Finite Group Databasebeta

← C61×#24475 #29527908

Subgroups — C61×#24475 #29527908

Order 15616.

1324 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3585C211yesmaximal, characteristic
2C61×#3069C211yesmaximal, characteristic, complemented
3C61×#3040C211yesmaximal, characteristic, complemented
4C61×#3022C211yesmaximal, characteristic, complemented
5C2×C61×#455C211yesmaximal, characteristic, complemented
6C61×#2901C211yesmaximal, characteristic, complemented
7C61×#2050C211yesmaximal, characteristic, complemented
8C61×#2048C211yesmaximal, characteristic, complemented
9C61×#2009C211yesmaximal, characteristic, complemented
10C61×#2003C211yesmaximal, characteristic, complemented
11C61×#1906C211yesmaximal, characteristic, complemented
12C61×#1903C211yesmaximal, characteristic, complemented
13C61×#1902C211yesmaximal, characteristic, complemented
14C61×#1861C211yesmaximal, characteristic, complemented
15C61×#1795C211yesmaximal, characteristic, complemented
16C61×#585C2211yescharacteristic
17C2×H(5,𝔽2)×C61C2211yescharacteristic
18C61×#577—22no—
19C61×#577—22no—
20C61×#576—22no—
21C61×#576—22no—
22C61×#575—22no—
23C61×#575C2211yescharacteristic
24C61×#575C2211yescharacteristic
25C2×#137×C61C2211yescharacteristic
26C2×#137×C61C2211yescharacteristic, complemented
27C2×#137×C61C2211yescharacteristic, complemented
28C2×AGL(1,ℤ/8)×C61—22no—
29C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
31C61×#568C2211yescharacteristic
32C61×#568C2211yescharacteristic, complemented
33C61×#536C2211yescharacteristic, complemented
34C2×#124×C61C2211yescharacteristic, complemented
35C4×#41×C61C2211yescharacteristic, complemented
36C61×#473—22no—
37C61×#471—22no—
38C61×#464—22no—
39C61×#463—22no—
40C61×#456—22no—
41C61×#455—22no—
42C61×#455—22no—
43C61×#455—22no—
44C61×#430C2211yescharacteristic, complemented
45C61×#423C2211yescharacteristic, complemented
46C61×#421—22no—
47C61×#421C2211yescharacteristic
48C61×#421C2211yescharacteristic
49C61×#421C2211yescharacteristic, complemented
50C61×#421C2211yescharacteristic, complemented
51C2×#104×C61—22no—
52C2×#104×C61C2211yescharacteristic
53C2×#104×C61C2211yescharacteristic, complemented
54C2×#104×C61C2211yescharacteristic, complemented
55C61×#419C2211yescharacteristic, complemented
56C61×#418C2211yescharacteristic, complemented
57C61×#418C2211yescharacteristic, complemented
58C61×#413C2211yescharacteristic, complemented
59C61×#413C2211yescharacteristic, complemented
60C2×#101×C61C2211yescharacteristic, complemented
61C2×#100×C61C2211yescharacteristic, complemented
62C61×#410C2211yescharacteristic, complemented
63C61×#344C2211yescharacteristic, complemented
64C61×#344C2211yescharacteristic, complemented
65C61×#339C2211yescharacteristic, complemented
66C61×#338C2211yescharacteristic, complemented
672−1+4×C61—21no—
682−1+4×C61—21no—
692−1+4×C61D412yes—
70H(5,𝔽2)×C61—22no—
71H(5,𝔽2)×C61—21no—
72H(5,𝔽2)×C61—22no—
73H(5,𝔽2)×C61—21no—
74H(5,𝔽2)×C61—22no—
75H(5,𝔽2)×C61—41no—
