Finite Group Databasebeta

← C61×#25890 #29529323

Subgroups — C61×#25890 #29529323

Order 15616.

1432 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#546C211yesmaximal, characteristic
2C2×C61×#488C211yesmaximal, characteristic, complemented
3C2×C61×#478C211yesmaximal, characteristic, complemented
4C61×#2562C211yesmaximal, characteristic, complemented
5C61×#2036C211yesmaximal, characteristic, complemented
6C61×#2035C211yesmaximal, characteristic, complemented
7C61×#2034C211yesmaximal, characteristic, complemented
8C61×#2033C211yesmaximal, characteristic, complemented
9C61×#1983C211yesmaximal, characteristic, complemented
10C61×#1954C211yesmaximal, characteristic, complemented
11C61×#1788C211yesmaximal, characteristic, complemented
12C61×#1788C211yesmaximal, characteristic, complemented
13C61×#1786C211yesmaximal, characteristic, complemented
14C61×#1786C211yesmaximal, characteristic, complemented
15C4×#102×C61C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C61×#546—24no—
19C61×#546—24no—
20C2×#125×C61C2211yescharacteristic, complemented
21C2×#124×C61C2211yescharacteristic
22C2×#123×C61—21no—
23C2×C22⋊Q8×C61C2211yescharacteristic
24C2×#121×C61—21no—
25C2×#121×C61C2211yescharacteristic
26C2×#120×C61—21no—
27C2×C4×D4×C61C2211yescharacteristic
28C2×C4×D4×C61C2211yescharacteristic
29C22×C22⋊C4×C61—21no—
30C61×#488—24no—
31C61×#478—24no—
32C2×#107×C61C2211yescharacteristic, complemented
33C2×#106×C61C2211yescharacteristic, complemented
34C2×C4⋊C8×C61C2211yescharacteristic, complemented
35C2×#103×C61C2211yescharacteristic, complemented
36C2×#103×C61C2211yescharacteristic, complemented
37C2×#103×C61C2211yescharacteristic, complemented
38C2×#103×C61C2211yescharacteristic, complemented
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×#102×C61C2211yescharacteristic
44C2×#102×C61C2211yescharacteristic
45C2×#102×C61C2211yescharacteristic
46C2×#102×C61C2211yescharacteristic
47C2×C22⋊C8×C61C2211yescharacteristic
48C2×C22⋊C8×C61C2211yescharacteristic
49C2×C22⋊C8×C61C2211yescharacteristic, complemented
50C2×C22⋊C8×C61C2211yescharacteristic, complemented
51C2×C4×C8×C61C2211yescharacteristic, complemented
52C61×#400—21no—
53C61×#394—21no—
54C61×#388—21no—
55C61×#388—21no—
56C61×#380C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#380C2211yescharacteristic, complemented
59C61×#380C2211yescharacteristic, complemented
60C4×C4⋊C4×C61C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C25×C61—21no—
64C2×#41×C61—22no—
65C2×#41×C61—22no—
66C2×#41×C61—22no—
67C2×#41×C61—22no—
68C2×#41×C61—41no—
69C2×#41×C61—41no—
70C22×Q8×C61C2311yescharacteristic
71C22×D4×C61—21no—
72C22×D4×C61—21no—
73C22×D4×C61—22no—
74C22×D4×C61—22no—
75C22×D4×C61—22no—
76C22×D4×C61—22no—
77C22×D4×C61—21no—
78C22×D4×C61—41no—
79C22×D4×C61—41no—
80C22×D4×C61D411yescharacteristic
81C22×D4×C61C2311yescharacteristic
82C22×D4×C61C2311yescharacteristic
83C23×C4×C61—21no—
84C23×C4×C61—21no—
85C23×C4×C61C2311yescharacteristic
86C23×C4×C61C2311yescharacteristic
87C22×C8×C61C2311yescharacteristic
88C22×C8×C61C2311yescharacteristic
89C22×C8×C61C2311yescharacteristic
90C22×C8×C61C2311yescharacteristic
91#125×C61—22no—
92#125×C61—22no—
93#124×C61—22no—
94#124×C61D414yes—
95#123×C61—28no—
96C22⋊Q8×C61—22no—
97C22⋊Q8×C61—22no—
98#121×C61—28no—
99#121×C61—22no—
100#121×C61—22no—
101#120×C61—28no—
102C4×D4×C61—22no—
103C4×D4×C61—22no—
104C4×D4×C61—22no—
