Finite Group Databasebeta

← C61×#24460 #29527893

Subgroups — C61×#24460 #29527893

Order 15616.

1352 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#577C211yesmaximal, characteristic, complemented
2C2×C61×#472C211yesmaximal, characteristic, complemented
3C61×#3045C211yesmaximal, characteristic, complemented
4C2×C61×#454C211yesmaximal, characteristic, complemented
5C61×#3008C211yesmaximal, characteristic, complemented
6C61×#2898C211yesmaximal, characteristic, complemented
7C61×#2052C211yesmaximal, characteristic, complemented
8C61×#2046C211yesmaximal, characteristic, complemented
9C61×#2012C211yesmaximal, characteristic, complemented
10C61×#2004C211yesmaximal, characteristic, complemented
11C61×#1907C211yesmaximal, characteristic, complemented
12C61×#1883C211yesmaximal, characteristic, complemented
13C61×#1876C211yesmaximal, characteristic, complemented
14C61×#1866C211yesmaximal, characteristic, complemented
15C61×#1792C211yesmaximal, characteristic, complemented
16C2×2−1+4×C61C2211yescharacteristic
17C2×H(5,𝔽2)×C61C2211yescharacteristic
18C61×#577—24no—
19C61×#577—24no—
20C2×#137×C61—21no—
21C2×#137×C61C2211yescharacteristic
22C2×AGL(1,ℤ/8)×C61—21no—
23C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
24C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C61C2211yescharacteristic, complemented
26C2×#135×C61—21no—
27C2×#135×C61C2211yescharacteristic
28C22×SD16×C61—21no—
29C22×SD16×C61C2211yescharacteristic
30C22×D8×C61C2211yescharacteristic
31C2×#131×C61C2211yescharacteristic
32C2×#131×C61C2211yescharacteristic, complemented
33C61×#535C2211yescharacteristic
34C2×#124×C61C2211yescharacteristic, complemented
35C61×#520C2211yescharacteristic, complemented
36C61×#472—24no—
37C61×#464—21no—
38C61×#463—21no—
39C61×#460—21no—
40C61×#459—21no—
41C61×#454—24no—
42C61×#449—21no—
43C61×#449—21no—
44C61×#447—21no—
45C61×#447—21no—
46C2×#108×C61C2211yescharacteristic, complemented
47C61×#424C2211yescharacteristic, complemented
48C2×#104×C61C2211yescharacteristic
49C2×#104×C61C2211yescharacteristic
50C2×#104×C61C2211yescharacteristic, complemented
51C61×#419—21no—
52C61×#419C2211yescharacteristic, complemented
53C61×#418C2211yescharacteristic
54C61×#417—21no—
55C61×#417C2211yescharacteristic
56C61×#417C2211yescharacteristic
57C61×#416—21no—
58C61×#416C2211yescharacteristic
59C2×#103×C61—21no—
60C2×#103×C61C2211yescharacteristic, complemented
61C2×#102×C61C2211yescharacteristic, complemented
62C2×#101×C61C2211yescharacteristic, complemented
63C2×#100×C61C2211yescharacteristic
64C2×#100×C61C2211yescharacteristic, complemented
65C61×#408C2211yescharacteristic
66C61×#390C2211yescharacteristic
67C61×#343C2211yescharacteristic, complemented
68C61×#341C2211yescharacteristic, complemented
69C61×#339C2211yescharacteristic, complemented
70C61×#336C2211yescharacteristic, complemented
712−1+4×C61—22no—
722−1+4×C61—22no—
732−1+4×C61—41no—
742−1+4×C61D414yescomplemented
75H(5,𝔽2)×C61—22no—
76H(5,𝔽2)×C61—22no—
77H(5,𝔽2)×C61—22no—
78H(5,𝔽2)×C61—41no—
79C2×#41×C61—21no—
80C2×#41×C61—21no—
81C2×#41×C61—21no—
82C2×#41×C61—21no—
