Finite Group Databasebeta

← C61×#24675 #29528108

Subgroups — C61×#24675 #29528108

Order 15616.

764 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3040C211yesmaximal, characteristic
2C2×C61×#464C211yesmaximal, characteristic, complemented
3C4×#137×C61C211yesmaximal, characteristic, complemented
4C61×#2925C211yesmaximal, characteristic, complemented
5C61×#2052C211yesmaximal, characteristic, complemented
6C61×#2051C211yesmaximal, characteristic
7C61×#2020C211yesmaximal, characteristic, complemented
8C61×#2019C211yesmaximal, characteristic
9C61×#1979C211yesmaximal, characteristic, complemented
10C61×#1977C211yesmaximal, characteristic, complemented
11C61×#1967C211yesmaximal, characteristic, complemented
12C61×#1950C211yesmaximal, characteristic, complemented
13C61×#1931C211yesmaximal, characteristic, complemented
14C61×#1930C211yesmaximal, characteristic, complemented
15C61×#1801C211yesmaximal, characteristic, complemented
16C2×#137×C61C2211yescharacteristic
17C2×#137×C61C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
19C22×Q16×C61C2211yescharacteristic
20C22×SD16×C61C2211yescharacteristic
21C2×#124×C61C2211yescharacteristic
22C4×#41×C61C2211yescharacteristic
23C2×C4×Q8×C61C2211yescharacteristic
24C61×#464—21no—
25C61×#464—21no—
26C61×#464—21no—
27C61×#464—21no—
28C61×#464—21no—
29C61×#464—21no—
30C61×#463—21no—
31C61×#463—21no—
32C61×#441—21no—
33C61×#440—21no—
34C4×Q16×C61—21no—
35C4×SD16×C61—21no—
36C61×#433—21no—
37C61×#433—21no—
38C61×#432—21no—
39C61×#431—21no—
40C2×#108×C61C2211yescharacteristic
41C2×#108×C61C2211yescharacteristic
42C61×#428C2211yescharacteristic
43C61×#423C2211yescharacteristic
44C61×#423C2211yescharacteristic
45C2×C4⋊C8×C61C2211yescharacteristic
46C61×#419C2211yescharacteristic
47C61×#419C2211yescharacteristic
48C61×#418C2211yescharacteristic
49C61×#417C2211yescharacteristic
50C2×#103×C61C2211yescharacteristic
51C2×#102×C61C2211yescharacteristic
52C2×#101×C61C2211yescharacteristic
53C2×#101×C61C2211yescharacteristic
54C2×#101×C61C2211yescharacteristic
55C2×#101×C61C2211yescharacteristic
56C2×#100×C61C2211yescharacteristic
57C2×#100×C61C2211yescharacteristic
58C61×#408C2211yescharacteristic
59C61×#408C2211yescharacteristic
60C61×#405C2211yescharacteristic
61C61×#405C2211yescharacteristic
62C4×M16×C61C2211yescharacteristic
63C61×#343C2211yescharacteristic
64C61×#343C2211yescharacteristic
65C61×#341C2211yescharacteristic
66C61×#341C2211yescharacteristic
67C2×#41×C61C2311yescharacteristic
68C22×Q8×C61C2311yescharacteristic
69C22×Q8×C61C2311yescharacteristic
70C22×D4×C61C2311yescharacteristic
71#137×C61—22no—
72#137×C61—22no—
73#137×C61—41no—
74#137×C61—41no—
75AGL(1,ℤ/8)×C61—41no—
76AGL(1,ℤ/8)×C61—41no—
77C2×Q16×C61—21no—
78C2×Q16×C61—21no—
79C2×Q16×C61—22no—
80C2×Q16×C61—21no—
81C2×Q16×C61—21no—
82C2×Q16×C61—41no—
83C2×SD16×C61—21no—
84C2×SD16×C61—21no—
85C2×SD16×C61—22no—
86C2×SD16×C61—21no—
87C2×SD16×C61—21no—
88C2×SD16×C61—21no—
89C2×SD16×C61—41no—
90C2×D8×C61—21no—
91C2×M16×C61C2311yescharacteristic
92C2×M16×C61C2311yescharacteristic
93C2×M16×C61C2311yescharacteristic
94C2×M16×C61C2311yescharacteristic
