Finite Group Databasebeta

← C61×#15079 #29518512

Subgroups — C61×#15079 #29518512

Order 15616.

1534 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#388C211yesmaximal, characteristic
2C2×C61×#388C212yesmaximal
3C2×C61×#387C212yesmaximal, complemented
4C2×C4×C4⋊C4×C61C211yesmaximal, characteristic, complemented
5C61×#1445C212yesmaximal, complemented
6C61×#1444C211yesmaximal, characteristic, complemented
7C61×#1444C211yesmaximal, characteristic, complemented
8C61×#1439C212yesmaximal
9C61×#1439C211yesmaximal, characteristic
10C61×#1439C211yesmaximal, characteristic
11C61×#1434C211yesmaximal, characteristic, complemented
12C22×C4⋊C4×C61C2211yescharacteristic
13C22×C4⋊C4×C61C2211yescharacteristic
14C22×C4⋊C4×C61C2211yescharacteristic
15C22×C4⋊C4×C61C2212yes—
16C22×C4⋊C4×C61C2212yes—
17C22×C22⋊C4×C61C2211yescharacteristic
18C22×C22⋊C4×C61C2211yescharacteristic
19C22×C22⋊C4×C61C2212yes—
20C22×C22⋊C4×C61C2211yescharacteristic
21C22×C22⋊C4×C61C2212yes—
22C22×C42×C61C2212yes—
23C22×C42×C61C2211yescharacteristic
24C61×#388—24no—
25C61×#388—28no—
26C61×#387—28no—
27C4×C4⋊C4×C61—24no—
28C2×#95×C61C2212yes—
29C2×#95×C61C2212yes—
30C2×#95×C61C2212yes—
31C2×#95×C61C2212yes—
32C2×#95×C61C2211yescharacteristic
33C2×#95×C61C2212yes—
34C2×#95×C61C2211yescharacteristic
35C2×#95×C61C2211yescharacteristic
36C2×#95×C61C2211yescharacteristic
37C2×#95×C61C2212yes—
38C2×#95×C61C2212yes—
39C25×C61C2311yescharacteristic
40C23×C4×C61C2311yescharacteristic
41C23×C4×C61C2311yescharacteristic
42C23×C4×C61C2311yescharacteristic
43C23×C4×C61C2312yes—
44C23×C4×C61C2312yes—
45C23×C4×C61C2312yes—
46C23×C4×C61C2312yes—
47C23×C4×C61C2311yescharacteristic
48C23×C4×C61C2311yescharacteristic
49C23×C4×C61C2311yescharacteristic
50C2×C4⋊C4×C61—22no—
51C2×C4⋊C4×C61—22no—
52C2×C4⋊C4×C61—24no—
53C2×C4⋊C4×C61—24no—
54C2×C4⋊C4×C61—24no—
55C2×C4⋊C4×C61—24no—
56C2×C4⋊C4×C61—24no—
57C2×C4⋊C4×C61—24no—
58C2×C4⋊C4×C61—24no—
59C2×C4⋊C4×C61—22no—
60C2×C4⋊C4×C61—24no—
61C2×C4⋊C4×C61—42no—
62C2×C22⋊C4×C61—22no—
63C2×C22⋊C4×C61—24no—
64C2×C22⋊C4×C61—24no—
65C2×C22⋊C4×C61—22no—
66C2×C22⋊C4×C61—24no—
67C2×C22⋊C4×C61—22no—
68C2×C22⋊C4×C61—24no—
69C2×C22⋊C4×C61—22no—
70C2×C22⋊C4×C61—22no—
71C2×C22⋊C4×C61—24no—
72C2×C22⋊C4×C61—24no—
73C2×C22⋊C4×C61—22no—
74C2×C22⋊C4×C61—22no—
75C2×C22⋊C4×C61—42no—
76C2×C42×C61—22no—
77C2×C42×C61—22no—
78C2×C42×C61—24no—
79C2×C42×C61—24no—
80C2×C42×C61—24no—
81C2×C42×C61D414yes—
82#95×C61—24no—
83#95×C61—24no—
84#95×C61—24no—
85#95×C61—24no—
86#95×C61—24no—
87#95×C61—22no—
88#95×C61—22no—
89#95×C61—22no—
90#95×C61—22no—
91#95×C61—42no—
92#95×C61D418yes—
93C24×C61—21no—
94C24×C61—22no—
95C24×C61—22no—
96C24×C61—21no—
97C24×C61—21no—
98C24×C61—22no—
99C24×C61—21no—
100C24×C61—21no—
101C24×C61—22no—
102C24×C61—21no—
103C24×C61#4112yes—
104C24×C61C2411yescharacteristic
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—21no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—22no—
123C22×C4×C61—21no—
124C22×C4×C61—22no—
125C22×C4×C61—21no—
126C22×C4×C61—22no—