83C2×#41×C61—41no—
84C2×#41×C61C2311yescharacteristic
85C2×#41×C61C2311yescharacteristic
86C2×#41×C61C2311yescharacteristic
87C22×Q8×C61—21no—
88C22×Q8×C61—21no—
89C22×Q8×C61C2311yescharacteristic
90C22×D4×C61—21no—
91C22×D4×C61—21no—
92C22×D4×C61—41no—
93C22×D4×C61C2311yescharacteristic
94C22×D4×C61C2311yescharacteristic
95#137×C61—28no—
96#137×C61—22no—
97#137×C61—22no—
98AGL(1,ℤ/8)×C61—28no—
99AGL(1,ℤ/8)×C61—22no—
100AGL(1,ℤ/8)×C61—22no—
101AGL(1,ℤ/8)×C61—22no—
102AGL(1,ℤ/8)×C61—22no—
103AGL(1,ℤ/8)×C61—22no—
104AGL(1,ℤ/8)×C61D414yescomplemented
105#135×C61—28no—
106#135×C61—22no—
107#135×C61—22no—
108C2×Q16×C61—21no—
109C2×Q16×C61D411yescharacteristic
110C2×SD16×C61—28no—
111C2×SD16×C61—21no—
112C2×SD16×C61—22no—
113C2×SD16×C61—21no—
114C2×SD16×C61—22no—
115C2×SD16×C61—21no—
116C2×SD16×C61—21no—
117C2×SD16×C61—21no—
118C2×SD16×C61—21no—
119C2×SD16×C61D411yescharacteristic
120C2×SD16×C61D411yescharacteristic
121C2×D8×C61—21no—
122C2×D8×C61—22no—
123C2×D8×C61—21no—
124C2×D8×C61—21no—
125C2×D8×C61—21no—
126C2×D8×C61—21no—
127C2×D8×C61—41no—
128C2×D8×C61D411yescharacteristic
129#131×C61—22no—
130#131×C61—22no—
131#131×C61—22no—
132#131×C61—41no—
133C2×M16×C61—21no—
134C2×M16×C61—21no—
135C2×M16×C61C2311yescharacteristic
136C2×M16×C61C2311yescharacteristic
137C2×M16×C61C2311yescharacteristic
138C2×M16×C61C2311yescharacteristic
139C22×C8×C61—21no—
140C22×C8×C61—21no—
141C22×C8×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143#127×C61—21no—
144#124×C61—21no—
145#124×C61—22no—
146#124×C61—41no—
147#121×C61—21no—
148#121×C61—21no—
149#120×C61—41no—
150C4×Q8×C61—21no—
151C4×D4×C61—21no—
152C4×D4×C61—41no—
153#117×C61—21no—
154#117×C61C2311yescharacteristic
155C2×C4⋊C4×C61—21no—
156C2×C4⋊C4×C61C2311yescharacteristic
157C2×C22⋊C4×C61—41no—
158C2×C22⋊C4×C61—41no—
159C2×C42×C61C2311yescharacteristic
160#108×C61—22no—
161C4⋊C8×C61—21no—
162C4⋊C8×C61—21no—
163#104×C61—22no—
164#104×C61—22no—
165#104×C61—41no—
166#103×C61—21no—
167#103×C61—21no—
168#103×C61—21no—
169#103×C61—21no—
170#103×C61—21no—
171#103×C61—21no—
172#103×C61D411yescharacteristic
173#103×C61D411yescharacteristic
174#102×C61—21no—
175#102×C61—21no—
176#102×C61—21no—
177#102×C61—21no—
178#102×C61—21no—
179#102×C61—21no—
180#102×C61D411yescharacteristic
181#102×C61D411yescharacteristic
182#101×C61—22no—
183#100×C61—22no—
184#100×C61—22no—
185C22⋊C8×C61—21no—
186C22⋊C8×C61—21no—
187C24×C61—21no—
188C24×C61—21no—
189C24×C61—41no—
190#41×C61—21no—
191#41×C61—21no—
192#41×C61—21no—
193#41×C61—21no—
194#41×C61—24no—
195#41×C61—24no—
196#41×C61—24no—
197#41×C61—21no—
198#41×C61—21no—
199#41×C61—21no—
200#41×C61—21no—
201#41×C61—44no—
202#41×C61—42no—
203#41×C61—42no—
204#41×C61—42no—
205#41×C61—44no—
206#41×C61—42no—
207#41×C61—42no—
208#41×C61C2×D412yes—
209#41×C61C2×D412yes—
210#41×C61C2×D412yes—
211#41×C61#4112yes—
212C2×Q8×C61—21no—
213C2×Q8×C61—24no—
214C2×Q8×C61—24no—
215C2×Q8×C61—21no—
216C2×Q8×C61—21no—
217C2×Q8×C61—21no—
218C2×Q8×C61—21no—
219C2×Q8×C61—41no—
220C2×Q8×C61—42no—
221C2×Q8×C61—42no—
222C2×Q8×C61C2×D412yes—
223C2×Q8×C61C2×D411yescharacteristic
