Finite Group Databasebeta

← C61×#26996 #29530429

Subgroups — C61×#26996 #29530429

Order 15616.

812 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3099C211yesmaximal, characteristic, complemented
2C61×#3062C211yesmaximal, characteristic, complemented
3C61×#3041C211yesmaximal, characteristic, complemented
4C61×#2946C211yesmaximal, characteristic, complemented
5C61×#2090C211yesmaximal, characteristic, complemented
6C61×#2037C211yesmaximal, characteristic, complemented
7C61×#2018C211yesmaximal, characteristic, complemented
8C61×#2006C211yesmaximal, characteristic, complemented
9C61×#1972C211yesmaximal, characteristic, complemented
10C61×#1938C211yesmaximal, characteristic, complemented
11C61×#1931C211yesmaximal, characteristic, complemented
12C61×#1907C211yesmaximal, characteristic, complemented
13C61×#1883C211yesmaximal, characteristic, complemented
14C61×#1856C211yesmaximal, characteristic, complemented
15C61×#1765C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
19C22×D8×C61C2211yescharacteristic
20C2×#131×C61C2211yescharacteristic
21C61×#537C2211yescharacteristic
22C61×#535C2211yescharacteristic
23C61×#520C2211yescharacteristic
24C61×#518C2211yescharacteristic
25C61×#485—21no—
26C61×#483—21no—
27C61×#482—21no—
28C61×#481—21no—
29C61×#469—21no—
30C61×#468—21no—
31C61×#466—21no—
32C61×#465—21no—
33C61×#463—21no—
34C61×#463—21no—
35C61×#459—21no—
36C61×#459—21no—
37C61×#442—21no—
38C61×#440—21no—
39C4×SD16×C61—21no—
40C4×D8×C61—21no—
41C61×#428C2211yescharacteristic
42C61×#428C2211yescharacteristic
43C61×#428C2211yescharacteristic
44C2×#106×C61C2211yescharacteristic
45C61×#424C2211yescharacteristic
46C2×#104×C61C2211yescharacteristic
47C2×#104×C61C2211yescharacteristic
48C61×#418C2211yescharacteristic
49C61×#417C2211yescharacteristic
50C61×#416C2211yescharacteristic
51C61×#416C2211yescharacteristic
52C2×#102×C61C2211yescharacteristic
53C2×#102×C61C2211yescharacteristic
54C2×#100×C61C2211yescharacteristic
55C2×#100×C61C2211yescharacteristic
56C61×#408C2211yescharacteristic
57C61×#405C2211yescharacteristic
58C2×#97×C61C2211yescharacteristic
59C61×#390C2211yescharacteristic
60C61×#390C2211yescharacteristic
61C61×#343C2211yescharacteristic
62C61×#343C2211yescharacteristic
63C61×#341C2211yescharacteristic
64C61×#341C2211yescharacteristic
65C61×#339C2211yescharacteristic
66C61×#339C2211yescharacteristic
67C2×#41×C61C2311yescharacteristic
68C2×#41×C61C2311yescharacteristic
69C22×D4×C61C2311yescharacteristic
70C22×D4×C61C2311yescharacteristic
71AGL(1,ℤ/8)×C61—22no—
72AGL(1,ℤ/8)×C61—22no—
73AGL(1,ℤ/8)×C61—22no—
74AGL(1,ℤ/8)×C61—22no—
75AGL(1,ℤ/8)×C61—41no—
76AGL(1,ℤ/8)×C61—41no—
77C2×SD16×C61—21no—
78C2×SD16×C61—21no—
79C2×SD16×C61—21no—
80C2×D8×C61—21no—
81C2×D8×C61—21no—
82C2×D8×C61—21no—
83C2×D8×C61—22no—
84C2×D8×C61—21no—
85C2×D8×C61—21no—
86C2×D8×C61—41no—
87#131×C61—22no—
88#131×C61—41no—
89C2×M16×C61—21no—
90C2×M16×C61C2311yescharacteristic
91C2×M16×C61C2311yescharacteristic
92C2×M16×C61C2311yescharacteristic
93C2×M16×C61C2311yescharacteristic
94C22×C8×C61—21no—
95C22×C8×C61C2311yescharacteristic
96C22×C8×C61C2311yescharacteristic
97#127×C61—21no—
98#124×C61—21no—
99C22⋊Q8×C61—21no—
100C22⋊Q8×C61—21no—
101#121×C61—21no—
