Finite Group Databasebeta

← C61×#24257 #29527690

Subgroups — C61×#24257 #29527690

Order 15616.

1650 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#546C211yesmaximal, characteristic, complemented
2C2×C61×#463C211yesmaximal, characteristic, complemented
3C2×C61×#449C211yesmaximal, characteristic, complemented
4C2×C61×#447C211yesmaximal, characteristic, complemented
5C2×C61×#442C211yesmaximal, characteristic, complemented
6C61×#2537C211yesmaximal, characteristic, complemented
7C61×#2035C211yesmaximal, characteristic, complemented
8C61×#2034C211yesmaximal, characteristic, complemented
9C61×#2000C211yesmaximal, characteristic, complemented
10C61×#1999C211yesmaximal, characteristic, complemented
11C61×#1959C211yesmaximal, characteristic, complemented
12C61×#1955C211yesmaximal, characteristic, complemented
13C61×#1802C211yesmaximal, characteristic, complemented
14C61×#1788C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic, complemented
19C22×D8×C61C2211yescharacteristic
20C22×D8×C61C2211yescharacteristic
21C61×#546—24no—
22C61×#546—24no—
23C2×#124×C61C2211yescharacteristic
24C2×#123×C61—21no—
25C2×C22⋊Q8×C61C2211yescharacteristic
26C2×#121×C61—21no—
27C2×#121×C61—21no—
28C2×#121×C61C2211yescharacteristic
29C2×#121×C61C2211yescharacteristic
30C2×#121×C61C2211yescharacteristic, complemented
31C2×#120×C61—21no—
32C2×C4×D4×C61C2211yescharacteristic
33C2×C4×D4×C61C2211yescharacteristic
34C2×C4×D4×C61C2211yescharacteristic, complemented
35C22×C22⋊C4×C61—21no—
36C61×#463—24no—
37C61×#449—24no—
38C61×#447—24no—
39C61×#442—24no—
40C2×#106×C61C2211yescharacteristic, complemented
41C2×C4⋊C8×C61C2211yescharacteristic, complemented
42C2×#103×C61C2211yescharacteristic, complemented
43C2×#103×C61C2211yescharacteristic, complemented
44C2×#103×C61C2211yescharacteristic, complemented
45C2×#102×C61C2211yescharacteristic
46C2×#102×C61C2211yescharacteristic
47C2×#102×C61C2211yescharacteristic
48C2×#102×C61C2211yescharacteristic
49C2×#102×C61C2211yescharacteristic
50C2×#102×C61C2211yescharacteristic
51C2×#102×C61C2211yescharacteristic, complemented
52C2×C22⋊C8×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic, complemented
55C2×C22⋊C8×C61C2211yescharacteristic, complemented
56C2×#97×C61C2211yescharacteristic, complemented
57C61×#394—21no—
58C61×#394—21no—
59C61×#384C2211yescharacteristic, complemented
60C61×#380—21no—
61C61×#380C2211yescharacteristic
62C61×#380C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C61×#340C2211yescharacteristic, complemented
65C25×C61—21no—
66C2×#41×C61—22no—
67C2×#41×C61—22no—
68C2×#41×C61—22no—
69C2×#41×C61—22no—
70C2×#41×C61—41no—
71C2×#41×C61—41no—
72C22×Q8×C61C2311yescharacteristic
73C22×D4×C61—21no—
74C22×D4×C61—21no—
75C22×D4×C61—22no—
76C22×D4×C61—22no—
77C22×D4×C61—22no—
78C22×D4×C61—22no—
79C22×D4×C61—21no—
80C22×D4×C61—21no—
81C22×D4×C61—21no—
82C22×D4×C61—41no—
83C22×D4×C61—41no—
84C22×D4×C61D411yescharacteristic
85C22×D4×C61C2311yescharacteristic
86C22×D4×C61C2311yescharacteristic
87C22×D4×C61C2311yescharacteristic
88C23×C4×C61—21no—
89C23×C4×C61—21no—
90C23×C4×C61—21no—
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2311yescharacteristic
93C2×SD16×C61—22no—
94C2×SD16×C61—22no—
95C2×SD16×C61—41no—
