Finite Group Databasebeta

← C61×#23894 #29527327

Subgroups — C61×#23894 #29527327

Order 15616.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3586C211yesmaximal, characteristic, complemented
2C61×#3585C211yesmaximal, characteristic, complemented
3C61×#3020C211yesmaximal, characteristic, complemented
4C61×#3019C211yesmaximal, characteristic, complemented
5C61×#3010C211yesmaximal, characteristic, complemented
6C61×#3009C211yesmaximal, characteristic, complemented
7C61×#2019C211yesmaximal, characteristic, complemented
8C61×#2017C211yesmaximal, characteristic, complemented
9C61×#2009C211yesmaximal, characteristic, complemented
10C61×#2008C211yesmaximal, characteristic, complemented
11C61×#1903C211yesmaximal, characteristic, complemented
12C61×#1902C211yesmaximal, characteristic, complemented
13C61×#1881C211yesmaximal, characteristic, complemented
14C61×#1881C211yesmaximal, characteristic, complemented
15C61×#1794C211yesmaximal, characteristic, complemented
16C61×#585C2211yescharacteristic
17C2×2−1+4×C61C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C61C2211yescharacteristic
19C61×#578—22no—
20C61×#578—22no—
21C61×#577—22no—
22C61×#577—22no—
23C61×#577—22no—
24C61×#577—22no—
25C61×#576—22no—
26C61×#576—22no—
27C61×#575—22no—
28C61×#575—22no—
29C61×#575C2211yescharacteristic
30C61×#575C2211yescharacteristic
31C61×#575C2211yescharacteristic
32C61×#575C2211yescharacteristic, complemented
33C61×#575C2211yescharacteristic, complemented
34C2×#137×C61—22no—
35C2×#137×C61C2211yescharacteristic
36C2×#137×C61C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)×C61—22no—
38C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
39C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
40C22×SD16×C61C2211yescharacteristic, complemented
41C61×#568C2211yescharacteristic
42C61×#568C2211yescharacteristic, complemented
43C61×#536C2211yescharacteristic, complemented
44C61×#535C2211yescharacteristic, complemented
45C61×#456—22no—
46C61×#455—22no—
47C61×#454—22no—
48C61×#453—22no—
49C61×#452—22no—
50C61×#450—22no—
51C61×#449—22no—
52C61×#448—22no—
53C61×#421C2211yescharacteristic
54C61×#421C2211yescharacteristic, complemented
55C61×#421C2211yescharacteristic, complemented
56C61×#421C2211yescharacteristic, complemented
57C61×#419C2211yescharacteristic, complemented
58C61×#418C2211yescharacteristic, complemented
59C61×#416C2211yescharacteristic
60C61×#416C2211yescharacteristic, complemented
61C2×#101×C61C2211yescharacteristic, complemented
62C2×#100×C61C2211yescharacteristic, complemented
63C61×#410C2211yescharacteristic, complemented
64C61×#408C2211yescharacteristic, complemented
65C61×#408C2211yescharacteristic, complemented
66C61×#408C2211yescharacteristic, complemented
67C61×#344C2211yescharacteristic, complemented
68C61×#344C2211yescharacteristic, complemented
69C61×#341C2211yescharacteristic, complemented
70C61×#338C2211yescharacteristic, complemented
712−1+4×C61—22no—
722−1+4×C61—21no—