95C2×M16×C61C2311yescharacteristic
96C2×M16×C61C2311yescharacteristic
97C22×C8×C61C2311yescharacteristic
98C22×C8×C61C2311yescharacteristic
99#124×C61—21no—
100#124×C61—21no—
101#124×C61—21no—
102#124×C61—21no—
103C4×Q8×C61—21no—
104C4×Q8×C61—21no—
105C4×Q8×C61—21no—
106C4×Q8×C61—21no—
107C4×Q8×C61D411yescharacteristic
108C4×Q8×C61D411yescharacteristic
109C4×D4×C61—21no—
110C4×D4×C61—21no—
111C4×D4×C61D411yescharacteristic
112C4×D4×C61D411yescharacteristic
113#117×C61—21no—
114#117×C61C2311yescharacteristic
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C42×C61—21no—
120C2×C42×C61—21no—
121C2×C42×C61C2311yescharacteristic
122#108×C61—41no—
123#108×C61—41no—
124#107×C61—21no—
125#106×C61—21no—
126C4⋊C8×C61—21no—
127C4⋊C8×C61—21no—
128C4⋊C8×C61—21no—
129C4⋊C8×C61—21no—
130C4⋊C8×C61D411yescharacteristic
131C4⋊C8×C61D411yescharacteristic
132C4⋊C8×C61D411yescharacteristic
133C4⋊C8×C61D411yescharacteristic
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#102×C61—21no—
142#102×C61—21no—
143#102×C61—21no—
144#102×C61—21no—
145#102×C61—21no—
146#101×C61—22no—
147#101×C61—41no—
148#101×C61—41no—
149#101×C61—41no—
150#100×C61—22no—
151#100×C61—41no—
152C22⋊C8×C61—21no—
153C22⋊C8×C61—21no—
154C22⋊C8×C61—21no—
155C22⋊C8×C61—21no—
156#97×C61—21no—
157#97×C61—21no—
158#97×C61—21no—
159C4×C8×C61—21no—
160C4×C8×C61—21no—
161C4×C8×C61—21no—
162C24×C61—21no—
163#41×C61—21no—
164#41×C61—21no—
165#41×C61—21no—
166#41×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61C2×D411yescharacteristic
179C2×Q8×C61#4112yes—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61C2×D411yescharacteristic
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61#4111yescharacteristic
195C22×C4×C61#4111yescharacteristic
196C22×C4×C61C2411yescharacteristic
197Q16×C61—24no—
198Q16×C61—42no—
199Q16×C61—42no—
200Q16×C61—42no—
201SD16×C61—24no—
202SD16×C61—42no—
203SD16×C61—42no—
204SD16×C61—42no—
205SD16×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—21no—
214M16×C61—21no—
215M16×C61—21no—
216M16×C61—21no—
217M16×C61—21no—
218M16×C61#4112yes—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61C2×D411yescharacteristic
230C2×C8×C61C2×D411yescharacteristic
231C2×C8×C61C2×D411yescharacteristic
232C2×C8×C61C2×D411yescharacteristic
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—41no—
238C4⋊C4×C61—41no—
239C4⋊C4×C61C2×D411yescharacteristic
240C4⋊C4×C61C2×D411yescharacteristic
241C22⋊C4×C61—21no—
242C22⋊C4×C61—21no—
243C22⋊C4×C61—21no—
244C22⋊C4×C61—41no—
245C22⋊C4×C61—41no—
246C22⋊C4×C61—41no—
247C22⋊C4×C61—41no—
248C42×C61—21no—
249C42×C61—21no—
250C42×C61—21no—
251C42×C61—41no—
252C42×C61—41no—
253C42×C61C2×D411yescharacteristic
254C42×C61C2×D411yescharacteristic
255C42×C61C2×D411yescharacteristic
256C42×C61C2×D411yescharacteristic
257C23×C61—21no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—81no—
262C23×C61—81no—
263C23×C61C2×#4111yescharacteristic
264Q8×C61—22no—
265Q8×C61—21no—
266Q8×C61—21no—
267Q8×C61—22no—
268Q8×C61—41no—
269Q8×C61—41no—
270Q8×C61—41no—
271Q8×C61—41no—
272Q8×C61—41no—
273Q8×C61—41no—
274D4×C61—21no—
275D4×C61—21no—
276D4×C61—41no—
