Finite Group Databasebeta

← C61×#23881 #29527314

Subgroups — C61×#23881 #29527314

Order 15616.

1714 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#575C211yesmaximal, characteristic, complemented
2C61×#3489C211yesmaximal, characteristic, complemented
3C2×C61×#456C211yesmaximal, characteristic, complemented
4C2×C61×#454C211yesmaximal, characteristic, complemented
5C61×#3005C211yesmaximal, characteristic, complemented
6C61×#2432C211yesmaximal, characteristic, complemented
7C61×#2007C211yesmaximal, characteristic, complemented
8C61×#2006C211yesmaximal, characteristic, complemented
9C61×#2005C211yesmaximal, characteristic, complemented
10C61×#2003C211yesmaximal, characteristic, complemented
11C61×#1901C211yesmaximal, characteristic, complemented
12C61×#1883C211yesmaximal, characteristic, complemented
13C61×#1882C211yesmaximal, characteristic, complemented
14C61×#1871C211yesmaximal, characteristic, complemented
15C61×#1789C211yesmaximal, characteristic, complemented
16C2×2−1+4×C61C2211yescharacteristic
17C22×#41×C61C2211yescharacteristic
18C22×#41×C61C2211yescharacteristic
19C61×#575—24no—
20C61×#575—24no—
21C2×#137×C61—21no—
22C2×#137×C61C2211yescharacteristic
23C2×#137×C61C2211yescharacteristic
24C2×#137×C61C2211yescharacteristic, complemented
25C2×AGL(1,ℤ/8)×C61—21no—
26C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C61C2211yescharacteristic, complemented
29C2×#135×C61—21no—
30C2×#135×C61—21no—
31C22×M16×C61C2211yescharacteristic
32D4×Q8×C61—21no—
33C61×#548—21no—
34C61×#547—21no—
35C61×#547—22no—
36C61×#546—21no—
37C61×#546—22no—
38C61×#537—21no—
39C61×#537C2211yescharacteristic
40C61×#536—21no—
41C61×#536C2211yescharacteristic
42C2×C4⋊Q8×C61C2211yescharacteristic, complemented
43C2×#124×C61C2211yescharacteristic, complemented
44C61×#525—21no—
45C61×#525C2211yescharacteristic
46C2×C22⋊Q8×C61—21no—
47C2×C22⋊Q8×C61C2211yescharacteristic
48C61×#520C2211yescharacteristic
49C61×#456—24no—
50C61×#454—24no—
51C61×#452—21no—
52C61×#452—21no—
53C61×#449—21no—
54C61×#449—21no—
55C2×#104×C61C2211yescharacteristic
56C2×#104×C61C2211yescharacteristic
57C2×#104×C61C2211yescharacteristic
58C2×#104×C61C2211yescharacteristic
59C2×#104×C61C2211yescharacteristic, complemented
60C2×#104×C61C2211yescharacteristic, complemented
61C61×#419C2211yescharacteristic, complemented
62C61×#418C2211yescharacteristic, complemented
63C2×#101×C61C2211yescharacteristic, complemented
64C2×#101×C61C2211yescharacteristic, complemented
65C61×#407C2211yescharacteristic
66C61×#394—22no—
67C61×#391C2211yescharacteristic, complemented
68C61×#390C2211yescharacteristic, complemented
69C61×#385—22no—
70C4×C22⋊C4×C61C2211yescharacteristic
71C61×#343C2211yescharacteristic, complemented
72C61×#343C2211yescharacteristic, complemented
73C61×#339C2211yescharacteristic, complemented
74C61×#339C2211yescharacteristic, complemented
752−1+4×C61—22no—
762−1+4×C61—22no—
772−1+4×C61—41no—
782−1+4×C61—41no—
79C2×#41×C61—21no—
80C2×#41×C61—21no—
81C2×#41×C61—21no—
82C2×#41×C61—22no—
83C2×#41×C61—21no—
84C2×#41×C61—22no—
85C2×#41×C61—22no—
86C2×#41×C61—22no—
87C2×#41×C61—22no—
88C2×#41×C61—21no—
89C2×#41×C61—21no—
90C2×#41×C61—21no—
91C2×#41×C61—21no—
92C2×#41×C61—41no—
