Finite Group Databasebeta

← C61×#25626 #29529059

Subgroups — C61×#25626 #29529059

Order 15616.

1076 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3507C211yesmaximal, characteristic, complemented
2C61×#3153C211yesmaximal, characteristic
3C61×#3140C211yesmaximal, characteristic, complemented
4C61×#2545C211yesmaximal, characteristic, complemented
5C61×#2005C212yesmaximal, complemented
6C61×#2003C212yesmaximal, complemented
7C61×#1986C211yesmaximal, characteristic, complemented
8C61×#1980C211yesmaximal, characteristic, complemented
9C61×#1883C212yesmaximal, complemented
10C61×#1882C212yesmaximal, complemented
11C4×#101×C61C211yesmaximal, characteristic, complemented
12C2×#137×C61C2212yes—
13C2×AGL(1,ℤ/8)×C61C2212yes—
14C61×#559—21no—
15C61×#557—21no—
16C61×#556—21no—
17C61×#556—22no—
18C61×#554—21no—
19C61×#552—22no—
20C61×#539—22no—
21C61×#536C2212yes—
22C61×#533C2211yescharacteristic
23C61×#532C2211yescharacteristic
24C2×C4⋊Q8×C61C2211yescharacteristic
25C61×#529—22no—
26C2×#124×C61C2211yescharacteristic
27C2×#124×C61C2211yescharacteristic
28C61×#520C2212yes—
29C2×C4×Q8×C61C2211yescharacteristic
30C61×#497—21no—
31C61×#496—21no—
32C61×#495—22no—
33C61×#489—21no—
34C61×#489—21no—
35C61×#488—22no—
36C2×#104×C61C2212yes—
37C2×#104×C61C2212yes—
38C61×#419C2212yes—
39C61×#418C2212yes—
40C2×#101×C61C2212yes—
41C4×M16×C61C2211yescharacteristic
42C4×M16×C61C2211yescharacteristic
43C61×#396—22no—
44C61×#391C2211yescharacteristic
45C61×#390C2211yescharacteristic
46C61×#388—22no—
47C4×C4⋊C4×C61C2211yescharacteristic
48C61×#343C2212yes—
49C61×#339C2212yes—
50C61×#339C2212yes—
51C2×#41×C61C2312yes—
52C22×Q8×C61C2311yescharacteristic
53C22×Q8×C61C2311yescharacteristic
54C22×D4×C61C2311yescharacteristic
55#137×C61—24no—
56#137×C61—42no—
57AGL(1,ℤ/8)×C61—24no—
58AGL(1,ℤ/8)×C61—42no—
59C2×Q16×C61—22no—
60C2×SD16×C61—22no—
61C2×SD16×C61—22no—
62C2×D8×C61—22no—
63C2×M16×C61C2312yes—
64C2×M16×C61C2312yes—
65C4⋊Q8×C61—22no—
66C4⋊Q8×C61—42no—
67C4⋊Q8×C61D411yescharacteristic
68C4⋊Q8×C61D411yescharacteristic
69C4⋊Q8×C61D411yescharacteristic
70#127×C61D411yescharacteristic
71#126×C61—24no—
72#126×C61—24no—
73#125×C61—24no—
74#125×C61—22no—
75#125×C61D412yes—
76#124×C61—22no—
77#124×C61—22no—
78#124×C61—21no—
79#124×C61—21no—
80#124×C61—21no—
81#124×C61—21no—
82#124×C61—42no—
83#124×C61D412yes—
84#123×C61—24no—
85#123×C61—24no—
86C22⋊Q8×C61—24no—
87C22⋊Q8×C61—21no—
88C22⋊Q8×C61—21no—
89C22⋊Q8×C61—22no—
90C22⋊Q8×C61—22no—
91#121×C61—21no—
92#121×C61—21no—
93C4×Q8×C61—22no—
94C4×Q8×C61—22no—
95C4×Q8×C61—21no—
96C4×Q8×C61—21no—
97C4×Q8×C61—21no—
98C4×Q8×C61—21no—
99C4×Q8×C61—21no—
100C4×Q8×C61—21no—
101C4×D4×C61—22no—
102C4×D4×C61—22no—
103C4×D4×C61—24no—
104C4×D4×C61—21no—
105C4×D4×C61—21no—
106#117×C61—24no—
107#117×C61—22no—
108#117×C61C2312yes—
109C2×C4⋊C4×C61—22no—
110C2×C4⋊C4×C61—22no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61D412yes—
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—22no—
116C2×C22⋊C4×C61—22no—
117C2×C22⋊C4×C61—21no—
118C2×C42×C61D412yes—
119C2×C42×C61C2311yescharacteristic
120C2×C42×C61C2311yescharacteristic
121C2×C42×C61C2311yescharacteristic
122#104×C61—42no—
123#104×C61—42no—
