Finite Group Databasebeta

← C61×#22097 #29525530

Subgroups — C61×#22097 #29525530

Order 15616.

712 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3091C211yesmaximal, characteristic
2C61×#2930C211yesmaximal, characteristic
3C61×#2905C211yesmaximal, characteristic, complemented
4C61×#1946C211yesmaximal, characteristic, complemented
5C61×#1945C211yesmaximal, characteristic, complemented
6C61×#1938C211yesmaximal, characteristic, complemented
7C61×#1937C211yesmaximal, characteristic, complemented
8C61×#1922C211yesmaximal, characteristic, complemented
9C61×#1922C211yesmaximal, characteristic, complemented
10C61×#1871C211yesmaximal, characteristic
11C61×#1866C211yesmaximal, characteristic, complemented
12C61×#1866C211yesmaximal, characteristic, complemented
13C61×#1855C211yesmaximal, characteristic, complemented
14C61×#1826C211yesmaximal, characteristic, complemented
15C61×#1753C211yesmaximal, characteristic, complemented
16C2×#131×C61C2211yescharacteristic
17C22×M16×C61C2211yescharacteristic
18C22×M16×C61C2211yescharacteristic
19C61×#525C2211yescharacteristic
20C2×#117×C61C2211yescharacteristic
21C61×#485C411yescharacteristic, complemented
22C61×#485C411yescharacteristic, complemented
23C61×#484C411yescharacteristic, complemented
24C61×#483C411yescharacteristic, complemented
25C61×#482C411yescharacteristic, complemented
26C61×#482C411yescharacteristic, complemented
27C61×#481C411yescharacteristic, complemented
28C61×#480C411yescharacteristic, complemented
29C61×#436—21no—
30C61×#436—21no—
31C61×#435—21no—
32C61×#435—21no—
33C2×#108×C61C2211yescharacteristic
34C2×#108×C61C2211yescharacteristic
35C61×#427C2211yescharacteristic
36C61×#427C2211yescharacteristic
37C61×#424—21no—
38C61×#424—21no—
39C61×#424C2211yescharacteristic
40C61×#424C2211yescharacteristic
41C61×#424C2211yescharacteristic
42C61×#424C2211yescharacteristic
43C61×#424C2211yescharacteristic
44C61×#423—21no—
45C61×#423—21no—
46C2×#104×C61C2211yescharacteristic
47C2×#104×C61C2211yescharacteristic
48C61×#416C2211yescharacteristic
49C61×#416C2211yescharacteristic
50C61×#408C2211yescharacteristic
51C61×#407C2211yescharacteristic
52C2×C22⋊C8×C61C2211yescharacteristic
53C61×#405C2211yescharacteristic
54C2×#97×C61C2211yescharacteristic
55C2×C4×C8×C61C2211yescharacteristic
56C4×C22⋊C4×C61C2211yescharacteristic
57C61×#341C2211yescharacteristic
58C61×#341C2211yescharacteristic
59C61×#339C2211yescharacteristic
60C61×#339C2211yescharacteristic
61C61×#339C2211yescharacteristic
62C61×#339C2211yescharacteristic
63C61×#339C2211yescharacteristic
64C61×#339C2211yescharacteristic
65C61×#336C2211yescharacteristic
66C61×#336C2211yescharacteristic
67C2×#41×C61C2311yescharacteristic
68C23×C4×C61C2311yescharacteristic
69#131×C61—41no—
70#131×C61—41no—
71C2×M16×C61—21no—
72C2×M16×C61—21no—
73C2×M16×C61—41no—
74C2×M16×C61—41no—
75C2×M16×C61—41no—
76C2×M16×C61—41no—
77C2×M16×C61D411yescharacteristic
78C2×M16×C61D411yescharacteristic
79C2×M16×C61D411yescharacteristic
