Finite Group Databasebeta

← C61×#24464 #29527897

Subgroups — C61×#24464 #29527897

Order 15616.

1600 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3488C211yesmaximal, characteristic, complemented
2C61×#3055C211yesmaximal, characteristic, complemented
3C2×C61×#453C211yesmaximal, characteristic, complemented
4C61×#3006C211yesmaximal, characteristic, complemented
5C22×#104×C61C211yesmaximal, characteristic, complemented
6C61×#2856C211yesmaximal, characteristic, complemented
7C61×#2039C211yesmaximal, characteristic, complemented
8C61×#2037C211yesmaximal, characteristic, complemented
9C61×#2006C211yesmaximal, characteristic, complemented
10C61×#2002C211yesmaximal, characteristic, complemented
11C61×#1900C211yesmaximal, characteristic, complemented
12C61×#1896C211yesmaximal, characteristic, complemented
13C61×#1883C211yesmaximal, characteristic, complemented
14C61×#1859C211yesmaximal, characteristic, complemented
15C61×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C61C2211yescharacteristic
17C22×#41×C61C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C61C2211yescharacteristic, complemented
20C2×AGL(1,ℤ/8)×C61C2211yescharacteristic, complemented
21C22×M16×C61C2211yescharacteristic, complemented
22C61×#550—21no—
23C61×#548—21no—
24C61×#546—21no—
25C61×#546—22no—
26D42×C61—22no—
27D42×C61—21no—
28C61×#537—21no—
29C61×#537C2211yescharacteristic
30C61×#535—21no—
31C61×#535C2211yescharacteristic
32C2×#127×C61C2211yescharacteristic, complemented
33C61×#525—21no—
34C61×#525C2211yescharacteristic
35C2×#121×C61—21no—
36C2×#121×C61—22no—
37C2×#121×C61C2211yescharacteristic
38C2×#121×C61C2211yescharacteristic, complemented
39C61×#520C2211yescharacteristic
40C22×C42×C61C2211yescharacteristic, complemented
41C61×#469—21no—
42C61×#468—21no—
43C61×#466—21no—
44C61×#465—21no—
45C61×#453—24no—
46C61×#449—21no—
47C61×#449—21no—
48C61×#448—21no—
49C61×#447—21no—
50C61×#428C2211yescharacteristic, complemented
51C2×#104×C61—24no—
52C2×#104×C61C2211yescharacteristic
53C2×#104×C61C2211yescharacteristic
54C2×#104×C61C2211yescharacteristic, complemented
55C2×#104×C61C2211yescharacteristic, complemented
56C2×#104×C61C2211yescharacteristic, complemented
57C2×#104×C61C2211yescharacteristic, complemented
58C61×#418C2211yescharacteristic, complemented
59C61×#417C2211yescharacteristic
60C61×#417C2211yescharacteristic, complemented
61C61×#417C2211yescharacteristic, complemented
62C2×#100×C61C2211yescharacteristic, complemented
63C2×#100×C61C2211yescharacteristic, complemented
64C61×#407C2211yescharacteristic, complemented
65C61×#390—22no—
66C61×#390C2211yescharacteristic, complemented
67C61×#390C2211yescharacteristic, complemented
68C61×#384C2211yescharacteristic, complemented
69C61×#343C2211yescharacteristic, complemented
70C61×#343C2211yescharacteristic, complemented
71C61×#339C2211yescharacteristic, complemented
72C61×#339C2211yescharacteristic, complemented
73H(5,𝔽2)×C61—22no—
74H(5,𝔽2)×C61—22no—
75H(5,𝔽2)×C61—41no—
76H(5,𝔽2)×C61—41no—
77C2×#41×C61—21no—
78C2×#41×C61—21no—
79C2×#41×C61—21no—
80C2×#41×C61—21no—
81C2×#41×C61—22no—
82C2×#41×C61—22no—
83C2×#41×C61—41no—
84C2×#41×C61—41no—
85C2×#41×C61D411yescharacteristic, complemented
86C2×#41×C61D411yescharacteristic, complemented
87C2×#41×C61C2311yescharacteristic
88C2×#41×C61C2311yescharacteristic
