Finite Group Databasebeta

← C61×#14402 #29517835

Subgroups — C61×#14402 #29517835

Order 15616.

1750 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#389C212yesmaximal, complemented
2C2×C61×#388C212yesmaximal
3C2×C61×#385C211yesmaximal, characteristic
4C2×C61×#380C212yesmaximal
5C61×#1444C212yesmaximal, complemented
6C61×#1441C212yesmaximal, complemented
7C61×#1439C211yesmaximal, characteristic
8C61×#1439C211yesmaximal, characteristic
9C61×#1436C212yesmaximal, complemented
10C24×C4×C61C2211yescharacteristic
11C22×C4⋊C4×C61C2212yes—
12C22×C4⋊C4×C61C2212yes—
13C22×C4⋊C4×C61C2212yes—
14C22×C4⋊C4×C61C2211yescharacteristic
15C22×C4⋊C4×C61C2212yes—
16C22×C4⋊C4×C61C2211yescharacteristic
17C22×C22⋊C4×C61C2212yes—
18C22×C22⋊C4×C61C2212yes—
19C22×C22⋊C4×C61C2211yescharacteristic
20C22×C22⋊C4×C61C2211yescharacteristic
21C22×C42×C61C2212yes—
22C61×#389—28no—
23C61×#388—28no—
24C61×#385C418yescomplemented
25C61×#380—28no—
26C2×#95×C61C2212yes—
27C2×#95×C61C2212yes—
28C2×#95×C61C2212yes—
29C2×#95×C61C2212yes—
30C2×#95×C61C2211yescharacteristic
31C2×#95×C61C2212yes—
32C2×#95×C61C2211yescharacteristic
33C2×#95×C61C2212yes—
34C2×#95×C61C2212yes—
35C25×C61C2311yescharacteristic
36C23×C4×C61—24no—
37C23×C4×C61—24no—
38C23×C4×C61—41no—
39C23×C4×C61—41no—
40C23×C4×C61C2×C414yes—
41C23×C4×C61C2312yes—
42C23×C4×C61C2312yes—
43C23×C4×C61C2311yescharacteristic
44C23×C4×C61C2311yescharacteristic
45C23×C4×C61C2312yes—
46C23×C4×C61C2312yes—
47C23×C4×C61C2312yes—
48C23×C4×C61C2312yes—
49C2×C4⋊C4×C61—24no—
50C2×C4⋊C4×C61—24no—
51C2×C4⋊C4×C61—24no—
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—42no—
59C2×C4⋊C4×C61—42no—
60C2×C4⋊C4×C61—42no—
61C2×C4⋊C4×C61—41no—
62C2×C4⋊C4×C61—42no—
63C2×C4⋊C4×C61—41no—
64C2×C4⋊C4×C61C2×C418yes—
65C2×C22⋊C4×C61—24no—
66C2×C22⋊C4×C61—24no—
67C2×C22⋊C4×C61—24no—
68C2×C22⋊C4×C61—24no—
69C2×C22⋊C4×C61—41no—
70C2×C22⋊C4×C61—41no—
71C2×C22⋊C4×C61—42no—
72C2×C22⋊C4×C61—42no—
73C2×C22⋊C4×C61C2×C414yes—
74C2×C22⋊C4×C61C2×C414yes—
75C2×C22⋊C4×C61D414yes—
76C2×C22⋊C4×C61Q814yes—
77C2×C42×C61—24no—
78C2×C42×C61—24no—
79C2×C42×C61—42no—
80#95×C61—24no—
81#95×C61—24no—
82#95×C61—24no—
83#95×C61—24no—
84#95×C61—42no—
85#95×C61—41no—
86#95×C61—41no—
87#95×C61C2×C418yes—
88#95×C61D418yes—
89C24×C61—22no—
90C24×C61—22no—
91C24×C61—22no—
92C24×C61—21no—
93C24×C61—21no—
94C24×C61—21no—
95C24×C61—21no—
96C24×C61—22no—
97C24×C61C22×C412yes—
98C24×C61C2×D412yes—
99C24×C61C2×Q812yes—
100C24×C61C2411yescharacteristic
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61—22no—
104C22×C4×C61—22no—
105C22×C4×C61—22no—
106C22×C4×C61—22no—
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—22no—
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
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—216no—
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—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—44no—
145C22×C4×C61—44no—
146C22×C4×C61—48no—
147C22×C4×C61—44no—