127C22×C4×C61—21no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—21no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—21no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—21no—
145C22×C4×C61—22no—
146C22×C4×C61—21no—
147C22×C4×C61—22no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—22no—
151C22×C4×C61—21no—
152C22×C4×C61—22no—
153C22×C4×C61—21no—
154C22×C4×C61C2×D412yes—
155C22×C4×C61C2×D414yes—
156C22×C4×C61C2×D414yes—
157C22×C4×C61C2×D412yes—
158C22×C4×C61C2×D414yes—
159C22×C4×C61C2×D412yes—
160C22×C4×C61#4114yes—
161C22×C4×C61#4112yes—
162C22×C4×C61#4114yes—
163C22×C4×C61#4112yes—
164C22×C4×C61#4112yes—
165C4⋊C4×C61—28no—
166C4⋊C4×C61—28no—
167C4⋊C4×C61—216no—
168C4⋊C4×C61—48no—
169C4⋊C4×C61—44no—
170C22⋊C4×C61—216no—
171C22⋊C4×C61—28no—
172C22⋊C4×C61—48no—
173C22⋊C4×C61—44no—
174C22⋊C4×C61—44no—
175C42×C61—28no—
176C42×C61—48no—
177C23×C61—22no—
178C23×C61—24no—
179C23×C61—24no—
180C23×C61—22no—
181C23×C61—22no—
182C23×C61—41no—
183C23×C61—41no—
184C23×C61—41no—
185C23×C61—42no—
186C23×C61—42no—
187C23×C61—42no—
188C23×C61—41no—
189C23×C61—41no—
190C23×C61—41no—
191C23×C61—42no—
192C23×C61—42no—
193C23×C61—42no—
194C23×C61—42no—
195C23×C61—42no—
196C23×C61—42no—
197C23×C61—41no—
198C23×C61—42no—
199C23×C61—41no—
200C23×C61C22×D411yescharacteristic
201C23×C61C22×D412yes—
202C23×C61C2×#4111yescharacteristic
203C23×C61C2×#4111yescharacteristic
204C23×C61C2×#4112yes—
205C23×C61C2×#4111yescharacteristic
206C23×C61C2×#4111yescharacteristic
207C23×C61C2×#4112yes—
208C23×C61H(5,𝔽2)11yescharacteristic
209C23×C612−1+412yes—
210C23×C612−1+411yescharacteristic
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—24no—
215C2×C4×C61—24no—
216C2×C4×C61—22no—
217C2×C4×C61—24no—
218C2×C4×C61—24no—
219C2×C4×C61—22no—
220C2×C4×C61—24no—
221C2×C4×C61—22no—
222C2×C4×C61—22no—
223C2×C4×C61—24no—
224C2×C4×C61—24no—
225C2×C4×C61—24no—
226C2×C4×C61—24no—
227C2×C4×C61—24no—
228C2×C4×C61—24no—
229C2×C4×C61—22no—
230C2×C4×C61—24no—
231C2×C4×C61—24no—
232C2×C4×C61—24no—
233C2×C4×C61—24no—
234C2×C4×C61—24no—
235C2×C4×C61—24no—
236C2×C4×C61—41no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—41no—
246C2×C4×C61—42no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61—41no—
253C2×C4×C61—42no—
254C2×C4×C61—41no—
255C2×C4×C61—42no—
256C2×C4×C61—41no—
257C2×C4×C61—42no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—42no—
266C2×C4×C61—42no—
267C2×C4×C61—42no—
268C2×C4×C61—42no—
269C2×C4×C61#12314yes—
270C2×C4×C61#12714yes—
271#15079C6111yesmaximal, characteristic, direct product factor, Sylow
272C22×C61—42no—
273C22×C61—42no—
274C22×C61—44no—
275C22×C61—44no—
276C22×C61—42no—
277C22×C61—81no—
278C22×C61—81no—
279C22×C61—82no—
280C22×C61—82no—
281C22×C61—81no—
282C22×C61—81no—
283C22×C61C2×#12311yescharacteristic
284C22×C61#52511yescharacteristic
285C22×C61#52511yescharacteristic
286C22×C61#52511yescharacteristic
287C22×C61#52512yes—
288C22×C61#52512yes—
289C22×C61#52912yes—
290C22×C61#52912yes—
291C22×C61C2×#12711yescharacteristic
292C22×C61#53611yescharacteristic