89C2×#41×C61C2311yescharacteristic
90C22×Q8×C61D411yescharacteristic, complemented
91C22×D4×C61—21no—
92C22×D4×C61—22no—
93C22×D4×C61—22no—
94C22×D4×C61—21no—
95C22×D4×C61—21no—
96C22×D4×C61—22no—
97C22×D4×C61—21no—
98C22×D4×C61D412yes—
99C22×D4×C61D411yescharacteristic, complemented
100C22×D4×C61C2311yescharacteristic
101C22×D4×C61C2311yescharacteristic
102C23×C4×C61—21no—
103C23×C4×C61—21no—
104C23×C4×C61C2311yescharacteristic
105AGL(1,ℤ/8)×C61—22no—
106AGL(1,ℤ/8)×C61—22no—
107AGL(1,ℤ/8)×C61—22no—
108AGL(1,ℤ/8)×C61—41no—
109AGL(1,ℤ/8)×C61—41no—
110AGL(1,ℤ/8)×C61—41no—
111C2×SD16×C61—21no—
112C2×SD16×C61—21no—
113C2×SD16×C61—21no—
114C2×D8×C61—21no—
115C2×D8×C61—21no—
116C2×D8×C61—21no—
117C2×M16×C61—21no—
118C2×M16×C61—22no—
119C2×M16×C61—41no—
120C2×M16×C61C2311yescharacteristic
121C2×M16×C61C2311yescharacteristic
122C2×M16×C61C2311yescharacteristic
123C2×M16×C61C2311yescharacteristic
124C22×C8×C61—21no—
125#127×C61—22no—
126#127×C61—21no—
127#127×C61—22no—
128#127×C61—41no—
129#124×C61—22no—
130#124×C61—21no—
131#123×C61—22no—
132#123×C61—21no—
133C22⋊Q8×C61—22no—
134C22⋊Q8×C61—21no—
135C22⋊Q8×C61—21no—
136C22⋊Q8×C61D411yescharacteristic, complemented
137C22⋊Q8×C61D411yescharacteristic, complemented
138#121×C61—22no—
139#121×C61—22no—
140#121×C61—22no—
141#121×C61—22no—
142#121×C61—22no—
143#121×C61—21no—
144#121×C61—21no—
145#121×C61—21no—
146#121×C61—22no—
147#121×C61—21no—
148#121×C61—21no—
149#121×C61—21no—
150#121×C61—21no—
151#121×C61—21no—
152#121×C61—21no—
153#121×C61—21no—
154#121×C61—21no—
155#121×C61—21no—
156#121×C61—48no—
157#121×C61D411yescharacteristic, complemented
158#121×C61D411yescharacteristic, complemented
159#120×C61—22no—
160#120×C61—22no—
161#120×C61—22no—
162#120×C61—22no—
163#120×C61—21no—
164C4×Q8×C61—21no—
165C4×D4×C61—22no—
166C4×D4×C61—22no—
167C4×D4×C61—21no—
168C4×D4×C61—22no—
169C4×D4×C61—21no—
170C4×D4×C61—21no—
171#117×C61—21no—
172#117×C61C2311yescharacteristic
173C2×C4⋊C4×C61—21no—
174C2×C4⋊C4×C61—22no—
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C22⋊C4×C61—22no—
178C2×C22⋊C4×C61—22no—
179C2×C22⋊C4×C61—21no—
180C2×C22⋊C4×C61—22no—
181C2×C22⋊C4×C61D412yes—
182C2×C42×C61—22no—
183C2×C42×C61—21no—
184C2×C42×C61—41no—
185C2×C42×C61C2311yescharacteristic
186C2×C42×C61C2311yescharacteristic
187#107×C61—21no—
188#106×C61—21no—
189#104×C61—22no—
190#104×C61—22no—
191#104×C61—22no—
192#104×C61—22no—
193#104×C61—41no—
194#104×C61D414yescomplemented
195#103×C61—21no—
196#103×C61—21no—
197#103×C61—21no—
198#102×C61—21no—
199#102×C61—21no—
200#102×C61—21no—
201#102×C61—21no—
202#102×C61—21no—
203#100×C61—22no—
204#100×C61—41no—
205C22⋊C8×C61—21no—
206C22⋊C8×C61—21no—
207C24×C61—22no—
208C24×C61—21no—
209C24×C61—21no—
210C24×C61C2×D411yescharacteristic
211C24×C61C2×D412yes—
212#41×C61—21no—
213#41×C61—21no—
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—42no—
225#41×C61—42no—
226#41×C61—41no—
227#41×C61—41no—
228#41×C61—42no—
229#41×C61—42no—
230#41×C61—42no—
231#41×C61—42no—
232#41×C61—42no—
233#41×C61—42no—
234#41×C61C2×D412yes—
235#41×C61#4112yes—
236C2×Q8×C61—21no—
237C2×Q8×C61—22no—
238C2×Q8×C61—41no—
239C2×Q8×C61C2×D411yescharacteristic
240C2×Q8×C61C2×D411yescharacteristic
241C2×Q8×C61C2×D411yescharacteristic
242C2×D4×C61—21no—
243C2×D4×C61—22no—
244C2×D4×C61—22no—
245C2×D4×C61—22no—
246C2×D4×C61—22no—