76H(5,𝔽2)×C61—41no—
77H(5,𝔽2)×C61D412yes—
78C2×#41×C61—22no—
79C2×#41×C61—22no—
80C2×#41×C61—21no—
81C2×#41×C61—21no—
82C2×#41×C61—41no—
83C2×#41×C61C2311yescharacteristic
84C2×#41×C61C2311yescharacteristic
85C2×#41×C61C2311yescharacteristic
86C2×#41×C61C2311yescharacteristic
87C22×Q8×C61C2311yescharacteristic
88C22×D4×C61—21no—
89C22×D4×C61—21no—
90C22×D4×C61—41no—
91C22×D4×C61C2311yescharacteristic
92#137×C61—24no—
93#137×C61—21no—
94#137×C61—21no—
95#137×C61—21no—
96#137×C61—22no—
97#137×C61—22no—
98#137×C61—22no—
99#137×C61—22no—
100#137×C61—22no—
101#137×C61—41no—
102#137×C61D412yes—
103AGL(1,ℤ/8)×C61—24no—
104AGL(1,ℤ/8)×C61—24no—
105AGL(1,ℤ/8)×C61—24no—
106AGL(1,ℤ/8)×C61—22no—
107AGL(1,ℤ/8)×C61—22no—
108AGL(1,ℤ/8)×C61—21no—
109AGL(1,ℤ/8)×C61—22no—
110AGL(1,ℤ/8)×C61—21no—
111AGL(1,ℤ/8)×C61—21no—
112AGL(1,ℤ/8)×C61—22no—
113AGL(1,ℤ/8)×C61D412yes—
114#135×C61—24no—
115#135×C61—24no—
116#135×C61—22no—
117#135×C61—22no—
118C2×Q16×C61—21no—
119C2×Q16×C61—21no—
120C2×Q16×C61—21no—
121C2×SD16×C61—24no—
122C2×SD16×C61—21no—
123C2×SD16×C61—21no—
124C2×SD16×C61—21no—
125C2×SD16×C61—21no—
126C2×SD16×C61D412yes—
127C2×D8×C61—24no—
128C2×D8×C61—21no—
129C2×D8×C61D412yes—
130#131×C61—22no—
131#131×C61—22no—
132#131×C61—22no—
133#131×C61—41no—
134C2×M16×C61—22no—
135C2×M16×C61—22no—
136C2×M16×C61C2311yescharacteristic
137C2×M16×C61C2311yescharacteristic
138C2×M16×C61C2311yescharacteristic
139C2×M16×C61C2311yescharacteristic
140C2×M16×C61C2311yescharacteristic
141C2×M16×C61C2311yescharacteristic
142C4⋊Q8×C61—21no—
143#124×C61—21no—
144#124×C61—22no—
145#124×C61—21no—
146#124×C61—21no—
147#123×C61—41no—
148C22⋊Q8×C61—41no—
149C4×Q8×C61—21no—
150C4×D4×C61—21no—
151C4×D4×C61—41no—
152#117×C61—21no—
153#117×C61C2311yescharacteristic
154#117×C61C2311yescharacteristic
155C2×C22⋊C4×C61—41no—
156C2×C42×C61—21no—
157C2×C42×C61C2311yescharacteristic
158#108×C61—22no—
159C4⋊C8×C61—22no—
160#104×C61—22no—
161#104×C61—22no—
162#104×C61—22no—
163#104×C61—22no—
164#104×C61—21no—
165#104×C61—21no—
166#104×C61—21no—
167#104×C61—21no—
168#104×C61D412yes—
169#104×C61D412yes—
170#103×C61—22no—
171#102×C61—22no—
172#102×C61—41no—
173#101×C61—21no—
174#101×C61—21no—
175#101×C61—22no—
176#100×C61—21no—
177#100×C61—21no—
178#100×C61—22no—
179#99×C61—41no—
180C24×C61—21no—
181C24×C61—41no—
182#41×C61—21no—
183#41×C61—21no—
184#41×C61—21no—
185#41×C61—21no—
186#41×C61—24no—
187#41×C61—22no—
188#41×C61—22no—
189#41×C61—22no—
190#41×C61—22no—
191#41×C61—21no—
192#41×C61—21no—
193#41×C61—21no—
194#41×C61—21no—
195#41×C61—21no—
196#41×C61—21no—
197#41×C61—21no—
198#41×C61—21no—
199#41×C61—42no—
200#41×C61—42no—
201#41×C61—42no—
202#41×C61—42no—
203#41×C61—42no—
204#41×C61—42no—
205#41×C61—41no—
206#41×C61—41no—
207#41×C61—42no—
208#41×C61C2×D412yes—
209#41×C61C2×D412yes—
210#41×C61C2×D412yes—
211#41×C61C2×D412yes—
212C2×Q8×C61—22no—
213C2×Q8×C61—22no—
214C2×Q8×C61—21no—
215C2×Q8×C61—21no—
216C2×Q8×C61—21no—
217C2×Q8×C61—21no—
218C2×Q8×C61—21no—
