Finite Group Databasebeta

← C61×#18468 #29521901

Subgroups — C61×#18468 #29521901

Order 15616.

870 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3559C211yesmaximal, characteristic
2C61×#3234C211yesmaximal, characteristic, complemented
3C61×#3232C211yesmaximal, characteristic, complemented
4C61×#2822C211yesmaximal, characteristic, complemented
5C61×#1616C212yesmaximal, complemented
6C61×#1615C212yesmaximal, complemented
7C61×#1610C212yesmaximal, complemented
8C61×#1609C212yesmaximal, complemented
9C61×#1517C211yesmaximal, characteristic, complemented
10C61×#1512C211yesmaximal, characteristic, complemented
11C61×#1470C211yesmaximal, characteristic, complemented
12C61×#563—21no—
13C61×#562—21no—
14C61×#554—21no—
15C61×#553—21no—
16C61×#553—21no—
17C61×#547—22no—
18C61×#547—21no—
19C61×#544—21no—
20C61×#540—21no—
21C61×#539—22no—
22C61×#539C2212yes—
23C61×#537C2212yes—
24C61×#532C2211yescharacteristic
25C61×#529C2211yescharacteristic
26C2×#125×C61C2211yescharacteristic
27C2×#125×C61C2211yescharacteristic
28C61×#501—21no—
29C61×#499—21no—
30C61×#490—21no—
31C61×#488—21no—
32C61×#484C2211yescharacteristic
33C61×#483C2211yescharacteristic
34C61×#481C2212yes—
35C61×#481C2211yescharacteristic
36C61×#480C2212yes—
37C61×#480C2211yescharacteristic
38C61×#479—21no—
39C61×#478—21no—
40C61×#478—22no—
41C61×#432C2211yescharacteristic
42C61×#431C2211yescharacteristic
43C61×#400—21no—
44C61×#400C2212yes—
45C61×#398—21no—
46C61×#398—22no—
47C61×#398C2212yes—
48C61×#382C2211yescharacteristic
49C61×#328C2212yes—
50C61×#327C2212yes—
51C61×#327C2212yes—
52C61×#327C2212yes—
53C61×#324C2212yes—
54C61×#324C2212yes—
55C2×#41×C61—21no—
56C2×#41×C61—22no—
57C4⋊Q8×C61—21no—
58C4⋊Q8×C61—22no—
59C4⋊Q8×C61D411yescharacteristic
60#127×C61D411yescharacteristic
61#126×C61—22no—
62#126×C61—22no—
63#126×C61—21no—
64#125×C61—21no—
65#125×C61—22no—
66#125×C61—21no—
67#125×C61—21no—
68#125×C61—21no—
69#125×C61—21no—
70#125×C61—21no—
71#125×C61—21no—
72#125×C61—21no—
73#125×C61—21no—
74#125×C61D411yescharacteristic
75#124×C61—21no—
76#124×C61D411yescharacteristic
77#123×C61—22no—
78#123×C61—22no—
79#123×C61—22no—
80#123×C61—22no—
81#123×C61—22no—
82#123×C61—22no—
83#123×C61—21no—
84C22⋊Q8×C61—22no—
85C22⋊Q8×C61—22no—
86C22⋊Q8×C61—22no—
87C22⋊Q8×C61—22no—
88C22⋊Q8×C61—22no—
89C22⋊Q8×C61—22no—
90C22⋊Q8×C61C2311yescharacteristic
91#121×C61—21no—
92#121×C61—22no—
93#121×C61—21no—
94#121×C61—22no—
95#121×C61—22no—
96#121×C61—21no—
97#121×C61—22no—
98#121×C61C2312yes—
99#121×C61C2311yescharacteristic
100C4×Q8×C61D411yescharacteristic
101C4×D4×C61—22no—
102C4×D4×C61—21no—
103C4×D4×C61—21no—
104C4×D4×C61—22no—
105C4×D4×C61—21no—
106C4×D4×C61—21no—
107C4×D4×C61D412yes—
108C4×D4×C61D411yescharacteristic
109#117×C61—21no—
110#117×C61—21no—
111C2×C4⋊C4×C61—22no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61—22no—
117C2×C4⋊C4×C61D411yescharacteristic
118C2×C4⋊C4×C61D412yes—
119C2×C4⋊C4×C61D411yescharacteristic
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2312yes—
123C2×C42×C61C2311yescharacteristic
124#107×C61—22no—
125#107×C61—21no—
126#107×C61—21no—
127#106×C61—22no—
128#106×C61—21no—
129#106×C61—21no—
