Finite Group Databasebeta

← C61×#25264 #29528697

Subgroups — C61×#25264 #29528697

Order 15616.

776 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3092C211yesmaximal, characteristic, complemented
2C2×C61×#480C211yesmaximal, characteristic, complemented
3C61×#3055C211yesmaximal, characteristic
4C61×#2933C211yesmaximal, characteristic, complemented
5C61×#2089C211yesmaximal, characteristic, complemented
6C61×#2078C211yesmaximal, characteristic, complemented
7C61×#2063C211yesmaximal, characteristic, complemented
8C61×#2051C211yesmaximal, characteristic, complemented
9C61×#1952C211yesmaximal, characteristic, complemented
10C61×#1931C211yesmaximal, characteristic, complemented
11C61×#1907C211yesmaximal, characteristic, complemented
12C61×#1900C211yesmaximal, characteristic, complemented
13C61×#1855C211yesmaximal, characteristic, complemented
14C61×#1816C211yesmaximal, characteristic, complemented
15C2×C61×#343C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
17C2×#131×C61C2211yescharacteristic
18C22×M16×C61C2211yescharacteristic
19C22×M16×C61C2211yescharacteristic
20C61×#525C2211yescharacteristic
21C2×#121×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C61×#484—21no—
24C61×#483—21no—
25C61×#481—21no—
26C61×#480—21no—
27C61×#480—21no—
28C61×#480—21no—
29C61×#480—21no—
30C61×#480—21no—
31C61×#469—21no—
32C61×#468—21no—
33C61×#466—21no—
34C61×#465—21no—
35C61×#436—21no—
36C61×#435—21no—
37C61×#435—21no—
38C8×D4×C61—21no—
39C2×#108×C61C2211yescharacteristic
40C2×#108×C61C2211yescharacteristic
41C61×#428C2211yescharacteristic
42C61×#428C2211yescharacteristic
43C61×#428C2211yescharacteristic
44C2×#107×C61C2211yescharacteristic
45C2×#107×C61C2211yescharacteristic
46C61×#424C2211yescharacteristic
47C61×#418C2211yescharacteristic
48C61×#417C2211yescharacteristic
49C61×#417C2211yescharacteristic
50C61×#417C2211yescharacteristic
51C2×#102×C61C2211yescharacteristic
52C2×#102×C61C2211yescharacteristic
53C2×#100×C61C2211yescharacteristic
54C2×#100×C61C2211yescharacteristic
55C61×#408C2211yescharacteristic
56C61×#407C2211yescharacteristic
57C2×C22⋊C8×C61C2211yescharacteristic
58C61×#405C2211yescharacteristic
59C61×#343C2211yescharacteristic
60C61×#343C2211yescharacteristic
61C61×#343C2211yescharacteristic
62C61×#343C2211yescharacteristic
63C61×#343C2211yescharacteristic
64C61×#343C2211yescharacteristic
65C61×#341C2211yescharacteristic
66C61×#341C2211yescharacteristic
67C2×#41×C61C2311yescharacteristic
68C22×D4×C61—21no—
69C22×D4×C61C2311yescharacteristic
70C23×C4×C61—21no—
71C23×C4×C61C2311yescharacteristic
72AGL(1,ℤ/8)×C61—22no—
73AGL(1,ℤ/8)×C61—41no—
74C2×SD16×C61—21no—
75C2×D8×C61—21no—
76#131×C61—22no—
77#131×C61—41no—
78C2×M16×C61—21no—
79C2×M16×C61—21no—
80C2×M16×C61—21no—
81C2×M16×C61—22no—
82C2×M16×C61—22no—
83C2×M16×C61—41no—
84C2×M16×C61—41no—
85C2×M16×C61C2311yescharacteristic
86C2×M16×C61C2311yescharacteristic
87C2×M16×C61C2311yescharacteristic
88C2×M16×C61C2311yescharacteristic
89C2×M16×C61C2311yescharacteristic
90C2×M16×C61C2311yescharacteristic
91C22×C8×C61—21no—
92C22×C8×C61—21no—
93C22×C8×C61—21no—
