Finite Group Databasebeta

← C61×#24030 #29527463

Subgroups — C61×#24030 #29527463

Order 15616.

1280 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3489C211yesmaximal, characteristic
2C61×#3092C211yesmaximal, characteristic, complemented
3C2×C61×#417C211yesmaximal, characteristic, complemented
4C61×#2502C211yesmaximal, characteristic, complemented
5C61×#2039C212yesmaximal, complemented
6C61×#2038C212yesmaximal, complemented
7C61×#1901C211yesmaximal, characteristic, complemented
8C61×#1871C211yesmaximal, characteristic, complemented
9C61×#1859C212yesmaximal, complemented
10C61×#1793C212yesmaximal, complemented
11C61×#1789C211yesmaximal, characteristic, complemented
12C2×2−1+4×C61C2211yescharacteristic
13C22×#41×C61C2211yescharacteristic
14C22×M16×C61C2211yescharacteristic
15D4×Q8×C61—21no—
16C61×#548—21no—
17C61×#547—21no—
18C61×#547—22no—
19C61×#546—21no—
20C61×#546—22no—
21C61×#537—21no—
22C61×#537C2211yescharacteristic
23C61×#536—21no—
24C61×#536C2211yescharacteristic
25C61×#525—21no—
26C61×#525C2211yescharacteristic
27C2×C22⋊Q8×C61—21no—
28C2×C22⋊Q8×C61C2211yescharacteristic
29C61×#520C2211yescharacteristic
30C22×C4⋊C4×C61C2211yescharacteristic
31C61×#484—21no—
32C61×#483—21no—
33C61×#481—21no—
34C61×#480—21no—
35C61×#428C2212yescomplemented
36C2×#104×C61C2212yes—
37C2×#104×C61C2212yes—
38C2×#104×C61C2212yescomplemented
39C61×#417—21no—
40C61×#417—21no—
41C61×#417C2212yes—
42C61×#417C2212yes—
43C61×#417C2212yescomplemented
44C2×#103×C61—21no—
45C2×#102×C61—21no—
46C2×#101×C61C2212yescomplemented
47C61×#407C2211yescharacteristic
48C61×#398—22no—
49C61×#391C2212yescomplemented
50C61×#385—22no—
51C61×#384C2212yescomplemented
52C4×C22⋊C4×C61C2211yescharacteristic
53C61×#343C2212yescomplemented
54C61×#339C2212yescomplemented
552−1+4×C61—24no—
562−1+4×C61—42no—
57C2×#41×C61—21no—
58C2×#41×C61—21no—
59C2×#41×C61—21no—
60C2×#41×C61—22no—
61C2×#41×C61—21no—
62C2×#41×C61—24no—
63C2×#41×C61—42no—
64C2×#41×C61D411yescharacteristic
65C2×#41×C61D411yescharacteristic
66C2×#41×C61C2311yescharacteristic
67C2×#41×C61C2311yescharacteristic
68C2×#41×C61C2311yescharacteristic
69C22×Q8×C61—21no—
70C22×Q8×C61—21no—
71C22×Q8×C61D411yescharacteristic
72C22×Q8×C61C2311yescharacteristic
73C22×D4×C61—21no—
74C22×D4×C61D411yescharacteristic
75C23×C4×C61—21no—
76C23×C4×C61—21no—
77C23×C4×C61C2311yescharacteristic
78C2×M16×C61—21no—
79C2×M16×C61—42no—
80C2×M16×C61C2312yes—
81C2×M16×C61C2312yes—
82C22×C8×C61—21no—
83C4⋊Q8×C61—22no—
84C4⋊Q8×C61—21no—
85#124×C61—22no—
86#124×C61—21no—
87#123×C61—22no—
88#123×C61—22no—
89#123×C61—22no—
90#123×C61—22no—
91#123×C61—21no—
92C22⋊Q8×C61—22no—
93C22⋊Q8×C61—22no—
94C22⋊Q8×C61—22no—
95C22⋊Q8×C61—21no—
96C22⋊Q8×C61—21no—
97C22⋊Q8×C61—21no—
98C22⋊Q8×C61—21no—
99C22⋊Q8×C61—21no—
100C22⋊Q8×C61—21no—
101C22⋊Q8×C61—21no—
102C22⋊Q8×C61—21no—
103C22⋊Q8×C61D411yescharacteristic
104C22⋊Q8×C61D411yescharacteristic
105#121×C61—22no—
106#121×C61—22no—
107#121×C61—22no—
108#121×C61—21no—
109#121×C61—21no—
110#121×C61—22no—
111#121×C61D411yescharacteristic
112#121×C61D411yescharacteristic
113#120×C61—22no—
114#120×C61—21no—
115C4×Q8×C61—21no—
116C4×D4×C61—22no—
117C4×D4×C61—22no—
118C4×D4×C61—21no—
