Finite Group Databasebeta

← C61×#24574 #29528007

Subgroups — C61×#24574 #29528007

Order 15616.

888 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
1C2×C61×#485C211yesmaximal, characteristic, complemented
2C61×#3007C211yesmaximal, characteristic
3C61×#2896C211yesmaximal, characteristic
4C61×#2880C211yesmaximal, characteristic
5C61×#2079C211yesmaximal, characteristic, complemented
6C61×#2078C211yesmaximal, characteristic, complemented
7C61×#2052C211yesmaximal, characteristic, complemented
8C61×#2052C211yesmaximal, characteristic, complemented
9C61×#1908C211yesmaximal, characteristic, complemented
10C61×#1908C211yesmaximal, characteristic, complemented
11C61×#1901C211yesmaximal, characteristic, complemented
12C61×#1855C211yesmaximal, characteristic, complemented
13C61×#1822C211yesmaximal, characteristic, complemented
14C61×#1816C211yesmaximal, characteristic, complemented
15C61×#1815C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C2×#137×C61C2211yescharacteristic
18C2×#137×C61C2211yescharacteristic
19C2×#131×C61C2211yescharacteristic
20C2×#131×C61C2211yescharacteristic
21C22×M16×C61C2211yescharacteristic
22C2×C22⋊Q8×C61C2211yescharacteristic
23C2×#117×C61C2211yescharacteristic
24C61×#485—21no—
25C61×#485—21no—
26C61×#485—21no—
27C61×#485—21no—
28C61×#452—21no—
29C61×#452—21no—
30C61×#451—21no—
31C61×#450—21no—
32C2×#108×C61C2211yescharacteristic, complemented
33C2×#108×C61C2211yescharacteristic, complemented
34C2×#107×C61C2211yescharacteristic, complemented
35C2×#106×C61C2211yescharacteristic, complemented
36C61×#419—21no—
37C61×#418—21no—
38C61×#417C2211yescharacteristic
39C61×#417C2211yescharacteristic
40C61×#417C2211yescharacteristic
41C61×#417C2211yescharacteristic
42C61×#417C2211yescharacteristic
43C61×#417C2211yescharacteristic
44C61×#416—21no—
45C61×#416—21no—
46C2×#103×C61C2211yescharacteristic, complemented
47C2×#103×C61C2211yescharacteristic, complemented
48C2×#101×C61C2211yescharacteristic, complemented
49C2×#101×C61C2211yescharacteristic, complemented
50C61×#408—21no—
51C61×#408—21no—
52C61×#408C2211yescharacteristic
53C61×#408C2211yescharacteristic
54C61×#407—21no—
55C61×#407C2211yescharacteristic
56C61×#407C2211yescharacteristic
57C2×C22⋊C8×C61—21no—
58C2×C22⋊C8×C61C2211yescharacteristic
59C61×#343C2211yescharacteristic, complemented
60C61×#343C2211yescharacteristic, complemented
61C61×#343C2211yescharacteristic, complemented
62C61×#343C2211yescharacteristic, complemented
63C61×#343C2211yescharacteristic, complemented
64C61×#343C2211yescharacteristic, complemented
65C61×#341C2211yescharacteristic, complemented
66C61×#341C2211yescharacteristic, complemented
67C2×#41×C61—21no—
68C2×#41×C61—21no—
69C2×#41×C61—22no—
70C2×#41×C61—22no—
71C2×#41×C61—41no—
72C2×#41×C61—41no—
73C2×#41×C61D411yescharacteristic
74C2×#41×C61D411yescharacteristic
75C2×#41×C61C2311yescharacteristic
76C2×#41×C61C2311yescharacteristic
77C22×Q8×C61D411yescharacteristic
78C22×Q8×C61C2311yescharacteristic
79C22×D4×C61—21no—
80C22×D4×C61D411yescharacteristic
81C23×C4×C61—21no—
82C23×C4×C61C2311yescharacteristic
83#137×C61—22no—
84#137×C61—22no—
85#137×C61—41no—
86#137×C61—41no—
87C2×Q16×C61—21no—
88C2×Q16×C61—21no—
89C2×SD16×C61—21no—
90C2×SD16×C61—21no—
91#131×C61—22no—
92#131×C61—22no—
93#131×C61—41no—
94#131×C61—41no—
95C2×M16×C61—21no—
96C2×M16×C61—21no—
97C2×M16×C61—21no—
98C2×M16×C61—41no—
99C2×M16×C61—41no—
100C2×M16×C61C2311yescharacteristic
101C2×M16×C61C2311yescharacteristic
102C2×M16×C61C2311yescharacteristic
103C2×M16×C61C2311yescharacteristic