94C22×C8×C61C2311yescharacteristic
95C22×C8×C61C2311yescharacteristic
96#123×C61—21no—
97C22⋊Q8×C61D411yescharacteristic
98C22⋊Q8×C61D411yescharacteristic
99#121×C61—21no—
100#121×C61—21no—
101#121×C61—21no—
102#121×C61—21no—
103#121×C61D411yescharacteristic
104#121×C61D411yescharacteristic
105#120×C61—21no—
106C4×D4×C61—21no—
107C4×D4×C61—21no—
108#117×C61C2311yescharacteristic
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C22⋊C4×C61—21no—
118#108×C61—22no—
119#108×C61—41no—
120#107×C61—21no—
121#107×C61—21no—
122#107×C61—21no—
123#107×C61—21no—
124#107×C61—21no—
125#107×C61—21no—
126#107×C61—21no—
127#106×C61—21no—
128#106×C61—21no—
129#106×C61—21no—
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132#103×C61—21no—
133#103×C61—21no—
134#103×C61—21no—
135#102×C61—21no—
136#102×C61—21no—
137#102×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#100×C61—22no—
145#100×C61—41no—
146C22⋊C8×C61—21no—
147C22⋊C8×C61—21no—
148C22⋊C8×C61—21no—
149C22⋊C8×C61—21no—
150C22⋊C8×C61D411yescharacteristic
151C22⋊C8×C61D411yescharacteristic
152C22⋊C8×C61D411yescharacteristic
153C22⋊C8×C61D411yescharacteristic
154#97×C61—21no—
155C4×C8×C61—21no—
156C24×C61—21no—
157C24×C61#4111yescharacteristic
158#41×C61—21no—
159#41×C61—21no—
160#41×C61—21no—
161#41×C61—21no—
162C2×Q8×C61C2×D411yescharacteristic
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—41no—
173C2×D4×C61—41no—
174C2×D4×C61—82no—
175C2×D4×C61C2×D411yescharacteristic
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—41no—
185C22×C4×C61—41no—
186C22×C4×C61—82no—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61#4111yescharacteristic
192C22×C4×C61C2411yescharacteristic
193SD16×C61—42no—
194D8×C61—42no—
195M16×C61—21no—
196M16×C61—21no—
197M16×C61—21no—
198M16×C61—21no—
199M16×C61—21no—
200M16×C61—21no—
201M16×C61—21no—
202M16×C61—21no—
203M16×C61—21no—
204M16×C61—21no—
205M16×C61—42no—
206M16×C61—42no—
207M16×C61—42no—
208M16×C61#4112yes—
209M16×C61#4112yes—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—42no—
221C2×C8×C61—42no—
222C2×C8×C61—42no—
223C2×C8×C61C2×D411yescharacteristic
224C2×C8×C61C2×D411yescharacteristic
225C2×C8×C61C2×D411yescharacteristic
226C2×C8×C61C2×D411yescharacteristic
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—41no—
236C4⋊C4×C61—41no—
237C4⋊C4×C61C2×D411yescharacteristic
238C4⋊C4×C61C2×D411yescharacteristic
239C22⋊C4×C61—21no—
240C22⋊C4×C61—21no—
241C22⋊C4×C61—21no—
242C22⋊C4×C61—21no—
243C22⋊C4×C61—21no—
244C22⋊C4×C61—41no—
245C22⋊C4×C61—41no—
246C42×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—22no—
250C23×C61—21no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—81no—
256C23×C61—81no—
257C23×C61#12111yescharacteristic
258C23×C61#12111yescharacteristic
259C23×C61C2×#4111yescharacteristic
260Q8×C61—21no—
261Q8×C61—21no—
262D4×C61—21no—
263D4×C61—21no—
264D4×C61—41no—
265D4×C61—41no—
266D4×C61—42no—
267D4×C61—41no—
268D4×C61—41no—
269D4×C61—41no—
270D4×C61—41no—
271D4×C61—81no—
272D4×C61—82no—
273D4×C61—82no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—82no—
293C2×C4×C61—82no—
294C2×C4×C61—81no—