105C4×D4×C61D414yes—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61D411yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C22⋊C4×C61—28no—
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61D411yescharacteristic
126C2×C22⋊C4×C61D411yescharacteristic
127C2×C42×C61—21no—
128C2×C42×C61C2311yescharacteristic
129#107×C61—22no—
130#106×C61—22no—
131C4⋊C8×C61—22no—
132#103×C61—22no—
133#103×C61—22no—
134#103×C61—41no—
135#103×C61—41no—
136#102×C61—22no—
137#102×C61—22no—
138#102×C61—22no—
139#102×C61—22no—
140#102×C61—22no—
141#102×C61—22no—
142#102×C61—41no—
143#102×C61—41no—
144C22⋊C8×C61—41no—
145C22⋊C8×C61—41no—
146C22⋊C8×C61—41no—
147C22⋊C8×C61—41no—
148C4×C8×C61—22no—
149#95×C61—21no—
150#95×C61—21no—
151#95×C61—21no—
152#95×C61—21no—
153#95×C61—21no—
154C24×C61—21no—
155C24×C61—24no—
156C24×C61—21no—
157C24×C61—42no—
158C24×C61—42no—
159C24×C61—42no—
160C24×C61—42no—
161C24×C61—81no—
162C24×C61—81no—
163C24×C61C2×D411yescharacteristic
164C24×C61C2×D411yescharacteristic
165#41×C61—44no—
166#41×C61—44no—
167#41×C61—44no—
168#41×C61—44no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61C2×D412yes—
175C2×D4×C61—24no—
176C2×D4×C61—24no—
177C2×D4×C61—22no—
178C2×D4×C61—24no—
179C2×D4×C61—22no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—41no—
189C2×D4×C61—42no—
190C2×D4×C61—42no—
191C2×D4×C61—44no—
192C2×D4×C61—44no—
193C2×D4×C61—44no—
194C2×D4×C61—42no—
195C2×D4×C61—42no—
196C2×D4×C61—44no—
197C2×D4×C61—81no—
198C2×D4×C61—81no—
199C2×D4×C61C2×D412yes—
200C2×D4×C61C2×D412yes—
201C2×D4×C61#4112yes—
202C2×D4×C61#4112yes—
203C22×C4×C61—24no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—24no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—42no—
224C22×C4×C61—42no—
225C22×C4×C61—81no—
226C22×C4×C61—81no—
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2411yescharacteristic
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C4⋊C4×C61—24no—
245C4⋊C4×C61—22no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—42no—
256C4⋊C4×C61—42no—
257C4⋊C4×C61C2×D412yes—
258C22⋊C4×C61—24no—
259C22⋊C4×C61—24no—
260C22⋊C4×C61—22no—
261C22⋊C4×C61—24no—
262C22⋊C4×C61—24no—
263C22⋊C4×C61—24no—
264C22⋊C4×C61—22no—
265C22⋊C4×C61—42no—
266C22⋊C4×C61—42no—
267C22⋊C4×C61—81no—
268C22⋊C4×C61—81no—
269C42×C61—81no—
270C42×C61C2×D412yes—
271C42×C61C2×D412yes—
272C23×C61—21no—
273C23×C61—22no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—22no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—48no—
290C23×C61—48no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—84no—
302C23×C61—84no—
303C23×C61—84no—
304C23×C61—84no—
305C23×C61—84no—
306C23×C61#13512yes—
307C23×C61C22×D411yescharacteristic
308Q8×C61—22no—
309Q8×C61—22no—
310Q8×C61—41no—
311Q8×C61—41no—
312D4×C61—22no—
313D4×C61—22no—
314D4×C61—22no—
315D4×C61—22no—
316D4×C61—22no—
317D4×C61—44no—
318D4×C61—48no—
319D4×C61—48no—
320D4×C61—41no—
321D4×C61—41no—
322D4×C61—84no—
323D4×C61#12414yes—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—22no—
329C2×C4×C61—21no—
330C2×C4×C61—22no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—48no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—84no—
362C2×C4×C61#12012yes—
363C2×C4×C61#12012yes—
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C2×#4111yescharacteristic
367C2×C4×C61C2×#4111yescharacteristic
368C2×C4×C61H(5,𝔽2)11yescharacteristic
369C2×C4×C61H(5,𝔽2)11yescharacteristic
370C8×C61—41no—
371C8×C61—41no—
372C8×C61—41no—
373C8×C61—41no—