247C2×D4×C61—21no—
248C2×D4×C61—21no—
249C2×D4×C61—21no—
250C2×D4×C61—21no—
251C2×D4×C61—21no—
252C2×D4×C61—22no—
253C2×D4×C61—22no—
254C2×D4×C61—22no—
255C2×D4×C61—21no—
256C2×D4×C61—22no—
257C2×D4×C61—21no—
258C2×D4×C61—21no—
259C2×D4×C61—21no—
260C2×D4×C61—21no—
261C2×D4×C61—21no—
262C2×D4×C61—21no—
263C2×D4×C61—21no—
264C2×D4×C61—21no—
265C2×D4×C61—21no—
266C2×D4×C61—21no—
267C2×D4×C61—21no—
268C2×D4×C61—21no—
269C2×D4×C61—21no—
270C2×D4×C61—41no—
271C2×D4×C61—42no—
272C2×D4×C61—42no—
273C2×D4×C61—44no—
274C2×D4×C61—44no—
275C2×D4×C61—44no—
276C2×D4×C61—42no—
277C2×D4×C61—42no—
278C2×D4×C61—44no—
279C2×D4×C61—44no—
280C2×D4×C61—42no—
281C2×D4×C61—42no—
282C2×D4×C61—44no—
283C2×D4×C61—44no—
284C2×D4×C61—41no—
285C2×D4×C61—41no—
286C2×D4×C61—84no—
287C2×D4×C61C2×D411yescharacteristic
288C2×D4×C61C2×D411yescharacteristic
289C2×D4×C61C2×D411yescharacteristic
290C22×C4×C61—21no—
291C22×C4×C61—21no—
292C22×C4×C61—21no—
293C22×C4×C61—21no—
294C22×C4×C61—21no—
295C22×C4×C61—21no—
296C22×C4×C61—22no—
297C22×C4×C61—24no—
298C22×C4×C61—21no—
299C22×C4×C61—21no—
300C22×C4×C61—22no—
301C22×C4×C61—21no—
302C22×C4×C61—21no—
303C22×C4×C61—21no—
304C22×C4×C61—21no—
305C22×C4×C61—21no—
306C22×C4×C61—42no—
307C22×C4×C61—42no—
308C22×C4×C61—42no—
309C22×C4×C61—42no—
310C22×C4×C61C2×D411yescharacteristic
311C22×C4×C61C2×D411yescharacteristic
312C22×C4×C61C2×D411yescharacteristic
313C22×C4×C61C2×D411yescharacteristic
314C22×C4×C61C2×D411yescharacteristic
315C22×C4×C61C2×D412yes—
316C22×C4×C61C2411yescharacteristic
317SD16×C61—42no—
318SD16×C61—42no—
319SD16×C61—42no—
320D8×C61—42no—
321D8×C61—42no—
322D8×C61—42no—
323M16×C61—21no—
324M16×C61—21no—
325M16×C61—21no—
326M16×C61—21no—
327M16×C61—21no—
328M16×C61—21no—
329M16×C61—21no—
330M16×C61—42no—
331M16×C61C2×D412yescomplemented
332C2×C8×C61—21no—
333C2×C8×C61—21no—
334C2×C8×C61—21no—
335C2×C8×C61—21no—
336C2×C8×C61—42no—
337C4⋊C4×C61—22no—
338C4⋊C4×C61—22no—
339C4⋊C4×C61—21no—
340C4⋊C4×C61—21no—
341C4⋊C4×C61—21no—
342C4⋊C4×C61—21no—
343C4⋊C4×C61—21no—
344C4⋊C4×C61—21no—
345C4⋊C4×C61—44no—
346C4⋊C4×C61C2×D411yescharacteristic
347C4⋊C4×C61C2×D411yescharacteristic
348C22⋊C4×C61—22no—
349C22⋊C4×C61—22no—
350C22⋊C4×C61—22no—
351C22⋊C4×C61—22no—
352C22⋊C4×C61—22no—
353C22⋊C4×C61—21no—
354C22⋊C4×C61—21no—
355C22⋊C4×C61—21no—
356C22⋊C4×C61—21no—
357C22⋊C4×C61—22no—
358C22⋊C4×C61—22no—
359C22⋊C4×C61—21no—
360C22⋊C4×C61—44no—
361C22⋊C4×C61—44no—
362C22⋊C4×C61—41no—
363C22⋊C4×C61—41no—
364C42×C61—22no—
365C42×C61—21no—
366C42×C61—21no—
367C42×C61—21no—
368C42×C61—21no—
369C42×C61—42no—
370C42×C61C2×D412yescomplemented
371C23×C61—21no—
372C23×C61—21no—
373C23×C61—21no—
374C23×C61—22no—
375C23×C61—22no—
376C23×C61—21no—
377C23×C61—21no—
378C23×C61—22no—
379C23×C61—22no—
380C23×C61—41no—
381C23×C61—42no—
382C23×C61—44no—
383C23×C61—42no—
384C23×C61—42no—
385C23×C61—42no—
386C23×C61—42no—
387C23×C61—42no—
388C23×C61—41no—
389C23×C61—41no—
390C23×C61—41no—
391C23×C61—81no—
392C23×C61—82no—
393C23×C61—82no—
394C23×C61#12011yescharacteristic
395C23×C61#12011yescharacteristic
396C23×C61C22×D411yescharacteristic
397Q8×C61—21no—
398Q8×C61—21no—
399Q8×C61—21no—
400Q8×C61—21no—
401Q8×C61—21no—
402Q8×C61—42no—
403Q8×C61#12112yescomplemented
404D4×C61—22no—
405D4×C61—22no—
406D4×C61—21no—
407D4×C61—21no—
408D4×C61—21no—
409D4×C61—21no—
