Finite Group Databasebeta

← C61×#24440 #29527873

Subgroups — C61×#24440 #29527873

Order 15616.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C61C211yesmaximal, characteristic, complemented
2C2×C61×#469C211yesmaximal, characteristic, complemented
3C2×C61×#447C211yesmaximal, characteristic, complemented
4C2×C61×#447C211yesmaximal, characteristic, complemented
5C2×C61×#418C211yesmaximal, characteristic, complemented
6C61×#2414C211yesmaximal, characteristic, complemented
7C61×#2041C211yesmaximal, characteristic, complemented
8C61×#2034C211yesmaximal, characteristic, complemented
9C61×#2011C211yesmaximal, characteristic, complemented
10C61×#1999C211yesmaximal, characteristic, complemented
11C61×#1879C211yesmaximal, characteristic, complemented
12C61×#1875C211yesmaximal, characteristic, complemented
13C61×#1870C211yesmaximal, characteristic, complemented
14C61×#1864C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C61—21no—
17C23×D4×C61C2211yescharacteristic
18C23×D4×C61C2211yescharacteristic
19C22×D8×C61C2211yescharacteristic
20C22×D8×C61C2211yescharacteristic, complemented
21C22×D8×C61C2211yescharacteristic, complemented
22C22×M16×C61C2211yescharacteristic, complemented
23D42×C61—24no—
24D42×C61—24no—
25C2×#127×C61C2211yescharacteristic
26C2×#121×C61—21no—
27C2×#121×C61C2211yescharacteristic
28C2×#121×C61C2211yescharacteristic
29C2×#121×C61C2211yescharacteristic, complemented
30C2×#121×C61C2211yescharacteristic, complemented
31C2×#120×C61—21no—
32C2×#120×C61—21no—
33C2×C4×D4×C61C2211yescharacteristic
34C2×C4×D4×C61C2211yescharacteristic
35C2×#117×C61C2211yescharacteristic, complemented
36C61×#469—24no—
37C61×#447—24no—
38C61×#447—24no—
39C2×#106×C61C2211yescharacteristic, complemented
40C61×#418—24no—
41C2×#102×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×#102×C61C2211yescharacteristic
44C2×#102×C61C2211yescharacteristic, complemented
45C2×#102×C61C2211yescharacteristic, complemented
46C2×#102×C61C2211yescharacteristic, complemented
47C2×#102×C61C2211yescharacteristic, complemented
48C2×#102×C61C2211yescharacteristic, complemented
49C2×#102×C61C2211yescharacteristic, complemented
50C2×#102×C61C2211yescharacteristic, complemented
51C2×C22⋊C8×C61C2211yescharacteristic, complemented
52C2×C22⋊C8×C61C2211yescharacteristic, complemented
53C2×C22⋊C8×C61C2211yescharacteristic, complemented
54C61×#394—21no—
55C61×#392—21no—
56C61×#390—21no—
57C61×#390C2211yescharacteristic, complemented
58C61×#389C2211yescharacteristic, complemented
59C61×#388—21no—
60C61×#380C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#336C2211yescharacteristic, complemented
64C61×#336C2211yescharacteristic, complemented
65C25×C61—21no—
66C25×C61—21no—
67C22×D4×C61—22no—
68C22×D4×C61—22no—
69C22×D4×C61—28no—
70C22×D4×C61—21no—
71C22×D4×C61—21no—
72C22×D4×C61—22no—
73C22×D4×C61—22no—
74C22×D4×C61—22no—
75C22×D4×C61—22no—
76C22×D4×C61—21no—
77C22×D4×C61—21no—
78C22×D4×C61—21no—
79C22×D4×C61—22no—
80C22×D4×C61—21no—
81C22×D4×C61—21no—
82C22×D4×C61—21no—
83C22×D4×C61—41no—
84C22×D4×C61—41no—
85C22×D4×C61—41no—
86C22×D4×C61—41no—
87C22×D4×C61—44no—