102#121×C61—21no—
103#121×C61—21no—
104#121×C61—21no—
105#121×C61—41no—
106#120×C61—41no—
107C4×Q8×C61—21no—
108C4×D4×C61—21no—
109C4×D4×C61—21no—
110C4×D4×C61—21no—
111C4×D4×C61—21no—
112C4×D4×C61—21no—
113C4×D4×C61—41no—
114#117×C61—21no—
115#117×C61C2311yescharacteristic
116#117×C61C2311yescharacteristic
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C22⋊C4×C61—41no—
121C2×C22⋊C4×C61—41no—
122C2×C22⋊C4×C61—41no—
123C2×C42×C61C2311yescharacteristic
124#107×C61—21no—
125#107×C61—21no—
126#107×C61—21no—
127#106×C61—21no—
128#106×C61—21no—
129#106×C61—21no—
130#106×C61—21no—
131#106×C61—21no—
132C4⋊C8×C61—21no—
133C4⋊C8×C61—21no—
134#104×C61—22no—
135#104×C61—41no—
136#103×C61—21no—
137#103×C61D411yescharacteristic
138#103×C61D411yescharacteristic
139#103×C61D411yescharacteristic
140#103×C61D411yescharacteristic
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#102×C61D411yescharacteristic
149#102×C61D411yescharacteristic
150#102×C61D411yescharacteristic
151#102×C61D411yescharacteristic
152#100×C61—22no—
153#100×C61—22no—
154C22⋊C8×C61—21no—
155C22⋊C8×C61—21no—
156#97×C61—21no—
157#97×C61—41no—
158C4×C8×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161#41×C61—21no—
162#41×C61—21no—
163#41×C61—21no—
164#41×C61—21no—
165#41×C61—21no—
166#41×C61—21no—
167#41×C61—21no—
168#41×C61—21no—
169C2×Q8×C61C2×D411yescharacteristic
170C2×Q8×C61C2×D411yescharacteristic
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—41no—
185C2×D4×C61—41no—
186C2×D4×C61—41no—
187C2×D4×C61C2×D411yescharacteristic
188C2×D4×C61C2×D411yescharacteristic
189C2×D4×C61#4112yes—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—41no—
196C22×C4×C61—41no—
197C22×C4×C61—41no—
198C22×C4×C61C2411yescharacteristic
199SD16×C61—24no—
200SD16×C61—42no—
201SD16×C61—42no—
202D8×C61—24no—
203D8×C61—42no—
204D8×C61—42no—
205D8×C61—42no—
206D8×C61—42no—
207M16×C61—21no—
208M16×C61—21no—
209M16×C61—21no—
210M16×C61—21no—
211M16×C61—21no—
212M16×C61—21no—
213M16×C61—42no—
214M16×C61#4112yes—
215M16×C61#4112yes—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—42no—
225C2×C8×C61C2×D411yescharacteristic
226C2×C8×C61C2×D411yescharacteristic
227C2×C8×C61C2×D411yescharacteristic
228C2×C8×C61C2×D411yescharacteristic
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—41no—
234C4⋊C4×C61—41no—
235C4⋊C4×C61C2×D411yescharacteristic
236C4⋊C4×C61C2×D411yescharacteristic
237C4⋊C4×C61C2×D411yescharacteristic
238C4⋊C4×C61C2×D411yescharacteristic
239C22⋊C4×C61—21no—
240C22⋊C4×C61—21no—
241C22⋊C4×C61—41no—
242C22⋊C4×C61—41no—
243C22⋊C4×C61—41no—
244C22⋊C4×C61—41no—
245C22⋊C4×C61—41no—
246C22⋊C4×C61—41no—
247C22⋊C4×C61—41no—
248C22⋊C4×C61—82no—
249C22⋊C4×C61—82no—
250C42×C61—21no—
251C42×C61—21no—
252C42×C61—21no—
253C42×C61—21no—
254C42×C61—41no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—22no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—81no—
264C23×C61—81no—
265C23×C61—81no—
266C23×C61—81no—
267C23×C61H(5,𝔽2)11yescharacteristic
268Q8×C61—21no—
269Q8×C61—21no—
270Q8×C61—21no—
271Q8×C61—21no—
272D4×C61—21no—
273D4×C61—22no—
274D4×C61—21no—
275D4×C61—22no—
276D4×C61—21no—
277D4×C61—21no—
278D4×C61—41no—
279D4×C61—41no—
280D4×C61—41no—
281D4×C61—41no—
