Finite Group Databasebeta

← C61×#24575 #29528008

Subgroups — C61×#24575 #29528008

Order 15616.

914 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#482C211yesmaximal, characteristic, complemented
2C61×#3006C211yesmaximal, characteristic
3C61×#2896C211yesmaximal, characteristic, complemented
4C61×#2880C211yesmaximal, characteristic, complemented
5C61×#2079C211yesmaximal, characteristic, complemented
6C61×#2078C211yesmaximal, characteristic, complemented
7C61×#2051C211yesmaximal, characteristic, complemented
8C61×#2051C211yesmaximal, characteristic, complemented
9C61×#1907C211yesmaximal, characteristic, complemented
10C61×#1907C211yesmaximal, characteristic, complemented
11C61×#1900C211yesmaximal, characteristic, complemented
12C61×#1855C211yesmaximal, characteristic, complemented
13C61×#1822C211yesmaximal, characteristic, complemented
14C61×#1816C211yesmaximal, characteristic, complemented
15C61×#1815C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
19C2×#131×C61C2211yescharacteristic
20C2×#131×C61C2211yescharacteristic
21C22×M16×C61C2211yescharacteristic
22C2×#121×C61C2211yescharacteristic
23C2×#117×C61C2211yescharacteristic
24C61×#482—21no—
25C61×#482—21no—
26C61×#482—21no—
27C61×#482—21no—
28C61×#449—21no—
29C61×#449—21no—
30C61×#448—21no—
31C61×#447—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×#102×C61C2211yescharacteristic, complemented
47C2×#102×C61C2211yescharacteristic, complemented
48C2×#100×C61C2211yescharacteristic, complemented
49C2×#100×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×D4×C61—21no—
79C22×D4×C61—21no—
80C22×D4×C61D411yescharacteristic
81C22×D4×C61C2311yescharacteristic
82C23×C4×C61—21no—
83C23×C4×C61C2311yescharacteristic
84AGL(1,ℤ/8)×C61—22no—
85AGL(1,ℤ/8)×C61—22no—
86AGL(1,ℤ/8)×C61—41no—
87AGL(1,ℤ/8)×C61—41no—
88C2×SD16×C61—21no—
89C2×SD16×C61—21no—
90C2×D8×C61—21no—
91C2×D8×C61—21no—
92#131×C61—22no—
93#131×C61—22no—
94#131×C61—41no—
95#131×C61—41no—
96C2×M16×C61—21no—
97C2×M16×C61—21no—
98C2×M16×C61—21no—
99C2×M16×C61—41no—
100C2×M16×C61—41no—
101C2×M16×C61C2311yescharacteristic
102C2×M16×C61C2311yescharacteristic
103C2×M16×C61C2311yescharacteristic
104C2×M16×C61C2311yescharacteristic
105C2×M16×C61C2311yescharacteristic
106C2×M16×C61C2311yescharacteristic
107C22×C8×C61—21no—
108C22×C8×C61—21no—
109C22×C8×C61—21no—
110C22×C8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112#121×C61—21no—
113#121×C61—21no—
114#121×C61—21no—
115#121×C61—21no—
116#117×C61—21no—
117#117×C61—21no—
118#117×C61—21no—
119#117×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#102×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141#102×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#100×C61—41no—
149#100×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—21no—
164C24×C61#4111yescharacteristic
165#41×C61—21no—
166#41×C61—21no—
167#41×C61—22no—
168#41×C61—22no—
169#41×C61—21no—
170#41×C61—21no—
171#41×C61—21no—
172#41×C61—21no—
173#41×C61—42no—
174#41×C61—42no—
175#41×C61—41no—
176#41×C61—41no—
177#41×C61—42no—
178#41×C61—42no—
179#41×C61#4112yes—
180#41×C61#4112yes—
181C2×Q8×C61—21no—
182C2×Q8×C61—22no—
183C2×Q8×C61—41no—
184C2×Q8×C61C2×D411yescharacteristic