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132#103×C61—21no—
133#103×C61—21no—
134#102×C61—21no—
135#102×C61—22no—
136#102×C61—21no—
137#102×C61—22no—
138C22⋊C8×C61C2311yescharacteristic
139C22⋊C8×C61C2311yescharacteristic
140C22⋊C8×C61C2312yes—
141#97×C61—21no—
142C4×C8×C61—21no—
143#95×C61—21no—
144#95×C61—22no—
145#95×C61—22no—
146#95×C61—22no—
147#95×C61C2312yes—
148#41×C61—81no—
149#41×C61—81no—
150#41×C61—82no—
151#41×C61—82no—
152C2×Q8×C61—22no—
153C2×Q8×C61—21no—
154C2×Q8×C61C2×D411yescharacteristic
155C2×D4×C61—22no—
156C2×D4×C61—21no—
157C2×D4×C61—22no—
158C2×D4×C61—22no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61C2×D411yescharacteristic
162C2×D4×C61C2×D412yes—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—21no—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61C2×D412yes—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D412yes—
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2411yescharacteristic
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—22no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—22no—
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—21no—
193C4⋊C4×C61—22no—
194C4⋊C4×C61—22no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—41no—
201C4⋊C4×C61—41no—
202C4⋊C4×C61—41no—
203C4⋊C4×C61—41no—
204C4⋊C4×C61—81no—
205C4⋊C4×C61—82no—
206C4⋊C4×C61C2×D412yes—
207C4⋊C4×C61C2×D411yescharacteristic
208C4⋊C4×C61C2×D411yescharacteristic
209C22⋊C4×C61—22no—
210C22⋊C4×C61—22no—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—22no—
214C22⋊C4×C61—21no—
215C22⋊C4×C61—21no—
216C22⋊C4×C61—21no—
217C22⋊C4×C61—21no—
218C22⋊C4×C61—22no—
219C22⋊C4×C61—21no—
220C22⋊C4×C61—22no—
221C42×C61—22no—
222C42×C61—21no—
223C42×C61C2×D411yescharacteristic
224C42×C61C2×D411yescharacteristic
225C42×C61C2×D411yescharacteristic
226C42×C61C2×D411yescharacteristic
227C23×C61—21no—
228C23×C61—22no—
229C23×C61C22×D411yescharacteristic
230Q8×C61—41no—
231Q8×C61—81no—
232Q8×C61—82no—
233D4×C61—42no—
234D4×C61—41no—
235D4×C61—42no—
236D4×C61—42no—
237D4×C61—41no—
238D4×C61—42no—
239D4×C61—41no—
240D4×C61—81no—
241D4×C61—82no—
242D4×C61—82no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—22no—
248C2×C4×C61—22no—
249C2×C4×C61—21no—
250C2×C4×C61—22no—
251C2×C4×C61—22no—
252C2×C4×C61—22no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—42no—
256C2×C4×C61—42no—
257C2×C4×C61—42no—
258C2×C4×C61—42no—
259C2×C4×C61—42no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—42no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—82no—
266C2×C4×C61—82no—
267C2×C4×C61—82no—
268C2×C4×C61—82no—
269C2×C4×C61#12011yescharacteristic
270C2×C4×C61#12011yescharacteristic
271C2×C4×C61#12011yescharacteristic
272C2×C4×C61#12011yescharacteristic
273C2×C4×C61C22×D411yescharacteristic
274C2×C4×C61C22×D411yescharacteristic
275C8×C61—42no—
276C8×C61—41no—
277C8×C61—41no—
278#18468C6111yesmaximal, characteristic, direct product factor, Sylow
279C22×C61—21no—
280C22×C61—21no—
281C22×C61—42no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—42no—
285C22×C61—42no—
286C22×C61—41no—
287C22×C61C2×#12011yescharacteristic
288C22×C61#57611yescharacteristic