295C2×C4×C61—81no—
296C2×C4×C61—81no—
297C2×C4×C61#12111yescharacteristic
298C2×C4×C61#12111yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C2×C4×C612−1+411yescharacteristic
305C8×C61—21no—
306C8×C61—21no—
307C8×C61—22no—
308C8×C61—22no—
309C8×C61—21no—
310C8×C61—21no—
311C8×C61—41no—
312C8×C61—41no—
313C8×C61—41no—
314C8×C61—41no—
315#25264C6111yesmaximal, characteristic, direct product factor, Sylow
316C22×C61—21no—
317C22×C61—21no—
318C22×C61—21no—
319C22×C61—21no—
320C22×C61—21no—
321C22×C61—21no—
322C22×C61—21no—
323C22×C61—42no—
324C22×C61—42no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—81no—
329C22×C61—81no—
330C22×C61—81no—
331C22×C61—161no—
332C22×C61—161no—
333C22×C61#47212yes—
334C22×C61C2×#12111yescharacteristic
335C22×C61#52911yescharacteristic
336C22×C61#53911yescharacteristic
337C4×C61—21no—
338C4×C61—21no—
339C4×C61—41no—
340C4×C61—41no—
341C4×C61—41no—
342C4×C61—81no—
343C4×C61—81no—
344C4×C61—81no—
345C4×C61#54611yescharacteristic
346C4×C61#54611yescharacteristic
347C4×C61#54711yescharacteristic
348C4×C61#54711yescharacteristic
349#3092C2×C6111yescharacteristic, complemented
350C2×#480C2×C6111yescharacteristic, complemented
351#3055C2×C6111yescharacteristic
352#2933C2×C6111yescharacteristic, complemented
353#2089C2×C6111yescharacteristic, complemented
354#2078C2×C6111yescharacteristic, complemented
355#2063C2×C6111yescharacteristic, complemented
356#2051C2×C6111yescharacteristic, complemented
357#1952C2×C6111yescharacteristic, complemented
358#1931C2×C6111yescharacteristic, complemented
359#1907C2×C6111yescharacteristic, complemented
360#1900C2×C6111yescharacteristic, complemented
361#1855C2×C6111yescharacteristic, complemented
362#1816C2×C6111yescharacteristic, complemented
363C2×#343C2×C6111yescharacteristic, complemented
364C2×C61—21no—
365C2×C61—21no—
366C2×C61—22no—
367C2×C61—41no—
368C2×C61—81no—
369C2×C61—161no—
370C2×C61#242511yescharacteristic
371C2×C61C2×#47211yescharacteristic
372C2×C61#306911yescharacteristic
373C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
374C2×#131C22×C6111yescharacteristic
375C22×M16C22×C6111yescharacteristic
376C22×M16C22×C6111yescharacteristic
377#525C22×C6111yescharacteristic
378C2×#121C22×C6111yescharacteristic
379C22×C4⋊C4C22×C6111yescharacteristic
380#484—21no—
381#483—21no—
382#481—21no—
383#480—21no—
384#480—21no—
385#480—21no—
386#480—21no—
387#480—21no—
388#469—21no—
389#468—21no—
390#466—21no—
391#465—21no—
392#436—21no—
393#435—21no—
394#435—21no—
395C8×D4—21no—
396C2×#108C22×C6111yescharacteristic
397C2×#108C22×C6111yescharacteristic
398#428C22×C6111yescharacteristic
399#428C22×C6111yescharacteristic
400#428C22×C6111yescharacteristic
401C2×#107C22×C6111yescharacteristic
402C2×#107C22×C6111yescharacteristic
403#424C22×C6111yescharacteristic
404#418C22×C6111yescharacteristic
405#417C22×C6111yescharacteristic
406#417C22×C6111yescharacteristic
407#417C22×C6111yescharacteristic
408C2×#102C22×C6111yescharacteristic
409C2×#102C22×C6111yescharacteristic
410C2×#100C22×C6111yescharacteristic
411C2×#100C22×C6111yescharacteristic
412#408C22×C6111yescharacteristic