282D4×C61—41no—
283D4×C61—41no—
284D4×C61—41no—
285D4×C61—41no—
286D4×C61—41no—
287D4×C61—41no—
288D4×C61—161no—
289D4×C61—161no—
290D4×C61—161no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—81no—
307C2×C4×C61—81no—
308C2×C4×C61—161no—
309C2×C4×C61—161no—
310C2×C4×C61—161no—
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C2×C4×C61H(5,𝔽2)11yescharacteristic
317C8×C61—22no—
318C8×C61—21no—
319C8×C61—21no—
320C8×C61—21no—
321C8×C61—21no—
322C8×C61—22no—
323C8×C61—41no—
324C8×C61—41no—
325#26996C6111yesmaximal, characteristic, direct product factor, Sylow
326C22×C61—21no—
327C22×C61—21no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61—42no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—82no—
336C22×C61—82no—
337C22×C61—81no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61—81no—
342C22×C61—161no—
343C22×C61—161no—
344C22×C61#54011yescharacteristic
345C22×C61D4211yescharacteristic
346C22×C61#55311yescharacteristic
347C4×C61—41no—
348C4×C61—41no—
349C4×C61—41no—
350C4×C61—41no—
351C4×C61—41no—
352C4×C61—41no—
353C4×C61—81no—
354C4×C61—81no—
355C4×C61—81no—
356C4×C61#52511yescharacteristic
357C4×C61#53211yescharacteristic
358C4×C61#54611yescharacteristic
359C4×C61#54611yescharacteristic
360#3099C2×C6111yescharacteristic, complemented
361#3062C2×C6111yescharacteristic, complemented
362#3041C2×C6111yescharacteristic, complemented
363#2946C2×C6111yescharacteristic, complemented
364#2090C2×C6111yescharacteristic, complemented
365#2037C2×C6111yescharacteristic, complemented
366#2018C2×C6111yescharacteristic, complemented
367#2006C2×C6111yescharacteristic, complemented
368#1972C2×C6111yescharacteristic, complemented
369#1938C2×C6111yescharacteristic, complemented
370#1931C2×C6111yescharacteristic, complemented
371#1907C2×C6111yescharacteristic, complemented
372#1883C2×C6111yescharacteristic, complemented
373#1856C2×C6111yescharacteristic, complemented
374#1765C2×C6111yescharacteristic, complemented
375C2×C61—21no—
376C2×C61—21no—
377C2×C61—81no—
378C2×C61—81no—
379C2×C61—82no—
380C2×C61—161no—
381C2×C61#246411yescharacteristic
382C2×C61#328811yescharacteristic
383C2×C61#328811yescharacteristic
384C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
385C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
386C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
387C22×D8C22×C6111yescharacteristic
388C2×#131C22×C6111yescharacteristic
389#537C22×C6111yescharacteristic
390#535C22×C6111yescharacteristic
391#520C22×C6111yescharacteristic
392#518C22×C6111yescharacteristic
393#485—21no—
394#483—21no—
395#482—21no—
396#481—21no—
397#469—21no—
398#468—21no—
399#466—21no—
400#465—21no—
401#463—21no—
402#463—21no—
403#459—21no—
404#459—21no—
405#442—21no—
406#440—21no—
407C4×SD16—21no—
408C4×D8—21no—
409#428C22×C6111yescharacteristic
410#428C22×C6111yescharacteristic
411#428C22×C6111yescharacteristic
412C2×#106C22×C6111yescharacteristic
413#424C22×C6111yescharacteristic
414C2×#104C22×C6111yescharacteristic
415C2×#104C22×C6111yescharacteristic
416#418C22×C6111yescharacteristic
417#417C22×C6111yescharacteristic
418#416C22×C6111yescharacteristic
419#416C22×C6111yescharacteristic
420C2×#102C22×C6111yescharacteristic
