Finite Group Databasebeta

← C61×#24050 #29527483

Subgroups — C61×#24050 #29527483

Order 15616.

1450 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#546C211yesmaximal, characteristic
2C2×C61×#485C211yesmaximal, characteristic, complemented
3C2×C61×#418C211yesmaximal, characteristic, complemented
4C61×#2485C211yesmaximal, characteristic, complemented
5C61×#2042C211yesmaximal, characteristic, complemented
6C61×#2042C211yesmaximal, characteristic, complemented
7C61×#2034C211yesmaximal, characteristic, complemented
8C61×#2033C211yesmaximal, characteristic, complemented
9C61×#1894C211yesmaximal, characteristic, complemented
10C61×#1870C211yesmaximal, characteristic, complemented
11C61×#1864C211yesmaximal, characteristic, complemented
12C61×#1862C211yesmaximal, characteristic, complemented
13C61×#1788C211yesmaximal, characteristic, complemented
14C61×#1788C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C22×M16×C61C2211yescharacteristic
19C61×#546—24no—
20C61×#546—24no—
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
29C2×#117×C61C2211yescharacteristic
30C22×C22⋊C4×C61—21no—
31C61×#485—24no—
32C2×#107×C61C2211yescharacteristic, complemented
33C2×#106×C61C2211yescharacteristic, complemented
34C61×#418—24no—
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, complemented
49C2×C22⋊C8×C61C2211yescharacteristic, complemented
50C61×#397—21no—
51C61×#394—21no—
52C61×#389C2211yescharacteristic, complemented
53C61×#389C2211yescharacteristic, complemented
54C61×#388—21no—
55C61×#387—21no—
56C61×#380C2211yescharacteristic
57C61×#380C2211yescharacteristic, complemented
58C61×#380C2211yescharacteristic, complemented
59C61×#340C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C61×#336C2211yescharacteristic, complemented
62C61×#336C2211yescharacteristic, 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—22no—
72C22×D4×C61—22no—
73C22×D4×C61—21no—
74C22×D4×C61—21no—
75C22×D4×C61—22no—
76C22×D4×C61—21no—
77C22×D4×C61—41no—
78C22×D4×C61—41no—
79C22×D4×C61D414yes—
80C22×D4×C61D411yescharacteristic
81C22×D4×C61C2311yescharacteristic
82C22×D4×C61C2311yescharacteristic
83C23×C4×C61—21no—
84C23×C4×C61—21no—
85C23×C4×C61C2311yescharacteristic
86C23×C4×C61C2311yescharacteristic
87C2×M16×C61—22no—
88C2×M16×C61—41no—
89C2×M16×C61—41no—
90C22×C8×C61C2311yescharacteristic
91C22×C8×C61C2311yescharacteristic
92C22×C8×C61C2311yescharacteristic
93C22×C8×C61C2311yescharacteristic
94#124×C61—22no—
95#124×C61—22no—
96#123×C61—28no—
97C22⋊Q8×C61—22no—
98C22⋊Q8×C61D414yes—
99#121×C61—28no—
100#121×C61—22no—
101#121×C61—22no—
102#120×C61—28no—
103C4×D4×C61—22no—
104C4×D4×C61—22no—
105C4×D4×C61—22no—
106C4×D4×C61—22no—
107#117×C61—22no—
108#117×C61—22no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61D411yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C22⋊C4×C61—28no—
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×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61D411yescharacteristic
129C2×C22⋊C4×C61D411yescharacteristic
130C2×C42×C61—21no—
131C2×C42×C61C2311yescharacteristic
132#107×C61—22no—
133#106×C61—22no—
134#103×C61—22no—
135#103×C61—22no—
136#103×C61—41no—
137#103×C61—41no—
138#102×C61—22no—
139#102×C61—22no—
140#102×C61—22no—
141#102×C61—22no—
142#102×C61—22no—
143#102×C61—22no—
144#102×C61—41no—
145#102×C61—41no—
146C22⋊C8×C61—22no—