410D4×C61—21no—
411D4×C61—42no—
412D4×C61—42no—
413D4×C61—44no—
414D4×C61—42no—
415D4×C61—44no—
416D4×C61—41no—
417D4×C61—41no—
418D4×C61—41no—
419D4×C61—41no—
420D4×C61—44no—
421D4×C61—42no—
422D4×C61—41no—
423D4×C61—41no—
424D4×C61—41no—
425D4×C61—41no—
426D4×C61—41no—
427D4×C61—41no—
428D4×C61—41no—
429D4×C61—41no—
430D4×C61—88no—
431D4×C61—81no—
432D4×C61—82no—
433D4×C61—82no—
434D4×C61—82no—
435D4×C61—82no—
436D4×C61—82no—
437D4×C61—82no—
438D4×C61#12112yescomplemented
439C2×C4×C61—22no—
440C2×C4×C61—22no—
441C2×C4×C61—21no—
442C2×C4×C61—22no—
443C2×C4×C61—21no—
444C2×C4×C61—21no—
445C2×C4×C61—21no—
446C2×C4×C61—21no—
447C2×C4×C61—21no—
448C2×C4×C61—21no—
449C2×C4×C61—21no—
450C2×C4×C61—21no—
451C2×C4×C61—22no—
452C2×C4×C61—21no—
453C2×C4×C61—21no—
454C2×C4×C61—22no—
455C2×C4×C61—22no—
456C2×C4×C61—21no—
457C2×C4×C61—22no—
458C2×C4×C61—21no—
459C2×C4×C61—21no—
460C2×C4×C61—21no—
461C2×C4×C61—42no—
462C2×C4×C61—42no—
463C2×C4×C61—42no—
464C2×C4×C61—48no—
465C2×C4×C61—44no—
466C2×C4×C61—41no—
467C2×C4×C61—41no—
468C2×C4×C61—41no—
469C2×C4×C61—41no—
470C2×C4×C61—41no—
471C2×C4×C61—41no—
472C2×C4×C61—42no—
473C2×C4×C61—42no—
474C2×C4×C61—41no—
475C2×C4×C61—82no—
476C2×C4×C61#12011yescharacteristic
477C2×C4×C61#12011yescharacteristic
478C2×C4×C61C22×D411yescharacteristic
479C2×C4×C61C22×D411yescharacteristic
480C2×C4×C61C22×D411yescharacteristic
481C2×C4×C61C2×#4111yescharacteristic
482C2×C4×C61H(5,𝔽2)11yescharacteristic
483C2×C4×C61H(5,𝔽2)11yescharacteristic
484C8×C61—22no—
485C8×C61—41no—
486C8×C61—41no—
487C8×C61—41no—
488#24464C6111yesmaximal, characteristic, direct product factor, Sylow
489C22×C61—21no—
490C22×C61—21no—
491C22×C61—21no—
492C22×C61—21no—
493C22×C61—21no—
494C22×C61—22no—
495C22×C61—21no—
496C22×C61—21no—
497C22×C61—42no—
498C22×C61—42no—
499C22×C61—41no—
500C22×C61—41no—
501C22×C61—41no—
502C22×C61—41no—
503C22×C61—42no—
504C22×C61—42no—
505C22×C61—41no—
506C22×C61—41no—
507C22×C61—41no—
508C22×C61—42no—
509C22×C61—41no—
510C22×C61—84no—
511C22×C61—82no—
512C22×C61—82no—
513C22×C61—82no—
514C22×C61—82no—
515C22×C61—81no—
516C22×C61—81no—
517C22×C61—81no—
518C22×C61—164no—
519C22×C61#45312yescomplemented
520C22×C61C2×#12011yescharacteristic
521C22×C61D4211yescharacteristic
522C22×C61#54611yescharacteristic
523C4×C61—24no—
524C4×C61—21no—
525C4×C61—21no—
526C4×C61—22no—
527C4×C61—42no—
528C4×C61—41no—
529C4×C61—41no—
530C4×C61—42no—
531C4×C61—41no—
532C4×C61—41no—
533C4×C61—81no—
534C4×C61C2×#12111yescharacteristic
535C4×C61#53411yescharacteristic
536C4×C61D4211yescharacteristic
537C4×C61#54611yescharacteristic
538#3488C2×C6111yescharacteristic, complemented
539#3055C2×C6111yescharacteristic, complemented
540C2×#453C2×C6111yescharacteristic, complemented
541#3006C2×C6111yescharacteristic, complemented
542C22×#104C2×C6111yescharacteristic, complemented
543#2856C2×C6111yescharacteristic, complemented
544#2039C2×C6111yescharacteristic, complemented
545#2037C2×C6111yescharacteristic, complemented
546#2006C2×C6111yescharacteristic, complemented
547#2002C2×C6111yescharacteristic, complemented
548#1900C2×C6111yescharacteristic, complemented
549#1896C2×C6111yescharacteristic, complemented
550#1883C2×C6111yescharacteristic, complemented
551#1859C2×C6111yescharacteristic, complemented
552#1792C2×C6111yescharacteristic, complemented
553C2×C61—21no—