80C2×M16×C61D411yescharacteristic
81C2×M16×C61C2311yescharacteristic
82C2×M16×C61C2311yescharacteristic
83C2×M16×C61C2311yescharacteristic
84C2×M16×C61C2311yescharacteristic
85C22×C8×C61—21no—
86C22×C8×C61—21no—
87C22×C8×C61C2311yescharacteristic
88C22×C8×C61C2311yescharacteristic
89C22×C8×C61C2311yescharacteristic
90C22×C8×C61C2311yescharacteristic
91#123×C61—21no—
92C22⋊Q8×C61C2×C411yescharacteristic
93C22⋊Q8×C61C2×C411yescharacteristic
94#121×C61C2×C411yescharacteristic
95#121×C61C2×C411yescharacteristic
96#120×C61—21no—
97C4×D4×C61—21no—
98C4×D4×C61—21no—
99#117×C61—21no—
100#117×C61—21no—
101#117×C61C2×C411yescharacteristic
102#117×C61C2×C411yescharacteristic
103#117×C61C2311yescharacteristic
104#117×C61C2311yescharacteristic
105#117×C61C2311yescharacteristic
106C2×C4⋊C4×C61C2×C411yescharacteristic
107C2×C4⋊C4×C61C2×C411yescharacteristic
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61—21no—
110C2×C42×C61—21no—
111C2×C42×C61C2311yescharacteristic
112C2×C42×C61C2311yescharacteristic
113#108×C61—41no—
114#108×C61—41no—
115#107×C61C2×C411yescharacteristic
116#107×C61C2×C411yescharacteristic
117#107×C61C2×C411yescharacteristic
118#107×C61C2×C411yescharacteristic
119#106×C61C2×C411yescharacteristic
120#106×C61C2×C411yescharacteristic
121#106×C61C2×C411yescharacteristic
122#106×C61C2×C411yescharacteristic
123C4⋊C8×C61—21no—
124C4⋊C8×C61—21no—
125C4⋊C8×C61—21no—
126C4⋊C8×C61—21no—
127C4⋊C8×C61—21no—
128C4⋊C8×C61—21no—
129C4⋊C8×C61—21no—
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61—21no—
133#104×C61—41no—
134#104×C61—41no—
135#103×C61C2×C411yescharacteristic
136#103×C61C2×C411yescharacteristic
137#103×C61C2×C411yescharacteristic
138#103×C61C2×C411yescharacteristic
139#102×C61C2×C411yescharacteristic
140#102×C61C2×C411yescharacteristic
141#102×C61C2×C411yescharacteristic
142#102×C61C2×C411yescharacteristic
143C22⋊C8×C61—21no—
144C22⋊C8×C61—21no—
145C22⋊C8×C61—21no—
146C22⋊C8×C61—21no—
147C22⋊C8×C61C2×C411yescharacteristic
148C22⋊C8×C61C2×C411yescharacteristic
149C22⋊C8×C61C2×C411yescharacteristic
150C22⋊C8×C61C2×C411yescharacteristic
151#97×C61—21no—
152#97×C61—41no—
153C4×C8×C61—21no—
154C4×C8×C61—41no—
155#95×C61—21no—
156C24×C61#4111yescharacteristic
157#41×C61—21no—
158#41×C61—21no—
159#41×C61—21no—
160#41×C61—21no—
161C2×Q8×C61C22×C411yescharacteristic
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61C22×C411yescharacteristic
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61C22×C411yescharacteristic
176C22×C4×C61C22×C411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61#4111yescharacteristic
180C22×C4×C61C2411yescharacteristic
181M16×C61—21no—
182M16×C61—21no—
183M16×C61—21no—
184M16×C61—21no—
185M16×C61—21no—
186M16×C61—21no—
187M16×C61—21no—
188M16×C61—21no—
189M16×C61—41no—
190M16×C61—41no—
191M16×C61—41no—
192M16×C61—41no—
193M16×C61—42no—
194M16×C61—42no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—42no—
208C2×C8×C61—42no—
209C2×C8×C61C22×C411yescharacteristic