147C22⋊C8×C61—41no—
148C22⋊C8×C61—41no—
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—21no—
156C24×C61—24no—
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—28no—
176C2×D4×C61—24no—
177C2×D4×C61—22no—
178C2×D4×C61—24no—
179C2×D4×C61—24no—
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—44no—
189C2×D4×C61—44no—
190C2×D4×C61—44no—
191C2×D4×C61—41no—
192C2×D4×C61—41no—
193C2×D4×C61—42no—
194C2×D4×C61—42no—
195C2×D4×C61—42no—
196C2×D4×C61—42no—
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—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—24no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—24no—
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—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—42no—
222C22×C4×C61—42no—
223C22×C4×C61—81no—
224C22×C4×C61—81no—
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D412yes—
230C22×C4×C61C2×D412yes—
231C22×C4×C61C2411yescharacteristic
232M16×C61—44no—
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—
244C2×C8×C61—21no—
245C4⋊C4×C61—24no—
246C4⋊C4×C61—22no—
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—21no—
256C4⋊C4×C61—42no—
257C4⋊C4×C61—81no—
258C4⋊C4×C61C2×D412yes—
259C22⋊C4×C61—24no—
260C22⋊C4×C61—24no—
261C22⋊C4×C61—24no—
262C22⋊C4×C61—24no—
263C22⋊C4×C61—22no—
264C22⋊C4×C61—24no—
265C22⋊C4×C61—22no—
266C22⋊C4×C61—42no—
267C22⋊C4×C61—42no—
268C22⋊C4×C61—81no—
269C22⋊C4×C61—81no—
270C42×C61—21no—
271C42×C61—21no—
272C42×C61—42no—
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—21no—
282C23×C61—22no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—48no—
291C23×C61—48no—
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—41no—
302C23×C61—84no—
303C23×C61—84no—
304C23×C61—84no—
305C23×C61—84no—
306C23×C61—84no—
307C23×C61#12012yes—
308C23×C61C22×D411yescharacteristic
309Q8×C61—22no—
310Q8×C61—22no—
311Q8×C61—41no—
312Q8×C61—41no—
313D4×C61—22no—
314D4×C61—22no—
315D4×C61—22no—
316D4×C61—22no—
317D4×C61—22no—
318D4×C61—48no—
319D4×C61—44no—
320D4×C61—48no—
321D4×C61—41no—
322D4×C61—41no—
323D4×C61—84no—
324D4×C61#12314yes—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—22no—
334C2×C4×C61—21no—
335C2×C4×C61—22no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—48no—
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—41no—
362C2×C4×C61—41no—
363C2×C4×C61—84no—
364C2×C4×C61#12012yes—
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C22×D411yescharacteristic
367C2×C4×C61C2×#4111yescharacteristic
368C2×C4×C61C2×#4111yescharacteristic
369C2×C4×C61H(5,𝔽2)11yescharacteristic
370C2×C4×C61H(5,𝔽2)11yescharacteristic
371C8×C61—41no—
372C8×C61—41no—
373C8×C61—41no—
374C8×C61—41no—
375#24050C6111yesmaximal, characteristic, direct product factor, Sylow
376C22×C61—22no—
377C22×C61—24no—
378C22×C61—22no—
379C22×C61—22no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—41no—
383C22×C61—42no—
384C22×C61—41no—
385C22×C61—42no—
386C22×C61—41no—
387C22×C61—42no—
388C22×C61—41no—
389C22×C61—42no—
390C22×C61—41no—
391C22×C61—42no—
392C22×C61—41no—
393C22×C61—42no—
394C22×C61—41no—
395C22×C61—42no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61—816no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61C2×#12011yescharacteristic
406C22×C61#54611yescharacteristic
407C22×C61#54611yescharacteristic
408C22×C61#57511yescharacteristic
