Finite Group Databasebeta

← C61×#15146 #29518579

Subgroups — C61×#15146 #29518579

Order 15616.

1294 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#400C212yesmaximal
2C2×C61×#389C211yesmaximal, characteristic
3C2×C61×#384C211yesmaximal, characteristic
4C61×#1442C212yesmaximal
5C61×#1442C212yesmaximal
6C61×#1441C212yesmaximal
7C61×C4⋊#95C211yesmaximal, characteristic
8C61×C4⋊#95C211yesmaximal, characteristic
9C61×C4⋊#95C211yesmaximal, characteristic
10C61×C4⋊#95C211yesmaximal, characteristic
11C4×#95×C61C211yesmaximal, characteristic
12C22×C4⋊C4×C61C2211yescharacteristic
13C22×C4⋊C4×C61C2211yescharacteristic
14C22×C4⋊C4×C61C2211yescharacteristic
15C22×C4⋊C4×C61C2212yes—
16C22×C4⋊C4×C61C2212yes—
17C22×C4⋊C4×C61C2212yes—
18C22×C4⋊C4×C61C2211yescharacteristic
19C22×C42×C61C2211yescharacteristic
20C22×C42×C61C2211yescharacteristic
21C22×C42×C61C2211yescharacteristic
22C61×#400—28no—
23C61×#389—24no—
24C61×#384—24no—
25C2×#95×C61C2212yes—
26C2×#95×C61C2212yes—
27C2×#95×C61C2212yes—
28C2×#95×C61C2212yes—
29C2×#95×C61C2212yes—
30C2×#95×C61C2211yescharacteristic
31C2×#95×C61C2211yescharacteristic
32C2×#95×C61C2212yes—
33C2×#95×C61C2212yes—
34C2×#95×C61C2212yes—
35C2×#95×C61C2212yes—
36C2×#95×C61C2211yescharacteristic
37C2×#95×C61C2211yescharacteristic
38C23×C4×C61C2312yes—
39C23×C4×C61C2312yes—
40C23×C4×C61C2312yes—
41C23×C4×C61C2311yescharacteristic
42C23×C4×C61C2311yescharacteristic
43C23×C4×C61C2312yes—
44C23×C4×C61C2311yescharacteristic
45C23×C4×C61C2311yescharacteristic
46C23×C4×C61C2311yescharacteristic
47C23×C4×C61C2311yescharacteristic
48C23×C4×C61C2311yescharacteristic
49C2×C4⋊C4×C61—22no—
50C2×C4⋊C4×C61—22no—
51C2×C4⋊C4×C61—24no—
52C2×C4⋊C4×C61—24no—
53C2×C4⋊C4×C61—22no—
54C2×C4⋊C4×C61—24no—
55C2×C4⋊C4×C61—22no—
56C2×C4⋊C4×C61—24no—
57C2×C4⋊C4×C61—24no—
58C2×C4⋊C4×C61—24no—
59C2×C4⋊C4×C61—22no—
60C2×C4⋊C4×C61—22no—
61C2×C4⋊C4×C61—22no—
62C2×C4⋊C4×C61—22no—
63C2×C4⋊C4×C61—22no—
64C2×C4⋊C4×C61—22no—
65C2×C4⋊C4×C61—22no—
66C2×C4⋊C4×C61—42no—
67C2×C4⋊C4×C61—42no—
68C2×C4⋊C4×C61—42no—
69C2×C4⋊C4×C61D414yes—
70C2×C42×C61—22no—
71C2×C42×C61—22no—
72C2×C42×C61—22no—
73C2×C42×C61—22no—
74C2×C42×C61—22no—
75C2×C42×C61—22no—
76C2×C42×C61—22no—
77C2×C42×C61—22no—
78C2×C42×C61Q814yes—
79#95×C61—24no—
80#95×C61—24no—
81#95×C61—24no—
82#95×C61—24no—
83#95×C61—24no—
84#95×C61—22no—
85#95×C61—22no—
86#95×C61—24no—
87#95×C61—42no—
88#95×C61—42no—
89#95×C61—42no—
90#95×C61D414yes—
91#95×C61Q814yes—
92C24×C61C2411yescharacteristic
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61—22no—
103C22×C4×C61—21no—
104C22×C4×C61—21no—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—21no—
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C22×C4×C61—22no—
119C22×C4×C61—22no—
120C22×C4×C61—22no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—22no—
135C22×C4×C61—22no—
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—22no—
139C22×C4×C61—22no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61C2×D412yes—
153C22×C4×C61C2×D412yes—
154C22×C4×C61C2×D414yes—
155C22×C4×C61C2×D412yes—
156C22×C4×C61C2×D412yes—
157C22×C4×C61C2×Q812yes—
158C22×C4×C61C2×Q812yes—
159C22×C4×C61C2×Q812yes—
160C22×C4×C61C2×Q812yes—
161C22×C4×C61C2×Q812yes—
162C22×C4×C61C2×Q812yes—
