Finite Group Databasebeta

← C61×#24218 #29527651

Subgroups — C61×#24218 #29527651

Order 15616.

1612 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#535C211yesmaximal, characteristic, complemented
2C2×C61×#463C211yesmaximal, characteristic, complemented
3C2×C61×#459C211yesmaximal, characteristic, complemented
4C2×C61×#449C211yesmaximal, characteristic, complemented
5C2×C61×#447C211yesmaximal, characteristic, complemented
6C61×#2324C211yesmaximal, characteristic, complemented
7C61×#2042C211yesmaximal, characteristic, complemented
8C61×#2041C211yesmaximal, characteristic, complemented
9C61×#2012C211yesmaximal, characteristic, complemented
10C61×#2011C211yesmaximal, characteristic, complemented
11C61×#1983C211yesmaximal, characteristic, complemented
12C61×#1982C211yesmaximal, characteristic, complemented
13C61×#1798C211yesmaximal, 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
21C22×D8×C61C2211yescharacteristic, complemented
22C61×#535—24no—
23C61×#535—24no—
24C2×#127×C61C2211yescharacteristic
25C2×#127×C61C2211yescharacteristic
26C2×#124×C61C2211yescharacteristic
27C2×#124×C61C2211yescharacteristic
28C2×#121×C61—21no—
29C2×#121×C61—21no—
30C2×#121×C61C2211yescharacteristic
31C2×#120×C61—21no—
32C2×#120×C61—21no—
33C2×C4×D4×C61C2211yescharacteristic, complemented
34C2×#117×C61C2211yescharacteristic
35C61×#463—24no—
36C61×#459—24no—
37C61×#449—24no—
38C61×#447—24no—
39C2×C4⋊C8×C61C2211yescharacteristic, complemented
40C2×C4⋊C8×C61C2211yescharacteristic, complemented
41C2×#103×C61C2211yescharacteristic, complemented
42C2×#103×C61C2211yescharacteristic, complemented
43C2×#103×C61C2211yescharacteristic, complemented
44C2×#102×C61C2211yescharacteristic
45C2×#102×C61C2211yescharacteristic
46C2×#102×C61C2211yescharacteristic
47C2×#102×C61C2211yescharacteristic
48C2×#102×C61C2211yescharacteristic
49C2×#102×C61C2211yescharacteristic
50C2×#102×C61C2211yescharacteristic, complemented
51C2×#102×C61C2211yescharacteristic, complemented
52C2×#102×C61C2211yescharacteristic, complemented
53C2×C22⋊C8×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C61×#390—21no—
56C61×#390C2211yescharacteristic, complemented
57C61×#389C2211yescharacteristic, complemented
58C61×#388—21no—
59C61×#386—21no—
60C61×#385—21no—
61C61×#380C2211yescharacteristic
62C4×C4⋊C4×C61C2211yescharacteristic, complemented
63C61×#336C2211yescharacteristic, complemented
64C61×#336C2211yescharacteristic, 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—21no—
78C22×D4×C61—21no—
79C22×D4×C61—21no—
80C22×D4×C61—21no—
81C22×D4×C61—21no—
82C22×D4×C61—22no—
83C22×D4×C61—22no—
84C22×D4×C61—41no—
85C22×D4×C61—41no—
86C22×D4×C61C2311yescharacteristic
87C22×D4×C61C2311yescharacteristic
88C22×D4×C61C2311yescharacteristic
89C22×D4×C61C2311yescharacteristic
90C23×C4×C61—21no—
91C23×C4×C61—21no—
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—22no—
101C2×D8×C61—22no—
102C2×D8×C61—41no—
103C2×D8×C61—41no—
104C2×D8×C61—41no—
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109#127×C61—22no—
110#127×C61—22no—
111#127×C61—22no—
112#127×C61D414yescomplemented
113#124×C61—22no—
114#124×C61—22no—
115#124×C61—22no—
116#124×C61D414yescomplemented
117#121×C61—28no—
118#121×C61—28no—
119#121×C61—22no—
120#121×C61D414yescomplemented
121#120×C61—28no—
122#120×C61—28no—
123C4×D4×C61—22no—
124C4×D4×C61—22no—
125#117×C61—22no—
126#117×C61—22no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61D411yescharacteristic
129C2×C4⋊C4×C61D411yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
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×C61D411yescharacteristic
143C2×C22⋊C4×C61D411yescharacteristic
144C2×C42×C61—21no—
145C2×C42×C61C2311yescharacteristic
146C2×C42×C61C2311yescharacteristic