293C22×C61#53711yescharacteristic
294C22×C61#54112yes—
295C22×C61#54212yes—
296C22×C61#54612yes—
297C22×C61#54712yes—
298C22×C61#54712yes—
299C22×C61#54812yes—
300C22×C61#55212yes—
301C22×C61#55211yescharacteristic
302C22×C61#55311yescharacteristic
303C22×C61#55511yescharacteristic
304C22×C61#55612yes—
305C22×C61#55611yescharacteristic
306C4×C61—24no—
307C4×C61—24no—
308C4×C61—44no—
309C4×C61—42no—
310C4×C61—44no—
311C4×C61—44no—
312C4×C61—42no—
313C4×C61—44no—
314C4×C61—81no—
315C4×C61—81no—
316C2×#388C2×C6111yescharacteristic
317C2×#388C2×C6112yes—
318C2×#387C2×C6112yescomplemented
319C2×C4×C4⋊C4C2×C6111yescharacteristic, complemented
320#1445C2×C6112yescomplemented
321#1444C2×C6111yescharacteristic, complemented
322#1444C2×C6111yescharacteristic, complemented
323#1439C2×C6111yescharacteristic
324#1439C2×C6112yes—
325#1439C2×C6111yescharacteristic
326#1434C2×C6111yescharacteristic, complemented
327C2×C61—82no—
328C2×C61#239711yescharacteristic
329C2×C61#246812yes—
330C2×C61#246912yes—
331C2×C61#247412yes—
332C2×C61#247512yes—
333C2×C61#248511yescharacteristic
334C2×C61#250111yescharacteristic
335C2×C61#254011yescharacteristic
336C2×C61#259911yescharacteristic
337C2×C61#263711yescharacteristic
338C2×C61#285311yescharacteristic
339C22×C4⋊C4C22×C6111yescharacteristic
340C22×C4⋊C4C22×C6111yescharacteristic
341C22×C4⋊C4C22×C6112yes—
342C22×C4⋊C4C22×C6111yescharacteristic
343C22×C4⋊C4C22×C6112yes—
344C22×C22⋊C4C22×C6112yes—
345C22×C22⋊C4C22×C6111yescharacteristic
346C22×C22⋊C4C22×C6111yescharacteristic
347C22×C22⋊C4C22×C6111yescharacteristic
348C22×C22⋊C4C22×C6112yes—
349C22×C42C22×C6112yes—
350C22×C42C22×C6111yescharacteristic
351#388—24no—
352#388—28no—
353#387—28no—
354C4×C4⋊C4—24no—
355C2×#95C22×C6111yescharacteristic
356C2×#95C22×C6111yescharacteristic
357C2×#95C22×C6112yes—
358C2×#95C22×C6112yes—
359C2×#95C22×C6112yes—
360C2×#95C22×C6112yes—
361C2×#95C22×C6111yescharacteristic
362C2×#95C22×C6112yes—
363C2×#95C22×C6111yescharacteristic
364C2×#95C22×C6112yes—
365C2×#95C22×C6112yes—
366C61#1507911yescharacteristic, direct product factor, Sylow
367C25C23×C6111yescharacteristic
368C23×C4C23×C6111yescharacteristic
369C23×C4C23×C6111yescharacteristic
370C23×C4C23×C6112yes—
371C23×C4C23×C6112yes—
372C23×C4C23×C6111yescharacteristic
373C23×C4C23×C6111yescharacteristic
374C23×C4C23×C6112yes—
375C23×C4C23×C6112yes—
376C23×C4C23×C6111yescharacteristic
377C23×C4C23×C6111yescharacteristic
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—42no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—42no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42D4×C6114yes—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—22no—
416#95—22no—
417#95—22no—
418#95—22no—
419#95—42no—
420#95D4×C6118yes—
421C24—21no—
422C24—22no—
423C24—22no—
424C24—21no—
425C24—21no—
426C24—22no—
427C24—21no—
428C24—21no—
429C24—22no—
430C24—21no—
431C24#41×C6112yes—
432C24C24×C6111yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4C2×D4×C6112yes—
483C22×C4C2×D4×C6114yes—
484C22×C4C2×D4×C6114yes—