163C22×C4×C61#4112yes—
164C22×C4×C61#4112yes—
165C22×C4×C61#4112yes—
166C22×C4×C61#4112yes—
167C22×C4×C61#4112yes—
168C22×C4×C61#4112yes—
169C22×C4×C61#4112yes—
170C4⋊C4×C61—28no—
171C4⋊C4×C61—48no—
172C4⋊C4×C61—48no—
173C4⋊C4×C61—48no—
174C4⋊C4×C61—44no—
175C4⋊C4×C61—44no—
176C4⋊C4×C61—44no—
177C42×C61—28no—
178C42×C61—44no—
179C42×C61—44no—
180C23×C61C22×D411yescharacteristic
181C23×C61C22×D411yescharacteristic
182C23×C61C22×Q811yescharacteristic
183C23×C61C22×Q811yescharacteristic
184C23×C61C2×#4111yescharacteristic
185C23×C61C2×#4111yescharacteristic
186C23×C61C2×#4111yescharacteristic
187C23×C61C2×#4111yescharacteristic
188C23×C61C2×#4111yescharacteristic
189C23×C61C2×#4111yescharacteristic
190C23×C61C2×#4111yescharacteristic
191C23×C61H(5,𝔽2)11yescharacteristic
192C23×C61H(5,𝔽2)11yescharacteristic
193C23×C612−1+411yescharacteristic
194C23×C612−1+411yescharacteristic
195C2×C4×C61—22no—
196C2×C4×C61—22no—
197C2×C4×C61—22no—
198C2×C4×C61—22no—
199C2×C4×C61—22no—
200C2×C4×C61—22no—
201C2×C4×C61—22no—
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—22no—
205C2×C4×C61—22no—
206C2×C4×C61—22no—
207C2×C4×C61—24no—
208C2×C4×C61—22no—
209C2×C4×C61—22no—
210C2×C4×C61—22no—
211C2×C4×C61—22no—
212C2×C4×C61—24no—
213C2×C4×C61—22no—
214C2×C4×C61—24no—
215C2×C4×C61—22no—
216C2×C4×C61—22no—
217C2×C4×C61—22no—
218C2×C4×C61—22no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—42no—
227C2×C4×C61—42no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—42no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
246C2×C4×C61—42no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61—42no—
251C2×C4×C61—42no—
252C2×C4×C61—42no—
253C2×C4×C61—42no—
254C2×C4×C61—42no—
255C2×C4×C61—42no—
256C2×C4×C61—42no—
257C2×C4×C61—42no—
258C2×C4×C61—42no—
259C2×C4×C61—42no—
260C2×C4×C61—42no—
261C2×C4×C61—42no—
262C2×C4×C61—42no—
263C2×C4×C61C22⋊Q814yes—
264C2×C4×C61#12314yes—
265C2×C4×C61#12414yes—
266C2×C4×C61#12514yes—
267C2×C4×C61#12514yes—
268C2×C4×C61#12514yes—
269C2×C4×C61#12614yes—
270C2×C4×C61#12614yes—
271C2×C4×C61C4⋊Q814yes—
272#15146C6111yesmaximal, characteristic, direct product factor, Sylow
273C22×C61C2×C22⋊Q811yescharacteristic
274C22×C61C2×#12311yescharacteristic
275C22×C61C2×#12411yescharacteristic
276C22×C61C2×#12511yescharacteristic
277C22×C61C2×#12511yescharacteristic
278C22×C61C2×#12511yescharacteristic
279C22×C61C2×#12611yescharacteristic
280C22×C61C2×#12611yescharacteristic
281C22×C61C2×C4⋊Q811yescharacteristic
282C22×C61#53211yescharacteristic
283C22×C61#53211yescharacteristic
284C22×C61#53311yescharacteristic
285C22×C61#53311yescharacteristic
286C22×C61#54011yescharacteristic
287C22×C61#54111yescharacteristic
288C22×C61#54211yescharacteristic
289C22×C61#54211yescharacteristic
290C22×C61#54411yescharacteristic
291C22×C61#54411yescharacteristic
292C22×C61D4211yescharacteristic
293C22×C61#54611yescharacteristic
294C22×C61#54711yescharacteristic
295C22×C61#54711yescharacteristic
296C22×C61#54811yescharacteristic
297C22×C61D4×Q811yescharacteristic
298C22×C61#55011yescharacteristic
299C22×C61#55211yescharacteristic
300C22×C61#55311yescharacteristic
301C22×C61#55411yescharacteristic
302C22×C61#55411yescharacteristic
303C22×C61#55511yescharacteristic