104C2×M16×C61C2311yescharacteristic
105C2×M16×C61C2311yescharacteristic
106C22×C8×C61—21no—
107C22×C8×C61—21no—
108C22×C8×C61—21no—
109C22×C8×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C22⋊Q8×C61—21no—
112C22⋊Q8×C61—21no—
113C22⋊Q8×C61—21no—
114C22⋊Q8×C61—21no—
115#117×C61—21no—
116#117×C61—21no—
117#117×C61—21no—
118#117×C61—21no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C42×C61—21no—
126#108×C61—41no—
127#108×C61—41no—
128#107×C61—21no—
129#107×C61—21no—
130#106×C61—21no—
131#106×C61—21no—
132#103×C61—21no—
133#103×C61—21no—
134#103×C61—21no—
135#103×C61—21no—
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#103×C61—21no—
140#103×C61—21no—
141#103×C61—21no—
142#102×C61—21no—
143#102×C61—21no—
144#102×C61—21no—
145#102×C61—21no—
146#102×C61—21no—
147#102×C61—21no—
148#101×C61—41no—
149#101×C61—41no—
150C22⋊C8×C61—21no—
151C22⋊C8×C61—21no—
152C22⋊C8×C61—21no—
153C22⋊C8×C61—21no—
154C22⋊C8×C61—21no—
155C22⋊C8×C61—21no—
156C22⋊C8×C61—21no—
157C22⋊C8×C61—21no—
158C22⋊C8×C61D411yescharacteristic
159C22⋊C8×C61D411yescharacteristic
160C22⋊C8×C61D411yescharacteristic
161C22⋊C8×C61D411yescharacteristic
162C24×C61—21no—
163C24×C61#4111yescharacteristic
164#41×C61—21no—
165#41×C61—21no—
166#41×C61—22no—
167#41×C61—22no—
168#41×C61—21no—
169#41×C61—21no—
170#41×C61—21no—
171#41×C61—21no—
172#41×C61—42no—
173#41×C61—42no—
174#41×C61—41no—
175#41×C61—41no—
176#41×C61—42no—
177#41×C61—42no—
178#41×C61#4112yes—
179#41×C61#4112yes—
180C2×Q8×C61—21no—
181C2×Q8×C61—22no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61—41no—
189C2×Q8×C61C2×D411yescharacteristic
190C2×Q8×C61C2×D411yescharacteristic
191C2×D4×C61—21no—
192C2×D4×C61—22no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—41no—
198C2×D4×C61—42no—
199C2×D4×C61—42no—
200C2×D4×C61C2×D411yescharacteristic
201C2×D4×C61C2×D411yescharacteristic
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—42no—
216C22×C4×C61—42no—
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61#4111yescharacteristic
222C22×C4×C61C2411yescharacteristic
223Q16×C61—42no—
224Q16×C61—42no—
225SD16×C61—42no—
226SD16×C61—42no—
227M16×C61—21no—
228M16×C61—21no—
229M16×C61—21no—
230M16×C61—21no—
231M16×C61—21no—
232M16×C61—21no—
233M16×C61—21no—
234M16×C61—21no—
235M16×C61—21no—
236M16×C61—21no—
237M16×C61—21no—
238M16×C61—21no—
239M16×C61—42no—
240M16×C61—42no—
241M16×C61—42no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—42no—
253C2×C8×C61—42no—
254C2×C8×C61—42no—
255C2×C8×C61C2×D411yescharacteristic
256C2×C8×C61C2×D411yescharacteristic
257C2×C8×C61C2×D411yescharacteristic
258C2×C8×C61C2×D411yescharacteristic
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—41no—
266C4⋊C4×C61—41no—
267C22⋊C4×C61—41no—
268C22⋊C4×C61—41no—
269C22⋊C4×C61—41no—
270C22⋊C4×C61—41no—
271C42×C61—41no—
272C42×C61—41no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—42no—
280C23×C61—42no—
281C23×C61—81no—
282C23×C61#12111yescharacteristic
283C23×C61#12111yescharacteristic
284C23×C61C2×#4111yescharacteristic
285Q8×C61—21no—
286Q8×C61—21no—
287Q8×C61—21no—
288Q8×C61—42no—
289Q8×C61—41no—
290Q8×C61—41no—
291Q8×C61—41no—
292Q8×C61—41no—
293Q8×C61#12312yes—
294D4×C61—22no—
295D4×C61—22no—
296D4×C61—21no—
297D4×C61—21no—
298D4×C61—21no—
299D4×C61—42no—
300D4×C61—42no—
301D4×C61—42no—
302D4×C61—41no—
303D4×C61—41no—
304D4×C61#12312yes—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—42no—
320C2×C4×C61—42no—
321C2×C4×C61—42no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—81no—
331C2×C4×C61—81no—
332C2×C4×C61—81no—