374#25890C6111yesmaximal, characteristic, direct product factor, Sylow
375C22×C61—24no—
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—41no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—41no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—41no—
386C22×C61—42no—
387C22×C61—41no—
388C22×C61—42no—
389C22×C61—41no—
390C22×C61—42no—
391C22×C61—41no—
392C22×C61—42no—
393C22×C61—41no—
394C22×C61—42no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—816no—
400C22×C61—81no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61C2×#12011yescharacteristic
405C22×C61#54611yescharacteristic
406C22×C61#54611yescharacteristic
407C22×C61C2×#13511yescharacteristic
408C22×C61#57511yescharacteristic
409C22×C61#57611yescharacteristic
410C22×C61#57711yescharacteristic
411C4×C61—22no—
412C4×C61—22no—
413C4×C61—41no—
414C4×C61—41no—
415C4×C61—42no—
416C4×C61—42no—
417C4×C61—81no—
418C4×C61—81no—
419C4×C61—81no—
420C4×C61—81no—
421C4×C61C2×#12411yescharacteristic
422C4×C61#53511yescharacteristic
423C4×C61#54611yescharacteristic
424C4×C61#54611yescharacteristic
425C2×#546C2×C6111yescharacteristic
426C2×#488C2×C6111yescharacteristic, complemented
427C2×#478C2×C6111yescharacteristic, complemented
428#2562C2×C6111yescharacteristic, complemented
429#2036C2×C6111yescharacteristic, complemented
430#2035C2×C6111yescharacteristic, complemented
431#2034C2×C6111yescharacteristic, complemented
432#2033C2×C6111yescharacteristic, complemented
433#1983C2×C6111yescharacteristic, complemented
434#1954C2×C6111yescharacteristic, complemented
435#1788C2×C6111yescharacteristic, complemented
436#1788C2×C6111yescharacteristic, complemented
437#1786C2×C6111yescharacteristic, complemented
438#1786C2×C6111yescharacteristic, complemented
439C4×#102C2×C6111yescharacteristic, complemented
440C2×C61—42no—
441C2×C61—44no—
442C2×C61—81no—
443C2×C61—82no—
444C2×C61#243511yescharacteristic
445C2×C61#300211yescharacteristic
446C2×C61#301211yescharacteristic
447C2×C61#329611yescharacteristic
448C2×C61#329711yescharacteristic
449C2×C61#332211yescharacteristic
450C2×C61#332311yescharacteristic
451C22×#41C22×C6111yescharacteristic
452C23×D4C22×C6111yescharacteristic
453#546—24no—
454#546—24no—
455C2×#125C22×C6111yescharacteristic, complemented
456C2×#124C22×C6111yescharacteristic
457C2×#123—21no—
458C2×C22⋊Q8C22×C6111yescharacteristic
459C2×#121—21no—
460C2×#121C22×C6111yescharacteristic
461C2×#120—21no—
462C2×C4×D4C22×C6111yescharacteristic
463C2×C4×D4C22×C6111yescharacteristic
464C22×C22⋊C4—21no—
465#488—24no—
466#478—24no—
467C2×#107C22×C6111yescharacteristic, complemented
468C2×#106C22×C6111yescharacteristic, complemented
469C2×C4⋊C8C22×C6111yescharacteristic, complemented
470C2×#103C22×C6111yescharacteristic, complemented
471C2×#103C22×C6111yescharacteristic, complemented
472C2×#103C22×C6111yescharacteristic, complemented
473C2×#103C22×C6111yescharacteristic, complemented
474C2×#102C22×C6111yescharacteristic
475C2×#102C22×C6111yescharacteristic
476C2×#102C22×C6111yescharacteristic
477C2×#102C22×C6111yescharacteristic
478C2×#102C22×C6111yescharacteristic
479C2×#102C22×C6111yescharacteristic
480C2×#102C22×C6111yescharacteristic
481C2×#102C22×C6111yescharacteristic
482C2×C22⋊C8C22×C6111yescharacteristic
483C2×C22⋊C8C22×C6111yescharacteristic
484C2×C22⋊C8C22×C6111yescharacteristic, complemented
485C2×C22⋊C8C22×C6111yescharacteristic, complemented
486C2×C4×C8C22×C6111yescharacteristic, complemented