148C22×C4×C61C22×C412yes—
149C22×C4×C61C22×C412yes—
150C22×C4×C61C22×C414yes—
151C22×C4×C61C22×C414yes—
152C22×C4×C61C2×D414yes—
153C22×C4×C61C2×D414yes—
154C22×C4×C61C2×D414yes—
155C22×C4×C61C2×D414yes—
156C22×C4×C61C2×Q814yes—
157C22×C4×C61#4114yes—
158C4⋊C4×C61—216no—
159C4⋊C4×C61—48no—
160C4⋊C4×C61—48no—
161C4⋊C4×C61—48no—
162C4⋊C4×C61—44no—
163C4⋊C4×C61—44no—
164C22⋊C4×C61—44no—
165C22⋊C4×C61—48no—
166C22⋊C4×C61—48no—
167C22⋊C4×C61C4⋊C4116yescomplemented
168C42×C61—48no—
169C23×C61—24no—
170C23×C61—22no—
171C23×C61—22no—
172C23×C61—24no—
173C23×C61—22no—
174C23×C61—22no—
175C23×C61—22no—
176C23×C61—22no—
177C23×C61—24no—
178C23×C61—24no—
179C23×C61—24no—
180C23×C61—24no—
181C23×C61—42no—
182C23×C61—42no—
183C23×C61—42no—
184C23×C61—42no—
185C23×C61—41no—
186C23×C61—42no—
187C23×C61—41no—
188C23×C61—41no—
189C23×C61—42no—
190C23×C61—41no—
191C23×C61C2×C4⋊C414yes—
192C23×C61C23×C411yescharacteristic
193C23×C61C22×D411yescharacteristic
194C23×C61C22×D412yes—
195C23×C61C22×Q811yescharacteristic
196C23×C61C2×#4112yes—
197C23×C61H(5,𝔽2)11yescharacteristic
198C23×C61H(5,𝔽2)11yescharacteristic
199C23×C61H(5,𝔽2)12yes—
200C23×C612−1+411yescharacteristic
201C23×C612−1+411yescharacteristic
202C23×C612−1+412yes—
203C2×C4×C61—24no—
204C2×C4×C61—24no—
205C2×C4×C61—24no—
206C2×C4×C61—24no—
207C2×C4×C61—24no—
208C2×C4×C61—24no—
209C2×C4×C61—24no—
210C2×C4×C61—24no—
211C2×C4×C61—24no—
212C2×C4×C61—24no—
213C2×C4×C61—24no—
214C2×C4×C61—24no—
215C2×C4×C61—24no—
216C2×C4×C61—22no—
217C2×C4×C61—22no—
218C2×C4×C61—24no—
219C2×C4×C61—24no—
220C2×C4×C61—24no—
221C2×C4×C61—24no—
222C2×C4×C61—24no—
223C2×C4×C61—24no—
224C2×C4×C61—24no—
225C2×C4×C61—416no—
226C2×C4×C61—42no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—41no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—42no—
237C2×C4×C61—42no—
238C2×C4×C61—42no—
239C2×C4×C61—41no—
240C2×C4×C61—42no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
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×C61C2×C4⋊C418yes—
255C2×C4×C61C4×D418yes—
256#14402C6111yesmaximal, characteristic, direct product factor, Sylow
257C22×C61—24no—
258C22×C61—28no—
259C22×C61—44no—
260C22×C61—42no—
261C22×C61—42no—
262C22×C61—44no—
263C22×C61—42no—
264C22×C61—42no—
265C22×C61—44no—
266C22×C61—42no—
267C22×C61—42no—
268C22×C61C22×C4⋊C411yescharacteristic
269C22×C61C2×C4×D412yes—
270C22×C61#51811yescharacteristic
271C22×C61#51911yescharacteristic
272C22×C61#52012yes—
273C22×C61#53612yes—
274C22×C61#53711yescharacteristic
275C22×C61#53711yescharacteristic
276C22×C61#53712yes—
277C22×C61#54112yes—
278C22×C61#54212yes—
279C22×C61#54411yescharacteristic
280C22×C61#54411yescharacteristic
281C22×C61D4212yes—
282C22×C61D4211yescharacteristic
283C22×C61#54612yes—
284C22×C61#54712yes—
285C22×C61D4×Q812yes—
286C22×C61#55111yescharacteristic
287C22×C61#55412yes—
288C22×C61#56011yescharacteristic
289C22×C61#56212yes—
290C22×C61#56311yescharacteristic
291C4×C61—28no—