119C4×D4×C61—22no—
120C4×D4×C61—21no—
121C4×D4×C61—21no—
122#117×C61—21no—
123#117×C61C2311yescharacteristic
124C2×C4⋊C4×C61—22no—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—24no—
132C2×C4⋊C4×C61D412yes—
133C2×C4⋊C4×C61C2312yes—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C22⋊C4×C61—22no—
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61D412yes—
138C2×C42×C61C2312yes—
139#107×C61—22no—
140#106×C61—22no—
141#104×C61—24no—
142#104×C61—42no—
143#104×C61—42no—
144#103×C61—22no—
145#103×C61—22no—
146#103×C61—22no—
147#102×C61—22no—
148#102×C61—22no—
149#102×C61—22no—
150#101×C61—42no—
151C22⋊C8×C61—21no—
152C22⋊C8×C61—21no—
153#95×C61—21no—
154#95×C61—24no—
155C24×C61—21no—
156C24×C61C2×D411yescharacteristic
157#41×C61—22no—
158#41×C61—22no—
159#41×C61—22no—
160#41×C61—22no—
161#41×C61—22no—
162#41×C61—22no—
163#41×C61—22no—
164#41×C61—44no—
165#41×C61—41no—
166#41×C61—41no—
167#41×C61—44no—
168#41×C61—44no—
169#41×C61—48no—
170#41×C61—42no—
171#41×C61—42no—
172#41×C61#4114yes—
173C2×Q8×C61—22no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61—22no—
178C2×Q8×C61—22no—
179C2×Q8×C61—22no—
180C2×Q8×C61—41no—
181C2×Q8×C61—44no—
182C2×Q8×C61—42no—
183C2×Q8×C61—42no—
184C2×Q8×C61C2×D411yescharacteristic
185C2×Q8×C61C2×D411yescharacteristic
186C2×Q8×C61C2×D411yescharacteristic
187C2×D4×C61—21no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—22no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—41no—
199C2×D4×C61—44no—
200C2×D4×C61C2×D411yescharacteristic
201C2×D4×C61C2×D411yescharacteristic
202C2×D4×C61C2×D411yescharacteristic
203C22×C4×C61—21no—
204C22×C4×C61—22no—
205C22×C4×C61—22no—
206C22×C4×C61—22no—
207C22×C4×C61—22no—
208C22×C4×C61—21no—
209C22×C4×C61—22no—
210C22×C4×C61—22no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—22no—
216C22×C4×C61—44no—
217C22×C4×C61—41no—
218C22×C4×C61—41no—
219C22×C4×C61—82no—
220C22×C4×C61C2×D412yes—
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D412yes—
227C22×C4×C61C2411yescharacteristic
228M16×C61—22no—
229M16×C61—22no—
230M16×C61—22no—
231M16×C61—22no—
232M16×C61—42no—
233C2×C8×C61—22no—
234C2×C8×C61—22no—
235C2×C8×C61—42no—
236C4⋊C4×C61—22no—
237C4⋊C4×C61—22no—
238C4⋊C4×C61—22no—
239C4⋊C4×C61—22no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—22no—
242C4⋊C4×C61—22no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—22no—
247C4⋊C4×C61—22no—
248C4⋊C4×C61—41no—
249C4⋊C4×C61—41no—
250C4⋊C4×C61—84no—
251C4⋊C4×C61C2×D411yescharacteristic
252C4⋊C4×C61C2×D411yescharacteristic
253C22⋊C4×C61—24no—
254C22⋊C4×C61—22no—
255C22⋊C4×C61—22no—
256C22⋊C4×C61—22no—
257C22⋊C4×C61—22no—
258C22⋊C4×C61—22no—
259C22⋊C4×C61—21no—
260C22⋊C4×C61—22no—
261C22⋊C4×C61—22no—
262C22⋊C4×C61—21no—
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61—21no—
266C42×C61—22no—
267C42×C61—21no—
268C42×C61—22no—
269C42×C61—22no—
270C23×C61—21no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—41no—
276C23×C61—42no—
277C23×C61—42no—
278C23×C61—81no—
279C23×C61#12011yescharacteristic
280C23×C61#12011yescharacteristic
281C23×C61C22×D411yescharacteristic
282Q8×C61—21no—
283Q8×C61—21no—
284Q8×C61—21no—
285Q8×C61—22no—
286Q8×C61—42no—
287Q8×C61—44no—