224C2×Q8×C61C2×D411yescharacteristic
225C2×Q8×C61C2×D411yescharacteristic
226C2×D4×C61—21no—
227C2×D4×C61—21no—
228C2×D4×C61—24no—
229C2×D4×C61—21no—
230C2×D4×C61—21no—
231C2×D4×C61—21no—
232C2×D4×C61—21no—
233C2×D4×C61—21no—
234C2×D4×C61—21no—
235C2×D4×C61—21no—
236C2×D4×C61—21no—
237C2×D4×C61—21no—
238C2×D4×C61—21no—
239C2×D4×C61—21no—
240C2×D4×C61—21no—
241C2×D4×C61—42no—
242C2×D4×C61—41no—
243C2×D4×C61—41no—
244C2×D4×C61—41no—
245C2×D4×C61—41no—
246C2×D4×C61—42no—
247C2×D4×C61—44no—
248C2×D4×C61—44no—
249C2×D4×C61—41no—
250C2×D4×C61—42no—
251C2×D4×C61C2×D412yes—
252C2×D4×C61C2×D411yescharacteristic
253C2×D4×C61C2×D411yescharacteristic
254C2×D4×C61C2×D411yescharacteristic
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61—21no—
261C22×C4×C61—41no—
262C22×C4×C61—41no—
263C22×C4×C61—41no—
264C22×C4×C61—41no—
265C22×C4×C61C2411yescharacteristic
266Q16×C61—24no—
267Q16×C61—22no—
268SD16×C61—24no—
269SD16×C61—24no—
270SD16×C61—24no—
271SD16×C61—22no—
272SD16×C61—24no—
273SD16×C61—22no—
274SD16×C61—42no—
275SD16×C61—42no—
276D8×C61—24no—
277D8×C61—22no—
278D8×C61—42no—
279D8×C61—42no—
280D8×C61—42no—
281D8×C61—42no—
282M16×C61—24no—
283M16×C61—21no—
284M16×C61—21no—
285M16×C61—21no—
286M16×C61—21no—
287M16×C61—21no—
288M16×C61—21no—
289M16×C61—21no—
290M16×C61—42no—
291M16×C61C2×D412yes—
292C2×C8×C61—24no—
293C2×C8×C61—21no—
294C2×C8×C61—21no—
295C2×C8×C61—21no—
296C2×C8×C61—21no—
297C2×C8×C61—21no—
298C2×C8×C61—21no—
299C2×C8×C61—21no—
300C2×C8×C61—21no—
301C2×C8×C61—42no—
302C2×C8×C61C2×D411yescharacteristic
303C2×C8×C61C2×D411yescharacteristic
304C2×C8×C61C2×D411yescharacteristic
305C2×C8×C61C2×D411yescharacteristic
306C4⋊C4×C61—21no—
307C4⋊C4×C61—21no—
308C4⋊C4×C61—41no—
309C4⋊C4×C61C2×D411yescharacteristic
310C4⋊C4×C61C2×D411yescharacteristic
311C22⋊C4×C61—21no—
312C22⋊C4×C61—41no—
313C22⋊C4×C61—41no—
314C22⋊C4×C61—41no—
315C22⋊C4×C61—44no—
316C22⋊C4×C61—82no—
317C42×C61—21no—
318C42×C61—21no—
319C42×C61—21no—
320C42×C61—41no—
321C23×C61—21no—
322C23×C61—21no—
323C23×C61—21no—
324C23×C61—22no—
325C23×C61—44no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61—81no—
332C23×C61—81no—
333C23×C61—81no—
334C23×C61—81no—
335C23×C61—161no—
336C23×C61—161no—
337C23×C61H(5,𝔽2)11yescharacteristic
338Q8×C61—21no—
339Q8×C61—21no—
340Q8×C61—22no—
341Q8×C61—21no—
342Q8×C61—22no—
343Q8×C61—21no—
344Q8×C61—44no—
345Q8×C61—41no—
346Q8×C61—41no—
347Q8×C61#12012yes—
348Q8×C61#12112yes—
349D4×C61—22no—
350D4×C61—22no—
351D4×C61—22no—
352D4×C61—22no—
353D4×C61—22no—
354D4×C61—21no—
355D4×C61—21no—
356D4×C61—22no—
357D4×C61—21no—
358D4×C61—21no—
359D4×C61—44no—
360D4×C61—44no—
361D4×C61—44no—
362D4×C61—41no—
363D4×C61—41no—
364D4×C61—41no—
365D4×C61—41no—
366D4×C61—41no—
367D4×C61—41no—
368D4×C61—41no—
369D4×C61—41no—
370D4×C61—161no—
371D4×C61—161no—
372D4×C61#12012yes—
373D4×C61#12112yes—
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—22no—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—21no—
384C2×C4×C61—44no—
385C2×C4×C61—44no—
386C2×C4×C61—44no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—81no—
396C2×C4×C61—161no—