93C2×#41×C61—41no—
94C2×#41×C61—41no—
95C2×#41×C61—41no—
96C2×#41×C61D411yescharacteristic
97C2×#41×C61D411yescharacteristic
98C2×#41×C61C2311yescharacteristic
99C2×#41×C61C2311yescharacteristic
100C2×#41×C61C2311yescharacteristic
101C22×Q8×C61—21no—
102C22×Q8×C61—21no—
103C22×Q8×C61D411yescharacteristic
104C22×Q8×C61C2311yescharacteristic
105C22×Q8×C61C2311yescharacteristic
106C22×D4×C61—21no—
107C22×D4×C61—21no—
108C22×D4×C61D411yescharacteristic
109C22×D4×C61C2311yescharacteristic
110C23×C4×C61—21no—
111C23×C4×C61—21no—
112C23×C4×C61C2311yescharacteristic
113#137×C61—28no—
114#137×C61—22no—
115#137×C61—22no—
116#137×C61—22no—
117#137×C61—22no—
118#137×C61—41no—
119#137×C61D414yescomplemented
120AGL(1,ℤ/8)×C61—28no—
121AGL(1,ℤ/8)×C61—22no—
122AGL(1,ℤ/8)×C61—22no—
123AGL(1,ℤ/8)×C61—22no—
124AGL(1,ℤ/8)×C61—22no—
125AGL(1,ℤ/8)×C61—41no—
126AGL(1,ℤ/8)×C61D414yescomplemented
127#135×C61—28no—
128#135×C61—28no—
129C2×Q16×C61—21no—
130C2×Q16×C61—21no—
131C2×Q16×C61—21no—
132C2×SD16×C61—21no—
133C2×SD16×C61—21no—
134C2×SD16×C61—21no—
135C2×SD16×C61—21no—
136C2×SD16×C61—21no—
137C2×SD16×C61—21no—
138C2×D8×C61—21no—
139C2×D8×C61—21no—
140C2×D8×C61—21no—
141C2×M16×C61—21no—
142C2×M16×C61—22no—
143C2×M16×C61—22no—
144C2×M16×C61C2311yescharacteristic
145C2×M16×C61C2311yescharacteristic
146C2×M16×C61C2311yescharacteristic
147C2×M16×C61C2311yescharacteristic
148C22×C8×C61—21no—
149C4⋊Q8×C61—22no—
150C4⋊Q8×C61—21no—
151C4⋊Q8×C61—22no—
152C4⋊Q8×C61—41no—
153#124×C61—22no—
154#124×C61—21no—
155#124×C61—22no—
156#124×C61—41no—
157#123×C61—22no—
158#123×C61—22no—
159#123×C61—22no—
160#123×C61—22no—
161#123×C61—21no—
162C22⋊Q8×C61—22no—
163C22⋊Q8×C61—22no—
164C22⋊Q8×C61—22no—
165C22⋊Q8×C61—21no—
166C22⋊Q8×C61—21no—
167C22⋊Q8×C61—21no—
168C22⋊Q8×C61—21no—
169C22⋊Q8×C61—21no—
170C22⋊Q8×C61—21no—
171C22⋊Q8×C61—21no—
172C22⋊Q8×C61—21no—
173C22⋊Q8×C61D411yescharacteristic
174C22⋊Q8×C61D411yescharacteristic
175#121×C61—22no—
176#121×C61—22no—
177#121×C61—22no—
178#121×C61—21no—
179#121×C61—21no—
180#121×C61—22no—
181#121×C61D411yescharacteristic
182#121×C61D411yescharacteristic
183#120×C61—22no—
184#120×C61—21no—
185C4×Q8×C61—21no—
186C4×D4×C61—22no—
187C4×D4×C61—22no—
188C4×D4×C61—21no—
189C4×D4×C61—22no—
190C4×D4×C61—21no—
191C4×D4×C61—21no—
192#117×C61—21no—
193#117×C61C2311yescharacteristic
194C2×C4⋊C4×C61—22no—
195C2×C4⋊C4×C61—21no—
196C2×C4⋊C4×C61—22no—
197C2×C4⋊C4×C61D412yes—
198C2×C4⋊C4×C61C2311yescharacteristic
199C2×C22⋊C4×C61—22no—
200C2×C22⋊C4×C61—21no—
201C2×C22⋊C4×C61—22no—
202C2×C22⋊C4×C61—22no—
203C2×C22⋊C4×C61D412yes—
204C2×C42×C61C2311yescharacteristic
205C2×C42×C61C2311yescharacteristic
206#104×C61—22no—
207#104×C61—22no—
208#104×C61—22no—
209#104×C61—22no—
210#104×C61—41no—
211#104×C61—41no—
212#103×C61—21no—
213#103×C61—21no—
214#102×C61—21no—
215#102×C61—21no—
216#101×C61—22no—
217#101×C61—22no—
218C22⋊C8×C61—21no—
219C22⋊C8×C61—21no—
220#95×C61—21no—
221#95×C61—22no—
222C24×C61—21no—
223C24×C61—21no—
224C24×C61C2×D411yescharacteristic
225#41×C61—21no—
226#41×C61—21no—
227#41×C61—24no—
228#41×C61—24no—
229#41×C61—22no—
230#41×C61—22no—
231#41×C61—21no—
232#41×C61—21no—
233#41×C61—21no—
234#41×C61—21no—
235#41×C61—21no—
236#41×C61—21no—