554C2×C61—21no—
555C2×C61—22no—
556C2×C61—41no—
557C2×C61—42no—
558C2×C61—81no—
559C2×C61—82no—
560C2×C61—81no—
561C2×C61—161no—
562C2×C61#241011yescharacteristic
563C2×C61C2×#45311yescharacteristic
564C2×C61#301811yescharacteristic
565C2×H(5,𝔽2)C22×C6111yescharacteristic
566C22×#41C22×C6111yescharacteristic
567C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
568C2×AGL(1,ℤ/8)C22×C6111yescharacteristic, complemented
569C2×AGL(1,ℤ/8)C22×C6111yescharacteristic, complemented
570C22×M16C22×C6111yescharacteristic, complemented
571#550—21no—
572#548—21no—
573#546—21no—
574#546—22no—
575D42—22no—
576D42—21no—
577#537—21no—
578#537C22×C6111yescharacteristic
579#535—21no—
580#535C22×C6111yescharacteristic
581C2×#127C22×C6111yescharacteristic, complemented
582#525—21no—
583#525C22×C6111yescharacteristic
584C2×#121—21no—
585C2×#121—22no—
586C2×#121C22×C6111yescharacteristic
587C2×#121C22×C6111yescharacteristic, complemented
588#520C22×C6111yescharacteristic
589C22×C42C22×C6111yescharacteristic, complemented
590#469—21no—
591#468—21no—
592#466—21no—
593#465—21no—
594#453—24no—
595#449—21no—
596#449—21no—
597#448—21no—
598#447—21no—
599#428C22×C6111yescharacteristic, complemented
600C2×#104—24no—
601C2×#104C22×C6111yescharacteristic
602C2×#104C22×C6111yescharacteristic
603C2×#104C22×C6111yescharacteristic, complemented
604C2×#104C22×C6111yescharacteristic, complemented
605C2×#104C22×C6111yescharacteristic, complemented
606C2×#104C22×C6111yescharacteristic, complemented
607#418C22×C6111yescharacteristic, complemented
608#417C22×C6111yescharacteristic
609#417C22×C6111yescharacteristic, complemented
610#417C22×C6111yescharacteristic, complemented
611C2×#100C22×C6111yescharacteristic, complemented
612C2×#100C22×C6111yescharacteristic, complemented
613#407C22×C6111yescharacteristic, complemented
614#390—22no—
615#390C22×C6111yescharacteristic, complemented
616#390C22×C6111yescharacteristic, complemented
617#384C22×C6111yescharacteristic, complemented
618#343C22×C6111yescharacteristic, complemented
619#343C22×C6111yescharacteristic, complemented
620#339C22×C6111yescharacteristic, complemented
621#339C22×C6111yescharacteristic, complemented
622C61#2446411yescharacteristic, direct product factor, Sylow
623H(5,𝔽2)—22no—
624H(5,𝔽2)—22no—
625H(5,𝔽2)—41no—
626H(5,𝔽2)—41no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41—21no—
630C2×#41—21no—
631C2×#41—22no—
632C2×#41—22no—
633C2×#41—41no—
634C2×#41—41no—
635C2×#41D4×C6111yescharacteristic, complemented
636C2×#41D4×C6111yescharacteristic, complemented
637C2×#41C23×C6111yescharacteristic
638C2×#41C23×C6111yescharacteristic
639C2×#41C23×C6111yescharacteristic
640C22×Q8D4×C6111yescharacteristic, complemented
641C22×D4—21no—
642C22×D4—22no—
643C22×D4—22no—
644C22×D4—21no—
645C22×D4—21no—
646C22×D4—21no—
647C22×D4—22no—
648C22×D4D4×C6112yes—
649C22×D4D4×C6111yescharacteristic, complemented
650C22×D4C23×C6111yescharacteristic
651C22×D4C23×C6111yescharacteristic
652C23×C4—21no—
653C23×C4—21no—
654C23×C4C23×C6111yescharacteristic
655AGL(1,ℤ/8)—22no—
656AGL(1,ℤ/8)—22no—
657AGL(1,ℤ/8)—22no—
658AGL(1,ℤ/8)—41no—
659AGL(1,ℤ/8)—41no—
660AGL(1,ℤ/8)—41no—
661C2×SD16—21no—
662C2×SD16—21no—
663C2×SD16—21no—
664C2×D8—21no—
665C2×D8—21no—
666C2×D8—21no—
667C2×M16—21no—
668C2×M16—22no—
669C2×M16—41no—
670C2×M16C23×C6111yescharacteristic