88C22×D4×C61—44no—
89C22×D4×C61D411yescharacteristic
90C22×D4×C61D414yescomplemented
91C22×D4×C61C2311yescharacteristic
92C22×D4×C61C2311yescharacteristic
93C22×D4×C61C2311yescharacteristic
94C22×D4×C61C2311yescharacteristic
95C23×C4×C61—21no—
96C23×C4×C61C2311yescharacteristic
97C23×C4×C61C2311yescharacteristic
98C2×D8×C61—22no—
99C2×D8×C61—22no—
100C2×D8×C61—22no—
101C2×D8×C61—22no—
102C2×D8×C61—22no—
103C2×D8×C61—22no—
104C2×D8×C61—41no—
105C2×D8×C61—41no—
106C2×D8×C61—41no—
107C2×M16×C61—22no—
108C2×M16×C61—22no—
109C2×M16×C61—41no—
110C22×C8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114#127×C61—22no—
115#127×C61—22no—
116#121×C61—28no—
117#121×C61—22no—
118#121×C61—22no—
119#121×C61—22no—
120#121×C61—22no—
121#121×C61—22no—
122#121×C61—22no—
123#121×C61—41no—
124#121×C61D414yescomplemented
125#120×C61—28no—
126#120×C61—28no—
127C4×D4×C61—22no—
128C4×D4×C61—22no—
129C4×D4×C61—22no—
130C4×D4×C61—22no—
131#117×C61—22no—
132#117×C61—41no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61D411yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61D411yescharacteristic
149C2×C22⋊C4×C61D411yescharacteristic
150C2×C42×C61—21no—
151C2×C42×C61C2311yescharacteristic
152#106×C61—22no—
153#102×C61—22no—
154#102×C61—22no—
155#102×C61—22no—
156#102×C61—22no—
157#102×C61—22no—
158#102×C61—22no—
159#102×C61—22no—
160#102×C61—22no—
161#102×C61—41no—
162#102×C61D414yescomplemented
163C22⋊C8×C61—22no—
164C22⋊C8×C61—22no—
165C22⋊C8×C61—41no—
166#95×C61—21no—
167#95×C61—21no—
168C24×C61—21no—
169C24×C61—24no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—24no—
173C24×C61—21no—
174C24×C61—42no—
175C24×C61—42no—
176C24×C61—42no—
177C24×C61—42no—
178C24×C61—42no—
179C24×C61—42no—
180C24×C61—42no—
181C24×C61—42no—
182C24×C61—81no—
183C24×C61—81no—
184C24×C61—81no—
185C24×C61—81no—
186C24×C61C2×D411yescharacteristic
187C24×C61C2×D411yescharacteristic
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61—28no—
191C2×D4×C61—24no—
192C2×D4×C61—24no—
193C2×D4×C61—24no—
194C2×D4×C61—24no—
195C2×D4×C61—24no—
196C2×D4×C61—24no—
197C2×D4×C61—22no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—21no—
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61—44no—
218C2×D4×C61—44no—
219C2×D4×C61—44no—
220C2×D4×C61—42no—
221C2×D4×C61—42no—
222C2×D4×C61—42no—
223C2×D4×C61—42no—
224C2×D4×C61—42no—
225C2×D4×C61—42no—
226C2×D4×C61—44no—
227C2×D4×C61—44no—
228C2×D4×C61—432no—
229C2×D4×C61—44no—
230C2×D4×C61—42no—
231C2×D4×C61—42no—
232C2×D4×C61—42no—
233C2×D4×C61—42no—
234C2×D4×C61—44no—
235C2×D4×C61—42no—
236C2×D4×C61—42no—
237C2×D4×C61—42no—
238C2×D4×C61—81no—
239C2×D4×C61—81no—
240C2×D4×C61—81no—
241C2×D4×C61—81no—
242C2×D4×C61—81no—
243C2×D4×C61C2×D412yes—
244C2×D4×C61C2×D412yes—
245C2×D4×C61C2×D412yes—
246C2×D4×C61C2×D412yes—
247C2×D4×C61#4112yes—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—24no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61—21no—
261C22×C4×C61—21no—
262C22×C4×C61—21no—
263C22×C4×C61—42no—
264C22×C4×C61—42no—
265C22×C4×C61C2×D411yescharacteristic
266C22×C4×C61C2×D411yescharacteristic
267C22×C4×C61C2×D411yescharacteristic