237#41×C61—21no—
238#41×C61—21no—
239#41×C61—42no—
240#41×C61—42no—
241#41×C61—41no—
242#41×C61—41no—
243#41×C61—42no—
244#41×C61—42no—
245#41×C61—42no—
246#41×C61—42no—
247#41×C61—42no—
248#41×C61—42no—
249#41×C61—44no—
250#41×C61—44no—
251#41×C61—42no—
252#41×C61—42no—
253#41×C61—42no—
254#41×C61—42no—
255#41×C61—42no—
256#41×C61—42no—
257#41×C61C2×D412yes—
258#41×C61C2×D412yes—
259C2×Q8×C61—22no—
260C2×Q8×C61—21no—
261C2×Q8×C61—21no—
262C2×Q8×C61—21no—
263C2×Q8×C61—21no—
264C2×Q8×C61—21no—
265C2×Q8×C61—21no—
266C2×Q8×C61—21no—
267C2×Q8×C61—21no—
268C2×Q8×C61—22no—
269C2×Q8×C61—21no—
270C2×Q8×C61—21no—
271C2×Q8×C61—21no—
272C2×Q8×C61—21no—
273C2×Q8×C61—41no—
274C2×Q8×C61—42no—
275C2×Q8×C61—42no—
276C2×Q8×C61—42no—
277C2×Q8×C61—42no—
278C2×Q8×C61C2×D411yescharacteristic
279C2×Q8×C61C2×D411yescharacteristic
280C2×Q8×C61C2×D412yes—
281C2×Q8×C61C2×D411yescharacteristic
282C2×D4×C61—21no—
283C2×D4×C61—22no—
284C2×D4×C61—22no—
285C2×D4×C61—21no—
286C2×D4×C61—21no—
287C2×D4×C61—21no—
288C2×D4×C61—21no—
289C2×D4×C61—21no—
290C2×D4×C61—22no—
291C2×D4×C61—21no—
292C2×D4×C61—21no—
293C2×D4×C61—21no—
294C2×D4×C61—21no—
295C2×D4×C61—21no—
296C2×D4×C61—21no—
297C2×D4×C61—21no—
298C2×D4×C61—41no—
299C2×D4×C61—42no—
300C2×D4×C61—42no—
301C2×D4×C61—42no—
302C2×D4×C61—42no—
303C2×D4×C61—41no—
304C2×D4×C61—41no—
305C2×D4×C61C2×D411yescharacteristic
306C2×D4×C61C2×D411yescharacteristic
307C2×D4×C61C2×D412yes—
308C2×D4×C61C2×D411yescharacteristic
309C22×C4×C61—21no—
310C22×C4×C61—21no—
311C22×C4×C61—21no—
312C22×C4×C61—21no—
313C22×C4×C61—21no—
314C22×C4×C61—22no—
315C22×C4×C61—22no—
316C22×C4×C61—21no—
317C22×C4×C61—21no—
318C22×C4×C61—21no—
319C22×C4×C61—22no—
320C22×C4×C61—21no—
321C22×C4×C61—21no—
322C22×C4×C61—21no—
323C22×C4×C61—21no—
324C22×C4×C61—21no—
325C22×C4×C61—42no—
326C22×C4×C61—42no—
327C22×C4×C61—42no—
328C22×C4×C61—42no—
329C22×C4×C61—41no—
330C22×C4×C61—41no—
331C22×C4×C61C2×D412yes—
332C22×C4×C61C2×D411yescharacteristic
333C22×C4×C61C2×D411yescharacteristic
334C22×C4×C61C2×D411yescharacteristic
335C22×C4×C61C2×D411yescharacteristic
336C22×C4×C61C2×D411yescharacteristic
337C22×C4×C61C2×D412yes—
338C22×C4×C61C2411yescharacteristic
339Q16×C61—24no—
340Q16×C61—24no—
341Q16×C61—42no—
342SD16×C61—24no—
343SD16×C61—24no—
344SD16×C61—24no—
345SD16×C61—24no—
346SD16×C61—42no—
347SD16×C61—42no—
348D8×C61—24no—
349D8×C61—24no—
350D8×C61—42no—
351M16×C61—24no—
352M16×C61—21no—
353M16×C61—21no—
354M16×C61—21no—
355M16×C61—21no—
356M16×C61—21no—
357M16×C61—21no—
358M16×C61C2×D412yes—
359M16×C61C2×D412yes—
360C2×C8×C61—24no—
361C2×C8×C61—21no—
362C2×C8×C61—21no—
363C2×C8×C61—21no—
364C2×C8×C61—21no—
365C4⋊C4×C61—22no—
366C4⋊C4×C61—22no—
367C4⋊C4×C61—22no—
368C4⋊C4×C61—22no—
369C4⋊C4×C61—21no—
370C4⋊C4×C61—22no—
371C4⋊C4×C61—22no—
372C4⋊C4×C61—21no—
373C4⋊C4×C61—21no—
374C4⋊C4×C61—21no—
375C4⋊C4×C61—44no—
376C4⋊C4×C61C2×D411yescharacteristic
377C4⋊C4×C61C2×D411yescharacteristic
378C22⋊C4×C61—22no—
379C22⋊C4×C61—22no—
380C22⋊C4×C61—22no—
381C22⋊C4×C61—22no—
382C22⋊C4×C61—22no—
383C22⋊C4×C61—21no—
384C22⋊C4×C61—22no—
385C22⋊C4×C61—22no—
386C22⋊C4×C61—21no—
387C22⋊C4×C61—21no—
388C22⋊C4×C61—21no—
389C22⋊C4×C61—21no—
390C22⋊C4×C61—44no—
391C22⋊C4×C61—44no—