210C2×C8×C61C22×C411yescharacteristic
211C2×C8×C61C22×C411yescharacteristic
212C2×C8×C61C22×C411yescharacteristic
213C2×C8×C61C2×D411yescharacteristic
214C2×C8×C61C2×D411yescharacteristic
215C2×C8×C61C2×D411yescharacteristic
216C2×C8×C61C2×D411yescharacteristic
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61C22×C411yescharacteristic
222C4⋊C4×C61C22×C411yescharacteristic
223C4⋊C4×C61C22×C411yescharacteristic
224C4⋊C4×C61C22×C411yescharacteristic
225C4⋊C4×C61C22×C411yescharacteristic
226C4⋊C4×C61C22×C411yescharacteristic
227C22⋊C4×C61—21no—
228C22⋊C4×C61—21no—
229C22⋊C4×C61—21no—
230C22⋊C4×C61—21no—
231C22⋊C4×C61—21no—
232C22⋊C4×C61—21no—
233C22⋊C4×C61—21no—
234C22⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C22⋊C4×C61—42no—
237C42×C61—21no—
238C42×C61—21no—
239C42×C61—21no—
240C42×C61—21no—
241C42×C61—21no—
242C42×C61—21no—
243C42×C61—21no—
244C42×C61—21no—
245C42×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61C4×D411yescharacteristic
252C23×C61C4×D411yescharacteristic
253C23×C61C2×#4111yescharacteristic
254Q8×C61—21no—
255Q8×C61—21no—
256D4×C61—21no—
257D4×C61—21no—
258D4×C61—41no—
259D4×C61—41no—
260D4×C61—81no—
261D4×C61—81no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—22no—
273C2×C4×C61—21no—
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—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—81no—
288C2×C4×C61—81no—
289C2×C4×C61C4×D411yescharacteristic
290C2×C4×C61C4×D411yescharacteristic
291C2×C4×C61C23×C411yescharacteristic
292C2×C4×C61C22×D411yescharacteristic
293C2×C4×C61H(5,𝔽2)11yescharacteristic
294C2×C4×C61H(5,𝔽2)11yescharacteristic
295C2×C4×C612−1+411yescharacteristic
296C2×C4×C612−1+411yescharacteristic
297C8×C61—21no—
298C8×C61—21no—
299C8×C61—21no—
300C8×C61—21no—
301C8×C61—21no—
302C8×C61—21no—
303C8×C61—21no—
304C8×C61—21no—
305C8×C61—41no—
306C8×C61—41no—
307C8×C61—41no—
308C8×C61—41no—
309#22097C6111yesmaximal, characteristic, direct product factor, Sylow
310C22×C61—21no—
311C22×C61—21no—
312C22×C61—21no—
313C22×C61—21no—
314C22×C61—21no—
315C22×C61—21no—
316C22×C61—21no—
317C22×C61—21no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—81no—
322C22×C61—81no—
323C22×C61C2×C4×D411yescharacteristic
324C22×C61#53911yescharacteristic
325C22×C61#53911yescharacteristic
326C4×C61—21no—
327C4×C61—21no—
328C4×C61—42no—
329C4×C61—41no—
330C4×C61—41no—
331C4×C61—41no—
332C4×C61—41no—
333C4×C61—41no—
334C4×C61—41no—
335C4×C61—41no—
336C4×C61—81no—
337C4×C61#52011yescharacteristic
338C4×C61#52011yescharacteristic
339C4×C61#53411yescharacteristic
340C4×C61#53611yescharacteristic
341#3091C2×C6111yescharacteristic
342#2930C2×C6111yescharacteristic
343#2905C2×C6111yescharacteristic, complemented
344#1946C2×C6111yescharacteristic, complemented
345#1945C2×C6111yescharacteristic, complemented
346#1938C2×C6111yescharacteristic, complemented
347#1937C2×C6111yescharacteristic, complemented
348#1922C2×C6111yescharacteristic, complemented
349#1922C2×C6111yescharacteristic, complemented