147C4⋊C8×C61—22no—
148C4⋊C8×C61—22no—
149#103×C61—22no—
150#103×C61—22no—
151#103×C61—41no—
152#102×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—41no—
159#102×C61—41no—
160#102×C61—41no—
161C22⋊C8×C61—22no—
162C22⋊C8×C61—22no—
163#95×C61—21no—
164#95×C61—21no—
165#95×C61—21no—
166C24×C61—24no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61—42no—
172C24×C61—42no—
173C24×C61—81no—
174C24×C61—81no—
175C24×C61—81no—
176C24×C61—81no—
177C24×C61C2×D411yescharacteristic
178#41×C61—44no—
179#41×C61—44no—
180#41×C61—44no—
181#41×C61—44no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61C2×D412yes—
188C2×D4×C61—24no—
189C2×D4×C61—24no—
190C2×D4×C61—24no—
191C2×D4×C61—24no—
192C2×D4×C61—24no—
193C2×D4×C61—24no—
194C2×D4×C61—24no—
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—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—44no—
216C2×D4×C61—44no—
217C2×D4×C61—44no—
218C2×D4×C61—44no—
219C2×D4×C61—42no—
220C2×D4×C61—42no—
221C2×D4×C61—42no—
222C2×D4×C61—42no—
223C2×D4×C61—81no—
224C2×D4×C61—81no—
225C2×D4×C61—81no—
226C2×D4×C61—81no—
227C2×D4×C61—81no—
228C2×D4×C61—81no—
229C2×D4×C61—81no—
230C2×D4×C61—81no—
231C2×D4×C61—81no—
232C2×D4×C61—81no—
233C2×D4×C61C2×D412yes—
234C2×D4×C61C2×D412yes—
235C2×D4×C61C2×D412yes—
236C2×D4×C61C2×D412yes—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—24no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—42no—
247C22×C4×C61—42no—
248C22×C4×C61—42no—
249C22×C4×C61—81no—
250C22×C4×C61—81no—
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D411yescharacteristic
254C22×C4×C61C2×D411yescharacteristic
255C22×C4×C61C2×D411yescharacteristic
256C22×C4×C61C2×D412yes—
257C22×C4×C61#4112yes—
258C22×C4×C61C2411yescharacteristic
259SD16×C61—44no—
260D8×C61—44no—
261D8×C61—44no—
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×C61—21no—
275C4⋊C4×C61—22no—
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—81no—
283C4⋊C4×C61C2×D412yes—
284C22⋊C4×C61—24no—
285C22⋊C4×C61—24no—
286C22⋊C4×C61—24no—
287C22⋊C4×C61—24no—
288C22⋊C4×C61—22no—
289C22⋊C4×C61—22no—
290C22⋊C4×C61—24no—
291C22⋊C4×C61—42no—
292C22⋊C4×C61—81no—
293C22⋊C4×C61—81no—
294C22⋊C4×C61—81no—
295C42×C61—21no—
296C42×C61—21no—
297C42×C61—81no—
298C42×C61C2×D412yes—
299C42×C61C2×D412yes—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—48no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
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—84no—
336C23×C61—84no—
337C23×C61—84no—
338C23×C61—84no—
339C23×C61—84no—
340C23×C61—84no—
341C23×C61#12112yes—
342C23×C61C22×D411yescharacteristic
343Q8×C61—22no—
344Q8×C61—22no—
345Q8×C61—41no—
346Q8×C61—41no—
347D4×C61—22no—
348D4×C61—22no—
349D4×C61—22no—
350D4×C61—22no—
351D4×C61—22no—
352D4×C61—22no—
353D4×C61—22no—
354D4×C61—22no—
355D4×C61—48no—
356D4×C61—48no—
357D4×C61—41no—
358D4×C61—41no—
359D4×C61—41no—
360D4×C61—41no—
361D4×C61—41no—
362D4×C61—41no—
363D4×C61—41no—
364D4×C61—41no—
365D4×C61—84no—
366D4×C61—84no—
367D4×C61—84no—
368D4×C61—84no—
369D4×C61—84no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—22no—
379C2×C4×C61—22no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—22no—
383C2×C4×C61—22no—
384C2×C4×C61—21no—
385C2×C4×C61—21no—
386C2×C4×C61—21no—
387C2×C4×C61—21no—
388C2×C4×C61—48no—
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—84no—
400C2×C4×C61#12012yes—
401C2×C4×C61#12012yes—
402C2×C4×C61#12112yes—
403C2×C4×C61C22×D411yescharacteristic
404C2×C4×C61C22×D411yescharacteristic
405C2×C4×C61C22×D411yescharacteristic
406C2×C4×C61C2×#4111yescharacteristic
407C2×C4×C61H(5,𝔽2)11yescharacteristic
408C2×C4×C61H(5,𝔽2)11yescharacteristic
409C8×C61—41no—
410C8×C61—41no—
411C8×C61—41no—
412C8×C61—41no—