185C2×Q8×C61C2×D411yescharacteristic
186C2×D4×C61—21no—
187C2×D4×C61—22no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—41no—
199C2×D4×C61—42no—
200C2×D4×C61—42no—
201C2×D4×C61—41no—
202C2×D4×C61—41no—
203C2×D4×C61—82no—
204C2×D4×C61C2×D411yescharacteristic
205C2×D4×C61C2×D411yescharacteristic
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—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—42no—
219C22×C4×C61—42no—
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61#4111yescharacteristic
225C22×C4×C61C2411yescharacteristic
226SD16×C61—42no—
227SD16×C61—42no—
228D8×C61—42no—
229D8×C61—42no—
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—21no—
240M16×C61—21no—
241M16×C61—21no—
242M16×C61—42no—
243M16×C61—42no—
244M16×C61—42no—
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—21no—
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C2×C8×C61—42no—
256C2×C8×C61—42no—
257C2×C8×C61—42no—
258C2×C8×C61C2×D411yescharacteristic
259C2×C8×C61C2×D411yescharacteristic
260C2×C8×C61C2×D411yescharacteristic
261C2×C8×C61C2×D411yescharacteristic
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C22⋊C4×C61—41no—
269C22⋊C4×C61—41no—
270C22⋊C4×C61—41no—
271C22⋊C4×C61—41no—
272C42×C61—41no—
273C42×C61—41no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—42no—
281C23×C61—42no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—81no—
286C23×C61—81no—
287C23×C61—81no—
288C23×C61#12111yescharacteristic
289C23×C61#12111yescharacteristic
290C23×C61C2×#4111yescharacteristic
291Q8×C61—21no—
292Q8×C61—21no—
293Q8×C61—21no—
294Q8×C61—42no—
295Q8×C61#12312yes—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—21no—
299D4×C61—21no—
300D4×C61—21no—
301D4×C61—42no—
302D4×C61—42no—
303D4×C61—42no—
304D4×C61—41no—
305D4×C61—41no—
306D4×C61—41no—
307D4×C61—41no—
308D4×C61—41no—
309D4×C61—41no—
310D4×C61—82no—
311D4×C61—82no—
312D4×C61#12312yes—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—42no—
328C2×C4×C61—42no—
329C2×C4×C61—42no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—81no—
336C2×C4×C61—81no—
337C2×C4×C61—81no—
338C2×C4×C61#12111yescharacteristic
339C2×C4×C61#12111yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C2×#4111yescharacteristic
343C2×C4×C61C2×#4111yescharacteristic
344C2×C4×C61H(5,𝔽2)11yescharacteristic
345C2×C4×C61H(5,𝔽2)11yescharacteristic
346C8×C61—21no—
347C8×C61—21no—
348C8×C61—21no—
349C8×C61—21no—
350C8×C61—41no—
351C8×C61—41no—
352C8×C61—41no—
353C8×C61—41no—
354C8×C61—41no—
355C8×C61—41no—
356#24575C6111yesmaximal, characteristic, direct product factor, Sylow
357C22×C61—21no—
358C22×C61—21no—
359C22×C61—21no—
360C22×C61—21no—
361C22×C61—22no—
362C22×C61—21no—
363C22×C61—21no—
364C22×C61—21no—
365C22×C61—21no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—81no—
372C22×C61—81no—
373C22×C61—84no—
374C22×C61—81no—
375C22×C61—81no—
376C22×C61—81no—
377C22×C61—161no—
378C22×C61—161no—
379C22×C61C2×#12111yescharacteristic
380C22×C61#55111yescharacteristic
381C22×C61#55111yescharacteristic
382C4×C61—21no—
383C4×C61—21no—
384C4×C61—22no—
385C4×C61—41no—
386C4×C61—81no—
387C4×C61—81no—
388C4×C61—81no—
389C4×C61C2×#12311yescharacteristic