671C2×M16C23×C6111yescharacteristic
672C2×M16C23×C6111yescharacteristic
673C2×M16C23×C6111yescharacteristic
674C22×C8—21no—
675#127—22no—
676#127—21no—
677#127—22no—
678#127—41no—
679#124—22no—
680#124—21no—
681#123—22no—
682#123—21no—
683C22⋊Q8—22no—
684C22⋊Q8—21no—
685C22⋊Q8—21no—
686C22⋊Q8D4×C6111yescharacteristic, complemented
687C22⋊Q8D4×C6111yescharacteristic, complemented
688#121—22no—
689#121—22no—
690#121—22no—
691#121—22no—
692#121—22no—
693#121—21no—
694#121—21no—
695#121—21no—
696#121—21no—
697#121—21no—
698#121—21no—
699#121—22no—
700#121—21no—
701#121—21no—
702#121—21no—
703#121—21no—
704#121—21no—
705#121—21no—
706#121—48no—
707#121D4×C6111yescharacteristic, complemented
708#121D4×C6111yescharacteristic, complemented
709#120—22no—
710#120—22no—
711#120—22no—
712#120—21no—
713#120—22no—
714C4×Q8—21no—
715C4×D4—22no—
716C4×D4—22no—
717C4×D4—21no—
718C4×D4—22no—
719C4×D4—21no—
720C4×D4—21no—
721#117—21no—
722#117C23×C6111yescharacteristic
723C2×C4⋊C4—21no—
724C2×C4⋊C4—22no—
725C2×C4⋊C4C23×C6111yescharacteristic
726C2×C4⋊C4C23×C6111yescharacteristic
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4D4×C6112yes—
732C2×C42—22no—
733C2×C42—21no—
734C2×C42—41no—
735C2×C42C23×C6111yescharacteristic
736C2×C42C23×C6111yescharacteristic
737#107—21no—
738#106—21no—
739#104—22no—
740#104—22no—
741#104—22no—
742#104—22no—
743#104—41no—
744#104D4×C6114yescomplemented
745#103—21no—
746#103—21no—
747#103—21no—
748#102—21no—
749#102—21no—
750#102—21no—
751#102—21no—
752#102—21no—
753#100—22no—
754#100—41no—
755C22⋊C8—21no—
756C22⋊C8—21no—
757C24—22no—
758C24—21no—
759C24—21no—
760C24C2×D4×C6111yescharacteristic
761C24C2×D4×C6112yes—
762#41—21no—
763#41—21no—
764#41—22no—
765#41—22no—
766#41—21no—
767#41—21no—
768#41—21no—
769#41—21no—
770#41—21no—
771#41—21no—
772#41—21no—
773#41—21no—
774#41—42no—
775#41—42no—
776#41—41no—
777#41—41no—
778#41—42no—
779#41—42no—
780#41—42no—
781#41—42no—
782#41—42no—
783#41—42no—
784#41C2×D4×C6112yes—
785#41#41×C6112yes—
786C2×Q8—21no—
787C2×Q8—22no—
788C2×Q8—41no—
789C2×Q8C2×D4×C6111yescharacteristic
790C2×Q8C2×D4×C6111yescharacteristic
791C2×Q8C2×D4×C6111yescharacteristic
792C2×D4—21no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—21no—
806C2×D4—22no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—41no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—44no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—44no—
829C2×D4—44no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—41no—
835C2×D4—41no—
836C2×D4—84no—
837C2×D4C2×D4×C6111yescharacteristic
838C2×D4C2×D4×C6111yescharacteristic
839C2×D4C2×D4×C6111yescharacteristic
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—24no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—42no—
857C22×C4—42no—
858C22×C4—42no—
859C22×C4—42no—
860C22×C4C2×D4×C6111yescharacteristic
861C22×C4C2×D4×C6111yescharacteristic
862C22×C4C2×D4×C6111yescharacteristic
863C22×C4C2×D4×C6111yescharacteristic
864C22×C4C2×D4×C6111yescharacteristic
865C22×C4C2×D4×C6112yes—
866C22×C4C24×C6111yescharacteristic
867SD16—42no—
868SD16—42no—
869SD16—42no—
870D8—42no—
871D8—42no—
872D8—42no—
873M16—21no—
874M16—21no—
875M16—21no—
876M16—21no—
877M16—21no—
878M16—21no—
879M16—21no—
880M16—42no—
881M16C2×D4×C6112yescomplemented