392C22⋊C4×C61—42no—
393C42×C61—22no—
394C42×C61—21no—
395C42×C61—21no—
396C42×C61—21no—
397C42×C61—21no—
398C42×C61—21no—
399C23×C61—21no—
400C23×C61—21no—
401C23×C61—21no—
402C23×C61—21no—
403C23×C61—21no—
404C23×C61—22no—
405C23×C61—41no—
406C23×C61—41no—
407C23×C61—42no—
408C23×C61—42no—
409C23×C61—42no—
410C23×C61—42no—
411C23×C61—41no—
412C23×C61—41no—
413C23×C61—81no—
414C23×C61#12011yescharacteristic
415C23×C61#12011yescharacteristic
416C23×C61C22×D411yescharacteristic
417Q8×C61—21no—
418Q8×C61—21no—
419Q8×C61—22no—
420Q8×C61—21no—
421Q8×C61—21no—
422Q8×C61—22no—
423Q8×C61—21no—
424Q8×C61—42no—
425Q8×C61—44no—
426Q8×C61—41no—
427Q8×C61—41no—
428Q8×C61—41no—
429Q8×C61—41no—
430Q8×C61—41no—
431Q8×C61—41no—
432Q8×C61#12012yes—
433D4×C61—22no—
434D4×C61—22no—
435D4×C61—21no—
436D4×C61—22no—
437D4×C61—21no—
438D4×C61—21no—
439D4×C61—21no—
440D4×C61—22no—
441D4×C61—21no—
442D4×C61—42no—
443D4×C61—42no—
444D4×C61—42no—
445D4×C61—42no—
446D4×C61—44no—
447D4×C61—44no—
448D4×C61—44no—
449D4×C61—41no—
450D4×C61—41no—
451D4×C61—41no—
452D4×C61—41no—
453D4×C61—41no—
454D4×C61—41no—
455D4×C61—81no—
456D4×C61—82no—
457D4×C61#12012yes—
458C2×C4×C61—21no—
459C2×C4×C61—21no—
460C2×C4×C61—21no—
461C2×C4×C61—21no—
462C2×C4×C61—21no—
463C2×C4×C61—21no—
464C2×C4×C61—21no—
465C2×C4×C61—21no—
466C2×C4×C61—21no—
467C2×C4×C61—21no—
468C2×C4×C61—21no—
469C2×C4×C61—22no—
470C2×C4×C61—22no—
471C2×C4×C61—22no—
472C2×C4×C61—21no—
473C2×C4×C61—22no—
474C2×C4×C61—21no—
475C2×C4×C61—21no—
476C2×C4×C61—22no—
477C2×C4×C61—21no—
478C2×C4×C61—22no—
479C2×C4×C61—22no—
480C2×C4×C61—22no—
481C2×C4×C61—42no—
482C2×C4×C61—42no—
483C2×C4×C61—42no—
484C2×C4×C61—44no—
485C2×C4×C61—44no—
486C2×C4×C61—44no—
487C2×C4×C61—41no—
488C2×C4×C61—44no—
489C2×C4×C61—41no—
490C2×C4×C61—41no—
491C2×C4×C61—41no—
492C2×C4×C61—41no—
493C2×C4×C61—41no—
494C2×C4×C61—41no—
495C2×C4×C61—41no—
496C2×C4×C61—42no—
497C2×C4×C61—41no—
498C2×C4×C61—41no—
499C2×C4×C61—41no—
500C2×C4×C61—82no—
501C2×C4×C61#12011yescharacteristic
502C2×C4×C61#12011yescharacteristic
503C2×C4×C61C22×D411yescharacteristic
504C2×C4×C61C22×D411yescharacteristic
505C2×C4×C61C22×D411yescharacteristic
506C2×C4×C61C22×D411yescharacteristic
507C2×C4×C61H(5,𝔽2)11yescharacteristic
508C2×C4×C61H(5,𝔽2)11yescharacteristic
509C8×C61—22no—
510C8×C61—22no—
511C8×C61—41no—
512C8×C61—41no—
513#23881C6111yesmaximal, characteristic, direct product factor, Sylow
514C22×C61—21no—
515C22×C61—21no—
516C22×C61—21no—
517C22×C61—21no—
518C22×C61—22no—
519C22×C61—21no—
520C22×C61—21no—
521C22×C61—21no—
522C22×C61—21no—
523C22×C61—44no—
524C22×C61—41no—
525C22×C61—41no—
526C22×C61—41no—
527C22×C61—41no—
528C22×C61—42no—
529C22×C61—41no—
530C22×C61—41no—
531C22×C61—41no—
532C22×C61—41no—
533C22×C61—81no—
534C22×C61—81no—
535C22×C61—82no—
536C22×C61—84no—
537C22×C61—81no—
538C22×C61—81no—
539C22×C61C2×#12011yescharacteristic
540C22×C61D4211yescharacteristic
541C22×C61D4211yescharacteristic
542C4×C61—21no—
543C4×C61—21no—
544C4×C61—22no—
545C4×C61—42no—
546C4×C61—42no—
547C4×C61—41no—
548C4×C61—42no—
549C4×C61—41no—
550C4×C61—42no—
551C4×C61—41no—
552C4×C61—41no—
553C4×C61—81no—
554C4×C61C2×#12011yescharacteristic
555C4×C61#53411yescharacteristic