288Q8×C61—41no—
289Q8×C61—41no—
290Q8×C61—42no—
291Q8×C61#12312yes—
292D4×C61—24no—
293D4×C61—21no—
294D4×C61—21no—
295D4×C61—21no—
296D4×C61—22no—
297D4×C61—42no—
298D4×C61—42no—
299D4×C61—42no—
300D4×C61—44no—
301D4×C61—42no—
302D4×C61—42no—
303D4×C61—42no—
304D4×C61—81no—
305D4×C61—82no—
306D4×C61#12312yes—
307C2×C4×C61—21no—
308C2×C4×C61—22no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—24no—
316C2×C4×C61—24no—
317C2×C4×C61—21no—
318C2×C4×C61—22no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—22no—
322C2×C4×C61—21no—
323C2×C4×C61—24no—
324C2×C4×C61—42no—
325C2×C4×C61—42no—
326C2×C4×C61—42no—
327C2×C4×C61—44no—
328C2×C4×C61—42no—
329C2×C4×C61—44no—
330C2×C4×C61—42no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—42no—
334C2×C4×C61—42no—
335C2×C4×C61—44no—
336C2×C4×C61—42no—
337C2×C4×C61—82no—
338C2×C4×C61—82no—
339C2×C4×C61—82no—
340C2×C4×C61#12011yescharacteristic
341C2×C4×C61#12011yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C2×#4112yes—
345C2×C4×C61H(5,𝔽2)12yes—
346C8×C61—42no—
347C8×C61—42no—
348#24030C6111yesmaximal, characteristic, direct product factor, Sylow
349C22×C61—21no—
350C22×C61—21no—
351C22×C61—21no—
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—22no—
355C22×C61—21no—
356C22×C61—21no—
357C22×C61—44no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—84no—
367C22×C61#45612yes—
368C22×C61C2×#12011yescharacteristic
369C22×C61#54612yes—
370C4×C61—21no—
371C4×C61—21no—
372C4×C61—22no—
373C4×C61—44no—
374C4×C61—42no—
375C4×C61—41no—
376C4×C61—41no—
377C4×C61—41no—
378C4×C61—42no—
379C4×C61—41no—
380C4×C61—82no—
381C4×C61C2×#12311yescharacteristic
382C4×C61#53411yescharacteristic
383C4×C61#54612yes—
384#3489C2×C6111yescharacteristic
385#3092C2×C6111yescharacteristic, complemented
386C2×#417C2×C6111yescharacteristic, complemented
387#2502C2×C6111yescharacteristic, complemented
388#2039C2×C6112yescomplemented
389#2038C2×C6112yescomplemented
390#1901C2×C6111yescharacteristic, complemented
391#1871C2×C6111yescharacteristic, complemented
392#1859C2×C6112yescomplemented
393#1793C2×C6112yescomplemented
394#1789C2×C6111yescharacteristic, complemented
395C2×C61—22no—
396C2×C61—22no—
397C2×C61—41no—
398C2×C61—42no—
399C2×C61—81no—
400C2×C61—81no—
401C2×C61#240511yescharacteristic
402C2×C61C2×#45611yescharacteristic
403C2×C61#302111yescharacteristic
404C2×2−1+4C22×C6111yescharacteristic
405C22×#41C22×C6111yescharacteristic
406C22×M16C22×C6111yescharacteristic
407D4×Q8—21no—
408#548—21no—
409#547—21no—
410#547—22no—
411#546—21no—
412#546—22no—
413#537—21no—
414#537C22×C6111yescharacteristic
415#536—21no—
416#536C22×C6111yescharacteristic
417#525—21no—
418#525C22×C6111yescharacteristic
419C2×C22⋊Q8—21no—
420C2×C22⋊Q8C22×C6111yescharacteristic
421#520C22×C6111yescharacteristic
422C22×C4⋊C4C22×C6111yescharacteristic
423#484—21no—
424#483—21no—
425#481—21no—
426#480—21no—
427#428C22×C6112yescomplemented
428C2×#104C22×C6112yes—
429C2×#104C22×C6112yes—
430C2×#104C22×C6112yescomplemented
431#417—21no—
432#417—21no—
433#417C22×C6112yes—
434#417C22×C6112yes—
435#417C22×C6112yescomplemented
436C2×#103—21no—
437C2×#102—21no—
438C2×#101C22×C6112yescomplemented
