Finite Group Databasebeta

← C61×#14410 #29517843

Subgroups — C61×#14410 #29517843

Order 15616.

1866 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#388C212yesmaximal, complemented
2C2×C61×#386C211yesmaximal, characteristic
3C2×C61×#380C212yesmaximal, complemented
4C61×#1442C212yesmaximal, complemented
5C61×#1439C212yesmaximal, complemented
6C61×#1438C211yesmaximal, characteristic
7C61×#1438C211yesmaximal, characteristic
8C61×#1437C212yesmaximal, complemented
9C61×#1436C212yesmaximal, complemented
10C23×D4×C61C2211yescharacteristic
11C24×C4×C61C2211yescharacteristic
12C22×C4⋊C4×C61C2212yes—
13C22×C4⋊C4×C61C2212yes—
14C22×C22⋊C4×C61C2212yes—
15C22×C22⋊C4×C61C2212yes—
16C22×C22⋊C4×C61C2211yescharacteristic
17C22×C22⋊C4×C61C2212yes—
18C22×C22⋊C4×C61C2212yes—
19C22×C22⋊C4×C61C2211yescharacteristic
20C22×C22⋊C4×C61C2211yescharacteristic
21C22×C42×C61C2212yes—
22C61×#388—28no—
23C61×#386C418yescomplemented
24C61×#380—28no—
25C2×#95×C61C2212yes—
26C2×#95×C61C2212yes—
27C2×#95×C61C2211yescharacteristic
28C2×#95×C61C2212yes—
29C2×#95×C61C2212yes—
30C2×#95×C61C2212yes—
31C2×#95×C61C2211yescharacteristic
32C2×#95×C61C2212yes—
33C2×#95×C61C2212yes—
34C25×C61C2311yescharacteristic
35C25×C61C2311yescharacteristic
36C22×D4×C61—24no—
37C22×D4×C61—42no—
38C22×D4×C61—41no—
39C22×D4×C61—41no—
40C22×D4×C61C2×C414yes—
41C23×C4×C61—24no—
42C23×C4×C61—24no—
43C23×C4×C61—41no—
44C23×C4×C61—41no—
45C23×C4×C61C2×C414yes—
46C23×C4×C61C2312yes—
47C23×C4×C61C2312yes—
48C23×C4×C61C2311yescharacteristic
49C23×C4×C61C2312yes—
50C23×C4×C61C2312yes—
51C23×C4×C61C2312yes—
52C23×C4×C61C2312yes—
53C2×C4⋊C4×C61—24no—
54C2×C4⋊C4×C61—24no—
55C2×C4⋊C4×C61—24no—
56C2×C4⋊C4×C61—24no—
57C2×C4⋊C4×C61—42no—
58C2×C4⋊C4×C61—42no—
59C2×C22⋊C4×C61—24no—
60C2×C22⋊C4×C61—24no—
61C2×C22⋊C4×C61—24no—
62C2×C22⋊C4×C61—24no—
63C2×C22⋊C4×C61—24no—
64C2×C22⋊C4×C61—24no—
65C2×C22⋊C4×C61—24no—
66C2×C22⋊C4×C61—24no—
67C2×C22⋊C4×C61—42no—
68C2×C22⋊C4×C61—41no—
69C2×C22⋊C4×C61—42no—
70C2×C22⋊C4×C61—42no—
71C2×C22⋊C4×C61—42no—
72C2×C22⋊C4×C61—42no—
73C2×C22⋊C4×C61—42no—
74C2×C22⋊C4×C61—41no—
75C2×C22⋊C4×C61C2×C418yes—
76C2×C22⋊C4×C61C2×C414yes—
77C2×C42×C61—24no—
78C2×C42×C61—42no—
79C2×C42×C61—42no—
80#95×C61—24no—
81#95×C61—24no—
82#95×C61—42no—
83#95×C61—42no—
84#95×C61—42no—
85#95×C61—41no—
86#95×C61—41no—
87#95×C61C2×C418yes—
88#95×C61D418yescomplemented
89C24×C61—22no—
90C24×C61—22no—
91C24×C61—22no—
92C24×C61—22no—
93C24×C61—21no—
94C24×C61—21no—
95C24×C61—22no—
96C24×C61—22no—
97C24×C61—22no—
98C24×C61—22no—
99C24×C61—22no—
100C24×C61—22no—
101C24×C61—21no—
102C24×C61—21no—
103C24×C61—22no—
104C24×C61C22×C412yes—
105C24×C61C22×C412yes—
106C24×C61#4114yes—
107C24×C61C2411yescharacteristic
108C2×D4×C61—28no—
109C2×D4×C61—44no—
110C2×D4×C61—44no—
111C2×D4×C61—48no—
112C2×D4×C61—48no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—22no—
122C22×C4×C61—22no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—22no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—216no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—44no—