219C2×Q8×C61—21no—
220C2×Q8×C61—41no—
221C2×Q8×C61C2×D411yescharacteristic
222C2×Q8×C61C2×D411yescharacteristic
223C2×Q8×C61C2×D411yescharacteristic
224C2×Q8×C61#4111yescharacteristic
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61—24no—
228C2×D4×C61—22no—
229C2×D4×C61—22no—
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—42no—
238C2×D4×C61—41no—
239C2×D4×C61—41no—
240C2×D4×C61—42no—
241C2×D4×C61—42no—
242C2×D4×C61—41no—
243C2×D4×C61—44no—
244C2×D4×C61—42no—
245C2×D4×C61—42no—
246C2×D4×C61—44no—
247C2×D4×C61—42no—
248C2×D4×C61C2×D411yescharacteristic
249C2×D4×C61C2×D411yescharacteristic
250C2×D4×C61C2×D412yes—
251C2×D4×C61C2×D411yescharacteristic
252C2×D4×C61#4111yescharacteristic
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—41no—
260C22×C4×C61—42no—
261C22×C4×C61—41no—
262C22×C4×C61C2411yescharacteristic
263Q16×C61—22no—
264Q16×C61—22no—
265Q16×C61—42no—
266Q16×C61—42no—
267Q16×C61—42no—
268SD16×C61—24no—
269SD16×C61—22no—
270SD16×C61—22no—
271SD16×C61—22no—
272SD16×C61—24no—
273SD16×C61—22no—
274SD16×C61—42no—
275SD16×C61—42no—
276SD16×C61—42no—
277D8×C61—24no—
278D8×C61—22no—
279D8×C61—22no—
280D8×C61—24no—
281M16×C61—24no—
282M16×C61—21no—
283M16×C61—21no—
284M16×C61—21no—
285M16×C61—21no—
286M16×C61—21no—
287M16×C61—21no—
288M16×C61—21no—
289M16×C61—21no—
290M16×C61—21no—
291M16×C61—21no—
292M16×C61—42no—
293M16×C61C2×D412yes—
294M16×C61C2×D412yes—
295C2×C8×C61—24no—
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×D412yes—
303C4⋊C4×C61—21no—
304C4⋊C4×C61—21no—
305C4⋊C4×C61—41no—
306C4⋊C4×C61—42no—
307C22⋊C4×C61—21no—
308C22⋊C4×C61—21no—
309C22⋊C4×C61—42no—
310C22⋊C4×C61—42no—
311C22⋊C4×C61—41no—
312C22⋊C4×C61—42no—
313C42×C61—21no—
314C42×C61—21no—
315C42×C61—21no—
316C42×C61—41no—
317C42×C61C2×D411yescharacteristic
318C42×C61C2×D411yescharacteristic
319C23×C61—21no—
320C23×C61—21no—
321C23×C61—21no—
322C23×C61—22no—
323C23×C61—21no—
324C23×C61—42no—
325C23×C61—44no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61—82no—
329C23×C61—162no—
330C23×C61H(5,𝔽2)11yescharacteristic
331Q8×C61—21no—
332Q8×C61—21no—
333Q8×C61—21no—
334Q8×C61—21no—
335Q8×C61—21no—
336Q8×C61—21no—
337Q8×C61—42no—
338Q8×C61—41no—
339Q8×C61—41no—
340Q8×C61—41no—
341Q8×C61—41no—
342Q8×C61#12012yes—
343Q8×C61#12112yes—
344D4×C61—22no—
345D4×C61—22no—
346D4×C61—22no—
347D4×C61—22no—
348D4×C61—21no—
349D4×C61—21no—
350D4×C61—22no—
351D4×C61—21no—
352D4×C61—21no—
353D4×C61—21no—
354D4×C61—21no—
355D4×C61—22no—
356D4×C61—42no—
357D4×C61—42no—
358D4×C61—44no—
359D4×C61—42no—
360D4×C61—44no—
361D4×C61—41no—
362D4×C61—41no—
363D4×C61—41no—
364D4×C61—41no—
365D4×C61—41no—
366D4×C61—41no—
367D4×C61#12012yes—
368D4×C61#12112yes—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—42no—
380C2×C4×C61—42no—
381C2×C4×C61—42no—
382C2×C4×C61—44no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—81no—
393C2×C4×C61—82no—
394C2×C4×C61C22×D411yescharacteristic
395C2×C4×C61C22×D411yescharacteristic