413#407C22×C6111yescharacteristic
414C2×C22⋊C8C22×C6111yescharacteristic
415#405C22×C6111yescharacteristic
416#343C22×C6111yescharacteristic
417#343C22×C6111yescharacteristic
418#343C22×C6111yescharacteristic
419#343C22×C6111yescharacteristic
420#343C22×C6111yescharacteristic
421#343C22×C6111yescharacteristic
422#341C22×C6111yescharacteristic
423#341C22×C6111yescharacteristic
424C61#2526411yescharacteristic, direct product factor, Sylow
425C2×#41C23×C6111yescharacteristic
426C22×D4—21no—
427C22×D4C23×C6111yescharacteristic
428C23×C4—21no—
429C23×C4C23×C6111yescharacteristic
430AGL(1,ℤ/8)—22no—
431AGL(1,ℤ/8)—41no—
432C2×SD16—21no—
433C2×D8—21no—
434#131—22no—
435#131—41no—
436C2×M16—21no—
437C2×M16—21no—
438C2×M16—21no—
439C2×M16—22no—
440C2×M16—22no—
441C2×M16—41no—
442C2×M16—41no—
443C2×M16C23×C6111yescharacteristic
444C2×M16C23×C6111yescharacteristic
445C2×M16C23×C6111yescharacteristic
446C2×M16C23×C6111yescharacteristic
447C2×M16C23×C6111yescharacteristic
448C2×M16C23×C6111yescharacteristic
449C22×C8—21no—
450C22×C8—21no—
451C22×C8—21no—
452C22×C8C23×C6111yescharacteristic
453C22×C8C23×C6111yescharacteristic
454#123—21no—
455C22⋊Q8D4×C6111yescharacteristic
456C22⋊Q8D4×C6111yescharacteristic
457#121—21no—
458#121—21no—
459#121—21no—
460#121—21no—
461#121D4×C6111yescharacteristic
462#121D4×C6111yescharacteristic
463#120—21no—
464C4×D4—21no—
465C4×D4—21no—
466#117C23×C6111yescharacteristic
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4C23×C6111yescharacteristic
473C2×C4⋊C4C23×C6111yescharacteristic
474C2×C4⋊C4C23×C6111yescharacteristic
475C2×C22⋊C4—21no—
476#108—22no—
477#108—41no—
478#107—21no—
479#107—21no—
480#107—21no—
481#107—21no—
482#107—21no—
483#107—21no—
484#107—21no—
485#106—21no—
486#106—21no—
487#106—21no—
488C4⋊C8—21no—
489C4⋊C8—21no—
490#103—21no—
491#103—21no—
492#103—21no—
493#102—21no—
494#102—21no—
495#102—21no—
496#102—21no—
497#102—21no—
498#102—21no—
499#102—21no—
500#102—21no—
501#102—21no—
502#100—22no—
503#100—41no—
504C22⋊C8—21no—
505C22⋊C8—21no—
506C22⋊C8—21no—
507C22⋊C8—21no—
508C22⋊C8D4×C6111yescharacteristic
509C22⋊C8D4×C6111yescharacteristic
510C22⋊C8D4×C6111yescharacteristic
511C22⋊C8D4×C6111yescharacteristic
512#97—21no—
513C4×C8—21no—
514C24—21no—
515C24#41×C6111yescharacteristic
516#41—21no—
517#41—21no—
518#41—21no—
519#41—21no—
520C2×Q8C2×D4×C6111yescharacteristic
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—82no—
533C2×D4C2×D4×C6111yescharacteristic
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—82no—
545C22×C4C2×D4×C6111yescharacteristic
546C22×C4C2×D4×C6111yescharacteristic
547C22×C4C2×D4×C6111yescharacteristic
548C22×C4C2×D4×C6111yescharacteristic
549C22×C4#41×C6111yescharacteristic
550C22×C4C24×C6111yescharacteristic
551SD16—42no—
552D8—42no—
553M16—21no—
554M16—21no—
555M16—21no—
556M16—21no—
557M16—21no—
558M16—21no—
559M16—21no—
560M16—21no—
561M16—21no—
562M16—21no—
563M16—42no—
564M16—42no—
565M16—42no—
566M16#41×C6112yes—
567M16#41×C6112yes—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—42no—
579C2×C8—42no—
580C2×C8—42no—