397C2×C4×C61C22×D411yescharacteristic
398C2×C4×C61C22×D411yescharacteristic
399C2×C4×C61C22×D411yescharacteristic
400C2×C4×C61C22×D411yescharacteristic
401C2×C4×C61C2×#4111yescharacteristic
402C2×C4×C61H(5,𝔽2)11yescharacteristic
403C8×C61—21no—
404C8×C61—22no—
405C8×C61—21no—
406C8×C61—21no—
407C8×C61—21no—
408C8×C61—41no—
409C8×C61—41no—
410C8×C61—41no—
411#24460C6111yesmaximal, characteristic, direct product factor, Sylow
412C22×C61—21no—
413C22×C61—21no—
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—41no—
420C22×C61—41no—
421C22×C61—42no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61—82no—
425C22×C61—82no—
426C22×C61—81no—
427C22×C61—81no—
428C22×C61—81no—
429C22×C61—81no—
430C22×C61—81no—
431C22×C61—161no—
432C22×C61—161no—
433C22×C61—164no—
434C22×C61#53411yescharacteristic
435C22×C61D4211yescharacteristic
436C22×C61#54611yescharacteristic
437C4×C61—22no—
438C4×C61—22no—
439C4×C61—41no—
440C4×C61—42no—
441C4×C61—41no—
442C4×C61—41no—
443C4×C61—81no—
444C4×C61—81no—
445C4×C61C2×#12011yescharacteristic
446C4×C61C2×#12111yescharacteristic
447C4×C61D4211yescharacteristic
448C4×C61#54611yescharacteristic
449C2×#577C2×C6111yescharacteristic, complemented
450C2×#472C2×C6111yescharacteristic, complemented
451#3045C2×C6111yescharacteristic, complemented
452C2×#454C2×C6111yescharacteristic, complemented
453#3008C2×C6111yescharacteristic, complemented
454#2898C2×C6111yescharacteristic, complemented
455#2052C2×C6111yescharacteristic, complemented
456#2046C2×C6111yescharacteristic, complemented
457#2012C2×C6111yescharacteristic, complemented
458#2004C2×C6111yescharacteristic, complemented
459#1907C2×C6111yescharacteristic, complemented
460#1883C2×C6111yescharacteristic, complemented
461#1876C2×C6111yescharacteristic, complemented
462#1866C2×C6111yescharacteristic, complemented
463#1792C2×C6111yescharacteristic, complemented
464C2×C61—21no—
465C2×C61—21no—
466C2×C61—42no—
467C2×C61—42no—
468C2×C61—81no—
469C2×C61—82no—
470C2×C61—161no—
471C2×C61#241011yescharacteristic
472C2×C61#328811yescharacteristic
473C2×C61#329011yescharacteristic
474C2×2−1+4C22×C6111yescharacteristic
475C2×H(5,𝔽2)C22×C6111yescharacteristic
476#577—24no—
477#577—24no—
478C2×#137—21no—
479C2×#137C22×C6111yescharacteristic
480C2×AGL(1,ℤ/8)—21no—
481C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
482C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
483C2×AGL(1,ℤ/8)C22×C6111yescharacteristic, complemented
484C2×#135—21no—
485C2×#135C22×C6111yescharacteristic
486C22×SD16—21no—
487C22×SD16C22×C6111yescharacteristic
488C22×D8C22×C6111yescharacteristic
489C2×#131C22×C6111yescharacteristic
490C2×#131C22×C6111yescharacteristic, complemented
491#535C22×C6111yescharacteristic
492C2×#124C22×C6111yescharacteristic, complemented
493#520C22×C6111yescharacteristic, complemented
494#472—24no—
495#464—21no—
496#463—21no—
497#460—21no—
498#459—21no—
499#454—24no—
500#449—21no—
501#449—21no—
502#447—21no—
503#447—21no—
504C2×#108C22×C6111yescharacteristic, complemented
505#424C22×C6111yescharacteristic, complemented
506C2×#104C22×C6111yescharacteristic