396C2×C4×C61C22×D411yescharacteristic
397C2×C4×C61C22×D411yescharacteristic
398C2×C4×C61C2×#4111yescharacteristic
399C2×C4×C61H(5,𝔽2)11yescharacteristic
400C8×C61—22no—
401C8×C61—22no—
402C8×C61—22no—
403C8×C61—41no—
404C8×C61—41no—
405C8×C61—41no—
406#24475C6111yesmaximal, characteristic, direct product factor, Sylow
407C22×C61—22no—
408C22×C61—22no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61—42no—
412C22×C61—41no—
413C22×C61—81no—
414C22×C61—81no—
415C22×C61—81no—
416C22×C61—82no—
417C22×C61—81no—
418C22×C61—82no—
419C22×C61—161no—
420C22×C61—162no—
421C22×C61—164no—
422C22×C61#53411yescharacteristic
423C22×C61D4211yescharacteristic
424C22×C61#54611yescharacteristic
425C4×C61—22no—
426C4×C61—22no—
427C4×C61—41no—
428C4×C61—41no—
429C4×C61—41no—
430C4×C61—41no—
431C4×C61—81no—
432C4×C61—81no—
433C4×C61—81no—
434C4×C61C2×#12011yescharacteristic
435C4×C61C2×#12111yescharacteristic
436C4×C61D4211yescharacteristic
437C4×C61#54611yescharacteristic
438#3585C2×C6111yescharacteristic
439#3069C2×C6111yescharacteristic, complemented
440#3040C2×C6111yescharacteristic, complemented
441#3022C2×C6111yescharacteristic, complemented
442C2×#455C2×C6111yescharacteristic, complemented
443#2901C2×C6111yescharacteristic, complemented
444#2050C2×C6111yescharacteristic, complemented
445#2048C2×C6111yescharacteristic, complemented
446#2009C2×C6111yescharacteristic, complemented
447#2003C2×C6111yescharacteristic, complemented
448#1906C2×C6111yescharacteristic, complemented
449#1903C2×C6111yescharacteristic, complemented
450#1902C2×C6111yescharacteristic, complemented
451#1861C2×C6111yescharacteristic, complemented
452#1795C2×C6111yescharacteristic, complemented
453C2×C61—21no—
454C2×C61—21no—
455C2×C61—21no—
456C2×C61—42no—
457C2×C61—42no—
458C2×C61—82no—
459C2×C61—81no—
460C2×C61—81no—
461C2×C61#241011yescharacteristic
462#585C22×C6111yescharacteristic
463C2×H(5,𝔽2)C22×C6111yescharacteristic
464#577—22no—
465#577—22no—
466#576—22no—
467#576—22no—
468#575—22no—
469#575C22×C6111yescharacteristic
470#575C22×C6111yescharacteristic
471C2×#137C22×C6111yescharacteristic
472C2×#137C22×C6111yescharacteristic, complemented
473C2×#137C22×C6111yescharacteristic, complemented
474C2×AGL(1,ℤ/8)—22no—
475C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
476C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
477#568C22×C6111yescharacteristic
478#568C22×C6111yescharacteristic, complemented
479#536C22×C6111yescharacteristic, complemented
480C2×#124C22×C6111yescharacteristic, complemented
481C4×#41C22×C6111yescharacteristic, complemented
482#473—22no—
483#471—22no—
484#464—22no—
485#463—22no—
486#456—22no—
487#455—22no—
488#455—22no—
489#455—22no—
490#430C22×C6111yescharacteristic, complemented
491#423C22×C6111yescharacteristic, complemented
492#421—22no—
493#421C22×C6111yescharacteristic
494#421C22×C6111yescharacteristic
495#421C22×C6111yescharacteristic, complemented
496#421C22×C6111yescharacteristic, complemented
497C2×#104—22no—