413#24218C6111yesmaximal, characteristic, direct product factor, Sylow
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—22no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—41no—
420C22×C61—41no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61—42no—
424C22×C61—42no—
425C22×C61—42no—
426C22×C61—42no—
427C22×C61—42no—
428C22×C61—42no—
429C22×C61—42no—
430C22×C61—42no—
431C22×C61—42no—
432C22×C61—42no—
433C22×C61—816no—
434C22×C61—81no—
435C22×C61—81no—
436C22×C61—81no—
437C22×C61—81no—
438C22×C61—81no—
439C22×C61—81no—
440C22×C61—81no—
441C22×C61—81no—
442C22×C61—81no—
443C22×C61—81no—
444C22×C61—81no—
445C22×C61—81no—
446C22×C61—81no—
447C22×C61—81no—
448C22×C61—81no—
449C22×C61—81no—
450C22×C61C2×#12011yescharacteristic
451C22×C61C2×#12111yescharacteristic
452C22×C61#53511yescharacteristic
453C22×C61#57611yescharacteristic
454C22×C61#57611yescharacteristic
455C22×C61#57611yescharacteristic
456C22×C61#57711yescharacteristic
457C4×C61—22no—
458C4×C61—22no—
459C4×C61—22no—
460C4×C61—42no—
461C4×C61—41no—
462C4×C61—41no—
463C4×C61—42no—
464C4×C61—81no—
465C4×C61—81no—
466C4×C61D4211yescharacteristic
467C4×C61D4211yescharacteristic
468C4×C61#54611yescharacteristic
469C4×C61#54611yescharacteristic
470C2×#535C2×C6111yescharacteristic, complemented
471C2×#463C2×C6111yescharacteristic, complemented
472C2×#459C2×C6111yescharacteristic, complemented
473C2×#449C2×C6111yescharacteristic, complemented
474C2×#447C2×C6111yescharacteristic, complemented
475#2324C2×C6111yescharacteristic, complemented
476#2042C2×C6111yescharacteristic, complemented
477#2041C2×C6111yescharacteristic, complemented
478#2012C2×C6111yescharacteristic, complemented
479#2011C2×C6111yescharacteristic, complemented
480#1983C2×C6111yescharacteristic, complemented
481#1982C2×C6111yescharacteristic, complemented
482#1798C2×C6111yescharacteristic, complemented
483#1788C2×C6111yescharacteristic, complemented
484#1786C2×C6111yescharacteristic, complemented
485C2×C61—42no—
486C2×C61—82no—
487C2×C61—82no—
488C2×C61—82no—
489C2×C61—82no—
490C2×C61#240811yescharacteristic
491C2×C61#300811yescharacteristic
492C2×C61#301211yescharacteristic
493C2×C61#304111yescharacteristic
494C2×C61#304511yescharacteristic
495C2×C61#322011yescharacteristic
496C2×C61#322411yescharacteristic
497C22×#41C22×C6111yescharacteristic
498C23×D4C22×C6111yescharacteristic
499C22×SD16C22×C6111yescharacteristic, complemented
500C22×D8C22×C6111yescharacteristic
501C22×D8C22×C6111yescharacteristic
502C22×D8C22×C6111yescharacteristic, complemented
503#535—24no—
504#535—24no—
505C2×#127C22×C6111yescharacteristic
506C2×#127C22×C6111yescharacteristic
507C2×#124C22×C6111yescharacteristic
508C2×#124C22×C6111yescharacteristic
509C2×#121—21no—
510C2×#121—21no—
511C2×#121C22×C6111yescharacteristic
512C2×#120—21no—
513C2×#120—21no—
514C2×C4×D4C22×C6111yescharacteristic, complemented
515C2×#117C22×C6111yescharacteristic
516#463—24no—
517#459—24no—
518#449—24no—
519#447—24no—
520C2×C4⋊C8C22×C6111yescharacteristic, complemented
521C2×C4⋊C8C22×C6111yescharacteristic, complemented
522C2×#103C22×C6111yescharacteristic, complemented
523C2×#103C22×C6111yescharacteristic, complemented
524C2×#103C22×C6111yescharacteristic, complemented
525C2×#102C22×C6111yescharacteristic
526C2×#102C22×C6111yescharacteristic
527C2×#102C22×C6111yescharacteristic
528C2×#102C22×C6111yescharacteristic
529C2×#102C22×C6111yescharacteristic
530C2×#102C22×C6111yescharacteristic
531C2×#102C22×C6111yescharacteristic, complemented
532C2×#102C22×C6111yescharacteristic, complemented
533C2×#102C22×C6111yescharacteristic, complemented
534C2×C22⋊C8C22×C6111yescharacteristic
535C2×C22⋊C8C22×C6111yescharacteristic
536#390—21no—
537#390C22×C6111yescharacteristic, complemented