487#400—21no—
488#394—21no—
489#388—21no—
490#388—21no—
491#380C22×C6111yescharacteristic
492#380C22×C6111yescharacteristic
493#380C22×C6111yescharacteristic, complemented
494#380C22×C6111yescharacteristic, complemented
495C4×C4⋊C4C22×C6111yescharacteristic, complemented
496#340C22×C6111yescharacteristic, complemented
497#340C22×C6111yescharacteristic, complemented
498C61#2589011yescharacteristic, direct product factor, Sylow
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C23×C6111yescharacteristic
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4D4×C6111yescharacteristic
517C22×D4C23×C6111yescharacteristic
518C22×D4C23×C6111yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C23×C6111yescharacteristic
522C23×C4C23×C6111yescharacteristic
523C22×C8C23×C6111yescharacteristic
524C22×C8C23×C6111yescharacteristic
525C22×C8C23×C6111yescharacteristic
526C22×C8C23×C6111yescharacteristic
527#125—22no—
528#125—22no—
529#124—22no—
530#124D4×C6114yes—
531#123—28no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534#121—28no—
535#121—22no—
536#121—22no—
537#120—28no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4D4×C6114yes—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4D4×C6111yescharacteristic
546C2×C4⋊C4C23×C6111yescharacteristic
547C2×C4⋊C4C23×C6111yescharacteristic
548C2×C4⋊C4C23×C6111yescharacteristic
549C2×C4⋊C4C23×C6111yescharacteristic
550C2×C4⋊C4C23×C6111yescharacteristic
551C2×C22⋊C4—28no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4D4×C6111yescharacteristic
562C2×C22⋊C4D4×C6111yescharacteristic
563C2×C42—21no—
564C2×C42C23×C6111yescharacteristic
565#107—22no—
566#106—22no—
567C4⋊C8—22no—
568#103—22no—
569#103—22no—
570#103—41no—
571#103—41no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—41no—
579#102—41no—
580C22⋊C8—41no—
581C22⋊C8—41no—
582C22⋊C8—41no—
583C22⋊C8—41no—
584C4×C8—22no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590C24—21no—
591C24—24no—
592C24—21no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—81no—
598C24—81no—
599C24C2×D4×C6111yescharacteristic
600C24C2×D4×C6111yescharacteristic
601#41—44no—
602#41—44no—
603#41—44no—
604#41—44no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8C2×D4×C6112yes—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C6112yes—
636C2×D4C2×D4×C6112yes—
637C2×D4#41×C6112yes—
638C2×D4#41×C6112yes—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4C2×D4×C6111yescharacteristic
664C22×C4C2×D4×C6111yescharacteristic
665C22×C4C2×D4×C6111yescharacteristic
666C22×C4C2×D4×C6111yescharacteristic
667C22×C4C24×C6111yescharacteristic
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C4⋊C4—24no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4C2×D4×C6112yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C42—81no—
706C42C2×D4×C6112yes—
707C42C2×D4×C6112yes—
708C23—21no—
709C23—21no—
710C23—22no—
711C23—22no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—22no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—48no—
726C23—48no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—84no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23#135×C6112yes—
743C23C22×D4×C6111yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—41no—
747Q8—41no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—44no—
754D4—48no—
755D4—48no—
756D4—41no—
757D4—41no—
758D4—84no—
759D4#124×C6114yes—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—84no—