421C2×#102C22×C6111yescharacteristic
422C2×#100C22×C6111yescharacteristic
423C2×#100C22×C6111yescharacteristic
424#408C22×C6111yescharacteristic
425#405C22×C6111yescharacteristic
426C2×#97C22×C6111yescharacteristic
427#390C22×C6111yescharacteristic
428#390C22×C6111yescharacteristic
429#343C22×C6111yescharacteristic
430#343C22×C6111yescharacteristic
431#341C22×C6111yescharacteristic
432#341C22×C6111yescharacteristic
433#339C22×C6111yescharacteristic
434#339C22×C6111yescharacteristic
435C61#2699611yescharacteristic, direct product factor, Sylow
436C2×#41C23×C6111yescharacteristic
437C2×#41C23×C6111yescharacteristic
438C22×D4C23×C6111yescharacteristic
439C22×D4C23×C6111yescharacteristic
440AGL(1,ℤ/8)—22no—
441AGL(1,ℤ/8)—22no—
442AGL(1,ℤ/8)—22no—
443AGL(1,ℤ/8)—22no—
444AGL(1,ℤ/8)—41no—
445AGL(1,ℤ/8)—41no—
446C2×SD16—21no—
447C2×SD16—21no—
448C2×SD16—21no—
449C2×D8—21no—
450C2×D8—21no—
451C2×D8—21no—
452C2×D8—22no—
453C2×D8—21no—
454C2×D8—21no—
455C2×D8—41no—
456#131—22no—
457#131—41no—
458C2×M16—21no—
459C2×M16C23×C6111yescharacteristic
460C2×M16C23×C6111yescharacteristic
461C2×M16C23×C6111yescharacteristic
462C2×M16C23×C6111yescharacteristic
463C22×C8—21no—
464C22×C8C23×C6111yescharacteristic
465C22×C8C23×C6111yescharacteristic
466#127—21no—
467#124—21no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470#121—21no—
471#121—21no—
472#121—21no—
473#121—21no—
474#121—41no—
475#120—41no—
476C4×Q8—21no—
477C4×D4—21no—
478C4×D4—21no—
479C4×D4—21no—
480C4×D4—21no—
481C4×D4—21no—
482C4×D4—41no—
483#117—21no—
484#117C23×C6111yescharacteristic
485#117C23×C6111yescharacteristic
486C2×C4⋊C4—21no—
487C2×C4⋊C4C23×C6111yescharacteristic
488C2×C4⋊C4C23×C6111yescharacteristic
489C2×C22⋊C4—41no—
490C2×C22⋊C4—41no—
491C2×C22⋊C4—41no—
492C2×C42C23×C6111yescharacteristic
493#107—21no—
494#107—21no—
495#107—21no—
496#106—21no—
497#106—21no—
498#106—21no—
499#106—21no—
500#106—21no—
501C4⋊C8—21no—
502C4⋊C8—21no—
503#104—22no—
504#104—41no—
505#103—21no—
506#103D4×C6111yescharacteristic
507#103D4×C6111yescharacteristic
508#103D4×C6111yescharacteristic
509#103D4×C6111yescharacteristic
510#102—21no—
511#102—21no—
512#102—21no—
513#102—21no—
514#102—21no—
515#102—21no—
516#102—21no—
517#102D4×C6111yescharacteristic
518#102D4×C6111yescharacteristic
519#102D4×C6111yescharacteristic
520#102D4×C6111yescharacteristic
521#100—22no—
522#100—22no—
523C22⋊C8—21no—
524C22⋊C8—21no—
525#97—21no—
526#97—41no—
527C4×C8—21no—
528C24—21no—
529C24—21no—
530#41—21no—
531#41—21no—
532#41—21no—
533#41—21no—
534#41—21no—
535#41—21no—
536#41—21no—
537#41—21no—
538C2×Q8C2×D4×C6111yescharacteristic
539C2×Q8C2×D4×C6111yescharacteristic
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4C2×D4×C6111yescharacteristic
557C2×D4C2×D4×C6111yescharacteristic
558C2×D4#41×C6112yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4C24×C6111yescharacteristic
568SD16—24no—
569SD16—42no—
570SD16—42no—
571D8—24no—
572D8—42no—
573D8—42no—
574D8—42no—
575D8—42no—
576M16—21no—
577M16—21no—
578M16—21no—
579M16—21no—
580M16—21no—
581M16—21no—
582M16—42no—
583M16#41×C6112yes—
584M16#41×C6112yes—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—42no—
594C2×C8C2×D4×C6111yescharacteristic