538#389C22×C6111yescharacteristic, complemented
539#388—21no—
540#386—21no—
541#385—21no—
542#380C22×C6111yescharacteristic
543C4×C4⋊C4C22×C6111yescharacteristic, complemented
544#336C22×C6111yescharacteristic, complemented
545#336C22×C6111yescharacteristic, complemented
546C61#2421811yescharacteristic, direct product factor, Sylow
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8C23×C6111yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—22no—
565C22×D4—22no—
566C22×D4—41no—
567C22×D4—41no—
568C22×D4C23×C6111yescharacteristic
569C22×D4C23×C6111yescharacteristic
570C22×D4C23×C6111yescharacteristic
571C22×D4C23×C6111yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C6111yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—41no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—41no—
585C2×D8—41no—
586C2×D8—41no—
587C22×C8C23×C6111yescharacteristic
588C22×C8C23×C6111yescharacteristic
589C22×C8C23×C6111yescharacteristic
590C22×C8C23×C6111yescharacteristic
591#127—22no—
592#127—22no—
593#127—22no—
594#127D4×C6114yescomplemented
595#124—22no—
596#124—22no—
597#124—22no—
598#124D4×C6114yescomplemented
599#121—28no—
600#121—28no—
601#121—22no—
602#121D4×C6114yescomplemented
603#120—28no—
604#120—28no—
605C4×D4—22no—
606C4×D4—22no—
607#117—22no—
608#117—22no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4D4×C6111yescharacteristic
611C2×C4⋊C4D4×C6111yescharacteristic
612C2×C4⋊C4C23×C6111yescharacteristic
613C2×C4⋊C4C23×C6111yescharacteristic
614C2×C4⋊C4C23×C6111yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
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⋊C4D4×C6111yescharacteristic
625C2×C22⋊C4D4×C6111yescharacteristic
626C2×C42—21no—
627C2×C42C23×C6111yescharacteristic
628C2×C42C23×C6111yescharacteristic
629C4⋊C8—22no—
630C4⋊C8—22no—
631#103—22no—
632#103—22no—
633#103—41no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—41no—
641#102—41no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645#95—21no—
646#95—21no—
647#95—21no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—42no—
654C24—42no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24—81no—
659C24C2×D4×C6111yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8C2×D4×C6112yes—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—24no—
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—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4—81no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4C2×D4×C6112yes—
716C2×D4C2×D4×C6112yes—
717C2×D4C2×D4×C6112yes—
718C2×D4C2×D4×C6112yes—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—24no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—81no—
732C22×C4—81no—
733C22×C4C2×D4×C6111yescharacteristic
734C22×C4C2×D4×C6111yescharacteristic
735C22×C4C2×D4×C6111yescharacteristic
736C22×C4C2×D4×C6111yescharacteristic
737C22×C4C2×D4×C6111yescharacteristic
738C22×C4C2×D4×C6112yes—
739C22×C4#41×C6112yes—
740C22×C4C24×C6111yescharacteristic
741SD16—44no—
742D8—44no—
743D8—44no—
744D8—44no—
745C2×C8—21no—
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—
757C4⋊C4—22no—
758C4⋊C4—22no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—81no—
765C4⋊C4C2×D4×C6112yes—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—24no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C22⋊C4—81no—
777C42—21no—
778C42—21no—
779C42—81no—
780C42C2×D4×C6112yes—
781C42C2×D4×C6112yes—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—48no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
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—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23#121×C6112yes—
824C23C22×D4×C6111yescharacteristic
825Q8—22no—
826Q8—22no—
827Q8—41no—