268C22×C4×C61C2×D412yes—
269C22×C4×C61C2×D412yes—
270C22×C4×C61C2×D411yescharacteristic
271C22×C4×C61C2411yescharacteristic
272D8×C61—44no—
273D8×C61—44no—
274D8×C61—44no—
275M16×C61—44no—
276C2×C8×C61—21no—
277C2×C8×C61—21no—
278C2×C8×C61—21no—
279C2×C8×C61—21no—
280C2×C8×C61—21no—
281C2×C8×C61—21no—
282C2×C8×C61—21no—
283C2×C8×C61—21no—
284C2×C8×C61—21no—
285C2×C8×C61—21no—
286C2×C8×C61—21no—
287C2×C8×C61C2×D412yescomplemented
288C4⋊C4×C61—22no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61—21no—
291C4⋊C4×C61—21no—
292C4⋊C4×C61—21no—
293C4⋊C4×C61—21no—
294C4⋊C4×C61—21no—
295C4⋊C4×C61—81no—
296C4⋊C4×C61C2×D412yes—
297C4⋊C4×C61C2×D412yescomplemented
298C22⋊C4×C61—24no—
299C22⋊C4×C61—24no—
300C22⋊C4×C61—22no—
301C22⋊C4×C61—24no—
302C22⋊C4×C61—22no—
303C22⋊C4×C61—42no—
304C22⋊C4×C61—42no—
305C22⋊C4×C61—42no—
306C22⋊C4×C61—42no—
307C22⋊C4×C61—81no—
308C22⋊C4×C61—81no—
309C42×C61—21no—
310C42×C61—21no—
311C42×C61—42no—
312C23×C61—21no—
313C23×C61—22no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—22no—
317C23×C61—21no—
318C23×C61—21no—
319C23×C61—22no—
320C23×C61—21no—
321C23×C61—21no—
322C23×C61—21no—
323C23×C61—21no—
324C23×C61—21no—
325C23×C61—21no—
326C23×C61—21no—
327C23×C61—22no—
328C23×C61—22no—
329C23×C61—48no—
330C23×C61—48no—
331C23×C61—48no—
332C23×C61—48no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61—41no—
336C23×C61—41no—
337C23×C61—41no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—41no—
355C23×C61—41no—
356C23×C61—84no—
357C23×C61—84no—
358C23×C61—84no—
359C23×C61—84no—
360C23×C61—84no—
361C23×C61—84no—
362C23×C61—84no—
363C23×C61—84no—
364C23×C61—84no—
365C23×C61—84no—
366C23×C61#12012yes—
367C23×C61AGL(1,ℤ/8)12yes—
368C23×C61C22×D411yescharacteristic
369D4×C61—28no—
370D4×C61—22no—
371D4×C61—22no—
372D4×C61—22no—
373D4×C61—22no—
374D4×C61—22no—
375D4×C61—22no—
376D4×C61—22no—
377D4×C61—48no—
378D4×C61—48no—
379D4×C61—48no—
380D4×C61—48no—
381D4×C61—48no—
382D4×C61—41no—
383D4×C61—41no—
384D4×C61—41no—
385D4×C61—41no—
386D4×C61—41no—
387D4×C61—41no—
388D4×C61—41no—
389D4×C61—41no—
390D4×C61—84no—
391D4×C61—84no—
392D4×C61—84no—
393D4×C61#12114yes—
394C2×C4×C61—21no—
395C2×C4×C61—21no—
396C2×C4×C61—21no—
397C2×C4×C61—21no—
398C2×C4×C61—22no—
399C2×C4×C61—22no—
400C2×C4×C61—22no—
401C2×C4×C61—22no—
402C2×C4×C61—21no—
403C2×C4×C61—21no—
404C2×C4×C61—22no—
405C2×C4×C61—22no—
406C2×C4×C61—21no—
407C2×C4×C61—21no—
408C2×C4×C61—21no—
409C2×C4×C61—21no—
410C2×C4×C61—48no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—41no—
424C2×C4×C61—41no—
425C2×C4×C61#12012yes—
426C2×C4×C61AGL(1,ℤ/8)12yes—
427C2×C4×C61C22×D411yescharacteristic
428C2×C4×C61C22×D411yescharacteristic
429C2×C4×C61C22×D411yescharacteristic
430C2×C4×C61C2×#4111yescharacteristic
431C2×C4×C61H(5,𝔽2)11yescharacteristic
432C2×C4×C61H(5,𝔽2)11yescharacteristic
433C8×C61—22no—
434C8×C61—41no—
435C8×C61—41no—
436C8×C61—41no—
437#24440C6111yesmaximal, characteristic, direct product factor, Sylow
438C22×C61—22no—
439C22×C61—24no—
440C22×C61—22no—
441C22×C61—22no—
442C22×C61—22no—
443C22×C61—22no—
444C22×C61—22no—