498C2×#104C22×C6111yescharacteristic
499C2×#104C22×C6111yescharacteristic, complemented
500C2×#104C22×C6111yescharacteristic, complemented
501#419C22×C6111yescharacteristic, complemented
502#418C22×C6111yescharacteristic, complemented
503#418C22×C6111yescharacteristic, complemented
504#413C22×C6111yescharacteristic, complemented
505#413C22×C6111yescharacteristic, complemented
506C2×#101C22×C6111yescharacteristic, complemented
507C2×#100C22×C6111yescharacteristic, complemented
508#410C22×C6111yescharacteristic, complemented
509#344C22×C6111yescharacteristic, complemented
510#344C22×C6111yescharacteristic, complemented
511#339C22×C6111yescharacteristic, complemented
512#338C22×C6111yescharacteristic, complemented
513C61#2447511yescharacteristic, direct product factor, Sylow
5142−1+4—21no—
5152−1+4—21no—
5162−1+4D4×C6112yes—
517H(5,𝔽2)—22no—
518H(5,𝔽2)—21no—
519H(5,𝔽2)—22no—
520H(5,𝔽2)—21no—
521H(5,𝔽2)—22no—
522H(5,𝔽2)—41no—
523H(5,𝔽2)—41no—
524H(5,𝔽2)D4×C6112yes—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—21no—
528C2×#41—21no—
529C2×#41—41no—
530C2×#41C23×C6111yescharacteristic
531C2×#41C23×C6111yescharacteristic
532C2×#41C23×C6111yescharacteristic
533C2×#41C23×C6111yescharacteristic
534C22×Q8C23×C6111yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—41no—
538C22×D4C23×C6111yescharacteristic
539#137—24no—
540#137—21no—
541#137—21no—
542#137—21no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—22no—
547#137—22no—
548#137—41no—
549#137D4×C6112yes—
550AGL(1,ℤ/8)—24no—
551AGL(1,ℤ/8)—24no—
552AGL(1,ℤ/8)—24no—
553AGL(1,ℤ/8)—22no—
554AGL(1,ℤ/8)—22no—
555AGL(1,ℤ/8)—21no—
556AGL(1,ℤ/8)—22no—
557AGL(1,ℤ/8)—21no—
558AGL(1,ℤ/8)—21no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)D4×C6112yes—
561#135—24no—
562#135—24no—
563#135—22no—
564#135—22no—
565C2×Q16—21no—
566C2×Q16—21no—
567C2×Q16—21no—
568C2×SD16—24no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16D4×C6112yes—
574C2×D8—24no—
575C2×D8—21no—
576C2×D8D4×C6112yes—
577#131—22no—
578#131—22no—
579#131—22no—
580#131—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16C23×C6111yescharacteristic
584C2×M16C23×C6111yescharacteristic
585C2×M16C23×C6111yescharacteristic
586C2×M16C23×C6111yescharacteristic
587C2×M16C23×C6111yescharacteristic
588C2×M16C23×C6111yescharacteristic
589C4⋊Q8—21no—
590#124—22no—
591#124—21no—
592#124—21no—
593#124—21no—
594#123—41no—
595C22⋊Q8—41no—
596C4×Q8—21no—
597C4×D4—21no—
598C4×D4—41no—
599#117—21no—
600#117C23×C6111yescharacteristic
601#117C23×C6111yescharacteristic
602C2×C22⋊C4—41no—
603C2×C42—21no—
604C2×C42C23×C6111yescharacteristic
605#108—22no—
606C4⋊C8—22no—
607#104—22no—
608#104—22no—
609#104—22no—
610#104—22no—
611#104—21no—
612#104—21no—
613#104—21no—
614#104—21no—
615#104D4×C6112yes—
616#104D4×C6112yes—
617#103—22no—
618#102—22no—
619#102—41no—
620#101—21no—
621#101—21no—
622#101—22no—
623#100—21no—
624#100—21no—
625#100—22no—
626#99—41no—
627C24—21no—