828Q8—41no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—48no—
838D4—48no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4—84no—
851D4—84no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—48no—
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—84no—
882C2×C4#120×C6112yes—
883C2×C4#120×C6112yes—
884C2×C4#121×C6112yes—
885C2×C4C22×D4×C6111yescharacteristic
886C2×C4C22×D4×C6111yescharacteristic
887C2×C4C22×D4×C6111yescharacteristic
888C2×C4C2×#41×C6111yescharacteristic
889C2×C4H(5,𝔽2)×C6111yescharacteristic
890C2×C4H(5,𝔽2)×C6111yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—816no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#120×C6111yescharacteristic
932C22C2×#121×C6111yescharacteristic
933C22C61×#53511yescharacteristic
934C22C61×#57611yescharacteristic
935C22C61×#57611yescharacteristic
936C22C61×#57611yescharacteristic
937C22C61×#57711yescharacteristic
938C4—22no—
939C4—22no—
940C4—22no—
941C4—42no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—81no—
946C4—81no—
947C4D42×C6111yescharacteristic
948C4D42×C6111yescharacteristic
949C4C61×#54611yescharacteristic
950C4C61×#54611yescharacteristic
951C2—42no—
952C2—82no—
953C2—82no—
954C2—82no—
955C2—82no—
956C2C61×#240811yescharacteristic
957C2C61×#300811yescharacteristic
958C2C61×#301211yescharacteristic
959C2C61×#304111yescharacteristic
960C2C61×#304511yescharacteristic
961C2C61×#322011yescharacteristic
962C2C61×#322411yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×#117×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#535C2semidirect
2. C2×C61×#463C2semidirect
3. C2×C61×#459C2semidirect
4. C2×C61×#449C2semidirect
5. C2×C61×#447C2semidirect
6. C61×#2324C2semidirect
7. C61×#2042C2semidirect
8. C61×#2041C2semidirect
9. C61×#2012C2semidirect
10. C61×#2011C2semidirect
11. C61×#1983C2semidirect
12. C61×#1982C2semidirect
13. C61×#1798C2semidirect
14. C61×#1788C2semidirect
15. C61×#1786C2semidirect
18. C22×SD16×C61C22semidirect
21. C22×D8×C61C22semidirect
33. C2×C4×D4×C61C22semidirect
39. C2×C4⋊C8×C61C22semidirect
40. C2×C4⋊C8×C61C22semidirect
41. C2×#103×C61C22semidirect
42. C2×#103×C61C22semidirect
43. C2×#103×C61C22semidirect
50. C2×#102×C61C22semidirect
51. C2×#102×C61C22semidirect
52. C2×#102×C61C22semidirect
56. C61×#390C22semidirect
57. C61×#389C22semidirect
62. C4×C4⋊C4×C61C22semidirect
63. C61×#336C22semidirect
64. C61×#336C22semidirect
112. #127×C61D4semidirect
116. #124×C61D4semidirect
120. #121×C61D4semidirect
413. #24218C61direct (N × H)
470. C2×#535C2×C61semidirect
471. C2×#463C2×C61semidirect
472. C2×#459C2×C61semidirect
473. C2×#449C2×C61semidirect
474. C2×#447C2×C61semidirect
475. #2324C2×C61semidirect
476. #2042C2×C61semidirect
477. #2041C2×C61semidirect
478. #2012C2×C61semidirect
479. #2011C2×C61semidirect
480. #1983C2×C61semidirect
481. #1982C2×C61semidirect
482. #1798C2×C61semidirect
483. #1788C2×C61semidirect
484. #1786C2×C61semidirect
499. C22×SD16C22×C61semidirect
502. C22×D8C22×C61semidirect
514. C2×C4×D4C22×C61semidirect
520. C2×C4⋊C8C22×C61semidirect
521. C2×C4⋊C8C22×C61semidirect
522. C2×#103C22×C61semidirect
523. C2×#103C22×C61semidirect
524. C2×#103C22×C61semidirect
531. C2×#102C22×C61semidirect
532. C2×#102C22×C61semidirect
533. C2×#102C22×C61semidirect
537. #390C22×C61semidirect
538. #389C22×C61semidirect
543. C4×C4⋊C4C22×C61semidirect
544. #336C22×C61semidirect
545. #336C22×C61semidirect
546. C61#24218direct (N × H)
594. #127D4×C61semidirect
598. #124D4×C61semidirect
602. #121D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5352
C2×C61×#4632
C2×C61×#4592
C2×C61×#4492
C2×C61×#4472
C61×#23242
C61×#20422
C61×#20412
C61×#20122
C61×#20112
C61×#19832
C61×#19822
C61×#17982
C61×#17882
C61×#17862
#2421861