556C4×C61D4211yescharacteristic
557C4×C61D4211yescharacteristic
558C2×#575C2×C6111yescharacteristic, complemented
559#3489C2×C6111yescharacteristic, complemented
560C2×#456C2×C6111yescharacteristic, complemented
561C2×#454C2×C6111yescharacteristic, complemented
562#3005C2×C6111yescharacteristic, complemented
563#2432C2×C6111yescharacteristic, complemented
564#2007C2×C6111yescharacteristic, complemented
565#2006C2×C6111yescharacteristic, complemented
566#2005C2×C6111yescharacteristic, complemented
567#2003C2×C6111yescharacteristic, complemented
568#1901C2×C6111yescharacteristic, complemented
569#1883C2×C6111yescharacteristic, complemented
570#1882C2×C6111yescharacteristic, complemented
571#1871C2×C6111yescharacteristic, complemented
572#1789C2×C6111yescharacteristic, complemented
573C2×C61—21no—
574C2×C61—21no—
575C2×C61—41no—
576C2×C61—41no—
577C2×C61—42no—
578C2×C61—81no—
579C2×C61—82no—
580C2×C61—81no—
581C2×C61#240311yescharacteristic
582C2×C61#301811yescharacteristic
583C2×C61#302011yescharacteristic
584C2×2−1+4C22×C6111yescharacteristic
585C22×#41C22×C6111yescharacteristic
586C22×#41C22×C6111yescharacteristic
587#575—24no—
588#575—24no—
589C2×#137—21no—
590C2×#137C22×C6111yescharacteristic
591C2×#137C22×C6111yescharacteristic
592C2×#137C22×C6111yescharacteristic, complemented
593C2×AGL(1,ℤ/8)—21no—
594C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
595C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
596C2×AGL(1,ℤ/8)C22×C6111yescharacteristic, complemented
597C2×#135—21no—
598C2×#135—21no—
599C22×M16C22×C6111yescharacteristic
600D4×Q8—21no—
601#548—21no—
602#547—21no—
603#547—22no—
604#546—21no—
605#546—22no—
606#537—21no—
607#537C22×C6111yescharacteristic
608#536—21no—
609#536C22×C6111yescharacteristic
610C2×C4⋊Q8C22×C6111yescharacteristic, complemented
611C2×#124C22×C6111yescharacteristic, complemented
612#525—21no—
613#525C22×C6111yescharacteristic
614C2×C22⋊Q8—21no—
615C2×C22⋊Q8C22×C6111yescharacteristic
616#520C22×C6111yescharacteristic
617#456—24no—
618#454—24no—
619#452—21no—
620#452—21no—
621#449—21no—
622#449—21no—
623C2×#104C22×C6111yescharacteristic
624C2×#104C22×C6111yescharacteristic
625C2×#104C22×C6111yescharacteristic
626C2×#104C22×C6111yescharacteristic
627C2×#104C22×C6111yescharacteristic, complemented
628C2×#104C22×C6111yescharacteristic, complemented
629#419C22×C6111yescharacteristic, complemented
630#418C22×C6111yescharacteristic, complemented
631C2×#101C22×C6111yescharacteristic, complemented
632C2×#101C22×C6111yescharacteristic, complemented
633#407C22×C6111yescharacteristic
634#394—22no—
635#391C22×C6111yescharacteristic, complemented
636#390C22×C6111yescharacteristic, complemented
637#385—22no—
638C4×C22⋊C4C22×C6111yescharacteristic
639#343C22×C6111yescharacteristic, complemented
640#343C22×C6111yescharacteristic, complemented
641#339C22×C6111yescharacteristic, complemented
642#339C22×C6111yescharacteristic, complemented
643C61#2388111yescharacteristic, direct product factor, Sylow
6442−1+4—22no—
6452−1+4—22no—
6462−1+4—41no—
6472−1+4—41no—
648C2×#41—21no—
649C2×#41—21no—
650C2×#41—21no—
651C2×#41—22no—
652C2×#41—21no—
653C2×#41—22no—
654C2×#41—22no—
655C2×#41—22no—
656C2×#41—22no—
657C2×#41—21no—