798C2×C4#120×C6112yes—
799C2×C4#120×C6112yes—
800C2×C4C22×D4×C6111yescharacteristic
801C2×C4C22×D4×C6111yescharacteristic
802C2×C4C2×#41×C6111yescharacteristic
803C2×C4C2×#41×C6111yescharacteristic
804C2×C4H(5,𝔽2)×C6111yescharacteristic
805C2×C4H(5,𝔽2)×C6111yescharacteristic
806C8—41no—
807C8—41no—
808C8—41no—
809C8—41no—
810C22—22no—
811C22—22no—
812C22—24no—
813C22—22no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—42no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—816no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C2×#120×C6111yescharacteristic
840C22C61×#54611yescharacteristic
841C22C61×#54611yescharacteristic
842C22C2×#135×C6111yescharacteristic
843C22C61×#57511yescharacteristic
844C22C61×#57611yescharacteristic
845C22C61×#57711yescharacteristic
846C4—22no—
847C4—22no—
848C4—41no—
849C4—41no—
850C4—42no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4C2×#124×C6111yescharacteristic
857C4C61×#53511yescharacteristic
858C4C61×#54611yescharacteristic
859C4C61×#54611yescharacteristic
860C2—42no—
861C2—44no—
862C2—81no—
863C2—82no—
864C2C61×#243511yescharacteristic
865C2C61×#300211yescharacteristic
866C2C61×#301211yescharacteristic
867C2C61×#329611yescharacteristic
868C2C61×#329711yescharacteristic
869C2C61×#332211yescharacteristic
870C2C61×#332311yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×C61×#546C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C4×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#488C2semidirect
3. C2×C61×#478C2semidirect
4. C61×#2562C2semidirect
5. C61×#2036C2semidirect
6. C61×#2035C2semidirect
7. C61×#2034C2semidirect
8. C61×#2033C2semidirect
9. C61×#1983C2semidirect
10. C61×#1954C2semidirect
11. C61×#1788C2semidirect
12. C61×#1788C2semidirect
13. C61×#1786C2semidirect
14. C61×#1786C2semidirect
15. C4×#102×C61C2semidirect
20. C2×#125×C61C22semidirect
32. C2×#107×C61C22semidirect
33. C2×#106×C61C22semidirect
34. C2×C4⋊C8×C61C22semidirect
35. C2×#103×C61C22semidirect
36. C2×#103×C61C22semidirect
37. C2×#103×C61C22semidirect
38. C2×#103×C61C22semidirect
49. C2×C22⋊C8×C61C22semidirect
50. C2×C22⋊C8×C61C22semidirect
51. C2×C4×C8×C61C22semidirect
58. C61×#380C22semidirect
59. C61×#380C22semidirect
60. C4×C4⋊C4×C61C22semidirect
61. C61×#340C22semidirect
62. C61×#340C22semidirect
374. #25890C61direct (N × H)
426. C2×#488C2×C61semidirect
427. C2×#478C2×C61semidirect
428. #2562C2×C61semidirect
429. #2036C2×C61semidirect
430. #2035C2×C61semidirect
431. #2034C2×C61semidirect
432. #2033C2×C61semidirect
433. #1983C2×C61semidirect
434. #1954C2×C61semidirect
435. #1788C2×C61semidirect
436. #1788C2×C61semidirect
437. #1786C2×C61semidirect
438. #1786C2×C61semidirect
439. C4×#102C2×C61semidirect
455. C2×#125C22×C61semidirect
467. C2×#107C22×C61semidirect
468. C2×#106C22×C61semidirect
469. C2×C4⋊C8C22×C61semidirect
470. C2×#103C22×C61semidirect
471. C2×#103C22×C61semidirect
472. C2×#103C22×C61semidirect
473. C2×#103C22×C61semidirect
484. C2×C22⋊C8C22×C61semidirect
485. C2×C22⋊C8C22×C61semidirect
486. C2×C4×C8C22×C61semidirect
493. #380C22×C61semidirect
494. #380C22×C61semidirect
495. C4×C4⋊C4C22×C61semidirect
496. #340C22×C61semidirect
497. #340C22×C61semidirect
498. C61#25890direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#5462
C2×C61×#4882
C2×C61×#4782
C61×#25622
C61×#20362
C61×#20352
C61×#20342
C61×#20332
C61×#19832
C61×#19542
C61×#17882
C61×#17862
C4×#102×C612
#2589061