390C4×C61#53411yescharacteristic
391C4×C61#54611yescharacteristic
392C4×C61#54611yescharacteristic
393C2×#482C2×C6111yescharacteristic, complemented
394#3006C2×C6111yescharacteristic
395#2896C2×C6111yescharacteristic, complemented
396#2880C2×C6111yescharacteristic, complemented
397#2079C2×C6111yescharacteristic, complemented
398#2078C2×C6111yescharacteristic, complemented
399#2051C2×C6111yescharacteristic, complemented
400#2051C2×C6111yescharacteristic, complemented
401#1907C2×C6111yescharacteristic, complemented
402#1907C2×C6111yescharacteristic, complemented
403#1900C2×C6111yescharacteristic, complemented
404#1855C2×C6111yescharacteristic, complemented
405#1822C2×C6111yescharacteristic, complemented
406#1816C2×C6111yescharacteristic, complemented
407#1815C2×C6111yescharacteristic, complemented
408C2×C61—21no—
409C2×C61—21no—
410C2×C61—41no—
411C2×C61—41no—
412C2×C61—42no—
413C2×C61—81no—
414C2×C61—161no—
415C2×C61#241211yescharacteristic
416C2×C61#306711yescharacteristic
417C2×C61#306811yescharacteristic
418C22×#41C22×C6111yescharacteristic
419C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
420C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
421C2×#131C22×C6111yescharacteristic
422C2×#131C22×C6111yescharacteristic
423C22×M16C22×C6111yescharacteristic
424C2×#121C22×C6111yescharacteristic
425C2×#117C22×C6111yescharacteristic
426#482—21no—
427#482—21no—
428#482—21no—
429#482—21no—
430#449—21no—
431#449—21no—
432#448—21no—
433#447—21no—
434C2×#108C22×C6111yescharacteristic, complemented
435C2×#108C22×C6111yescharacteristic, complemented
436C2×#107C22×C6111yescharacteristic, complemented
437C2×#106C22×C6111yescharacteristic, complemented
438#419—21no—
439#418—21no—
440#417C22×C6111yescharacteristic
441#417C22×C6111yescharacteristic
442#417C22×C6111yescharacteristic
443#417C22×C6111yescharacteristic
444#417C22×C6111yescharacteristic
445#417C22×C6111yescharacteristic
446#416—21no—
447#416—21no—
448C2×#102C22×C6111yescharacteristic, complemented
449C2×#102C22×C6111yescharacteristic, complemented
450C2×#100C22×C6111yescharacteristic, complemented
451C2×#100C22×C6111yescharacteristic, complemented
452#408—21no—
453#408—21no—
454#408C22×C6111yescharacteristic
455#408C22×C6111yescharacteristic
456#407—21no—
457#407C22×C6111yescharacteristic
458#407C22×C6111yescharacteristic
459C2×C22⋊C8—21no—
460C2×C22⋊C8C22×C6111yescharacteristic
461#343C22×C6111yescharacteristic, complemented
462#343C22×C6111yescharacteristic, complemented
463#343C22×C6111yescharacteristic, complemented
464#343C22×C6111yescharacteristic, complemented
465#343C22×C6111yescharacteristic, complemented
466#343C22×C6111yescharacteristic, complemented
467#341C22×C6111yescharacteristic, complemented
468#341C22×C6111yescharacteristic, complemented
469C61#2457511yescharacteristic, direct product factor, Sylow
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—22no—
473C2×#41—22no—
474C2×#41—41no—
475C2×#41—41no—
476C2×#41D4×C6111yescharacteristic
477C2×#41D4×C6111yescharacteristic
478C2×#41C23×C6111yescharacteristic
479C2×#41C23×C6111yescharacteristic
480C22×Q8D4×C6111yescharacteristic
481C22×D4—21no—
482C22×D4—21no—
483C22×D4D4×C6111yescharacteristic