732−1+4×C61—22no—
742−1+4×C61—21no—
752−1+4×C61—22no—
762−1+4×C61—41no—
772−1+4×C61D412yescomplemented
78H(5,𝔽2)×C61—22no—
79H(5,𝔽2)×C61—21no—
80H(5,𝔽2)×C61—22no—
81H(5,𝔽2)×C61—21no—
82H(5,𝔽2)×C61—22no—
83H(5,𝔽2)×C61—41no—
84H(5,𝔽2)×C61—41no—
85H(5,𝔽2)×C61D412yescomplemented
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×C61C2311yescharacteristic
95C2×#41×C61C2311yescharacteristic
96C2×#41×C61C2311yescharacteristic
97C2×#41×C61C2311yescharacteristic
98C2×#41×C61C2311yescharacteristic
99C22×Q8×C61—21no—
100C22×Q8×C61—21no—
101C22×Q8×C61C2311yescharacteristic
102C22×D4×C61—21no—
103C22×D4×C61—21no—
104C22×D4×C61—41no—
105C22×D4×C61C2311yescharacteristic
106#137×C61—24no—
107#137×C61—24no—
108#137×C61—24no—
109#137×C61—24no—
110#137×C61—22no—
111#137×C61—22no—
112#137×C61—21no—
113#137×C61—22no—
114#137×C61—21no—
115#137×C61—21no—
116#137×C61—21no—
117#137×C61—21no—
118#137×C61—21no—
119#137×C61—21no—
120#137×C61—21no—
121#137×C61—22no—
122#137×C61D412yes—
123#137×C61D412yescomplemented
124AGL(1,ℤ/8)×C61—24no—
125AGL(1,ℤ/8)×C61—24no—
126AGL(1,ℤ/8)×C61—24no—
127AGL(1,ℤ/8)×C61—24no—
128AGL(1,ℤ/8)×C61—22no—
129AGL(1,ℤ/8)×C61—22no—
130AGL(1,ℤ/8)×C61—21no—
131AGL(1,ℤ/8)×C61—22no—
132AGL(1,ℤ/8)×C61—21no—
133AGL(1,ℤ/8)×C61—21no—
134AGL(1,ℤ/8)×C61—21no—
135AGL(1,ℤ/8)×C61—21no—
136AGL(1,ℤ/8)×C61—21no—
137AGL(1,ℤ/8)×C61—21no—
138AGL(1,ℤ/8)×C61—21no—
139AGL(1,ℤ/8)×C61—22no—
140AGL(1,ℤ/8)×C61D412yes—
141AGL(1,ℤ/8)×C61D412yescomplemented
142#135×C61—24no—
143#135×C61—24no—
144#135×C61—24no—
145#135×C61—24no—
146#135×C61—22no—
147#135×C61—22no—
148#135×C61—22no—
149#135×C61—22no—
150#135×C61—41no—
151C2×Q16×C61—24no—
152C2×Q16×C61—21no—
153C2×Q16×C61D412yescomplemented
154C2×SD16×C61—24no—
155C2×SD16×C61—24no—
156C2×SD16×C61—21no—
157C2×SD16×C61—21no—
158C2×SD16×C61—22no—
159C2×SD16×C61—22no—
160C2×SD16×C61—41no—
161C2×SD16×C61D412yes—
162C2×SD16×C61D412yescomplemented
163C2×D8×C61—24no—
164C2×D8×C61—21no—
165C2×D8×C61D412yes—
166#131×C61—22no—
167#131×C61—22no—
168#131×C61—22no—
169#131×C61—22no—
170C2×M16×C61—22no—
171C2×M16×C61—22no—
172C2×M16×C61C2311yescharacteristic
173C2×M16×C61C2311yescharacteristic
174C2×M16×C61C2311yescharacteristic
175C2×M16×C61C2311yescharacteristic
176C2×M16×C61C2311yescharacteristic
177C22×C8×C61C2311yescharacteristic
178C4⋊Q8×C61—21no—
179#127×C61—21no—
180#124×C61—21no—
181#124×C61—21no—
182#123×C61—41no—
183C22⋊Q8×C61—22no—
184#121×C61—22no—
185#120×C61—41no—
186#117×C61C2311yescharacteristic
187#117×C61C2311yescharacteristic
188#104×C61—22no—
189#104×C61—22no—
190#104×C61—22no—
191#104×C61—22no—
192#103×C61—21no—
193#103×C61—21no—
194#103×C61—22no—
195#102×C61—21no—
196#102×C61—21no—
197#102×C61—22no—
198#101×C61—22no—
199#100×C61—22no—
200#99×C61—41no—
201C22⋊C8×C61—22no—
202C22⋊C8×C61—22no—
203C22⋊C8×C61—41no—
204C24×C61—21no—
205C24×C61—41no—
206#41×C61—21no—
207#41×C61—21no—
208#41×C61—21no—
209#41×C61—21no—
210#41×C61—24no—
211#41×C61—24no—