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—42no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—44no—
896C4⋊C4C2×D4×C6111yescharacteristic
897C4⋊C4C2×D4×C6111yescharacteristic
898C22⋊C4—22no—
899C22⋊C4—22no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—22no—
903C22⋊C4—21no—
904C22⋊C4—21no—
905C22⋊C4—21no—
906C22⋊C4—21no—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—21no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—41no—
913C22⋊C4—41no—
914C42—22no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—42no—
920C42C2×D4×C6112yescomplemented
921C23—21no—
922C23—21no—
923C23—22no—
924C23—21no—
925C23—22no—
926C23—21no—
927C23—21no—
928C23—22no—
929C23—22no—
930C23—41no—
931C23—42no—
932C23—44no—
933C23—42no—
934C23—42no—
935C23—42no—
936C23—42no—
937C23—42no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—81no—
942C23—82no—
943C23—82no—
944C23#120×C6111yescharacteristic
945C23#120×C6111yescharacteristic
946C23C22×D4×C6111yescharacteristic
947Q8—21no—
948Q8—21no—
949Q8—21no—
950Q8—21no—
951Q8—21no—
952Q8—42no—
953Q8#121×C6112yescomplemented
954D4—22no—
955D4—22no—
956D4—21no—
957D4—21no—
958D4—21no—
959D4—21no—
960D4—21no—
961D4—42no—
962D4—42no—
963D4—44no—
964D4—42no—
965D4—44no—
966D4—41no—
967D4—41no—
968D4—41no—
969D4—41no—
970D4—44no—
971D4—42no—
972D4—41no—
973D4—41no—
974D4—41no—
975D4—41no—
976D4—41no—
977D4—41no—
978D4—41no—
979D4—41no—
980D4—88no—
981D4—81no—
982D4—82no—
983D4—82no—
984D4—82no—
985D4—82no—
986D4—82no—
987D4—82no—
988D4#121×C6112yescomplemented
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—22no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—22no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—22no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—42no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—48no—
1015C2×C4—44no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—42no—
1023C2×C4—42no—
1024C2×C4—41no—
1025C2×C4—82no—
1026C2×C4#120×C6111yescharacteristic
1027C2×C4#120×C6111yescharacteristic
1028C2×C4C22×D4×C6111yescharacteristic
1029C2×C4C22×D4×C6111yescharacteristic
1030C2×C4C22×D4×C6111yescharacteristic
1031C2×C4C2×#41×C6111yescharacteristic
1032C2×C4H(5,𝔽2)×C6111yescharacteristic
1033C2×C4H(5,𝔽2)×C6111yescharacteristic
1034C8—22no—
1035C8—41no—
1036C8—41no—
1037C8—41no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—22no—
1044C22—21no—
1045C22—21no—
1046C22—42no—
1047C22—42no—
1048C22—41no—
1049C22—41no—
1050C22—41no—
1051C22—41no—
1052C22—42no—
1053C22—42no—
1054C22—41no—
1055C22—41no—
1056C22—41no—
1057C22—42no—
1058C22—41no—
1059C22—84no—
1060C22—82no—
1061C22—82no—
1062C22—82no—
1063C22—82no—
1064C22—81no—
1065C22—81no—
1066C22—81no—
1067C22—164no—
1068C22C61×#45312yescomplemented
1069C22C2×#120×C6111yescharacteristic
1070C22D42×C6111yescharacteristic
1071C22C61×#54611yescharacteristic
1072C4—24no—
1073C4—21no—
1074C4—21no—
1075C4—22no—
1076C4—42no—
1077C4—41no—
1078C4—41no—
1079C4—42no—
1080C4—41no—
1081C4—41no—
1082C4—81no—
1083C4C2×#121×C6111yescharacteristic
1084C4C61×#53411yescharacteristic
1085C4D42×C6111yescharacteristic
1086C4C61×#54611yescharacteristic
1087C2—21no—
1088C2—21no—
1089C2—22no—
1090C2—41no—
1091C2—42no—
1092C2—81no—
1093C2—82no—
1094C2—81no—
1095C2—161no—
1096C2C61×#241011yescharacteristic
1097C2C2×C61×#45311yescharacteristic
1098C2C61×#301811yescharacteristic