658C2×#41—21no—
659C2×#41—21no—
660C2×#41—21no—
661C2×#41—41no—
662C2×#41—41no—
663C2×#41—41no—
664C2×#41—41no—
665C2×#41D4×C6111yescharacteristic
666C2×#41D4×C6111yescharacteristic
667C2×#41C23×C6111yescharacteristic
668C2×#41C23×C6111yescharacteristic
669C2×#41C23×C6111yescharacteristic
670C22×Q8—21no—
671C22×Q8—21no—
672C22×Q8D4×C6111yescharacteristic
673C22×Q8C23×C6111yescharacteristic
674C22×Q8C23×C6111yescharacteristic
675C22×D4—21no—
676C22×D4—21no—
677C22×D4D4×C6111yescharacteristic
678C22×D4C23×C6111yescharacteristic
679C23×C4—21no—
680C23×C4—21no—
681C23×C4C23×C6111yescharacteristic
682#137—28no—
683#137—22no—
684#137—22no—
685#137—22no—
686#137—22no—
687#137—41no—
688#137D4×C6114yescomplemented
689AGL(1,ℤ/8)—28no—
690AGL(1,ℤ/8)—22no—
691AGL(1,ℤ/8)—22no—
692AGL(1,ℤ/8)—22no—
693AGL(1,ℤ/8)—22no—
694AGL(1,ℤ/8)—41no—
695AGL(1,ℤ/8)D4×C6114yescomplemented
696#135—28no—
697#135—28no—
698C2×Q16—21no—
699C2×Q16—21no—
700C2×Q16—21no—
701C2×SD16—21no—
702C2×SD16—21no—
703C2×SD16—21no—
704C2×SD16—21no—
705C2×SD16—21no—
706C2×SD16—21no—
707C2×D8—21no—
708C2×D8—21no—
709C2×D8—21no—
710C2×M16—21no—
711C2×M16—22no—
712C2×M16—22no—
713C2×M16C23×C6111yescharacteristic
714C2×M16C23×C6111yescharacteristic
715C2×M16C23×C6111yescharacteristic
716C2×M16C23×C6111yescharacteristic
717C22×C8—21no—
718C4⋊Q8—22no—
719C4⋊Q8—21no—
720C4⋊Q8—22no—
721C4⋊Q8—41no—
722#124—22no—
723#124—21no—
724#124—22no—
725#124—41no—
726#123—22no—
727#123—22no—
728#123—22no—
729#123—21no—
730#123—22no—
731C22⋊Q8—22no—
732C22⋊Q8—22no—
733C22⋊Q8—22no—
734C22⋊Q8—21no—
735C22⋊Q8—21no—
736C22⋊Q8—21no—
737C22⋊Q8—21no—
738C22⋊Q8—21no—
739C22⋊Q8—21no—
740C22⋊Q8—21no—
741C22⋊Q8—21no—
742C22⋊Q8D4×C6111yescharacteristic
743C22⋊Q8D4×C6111yescharacteristic
744#121—22no—
745#121—22no—
746#121—22no—
747#121—21no—
748#121—21no—
749#121—22no—
750#121D4×C6111yescharacteristic
751#121D4×C6111yescharacteristic
752#120—22no—
753#120—21no—
754C4×Q8—21no—
755C4×D4—22no—
756C4×D4—22no—
757C4×D4—21no—
758C4×D4—22no—
759C4×D4—21no—
760C4×D4—21no—
761#117—21no—
762#117C23×C6111yescharacteristic
763C2×C4⋊C4—22no—
764C2×C4⋊C4—21no—
765C2×C4⋊C4—22no—
766C2×C4⋊C4D4×C6112yes—
767C2×C4⋊C4C23×C6111yescharacteristic
768C2×C22⋊C4—22no—
769C2×C22⋊C4—21no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4D4×C6112yes—
773C2×C42C23×C6111yescharacteristic
774C2×C42C23×C6111yescharacteristic
775#104—22no—
776#104—22no—
777#104—22no—
778#104—22no—
779#104—41no—
780#104—41no—
781#103—21no—
782#103—21no—
783#102—21no—
784#102—21no—
785#101—22no—
786#101—22no—
787C22⋊C8—21no—
788C22⋊C8—21no—
789#95—21no—
790#95—22no—
791C24—21no—
792C24—21no—
793C24C2×D4×C6111yescharacteristic
794#41—21no—
795#41—21no—
796#41—24no—
797#41—24no—
798#41—22no—
799#41—22no—
800#41—21no—
801#41—21no—
802#41—21no—
803#41—21no—
804#41—21no—
805#41—21no—
806#41—21no—
807#41—21no—
808#41—42no—
809#41—42no—
810#41—41no—
811#41—41no—
812#41—42no—
813#41—42no—
814#41—42no—
815#41—42no—
816#41—42no—
817#41—42no—
818#41—44no—
819#41—44no—
820#41—42no—
821#41—42no—
822#41—42no—
823#41—42no—
824#41—42no—
825#41—42no—
826#41C2×D4×C6112yes—
827#41C2×D4×C6112yes—
828C2×Q8—22no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—22no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—41no—