212#41×C61—22no—
213#41×C61—22no—
214#41×C61—22no—
215#41×C61—22no—
216#41×C61—21no—
217#41×C61—21no—
218#41×C61—21no—
219#41×C61—21no—
220#41×C61—21no—
221#41×C61—21no—
222#41×C61—21no—
223#41×C61—21no—
224#41×C61—21no—
225#41×C61—21no—
226#41×C61—21no—
227#41×C61—21no—
228#41×C61—42no—
229#41×C61—42no—
230#41×C61—42no—
231#41×C61—42no—
232#41×C61—42no—
233#41×C61—44no—
234#41×C61—42no—
235#41×C61—42no—
236#41×C61—42no—
237#41×C61—41no—
238#41×C61—41no—
239#41×C61—44no—
240#41×C61—42no—
241#41×C61—42no—
242#41×C61C2×D412yes—
243#41×C61C2×D412yes—
244#41×C61C2×D412yes—
245#41×C61C2×D412yes—
246C2×Q8×C61—21no—
247C2×Q8×C61—24no—
248C2×Q8×C61—22no—
249C2×Q8×C61—22no—
250C2×Q8×C61—21no—
251C2×Q8×C61—21no—
252C2×Q8×C61—21no—
253C2×Q8×C61—21no—
254C2×Q8×C61—41no—
255C2×Q8×C61—42no—
256C2×Q8×C61—42no—
257C2×Q8×C61—41no—
258C2×Q8×C61—42no—
259C2×Q8×C61C2×D412yes—
260C2×Q8×C61C2×D411yescharacteristic
261C2×Q8×C61C2×D411yescharacteristic
262C2×Q8×C61C2×D411yescharacteristic
263C2×Q8×C61C2×D411yescharacteristic
264C2×Q8×C61C2×D411yescharacteristic
265C2×D4×C61—21no—
266C2×D4×C61—21no—
267C2×D4×C61—24no—
268C2×D4×C61—22no—
269C2×D4×C61—22no—
270C2×D4×C61—21no—
271C2×D4×C61—21no—
272C2×D4×C61—21no—
273C2×D4×C61—21no—
274C2×D4×C61—21no—
275C2×D4×C61—21no—
276C2×D4×C61—21no—
277C2×D4×C61—21no—
278C2×D4×C61—42no—
279C2×D4×C61—41no—
280C2×D4×C61—41no—
281C2×D4×C61—42no—
282C2×D4×C61—42no—
283C2×D4×C61—41no—
284C2×D4×C61—44no—
285C2×D4×C61—42no—
286C2×D4×C61—42no—
287C2×D4×C61—44no—
288C2×D4×C61—41no—
289C2×D4×C61—42no—
290C2×D4×C61—42no—
291C2×D4×C61C2×D412yes—
292C2×D4×C61C2×D411yescharacteristic
293C2×D4×C61C2×D411yescharacteristic
294C2×D4×C61C2×D411yescharacteristic
295C2×D4×C61C2×D411yescharacteristic
296C2×D4×C61C2×D411yescharacteristic
297C22×C4×C61—21no—
298C22×C4×C61—21no—
299C22×C4×C61—21no—
300C22×C4×C61—21no—
301C22×C4×C61—21no—
302C22×C4×C61—21no—
303C22×C4×C61—41no—
304C22×C4×C61—42no—
305C22×C4×C61—41no—
306C22×C4×C61—41no—
307C22×C4×C61C2411yescharacteristic
308Q16×C61—24no—
309Q16×C61—22no—
310Q16×C61—22no—
311Q16×C61—22no—
312Q16×C61—24no—
313Q16×C61—22no—
314Q16×C61—41no—
315SD16×C61—24no—
316SD16×C61—22no—
317SD16×C61—24no—
318SD16×C61—22no—
319SD16×C61—22no—
320SD16×C61—22no—
321SD16×C61—22no—
322SD16×C61—24no—
323SD16×C61—22no—
324SD16×C61—22no—
325SD16×C61—24no—
326SD16×C61—22no—
327SD16×C61—44no—
328SD16×C61—41no—
329SD16×C61—41no—
330D8×C61—24no—
331D8×C61—22no—
332D8×C61—22no—
333D8×C61—22no—
334D8×C61—24no—
335D8×C61—22no—
336D8×C61—41no—
337M16×C61—24no—
338M16×C61—24no—
339M16×C61—21no—
340M16×C61—21no—
341M16×C61—21no—
342M16×C61—21no—
343M16×C61—21no—
344M16×C61—21no—
345M16×C61—21no—
346M16×C61—21no—
347M16×C61C2×D412yes—
348M16×C61C2×D412yes—
349C2×C8×C61—24no—
350C2×C8×C61—24no—
351C2×C8×C61—21no—
352C2×C8×C61—21no—
353C2×C8×C61—21no—
354C2×C8×C61—21no—
355C2×C8×C61—21no—
356C2×C8×C61—21no—
357C2×C8×C61C2×D412yes—
358C2×C8×C61C2×D412yes—
359C4⋊C4×C61—21no—