304C22×C61#55611yescharacteristic
305C22×C61#55611yescharacteristic
306C22×C61#55711yescharacteristic
307C22×C61#55911yescharacteristic
308C4×C61—24no—
309C4×C61—24no—
310C4×C61—44no—
311C4×C61—42no—
312C4×C61—42no—
313C4×C61—42no—
314C4×C61—42no—
315C4×C61—82no—
316C4×C61—82no—
317C4×C61—82no—
318C4×C61#40018yescomplemented
319C2×#400C2×C6112yes—
320C2×#389C2×C6111yescharacteristic
321C2×#384C2×C6111yescharacteristic
322#1442C2×C6112yes—
323#1442C2×C6112yes—
324#1441C2×C6112yes—
325C4⋊#95C2×C6111yescharacteristic
326C4⋊#95C2×C6111yescharacteristic
327C4⋊#95C2×C6111yescharacteristic
328C4⋊#95C2×C6111yescharacteristic
329C4×#95C2×C6111yescharacteristic
330C2×C61C2×#40011yescharacteristic
331C2×C61#244011yescharacteristic
332C2×C61#244211yescharacteristic
333C2×C61#244511yescharacteristic
334C2×C61#244611yescharacteristic
335C2×C61#249111yescharacteristic
336C2×C61#249211yescharacteristic
337C2×C61#249611yescharacteristic
338C2×C61#249711yescharacteristic
339C2×C61#251111yescharacteristic
340C2×C61#251211yescharacteristic
341C2×C61#255211yescharacteristic
342C2×C61#257111yescharacteristic
343C2×C61#264711yescharacteristic
344C2×C61#285911yescharacteristic
345C22×C4⋊C4C22×C6111yescharacteristic
346C22×C4⋊C4C22×C6111yescharacteristic
347C22×C4⋊C4C22×C6111yescharacteristic
348C22×C4⋊C4C22×C6112yes—
349C22×C4⋊C4C22×C6112yes—
350C22×C4⋊C4C22×C6112yes—
351C22×C4⋊C4C22×C6111yescharacteristic
352C22×C42C22×C6111yescharacteristic
353C22×C42C22×C6111yescharacteristic
354C22×C42C22×C6111yescharacteristic
355#400—28no—
356#389—24no—
357#384—24no—
358C2×#95C22×C6112yes—
359C2×#95C22×C6112yes—
360C2×#95C22×C6112yes—
361C2×#95C22×C6112yes—
362C2×#95C22×C6111yescharacteristic
363C2×#95C22×C6111yescharacteristic
364C2×#95C22×C6112yes—
365C2×#95C22×C6112yes—
366C2×#95C22×C6112yes—
367C2×#95C22×C6112yes—
368C2×#95C22×C6112yes—
369C2×#95C22×C6111yescharacteristic
370C2×#95C22×C6111yescharacteristic
371C61#1514611yescharacteristic, direct product factor, Sylow
372C23×C4C23×C6112yes—
373C23×C4C23×C6112yes—
374C23×C4C23×C6112yes—
375C23×C4C23×C6112yes—
376C23×C4C23×C6111yescharacteristic
377C23×C4C23×C6111yescharacteristic
378C23×C4C23×C6111yescharacteristic
379C23×C4C23×C6111yescharacteristic
380C23×C4C23×C6111yescharacteristic
381C23×C4C23×C6111yescharacteristic
382C23×C4C23×C6111yescharacteristic
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—42no—
401C2×C4⋊C4—42no—
402C2×C4⋊C4—42no—
403C2×C4⋊C4D4×C6114yes—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42Q8×C6114yes—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—22no—
419#95—22no—
420#95—24no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95D4×C6114yes—
425#95Q8×C6114yes—
426C24C24×C6111yescharacteristic
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4C2×D4×C6112yes—
487C22×C4C2×D4×C6112yes—
488C22×C4C2×D4×C6114yes—
489C22×C4C2×D4×C6112yes—
490C22×C4C2×D4×C6112yes—
491C22×C4C2×Q8×C6112yes—
492C22×C4C2×Q8×C6112yes—
493C22×C4C2×Q8×C6112yes—
494C22×C4C2×Q8×C6112yes—
495C22×C4C2×Q8×C6112yes—
496C22×C4C2×Q8×C6112yes—
497C22×C4#41×C6112yes—
498C22×C4#41×C6112yes—
499C22×C4#41×C6112yes—
500C22×C4#41×C6112yes—
501C22×C4#41×C6112yes—
502C22×C4#41×C6112yes—
503C22×C4#41×C6112yes—