409C22×C61#57511yescharacteristic
410C22×C61#57611yescharacteristic
411C22×C61#57711yescharacteristic
412C4×C61—22no—
413C4×C61—41no—
414C4×C61—42no—
415C4×C61—41no—
416C4×C61—41no—
417C4×C61—42no—
418C4×C61—81no—
419C4×C61—81no—
420C4×C61—81no—
421C4×C61—81no—
422C4×C61C2×#12311yescharacteristic
423C4×C61#53411yescharacteristic
424C4×C61#54611yescharacteristic
425C4×C61#54611yescharacteristic
426C2×#546C2×C6111yescharacteristic
427C2×#485C2×C6111yescharacteristic, complemented
428C2×#418C2×C6111yescharacteristic, complemented
429#2485C2×C6111yescharacteristic, complemented
430#2042C2×C6111yescharacteristic, complemented
431#2042C2×C6111yescharacteristic, complemented
432#2034C2×C6111yescharacteristic, complemented
433#2033C2×C6111yescharacteristic, complemented
434#1894C2×C6111yescharacteristic, complemented
435#1870C2×C6111yescharacteristic, complemented
436#1864C2×C6111yescharacteristic, complemented
437#1862C2×C6111yescharacteristic, complemented
438#1788C2×C6111yescharacteristic, complemented
439#1788C2×C6111yescharacteristic, complemented
440#1786C2×C6111yescharacteristic, complemented
441C2×C61—42no—
442C2×C61—44no—
443C2×C61—81no—
444C2×C61—82no—
445C2×C61#240511yescharacteristic
446C2×C61#300511yescharacteristic
447C2×C61#301211yescharacteristic
448C2×C61#331111yescharacteristic
449C2×C61#331911yescharacteristic
450C2×C61#332211yescharacteristic
451C2×C61#332311yescharacteristic
452C22×#41C22×C6111yescharacteristic
453C23×D4C22×C6111yescharacteristic
454C22×M16C22×C6111yescharacteristic
455#546—24no—
456#546—24no—
457C2×#124C22×C6111yescharacteristic
458C2×#123—21no—
459C2×C22⋊Q8C22×C6111yescharacteristic
460C2×#121—21no—
461C2×#121C22×C6111yescharacteristic
462C2×#120—21no—
463C2×C4×D4C22×C6111yescharacteristic
464C2×C4×D4C22×C6111yescharacteristic
465C2×#117C22×C6111yescharacteristic
466C22×C22⋊C4—21no—
467#485—24no—
468C2×#107C22×C6111yescharacteristic, complemented
469C2×#106C22×C6111yescharacteristic, complemented
470#418—24no—
471C2×#103C22×C6111yescharacteristic, complemented
472C2×#103C22×C6111yescharacteristic, complemented
473C2×#103C22×C6111yescharacteristic, complemented
474C2×#103C22×C6111yescharacteristic, complemented
475C2×#102C22×C6111yescharacteristic
476C2×#102C22×C6111yescharacteristic
477C2×#102C22×C6111yescharacteristic
478C2×#102C22×C6111yescharacteristic
479C2×#102C22×C6111yescharacteristic
480C2×#102C22×C6111yescharacteristic
481C2×#102C22×C6111yescharacteristic
482C2×#102C22×C6111yescharacteristic
483C2×C22⋊C8C22×C6111yescharacteristic
484C2×C22⋊C8C22×C6111yescharacteristic, complemented
485C2×C22⋊C8C22×C6111yescharacteristic, complemented
486#397—21no—
487#394—21no—
488#389C22×C6111yescharacteristic, complemented
489#389C22×C6111yescharacteristic, complemented
490#388—21no—
491#387—21no—
492#380C22×C6111yescharacteristic
493#380C22×C6111yescharacteristic, complemented
494#380C22×C6111yescharacteristic, complemented
495#340C22×C6111yescharacteristic, complemented
496#340C22×C6111yescharacteristic, complemented
497#336C22×C6111yescharacteristic, complemented
498#336C22×C6111yescharacteristic, complemented
499C61#2405011yescharacteristic, direct product factor, Sylow
500C25—21no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—41no—
506C2×#41—41no—
507C22×Q8C23×C6111yescharacteristic