360C4⋊C4×C61—21no—
361C4⋊C4×C61—42no—
362C22⋊C4×C61—21no—
363C22⋊C4×C61—21no—
364C22⋊C4×C61—42no—
365C22⋊C4×C61—42no—
366C42×C61—21no—
367C42×C61—21no—
368C23×C61—21no—
369C23×C61—21no—
370C23×C61—21no—
371C23×C61—21no—
372C23×C61—21no—
373C23×C61—22no—
374C23×C61—42no—
375C23×C61—44no—
376C23×C61—41no—
377C23×C61—41no—
378C23×C61—161no—
379C23×C61—162no—
380C23×C61H(5,𝔽2)11yescharacteristic
381Q8×C61—21no—
382Q8×C61—21no—
383Q8×C61—21no—
384Q8×C61—21no—
385Q8×C61—22no—
386Q8×C61—21no—
387Q8×C61—21no—
388Q8×C61—22no—
389Q8×C61—21no—
390Q8×C61—21no—
391Q8×C61—42no—
392Q8×C61—44no—
393Q8×C61—41no—
394Q8×C61—41no—
395Q8×C61#12012yes—
396Q8×C61#12012yes—
397D4×C61—22no—
398D4×C61—22no—
399D4×C61—22no—
400D4×C61—22no—
401D4×C61—21no—
402D4×C61—21no—
403D4×C61—22no—
404D4×C61—21no—
405D4×C61—21no—
406D4×C61—21no—
407D4×C61—21no—
408D4×C61—21no—
409D4×C61—21no—
410D4×C61—22no—
411D4×C61—42no—
412D4×C61—42no—
413D4×C61—44no—
414D4×C61—42no—
415D4×C61—44no—
416D4×C61—44no—
417D4×C61—41no—
418D4×C61—41no—
419D4×C61—41no—
420D4×C61—41no—
421D4×C61—41no—
422D4×C61—41no—
423D4×C61—41no—
424D4×C61—41no—
425D4×C61—162no—
426D4×C61#12012yes—
427D4×C61#12012yes—
428C2×C4×C61—21no—
429C2×C4×C61—21no—
430C2×C4×C61—22no—
431C2×C4×C61—22no—
432C2×C4×C61—22no—
433C2×C4×C61—22no—
434C2×C4×C61—21no—
435C2×C4×C61—21no—
436C2×C4×C61—22no—
437C2×C4×C61—21no—
438C2×C4×C61—42no—
439C2×C4×C61—42no—
440C2×C4×C61—42no—
441C2×C4×C61—44no—
442C2×C4×C61—44no—
443C2×C4×C61—44no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—41no—
447C2×C4×C61—41no—
448C2×C4×C61—41no—
449C2×C4×C61—41no—
450C2×C4×C61—41no—
451C2×C4×C61—41no—
452C2×C4×C61—41no—
453C2×C4×C61—41no—
454C2×C4×C61C22×D411yescharacteristic
455C2×C4×C61C22×D411yescharacteristic
456C2×C4×C61C22×D411yescharacteristic
457C2×C4×C61C22×D411yescharacteristic
458C2×C4×C61C22×D411yescharacteristic
459C2×C4×C61H(5,𝔽2)11yescharacteristic
460C8×C61—22no—
461C8×C61—22no—
462C8×C61—22no—
463C8×C61—22no—
464C8×C61—41no—
465C8×C61—41no—
466#23894C6111yesmaximal, characteristic, direct product factor, Sylow
467C22×C61—22no—
468C22×C61—22no—
469C22×C61—41no—
470C22×C61—42no—
471C22×C61—42no—
472C22×C61—41no—
473C22×C61—41no—
474C22×C61—41no—
475C22×C61—42no—
476C22×C61—81no—
477C22×C61—81no—
478C22×C61—82no—
479C22×C61—81no—
480C22×C61—82no—
481C22×C61—161no—
482C22×C61—162no—
483C22×C61—164no—
484C22×C61#53411yescharacteristic
485C22×C61D4211yescharacteristic
486C22×C61D4211yescharacteristic
487C4×C61—22no—
488C4×C61—22no—
489C4×C61—41no—
490C4×C61—41no—
491C4×C61—41no—
492C4×C61—42no—
493C4×C61—81no—
494C4×C61—81no—
495C4×C61C2×#12011yescharacteristic
496C4×C61C2×#12011yescharacteristic
497C4×C61D4211yescharacteristic
498C4×C61D4211yescharacteristic
499#3586C2×C6111yescharacteristic, complemented
500#3585C2×C6111yescharacteristic, complemented
501#3020C2×C6111yescharacteristic, complemented
502#3019C2×C6111yescharacteristic, complemented
503#3010C2×C6111yescharacteristic, complemented