504C4⋊C4—28no—
505C4⋊C4—48no—
506C4⋊C4—48no—
507C4⋊C4—48no—
508C4⋊C4—44no—
509C4⋊C4—44no—
510C4⋊C4—44no—
511C42—28no—
512C42—44no—
513C42—44no—
514C23C22×D4×C6111yescharacteristic
515C23C22×D4×C6111yescharacteristic
516C23C22×Q8×C6111yescharacteristic
517C23C22×Q8×C6111yescharacteristic
518C23C2×#41×C6111yescharacteristic
519C23C2×#41×C6111yescharacteristic
520C23C2×#41×C6111yescharacteristic
521C23C2×#41×C6111yescharacteristic
522C23C2×#41×C6111yescharacteristic
523C23C2×#41×C6111yescharacteristic
524C23C2×#41×C6111yescharacteristic
525C23H(5,𝔽2)×C6111yescharacteristic
526C23H(5,𝔽2)×C6111yescharacteristic
527C232−1+4×C6111yescharacteristic
528C232−1+4×C6111yescharacteristic
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4C22⋊Q8×C6114yes—
598C2×C4#123×C6114yes—
599C2×C4#124×C6114yes—
600C2×C4#125×C6114yes—
601C2×C4#125×C6114yes—
602C2×C4#125×C6114yes—
603C2×C4#126×C6114yes—
604C2×C4#126×C6114yes—
605C2×C4C4⋊Q8×C6114yes—
606C22C2×C22⋊Q8×C6111yescharacteristic
607C22C2×#123×C6111yescharacteristic
608C22C2×#124×C6111yescharacteristic
609C22C2×#125×C6111yescharacteristic
610C22C2×#125×C6111yescharacteristic
611C22C2×#125×C6111yescharacteristic
612C22C2×#126×C6111yescharacteristic
613C22C2×#126×C6111yescharacteristic
614C22C2×C4⋊Q8×C6111yescharacteristic
615C22C61×#53211yescharacteristic
616C22C61×#53211yescharacteristic
617C22C61×#53311yescharacteristic
618C22C61×#53311yescharacteristic
619C22C61×#54011yescharacteristic
620C22C61×#54111yescharacteristic
621C22C61×#54211yescharacteristic
622C22C61×#54211yescharacteristic
623C22C61×#54411yescharacteristic
624C22C61×#54411yescharacteristic
625C22D42×C6111yescharacteristic
626C22C61×#54611yescharacteristic
627C22C61×#54711yescharacteristic
628C22C61×#54711yescharacteristic
629C22C61×#54811yescharacteristic
630C22D4×Q8×C6111yescharacteristic
631C22C61×#55011yescharacteristic
632C22C61×#55211yescharacteristic
633C22C61×#55311yescharacteristic
634C22C61×#55411yescharacteristic
635C22C61×#55411yescharacteristic
636C22C61×#55511yescharacteristic
637C22C61×#55611yescharacteristic
638C22C61×#55611yescharacteristic
639C22C61×#55711yescharacteristic
640C22C61×#55911yescharacteristic
641C4—24no—
642C4—24no—
643C4—44no—
644C4—42no—
645C4—42no—
646C4—42no—
647C4—42no—
648C4—82no—
649C4—82no—
650C4—82no—
651C4C61×#40018yescomplemented
652C2C2×C61×#40011yescharacteristic
653C2C61×#244011yescharacteristic
654C2C61×#244211yescharacteristic
655C2C61×#244511yescharacteristic
656C2C61×#244611yescharacteristic
657C2C61×#249111yescharacteristic
658C2C61×#249211yescharacteristic
659C2C61×#249611yescharacteristic
660C2C61×#249711yescharacteristic
661C2C61×#251111yescharacteristic
662C2C61×#251211yescharacteristic
663C2C61×#255211yescharacteristic
664C2C61×#257111yescharacteristic
665C2C61×#264711yescharacteristic
666C2C61×#285911yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C61C24
commutator, Frattini, cosocleC24C24×C61
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
272. #15146C61direct (N × H)
318. C4×C61#400semidirect
371. C61#15146direct (N × H)
651. C4C61×#400semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4002
C2×C61×#3892
C2×C61×#3842
C61×#14422
C61×#14412
C61×C4⋊#952
C4×#95×C612
#1514661