484C22×D4C23×C6111yescharacteristic
485C23×C4—21no—
486C23×C4C23×C6111yescharacteristic
487AGL(1,ℤ/8)—22no—
488AGL(1,ℤ/8)—22no—
489AGL(1,ℤ/8)—41no—
490AGL(1,ℤ/8)—41no—
491C2×SD16—21no—
492C2×SD16—21no—
493C2×D8—21no—
494C2×D8—21no—
495#131—22no—
496#131—22no—
497#131—41no—
498#131—41no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—41no—
503C2×M16—41no—
504C2×M16C23×C6111yescharacteristic
505C2×M16C23×C6111yescharacteristic
506C2×M16C23×C6111yescharacteristic
507C2×M16C23×C6111yescharacteristic
508C2×M16C23×C6111yescharacteristic
509C2×M16C23×C6111yescharacteristic
510C22×C8—21no—
511C22×C8—21no—
512C22×C8—21no—
513C22×C8C23×C6111yescharacteristic
514C22×C8C23×C6111yescharacteristic
515#121—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#117—21no—
520#117—21no—
521#117—21no—
522#117—21no—
523C2×C4⋊C4C23×C6111yescharacteristic
524C2×C4⋊C4C23×C6111yescharacteristic
525C2×C4⋊C4C23×C6111yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C42—21no—
529#108—41no—
530#108—41no—
531#107—21no—
532#107—21no—
533#106—21no—
534#106—21no—
535#103—21no—
536#103—21no—
537#103—21no—
538#103—21no—
539#103—21no—
540#103—21no—
541#102—21no—
542#102—21no—
543#102—21no—
544#102—21no—
545#102—21no—
546#102—21no—
547#102—21no—
548#102—21no—
549#102—21no—
550#102—21no—
551#100—41no—
552#100—41no—
553C22⋊C8—21no—
554C22⋊C8—21no—
555C22⋊C8—21no—
556C22⋊C8—21no—
557C22⋊C8—21no—
558C22⋊C8—21no—
559C22⋊C8—21no—
560C22⋊C8—21no—
561C22⋊C8D4×C6111yescharacteristic
562C22⋊C8D4×C6111yescharacteristic
563C22⋊C8D4×C6111yescharacteristic
564C22⋊C8D4×C6111yescharacteristic
565C24—21no—
566C24—21no—
567C24#41×C6111yescharacteristic
568#41—21no—
569#41—21no—
570#41—22no—
571#41—22no—
572#41—21no—
573#41—21no—
574#41—21no—
575#41—21no—
576#41—42no—
577#41—42no—
578#41—41no—
579#41—41no—
580#41—42no—
581#41—42no—
582#41#41×C6112yes—
583#41#41×C6112yes—
584C2×Q8—21no—
585C2×Q8—22no—
586C2×Q8—41no—
587C2×Q8C2×D4×C6111yescharacteristic
588C2×Q8C2×D4×C6111yescharacteristic
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—41no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—82no—
607C2×D4C2×D4×C6111yescharacteristic
608C2×D4C2×D4×C6111yescharacteristic
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4C2×D4×C6111yescharacteristic
624C22×C4C2×D4×C6111yescharacteristic
625C22×C4C2×D4×C6111yescharacteristic
626C22×C4C2×D4×C6111yescharacteristic
627C22×C4#41×C6111yescharacteristic
628C22×C4C24×C6111yescharacteristic
629SD16—42no—
630SD16—42no—
631D8—42no—
632D8—42no—
633M16—21no—
634M16—21no—
635M16—21no—
636M16—21no—
637M16—21no—
638M16—21no—
639M16—21no—
640M16—21no—
641M16—21no—
642M16—21no—
643M16—21no—
644M16—21no—
645M16—42no—
646M16—42no—
647M16—42no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—42no—
659C2×C8—42no—
660C2×C8—42no—
661C2×C8C2×D4×C6111yescharacteristic
662C2×C8C2×D4×C6111yescharacteristic
663C2×C8C2×D4×C6111yescharacteristic
664C2×C8C2×D4×C6111yescharacteristic
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C22⋊C4—41no—
672C22⋊C4—41no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C42—41no—
676C42—41no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—41no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—81no—