289C22×C61#57711yescharacteristic
290C4×C61—21no—
291C4×C61—21no—
292C4×C61—21no—
293C4×C61—21no—
294C4×C61—21no—
295C4×C61—21no—
296C4×C61—42no—
297C4×C61—42no—
298C4×C61—41no—
299C4×C61—41no—
300C4×C61—42no—
301C4×C61—41no—
302C4×C61—82no—
303C4×C61—81no—
304C4×C61—81no—
305#3559C2×C6111yescharacteristic
306#3234C2×C6111yescharacteristic, complemented
307#3232C2×C6111yescharacteristic, complemented
308#2822C2×C6111yescharacteristic, complemented
309#1616C2×C6112yescomplemented
310#1615C2×C6112yescomplemented
311#1610C2×C6112yescomplemented
312#1609C2×C6112yescomplemented
313#1517C2×C6111yescharacteristic, complemented
314#1512C2×C6111yescharacteristic, complemented
315#1470C2×C6111yescharacteristic, complemented
316C2×C61—21no—
317C2×C61—21no—
318C2×C61—81no—
319C2×C61—82no—
320C2×C61#301211yescharacteristic
321C2×C61#302011yescharacteristic
322C2×C61#302811yescharacteristic
323#563—21no—
324#562—21no—
325#554—21no—
326#553—21no—
327#553—21no—
328#547—22no—
329#547—21no—
330#544—21no—
331#540—21no—
332#539—22no—
333#539C22×C6112yes—
334#537C22×C6112yes—
335#532C22×C6111yescharacteristic
336#529C22×C6111yescharacteristic
337C2×#125C22×C6111yescharacteristic
338C2×#125C22×C6111yescharacteristic
339#501—21no—
340#499—21no—
341#490—21no—
342#488—21no—
343#484C22×C6111yescharacteristic
344#483C22×C6111yescharacteristic
345#481C22×C6112yes—
346#481C22×C6111yescharacteristic
347#480C22×C6112yes—
348#480C22×C6111yescharacteristic
349#479—21no—
350#478—21no—
351#478—22no—
352#432C22×C6111yescharacteristic
353#431C22×C6111yescharacteristic
354#400—21no—
355#400C22×C6112yes—
356#398—21no—
357#398—22no—
358#398C22×C6112yes—
359#382C22×C6111yescharacteristic
360#328C22×C6112yes—
361#327C22×C6112yes—
362#327C22×C6112yes—
363#327C22×C6112yes—
364#324C22×C6112yes—
365#324C22×C6112yes—
366C61#1846811yescharacteristic, direct product factor, Sylow
367C2×#41—21no—
368C2×#41—22no—
369C4⋊Q8—21no—
370C4⋊Q8—22no—
371C4⋊Q8D4×C6111yescharacteristic
372#127D4×C6111yescharacteristic
373#126—22no—
374#126—22no—
375#126—21no—
376#125—21no—
377#125—22no—
378#125—21no—
379#125—21no—
380#125—21no—
381#125—21no—
382#125—21no—
383#125—21no—
384#125—21no—
385#125—21no—
386#125D4×C6111yescharacteristic
387#124—21no—
388#124D4×C6111yescharacteristic
389#123—22no—
390#123—22no—
391#123—22no—
392#123—22no—
393#123—22no—
394#123—21no—
395#123—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8C23×C6111yescharacteristic
403#121—21no—
404#121—22no—
405#121—21no—
406#121—22no—
407#121—22no—
408#121—21no—
409#121—22no—
410#121C23×C6111yescharacteristic
411#121C23×C6112yes—
412C4×Q8D4×C6111yescharacteristic
413C4×D4—22no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4—22no—
418C4×D4—21no—
419C4×D4D4×C6111yescharacteristic
420C4×D4D4×C6112yes—
421#117—21no—
422#117—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4D4×C6111yescharacteristic
430C2×C4⋊C4D4×C6112yes—
431C2×C4⋊C4D4×C6111yescharacteristic
432C2×C4⋊C4C23×C6111yescharacteristic
433C2×C4⋊C4C23×C6111yescharacteristic
434C2×C4⋊C4C23×C6112yes—
435C2×C42C23×C6111yescharacteristic
436#107—22no—
437#107—21no—
438#107—21no—
439#106—22no—
440#106—21no—