124#103×C61—22no—
125#103×C61—22no—
126#102×C61—22no—
127#102×C61—22no—
128#101×C61—24no—
129#97×C61—21no—
130#97×C61—21no—
131C4×C8×C61—21no—
132C4×C8×C61—21no—
133#95×C61—21no—
134#95×C61—22no—
135C24×C61—21no—
136#41×C61—22no—
137#41×C61—22no—
138#41×C61—22no—
139#41×C61—22no—
140C2×Q8×C61—21no—
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—22no—
145C2×Q8×C61—22no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—22no—
149C2×Q8×C61—22no—
150C2×Q8×C61C2×D412yes—
151C2×D4×C61—22no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—22no—
157C2×D4×C61—22no—
158C2×D4×C61C2×D412yes—
159C22×C4×C61—21no—
160C22×C4×C61—24no—
161C22×C4×C61—22no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61C2×D412yes—
165C22×C4×C61C2×D412yes—
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2411yescharacteristic
169Q16×C61—44no—
170SD16×C61—44no—
171SD16×C61—44no—
172D8×C61—44no—
173M16×C61—22no—
174M16×C61—22no—
175M16×C61—22no—
176M16×C61#4114yes—
177C2×C8×C61—22no—
178C2×C8×C61—22no—
179C4⋊C4×C61—24no—
180C4⋊C4×C61—24no—
181C4⋊C4×C61—24no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61—22no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—22no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—42no—
193C4⋊C4×C61—44no—
194C4⋊C4×C61C2×D412yes—
195C4⋊C4×C61C2×D412yes—
196C22⋊C4×C61—24no—
197C22⋊C4×C61—24no—
198C22⋊C4×C61—24no—
199C22⋊C4×C61—22no—
200C22⋊C4×C61—22no—
201C22⋊C4×C61—22no—
202C22⋊C4×C61—44no—
203C22⋊C4×C61—44no—
204C22⋊C4×C61—41no—
205C22⋊C4×C61—41no—
206C22⋊C4×C61—41no—
207C22⋊C4×C61—41no—
208C42×C61—24no—
209C42×C61—22no—
210C42×C61—22no—
211C42×C61—22no—
212C42×C61—22no—
213C42×C61—22no—
214C42×C61C2×D411yescharacteristic
215C42×C61C2×D411yescharacteristic
216C42×C61C2×D411yescharacteristic
217C42×C61C2×D411yescharacteristic
218C23×C61—22no—
219C23×C61—42no—
220C23×C61—42no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61—41no—
224C23×C61C22×D411yescharacteristic
225Q8×C61—22no—
226Q8×C61—22no—
227Q8×C61—42no—
228Q8×C61—42no—
229Q8×C61—42no—
230Q8×C61—42no—
231Q8×C61—42no—
232Q8×C61—81no—
233D4×C61—22no—
234D4×C61—22no—
235D4×C61—42no—
236D4×C61—42no—
237D4×C61—42no—
238D4×C61—42no—
239D4×C61—42no—
240D4×C61—81no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—22no—
248C2×C4×C61—22no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—42no—
254C2×C4×C61—42no—
255C2×C4×C61—42no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—84no—
263C2×C4×C61#12011yescharacteristic
264C2×C4×C61#12011yescharacteristic
265C2×C4×C61#12011yescharacteristic
266C2×C4×C61#12011yescharacteristic
267C2×C4×C61C22×D411yescharacteristic
268C2×C4×C61C22×D411yescharacteristic
269C2×C4×C61C2×#4112yes—
270C2×C4×C61H(5,𝔽2)12yes—
271C8×C61—24no—
272C8×C61—42no—
273#25626C6111yesmaximal, characteristic, direct product factor, Sylow
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—42no—
277C22×C61—42no—
278C22×C61—42no—
279C22×C61—82no—
280C22×C61—82no—
281C22×C61—81no—
282C22×C61—81no—
283C22×C61—81no—
284C22×C61C2×#12011yescharacteristic
285C22×C61#53211yescharacteristic
286C22×C61#53511yescharacteristic
287C4×C61—21no—
288C4×C61—21no—
289C4×C61—21no—
290C4×C61—21no—
291C4×C61—42no—