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—22no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4D4×C6114yes—
517C22×D4D4×C6111yescharacteristic
518C22×D4C23×C6111yescharacteristic
519C22×D4C23×C6111yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C6111yescharacteristic
523C23×C4C23×C6111yescharacteristic
524C2×M16—22no—
525C2×M16—41no—
526C2×M16—41no—
527C22×C8C23×C6111yescharacteristic
528C22×C8C23×C6111yescharacteristic
529C22×C8C23×C6111yescharacteristic
530C22×C8C23×C6111yescharacteristic
531#124—22no—
532#124—22no—
533#123—28no—
534C22⋊Q8—22no—
535C22⋊Q8D4×C6114yes—
536#121—28no—
537#121—22no—
538#121—22no—
539#120—28no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544#117—22no—
545#117—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4D4×C6111yescharacteristic
550C2×C4⋊C4C23×C6111yescharacteristic
551C2×C4⋊C4C23×C6111yescharacteristic
552C2×C4⋊C4C23×C6111yescharacteristic
553C2×C4⋊C4C23×C6111yescharacteristic
554C2×C4⋊C4C23×C6111yescharacteristic
555C2×C22⋊C4—28no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4D4×C6111yescharacteristic
566C2×C22⋊C4D4×C6111yescharacteristic
567C2×C42—21no—
568C2×C42C23×C6111yescharacteristic
569#107—22no—
570#106—22no—
571#103—22no—
572#103—22no—
573#103—41no—
574#103—41no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—22no—
579#102—22no—
580#102—22no—
581#102—41no—
582#102—41no—
583C22⋊C8—22no—
584C22⋊C8—41no—
585C22⋊C8—41no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590#95—21no—
591C24—21no—
592C24—21no—
593C24—24no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—42no—
598C24—81no—
599C24—81no—
600C24C2×D4×C6111yescharacteristic
601C24C2×D4×C6111yescharacteristic
602#41—44no—
603#41—44no—
604#41—44no—
605#41—44no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8C2×D4×C6112yes—
612C2×D4—28no—
613C2×D4—24no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—44no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—81no—
635C2×D4—81no—
636C2×D4C2×D4×C6112yes—
637C2×D4C2×D4×C6112yes—
638C2×D4#41×C6112yes—
639C2×D4#41×C6112yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—24no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C2×D4×C6111yescharacteristic
663C22×C4C2×D4×C6111yescharacteristic
664C22×C4C2×D4×C6111yescharacteristic
665C22×C4C2×D4×C6111yescharacteristic
666C22×C4C2×D4×C6112yes—
667C22×C4C2×D4×C6112yes—
668C22×C4C24×C6111yescharacteristic
669M16—44no—
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—
680C2×C8—21no—
681C2×C8—21no—
682C4⋊C4—24no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—42no—
694C4⋊C4—81no—
695C4⋊C4C2×D4×C6112yes—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—24no—
702C22⋊C4—22no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C42—21no—
708C42—21no—
709C42—42no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—22no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—22no—
726C23—21no—
727C23—48no—
728C23—48no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23—84no—
743C23—84no—
744C23#120×C6112yes—
745C23C22×D4×C6111yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—41no—
749Q8—41no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—44no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4#123×C6114yes—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—48no—