277D4×C61—41no—
278D4×C61—41no—
279D4×C61—41no—
280D4×C61—41no—
281D4×C61—41no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—22no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—42no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—81no—
298C2×C4×C61—81no—
299C2×C4×C61#12111yescharacteristic
300C2×C4×C61#12111yescharacteristic
301C2×C4×C61#12111yescharacteristic
302C2×C4×C61#12111yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61H(5,𝔽2)11yescharacteristic
308C2×C4×C61H(5,𝔽2)11yescharacteristic
309C8×C61—22no—
310C8×C61—21no—
311C8×C61—21no—
312C8×C61—21no—
313C8×C61—21no—
314C8×C61—41no—
315C8×C61—41no—
316C8×C61—41no—
317C8×C61—41no—
318C8×C61—41no—
319#24675C6111yesmaximal, characteristic, direct product factor, Sylow
320C22×C61—21no—
321C22×C61—21no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61—81no—
326C22×C61—81no—
327C22×C61—81no—
328C22×C61—161no—
329C22×C61—161no—
330C22×C61C2×#12111yescharacteristic
331C22×C61#55311yescharacteristic
332C22×C61#55511yescharacteristic
333C4×C61—21no—
334C4×C61—21no—
335C4×C61—21no—
336C4×C61—21no—
337C4×C61—41no—
338C4×C61—42no—
339C4×C61—41no—
340C4×C61—41no—
341C4×C61—81no—
342C4×C61—81no—
343C4×C61#52511yescharacteristic
344C4×C61#53511yescharacteristic
345C4×C61#54611yescharacteristic
346C4×C61#55011yescharacteristic
347#3040C2×C6111yescharacteristic
348C2×#464C2×C6111yescharacteristic, complemented
349C4×#137C2×C6111yescharacteristic, complemented
350#2925C2×C6111yescharacteristic, complemented
351#2052C2×C6111yescharacteristic, complemented
352#2051C2×C6111yescharacteristic
353#2020C2×C6111yescharacteristic, complemented
354#2019C2×C6111yescharacteristic
355#1979C2×C6111yescharacteristic, complemented
356#1977C2×C6111yescharacteristic, complemented
357#1967C2×C6111yescharacteristic, complemented
358#1950C2×C6111yescharacteristic, complemented
359#1931C2×C6111yescharacteristic, complemented
360#1930C2×C6111yescharacteristic, complemented
361#1801C2×C6111yescharacteristic, complemented
362C2×C61—21no—
363C2×C61—21no—
364C2×C61—81no—
365C2×C61—161no—
366C2×C61#241411yescharacteristic
367C2×C61#306711yescharacteristic
368C2×C61#306911yescharacteristic
369C2×#137C22×C6111yescharacteristic
370C2×#137C22×C6111yescharacteristic
371C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
372C22×Q16C22×C6111yescharacteristic
373C22×SD16C22×C6111yescharacteristic
374C2×#124C22×C6111yescharacteristic
375C4×#41C22×C6111yescharacteristic
376C2×C4×Q8C22×C6111yescharacteristic
377#464—21no—
378#464—21no—
379#464—21no—
380#464—21no—
381#464—21no—
382#464—21no—
383#463—21no—
384#463—21no—
385#441—21no—
386#440—21no—
387C4×Q16—21no—
388C4×SD16—21no—
389#433—21no—
390#433—21no—
391#432—21no—
392#431—21no—
393C2×#108C22×C6111yescharacteristic
394C2×#108C22×C6111yescharacteristic
395#428C22×C6111yescharacteristic
396#423C22×C6111yescharacteristic
397#423C22×C6111yescharacteristic
398C2×C4⋊C8C22×C6111yescharacteristic
399#419C22×C6111yescharacteristic
400#419C22×C6111yescharacteristic
401#418C22×C6111yescharacteristic
402#417C22×C6111yescharacteristic
403C2×#103C22×C6111yescharacteristic