507C2×#104C22×C6111yescharacteristic
508C2×#104C22×C6111yescharacteristic, complemented
509#419—21no—
510#419C22×C6111yescharacteristic, complemented
511#418C22×C6111yescharacteristic
512#417—21no—
513#417C22×C6111yescharacteristic
514#417C22×C6111yescharacteristic
515#416—21no—
516#416C22×C6111yescharacteristic
517C2×#103—21no—
518C2×#103C22×C6111yescharacteristic, complemented
519C2×#102C22×C6111yescharacteristic, complemented
520C2×#101C22×C6111yescharacteristic, complemented
521C2×#100C22×C6111yescharacteristic
522C2×#100C22×C6111yescharacteristic, complemented
523#408C22×C6111yescharacteristic
524#390C22×C6111yescharacteristic
525#343C22×C6111yescharacteristic, complemented
526#341C22×C6111yescharacteristic, complemented
527#339C22×C6111yescharacteristic, complemented
528#336C22×C6111yescharacteristic, complemented
529C61#2446011yescharacteristic, direct product factor, Sylow
5302−1+4—22no—
5312−1+4—22no—
5322−1+4—41no—
5332−1+4D4×C6114yescomplemented
534H(5,𝔽2)—22no—
535H(5,𝔽2)—22no—
536H(5,𝔽2)—22no—
537H(5,𝔽2)—41no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—41no—
543C2×#41C23×C6111yescharacteristic
544C2×#41C23×C6111yescharacteristic
545C2×#41C23×C6111yescharacteristic
546C22×Q8—21no—
547C22×Q8—21no—
548C22×Q8C23×C6111yescharacteristic
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—41no—
552C22×D4C23×C6111yescharacteristic
553C22×D4C23×C6111yescharacteristic
554#137—28no—
555#137—22no—
556#137—22no—
557AGL(1,ℤ/8)—28no—
558AGL(1,ℤ/8)—22no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—22no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)D4×C6114yescomplemented
564#135—28no—
565#135—22no—
566#135—22no—
567C2×Q16—21no—
568C2×Q16D4×C6111yescharacteristic
569C2×SD16—28no—
570C2×SD16—21no—
571C2×SD16—22no—
572C2×SD16—21no—
573C2×SD16—22no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16D4×C6111yescharacteristic
579C2×SD16D4×C6111yescharacteristic
580C2×D8—21no—
581C2×D8—22no—
582C2×D8—21no—
583C2×D8—21no—
584C2×D8—21no—
585C2×D8—21no—
586C2×D8—41no—
587C2×D8D4×C6111yescharacteristic
588#131—22no—
589#131—22no—
590#131—22no—
591#131—41no—
592C2×M16—21no—
593C2×M16—21no—
594C2×M16C23×C6111yescharacteristic
595C2×M16C23×C6111yescharacteristic
596C2×M16C23×C6111yescharacteristic
597C2×M16C23×C6111yescharacteristic
598C22×C8—21no—
599C22×C8—21no—
600C22×C8C23×C6111yescharacteristic
601C22×C8C23×C6111yescharacteristic
602#127—21no—
603#124—22no—
604#124—21no—
605#124—41no—
606#121—21no—
607#121—21no—
608#120—41no—
609C4×Q8—21no—
610C4×D4—21no—
611C4×D4—41no—
612#117—21no—
613#117C23×C6111yescharacteristic
614C2×C4⋊C4—21no—
615C2×C4⋊C4C23×C6111yescharacteristic
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C42C23×C6111yescharacteristic
619#108—22no—
620C4⋊C8—21no—
621C4⋊C8—21no—
622#104—22no—
623#104—22no—
624#104—41no—
625#103—21no—
626#103—21no—
627#103—21no—
628#103—21no—
629#103—21no—
630#103—21no—
631#103D4×C6111yescharacteristic
632#103D4×C6111yescharacteristic
633#102—21no—
634#102—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102D4×C6111yescharacteristic