439#407C22×C6111yescharacteristic
440#398—22no—
441#391C22×C6112yescomplemented
442#385—22no—
443#384C22×C6112yescomplemented
444C4×C22⋊C4C22×C6111yescharacteristic
445#343C22×C6112yescomplemented
446#339C22×C6112yescomplemented
447C61#2403011yescharacteristic, direct product factor, Sylow
4482−1+4—24no—
4492−1+4—42no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—22no—
454C2×#41—21no—
455C2×#41—24no—
456C2×#41—42no—
457C2×#41D4×C6111yescharacteristic
458C2×#41D4×C6111yescharacteristic
459C2×#41C23×C6111yescharacteristic
460C2×#41C23×C6111yescharacteristic
461C2×#41C23×C6111yescharacteristic
462C22×Q8—21no—
463C22×Q8—21no—
464C22×Q8D4×C6111yescharacteristic
465C22×Q8C23×C6111yescharacteristic
466C22×D4—21no—
467C22×D4D4×C6111yescharacteristic
468C23×C4—21no—
469C23×C4—21no—
470C23×C4C23×C6111yescharacteristic
471C2×M16—21no—
472C2×M16—42no—
473C2×M16C23×C6112yes—
474C2×M16C23×C6112yes—
475C22×C8—21no—
476C4⋊Q8—22no—
477C4⋊Q8—21no—
478#124—22no—
479#124—21no—
480#123—22no—
481#123—22no—
482#123—22no—
483#123—21no—
484#123—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8D4×C6111yescharacteristic
497C22⋊Q8D4×C6111yescharacteristic
498#121—22no—
499#121—22no—
500#121—22no—
501#121—21no—
502#121—21no—
503#121—22no—
504#121D4×C6111yescharacteristic
505#121D4×C6111yescharacteristic
506#120—22no—
507#120—21no—
508C4×Q8—21no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—21no—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515#117—21no—
516#117C23×C6111yescharacteristic
517C2×C4⋊C4—22no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—24no—
525C2×C4⋊C4D4×C6112yes—
526C2×C4⋊C4C23×C6112yes—
527C2×C4⋊C4C23×C6111yescharacteristic
528C2×C22⋊C4—22no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4D4×C6112yes—
531C2×C42C23×C6112yes—
532#107—22no—
533#106—22no—
534#104—24no—
535#104—42no—
536#104—42no—
537#103—22no—
538#103—22no—
539#103—22no—
540#102—22no—
541#102—22no—
542#102—22no—
543#101—42no—
544C22⋊C8—21no—
545C22⋊C8—21no—
546#95—21no—
547#95—24no—
548C24—21no—
549C24C2×D4×C6111yescharacteristic
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—44no—
558#41—41no—
559#41—41no—
560#41—44no—
561#41—44no—
562#41—48no—
563#41—42no—
564#41—42no—
565#41#41×C6114yes—
566C2×Q8—22no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—41no—
574C2×Q8—44no—
575C2×Q8—42no—
576C2×Q8—42no—
577C2×Q8C2×D4×C6111yescharacteristic
578C2×Q8C2×D4×C6111yescharacteristic
579C2×Q8C2×D4×C6111yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—41no—
592C2×D4—44no—
593C2×D4C2×D4×C6111yescharacteristic
594C2×D4C2×D4×C6111yescharacteristic
595C2×D4C2×D4×C6111yescharacteristic
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—44no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—82no—
613C22×C4C2×D4×C6112yes—
614C22×C4C2×D4×C6111yescharacteristic
615C22×C4C2×D4×C6111yescharacteristic
616C22×C4C2×D4×C6111yescharacteristic
617C22×C4C2×D4×C6111yescharacteristic
618C22×C4C2×D4×C6111yescharacteristic
619C22×C4C2×D4×C6112yes—
620C22×C4C24×C6111yescharacteristic
621M16—22no—
622M16—22no—
623M16—22no—
624M16—22no—
625M16—42no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—42no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—21no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—41no—