155C22×C4×C61—44no—
156C22×C4×C61—48no—
157C22×C4×C61—44no—
158C22×C4×C61C22×C412yes—
159C22×C4×C61C22×C414yes—
160C22×C4×C61C22×C414yes—
161C22×C4×C61C2×D414yes—
162C22×C4×C61C2×D414yes—
163C22×C4×C61C2×D414yes—
164C22×C4×C61#4114yes—
165C4⋊C4×C61—48no—
166C4⋊C4×C61—48no—
167C22⋊C4×C61—216no—
168C22⋊C4×C61—44no—
169C22⋊C4×C61—44no—
170C22⋊C4×C61—48no—
171C22⋊C4×C61—48no—
172C22⋊C4×C61—48no—
173C22⋊C4×C61—44no—
174C42×C61—48no—
175C23×C61—24no—
176C23×C61—22no—
177C23×C61—22no—
178C23×C61—24no—
179C23×C61—24no—
180C23×C61—24no—
181C23×C61—24no—
182C23×C61—24no—
183C23×C61—24no—
184C23×C61—24no—
185C23×C61—22no—
186C23×C61—24no—
187C23×C61—22no—
188C23×C61—22no—
189C23×C61—24no—
190C23×C61—42no—
191C23×C61—42no—
192C23×C61—42no—
193C23×C61—42no—
194C23×C61—41no—
195C23×C61—42no—
196C23×C61—41no—
197C23×C61—41no—
198C23×C61—42no—
199C23×C61—41no—
200C23×C61—42no—
201C23×C61—42no—
202C23×C61—42no—
203C23×C61—42no—
204C23×C61—42no—
205C23×C61—42no—
206C23×C61—41no—
207C23×C61—42no—
208C23×C61—42no—
209C23×C61—42no—
210C23×C61—41no—
211C23×C61—42no—
212C23×C61—42no—
213C23×C61—41no—
214C23×C61—42no—
215C23×C61—41no—
216C23×C61#11714yes—
217C23×C61C23×C411yescharacteristic
218C23×C61C22×D412yes—
219C23×C61C2×#4112yes—
220C23×C61C2×#4112yes—
221C23×C61H(5,𝔽2)12yes—
222C23×C61H(5,𝔽2)11yescharacteristic
223C23×C61H(5,𝔽2)11yescharacteristic
224C23×C61H(5,𝔽2)12yes—
225C23×C612−1+412yes—
226D4×C61—416no—
227C2×C4×C61—24no—
228C2×C4×C61—24no—
229C2×C4×C61—24no—
230C2×C4×C61—24no—
231C2×C4×C61—24no—
232C2×C4×C61—24no—
233C2×C4×C61—22no—
234C2×C4×C61—24no—
235C2×C4×C61—24no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—24no—
239C2×C4×C61—24no—
240C2×C4×C61—24no—
241C2×C4×C61—24no—
242C2×C4×C61—24no—
243C2×C4×C61—24no—
244C2×C4×C61—24no—
245C2×C4×C61—416no—
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—42no—
253C2×C4×C61—42no—
254C2×C4×C61—42no—
255C2×C4×C61—42no—
256C2×C4×C61—42no—
257C2×C4×C61—42no—
258C2×C4×C61—42no—
259C2×C4×C61—42no—
260C2×C4×C61—42no—
261C2×C4×C61—42no—
262C2×C4×C61—42no—
263C2×C4×C61—42no—
264C2×C4×C61—42no—
265C2×C4×C61—42no—
266C2×C4×C61—42no—
267C2×C4×C61—42no—
268C2×C4×C61—42no—
269C2×C4×C61—42no—
270C2×C4×C61—42no—
271C2×C4×C61—42no—
272C2×C4×C61—42no—
273C2×C4×C61—42no—
274C2×C4×C61C4×D418yes—
275#14410C6111yesmaximal, characteristic, direct product factor, Sylow
276C22×C61—24no—
277C22×C61—28no—
278C22×C61—44no—
279C22×C61—42no—
280C22×C61—42no—
281C22×C61—44no—
282C22×C61—44no—
283C22×C61—44no—
284C22×C61—44no—
285C22×C61—42no—
286C22×C61—44no—
287C22×C61—44no—
288C22×C61—42no—
289C22×C61—42no—
290C22×C61—82no—
291C22×C61—82no—
292C22×C61—82no—
293C22×C61—82no—
294C22×C61C2×#11711yescharacteristic
295C22×C61C2×C4×D412yes—
296C22×C61#51811yescharacteristic
297C22×C61#51811yescharacteristic
298C22×C61#52012yes—
299C22×C61#53512yes—
300C22×C61#53712yes—
301C22×C61#53812yes—
302C22×C61#53812yes—
303C22×C61#54012yes—
304C22×C61#54212yes—