445C22×C61—41no—
446C22×C61—42no—
447C22×C61—41no—
448C22×C61—42no—
449C22×C61—41no—
450C22×C61—42no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—42no—
454C22×C61—41no—
455C22×C61—42no—
456C22×C61—41no—
457C22×C61—41no—
458C22×C61—42no—
459C22×C61—42no—
460C22×C61—42no—
461C22×C61—42no—
462C22×C61—42no—
463C22×C61—42no—
464C22×C61—42no—
465C22×C61—816no—
466C22×C61—816no—
467C22×C61—81no—
468C22×C61—81no—
469C22×C61—81no—
470C22×C61—81no—
471C22×C61—81no—
472C22×C61—81no—
473C22×C61—81no—
474C22×C61—81no—
475C22×C61—81no—
476C22×C61—81no—
477C22×C61—81no—
478C22×C61—81no—
479C22×C61—81no—
480C22×C61—81no—
481C22×C61—81no—
482C22×C61C2×#12011yescharacteristic
483C22×C61D4211yescharacteristic
484C22×C61#54611yescharacteristic
485C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
486C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
487C22×C61#57611yescharacteristic
488C22×C61#57611yescharacteristic
489C4×C61—22no—
490C4×C61—22no—
491C4×C61—41no—
492C4×C61—42no—
493C4×C61—41no—
494C4×C61—42no—
495C4×C61—81no—
496C4×C61—81no—
497C4×C61C2×#12111yescharacteristic
498C4×C61#53411yescharacteristic
499C4×C61D4211yescharacteristic
500C4×C61#54611yescharacteristic
501C2×D42C2×C6111yescharacteristic, complemented
502C2×#469C2×C6111yescharacteristic, complemented
503C2×#447C2×C6111yescharacteristic, complemented
504C2×#447C2×C6111yescharacteristic, complemented
505C2×#418C2×C6111yescharacteristic, complemented
506#2414C2×C6111yescharacteristic, complemented
507#2041C2×C6111yescharacteristic, complemented
508#2034C2×C6111yescharacteristic, complemented
509#2011C2×C6111yescharacteristic, complemented
510#1999C2×C6111yescharacteristic, complemented
511#1879C2×C6111yescharacteristic, complemented
512#1875C2×C6111yescharacteristic, complemented
513#1870C2×C6111yescharacteristic, complemented
514#1864C2×C6111yescharacteristic, complemented
515#1786C2×C6111yescharacteristic, complemented
516C2×C61—42no—
517C2×C61—42no—
518C2×C61—44no—
519C2×C61—82no—
520C2×C61—82no—
521C2×C61—161no—
522C2×C61#241011yescharacteristic
523C2×C61#300311yescharacteristic
524C2×C61#300811yescharacteristic
525C2×C61#326411yescharacteristic
526C2×C61#327411yescharacteristic
527C2×C61#331811yescharacteristic
528C2×C61#332511yescharacteristic
529C23×D4—21no—
530C23×D4C22×C6111yescharacteristic
531C23×D4C22×C6111yescharacteristic
532C22×D8C22×C6111yescharacteristic
533C22×D8C22×C6111yescharacteristic, complemented
534C22×D8C22×C6111yescharacteristic, complemented
535C22×M16C22×C6111yescharacteristic, complemented
536D42—24no—
537D42—24no—
538C2×#127C22×C6111yescharacteristic
539C2×#121—21no—
540C2×#121C22×C6111yescharacteristic
541C2×#121C22×C6111yescharacteristic
542C2×#121C22×C6111yescharacteristic, complemented
543C2×#121C22×C6111yescharacteristic, complemented
544C2×#120—21no—
545C2×#120—21no—
546C2×C4×D4C22×C6111yescharacteristic
547C2×C4×D4C22×C6111yescharacteristic
548C2×#117C22×C6111yescharacteristic, complemented
549#469—24no—
550#447—24no—
551#447—24no—
552C2×#106C22×C6111yescharacteristic, complemented
553#418—24no—
554C2×#102C22×C6111yescharacteristic