333C2×C4×C61#12111yescharacteristic
334C2×C4×C61#12111yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C2×#4111yescharacteristic
338C2×C4×C61C2×#4111yescharacteristic
339C2×C4×C61H(5,𝔽2)11yescharacteristic
340C2×C4×C61H(5,𝔽2)11yescharacteristic
341C8×C61—21no—
342C8×C61—21no—
343C8×C61—21no—
344C8×C61—21no—
345C8×C61—41no—
346C8×C61—41no—
347C8×C61—41no—
348C8×C61—41no—
349C8×C61—41no—
350C8×C61—41no—
351#24574C6111yesmaximal, characteristic, direct product factor, Sylow
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—21no—
356C22×C61—22no—
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—21no—
360C22×C61—21no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—84no—
369C22×C61C2×#12111yescharacteristic
370C22×C61#55111yescharacteristic
371C22×C61#55111yescharacteristic
372C4×C61—21no—
373C4×C61—21no—
374C4×C61—22no—
375C4×C61—41no—
376C4×C61—81no—
377C4×C61—81no—
378C4×C61—81no—
379C4×C61—81no—
380C4×C61C2×#12311yescharacteristic
381C4×C61#53411yescharacteristic
382C4×C61#54611yescharacteristic
383C4×C61#54611yescharacteristic
384C2×#485C2×C6111yescharacteristic, complemented
385#3007C2×C6111yescharacteristic
386#2896C2×C6111yescharacteristic
387#2880C2×C6111yescharacteristic
388#2079C2×C6111yescharacteristic, complemented
389#2078C2×C6111yescharacteristic, complemented
390#2052C2×C6111yescharacteristic, complemented
391#2052C2×C6111yescharacteristic, complemented
392#1908C2×C6111yescharacteristic, complemented
393#1908C2×C6111yescharacteristic, complemented
394#1901C2×C6111yescharacteristic, complemented
395#1855C2×C6111yescharacteristic, complemented
396#1822C2×C6111yescharacteristic, complemented
397#1816C2×C6111yescharacteristic, complemented
398#1815C2×C6111yescharacteristic, complemented
399C2×C61—21no—
400C2×C61—21no—
401C2×C61—41no—
402C2×C61—41no—
403C2×C61—42no—
404C2×C61—81no—
405C2×C61#241211yescharacteristic
406C2×C61#306711yescharacteristic
407C2×C61#306911yescharacteristic
408C22×#41C22×C6111yescharacteristic
409C2×#137C22×C6111yescharacteristic
410C2×#137C22×C6111yescharacteristic
411C2×#131C22×C6111yescharacteristic
412C2×#131C22×C6111yescharacteristic
413C22×M16C22×C6111yescharacteristic
414C2×C22⋊Q8C22×C6111yescharacteristic
415C2×#117C22×C6111yescharacteristic
416#485—21no—
417#485—21no—
418#485—21no—
419#485—21no—
420#452—21no—
421#452—21no—
422#451—21no—
423#450—21no—
424C2×#108C22×C6111yescharacteristic, complemented
425C2×#108C22×C6111yescharacteristic, complemented
426C2×#107C22×C6111yescharacteristic, complemented
427C2×#106C22×C6111yescharacteristic, complemented
428#419—21no—
429#418—21no—
430#417C22×C6111yescharacteristic
431#417C22×C6111yescharacteristic
432#417C22×C6111yescharacteristic
433#417C22×C6111yescharacteristic
434#417C22×C6111yescharacteristic
435#417C22×C6111yescharacteristic
436#416—21no—
437#416—21no—
438C2×#103C22×C6111yescharacteristic, complemented
439C2×#103C22×C6111yescharacteristic, complemented
440C2×#101C22×C6111yescharacteristic, complemented
441C2×#101C22×C6111yescharacteristic, complemented
442#408—21no—
443#408—21no—
444#408C22×C6111yescharacteristic
445#408C22×C6111yescharacteristic
446#407—21no—
447#407C22×C6111yescharacteristic
448#407C22×C6111yescharacteristic
449C2×C22⋊C8—21no—
450C2×C22⋊C8C22×C6111yescharacteristic
451#343C22×C6111yescharacteristic, complemented
452#343C22×C6111yescharacteristic, complemented
453#343C22×C6111yescharacteristic, complemented
454#343C22×C6111yescharacteristic, complemented
455#343C22×C6111yescharacteristic, complemented
456#343C22×C6111yescharacteristic, complemented