305C22×C61D4211yescharacteristic
306C22×C61#54612yes—
307C22×C61#54612yes—
308C22×C61#54812yes—
309C22×C61#55111yescharacteristic
310C22×C61#55212yes—
311C22×C61#55312yes—
312C22×C61#56011yescharacteristic
313C22×C61#56212yes—
314C22×C61#56311yescharacteristic
315C4×C61—28no—
316C4×C61—42no—
317C4×C61—44no—
318C4×C61—44no—
319C4×C61—44no—
320C4×C61—82no—
321C4×C61—82no—
322C2×#388C2×C6112yescomplemented
323C2×#386C2×C6111yescharacteristic
324C2×#380C2×C6112yescomplemented
325#1442C2×C6112yescomplemented
326#1439C2×C6112yescomplemented
327#1438C2×C6111yescharacteristic
328#1438C2×C6111yescharacteristic
329#1437C2×C6112yescomplemented
330#1436C2×C6112yescomplemented
331C2×C61—44no—
332C2×C61—82no—
333C2×C61#231211yescharacteristic
334C2×C61#232412yes—
335C2×C61#235212yes—
336C2×C61#235811yescharacteristic
337C2×C61#237611yescharacteristic
338C2×C61#267612yes—
339C2×C61#270212yes—
340C2×C61#270312yes—
341C2×C61#274112yes—
342C23×D4C22×C6111yescharacteristic
343C24×C4C22×C6111yescharacteristic
344C22×C4⋊C4C22×C6112yes—
345C22×C4⋊C4C22×C6112yes—
346C22×C22⋊C4C22×C6112yes—
347C22×C22⋊C4C22×C6112yes—
348C22×C22⋊C4C22×C6111yescharacteristic
349C22×C22⋊C4C22×C6112yes—
350C22×C22⋊C4C22×C6112yes—
351C22×C22⋊C4C22×C6111yescharacteristic
352C22×C22⋊C4C22×C6111yescharacteristic
353C22×C42C22×C6112yes—
354#388—28no—
355#386C4×C6118yescomplemented
356#380—28no—
357C2×#95C22×C6112yes—
358C2×#95C22×C6112yes—
359C2×#95C22×C6111yescharacteristic
360C2×#95C22×C6112yes—
361C2×#95C22×C6112yes—
362C2×#95C22×C6112yes—
363C2×#95C22×C6111yescharacteristic
364C2×#95C22×C6112yes—
365C2×#95C22×C6112yes—
366C61#1441011yescharacteristic, direct product factor, Sylow
367C25C23×C6111yescharacteristic
368C25C23×C6111yescharacteristic
369C22×D4—24no—
370C22×D4—42no—
371C22×D4—41no—
372C22×D4—41no—
373C22×D4C2×C4×C6114yes—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—41no—
377C23×C4—41no—
378C23×C4C2×C4×C6114yes—
379C23×C4C23×C6112yes—
380C23×C4C23×C6112yes—
381C23×C4C23×C6112yes—
382C23×C4C23×C6111yescharacteristic
383C23×C4C23×C6112yes—
384C23×C4C23×C6112yes—
385C23×C4C23×C6112yes—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—42no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—41no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4C2×C4×C6118yes—
409C2×C22⋊C4C2×C4×C6114yes—
410C2×C42—24no—
411C2×C42—42no—
412C2×C42—42no—
413#95—24no—
414#95—24no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—41no—
419#95—41no—
420#95C2×C4×C6118yes—
421#95D4×C6118yescomplemented
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—21no—
435C24—21no—
436C24—22no—
437C24C22×C4×C6112yes—
438C24C22×C4×C6112yes—
439C24#41×C6114yes—
440C24C24×C6111yescharacteristic
441C2×D4—28no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—48no—
445C2×D4—48no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—216no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—48no—
490C22×C4—44no—
491C22×C4C22×C4×C6112yes—
492C22×C4C22×C4×C6114yes—
493C22×C4C22×C4×C6114yes—
494C22×C4C2×D4×C6114yes—