843C2×Q8—42no—
844C2×Q8—42no—
845C2×Q8—42no—
846C2×Q8—42no—
847C2×Q8C2×D4×C6111yescharacteristic
848C2×Q8C2×D4×C6111yescharacteristic
849C2×Q8C2×D4×C6112yes—
850C2×Q8C2×D4×C6111yescharacteristic
851C2×D4—21no—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—22no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—41no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—41no—
873C2×D4—41no—
874C2×D4C2×D4×C6111yescharacteristic
875C2×D4C2×D4×C6111yescharacteristic
876C2×D4C2×D4×C6112yes—
877C2×D4C2×D4×C6111yescharacteristic
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—22no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—41no—
899C22×C4—41no—
900C22×C4C2×D4×C6112yes—
901C22×C4C2×D4×C6111yescharacteristic
902C22×C4C2×D4×C6111yescharacteristic
903C22×C4C2×D4×C6111yescharacteristic
904C22×C4C2×D4×C6111yescharacteristic
905C22×C4C2×D4×C6111yescharacteristic
906C22×C4C2×D4×C6112yes—
907C22×C4C24×C6111yescharacteristic
908Q16—24no—
909Q16—24no—
910Q16—42no—
911SD16—24no—
912SD16—24no—
913SD16—24no—
914SD16—24no—
915SD16—42no—
916SD16—42no—
917D8—24no—
918D8—24no—
919D8—42no—
920M16—24no—
921M16—21no—
922M16—21no—
923M16—21no—
924M16—21no—
925M16—21no—
926M16—21no—
927M16C2×D4×C6112yes—
928M16C2×D4×C6112yes—
929C2×C8—24no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—21no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—44no—
945C4⋊C4C2×D4×C6111yescharacteristic
946C4⋊C4C2×D4×C6111yescharacteristic
947C22⋊C4—22no—
948C22⋊C4—22no—
949C22⋊C4—22no—
950C22⋊C4—22no—
951C22⋊C4—22no—
952C22⋊C4—21no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—21no—
956C22⋊C4—21no—
957C22⋊C4—21no—
958C22⋊C4—21no—
959C22⋊C4—44no—
960C22⋊C4—44no—
961C22⋊C4—42no—
962C42—22no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—21no—
968C23—21no—
969C23—21no—
970C23—21no—
971C23—22no—
972C23—21no—
973C23—21no—
974C23—41no—
975C23—41no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—41no—
981C23—41no—
982C23—81no—
983C23#120×C6111yescharacteristic
984C23#120×C6111yescharacteristic
985C23C22×D4×C6111yescharacteristic
986Q8—21no—
987Q8—21no—
988Q8—21no—
989Q8—22no—
990Q8—21no—
991Q8—21no—
992Q8—22no—
993Q8—42no—
994Q8—44no—
995Q8—41no—
996Q8—41no—
997Q8—41no—
998Q8—41no—
999Q8—41no—
1000Q8—41no—
1001Q8#120×C6112yes—
1002D4—22no—
1003D4—22no—
1004D4—21no—
1005D4—21no—
1006D4—21no—
1007D4—22no—
1008D4—21no—
1009D4—21no—
1010D4—22no—
1011D4—42no—
1012D4—42no—
1013D4—42no—
1014D4—42no—
1015D4—44no—
1016D4—44no—
1017D4—44no—
1018D4—41no—
1019D4—41no—
1020D4—41no—
1021D4—41no—
1022D4—41no—
1023D4—41no—
1024D4—81no—
1025D4—82no—
1026D4#120×C6112yes—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—21no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—42no—
1053C2×C4—44no—
1054C2×C4—44no—
1055C2×C4—44no—
1056C2×C4—41no—
1057C2×C4—44no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—42no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—82no—
1070C2×C4#120×C6111yescharacteristic
1071C2×C4#120×C6111yescharacteristic
1072C2×C4C22×D4×C6111yescharacteristic
1073C2×C4C22×D4×C6111yescharacteristic
1074C2×C4C22×D4×C6111yescharacteristic
1075C2×C4C22×D4×C6111yescharacteristic