457#341C22×C6111yescharacteristic, complemented
458#341C22×C6111yescharacteristic, complemented
459C61#2457411yescharacteristic, direct product factor, Sylow
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—41no—
465C2×#41—41no—
466C2×#41D4×C6111yescharacteristic
467C2×#41D4×C6111yescharacteristic
468C2×#41C23×C6111yescharacteristic
469C2×#41C23×C6111yescharacteristic
470C22×Q8D4×C6111yescharacteristic
471C22×Q8C23×C6111yescharacteristic
472C22×D4—21no—
473C22×D4D4×C6111yescharacteristic
474C23×C4—21no—
475C23×C4C23×C6111yescharacteristic
476#137—22no—
477#137—22no—
478#137—41no—
479#137—41no—
480C2×Q16—21no—
481C2×Q16—21no—
482C2×SD16—21no—
483C2×SD16—21no—
484#131—22no—
485#131—22no—
486#131—41no—
487#131—41no—
488C2×M16—21no—
489C2×M16—21no—
490C2×M16—21no—
491C2×M16—41no—
492C2×M16—41no—
493C2×M16C23×C6111yescharacteristic
494C2×M16C23×C6111yescharacteristic
495C2×M16C23×C6111yescharacteristic
496C2×M16C23×C6111yescharacteristic
497C2×M16C23×C6111yescharacteristic
498C2×M16C23×C6111yescharacteristic
499C22×C8—21no—
500C22×C8—21no—
501C22×C8—21no—
502C22×C8C23×C6111yescharacteristic
503C22×C8C23×C6111yescharacteristic
504C22⋊Q8—21no—
505C22⋊Q8—21no—
506C22⋊Q8—21no—
507C22⋊Q8—21no—
508#117—21no—
509#117—21no—
510#117—21no—
511#117—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4C23×C6111yescharacteristic
514C2×C4⋊C4C23×C6111yescharacteristic
515C2×C4⋊C4C23×C6111yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C42—21no—
519#108—41no—
520#108—41no—
521#107—21no—
522#107—21no—
523#106—21no—
524#106—21no—
525#103—21no—
526#103—21no—
527#103—21no—
528#103—21no—
529#103—21no—
530#103—21no—
531#103—21no—
532#103—21no—
533#103—21no—
534#103—21no—
535#102—21no—
536#102—21no—
537#102—21no—
538#102—21no—
539#102—21no—
540#102—21no—
541#101—41no—
542#101—41no—
543C22⋊C8—21no—
544C22⋊C8—21no—
545C22⋊C8—21no—
546C22⋊C8—21no—
547C22⋊C8—21no—
548C22⋊C8—21no—
549C22⋊C8—21no—
550C22⋊C8—21no—
551C22⋊C8D4×C6111yescharacteristic
552C22⋊C8D4×C6111yescharacteristic
553C22⋊C8D4×C6111yescharacteristic
554C22⋊C8D4×C6111yescharacteristic
555C24—21no—
556C24#41×C6111yescharacteristic
557#41—21no—
558#41—21no—
559#41—22no—
560#41—22no—
561#41—21no—
562#41—21no—
563#41—21no—
564#41—21no—
565#41—42no—
566#41—42no—
567#41—41no—
568#41—41no—
569#41—42no—
570#41—42no—
571#41#41×C6112yes—
572#41#41×C6112yes—
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—41no—
582C2×Q8C2×D4×C6111yescharacteristic
583C2×Q8C2×D4×C6111yescharacteristic
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—41no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4C2×D4×C6111yescharacteristic
594C2×D4C2×D4×C6111yescharacteristic
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4C2×D4×C6111yescharacteristic
611C22×C4C2×D4×C6111yescharacteristic
612C22×C4C2×D4×C6111yescharacteristic
613C22×C4C2×D4×C6111yescharacteristic
614C22×C4#41×C6111yescharacteristic
615C22×C4C24×C6111yescharacteristic
616Q16—42no—
617Q16—42no—
618SD16—42no—
619SD16—42no—
620M16—21no—
621M16—21no—
622M16—21no—
623M16—21no—
624M16—21no—
625M16—21no—
626M16—21no—
627M16—21no—
628M16—21no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—42no—
633M16—42no—
634M16—42no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—42no—
646C2×C8—42no—
647C2×C8—42no—
648C2×C8C2×D4×C6111yescharacteristic
649C2×C8C2×D4×C6111yescharacteristic
650C2×C8C2×D4×C6111yescharacteristic
651C2×C8C2×D4×C6111yescharacteristic
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C22⋊C4—41no—
661C22⋊C4—41no—
662C22⋊C4—41no—