504#3009C2×C6111yescharacteristic, complemented
505#2019C2×C6111yescharacteristic, complemented
506#2017C2×C6111yescharacteristic, complemented
507#2009C2×C6111yescharacteristic, complemented
508#2008C2×C6111yescharacteristic, complemented
509#1903C2×C6111yescharacteristic, complemented
510#1902C2×C6111yescharacteristic, complemented
511#1881C2×C6111yescharacteristic, complemented
512#1881C2×C6111yescharacteristic, complemented
513#1794C2×C6111yescharacteristic, complemented
514C2×C61—21no—
515C2×C61—21no—
516C2×C61—21no—
517C2×C61—42no—
518C2×C61—42no—
519C2×C61—81no—
520C2×C61—81no—
521C2×C61—82no—
522C2×C61—81no—
523C2×C61#240311yescharacteristic
524#585C22×C6111yescharacteristic
525C2×2−1+4C22×C6111yescharacteristic, complemented
526C2×H(5,𝔽2)C22×C6111yescharacteristic
527#578—22no—
528#578—22no—
529#577—22no—
530#577—22no—
531#577—22no—
532#577—22no—
533#576—22no—
534#576—22no—
535#575—22no—
536#575—22no—
537#575C22×C6111yescharacteristic
538#575C22×C6111yescharacteristic
539#575C22×C6111yescharacteristic
540#575C22×C6111yescharacteristic, complemented
541#575C22×C6111yescharacteristic, complemented
542C2×#137—22no—
543C2×#137C22×C6111yescharacteristic
544C2×#137C22×C6111yescharacteristic, complemented
545C2×AGL(1,ℤ/8)—22no—
546C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
547C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
548C22×SD16C22×C6111yescharacteristic, complemented
549#568C22×C6111yescharacteristic
550#568C22×C6111yescharacteristic, complemented
551#536C22×C6111yescharacteristic, complemented
552#535C22×C6111yescharacteristic, complemented
553#456—22no—
554#455—22no—
555#454—22no—
556#453—22no—
557#452—22no—
558#450—22no—
559#449—22no—
560#448—22no—
561#421C22×C6111yescharacteristic
562#421C22×C6111yescharacteristic, complemented
563#421C22×C6111yescharacteristic, complemented
564#421C22×C6111yescharacteristic, complemented
565#419C22×C6111yescharacteristic, complemented
566#418C22×C6111yescharacteristic, complemented
567#416C22×C6111yescharacteristic
568#416C22×C6111yescharacteristic, complemented
569C2×#101C22×C6111yescharacteristic, complemented
570C2×#100C22×C6111yescharacteristic, complemented
571#410C22×C6111yescharacteristic, complemented
572#408C22×C6111yescharacteristic, complemented
573#408C22×C6111yescharacteristic, complemented
574#408C22×C6111yescharacteristic, complemented
575#344C22×C6111yescharacteristic, complemented
576#344C22×C6111yescharacteristic, complemented
577#341C22×C6111yescharacteristic, complemented
578#338C22×C6111yescharacteristic, complemented
579C61#2389411yescharacteristic, direct product factor, Sylow
5802−1+4—22no—
5812−1+4—21no—
5822−1+4—22no—
5832−1+4—21no—
5842−1+4—22no—
5852−1+4—41no—
5862−1+4D4×C6112yescomplemented
587H(5,𝔽2)—22no—
588H(5,𝔽2)—21no—
589H(5,𝔽2)—22no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—22no—
592H(5,𝔽2)—41no—
593H(5,𝔽2)—41no—
594H(5,𝔽2)D4×C6112yescomplemented
