C2×D411yescharacteristic
208C42×C61C2×D411yescharacteristic
209C42×C61C2×D411yescharacteristic
210C42×C61C2411yescharacteristic
211C23×C61—22no—
212C23×C61—21no—
213C23×C61—42no—
214C23×C61—82no—
215C23×C61—82no—
216C23×C61—82no—
217C23×C61#12011yescharacteristic
218Q8×C61—42no—
219Q8×C61—41no—
220Q8×C61—82no—
221D4×C61—42no—
222D4×C61—41no—
223D4×C61—44no—
224D4×C61—42no—
225D4×C61—42no—
226D4×C61—44no—
227D4×C61—44no—
228D4×C61—42no—
229D4×C61—42no—
230D4×C61—81no—
231D4×C61—82no—
232D4×C61—82no—
233D4×C61—82no—
234D4×C61—82no—
235D4×C61—82no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—21no—
243C2×C4×C61—22no—
244C2×C4×C61—41no—
245C2×C4×C61—42no—
246C2×C4×C61—42no—
247C2×C4×C61—82no—
248C2×C4×C61—81no—
249C2×C4×C61—82no—
250C2×C4×C61—82no—
251C2×C4×C61—82no—
252C2×C4×C61#12011yescharacteristic
253C2×C4×C61#12011yescharacteristic
254C2×C4×C61#12011yescharacteristic
255C2×C4×C61C22×D411yescharacteristic
256C2×C4×C61C22×D411yescharacteristic
257C2×C4×C61C22×D411yescharacteristic
258C8×C61—24no—
259C8×C61—42no—
260C8×C61—42no—
261#19016C6111yesmaximal, characteristic, direct product factor, Sylow
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—42no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—42no—
268C22×C61—42no—
269C22×C61—41no—
270C22×C61—82no—
271C22×C61—82no—
272C22×C61—82no—
273C22×C61—164no—
274C22×C61#45312yes—
275C22×C61C2×#12011yescharacteristic
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—21no—
279C4×C61—21no—
280C4×C61—21no—
281C4×C61—42no—
282C4×C61—42no—
283C4×C61—41no—
284C4×C61—41no—
285C4×C61—42no—
286C4×C61—41no—
287C4×C61#45412yes—
288#3559C2×C6111yescharacteristic, complemented
289#3217C2×C6111yescharacteristic, complemented
290#3151C2×C6111yescharacteristic, complemented
291C2×#490C2×C6111yescharacteristic, complemented
292#1657C2×C6114yescomplemented
293#1656C2×C6114yescomplemented
294#1530C2×C6111yescharacteristic, complemented
295#1528C2×C6111yescharacteristic, complemented
296#1524C2×C6111yescharacteristic, complemented
297C2×C61—22no—
298C2×C61—82no—
299C2×C61—81no—
300C2×C61—162no—
301C2×C61C2×#45311yescharacteristic
302C2×C61C2×#45411yescharacteristic
303C2×C61#302111yescharacteristic
304C2×AGL(1,ℤ/8)—22no—
305#563C22×C6112yescomplemented
306#562C22×C6112yescomplemented
307#554—21no—
308#553—21no—
309#553—21no—
310#547—22no—
311#547—21no—
312#544—21no—
313#540—21no—
314#539—22no—
315#539—21no—
316#537—21no—
317#532C22×C6111yescharacteristic
318C2×#127C22×C6111yescharacteristic
319#529C22×C6111yescharacteristic
320C2×#125C22×C6111yescharacteristic
321#496C22×C6114yes—
322#496C22×C6112yes—
323#493—21no—
324#492—21no—
325#490—22no—
326#490C22×C6114yes—
327#490C22×C6112yes—
328#460—21no—
329#459—21no—
330#450—21no—
331#447—21no—
332#432C22×C6111yescharacteristic
333C2×#102—21no—
334C2×#102—21no—
335C4×M16C22×C6111yescharacteristic
336C2×#97C22×C6111yescharacteristic
337#330C22×C6114yescomplemented
338#330C22×C6112yescomplemented
339#329C22×C6112yescomplemented
340#329C22×C6114yescomplemented
341C61#1901611yescharacteristic, direct product factor, Sylow
342C2×#41—22no—
343C2×#41D4×C6112yes—
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—21no—
347AGL(1,ℤ/8)—48no—
348C2×SD16—24no—
349C2×SD16—22no—
350C2×D8—24no—
351C2×D8—22no—
352C2×M16—21no—
353C22×C8—21no—
354C4⋊Q8—21no—
355C4⋊Q8—22no—
356C4⋊Q8D4×C6111yescharacteristic
357#127—21no—
358#127—21no—
359#127—21no—
360#127D4×C6111yescharacteristic
361#127C23×C6112yes—
362#126—22no—
363#126—22no—
364#126—21no—
365#125—22no—
366#125—21no—
367#125—21no—
368#125—21no—
369#125D4×C6112yes—
370#125C23×C6112yes—
371#125C23×C6111yescharacteristic
372#124C23×C6111yescharacteristic
373#124C23×C6112yes—
374#123—22no—
375#123—22no—
376#123—22no—
377#123—22no—
378#123—21no—
379#123—22no—
380#123—22no—
381C22⋊Q8—22no—
382C22⋊Q8—22no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8—22no—
386C22⋊Q8—22no—