96C2×D8×C61—22no—
97C2×D8×C61—22no—
98C2×D8×C61—22no—
99C2×D8×C61—22no—
100C2×D8×C61—41no—
101C2×D8×C61D414yescomplemented
102C22×C8×C61C2311yescharacteristic
103C22×C8×C61C2311yescharacteristic
104C22×C8×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106#124×C61—22no—
107#124×C61D414yescomplemented
108#123×C61—28no—
109C22⋊Q8×C61—22no—
110C22⋊Q8×C61—22no—
111#121×C61—28no—
112#121×C61—22no—
113#121×C61—22no—
114#121×C61—22no—
115#121×C61—22no—
116#121×C61—41no—
117#121×C61—41no—
118#121×C61—44no—
119#120×C61—28no—
120C4×D4×C61—22no—
121C4×D4×C61—22no—
122C4×D4×C61—22no—
123C4×D4×C61—22no—
124C4×D4×C61—22no—
125C4×D4×C61D414yescomplemented
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61D411yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—28no—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
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×C61D411yescharacteristic
146C2×C22⋊C4×C61D411yescharacteristic
147C2×C42×C61C2311yescharacteristic
148#106×C61—22no—
149C4⋊C8×C61—22no—
150#103×C61—22no—
151#103×C61—22no—
152#103×C61—41no—
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—41no—
160C22⋊C8×C61—22no—
161C22⋊C8×C61—22no—
162C22⋊C8×C61—41no—
163C22⋊C8×C61—41no—
164#97×C61—22no—
165#95×C61—21no—
166#95×C61—21no—
167C24×C61—21no—
168C24×C61—24no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61—42no—
172C24×C61—42no—
173C24×C61—42no—
174C24×C61—42no—
175C24×C61—81no—
176C24×C61—81no—
177C24×C61C2×D411yescharacteristic
178C24×C61C2×D411yescharacteristic
179#41×C61—44no—
180#41×C61—44no—
181#41×C61—44no—
182#41×C61—44no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61C2×D412yes—
189C2×D4×C61—24no—
190C2×D4×C61—24no—
191C2×D4×C61—22no—
192C2×D4×C61—24no—
193C2×D4×C61—22no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
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—41no—
208C2×D4×C61—42no—
209C2×D4×C61—42no—
210C2×D4×C61—44no—
211C2×D4×C61—44no—
212C2×D4×C61—44no—
213C2×D4×C61—42no—
214C2×D4×C61—42no—
215C2×D4×C61—44no—
216C2×D4×C61—42no—
217C2×D4×C61—42no—
218C2×D4×C61—42no—
219C2×D4×C61—42no—
220C2×D4×C61—81no—
221C2×D4×C61—81no—
222C2×D4×C61—81no—
223C2×D4×C61—81no—
224C2×D4×C61C2×D412yes—
225C2×D4×C61C2×D412yes—
226C2×D4×C61C2×D412yes—
227C2×D4×C61C2×D412yes—
228C2×D4×C61#4112yes—
229C22×C4×C61—24no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—24no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—42no—
249C22×C4×C61—42no—
250C22×C4×C61—42no—
251C22×C4×C61—42no—
252C22×C4×C61—42no—
253C22×C4×C61—81no—
254C22×C4×C61—81no—
255C22×C4×C61C2×D411yescharacteristic
256C22×C4×C61C2×D411yescharacteristic
257C22×C4×C61C2×D411yescharacteristic
258C22×C4×C61C2×D411yescharacteristic
259C22×C4×C61C2411yescharacteristic
260SD16×C61—44no—
261D8×C61—28no—
262D8×C61—44no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61—21no—
270C2×C8×C61—21no—
271C2×C8×C61—21no—
272C2×C8×C61—21no—
273C2×C8×C61—21no—
274C2×C8×C61C2×D412yes—
275C4⋊C4×C61—24no—
276C4⋊C4×C61—22no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61—42no—
285C4⋊C4×C61—81no—
286C4⋊C4×C61C2×D412yes—
287C22⋊C4×C61—24no—
288C22⋊C4×C61—24no—
289C22⋊C4×C61—22no—
290C22⋊C4×C61—24no—
291C22⋊C4×C61—24no—
292C22⋊C4×C61—24no—
293C22⋊C4×C61—22no—