555C2×#102C22×C6111yescharacteristic
556C2×#102C22×C6111yescharacteristic
557C2×#102C22×C6111yescharacteristic, complemented
558C2×#102C22×C6111yescharacteristic, complemented
559C2×#102C22×C6111yescharacteristic, complemented
560C2×#102C22×C6111yescharacteristic, complemented
561C2×#102C22×C6111yescharacteristic, complemented
562C2×#102C22×C6111yescharacteristic, complemented
563C2×#102C22×C6111yescharacteristic, complemented
564C2×C22⋊C8C22×C6111yescharacteristic, complemented
565C2×C22⋊C8C22×C6111yescharacteristic, complemented
566C2×C22⋊C8C22×C6111yescharacteristic, complemented
567#394—21no—
568#392—21no—
569#390—21no—
570#390C22×C6111yescharacteristic, complemented
571#389C22×C6111yescharacteristic, complemented
572#388—21no—
573#380C22×C6111yescharacteristic, complemented
574#340C22×C6111yescharacteristic, complemented
575#340C22×C6111yescharacteristic, complemented
576#336C22×C6111yescharacteristic, complemented
577#336C22×C6111yescharacteristic, complemented
578C61#2444011yescharacteristic, direct product factor, Sylow
579C25—21no—
580C25—21no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—28no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—41no—
598C22×D4—41no—
599C22×D4—41no—
600C22×D4—41no—
601C22×D4—44no—
602C22×D4—44no—
603C22×D4D4×C6111yescharacteristic
604C22×D4D4×C6114yescomplemented
605C22×D4C23×C6111yescharacteristic
606C22×D4C23×C6111yescharacteristic
607C22×D4C23×C6111yescharacteristic
608C22×D4C23×C6111yescharacteristic
609C23×C4—21no—
610C23×C4C23×C6111yescharacteristic
611C23×C4C23×C6111yescharacteristic
612C2×D8—22no—
613C2×D8—22no—
614C2×D8—22no—
615C2×D8—22no—
616C2×D8—22no—
617C2×D8—22no—
618C2×D8—41no—
619C2×D8—41no—
620C2×D8—41no—
621C2×M16—22no—
622C2×M16—22no—
623C2×M16—41no—
624C22×C8C23×C6111yescharacteristic
625C22×C8C23×C6111yescharacteristic
626C22×C8C23×C6111yescharacteristic
627C22×C8C23×C6111yescharacteristic
628#127—22no—
629#127—22no—
630#121—28no—
631#121—22no—
632#121—22no—
633#121—22no—
634#121—22no—
635#121—22no—
636#121—22no—
637#121—41no—
638#121D4×C6114yescomplemented
639#120—28no—
640#120—28no—
641C4×D4—22no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645#117—22no—
646#117—41no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4D4×C6111yescharacteristic
649C2×C4⋊C4C23×C6111yescharacteristic
650C2×C4⋊C4C23×C6111yescharacteristic
651C2×C4⋊C4C23×C6111yescharacteristic
652C2×C4⋊C4C23×C6111yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4D4×C6111yescharacteristic
663C2×C22⋊C4D4×C6111yescharacteristic
664C2×C42—21no—
665C2×C42C23×C6111yescharacteristic
666#106—22no—
667#102—22no—
668#102—22no—
669#102—22no—
670#102—22no—
671#102—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—41no—
676#102D4×C6114yescomplemented
677C22⋊C8—22no—
678C22⋊C8—22no—
679C22⋊C8—41no—
680#95—21no—
681#95—21no—
682C24—21no—
683C24—24no—
684C24—21no—
685C24—21no—
686C24—24no—
687C24—21no—
688C24—42no—
689C24—42no—
690C24—42no—
691C24—42no—
692C24—42no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24—81no—
700C24C2×D4×C6111yescharacteristic
701C24C2×D4×C6111yescharacteristic