387C22⋊Q8D4×C6111yescharacteristic
388#121—22no—
389#121—22no—
390#121—21no—
391#121—21no—
392#121—22no—
393#121—22no—
394#121—21no—
395#121—21no—
396#121D4×C6111yescharacteristic
397C4×Q8D4×C6111yescharacteristic
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4D4×C6111yescharacteristic
406#117—21no—
407#117—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4D4×C6111yescharacteristic
413C2×C4⋊C4D4×C6111yescharacteristic
414C2×C42C23×C6111yescharacteristic
415C4⋊C8—21no—
416#102—24no—
417#102—24no—
418#102—22no—
419#102—22no—
420C22⋊C8—21no—
421#97—21no—
422#97C23×C6112yes—
423#97C23×C6112yes—
424#97C23×C6112yes—
425C4×C8—21no—
426C24—41no—
427#41—44no—
428#41—84no—
429C2×Q8—22no—
430C2×Q8C2×D4×C6111yescharacteristic
431C2×Q8C2×D4×C6112yes—
432C2×D4—22no—
433C2×D4—21no—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—82no—
447C2×D4C2×D4×C6111yescharacteristic
448C2×D4C2×D4×C6112yes—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4C2×D4×C6111yescharacteristic
457C22×C4C2×D4×C6111yescharacteristic
458C22×C4C2×D4×C6111yescharacteristic
459SD16—48no—
460SD16—82no—
461D8—48no—
462D8—82no—
463M16—24no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—42no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4C2×D4×C6112yes—
485C4⋊C4C2×D4×C6112yes—
486C4⋊C4C2×D4×C6111yescharacteristic
487C4⋊C4C2×D4×C6111yescharacteristic
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C22⋊C4—21no—
500C42—22no—
501C42—21no—
502C42C2×D4×C6111yescharacteristic
503C42C2×D4×C6111yescharacteristic
504C42C2×D4×C6111yescharacteristic
505C42C24×C6111yescharacteristic
506C23—22no—
507C23—21no—
508C23—42no—
509C23—82no—
510C23—82no—
511C23—82no—
512C23#120×C6111yescharacteristic
513Q8—42no—
514Q8—41no—
515Q8—82no—
516D4—42no—
517D4—41no—
518D4—44no—
519D4—42no—
520D4—42no—
521D4—44no—
522D4—44no—
523D4—42no—
524D4—42no—
525D4—81no—
526D4—82no—
527D4—82no—
528D4—82no—
529D4—82no—
530D4—82no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—82no—
543C2×C4—81no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4#120×C6111yescharacteristic
548C2×C4#120×C6111yescharacteristic
549C2×C4#120×C6111yescharacteristic
550C2×C4C22×D4×C6111yescharacteristic
551C2×C4C22×D4×C6111yescharacteristic
552C2×C4C22×D4×C6111yescharacteristic
553C8—24no—
554C8—42no—
555C8—42no—
556C22—21no—
557C22—21no—
558C22—42no—
559C22—41no—
560C22—41no—
561C22—42no—
562C22—42no—
563C22—41no—
564C22—82no—
565C22—82no—
566C22—82no—
567C22—164no—
568C22C61×#45312yes—
569C22C2×#120×C6111yescharacteristic
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—42no—
576C4—42no—
577C4—41no—
578C4—41no—
579C4—42no—
580C4—41no—
581C4C61×#45412yes—
582C2—22no—
583C2—82no—
584C2—81no—
585C2—162no—
586C2C2×C61×#45311yescharacteristic
587C2C2×C61×#45411yescharacteristic
588C2C61×#302111yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC42C24×C61
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3559C2semidirect
2. C61×#3217C2semidirect
3. C61×#3151C2semidirect
4. C2×C61×#490C2semidirect
5. C61×#1657C2semidirect
6. C61×#1656C2semidirect
7. C61×#1530C2semidirect
8. C61×#1528C2semidirect
9. C61×#1524C2semidirect
11. C61×#563C22semidirect
12. C61×#562C22semidirect
43. C61×#330C22semidirect
44. C61×#330C22semidirect
45. C61×#329C22semidirect
46. C61×#329C22semidirect
261. #19016C61direct (N × H)
288. #3559C2×C61semidirect
289. #3217C2×C61semidirect
290. #3151C2×C61semidirect
291. C2×#490C2×C61semidirect
292. #1657C2×C61semidirect
293. #1656C2×C61semidirect
294. #1530C2×C61semidirect
295. #1528C2×C61semidirect
296. #1524C2×C61semidirect
305. #563C22×C61semidirect
306. #562C22×C61semidirect
337. #330C22×C61semidirect
338. #330C22×C61semidirect
339. #329C22×C61semidirect
340. #329C22×C61semidirect
341. C61#19016direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35592
C61×#32172
C61×#31512
C2×C61×#4902
C61×#16572
C61×#16562
C61×#15302
C61×#15282
C61×#15242
#1901661