485C22×C4C2×D4×C6112yes—
486C22×C4C2×D4×C6114yes—
487C22×C4C2×D4×C6112yes—
488C22×C4#41×C6114yes—
489C22×C4#41×C6114yes—
490C22×C4#41×C6112yes—
491C22×C4#41×C6112yes—
492C22×C4#41×C6112yes—
493C4⋊C4—28no—
494C4⋊C4—28no—
495C4⋊C4—216no—
496C4⋊C4—48no—
497C4⋊C4—44no—
498C22⋊C4—216no—
499C22⋊C4—28no—
500C22⋊C4—48no—
501C22⋊C4—44no—
502C22⋊C4—44no—
503C42—28no—
504C42—48no—
505C23—24no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—24no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—41no—
520C23—42no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23C22×D4×C6111yescharacteristic
529C23C22×D4×C6112yes—
530C23C2×#41×C6112yes—
531C23C2×#41×C6112yes—
532C23C2×#41×C6111yescharacteristic
533C23C2×#41×C6111yescharacteristic
534C23C2×#41×C6111yescharacteristic
535C23C2×#41×C6111yescharacteristic
536C23H(5,𝔽2)×C6111yescharacteristic
537C232−1+4×C6112yes—
538C232−1+4×C6111yescharacteristic
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—42no—
565C2×C4—42no—
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—42no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4#123×C6114yes—
598C2×C4#127×C6114yes—
599C22—42no—
600C22—42no—
601C22—44no—
602C22—44no—
603C22—42no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—82no—
608C22—82no—
609C22—81no—
610C22C2×#123×C6111yescharacteristic
611C22C61×#52511yescharacteristic
612C22C61×#52511yescharacteristic
613C22C61×#52511yescharacteristic
614C22C61×#52512yes—
615C22C61×#52512yes—
616C22C61×#52912yes—
617C22C61×#52912yes—
618C22C2×#127×C6111yescharacteristic
619C22C61×#53611yescharacteristic
620C22C61×#53711yescharacteristic
621C22C61×#54112yes—
622C22C61×#54212yes—
623C22C61×#54612yes—
624C22C61×#54712yes—
625C22C61×#54712yes—
626C22C61×#54812yes—
627C22C61×#55212yes—
628C22C61×#55211yescharacteristic
629C22C61×#55311yescharacteristic
630C22C61×#55511yescharacteristic
631C22C61×#55612yes—
632C22C61×#55611yescharacteristic
633C4—24no—
634C4—24no—
635C4—44no—
636C4—44no—
637C4—42no—
638C4—44no—
639C4—44no—
640C4—42no—
641C4—81no—
642C4—81no—
643C2—82no—
644C2C61×#239711yescharacteristic
645C2C61×#246812yes—
646C2C61×#246912yes—
647C2C61×#247412yes—
648C2C61×#247512yes—
649C2C61×#248511yescharacteristic
650C2C61×#250111yescharacteristic
651C2C61×#254011yescharacteristic
652C2C61×#259911yescharacteristic
653C2C61×#263711yescharacteristic
654C2C61×#285311yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC24C24×C61
prime radicalC25×C61C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C61×#387C2semidirect
4. C2×C4×C4⋊C4×C61C2semidirect
5. C61×#1445C2semidirect
6. C61×#1444C2semidirect
7. C61×#1444C2semidirect
11. C61×#1434C2semidirect
271. #15079C61direct (N × H)
318. C2×#387C2×C61semidirect
319. C2×C4×C4⋊C4C2×C61semidirect
320. #1445C2×C61semidirect
321. #1444C2×C61semidirect
322. #1444C2×C61semidirect
326. #1434C2×C61semidirect
366. C61#15079direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#3882
C2×C61×#3872
C2×C4×C4⋊C4×C612
C61×#14452
C61×#14442
C61×#14392
C61×#14342
#1507961