689C23—81no—
690C23—81no—
691C23#121×C6111yescharacteristic
692C23#121×C6111yescharacteristic
693C23C2×#41×C6111yescharacteristic
694Q8—21no—
695Q8—21no—
696Q8—21no—
697Q8—42no—
698Q8#123×C6112yes—
699D4—22no—
700D4—22no—
701D4—21no—
702D4—21no—
703D4—21no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—82no—
714D4—82no—
715D4#123×C6112yes—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4#121×C6111yescharacteristic
742C2×C4#121×C6111yescharacteristic
743C2×C4C22×D4×C6111yescharacteristic
744C2×C4C22×D4×C6111yescharacteristic
745C2×C4C2×#41×C6111yescharacteristic
746C2×C4C2×#41×C6111yescharacteristic
747C2×C4H(5,𝔽2)×C6111yescharacteristic
748C2×C4H(5,𝔽2)×C6111yescharacteristic
749C8—21no—
750C8—21no—
751C8—21no—
752C8—21no—
753C8—41no—
754C8—41no—
755C8—41no—
756C8—41no—
757C8—41no—
758C8—41no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—81no—
774C22—81no—
775C22—84no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—161no—
780C22—161no—
781C22C2×#121×C6111yescharacteristic
782C22C61×#55111yescharacteristic
783C22C61×#55111yescharacteristic
784C4—21no—
785C4—21no—
786C4—22no—
787C4—41no—
788C4—81no—
789C4—81no—
790C4—81no—
791C4C2×#123×C6111yescharacteristic
792C4C61×#53411yescharacteristic
793C4C61×#54611yescharacteristic
794C4C61×#54611yescharacteristic
795C2—21no—
796C2—21no—
797C2—41no—
798C2—41no—
799C2—42no—
800C2—81no—
801C2—161no—
802C2C61×#241211yescharacteristic
803C2C61×#306711yescharacteristic
804C2C61×#306811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3006C2
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×#482C2semidirect
3. C61×#2896C2semidirect
4. C61×#2880C2semidirect
5. C61×#2079C2semidirect
6. C61×#2078C2semidirect
7. C61×#2051C2semidirect
8. C61×#2051C2semidirect
9. C61×#1907C2semidirect
10. C61×#1907C2semidirect
11. C61×#1900C2semidirect
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×#102×C61C22semidirect
47. C2×#102×C61C22semidirect
48. C2×#100×C61C22semidirect
49. C2×#100×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
356. #24575C61direct (N × H)
393. C2×#482C2×C61semidirect
395. #2896C2×C61semidirect
396. #2880C2×C61semidirect
397. #2079C2×C61semidirect
398. #2078C2×C61semidirect
399. #2051C2×C61semidirect
400. #2051C2×C61semidirect
401. #1907C2×C61semidirect
402. #1907C2×C61semidirect
403. #1900C2×C61semidirect
404. #1855C2×C61semidirect
405. #1822C2×C61semidirect
406. #1816C2×C61semidirect
407. #1815C2×C61semidirect
434. C2×#108C22×C61semidirect
435. C2×#108C22×C61semidirect
436. C2×#107C22×C61semidirect
437. C2×#106C22×C61semidirect
448. C2×#102C22×C61semidirect
449. C2×#102C22×C61semidirect
450. C2×#100C22×C61semidirect
451. C2×#100C22×C61semidirect
461. #343C22×C61semidirect
462. #343C22×C61semidirect
463. #343C22×C61semidirect
464. #343C22×C61semidirect
465. #343C22×C61semidirect
466. #343C22×C61semidirect
467. #341C22×C61semidirect
468. #341C22×C61semidirect
469. C61#24575direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#4822
C61×#30062
C61×#28962
C61×#28802
C61×#20792
C61×#20782
C61×#20512
C61×#19072
C61×#19002
C61×#18552
C61×#18222
C61×#18162
C61×#18152
#2457561