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. C61×#3488C2semidirect
2. C61×#3055C2semidirect
3. C2×C61×#453C2semidirect
4. C61×#3006C2semidirect
5. C22×#104×C61C2semidirect
6. C61×#2856C2semidirect
7. C61×#2039C2semidirect
8. C61×#2037C2semidirect
9. C61×#2006C2semidirect
10. C61×#2002C2semidirect
11. C61×#1900C2semidirect
12. C61×#1896C2semidirect
13. C61×#1883C2semidirect
14. C61×#1859C2semidirect
15. C61×#1792C2semidirect
19. C2×AGL(1,ℤ/8)×C61C22semidirect
20. C2×AGL(1,ℤ/8)×C61C22semidirect
21. C22×M16×C61C22semidirect
32. C2×#127×C61C22semidirect
38. C2×#121×C61C22semidirect
40. C22×C42×C61C22semidirect
50. C61×#428C22semidirect
54. C2×#104×C61C22semidirect
55. C2×#104×C61C22semidirect
56. C2×#104×C61C22semidirect
57. C2×#104×C61C22semidirect
58. C61×#418C22semidirect
60. C61×#417C22semidirect
61. C61×#417C22semidirect
62. C2×#100×C61C22semidirect
63. C2×#100×C61C22semidirect
64. C61×#407C22semidirect
66. C61×#390C22semidirect
67. C61×#390C22semidirect
68. C61×#384C22semidirect
69. C61×#343C22semidirect
70. C61×#343C22semidirect
71. C61×#339C22semidirect
72. C61×#339C22semidirect
85. C2×#41×C61D4semidirect
86. C2×#41×C61D4semidirect
90. C22×Q8×C61D4semidirect
99. C22×D4×C61D4semidirect
136. C22⋊Q8×C61D4semidirect
137. C22⋊Q8×C61D4semidirect
157. #121×C61D4semidirect
158. #121×C61D4semidirect
194. #104×C61D4semidirect
331. M16×C61C2×D4semidirect
370. C42×C61C2×D4semidirect
403. Q8×C61#121semidirect
438. D4×C61#121semidirect
488. #24464C61direct (N × H)
519. C22×C61#453semidirect
538. #3488C2×C61semidirect
539. #3055C2×C61semidirect
540. C2×#453C2×C61semidirect
541. #3006C2×C61semidirect
542. C22×#104C2×C61semidirect
543. #2856C2×C61semidirect
544. #2039C2×C61semidirect
545. #2037C2×C61semidirect
546. #2006C2×C61semidirect
547. #2002C2×C61semidirect
548. #1900C2×C61semidirect
549. #1896C2×C61semidirect
550. #1883C2×C61semidirect
551. #1859C2×C61semidirect
552. #1792C2×C61semidirect
568. C2×AGL(1,ℤ/8)C22×C61semidirect
569. C2×AGL(1,ℤ/8)C22×C61semidirect
570. C22×M16C22×C61semidirect
581. C2×#127C22×C61semidirect
587. C2×#121C22×C61semidirect
589. C22×C42C22×C61semidirect
599. #428C22×C61semidirect
603. C2×#104C22×C61semidirect
604. C2×#104C22×C61semidirect
605. C2×#104C22×C61semidirect
606. C2×#104C22×C61semidirect
607. #418C22×C61semidirect
609. #417C22×C61semidirect
610. #417C22×C61semidirect
611. C2×#100C22×C61semidirect
612. C2×#100C22×C61semidirect
613. #407C22×C61semidirect
615. #390C22×C61semidirect
616. #390C22×C61semidirect
617. #384C22×C61semidirect
618. #343C22×C61semidirect
619. #343C22×C61semidirect
620. #339C22×C61semidirect
621. #339C22×C61semidirect
622. C61#24464direct (N × H)
635. C2×#41D4×C61semidirect
636. C2×#41D4×C61semidirect
640. C22×Q8D4×C61semidirect
649. C22×D4D4×C61semidirect
686. C22⋊Q8D4×C61semidirect
687. C22⋊Q8D4×C61semidirect
707. #121D4×C61semidirect
708. #121D4×C61semidirect
744. #104D4×C61semidirect
881. M16C2×D4×C61semidirect
920. C42C2×D4×C61semidirect
953. Q8#121×C61semidirect
988. D4#121×C61semidirect
1068. C22C61×#453semidirect

Maximal subgroups

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

subgroupindex
C61×#34882
C61×#30552
C2×C61×#4532
C61×#30062
C22×#104×C612
C61×#28562
C61×#20392
C61×#20372
C61×#20062
C61×#20022
C61×#19002
C61×#18962
C61×#18832
C61×#18592
C61×#17922
#2446461