294C22⋊C4×C61—42no—
295C22⋊C4×C61—42no—
296C22⋊C4×C61—42no—
297C22⋊C4×C61—42no—
298C22⋊C4×C61—42no—
299C42×C61C2×D412yes—
300C42×C61C2×D412yes—
301C23×C61—21no—
302C23×C61—22no—
303C23×C61—21no—
304C23×C61—22no—
305C23×C61—21no—
306C23×C61—22no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—22no—
311C23×C61—21no—
312C23×C61—22no—
313C23×C61—21no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—21no—
318C23×C61—21no—
319C23×C61—48no—
320C23×C61—48no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61—41no—
336C23×C61—41no—
337C23×C61—84no—
338C23×C61—84no—
339C23×C61—84no—
340C23×C61—84no—
341C23×C61—84no—
342C23×C61AGL(1,ℤ/8)12yes—
343C23×C61C22×D411yescharacteristic
344Q8×C61—22no—
345Q8×C61—22no—
346Q8×C61—41no—
347Q8×C61—41no—
348D4×C61—22no—
349D4×C61—22no—
350D4×C61—22no—
351D4×C61—22no—
352D4×C61—22no—
353D4×C61—22no—
354D4×C61—22no—
355D4×C61—44no—
356D4×C61—48no—
357D4×C61—48no—
358D4×C61—41no—
359D4×C61—41no—
360D4×C61—41no—
361D4×C61—41no—
362D4×C61—84no—
363D4×C61—84no—
364D4×C61—84no—
365D4×C61#12114yescomplemented
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—22no—
371C2×C4×C61—21no—
372C2×C4×C61—22no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—48no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—84no—
401C2×C4×C61—84no—
402C2×C4×C61#12012yes—
403C2×C4×C61#12012yes—
404C2×C4×C61C22×D411yescharacteristic
405C2×C4×C61C22×D411yescharacteristic
406C2×C4×C61C22×D411yescharacteristic
407C2×C4×C61C2×#4111yescharacteristic
408C2×C4×C61H(5,𝔽2)11yescharacteristic
409C2×C4×C61H(5,𝔽2)11yescharacteristic
410C8×C61—22no—
411C8×C61—41no—
412C8×C61—41no—
413C8×C61—41no—
414#24257C6111yesmaximal, characteristic, direct product factor, Sylow
415C22×C61—24no—
416C22×C61—22no—
417C22×C61—22no—
418C22×C61—22no—
419C22×C61—41no—
420C22×C61—42no—
421C22×C61—42no—
422C22×C61—41no—
423C22×C61—42no—
424C22×C61—42no—
425C22×C61—41no—
426C22×C61—42no—
427C22×C61—41no—
428C22×C61—42no—
429C22×C61—41no—
430C22×C61—42no—
431C22×C61—42no—
432C22×C61—41no—
433C22×C61—42no—
434C22×C61—41no—
435C22×C61—42no—
436C22×C61—41no—
437C22×C61—42no—
438C22×C61—41no—
439C22×C61—42no—
440C22×C61—41no—
441C22×C61—41no—
442C22×C61—816no—
443C22×C61—81no—
444C22×C61—81no—
445C22×C61—81no—
446C22×C61—81no—
447C22×C61—81no—
448C22×C61—81no—
449C22×C61—81no—
450C22×C61—81no—
451C22×C61C2×#12011yescharacteristic
452C22×C61D4211yescharacteristic
453C22×C61#54611yescharacteristic
454C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
455C22×C61#57511yescharacteristic
456C22×C61#57611yescharacteristic
457C22×C61#57711yescharacteristic
458C4×C61—22no—
459C4×C61—22no—
460C4×C61—41no—
461C4×C61—41no—
462C4×C61—42no—
463C4×C61—42no—
464C4×C61—81no—
465C4×C61—81no—
466C4×C61—81no—
467C4×C61C2×#12111yescharacteristic
468C4×C61#53511yescharacteristic
469C4×C61D4211yescharacteristic
470C4×C61#54611yescharacteristic
471C2×#546C2×C6111yescharacteristic, complemented
472C2×#463C2×C6111yescharacteristic, complemented
473C2×#449C2×C6111yescharacteristic, complemented
474C2×#447C2×C6111yescharacteristic, complemented
475C2×#442C2×C6111yescharacteristic, complemented
476#2537C2×C6111yescharacteristic, complemented
477#2035C2×C6111yescharacteristic, complemented