350#1871C2×C6111yescharacteristic
351#1866C2×C6111yescharacteristic, complemented
352#1866C2×C6111yescharacteristic, complemented
353#1855C2×C6111yescharacteristic, complemented
354#1826C2×C6111yescharacteristic, complemented
355#1753C2×C6111yescharacteristic, complemented
356C2×C61—21no—
357C2×C61—21no—
358C2×C61—41no—
359C2×C61—41no—
360C2×C61—81no—
361C2×C61#232211yescharacteristic
362C2×C61#295611yescharacteristic
363C2×C61#295711yescharacteristic
364C2×#131C22×C6111yescharacteristic
365C22×M16C22×C6111yescharacteristic
366C22×M16C22×C6111yescharacteristic
367#525C22×C6111yescharacteristic
368C2×#117C22×C6111yescharacteristic
369#485C4×C6111yescharacteristic, complemented
370#485C4×C6111yescharacteristic, complemented
371#484C4×C6111yescharacteristic, complemented
372#483C4×C6111yescharacteristic, complemented
373#482C4×C6111yescharacteristic, complemented
374#482C4×C6111yescharacteristic, complemented
375#481C4×C6111yescharacteristic, complemented
376#480C4×C6111yescharacteristic, complemented
377#436—21no—
378#436—21no—
379#435—21no—
380#435—21no—
381C2×#108C22×C6111yescharacteristic
382C2×#108C22×C6111yescharacteristic
383#427C22×C6111yescharacteristic
384#427C22×C6111yescharacteristic
385#424—21no—
386#424—21no—
387#424C22×C6111yescharacteristic
388#424C22×C6111yescharacteristic
389#424C22×C6111yescharacteristic
390#424C22×C6111yescharacteristic
391#424C22×C6111yescharacteristic
392#423—21no—
393#423—21no—
394C2×#104C22×C6111yescharacteristic
395C2×#104C22×C6111yescharacteristic
396#416C22×C6111yescharacteristic
397#416C22×C6111yescharacteristic
398#408C22×C6111yescharacteristic
399#407C22×C6111yescharacteristic
400C2×C22⋊C8C22×C6111yescharacteristic
401#405C22×C6111yescharacteristic
402C2×#97C22×C6111yescharacteristic
403C2×C4×C8C22×C6111yescharacteristic
404C4×C22⋊C4C22×C6111yescharacteristic
405#341C22×C6111yescharacteristic
406#341C22×C6111yescharacteristic
407#339C22×C6111yescharacteristic
408#339C22×C6111yescharacteristic
409#339C22×C6111yescharacteristic
410#339C22×C6111yescharacteristic
411#339C22×C6111yescharacteristic
412#339C22×C6111yescharacteristic
413#336C22×C6111yescharacteristic
414#336C22×C6111yescharacteristic
415C61#2209711yescharacteristic, direct product factor, Sylow
416C2×#41C23×C6111yescharacteristic
417C23×C4C23×C6111yescharacteristic
418#131—41no—
419#131—41no—
420C2×M16—21no—
421C2×M16—21no—
422C2×M16—41no—
423C2×M16—41no—
424C2×M16—41no—
425C2×M16—41no—
426C2×M16D4×C6111yescharacteristic
427C2×M16D4×C6111yescharacteristic
428C2×M16D4×C6111yescharacteristic
429C2×M16D4×C6111yescharacteristic
430C2×M16C23×C6111yescharacteristic
431C2×M16C23×C6111yescharacteristic
432C2×M16C23×C6111yescharacteristic
433C2×M16C23×C6111yescharacteristic
434C22×C8—21no—
435C22×C8—21no—
436C22×C8C23×C6111yescharacteristic
437C22×C8C23×C6111yescharacteristic
438C22×C8C23×C6111yescharacteristic
439C22×C8C23×C6111yescharacteristic
440#123—21no—
441C22⋊Q8C2×C4×C6111yescharacteristic
442C22⋊Q8C2×C4×C6111yescharacteristic