640#102D4×C6111yescharacteristic
641#101—22no—
642#100—22no—
643#100—22no—
644C22⋊C8—21no—
645C22⋊C8—21no—
646C24—21no—
647C24—21no—
648C24—41no—
649#41—21no—
650#41—21no—
651#41—21no—
652#41—21no—
653#41—24no—
654#41—24no—
655#41—24no—
656#41—21no—
657#41—21no—
658#41—21no—
659#41—21no—
660#41—44no—
661#41—42no—
662#41—42no—
663#41—42no—
664#41—44no—
665#41—42no—
666#41—42no—
667#41C2×D4×C6112yes—
668#41C2×D4×C6112yes—
669#41C2×D4×C6112yes—
670#41#41×C6112yes—
671C2×Q8—21no—
672C2×Q8—24no—
673C2×Q8—24no—
674C2×Q8—21no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—41no—
679C2×Q8—42no—
680C2×Q8—42no—
681C2×Q8C2×D4×C6112yes—
682C2×Q8C2×D4×C6111yescharacteristic
683C2×Q8C2×D4×C6111yescharacteristic
684C2×Q8C2×D4×C6111yescharacteristic
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—24no—
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—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—42no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4—41no—
705C2×D4—42no—
706C2×D4—44no—
707C2×D4—44no—
708C2×D4—41no—
709C2×D4—42no—
710C2×D4C2×D4×C6112yes—
711C2×D4C2×D4×C6111yescharacteristic
712C2×D4C2×D4×C6111yescharacteristic
713C2×D4C2×D4×C6111yescharacteristic
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4—41no—
724C22×C4C24×C6111yescharacteristic
725Q16—24no—
726Q16—22no—
727SD16—24no—
728SD16—24no—
729SD16—24no—
730SD16—22no—
731SD16—24no—
732SD16—22no—
733SD16—42no—
734SD16—42no—
735D8—24no—
736D8—22no—
737D8—42no—
738D8—42no—
739D8—42no—
740D8—42no—
741M16—24no—
742M16—21no—
743M16—21no—
744M16—21no—
745M16—21no—
746M16—21no—
747M16—21no—
748M16—21no—
749M16—42no—
750M16C2×D4×C6112yes—
751C2×C8—24no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—42no—
761C2×C8C2×D4×C6111yescharacteristic
762C2×C8C2×D4×C6111yescharacteristic
763C2×C8C2×D4×C6111yescharacteristic
764C2×C8C2×D4×C6111yescharacteristic
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—41no—
768C4⋊C4C2×D4×C6111yescharacteristic
769C4⋊C4C2×D4×C6111yescharacteristic
770C22⋊C4—21no—
771C22⋊C4—41no—
772C22⋊C4—41no—
773C22⋊C4—41no—
774C22⋊C4—44no—
775C22⋊C4—82no—
776C42—21no—
777C42—21no—
778C42—21no—
779C42—41no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—22no—
784C23—44no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—81no—
791C23—81no—
792C23—81no—
793C23—81no—
794C23—161no—
795C23—161no—
796C23H(5,𝔽2)×C6111yescharacteristic
797Q8—21no—
798Q8—21no—
799Q8—21no—
800Q8—22no—
801Q8—21no—
802Q8—22no—
803Q8—44no—
804Q8—41no—
805Q8—41no—
806Q8#120×C6112yes—
807Q8#121×C6112yes—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—21no—
813D4—22no—
814D4—21no—
815D4—21no—
816D4—22no—
817D4—21no—
818D4—44no—
819D4—44no—
820D4—44no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—161no—
830D4—161no—
831D4#120×C6112yes—
832D4#121×C6112yes—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—81no—
855C2×C4—161no—
856C2×C4C22×D4×C6111yescharacteristic
857C2×C4C22×D4×C6111yescharacteristic
858C2×C4C22×D4×C6111yescharacteristic
859C2×C4C22×D4×C6111yescharacteristic
860C2×C4C2×#41×C6111yescharacteristic
861C2×C4H(5,𝔽2)×C6111yescharacteristic