404C2×#102C22×C6111yescharacteristic
405C2×#101C22×C6111yescharacteristic
406C2×#101C22×C6111yescharacteristic
407C2×#101C22×C6111yescharacteristic
408C2×#101C22×C6111yescharacteristic
409C2×#100C22×C6111yescharacteristic
410C2×#100C22×C6111yescharacteristic
411#408C22×C6111yescharacteristic
412#408C22×C6111yescharacteristic
413#405C22×C6111yescharacteristic
414#405C22×C6111yescharacteristic
415C4×M16C22×C6111yescharacteristic
416#343C22×C6111yescharacteristic
417#343C22×C6111yescharacteristic
418#341C22×C6111yescharacteristic
419#341C22×C6111yescharacteristic
420C61#2467511yescharacteristic, direct product factor, Sylow
421C2×#41C23×C6111yescharacteristic
422C22×Q8C23×C6111yescharacteristic
423C22×Q8C23×C6111yescharacteristic
424C22×D4C23×C6111yescharacteristic
425#137—22no—
426#137—22no—
427#137—41no—
428#137—41no—
429AGL(1,ℤ/8)—41no—
430AGL(1,ℤ/8)—41no—
431C2×Q16—21no—
432C2×Q16—21no—
433C2×Q16—22no—
434C2×Q16—21no—
435C2×Q16—21no—
436C2×Q16—41no—
437C2×SD16—21no—
438C2×SD16—21no—
439C2×SD16—22no—
440C2×SD16—21no—
441C2×SD16—21no—
442C2×SD16—21no—
443C2×SD16—41no—
444C2×D8—21no—
445C2×M16C23×C6111yescharacteristic
446C2×M16C23×C6111yescharacteristic
447C2×M16C23×C6111yescharacteristic
448C2×M16C23×C6111yescharacteristic
449C2×M16C23×C6111yescharacteristic
450C2×M16C23×C6111yescharacteristic
451C22×C8C23×C6111yescharacteristic
452C22×C8C23×C6111yescharacteristic
453#124—21no—
454#124—21no—
455#124—21no—
456#124—21no—
457C4×Q8—21no—
458C4×Q8—21no—
459C4×Q8—21no—
460C4×Q8—21no—
461C4×Q8D4×C6111yescharacteristic
462C4×Q8D4×C6111yescharacteristic
463C4×D4—21no—
464C4×D4—21no—
465C4×D4D4×C6111yescharacteristic
466C4×D4D4×C6111yescharacteristic
467#117—21no—
468#117C23×C6111yescharacteristic
469C2×C4⋊C4—21no—
470C2×C4⋊C4C23×C6111yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42C23×C6111yescharacteristic
476#108—41no—
477#108—41no—
478#107—21no—
479#106—21no—
480C4⋊C8—21no—
481C4⋊C8—21no—
482C4⋊C8—21no—
483C4⋊C8—21no—
484C4⋊C8D4×C6111yescharacteristic
485C4⋊C8D4×C6111yescharacteristic
486C4⋊C8D4×C6111yescharacteristic
487C4⋊C8D4×C6111yescharacteristic
488#103—21no—
489#103—21no—
490#103—21no—
491#103—21no—
492#103—21no—
493#103—21no—
494#103—21no—
495#102—21no—
496#102—21no—
497#102—21no—
498#102—21no—
499#102—21no—
500#101—22no—
501#101—41no—
502#101—41no—
503#101—41no—
504#100—22no—
505#100—41no—
506C22⋊C8—21no—
507C22⋊C8—21no—
508C22⋊C8—21no—
509C22⋊C8—21no—
510#97—21no—
511#97—21no—
512#97—21no—
513C4×C8—21no—
514C4×C8—21no—
515C4×C8—21no—
516C24—21no—
517#41—21no—
518#41—21no—
519#41—21no—
520#41—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8C2×D4×C6111yescharacteristic
533C2×Q8#41×C6112yes—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4C2×D4×C6111yescharacteristic
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4#41×C6111yescharacteristic
549C22×C4#41×C6111yescharacteristic
550C22×C4C24×C6111yescharacteristic
551Q16—24no—
552Q16—42no—
553Q16—42no—
554Q16—42no—
555SD16—24no—
556SD16—42no—
557SD16—42no—
558SD16—42no—
559SD16—42no—
560D8—42no—
561M16—21no—
562M16—21no—
563M16—21no—
564M16—21no—
565M16—21no—