292C4×C61—42no—
293C4×C61—42no—
294C4×C61—42no—
295C4×C61—42no—
296C4×C61—42no—
297C4×C61—81no—
298C4×C61—81no—
299C4×C61#54612yes—
300C4×C61#55012yes—
301#3507C2×C6111yescharacteristic, complemented
302#3153C2×C6111yescharacteristic
303#3140C2×C6111yescharacteristic, complemented
304#2545C2×C6111yescharacteristic, complemented
305#2005C2×C6112yescomplemented
306#2003C2×C6112yescomplemented
307#1986C2×C6111yescharacteristic, complemented
308#1980C2×C6111yescharacteristic, complemented
309#1883C2×C6112yescomplemented
310#1882C2×C6112yescomplemented
311C4×#101C2×C6111yescharacteristic, complemented
312C2×C61—21no—
313C2×C61—21no—
314C2×C61—82no—
315C2×C61—161no—
316C2×C61#243111yescharacteristic
317C2×C61#301811yescharacteristic
318C2×C61#302011yescharacteristic
319C2×#137C22×C6112yes—
320C2×AGL(1,ℤ/8)C22×C6112yes—
321#559—21no—
322#557—21no—
323#556—21no—
324#556—22no—
325#554—21no—
326#552—22no—
327#539—22no—
328#536C22×C6112yes—
329#533C22×C6111yescharacteristic
330#532C22×C6111yescharacteristic
331C2×C4⋊Q8C22×C6111yescharacteristic
332#529—22no—
333C2×#124C22×C6111yescharacteristic
334C2×#124C22×C6111yescharacteristic
335#520C22×C6112yes—
336C2×C4×Q8C22×C6111yescharacteristic
337#497—21no—
338#496—21no—
339#495—22no—
340#489—21no—
341#489—21no—
342#488—22no—
343C2×#104C22×C6112yes—
344C2×#104C22×C6112yes—
345#419C22×C6112yes—
346#418C22×C6112yes—
347C2×#101C22×C6112yes—
348C4×M16C22×C6111yescharacteristic
349C4×M16C22×C6111yescharacteristic
350#396—22no—
351#391C22×C6111yescharacteristic
352#390C22×C6111yescharacteristic
353#388—22no—
354C4×C4⋊C4C22×C6111yescharacteristic
355#343C22×C6112yes—
356#339C22×C6112yes—
357#339C22×C6112yes—
358C61#2562611yescharacteristic, direct product factor, Sylow
359C2×#41C23×C6112yes—
360C22×Q8C23×C6111yescharacteristic
361C22×Q8C23×C6111yescharacteristic
362C22×D4C23×C6111yescharacteristic
363#137—24no—
364#137—42no—
365AGL(1,ℤ/8)—24no—
366AGL(1,ℤ/8)—42no—
367C2×Q16—22no—
368C2×SD16—22no—
369C2×SD16—22no—
370C2×D8—22no—
371C2×M16C23×C6112yes—
372C2×M16C23×C6112yes—
373C4⋊Q8—22no—
374C4⋊Q8—42no—
375C4⋊Q8D4×C6111yescharacteristic
376C4⋊Q8D4×C6111yescharacteristic
377C4⋊Q8D4×C6111yescharacteristic
378#127D4×C6111yescharacteristic
379#126—24no—
380#126—24no—
381#125—22no—
382#125—24no—
383#125D4×C6112yes—
384#124—22no—
385#124—22no—
386#124—21no—
387#124—21no—
388#124—21no—
389#124—21no—
390#124—42no—
391#124D4×C6112yes—
392#123—24no—
393#123—24no—
394C22⋊Q8—24no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399#121—21no—
400#121—21no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—24no—
412C4×D4—21no—
413C4×D4—21no—
414#117—24no—
415#117—22no—
416#117C23×C6112yes—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4D4×C6112yes—
421C2×C4⋊C4C23×C6111yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—22no—
426C2×C42D4×C6112yes—
427C2×C42C23×C6111yescharacteristic
428C2×C42C23×C6111yescharacteristic
429C2×C42C23×C6111yescharacteristic
430#104—42no—
431#104—42no—
432#103—22no—
433#103—22no—
434#102—22no—
435#102—22no—
436#101—24no—
437#97—21no—
438#97—21no—
439C4×C8—21no—
440C4×C8—21no—
441#95—21no—
442#95—22no—
443C24—21no—
444#41—22no—
445#41—22no—