663C22⋊C4—41no—
664C42—41no—
665C42—41no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—41no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—81no—
675C23#121×C6111yescharacteristic
676C23#121×C6111yescharacteristic
677C23C2×#41×C6111yescharacteristic
678Q8—21no—
679Q8—21no—
680Q8—21no—
681Q8—42no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8#123×C6112yes—
687D4—22no—
688D4—22no—
689D4—21no—
690D4—21no—
691D4—21no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—41no—
696D4—41no—
697D4#123×C6112yes—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4#121×C6111yescharacteristic
727C2×C4#121×C6111yescharacteristic
728C2×C4C22×D4×C6111yescharacteristic
729C2×C4C22×D4×C6111yescharacteristic
730C2×C4C2×#41×C6111yescharacteristic
731C2×C4C2×#41×C6111yescharacteristic
732C2×C4H(5,𝔽2)×C6111yescharacteristic
733C2×C4H(5,𝔽2)×C6111yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—41no—
739C8—41no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—41no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—22no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—81no—
759C22—81no—
760C22—84no—
761C22C2×#121×C6111yescharacteristic
762C22C61×#55111yescharacteristic
763C22C61×#55111yescharacteristic
764C4—21no—
765C4—21no—
766C4—22no—
767C4—41no—
768C4—81no—
769C4—81no—
770C4—81no—
771C4—81no—
772C4C2×#123×C6111yescharacteristic
773C4C61×#53411yescharacteristic
774C4C61×#54611yescharacteristic
775C4C61×#54611yescharacteristic
776C2—21no—
777C2—21no—
778C2—41no—
779C2—41no—
780C2—42no—
781C2—81no—
782C2C61×#241211yescharacteristic
783C2C61×#306711yescharacteristic
784C2C61×#306911yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC22×#41×C61C22
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. C2×C61×#485C2semidirect
5. C61×#2079C2semidirect
6. C61×#2078C2semidirect
7. C61×#2052C2semidirect
8. C61×#2052C2semidirect
9. C61×#1908C2semidirect
10. C61×#1908C2semidirect
11. C61×#1901C2semidirect
12. C61×#1855C2semidirect
13. C61×#1822C2semidirect
14. C61×#1816C2semidirect
15. C61×#1815C2semidirect
32. C2×#108×C61C22semidirect
33. C2×#108×C61C22semidirect
34. C2×#107×C61C22semidirect
35. C2×#106×C61C22semidirect
46. C2×#103×C61C22semidirect
47. C2×#103×C61C22semidirect
48. C2×#101×C61C22semidirect
49. C2×#101×C61C22semidirect
59. C61×#343C22semidirect
60. C61×#343C22semidirect
61. C61×#343C22semidirect
62. C61×#343C22semidirect
63. C61×#343C22semidirect
64. C61×#343C22semidirect
65. C61×#341C22semidirect
66. C61×#341C22semidirect
351. #24574C61direct (N × H)
384. C2×#485C2×C61semidirect
388. #2079C2×C61semidirect
389. #2078C2×C61semidirect
390. #2052C2×C61semidirect
391. #2052C2×C61semidirect
392. #1908C2×C61semidirect
393. #1908C2×C61semidirect
394. #1901C2×C61semidirect
395. #1855C2×C61semidirect
396. #1822C2×C61semidirect
397. #1816C2×C61semidirect
398. #1815C2×C61semidirect
424. C2×#108C22×C61semidirect
425. C2×#108C22×C61semidirect
426. C2×#107C22×C61semidirect
427. C2×#106C22×C61semidirect
438. C2×#103C22×C61semidirect
439. C2×#103C22×C61semidirect
440. C2×#101C22×C61semidirect
441. C2×#101C22×C61semidirect
451. #343C22×C61semidirect
452. #343C22×C61semidirect
453. #343C22×C61semidirect
454. #343C22×C61semidirect
455. #343C22×C61semidirect
456. #343C22×C61semidirect
457. #341C22×C61semidirect
458. #341C22×C61semidirect
459. C61#24574direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#4852
C61×#30072
C61×#28962
C61×#28802
C61×#20792
C61×#20782
C61×#20522
C61×#19082
C61×#19012
C61×#18552
C61×#18222
C61×#18162
C61×#18152
#2457461