595C2×#41—22no—
596C2×#41—22no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—41no—
602C2×#41—41no—
603C2×#41C23×C6111yescharacteristic
604C2×#41C23×C6111yescharacteristic
605C2×#41C23×C6111yescharacteristic
606C2×#41C23×C6111yescharacteristic
607C2×#41C23×C6111yescharacteristic
608C22×Q8—21no—
609C22×Q8—21no—
610C22×Q8C23×C6111yescharacteristic
611C22×D4—21no—
612C22×D4—21no—
613C22×D4—41no—
614C22×D4C23×C6111yescharacteristic
615#137—24no—
616#137—24no—
617#137—24no—
618#137—24no—
619#137—22no—
620#137—22no—
621#137—21no—
622#137—22no—
623#137—21no—
624#137—21no—
625#137—21no—
626#137—21no—
627#137—21no—
628#137—21no—
629#137—21no—
630#137—22no—
631#137D4×C6112yes—
632#137D4×C6112yescomplemented
633AGL(1,ℤ/8)—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—22no—
638AGL(1,ℤ/8)—22no—
639AGL(1,ℤ/8)—21no—
640AGL(1,ℤ/8)—22no—
641AGL(1,ℤ/8)—21no—
642AGL(1,ℤ/8)—21no—
643AGL(1,ℤ/8)—21no—
644AGL(1,ℤ/8)—21no—
645AGL(1,ℤ/8)—21no—
646AGL(1,ℤ/8)—21no—
647AGL(1,ℤ/8)—21no—
648AGL(1,ℤ/8)—22no—
649AGL(1,ℤ/8)D4×C6112yes—
650AGL(1,ℤ/8)D4×C6112yescomplemented
651#135—24no—
652#135—24no—
653#135—24no—
654#135—24no—
655#135—22no—
656#135—22no—
657#135—22no—
658#135—22no—
659#135—41no—
660C2×Q16—24no—
661C2×Q16—21no—
662C2×Q16D4×C6112yescomplemented
663C2×SD16—24no—
664C2×SD16—24no—
665C2×SD16—21no—
666C2×SD16—21no—
667C2×SD16—22no—
668C2×SD16—22no—
669C2×SD16—41no—
670C2×SD16D4×C6112yes—
671C2×SD16D4×C6112yescomplemented
672C2×D8—24no—
673C2×D8—21no—
674C2×D8D4×C6112yes—
675#131—22no—
676#131—22no—
677#131—22no—
678#131—22no—
679C2×M16—22no—
680C2×M16—22no—
681C2×M16C23×C6111yescharacteristic
682C2×M16C23×C6111yescharacteristic
683C2×M16C23×C6111yescharacteristic
684C2×M16C23×C6111yescharacteristic
685C2×M16C23×C6111yescharacteristic
686C22×C8C23×C6111yescharacteristic
687C4⋊Q8—21no—
688#127—21no—
689#124—21no—
690#124—21no—
691#123—41no—
692C22⋊Q8—22no—
693#121—22no—
694#120—41no—
695#117C23×C6111yescharacteristic
696#117C23×C6111yescharacteristic
697#104—22no—
698#104—22no—
699#104—22no—
700#104—22no—
701#103—21no—
702#103—21no—
703#103—22no—
704#102—21no—
705#102—21no—
706#102—22no—
707#101—22no—
708#100—22no—
709#99—41no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—41no—
713C24—21no—
714C24—41no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—24no—
720#41—24no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—42no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—44no—
743#41—42no—
744#41—42no—
745#41—42no—
746#41—41no—
747#41—41no—
748#41—44no—
749#41—42no—
750#41—42no—
751#41C2×D4×C6112yes—
752#41C2×D4×C6112yes—
753#41C2×D4×C6112yes—
754#41C2×D4×C6112yes—
755C2×Q8—21no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—41no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—41no—
767C2×Q8—42no—
768C2×Q8C2×D4×C6112yes—
769C2×Q8C2×D4×C6111yescharacteristic
770C2×Q8C2×D4×C6111yescharacteristic
771C2×Q8C2×D4×C6111yescharacteristic
772C2×Q8C2×D4×C6111yescharacteristic