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—24no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—22no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—432no—
743C2×D4—44no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—44no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4—81no—
757C2×D4C2×D4×C6112yes—
758C2×D4C2×D4×C6112yes—
759C2×D4C2×D4×C6112yes—
760C2×D4C2×D4×C6112yes—
761C2×D4#41×C6112yes—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4C2×D4×C6111yescharacteristic
780C22×C4C2×D4×C6111yescharacteristic
781C22×C4C2×D4×C6111yescharacteristic
782C22×C4C2×D4×C6112yes—
783C22×C4C2×D4×C6112yes—
784C22×C4C2×D4×C6111yescharacteristic
785C22×C4C24×C6111yescharacteristic
786D8—44no—
787D8—44no—
788D8—44no—
789M16—44no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8C2×D4×C6112yescomplemented
802C4⋊C4—22no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—81no—
810C4⋊C4C2×D4×C6112yes—
811C4⋊C4C2×D4×C6112yescomplemented
812C22⋊C4—24no—
813C22⋊C4—24no—
814C22⋊C4—22no—
815C22⋊C4—24no—
816C22⋊C4—22no—
817C22⋊C4—42no—
818C22⋊C4—42no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—81no—
822C22⋊C4—81no—
823C42—21no—
824C42—21no—
825C42—42no—
826C23—21no—
827C23—21no—
828C23—22no—
829C23—21no—
830C23—21no—
831C23—22no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—48no—
844C23—48no—
845C23—48no—
846C23—48no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—84no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23#120×C6112yes—
881C23AGL(1,ℤ/8)×C6112yes—
882C23C22×D4×C6111yescharacteristic
883D4—28no—
884D4—22no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—48no—
892D4—48no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—41no—
901D4—41no—
902D4—41no—
903D4—41no—
904D4—84no—
905D4—84no—
906D4—84no—
907D4#121×C6114yes—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—22no—
924C2×C4—48no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4#120×C6112yes—
940C2×C4AGL(1,ℤ/8)×C6112yes—
941C2×C4C22×D4×C6111yescharacteristic
942C2×C4C22×D4×C6111yescharacteristic
943C2×C4C22×D4×C6111yescharacteristic
944C2×C4C2×#41×C6111yescharacteristic
945C2×C4H(5,𝔽2)×C6111yescharacteristic
946C2×C4H(5,𝔽2)×C6111yescharacteristic
947C8—22no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—22no—
953C22—24no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—41no—
959C22—42no—
960C22—41no—
961C22—41no—
962C22—42no—
963C22—41no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—816no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22C2×#120×C6111yescharacteristic
996C22D42×C6111yescharacteristic
997C22C61×#54611yescharacteristic
998C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
999C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
1000C22C61×#57611yescharacteristic
1001C22C61×#57611yescharacteristic
1002C4—22no—
1003C4—22no—
1004C4—41no—
1005C4—42no—
1006C4—41no—
1007C4—42no—
1008C4—81no—
1009C4—81no—
1010C4C2×#121×C6111yescharacteristic
1011C4C61×#53411yescharacteristic
1012C4D42×C6111yescharacteristic
1013C4C61×#54611yescharacteristic
1014C2—42no—
1015C2—42no—
1016C2—44no—
1017C2—82no—