566M16—21no—
567M16—21no—
568M16—21no—
569M16—21no—
570M16—21no—
571M16—21no—
572M16#41×C6112yes—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8C2×D4×C6111yescharacteristic
584C2×C8C2×D4×C6111yescharacteristic
585C2×C8C2×D4×C6111yescharacteristic
586C2×C8C2×D4×C6111yescharacteristic
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4C2×D4×C6111yescharacteristic
594C4⋊C4C2×D4×C6111yescharacteristic
595C22⋊C4—21no—
596C22⋊C4—21no—
597C22⋊C4—21no—
598C22⋊C4—41no—
599C22⋊C4—41no—
600C22⋊C4—41no—
601C22⋊C4—41no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—41no—
606C42—41no—
607C42C2×D4×C6111yescharacteristic
608C42C2×D4×C6111yescharacteristic
609C42C2×D4×C6111yescharacteristic
610C42C2×D4×C6111yescharacteristic
611C23—21no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—81no—
616C23—81no—
617C23C2×#41×C6111yescharacteristic
618Q8—21no—
619Q8—22no—
620Q8—22no—
621Q8—21no—
622Q8—41no—
623Q8—41no—
624Q8—41no—
625Q8—41no—
626Q8—41no—
627Q8—41no—
628D4—21no—
629D4—21no—
630D4—41no—
631D4—41no—
632D4—41no—
633D4—41no—
634D4—41no—
635D4—41no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—42no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—81no—
652C2×C4—81no—
653C2×C4#121×C6111yescharacteristic
654C2×C4#121×C6111yescharacteristic
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×C4H(5,𝔽2)×C6111yescharacteristic
663C8—21no—
664C8—21no—
665C8—21no—
666C8—21no—
667C8—22no—
668C8—41no—
669C8—41no—
670C8—41no—
671C8—41no—
672C8—41no—
673C22—21no—
674C22—21no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—161no—
682C22—161no—
683C22C2×#121×C6111yescharacteristic
684C22C61×#55311yescharacteristic
685C22C61×#55511yescharacteristic
686C4—21no—
687C4—21no—
688C4—21no—
689C4—21no—
690C4—41no—
691C4—41no—
692C4—41no—
693C4—42no—
694C4—81no—
695C4—81no—
696C4C61×#52511yescharacteristic
697C4C61×#53511yescharacteristic
698C4C61×#54611yescharacteristic
699C4C61×#55011yescharacteristic
700C2—21no—
701C2—21no—
702C2—81no—
703C2—161no—
704C2C61×#241411yescharacteristic
705C2C61×#306711yescharacteristic
706C2C61×#306911yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×AGL(1,ℤ/8)×C61C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C61×#464C2semidirect
3. C4×#137×C61C2semidirect
4. C61×#2925C2semidirect
5. C61×#2052C2semidirect
7. C61×#2020C2semidirect
9. C61×#1979C2semidirect
10. C61×#1977C2semidirect
11. C61×#1967C2semidirect
12. C61×#1950C2semidirect
13. C61×#1931C2semidirect
14. C61×#1930C2semidirect
15. C61×#1801C2semidirect
319. #24675C61direct (N × H)
348. C2×#464C2×C61semidirect
349. C4×#137C2×C61semidirect
350. #2925C2×C61semidirect
351. #2052C2×C61semidirect
353. #2020C2×C61semidirect
355. #1979C2×C61semidirect
356. #1977C2×C61semidirect
357. #1967C2×C61semidirect
358. #1950C2×C61semidirect
359. #1931C2×C61semidirect
360. #1930C2×C61semidirect
361. #1801C2×C61semidirect
420. C61#24675direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#30402
C2×C61×#4642
C4×#137×C612
C61×#29252
C61×#20522
C61×#20512
C61×#20202
C61×#20192
C61×#19792
C61×#19772
C61×#19672
C61×#19502
C61×#19312
C61×#19302
C61×#18012
#2467561