773C2×Q8C2×D4×C6111yescharacteristic
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—42no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—41no—
793C2×D4—44no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—44no—
797C2×D4—41no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4C2×D4×C6112yes—
801C2×D4C2×D4×C6111yescharacteristic
802C2×D4C2×D4×C6111yescharacteristic
803C2×D4C2×D4×C6111yescharacteristic
804C2×D4C2×D4×C6111yescharacteristic
805C2×D4C2×D4×C6111yescharacteristic
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4C24×C6111yescharacteristic
817Q16—24no—
818Q16—22no—
819Q16—22no—
820Q16—22no—
821Q16—24no—
822Q16—22no—
823Q16—41no—
824SD16—24no—
825SD16—22no—
826SD16—24no—
827SD16—22no—
828SD16—22no—
829SD16—22no—
830SD16—22no—
831SD16—24no—
832SD16—22no—
833SD16—22no—
834SD16—24no—
835SD16—22no—
836SD16—44no—
837SD16—41no—
838SD16—41no—
839D8—24no—
840D8—22no—
841D8—22no—
842D8—22no—
843D8—24no—
844D8—22no—
845D8—41no—
846M16—24no—
847M16—24no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16C2×D4×C6112yes—
857M16C2×D4×C6112yes—
858C2×C8—24no—
859C2×C8—24no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8C2×D4×C6112yes—
867C2×C8C2×D4×C6112yes—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—42no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C42—21no—
876C42—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—22no—
883C23—42no—
884C23—44no—
885C23—41no—
886C23—41no—
887C23—161no—
888C23—162no—
889C23H(5,𝔽2)×C6111yescharacteristic
890Q8—21no—
891Q8—21no—
892Q8—22no—
893Q8—21no—
894Q8—21no—
895Q8—21no—
896Q8—21no—
897Q8—22no—
898Q8—21no—
899Q8—21no—
900Q8—42no—
901Q8—44no—
902Q8—41no—
903Q8—41no—
904Q8#120×C6112yes—
905Q8#120×C6112yes—
906D4—22no—
907D4—22no—
908D4—22no—
909D4—22no—
910D4—21no—
911D4—21no—
912D4—21no—
913D4—21no—
914D4—22no—
915D4—21no—
916D4—21no—
917D4—22no—
918D4—21no—
919D4—21no—
920D4—42no—
921D4—42no—
922D4—44no—
923D4—42no—
924D4—44no—
925D4—44no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—162no—
935D4#120×C6112yes—
936D4#120×C6112yes—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4C22×D4×C6111yescharacteristic
964C2×C4C22×D4×C6111yescharacteristic
965C2×C4C22×D4×C6111yescharacteristic
966C2×C4C22×D4×C6111yescharacteristic
967C2×C4C22×D4×C6111yescharacteristic
968C2×C4H(5,𝔽2)×C6111yescharacteristic
969C8—22no—
970C8—22no—
971C8—22no—
972C8—22no—
973C8—41no—
974C8—41no—
975C22—22no—
976C22—22no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—42no—
984C22—81no—
985C22—81no—
986C22—82no—
987C22—81no—
988C22—82no—
989C22—161no—
990C22—162no—
991C22—164no—
992C22C61×#53411yescharacteristic
993C22D42×C6111yescharacteristic
994C22D42×C6111yescharacteristic
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C6111yescharacteristic
1004C4C2×#120×C6111yescharacteristic
1005C4D42×C6111yescharacteristic
1006C4D42×C6111yescharacteristic
1007C2—21no—
1008C2—21no—
1009C2—21no—
1010C2—42no—