495C22×C4C2×D4×C6114yes—
496C22×C4C2×D4×C6114yes—
497C22×C4#41×C6114yes—
498C4⋊C4—48no—
499C4⋊C4—48no—
500C22⋊C4—216no—
501C22⋊C4—44no—
502C22⋊C4—44no—
503C22⋊C4—48no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—44no—
507C42—48no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—22no—
516C23—22no—
517C23—24no—
518C23—22no—
519C23—24no—
520C23—22no—
521C23—22no—
522C23—24no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—41no—
528C23—42no—
529C23—41no—
530C23—41no—
531C23—42no—
532C23—41no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—41no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—41no—
544C23—42no—
545C23—42no—
546C23—41no—
547C23—42no—
548C23—41no—
549C23#117×C6114yes—
550C23C23×C4×C6111yescharacteristic
551C23C22×D4×C6112yes—
552C23C2×#41×C6112yes—
553C23C2×#41×C6112yes—
554C23H(5,𝔽2)×C6112yes—
555C23H(5,𝔽2)×C6112yes—
556C23H(5,𝔽2)×C6111yescharacteristic
557C23H(5,𝔽2)×C6111yescharacteristic
558C232−1+4×C6112yes—
559D4—416no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—416no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4C4×D4×C6118yes—
608C22—24no—
609C22—28no—
610C22—44no—
611C22—42no—
612C22—42no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—42no—
618C22—44no—
619C22—44no—
620C22—42no—
621C22—42no—
622C22—82no—
623C22—82no—
624C22—82no—
625C22—82no—
626C22C2×#117×C6111yescharacteristic
627C22C2×C4×D4×C6112yes—
628C22C61×#51811yescharacteristic
629C22C61×#51811yescharacteristic
630C22C61×#52012yes—
631C22C61×#53512yes—
632C22C61×#53712yes—
633C22C61×#53812yes—
634C22C61×#53812yes—
635C22C61×#54012yes—
636C22C61×#54212yes—
637C22D42×C6111yescharacteristic
638C22C61×#54612yes—
639C22C61×#54612yes—
640C22C61×#54812yes—
641C22C61×#55111yescharacteristic
642C22C61×#55212yes—
643C22C61×#55312yes—
644C22C61×#56011yescharacteristic
645C22C61×#56212yes—
646C22C61×#56311yescharacteristic
647C4—28no—
648C4—42no—
649C4—44no—
650C4—44no—
651C4—44no—
652C4—82no—
653C4—82no—
654C2—44no—
655C2—82no—
656C2C61×#231211yescharacteristic
657C2C61×#232412yes—
658C2C61×#235212yes—
659C2C61×#235811yescharacteristic
660C2C61×#237611yescharacteristic
661C2C61×#267612yes—
662C2C61×#270212yes—
663C2C61×#270312yes—
664C2C61×#274112yes—
subgroupG/H
center, socleC24×C61C24
commutatorC23C23×C4×C61
Frattini, cosocleC24C24×C61
prime radicalC23×D4×C61C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#388C2semidirect
3. C2×C61×#380C2semidirect
4. C61×#1442C2semidirect
5. C61×#1439C2semidirect
8. C61×#1437C2semidirect
9. C61×#1436C2semidirect
23. C61×#386C4semidirect
88. #95×C61D4semidirect
275. #14410C61direct (N × H)
322. C2×#388C2×C61semidirect
324. C2×#380C2×C61semidirect
325. #1442C2×C61semidirect
326. #1439C2×C61semidirect
329. #1437C2×C61semidirect
330. #1436C2×C61semidirect
355. #386C4×C61semidirect
366. C61#14410direct (N × H)
421. #95D4×C61semidirect

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×#3862
C2×C61×#3802
C61×#14422
C61×#14392
C61×#14382
C61×#14372
C61×#14362
#1441061