642C4⋊C4—41no—
643C4⋊C4—84no—
644C4⋊C4C2×D4×C6111yescharacteristic
645C4⋊C4C2×D4×C6111yescharacteristic
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—24no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C42—22no—
660C42—21no—
661C42—22no—
662C42—22no—
663C23—22no—
664C23—22no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—41no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23#120×C6111yescharacteristic
673C23#120×C6111yescharacteristic
674C23C22×D4×C6111yescharacteristic
675Q8—21no—
676Q8—21no—
677Q8—22no—
678Q8—21no—
679Q8—42no—
680Q8—44no—
681Q8—41no—
682Q8—42no—
683Q8—41no—
684Q8#123×C6112yes—
685D4—24no—
686D4—21no—
687D4—21no—
688D4—22no—
689D4—21no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—44no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—81no—
698D4—82no—
699D4#123×C6112yes—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—42no—
730C2×C4—82no—
731C2×C4—82no—
732C2×C4—82no—
733C2×C4#120×C6111yescharacteristic
734C2×C4#120×C6111yescharacteristic
735C2×C4C22×D4×C6111yescharacteristic
736C2×C4C22×D4×C6111yescharacteristic
737C2×C4C2×#41×C6112yes—
738C2×C4H(5,𝔽2)×C6112yes—
739C8—42no—
740C8—42no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—22no—
747C22—21no—
748C22—21no—
749C22—44no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—84no—
759C22C61×#45612yes—
760C22C2×#120×C6111yescharacteristic
761C22C61×#54612yes—
762C4—21no—
763C4—21no—
764C4—22no—
765C4—44no—
766C4—42no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—41no—
772C4—82no—
773C4C2×#123×C6111yescharacteristic
774C4C61×#53411yescharacteristic
775C4C61×#54612yes—
776C2—22no—
777C2—22no—
778C2—41no—
779C2—42no—
780C2—81no—
781C2—81no—
782C2C61×#240511yescharacteristic
783C2C2×C61×#45611yescharacteristic
784C2C61×#302111yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3489C2
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
2. C61×#3092C2semidirect
3. C2×C61×#417C2semidirect
4. C61×#2502C2semidirect
5. C61×#2039C2semidirect
6. C61×#2038C2semidirect
7. C61×#1901C2semidirect
8. C61×#1871C2semidirect
9. C61×#1859C2semidirect
10. C61×#1793C2semidirect
11. C61×#1789C2semidirect
35. C61×#428C22semidirect
38. C2×#104×C61C22semidirect
43. C61×#417C22semidirect
46. C2×#101×C61C22semidirect
49. C61×#391C22semidirect
51. C61×#384C22semidirect
53. C61×#343C22semidirect
54. C61×#339C22semidirect
348. #24030C61direct (N × H)
385. #3092C2×C61semidirect
386. C2×#417C2×C61semidirect
387. #2502C2×C61semidirect
388. #2039C2×C61semidirect
389. #2038C2×C61semidirect
390. #1901C2×C61semidirect
391. #1871C2×C61semidirect
392. #1859C2×C61semidirect
393. #1793C2×C61semidirect
394. #1789C2×C61semidirect
427. #428C22×C61semidirect
430. C2×#104C22×C61semidirect
435. #417C22×C61semidirect
438. C2×#101C22×C61semidirect
441. #391C22×C61semidirect
443. #384C22×C61semidirect
445. #343C22×C61semidirect
446. #339C22×C61semidirect
447. C61#24030direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#34892
C61×#30922
C2×C61×#4172
C61×#25022
C61×#20392
C61×#20382
C61×#19012
C61×#18712
C61×#18592
C61×#17932
C61×#17892
#2403061