478#2034C2×C6111yescharacteristic, complemented
479#2000C2×C6111yescharacteristic, complemented
480#1999C2×C6111yescharacteristic, complemented
481#1959C2×C6111yescharacteristic, complemented
482#1955C2×C6111yescharacteristic, complemented
483#1802C2×C6111yescharacteristic, complemented
484#1788C2×C6111yescharacteristic, complemented
485#1786C2×C6111yescharacteristic, complemented
486C2×C61—42no—
487C2×C61—44no—
488C2×C61—81no—
489C2×C61—82no—
490C2×C61—82no—
491C2×C61#240811yescharacteristic
492C2×C61#300611yescharacteristic
493C2×C61#301211yescharacteristic
494C2×C61#326411yescharacteristic
495C2×C61#326711yescharacteristic
496C2×C61#330611yescharacteristic
497C2×C61#331911yescharacteristic
498C22×#41C22×C6111yescharacteristic
499C23×D4C22×C6111yescharacteristic
500C22×SD16C22×C6111yescharacteristic, complemented
501C22×D8C22×C6111yescharacteristic
502C22×D8C22×C6111yescharacteristic
503#546—24no—
504#546—24no—
505C2×#124C22×C6111yescharacteristic
506C2×#123—21no—
507C2×C22⋊Q8C22×C6111yescharacteristic
508C2×#121—21no—
509C2×#121—21no—
510C2×#121C22×C6111yescharacteristic
511C2×#121C22×C6111yescharacteristic
512C2×#121C22×C6111yescharacteristic, complemented
513C2×#120—21no—
514C2×C4×D4C22×C6111yescharacteristic
515C2×C4×D4C22×C6111yescharacteristic
516C2×C4×D4C22×C6111yescharacteristic, complemented
517C22×C22⋊C4—21no—
518#463—24no—
519#449—24no—
520#447—24no—
521#442—24no—
522C2×#106C22×C6111yescharacteristic, complemented
523C2×C4⋊C8C22×C6111yescharacteristic, complemented
524C2×#103C22×C6111yescharacteristic, complemented
525C2×#103C22×C6111yescharacteristic, complemented
526C2×#103C22×C6111yescharacteristic, complemented
527C2×#102C22×C6111yescharacteristic
528C2×#102C22×C6111yescharacteristic
529C2×#102C22×C6111yescharacteristic
530C2×#102C22×C6111yescharacteristic
531C2×#102C22×C6111yescharacteristic
532C2×#102C22×C6111yescharacteristic
533C2×#102C22×C6111yescharacteristic, complemented
534C2×C22⋊C8C22×C6111yescharacteristic
535C2×C22⋊C8C22×C6111yescharacteristic
536C2×C22⋊C8C22×C6111yescharacteristic, complemented
537C2×C22⋊C8C22×C6111yescharacteristic, complemented
538C2×#97C22×C6111yescharacteristic, complemented
539#394—21no—
540#394—21no—
541#384C22×C6111yescharacteristic, complemented
542#380—21no—
543#380C22×C6111yescharacteristic
544#380C22×C6111yescharacteristic, complemented
545#340C22×C6111yescharacteristic, complemented
546#340C22×C6111yescharacteristic, complemented
547C61#2425711yescharacteristic, direct product factor, Sylow
548C25—21no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—41no—
554C2×#41—41no—
555C22×Q8C23×C6111yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C6111yescharacteristic
568C22×D4C23×C6111yescharacteristic
569C22×D4C23×C6111yescharacteristic
570C22×D4C23×C6111yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C6111yescharacteristic
575C23×C4C23×C6111yescharacteristic
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—41no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—41no—
584C2×D8D4×C6114yescomplemented
585C22×C8C23×C6111yescharacteristic
586C22×C8C23×C6111yescharacteristic
587C22×C8C23×C6111yescharacteristic
588C22×C8C23×C6111yescharacteristic
589#124—22no—
590#124D4×C6114yescomplemented