862C8—21no—
863C8—21no—
864C8—21no—
865C8—22no—
866C8—21no—
867C8—41no—
868C8—41no—
869C8—41no—
870C22—21no—
871C22—21no—
872C22—22no—
873C22—22no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—42no—
882C22—82no—
883C22—82no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—161no—
890C22—161no—
891C22—164no—
892C22C61×#53411yescharacteristic
893C22D42×C6111yescharacteristic
894C22C61×#54611yescharacteristic
895C4—22no—
896C4—22no—
897C4—41no—
898C4—41no—
899C4—41no—
900C4—42no—
901C4—81no—
902C4—81no—
903C4C2×#120×C6111yescharacteristic
904C4C2×#121×C6111yescharacteristic
905C4D42×C6111yescharacteristic
906C4C61×#54611yescharacteristic
907C2—21no—
908C2—21no—
909C2—42no—
910C2—42no—
911C2—81no—
912C2—82no—
913C2—161no—
914C2C61×#241011yescharacteristic
915C2C61×#328811yescharacteristic
916C2C61×#329011yescharacteristic
subgroupG/H
center, socleC22×C61D42
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C22×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#577C2semidirect
2. C2×C61×#472C2semidirect
3. C61×#3045C2semidirect
4. C2×C61×#454C2semidirect
5. C61×#3008C2semidirect
6. C61×#2898C2semidirect
7. C61×#2052C2semidirect
8. C61×#2046C2semidirect
9. C61×#2012C2semidirect
10. C61×#2004C2semidirect
11. C61×#1907C2semidirect
12. C61×#1883C2semidirect
13. C61×#1876C2semidirect
14. C61×#1866C2semidirect
15. C61×#1792C2semidirect
25. C2×AGL(1,ℤ/8)×C61C22semidirect
32. C2×#131×C61C22semidirect
34. C2×#124×C61C22semidirect
35. C61×#520C22semidirect
46. C2×#108×C61C22semidirect
47. C61×#424C22semidirect
50. C2×#104×C61C22semidirect
52. C61×#419C22semidirect
60. C2×#103×C61C22semidirect
61. C2×#102×C61C22semidirect
62. C2×#101×C61C22semidirect
64. C2×#100×C61C22semidirect
67. C61×#343C22semidirect
68. C61×#341C22semidirect
69. C61×#339C22semidirect
70. C61×#336C22semidirect
74. 2−1+4×C61D4semidirect
104. AGL(1,ℤ/8)×C61D4semidirect
411. #24460C61direct (N × H)
449. C2×#577C2×C61semidirect
450. C2×#472C2×C61semidirect
451. #3045C2×C61semidirect
452. C2×#454C2×C61semidirect
453. #3008C2×C61semidirect
454. #2898C2×C61semidirect
455. #2052C2×C61semidirect
456. #2046C2×C61semidirect
457. #2012C2×C61semidirect
458. #2004C2×C61semidirect
459. #1907C2×C61semidirect
460. #1883C2×C61semidirect
461. #1876C2×C61semidirect
462. #1866C2×C61semidirect
463. #1792C2×C61semidirect
483. C2×AGL(1,ℤ/8)C22×C61semidirect
490. C2×#131C22×C61semidirect
492. C2×#124C22×C61semidirect
493. #520C22×C61semidirect
504. C2×#108C22×C61semidirect
505. #424C22×C61semidirect
508. C2×#104C22×C61semidirect
510. #419C22×C61semidirect
518. C2×#103C22×C61semidirect
519. C2×#102C22×C61semidirect
520. C2×#101C22×C61semidirect
522. C2×#100C22×C61semidirect
525. #343C22×C61semidirect
526. #341C22×C61semidirect
527. #339C22×C61semidirect
528. #336C22×C61semidirect
529. C61#24460direct (N × H)
533. 2−1+4D4×C61semidirect
563. 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×#5772
C2×C61×#4722
C61×#30452
C2×C61×#4542
C61×#30082
C61×#28982
C61×#20522
C61×#20462
C61×#20122
C61×#20042
C61×#19072
C61×#18832
C61×#18762
C61×#18662
C61×#17922
#2446061