292C4×C61—28no—
293C4×C61—42no—
294C4×C61—42no—
295C4×C61—44no—
296C4×C61—44no—
297C4×C61—82no—
298C4×C61—82no—
299C2×#389C2×C6112yescomplemented
300C2×#388C2×C6112yes—
301C2×#385C2×C6111yescharacteristic
302C2×#380C2×C6112yes—
303#1444C2×C6112yescomplemented
304#1441C2×C6112yescomplemented
305#1439C2×C6111yescharacteristic
306#1439C2×C6111yescharacteristic
307#1436C2×C6112yescomplemented
308C2×C61—44no—
309C2×C61#231611yescharacteristic
310C2×C61#232312yes—
311C2×C61D4×C4⋊C412yes—
312C2×C61#235811yescharacteristic
313C2×C61#237611yescharacteristic
314C2×C61#267212yes—
315C2×C61#267511yescharacteristic
316C2×C61#267711yescharacteristic
317C2×C61#270412yes—
318C2×C61#272211yescharacteristic
319C2×C61#274211yescharacteristic
320C24×C4C22×C6111yescharacteristic
321C22×C4⋊C4C22×C6112yes—
322C22×C4⋊C4C22×C6111yescharacteristic
323C22×C4⋊C4C22×C6112yes—
324C22×C4⋊C4C22×C6112yes—
325C22×C4⋊C4C22×C6112yes—
326C22×C4⋊C4C22×C6111yescharacteristic
327C22×C22⋊C4C22×C6112yes—
328C22×C22⋊C4C22×C6112yes—
329C22×C22⋊C4C22×C6111yescharacteristic
330C22×C22⋊C4C22×C6111yescharacteristic
331C22×C42C22×C6112yes—
332#389—28no—
333#388—28no—
334#385C4×C6118yescomplemented
335#380—28no—
336C2×#95C22×C6112yes—
337C2×#95C22×C6112yes—
338C2×#95C22×C6112yes—
339C2×#95C22×C6112yes—
340C2×#95C22×C6111yescharacteristic
341C2×#95C22×C6112yes—
342C2×#95C22×C6111yescharacteristic
343C2×#95C22×C6112yes—
344C2×#95C22×C6112yes—
345C61#1440211yescharacteristic, direct product factor, Sylow
346C25C23×C6111yescharacteristic
347C23×C4—24no—
348C23×C4—24no—
349C23×C4—41no—
350C23×C4—41no—
351C23×C4C2×C4×C6114yes—
352C23×C4C23×C6112yes—
353C23×C4C23×C6112yes—
354C23×C4C23×C6111yescharacteristic
355C23×C4C23×C6111yescharacteristic
356C23×C4C23×C6112yes—
357C23×C4C23×C6112yes—
358C23×C4C23×C6112yes—
359C23×C4C23×C6112yes—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—41no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—41no—
375C2×C4⋊C4C2×C4×C6118yes—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—41no—
381C2×C22⋊C4—41no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4C2×C4×C6114yes—
385C2×C22⋊C4C2×C4×C6114yes—
386C2×C22⋊C4D4×C6114yes—
387C2×C22⋊C4Q8×C6114yes—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—42no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—42no—
396#95—41no—
397#95—41no—
398#95C2×C4×C6118yes—
399#95D4×C6118yes—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—22no—
408C24C22×C4×C6112yes—
409C24C2×D4×C6112yes—
410C24C2×Q8×C6112yes—
411C24C24×C6111yescharacteristic
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—216no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
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—44no—
456C22×C4—44no—
457C22×C4—48no—
458C22×C4—44no—
459C22×C4C22×C4×C6112yes—
460C22×C4C22×C4×C6112yes—
461C22×C4C22×C4×C6114yes—
462C22×C4C22×C4×C6114yes—
463C22×C4C2×D4×C6114yes—
464C22×C4C2×D4×C6114yes—
465C22×C4C2×D4×C6114yes—
466C22×C4C2×D4×C6114yes—