443#121C2×C4×C6111yescharacteristic
444#121C2×C4×C6111yescharacteristic
445#120—21no—
446C4×D4—21no—
447C4×D4—21no—
448#117—21no—
449#117—21no—
450#117C2×C4×C6111yescharacteristic
451#117C2×C4×C6111yescharacteristic
452#117C23×C6111yescharacteristic
453#117C23×C6111yescharacteristic
454#117C23×C6111yescharacteristic
455C2×C4⋊C4C2×C4×C6111yescharacteristic
456C2×C4⋊C4C2×C4×C6111yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C42—21no—
460C2×C42C23×C6111yescharacteristic
461C2×C42C23×C6111yescharacteristic
462#108—41no—
463#108—41no—
464#107C2×C4×C6111yescharacteristic
465#107C2×C4×C6111yescharacteristic
466#107C2×C4×C6111yescharacteristic
467#107C2×C4×C6111yescharacteristic
468#106C2×C4×C6111yescharacteristic
469#106C2×C4×C6111yescharacteristic
470#106C2×C4×C6111yescharacteristic
471#106C2×C4×C6111yescharacteristic
472C4⋊C8—21no—
473C4⋊C8—21no—
474C4⋊C8—21no—
475C4⋊C8—21no—
476C4⋊C8—21no—
477C4⋊C8—21no—
478C4⋊C8—21no—
479C4⋊C8—21no—
480C4⋊C8—21no—
481C4⋊C8—21no—
482#104—41no—
483#104—41no—
484#103C2×C4×C6111yescharacteristic
485#103C2×C4×C6111yescharacteristic
486#103C2×C4×C6111yescharacteristic
487#103C2×C4×C6111yescharacteristic
488#102C2×C4×C6111yescharacteristic
489#102C2×C4×C6111yescharacteristic
490#102C2×C4×C6111yescharacteristic
491#102C2×C4×C6111yescharacteristic
492C22⋊C8—21no—
493C22⋊C8—21no—
494C22⋊C8—21no—
495C22⋊C8—21no—
496C22⋊C8C2×C4×C6111yescharacteristic
497C22⋊C8C2×C4×C6111yescharacteristic
498C22⋊C8C2×C4×C6111yescharacteristic
499C22⋊C8C2×C4×C6111yescharacteristic
500#97—21no—
501#97—41no—
502C4×C8—21no—
503C4×C8—41no—
504#95—21no—
505C24#41×C6111yescharacteristic
506#41—21no—
507#41—21no—
508#41—21no—
509#41—21no—
510C2×Q8C22×C4×C6111yescharacteristic
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4C22×C4×C6111yescharacteristic
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4C22×C4×C6111yescharacteristic
525C22×C4C22×C4×C6111yescharacteristic
526C22×C4C2×D4×C6111yescharacteristic
527C22×C4C2×D4×C6111yescharacteristic
528C22×C4#41×C6111yescharacteristic
529C22×C4C24×C6111yescharacteristic
530M16—21no—
531M16—21no—
532M16—21no—
533M16—21no—
534M16—21no—
535M16—21no—
536M16—21no—
537M16—21no—
538M16—41no—
539M16—41no—
540M16—41no—
541M16—41no—
542M16—42no—
543M16—42no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—42no—
557C2×C8—42no—
558C2×C8C22×C4×C6111yescharacteristic
559C2×C8C22×C4×C6111yescharacteristic
560C2×C8C22×C4×C6111yescharacteristic
561C2×C8C22×C4×C6111yescharacteristic
562C2×C8C2×D4×C6111yescharacteristic
563C2×C8C2×D4×C6111yescharacteristic
564C2×C8C2×D4×C6111yescharacteristic
565C2×C8C2×D4×C6111yescharacteristic
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4C22×C4×C6111yescharacteristic
571C4⋊C4C22×C4×C6111yescharacteristic
572C4⋊C4C22×C4×C6111yescharacteristic
573C4⋊C4C22×C4×C6111yescharacteristic
574C4⋊C4C22×C4×C6111yescharacteristic
575C4⋊C4C22×C4×C6111yescharacteristic
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—21no—