1011C2—42no—
1012C2—81no—
1013C2—81no—
1014C2—82no—
1015C2—81no—
1016C2C61×#240311yescharacteristic
subgroupG/H
center, socleC2×C61#2403
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C61 ◁ C22×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3586C2semidirect
2. C61×#3585C2semidirect
3. C61×#3020C2semidirect
4. C61×#3019C2semidirect
5. C61×#3010C2semidirect
6. C61×#3009C2semidirect
7. C61×#2019C2semidirect
8. C61×#2017C2semidirect
9. C61×#2009C2semidirect
10. C61×#2008C2semidirect
11. C61×#1903C2semidirect
12. C61×#1902C2semidirect
13. C61×#1881C2semidirect
14. C61×#1881C2semidirect
15. C61×#1794C2semidirect
17. C2×2−1+4×C61C22semidirect
32. C61×#575C22semidirect
33. C61×#575C22semidirect
36. C2×#137×C61C22semidirect
40. C22×SD16×C61C22semidirect
42. C61×#568C22semidirect
43. C61×#536C22semidirect
44. C61×#535C22semidirect
54. C61×#421C22semidirect
55. C61×#421C22semidirect
56. C61×#421C22semidirect
57. C61×#419C22semidirect
58. C61×#418C22semidirect
60. C61×#416C22semidirect
61. C2×#101×C61C22semidirect
62. C2×#100×C61C22semidirect
63. C61×#410C22semidirect
64. C61×#408C22semidirect
65. C61×#408C22semidirect
66. C61×#408C22semidirect
67. C61×#344C22semidirect
68. C61×#344C22semidirect
69. C61×#341C22semidirect
70. C61×#338C22semidirect
77. 2−1+4×C61D4semidirect
85. H(5,𝔽2)×C61D4semidirect
123. #137×C61D4semidirect
141. AGL(1,ℤ/8)×C61D4semidirect
153. C2×Q16×C61D4semidirect
162. C2×SD16×C61D4semidirect
466. #23894C61direct (N × H)
499. #3586C2×C61semidirect
500. #3585C2×C61semidirect
501. #3020C2×C61semidirect
502. #3019C2×C61semidirect
503. #3010C2×C61semidirect
504. #3009C2×C61semidirect
505. #2019C2×C61semidirect
506. #2017C2×C61semidirect
507. #2009C2×C61semidirect
508. #2008C2×C61semidirect
509. #1903C2×C61semidirect
510. #1902C2×C61semidirect
511. #1881C2×C61semidirect
512. #1881C2×C61semidirect
513. #1794C2×C61semidirect
525. C2×2−1+4C22×C61semidirect
540. #575C22×C61semidirect
541. #575C22×C61semidirect
544. C2×#137C22×C61semidirect
548. C22×SD16C22×C61semidirect
550. #568C22×C61semidirect
551. #536C22×C61semidirect
552. #535C22×C61semidirect
562. #421C22×C61semidirect
563. #421C22×C61semidirect
564. #421C22×C61semidirect
565. #419C22×C61semidirect
566. #418C22×C61semidirect
568. #416C22×C61semidirect
569. C2×#101C22×C61semidirect
570. C2×#100C22×C61semidirect
571. #410C22×C61semidirect
572. #408C22×C61semidirect
573. #408C22×C61semidirect
574. #408C22×C61semidirect
575. #344C22×C61semidirect
576. #344C22×C61semidirect
577. #341C22×C61semidirect
578. #338C22×C61semidirect
579. C61#23894direct (N × H)
586. 2−1+4D4×C61semidirect
594. H(5,𝔽2)D4×C61semidirect
632. #137D4×C61semidirect
650. AGL(1,ℤ/8)D4×C61semidirect
662. C2×Q16D4×C61semidirect
671. C2×SD16D4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#35862
C61×#35852
C61×#30202
C61×#30192
C61×#30102
C61×#30092
C61×#20192
C61×#20172
C61×#20092
C61×#20082
C61×#19032
C61×#19022
C61×#18812
C61×#17942
#2389461