1018C2—82no—
1019C2—161no—
1020C2C61×#241011yescharacteristic
1021C2C61×#300311yescharacteristic
1022C2C61×#300811yescharacteristic
1023C2C61×#326411yescharacteristic
1024C2C61×#327411yescharacteristic
1025C2C61×#331811yescharacteristic
1026C2C61×#332511yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
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
1. C2×D42×C61C2semidirect
2. C2×C61×#469C2semidirect
3. C2×C61×#447C2semidirect
4. C2×C61×#447C2semidirect
5. C2×C61×#418C2semidirect
6. C61×#2414C2semidirect
7. C61×#2041C2semidirect
8. C61×#2034C2semidirect
9. C61×#2011C2semidirect
10. C61×#1999C2semidirect
11. C61×#1879C2semidirect
12. C61×#1875C2semidirect
13. C61×#1870C2semidirect
14. C61×#1864C2semidirect
15. C61×#1786C2semidirect
20. C22×D8×C61C22semidirect
21. C22×D8×C61C22semidirect
22. C22×M16×C61C22semidirect
29. C2×#121×C61C22semidirect
30. C2×#121×C61C22semidirect
35. C2×#117×C61C22semidirect
39. C2×#106×C61C22semidirect
44. C2×#102×C61C22semidirect
45. C2×#102×C61C22semidirect
46. C2×#102×C61C22semidirect
47. C2×#102×C61C22semidirect
48. C2×#102×C61C22semidirect
49. C2×#102×C61C22semidirect
50. C2×#102×C61C22semidirect
51. C2×C22⋊C8×C61C22semidirect
52. C2×C22⋊C8×C61C22semidirect
53. C2×C22⋊C8×C61C22semidirect
57. C61×#390C22semidirect
58. C61×#389C22semidirect
60. C61×#380C22semidirect
61. C61×#340C22semidirect
62. C61×#340C22semidirect
63. C61×#336C22semidirect
64. C61×#336C22semidirect
90. C22×D4×C61D4semidirect
124. #121×C61D4semidirect
162. #102×C61D4semidirect
287. C2×C8×C61C2×D4semidirect
297. C4⋊C4×C61C2×D4semidirect
437. #24440C61direct (N × H)
501. C2×D42C2×C61semidirect
502. C2×#469C2×C61semidirect
503. C2×#447C2×C61semidirect
504. C2×#447C2×C61semidirect
505. C2×#418C2×C61semidirect
506. #2414C2×C61semidirect
507. #2041C2×C61semidirect
508. #2034C2×C61semidirect
509. #2011C2×C61semidirect
510. #1999C2×C61semidirect
511. #1879C2×C61semidirect
512. #1875C2×C61semidirect
513. #1870C2×C61semidirect
514. #1864C2×C61semidirect
515. #1786C2×C61semidirect
533. C22×D8C22×C61semidirect
534. C22×D8C22×C61semidirect
535. C22×M16C22×C61semidirect
542. C2×#121C22×C61semidirect
543. C2×#121C22×C61semidirect
548. C2×#117C22×C61semidirect
552. C2×#106C22×C61semidirect
557. C2×#102C22×C61semidirect
558. C2×#102C22×C61semidirect
559. C2×#102C22×C61semidirect
560. C2×#102C22×C61semidirect
561. C2×#102C22×C61semidirect
562. C2×#102C22×C61semidirect
563. C2×#102C22×C61semidirect
564. C2×C22⋊C8C22×C61semidirect
565. C2×C22⋊C8C22×C61semidirect
566. C2×C22⋊C8C22×C61semidirect
570. #390C22×C61semidirect
571. #389C22×C61semidirect
573. #380C22×C61semidirect
574. #340C22×C61semidirect
575. #340C22×C61semidirect
576. #336C22×C61semidirect
577. #336C22×C61semidirect
578. C61#24440direct (N × H)
604. C22×D4D4×C61semidirect
638. #121D4×C61semidirect
676. #102D4×C61semidirect
801. C2×C8C2×D4×C61semidirect
811. C4⋊C4C2×D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C612
C2×C61×#4692
C2×C61×#4472
C2×C61×#4182
C61×#24142
C61×#20412
C61×#20342
C61×#20112
C61×#19992
C61×#18792
C61×#18752
C61×#18702
C61×#18642
C61×#17862
#2444061