628C24—41no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—24no—
634#41—22no—
635#41—22no—
636#41—22no—
637#41—22no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—42no—
647#41—42no—
648#41—42no—
649#41—42no—
650#41—42no—
651#41—42no—
652#41—41no—
653#41—41no—
654#41—42no—
655#41C2×D4×C6112yes—
656#41C2×D4×C6112yes—
657#41C2×D4×C6112yes—
658#41C2×D4×C6112yes—
659C2×Q8—22no—
660C2×Q8—22no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—41no—
668C2×Q8C2×D4×C6111yescharacteristic
669C2×Q8C2×D4×C6111yescharacteristic
670C2×Q8C2×D4×C6111yescharacteristic
671C2×Q8#41×C6111yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—42no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—41no—
690C2×D4—44no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—42no—
695C2×D4C2×D4×C6111yescharacteristic
696C2×D4C2×D4×C6111yescharacteristic
697C2×D4C2×D4×C6112yes—
698C2×D4C2×D4×C6111yescharacteristic
699C2×D4#41×C6111yescharacteristic
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—41no—
707C22×C4—42no—
708C22×C4—41no—
709C22×C4C24×C6111yescharacteristic
710Q16—22no—
711Q16—22no—
712Q16—42no—
713Q16—42no—
714Q16—42no—
715SD16—24no—
716SD16—22no—
717SD16—22no—
718SD16—22no—
719SD16—24no—
720SD16—22no—
721SD16—42no—
722SD16—42no—
723SD16—42no—
724D8—24no—
725D8—22no—
726D8—22no—
727D8—24no—
728M16—24no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16—21no—
739M16—42no—
740M16C2×D4×C6112yes—
741M16C2×D4×C6112yes—
742C2×C8—24no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—42no—
749C2×C8C2×D4×C6112yes—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—41no—
753C4⋊C4—42no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—41no—
759C22⋊C4—42no—
760C42—21no—
761C42—21no—
762C42—21no—
763C42—41no—
764C42C2×D4×C6111yescharacteristic
765C42C2×D4×C6111yescharacteristic
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—21no—
771C23—42no—
772C23—44no—
773C23—41no—
774C23—41no—
775C23—82no—
776C23—162no—
777C23H(5,𝔽2)×C6111yescharacteristic
778Q8—21no—
779Q8—21no—
780Q8—21no—
781Q8—21no—
782Q8—21no—
783Q8—21no—
784Q8—42no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8#120×C6112yes—
790Q8#121×C6112yes—
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—21no—
796D4—21no—
797D4—21no—
798D4—22no—
799D4—21no—
800D4—21no—
801D4—22no—
802D4—21no—
803D4—42no—
804D4—42no—
805D4—44no—
806D4—42no—
807D4—44no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4#120×C6112yes—
815D4#121×C6112yes—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—81no—
840C2×C4—82no—
841C2×C4C22×D4×C6111yescharacteristic
842C2×C4C22×D4×C6111yescharacteristic
843C2×C4C22×D4×C6111yescharacteristic
844C2×C4C22×D4×C6111yescharacteristic
845C2×C4C2×#41×C6111yescharacteristic
846C2×C4H(5,𝔽2)×C6111yescharacteristic
847C8—22no—
848C8—22no—
849C8—22no—
850C8—41no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—41no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—82no—
863C22—81no—
864C22—82no—
865C22—161no—
866C22—162no—
867C22—164no—