581C22⋊C4—21no—
582C22⋊C4—21no—
583C22⋊C4—21no—
584C22⋊C4—21no—
585C22⋊C4—42no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—41no—
599C23—41no—
600C23C4×D4×C6111yescharacteristic
601C23C4×D4×C6111yescharacteristic
602C23C2×#41×C6111yescharacteristic
603Q8—21no—
604Q8—21no—
605D4—21no—
606D4—21no—
607D4—41no—
608D4—41no—
609D4—81no—
610D4—81no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—81no—
637C2×C4—81no—
638C2×C4C4×D4×C6111yescharacteristic
639C2×C4C4×D4×C6111yescharacteristic
640C2×C4C23×C4×C6111yescharacteristic
641C2×C4C22×D4×C6111yescharacteristic
642C2×C4H(5,𝔽2)×C6111yescharacteristic
643C2×C4H(5,𝔽2)×C6111yescharacteristic
644C2×C42−1+4×C6111yescharacteristic
645C2×C42−1+4×C6111yescharacteristic
646C8—21no—
647C8—21no—
648C8—21no—
649C8—21no—
650C8—21no—
651C8—21no—
652C8—21no—
653C8—21no—
654C8—41no—
655C8—41no—
656C8—41no—
657C8—41no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—81no—
670C22—81no—
671C22C2×C4×D4×C6111yescharacteristic
672C22C61×#53911yescharacteristic
673C22C61×#53911yescharacteristic
674C4—21no—
675C4—21no—
676C4—42no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—81no—
685C4C61×#52011yescharacteristic
686C4C61×#52011yescharacteristic
687C4C61×#53411yescharacteristic
688C4C61×#53611yescharacteristic
689C2—21no—
690C2—21no—
691C2—41no—
692C2—41no—
693C2—81no—
694C2C61×#232211yescharacteristic
695C2C61×#295611yescharacteristic
696C2C61×#295711yescharacteristic
subgroupG/H
centerC2×C4×C61C22×D4
commutatorC2×C4C23×C4×C61
Frattini, cosocleC22×C4C24×C61
socleC22×C61C2×C4×D4
prime radicalC61×#525C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C22×M16×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C61×#2905C2semidirect
4. C61×#1946C2semidirect
5. C61×#1945C2semidirect
6. C61×#1938C2semidirect
7. C61×#1937C2semidirect
8. C61×#1922C2semidirect
9. C61×#1922C2semidirect
11. C61×#1866C2semidirect
12. C61×#1866C2semidirect
13. C61×#1855C2semidirect
14. C61×#1826C2semidirect
15. C61×#1753C2semidirect
21. C61×#485C4semidirect
22. C61×#485C4semidirect
23. C61×#484C4semidirect
24. C61×#483C4semidirect
25. C61×#482C4semidirect
26. C61×#482C4semidirect
27. C61×#481C4semidirect
28. C61×#480C4semidirect
309. #22097C61direct (N × H)
343. #2905C2×C61semidirect
344. #1946C2×C61semidirect
345. #1945C2×C61semidirect
346. #1938C2×C61semidirect
347. #1937C2×C61semidirect
348. #1922C2×C61semidirect
349. #1922C2×C61semidirect
351. #1866C2×C61semidirect
352. #1866C2×C61semidirect
353. #1855C2×C61semidirect
354. #1826C2×C61semidirect
355. #1753C2×C61semidirect
369. #485C4×C61semidirect
370. #485C4×C61semidirect
371. #484C4×C61semidirect
372. #483C4×C61semidirect
373. #482C4×C61semidirect
374. #482C4×C61semidirect
375. #481C4×C61semidirect
376. #480C4×C61semidirect
415. C61#22097direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#30912
C61×#29302
C61×#29052
C61×#19462
C61×#19452
C61×#19382
C61×#19372
C61×#19222
C61×#18712
C61×#18662
C61×#18552
C61×#18262
C61×#17532
#2209761