467C22×C4C2×Q8×C6114yes—
468C22×C4#41×C6114yes—
469C4⋊C4—216no—
470C4⋊C4—48no—
471C4⋊C4—48no—
472C4⋊C4—48no—
473C4⋊C4—44no—
474C4⋊C4—44no—
475C22⋊C4—44no—
476C22⋊C4—48no—
477C22⋊C4—48no—
478C22⋊C4C4⋊C4×C61116yescomplemented
479C42—48no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—24no—
485C23—24no—
486C23—24no—
487C23—24no—
488C23—24no—
489C23—22no—
490C23—22no—
491C23—24no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—41no—
497C23—42no—
498C23—41no—
499C23—41no—
500C23—42no—
501C23—41no—
502C23C2×C4⋊C4×C6114yes—
503C23C23×C4×C6111yescharacteristic
504C23C22×D4×C6112yes—
505C23C22×D4×C6111yescharacteristic
506C23C22×Q8×C6111yescharacteristic
507C23C2×#41×C6112yes—
508C23H(5,𝔽2)×C6112yes—
509C23H(5,𝔽2)×C6111yescharacteristic
510C23H(5,𝔽2)×C6111yescharacteristic
511C232−1+4×C6111yescharacteristic
512C232−1+4×C6112yes—
513C232−1+4×C6111yescharacteristic
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—24no—
536C2×C4—416no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4C2×C4⋊C4×C6118yes—
566C2×C4C4×D4×C6118yes—
567C22—24no—
568C22—28no—
569C22—44no—
570C22—42no—
571C22—42no—
572C22—44no—
573C22—42no—
574C22—42no—
575C22—44no—
576C22—42no—
577C22—42no—
578C22C22×C4⋊C4×C6111yescharacteristic
579C22C2×C4×D4×C6112yes—
580C22C61×#51811yescharacteristic
581C22C61×#51911yescharacteristic
582C22C61×#52012yes—
583C22C61×#53612yes—
584C22C61×#53711yescharacteristic
585C22C61×#53711yescharacteristic
586C22C61×#53712yes—
587C22C61×#54112yes—
588C22C61×#54212yes—
589C22C61×#54411yescharacteristic
590C22C61×#54411yescharacteristic
591C22D42×C6112yes—
592C22D42×C6111yescharacteristic
593C22C61×#54612yes—
594C22C61×#54712yes—
595C22D4×Q8×C6112yes—
596C22C61×#55111yescharacteristic
597C22C61×#55412yes—
598C22C61×#56011yescharacteristic
599C22C61×#56212yes—
600C22C61×#56311yescharacteristic
601C4—28no—
602C4—28no—
603C4—42no—
604C4—42no—
605C4—44no—
606C4—44no—
607C4—82no—
608C4—82no—
609C2—44no—
610C2C61×#231611yescharacteristic
611C2C61×#232312yes—
612C2D4×C4⋊C4×C6112yes—
613C2C61×#235811yescharacteristic
614C2C61×#237611yescharacteristic
615C2C61×#267212yes—
616C2C61×#267511yescharacteristic
617C2C61×#267711yescharacteristic
618C2C61×#270412yes—
619C2C61×#272211yescharacteristic
620C2C61×#274211yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutatorC23C23×C4×C61
Frattini, cosocleC24C24×C61
prime radicalC25×C61C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#389C2semidirect
5. C61×#1444C2semidirect
6. C61×#1441C2semidirect
9. C61×#1436C2semidirect
24. C61×#385C4semidirect
167. C22⋊C4×C61C4⋊C4semidirect
256. #14402C61direct (N × H)
299. C2×#389C2×C61semidirect
303. #1444C2×C61semidirect
304. #1441C2×C61semidirect
307. #1436C2×C61semidirect
334. #385C4×C61semidirect
345. C61#14402direct (N × H)
478. C22⋊C4C4⋊C4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#3892
C2×C61×#3882
C2×C61×#3852
C2×C61×#3802
C61×#14442
C61×#14412
C61×#14392
C61×#14362
#1440261