868C22C61×#53411yescharacteristic
869C22D42×C6111yescharacteristic
870C22C61×#54611yescharacteristic
871C4—22no—
872C4—22no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—81no—
878C4—81no—
879C4—81no—
880C4C2×#120×C6111yescharacteristic
881C4C2×#121×C6111yescharacteristic
882C4D42×C6111yescharacteristic
883C4C61×#54611yescharacteristic
884C2—21no—
885C2—21no—
886C2—21no—
887C2—42no—
888C2—42no—
889C2—82no—
890C2—81no—
891C2—81no—
892C2C61×#241011yescharacteristic
subgroupG/H
center, socleC2×C61#2410
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3585C2
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
2. C61×#3069C2semidirect
3. C61×#3040C2semidirect
4. C61×#3022C2semidirect
5. C2×C61×#455C2semidirect
6. C61×#2901C2semidirect
7. C61×#2050C2semidirect
8. C61×#2048C2semidirect
9. C61×#2009C2semidirect
10. C61×#2003C2semidirect
11. C61×#1906C2semidirect
12. C61×#1903C2semidirect
13. C61×#1902C2semidirect
14. C61×#1861C2semidirect
15. C61×#1795C2semidirect
26. C2×#137×C61C22semidirect
27. C2×#137×C61C22semidirect
32. C61×#568C22semidirect
33. C61×#536C22semidirect
34. C2×#124×C61C22semidirect
35. C4×#41×C61C22semidirect
44. C61×#430C22semidirect
45. C61×#423C22semidirect
49. C61×#421C22semidirect
50. C61×#421C22semidirect
53. C2×#104×C61C22semidirect
54. C2×#104×C61C22semidirect
55. C61×#419C22semidirect
56. C61×#418C22semidirect
57. C61×#418C22semidirect
58. C61×#413C22semidirect
59. C61×#413C22semidirect
60. C2×#101×C61C22semidirect
61. C2×#100×C61C22semidirect
62. C61×#410C22semidirect
63. C61×#344C22semidirect
64. C61×#344C22semidirect
65. C61×#339C22semidirect
66. C61×#338C22semidirect
406. #24475C61direct (N × H)
439. #3069C2×C61semidirect
440. #3040C2×C61semidirect
441. #3022C2×C61semidirect
442. C2×#455C2×C61semidirect
443. #2901C2×C61semidirect
444. #2050C2×C61semidirect
445. #2048C2×C61semidirect
446. #2009C2×C61semidirect
447. #2003C2×C61semidirect
448. #1906C2×C61semidirect
449. #1903C2×C61semidirect
450. #1902C2×C61semidirect
451. #1861C2×C61semidirect
452. #1795C2×C61semidirect
472. C2×#137C22×C61semidirect
473. C2×#137C22×C61semidirect
478. #568C22×C61semidirect
479. #536C22×C61semidirect
480. C2×#124C22×C61semidirect
481. C4×#41C22×C61semidirect
490. #430C22×C61semidirect
491. #423C22×C61semidirect
495. #421C22×C61semidirect
496. #421C22×C61semidirect
499. C2×#104C22×C61semidirect
500. C2×#104C22×C61semidirect
501. #419C22×C61semidirect
502. #418C22×C61semidirect
503. #418C22×C61semidirect
504. #413C22×C61semidirect
505. #413C22×C61semidirect
506. C2×#101C22×C61semidirect
507. C2×#100C22×C61semidirect
508. #410C22×C61semidirect
509. #344C22×C61semidirect
510. #344C22×C61semidirect
511. #339C22×C61semidirect
512. #338C22×C61semidirect
513. C61#24475direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35852
C61×#30692
C61×#30402
C61×#30222
C2×C61×#4552
C61×#29012
C61×#20502
C61×#20482
C61×#20092
C61×#20032
C61×#19062
C61×#19032
C61×#19022
C61×#18612
C61×#17952
#2447561