595C2×C8C2×D4×C6111yescharacteristic
596C2×C8C2×D4×C6111yescharacteristic
597C2×C8C2×D4×C6111yescharacteristic
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4C2×D4×C6111yescharacteristic
605C4⋊C4C2×D4×C6111yescharacteristic
606C4⋊C4C2×D4×C6111yescharacteristic
607C4⋊C4C2×D4×C6111yescharacteristic
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—41no—
611C22⋊C4—41no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4—41no—
615C22⋊C4—41no—
616C22⋊C4—41no—
617C22⋊C4—82no—
618C22⋊C4—82no—
619C42—21no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—41no—
624C23—21no—
625C23—21no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—81no—
633C23—81no—
634C23—81no—
635C23—81no—
636C23H(5,𝔽2)×C6111yescharacteristic
637Q8—21no—
638Q8—21no—
639Q8—21no—
640Q8—21no—
641D4—21no—
642D4—22no—
643D4—21no—
644D4—21no—
645D4—21no—
646D4—22no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—161no—
658D4—161no—
659D4—161no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—81no—
676C2×C4—81no—
677C2×C4—161no—
678C2×C4—161no—
679C2×C4—161no—
680C2×C4C22×D4×C6111yescharacteristic
681C2×C4C22×D4×C6111yescharacteristic
682C2×C4C2×#41×C6111yescharacteristic
683C2×C4C2×#41×C6111yescharacteristic
684C2×C4C2×#41×C6111yescharacteristic
685C2×C4H(5,𝔽2)×C6111yescharacteristic
686C8—21no—
687C8—21no—
688C8—21no—
689C8—21no—
690C8—22no—
691C8—22no—
692C8—41no—
693C8—41no—
694C22—21no—
695C22—21no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—42no—
703C22—82no—
704C22—82no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—161no—
711C22—161no—
712C22C61×#54011yescharacteristic
713C22D42×C6111yescharacteristic
714C22C61×#55311yescharacteristic
715C4—41no—
716C4—41no—
717C4—41no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—81no—
722C4—81no—
723C4—81no—
724C4C61×#52511yescharacteristic
725C4C61×#53211yescharacteristic
726C4C61×#54611yescharacteristic
727C4C61×#54611yescharacteristic
728C2—21no—
729C2—21no—
730C2—81no—
731C2—81no—
732C2—82no—
733C2—161no—
734C2C61×#246411yescharacteristic
735C2C61×#328811yescharacteristic
736C2C61×#328811yescharacteristic
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. C61×#3099C2semidirect
2. C61×#3062C2semidirect
3. C61×#3041C2semidirect
4. C61×#2946C2semidirect
5. C61×#2090C2semidirect
6. C61×#2037C2semidirect
7. C61×#2018C2semidirect
8. C61×#2006C2semidirect
9. C61×#1972C2semidirect
10. C61×#1938C2semidirect
11. C61×#1931C2semidirect
12. C61×#1907C2semidirect
13. C61×#1883C2semidirect
14. C61×#1856C2semidirect
15. C61×#1765C2semidirect
325. #26996C61direct (N × H)
360. #3099C2×C61semidirect
361. #3062C2×C61semidirect
362. #3041C2×C61semidirect
363. #2946C2×C61semidirect
364. #2090C2×C61semidirect
365. #2037C2×C61semidirect
366. #2018C2×C61semidirect
367. #2006C2×C61semidirect
368. #1972C2×C61semidirect
369. #1938C2×C61semidirect
370. #1931C2×C61semidirect
371. #1907C2×C61semidirect
372. #1883C2×C61semidirect
373. #1856C2×C61semidirect
374. #1765C2×C61semidirect
435. C61#26996direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#30992
C61×#30622
C61×#30412
C61×#29462
C61×#20902
C61×#20372
C61×#20182
C61×#20062
C61×#19722
C61×#19382
C61×#19312
C61×#19072
C61×#18832
C61×#18562
C61×#17652
#2699661