1076C2×C4H(5,𝔽2)×C6111yescharacteristic
1077C2×C4H(5,𝔽2)×C6111yescharacteristic
1078C8—22no—
1079C8—22no—
1080C8—41no—
1081C8—41no—
1082C22—21no—
1083C22—21no—
1084C22—21no—
1085C22—21no—
1086C22—22no—
1087C22—21no—
1088C22—21no—
1089C22—21no—
1090C22—21no—
1091C22—44no—
1092C22—41no—
1093C22—41no—
1094C22—41no—
1095C22—41no—
1096C22—42no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—81no—
1102C22—81no—
1103C22—82no—
1104C22—84no—
1105C22—81no—
1106C22—81no—
1107C22C2×#120×C6111yescharacteristic
1108C22D42×C6111yescharacteristic
1109C22D42×C6111yescharacteristic
1110C4—21no—
1111C4—21no—
1112C4—22no—
1113C4—42no—
1114C4—42no—
1115C4—42no—
1116C4—41no—
1117C4—41no—
1118C4—42no—
1119C4—41no—
1120C4—41no—
1121C4—81no—
1122C4C2×#120×C6111yescharacteristic
1123C4C61×#53411yescharacteristic
1124C4D42×C6111yescharacteristic
1125C4D42×C6111yescharacteristic
1126C2—21no—
1127C2—21no—
1128C2—41no—
1129C2—41no—
1130C2—42no—
1131C2—82no—
1132C2—81no—
1133C2—81no—
1134C2C61×#240311yescharacteristic
1135C2C61×#301811yescharacteristic
1136C2C61×#302011yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#575C2semidirect
2. C61×#3489C2semidirect
3. C2×C61×#456C2semidirect
4. C2×C61×#454C2semidirect
5. C61×#3005C2semidirect
6. C61×#2432C2semidirect
7. C61×#2007C2semidirect
8. C61×#2006C2semidirect
9. C61×#2005C2semidirect
10. C61×#2003C2semidirect
11. C61×#1901C2semidirect
12. C61×#1883C2semidirect
13. C61×#1882C2semidirect
14. C61×#1871C2semidirect
15. C61×#1789C2semidirect
24. C2×#137×C61C22semidirect
28. C2×AGL(1,ℤ/8)×C61C22semidirect
42. C2×C4⋊Q8×C61C22semidirect
43. C2×#124×C61C22semidirect
59. C2×#104×C61C22semidirect
60. C2×#104×C61C22semidirect
61. C61×#419C22semidirect
62. C61×#418C22semidirect
63. C2×#101×C61C22semidirect
64. C2×#101×C61C22semidirect
67. C61×#391C22semidirect
68. C61×#390C22semidirect
71. C61×#343C22semidirect
72. C61×#343C22semidirect
73. C61×#339C22semidirect
74. C61×#339C22semidirect
119. #137×C61D4semidirect
126. AGL(1,ℤ/8)×C61D4semidirect
513. #23881C61direct (N × H)
558. C2×#575C2×C61semidirect
559. #3489C2×C61semidirect
560. C2×#456C2×C61semidirect
561. C2×#454C2×C61semidirect
562. #3005C2×C61semidirect
563. #2432C2×C61semidirect
564. #2007C2×C61semidirect
565. #2006C2×C61semidirect
566. #2005C2×C61semidirect
567. #2003C2×C61semidirect
568. #1901C2×C61semidirect
569. #1883C2×C61semidirect
570. #1882C2×C61semidirect
571. #1871C2×C61semidirect
572. #1789C2×C61semidirect
592. C2×#137C22×C61semidirect
596. C2×AGL(1,ℤ/8)C22×C61semidirect
610. C2×C4⋊Q8C22×C61semidirect
611. C2×#124C22×C61semidirect
627. C2×#104C22×C61semidirect
628. C2×#104C22×C61semidirect
629. #419C22×C61semidirect
630. #418C22×C61semidirect
631. C2×#101C22×C61semidirect
632. C2×#101C22×C61semidirect
635. #391C22×C61semidirect
636. #390C22×C61semidirect
639. #343C22×C61semidirect
640. #343C22×C61semidirect
641. #339C22×C61semidirect
642. #339C22×C61semidirect
643. C61#23881direct (N × H)
688. #137D4×C61semidirect
695. AGL(1,ℤ/8)D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5752
C61×#34892
C2×C61×#4562
C2×C61×#4542
C61×#30052
C61×#24322
C61×#20072
C61×#20062
C61×#20052
C61×#20032
C61×#19012
C61×#18832
C61×#18822
C61×#18712
C61×#17892
#2388161