446#41—22no—
447#41—22no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8C2×D4×C6112yes—
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4C2×D4×C6112yes—
467C22×C4—21no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4C2×D4×C6112yes—
473C22×C4C2×D4×C6112yes—
474C22×C4C2×D4×C6111yescharacteristic
475C22×C4C2×D4×C6111yescharacteristic
476C22×C4C24×C6111yescharacteristic
477Q16—44no—
478SD16—44no—
479SD16—44no—
480D8—44no—
481M16—22no—
482M16—22no—
483M16—22no—
484M16#41×C6114yes—
485C2×C8—22no—
486C2×C8—22no—
487C4⋊C4—24no—
488C4⋊C4—24no—
489C4⋊C4—24no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—42no—
501C4⋊C4—44no—
502C4⋊C4C2×D4×C6112yes—
503C4⋊C4C2×D4×C6112yes—
504C22⋊C4—24no—
505C22⋊C4—24no—
506C22⋊C4—24no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—44no—
511C22⋊C4—44no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C42—24no—
517C42—22no—
518C42—22no—
519C42—22no—
520C42—22no—
521C42—22no—
522C42C2×D4×C6111yescharacteristic
523C42C2×D4×C6111yescharacteristic
524C42C2×D4×C6111yescharacteristic
525C42C2×D4×C6111yescharacteristic
526C23—22no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23C22×D4×C6111yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—42no—
536Q8—42no—
537Q8—42no—
538Q8—42no—
539Q8—42no—
540Q8—81no—
541D4—22no—
542D4—22no—
543D4—42no—
544D4—42no—
545D4—42no—
546D4—42no—
547D4—42no—
548D4—81no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—84no—
571C2×C4#120×C6111yescharacteristic
572C2×C4#120×C6111yescharacteristic
573C2×C4#120×C6111yescharacteristic
574C2×C4#120×C6111yescharacteristic
575C2×C4C22×D4×C6111yescharacteristic
576C2×C4C22×D4×C6111yescharacteristic
577C2×C4C2×#41×C6112yes—
578C2×C4H(5,𝔽2)×C6112yes—
579C8—24no—
580C8—42no—
581C22—21no—
582C22—21no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—82no—
587C22—82no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22C2×#120×C6111yescharacteristic
592C22C61×#53211yescharacteristic
593C22C61×#53511yescharacteristic
594C4—21no—
595C4—21no—
596C4—21no—
597C4—21no—
598C4—42no—
599C4—42no—
600C4—42no—
601C4—42no—
602C4—42no—
603C4—42no—
604C4—81no—
605C4—81no—
606C4C61×#54612yes—
607C4C61×#55012yes—
608C2—21no—
609C2—21no—
610C2—82no—
611C2—161no—
612C2C61×#243111yescharacteristic
613C2C61×#301811yescharacteristic
614C2C61×#302011yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3153C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3507C2semidirect
3. C61×#3140C2semidirect
4. C61×#2545C2semidirect
5. C61×#2005C2semidirect
6. C61×#2003C2semidirect
7. C61×#1986C2semidirect
8. C61×#1980C2semidirect
9. C61×#1883C2semidirect
10. C61×#1882C2semidirect
11. C4×#101×C61C2semidirect
273. #25626C61direct (N × H)
301. #3507C2×C61semidirect
303. #3140C2×C61semidirect
304. #2545C2×C61semidirect
305. #2005C2×C61semidirect
306. #2003C2×C61semidirect
307. #1986C2×C61semidirect
308. #1980C2×C61semidirect
309. #1883C2×C61semidirect
310. #1882C2×C61semidirect
311. C4×#101C2×C61semidirect
358. C61#25626direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35072
C61×#31532
C61×#31402
C61×#25452
C61×#20052
C61×#20032
C61×#19862
C61×#19802
C61×#18832
C61×#18822
C4×#101×C612
#2562661