591#123—28no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—41no—
600#121—41no—
601#121—44no—
602#120—28no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4D4×C6114yescomplemented
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4D4×C6111yescharacteristic
613C2×C4⋊C4C23×C6111yescharacteristic
614C2×C4⋊C4C23×C6111yescharacteristic
615C2×C4⋊C4C23×C6111yescharacteristic
616C2×C4⋊C4C23×C6111yescharacteristic
617C2×C22⋊C4—28no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4D4×C6111yescharacteristic
629C2×C22⋊C4D4×C6111yescharacteristic
630C2×C42C23×C6111yescharacteristic
631#106—22no—
632C4⋊C8—22no—
633#103—22no—
634#103—22no—
635#103—41no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645C22⋊C8—41no—
646C22⋊C8—41no—
647#97—22no—
648#95—21no—
649#95—21no—
650C24—21no—
651C24—24no—
652C24—21no—
653C24—21no—
654C24—42no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—81no—
659C24—81no—
660C24C2×D4×C6111yescharacteristic
661C24C2×D4×C6111yescharacteristic
662#41—44no—
663#41—44no—
664#41—44no—
665#41—44no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8C2×D4×C6112yes—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—44no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4C2×D4×C6112yes—
708C2×D4C2×D4×C6112yes—
709C2×D4C2×D4×C6112yes—
710C2×D4C2×D4×C6112yes—
711C2×D4#41×C6112yes—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—24no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—81no—
737C22×C4—81no—
738C22×C4C2×D4×C6111yescharacteristic
739C22×C4C2×D4×C6111yescharacteristic
740C22×C4C2×D4×C6111yescharacteristic
741C22×C4C2×D4×C6111yescharacteristic
742C22×C4C24×C6111yescharacteristic
743SD16—44no—
744D8—28no—
745D8—44no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8C2×D4×C6112yes—
758C4⋊C4—24no—
759C4⋊C4—22no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C6112yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—42no—
778C22⋊C4—42no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C42C2×D4×C6112yes—
783C42C2×D4×C6112yes—
784C23—21no—
785C23—22no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—22no—
793C23—22no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—22no—
801C23—21no—
802C23—48no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23AGL(1,ℤ/8)×C6112yes—
826C23C22×D4×C6111yescharacteristic
827Q8—22no—
828Q8—22no—
829Q8—41no—
830Q8—41no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—44no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—84no—
846D4—84no—
847D4—84no—
848D4#121×C6114yescomplemented
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—22no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—84no—
884C2×C4—84no—
885C2×C4#120×C6112yes—
886C2×C4#120×C6112yes—
887C2×C4C22×D4×C6111yescharacteristic
888C2×C4C22×D4×C6111yescharacteristic
889C2×C4C22×D4×C6111yescharacteristic
890C2×C4C2×#41×C6111yescharacteristic
891C2×C4H(5,𝔽2)×C6111yescharacteristic
892C2×C4H(5,𝔽2)×C6111yescharacteristic
893C8—22no—
894C8—41no—
895C8—41no—
896C8—41no—
897C22—22no—
898C22—24no—
899C22—22no—
900C22—22no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—42no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—42no—
915C22—42no—
916C22—41no—