441#106—21no—
442C4⋊C8—21no—
443C4⋊C8—21no—
444#103—21no—
445#103—21no—
446#102—21no—
447#102—22no—
448#102—21no—
449#102—22no—
450C22⋊C8C23×C6111yescharacteristic
451C22⋊C8C23×C6111yescharacteristic
452C22⋊C8C23×C6112yes—
453#97—21no—
454C4×C8—21no—
455#95—21no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95C23×C6112yes—
460#41—81no—
461#41—81no—
462#41—82no—
463#41—82no—
464C2×Q8—22no—
465C2×Q8—21no—
466C2×Q8C2×D4×C6111yescharacteristic
467C2×D4—21no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4C2×D4×C6111yescharacteristic
474C2×D4C2×D4×C6112yes—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4C2×D4×C6112yes—
484C22×C4C2×D4×C6111yescharacteristic
485C22×C4C2×D4×C6112yes—
486C22×C4C2×D4×C6111yescharacteristic
487C22×C4C24×C6111yescharacteristic
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—81no—
517C4⋊C4—82no—
518C4⋊C4C2×D4×C6112yes—
519C4⋊C4C2×D4×C6111yescharacteristic
520C4⋊C4C2×D4×C6111yescharacteristic
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—22no—
531C22⋊C4—21no—
532C22⋊C4—22no—
533C42—22no—
534C42—21no—
535C42C2×D4×C6111yescharacteristic
536C42C2×D4×C6111yescharacteristic
537C42C2×D4×C6111yescharacteristic
538C42C2×D4×C6111yescharacteristic
539C23—21no—
540C23—22no—
541C23C22×D4×C6111yescharacteristic
542Q8—41no—
543Q8—81no—
544Q8—82no—
545D4—42no—
546D4—41no—
547D4—42no—
548D4—42no—
549D4—41no—
550D4—42no—
551D4—41no—
552D4—81no—
553D4—82no—
554D4—82no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4—82no—
580C2×C4—82no—
581C2×C4#120×C6111yescharacteristic
582C2×C4#120×C6111yescharacteristic
583C2×C4#120×C6111yescharacteristic
584C2×C4#120×C6111yescharacteristic
585C2×C4C22×D4×C6111yescharacteristic
586C2×C4C22×D4×C6111yescharacteristic
587C8—42no—
588C8—41no—
589C8—41no—
590C22—21no—
591C22—21no—
592C22—42no—
593C22—41no—
594C22—41no—
595C22—42no—
596C22—42no—
597C22—41no—
598C22C2×#120×C6111yescharacteristic
599C22C61×#57611yescharacteristic
600C22C61×#57711yescharacteristic
601C4—21no—
602C4—21no—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—21no—
607C4—42no—
608C4—42no—
609C4—41no—
610C4—41no—
611C4—42no—
612C4—41no—
613C4—82no—
614C4—81no—
615C4—81no—
616C2—21no—
617C2—21no—
618C2—81no—
619C2—82no—
620C2C61×#301211yescharacteristic
621C2C61×#302011yescharacteristic
622C2C61×#302811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3559C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#3234C2semidirect
3. C61×#3232C2semidirect
4. C61×#2822C2semidirect
5. C61×#1616C2semidirect
6. C61×#1615C2semidirect
7. C61×#1610C2semidirect
8. C61×#1609C2semidirect
9. C61×#1517C2semidirect
10. C61×#1512C2semidirect
11. C61×#1470C2semidirect
278. #18468C61direct (N × H)
306. #3234C2×C61semidirect
307. #3232C2×C61semidirect
308. #2822C2×C61semidirect
309. #1616C2×C61semidirect
310. #1615C2×C61semidirect
311. #1610C2×C61semidirect
312. #1609C2×C61semidirect
313. #1517C2×C61semidirect
314. #1512C2×C61semidirect
315. #1470C2×C61semidirect
366. C61#18468direct (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×#32342
C61×#32322
C61×#28222
C61×#16162
C61×#16152
C61×#16102
C61×#16092
C61×#15172
C61×#15122
C61×#14702
#1846861