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—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—84no—
801C2×C4#120×C6112yes—
802C2×C4C22×D4×C6111yescharacteristic
803C2×C4C22×D4×C6111yescharacteristic
804C2×C4C2×#41×C6111yescharacteristic
805C2×C4C2×#41×C6111yescharacteristic
806C2×C4H(5,𝔽2)×C6111yescharacteristic
807C2×C4H(5,𝔽2)×C6111yescharacteristic
808C8—41no—
809C8—41no—
810C8—41no—
811C8—41no—
812C22—22no—
813C22—24no—
814C22—22no—
815C22—22no—
816C22—41no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—41no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—41no—
835C22—42no—
836C22—816no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22C2×#120×C6111yescharacteristic
842C22C61×#54611yescharacteristic
843C22C61×#54611yescharacteristic
844C22C61×#57511yescharacteristic
845C22C61×#57511yescharacteristic
846C22C61×#57611yescharacteristic
847C22C61×#57711yescharacteristic
848C4—22no—
849C4—41no—
850C4—42no—
851C4—41no—
852C4—41no—
853C4—42no—
854C4—81no—
855C4—81no—
856C4—81no—
857C4—81no—
858C4C2×#123×C6111yescharacteristic
859C4C61×#53411yescharacteristic
860C4C61×#54611yescharacteristic
861C4C61×#54611yescharacteristic
862C2—42no—
863C2—44no—
864C2—81no—
865C2—82no—
866C2C61×#240511yescharacteristic
867C2C61×#300511yescharacteristic
868C2C61×#301211yescharacteristic
869C2C61×#331111yescharacteristic
870C2C61×#331911yescharacteristic
871C2C61×#332211yescharacteristic
872C2C61×#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×#485C2semidirect
3. C2×C61×#418C2semidirect
4. C61×#2485C2semidirect
5. C61×#2042C2semidirect
6. C61×#2042C2semidirect
7. C61×#2034C2semidirect
8. C61×#2033C2semidirect
9. C61×#1894C2semidirect
10. C61×#1870C2semidirect
11. C61×#1864C2semidirect
12. C61×#1862C2semidirect
13. C61×#1788C2semidirect
14. C61×#1788C2semidirect
15. C61×#1786C2semidirect
32. C2×#107×C61C22semidirect
33. C2×#106×C61C22semidirect
35. C2×#103×C61C22semidirect
36. C2×#103×C61C22semidirect
37. C2×#103×C61C22semidirect
38. C2×#103×C61C22semidirect
48. C2×C22⋊C8×C61C22semidirect
49. C2×C22⋊C8×C61C22semidirect
52. C61×#389C22semidirect
53. C61×#389C22semidirect
57. C61×#380C22semidirect
58. C61×#380C22semidirect
59. C61×#340C22semidirect
60. C61×#340C22semidirect
61. C61×#336C22semidirect
62. C61×#336C22semidirect
375. #24050C61direct (N × H)
427. C2×#485C2×C61semidirect
428. C2×#418C2×C61semidirect
429. #2485C2×C61semidirect
430. #2042C2×C61semidirect
431. #2042C2×C61semidirect
432. #2034C2×C61semidirect
433. #2033C2×C61semidirect
434. #1894C2×C61semidirect
435. #1870C2×C61semidirect
436. #1864C2×C61semidirect
437. #1862C2×C61semidirect
438. #1788C2×C61semidirect
439. #1788C2×C61semidirect
440. #1786C2×C61semidirect
468. C2×#107C22×C61semidirect
469. C2×#106C22×C61semidirect
471. C2×#103C22×C61semidirect
472. C2×#103C22×C61semidirect
473. C2×#103C22×C61semidirect
474. C2×#103C22×C61semidirect
484. C2×C22⋊C8C22×C61semidirect
485. C2×C22⋊C8C22×C61semidirect
488. #389C22×C61semidirect
489. #389C22×C61semidirect
493. #380C22×C61semidirect
494. #380C22×C61semidirect
495. #340C22×C61semidirect
496. #340C22×C61semidirect
497. #336C22×C61semidirect
498. #336C22×C61semidirect
499. C61#24050direct (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×#4852
C2×C61×#4182
C61×#24852
C61×#20422
C61×#20342
C61×#20332
C61×#18942
C61×#18702
C61×#18642
C61×#18622
C61×#17882
C61×#17862
#2405061