917C22—42no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—42no—
922C22—41no—
923C22—42no—
924C22—816no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22C2×#120×C6111yescharacteristic
934C22D42×C6111yescharacteristic
935C22C61×#54611yescharacteristic
936C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
937C22C61×#57511yescharacteristic
938C22C61×#57611yescharacteristic
939C22C61×#57711yescharacteristic
940C4—22no—
941C4—22no—
942C4—41no—
943C4—41no—
944C4—42no—
945C4—42no—
946C4—81no—
947C4—81no—
948C4—81no—
949C4C2×#121×C6111yescharacteristic
950C4C61×#53511yescharacteristic
951C4D42×C6111yescharacteristic
952C4C61×#54611yescharacteristic
953C2—42no—
954C2—44no—
955C2—81no—
956C2—82no—
957C2—82no—
958C2C61×#240811yescharacteristic
959C2C61×#300611yescharacteristic
960C2C61×#301211yescharacteristic
961C2C61×#326411yescharacteristic
962C2C61×#326711yescharacteristic
963C2C61×#330611yescharacteristic
964C2C61×#331911yescharacteristic
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×C61×#546C2semidirect
2. C2×C61×#463C2semidirect
3. C2×C61×#449C2semidirect
4. C2×C61×#447C2semidirect
5. C2×C61×#442C2semidirect
6. C61×#2537C2semidirect
7. C61×#2035C2semidirect
8. C61×#2034C2semidirect
9. C61×#2000C2semidirect
10. C61×#1999C2semidirect
11. C61×#1959C2semidirect
12. C61×#1955C2semidirect
13. C61×#1802C2semidirect
14. C61×#1788C2semidirect
15. C61×#1786C2semidirect
18. C22×SD16×C61C22semidirect
30. C2×#121×C61C22semidirect
34. C2×C4×D4×C61C22semidirect
40. C2×#106×C61C22semidirect
41. C2×C4⋊C8×C61C22semidirect
42. C2×#103×C61C22semidirect
43. C2×#103×C61C22semidirect
44. C2×#103×C61C22semidirect
51. C2×#102×C61C22semidirect
54. C2×C22⋊C8×C61C22semidirect
55. C2×C22⋊C8×C61C22semidirect
56. C2×#97×C61C22semidirect
59. C61×#384C22semidirect
62. C61×#380C22semidirect
63. C61×#340C22semidirect
64. C61×#340C22semidirect
101. C2×D8×C61D4semidirect
107. #124×C61D4semidirect
125. C4×D4×C61D4semidirect
365. D4×C61#121semidirect
414. #24257C61direct (N × H)
471. C2×#546C2×C61semidirect
472. C2×#463C2×C61semidirect
473. C2×#449C2×C61semidirect
474. C2×#447C2×C61semidirect
475. C2×#442C2×C61semidirect
476. #2537C2×C61semidirect
477. #2035C2×C61semidirect
478. #2034C2×C61semidirect
479. #2000C2×C61semidirect
480. #1999C2×C61semidirect
481. #1959C2×C61semidirect
482. #1955C2×C61semidirect
483. #1802C2×C61semidirect
484. #1788C2×C61semidirect
485. #1786C2×C61semidirect
500. C22×SD16C22×C61semidirect
512. C2×#121C22×C61semidirect
516. C2×C4×D4C22×C61semidirect
522. C2×#106C22×C61semidirect
523. C2×C4⋊C8C22×C61semidirect
524. C2×#103C22×C61semidirect
525. C2×#103C22×C61semidirect
526. C2×#103C22×C61semidirect
533. C2×#102C22×C61semidirect
536. C2×C22⋊C8C22×C61semidirect
537. C2×C22⋊C8C22×C61semidirect
538. C2×#97C22×C61semidirect
541. #384C22×C61semidirect
544. #380C22×C61semidirect
545. #340C22×C61semidirect
546. #340C22×C61semidirect
547. C61#24257direct (N × H)
584. C2×D8D4×C61semidirect
590. #124D4×C61semidirect
608. C4×D4D4×C61semidirect
848. D4#121×C61semidirect

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×#4632
C2×C61×#4492
C2×C61×#4472
C2×C61×#4422
C61×#25372
C61×#20352
C61×#20342
C61×#20002
C61×#19992
C61×#19592
C61×#19552
C61×#18022
C61×#17882
C61×#17862
#2425761