581C2×C8C2×D4×C6111yescharacteristic
582C2×C8C2×D4×C6111yescharacteristic
583C2×C8C2×D4×C6111yescharacteristic
584C2×C8C2×D4×C6111yescharacteristic
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4C2×D4×C6111yescharacteristic
596C4⋊C4C2×D4×C6111yescharacteristic
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—41no—
603C22⋊C4—41no—
604C42—21no—
605C23—21no—
606C23—22no—
607C23—21no—
608C23—21no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—81no—
614C23—81no—
615C23#121×C6111yescharacteristic
616C23#121×C6111yescharacteristic
617C23C2×#41×C6111yescharacteristic
618Q8—21no—
619Q8—21no—
620D4—21no—
621D4—21no—
622D4—41no—
623D4—42no—
624D4—41no—
625D4—41no—
626D4—41no—
627D4—41no—
628D4—41no—
629D4—81no—
630D4—82no—
631D4—82no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—82no—
651C2×C4—82no—
652C2×C4—81no—
653C2×C4—81no—
654C2×C4—81no—
655C2×C4#121×C6111yescharacteristic
656C2×C4#121×C6111yescharacteristic
657C2×C4C22×D4×C6111yescharacteristic
658C2×C4C22×D4×C6111yescharacteristic
659C2×C4C2×#41×C6111yescharacteristic
660C2×C4C2×#41×C6111yescharacteristic
661C2×C4H(5,𝔽2)×C6111yescharacteristic
662C2×C42−1+4×C6111yescharacteristic
663C8—21no—
664C8—21no—
665C8—22no—
666C8—22no—
667C8—21no—
668C8—21no—
669C8—41no—
670C8—41no—
671C8—41no—
672C8—41no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—42no—
681C22—42no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—161no—
689C22—161no—
690C22C61×#47212yes—
691C22C2×#121×C6111yescharacteristic
692C22C61×#52911yescharacteristic
693C22C61×#53911yescharacteristic
694C4—21no—
695C4—21no—
696C4—41no—
697C4—41no—
698C4—41no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4C61×#54611yescharacteristic
703C4C61×#54611yescharacteristic
704C4C61×#54711yescharacteristic
705C4C61×#54711yescharacteristic
706C2—21no—
707C2—21no—
708C2—22no—
709C2—41no—
710C2—81no—
711C2—161no—
712C2C61×#242511yescharacteristic
713C2C2×C61×#47211yescharacteristic
714C2C61×#306911yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3055C2
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. C61×#3092C2semidirect
2. C2×C61×#480C2semidirect
4. C61×#2933C2semidirect
5. C61×#2089C2semidirect
6. C61×#2078C2semidirect
7. C61×#2063C2semidirect
8. C61×#2051C2semidirect
9. C61×#1952C2semidirect
10. C61×#1931C2semidirect
11. C61×#1907C2semidirect
12. C61×#1900C2semidirect
13. C61×#1855C2semidirect
14. C61×#1816C2semidirect
15. C2×C61×#343C2semidirect
315. #25264C61direct (N × H)
349. #3092C2×C61semidirect
350. C2×#480C2×C61semidirect
352. #2933C2×C61semidirect
353. #2089C2×C61semidirect
354. #2078C2×C61semidirect
355. #2063C2×C61semidirect
356. #2051C2×C61semidirect
357. #1952C2×C61semidirect
358. #1931C2×C61semidirect
359. #1907C2×C61semidirect
360. #1900C2×C61semidirect
361. #1855C2×C61semidirect
362. #1816C2×C61semidirect
363. C2×#343C2×C61semidirect
424. C61#25264direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#30922
C2×C61×#4802
C61×#30552
C61×#29332
C61×#20892
C61×#20782
C61×#20632
C61×#20512
C61×#19522
C61×#19312
C61×#19072
C61×#19002
C61×#18552
C61×#18162
C2×C61×#3432
#2526461