Finite Group Databasebeta

← C61×#15113 #29518546

Subgroups — C61×#15113 #29518546

Order 15616.

2062 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#117×C61C211yesmaximal, characteristic, complemented
2C2×C61×#388C212yesmaximal, complemented
3C2×C61×#386C211yesmaximal, characteristic
4C61×#1444C211yesmaximal, characteristic, complemented
5C61×#1442C211yesmaximal, characteristic, complemented
6C61×#1439C212yesmaximal, complemented
7C61×#1439C211yesmaximal, characteristic, complemented
8C61×#1439C211yesmaximal, characteristic, complemented
9C61×#1438C212yesmaximal
10C61×#1434C212yesmaximal, complemented
11C61×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C61C2211yescharacteristic
13C24×C4×C61C2211yescharacteristic
14C2×#117×C61—24no—
15C2×#117×C61—28no—
16C22×C4⋊C4×C61C2211yescharacteristic
17C22×C4⋊C4×C61C2211yescharacteristic
18C22×C4⋊C4×C61C2212yes—
19C22×C22⋊C4×C61C2211yescharacteristic
20C22×C22⋊C4×C61C2211yescharacteristic
21C22×C22⋊C4×C61C2212yes—
22C22×C22⋊C4×C61C2212yes—
23C22×C22⋊C4×C61C2212yes—
24C22×C22⋊C4×C61C2211yescharacteristic
25C22×C22⋊C4×C61C2212yes—
26C22×C42×C61C2212yes—
27C61×#388—28no—
28C61×#386—24no—
29C2×#95×C61C2211yescharacteristic
30C2×#95×C61C2211yescharacteristic
31C2×#95×C61C2212yes—
32C2×#95×C61C2212yes—
33C2×#95×C61C2211yescharacteristic
34C2×#95×C61C2211yescharacteristic
35C2×#95×C61C2212yes—
36C2×#95×C61C2212yes—
37C2×#95×C61C2212yes—
38C2×#95×C61C2212yes—
39C25×C61C2311yescharacteristic
40C25×C61C2311yescharacteristic
41C22×D4×C61—22no—
42C22×D4×C61—22no—
43C22×D4×C61—24no—
44C22×D4×C61—22no—
45C22×D4×C61—42no—
46C23×C4×C61—24no—
47C23×C4×C61—24no—
48C23×C4×C61—22no—
49C23×C4×C61—22no—
50C23×C4×C61D414yes—
51C23×C4×C61C2312yes—
52C23×C4×C61C2311yescharacteristic
53C23×C4×C61C2311yescharacteristic
54C23×C4×C61C2312yes—
55C23×C4×C61C2312yes—
56C23×C4×C61C2311yescharacteristic
57C23×C4×C61C2312yes—
58C23×C4×C61C2311yescharacteristic
59C23×C4×C61C2311yescharacteristic
60#117×C61—232no—
61C2×C4⋊C4×C61—24no—
62C2×C4⋊C4×C61—24no—
63C2×C4⋊C4×C61—22no—
64C2×C4⋊C4×C61—22no—
65C2×C4⋊C4×C61—24no—
66C2×C4⋊C4×C61—42no—
67C2×C4⋊C4×C61—42no—
68C2×C22⋊C4×C61—24no—
69C2×C22⋊C4×C61—24no—
70C2×C22⋊C4×C61—24no—
71C2×C22⋊C4×C61—24no—
72C2×C22⋊C4×C61—24no—
73C2×C22⋊C4×C61—24no—
74C2×C22⋊C4×C61—22no—
75C2×C22⋊C4×C61—24no—
76C2×C22⋊C4×C61—22no—
77C2×C22⋊C4×C61—22no—
78C2×C22⋊C4×C61—24no—
79C2×C22⋊C4×C61—24no—
80C2×C22⋊C4×C61—24no—
81C2×C22⋊C4×C61—22no—
82C2×C22⋊C4×C61—22no—
83C2×C22⋊C4×C61—42no—
84C2×C22⋊C4×C61—42no—
85C2×C22⋊C4×C61—42no—
86C2×C22⋊C4×C61—42no—
87C2×C42×C61—24no—
88C2×C42×C61—24no—
89C2×C42×C61D418yescomplemented
90#95×C61—22no—
91#95×C61—22no—
92#95×C61—24no—
93#95×C61—24no—
94#95×C61—22no—
95#95×C61—24no—
96#95×C61—24no—
97#95×C61—22no—
98#95×C61—42no—
99#95×C61—42no—
100C24×C61—22no—
101C24×C61—22no—
102C24×C61—21no—
103C24×C61—21no—
104C24×C61—21no—
105C24×C61—21no—
106C24×C61—21no—
107C24×C61—22no—
108C24×C61—21no—
109C24×C61—22no—
110C24×C61—21no—
111C24×C61—22no—
112C24×C61—21no—
113C24×C61—21no—
114C24×C61—21no—
115C24×C61—22no—
116C24×C61—21no—
117C24×C61—22no—
118C24×C61—21no—
119C24×C61C2×D412yes—
120C24×C61#4112yes—
121C24×C61#4114yes—
122C24×C61C2411yescharacteristic
123C2×D4×C61—28no—
124C2×D4×C61—48no—
125C2×D4×C61—48no—
126C2×D4×C61—44no—
127C2×D4×C61—44no—
128C22×C4×C61—216no—
129C22×C4×C61—216no—
130C22×C4×C61—28no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—22no—
136C22×C4×C61—28no—
137C22×C4×C61—28no—
138C22×C4×C61—21no—
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—21no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—22no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61C2×D414yes—
178C22×C4×C61C2×D414yes—
179C22×C4×C61C2×D412yes—
180C22×C4×C61C2×D414yes—
181C22×C4×C61C2×D412yes—
182C22×C4×C61#4112yes—
183C22×C4×C61#4114yes—
184C22×C4×C61#4112yes—
185C22×C4×C61#4112yes—
186C4⋊C4×C61—28no—
187C4⋊C4×C61—28no—
188C4⋊C4×C61—48no—
189C22⋊C4×C61—216no—
190C22⋊C4×C61—216no—
191C22⋊C4×C61—48no—
192C22⋊C4×C61—48no—
193C22⋊C4×C61—44no—
194C22⋊C4×C61—44no—
195C22⋊C4×C61—44no—
196C42×C61—216no—
197C23×C61—22no—
198C23×C61—22no—
199C23×C61—24no—
200C23×C61—24no—
201C23×C61—22no—
202C23×C61—22no—
203C23×C61—22no—
204C23×C61—22no—
205C23×C61—24no—
206C23×C61—24no—
207C23×C61—24no—
208C23×C61—24no—
209C23×C61—24no—
210C23×C61—22no—
211C23×C61—24no—
212C23×C61—22no—
213C23×C61—22no—
214C23×C61—42no—
215C23×C61—42no—
216C23×C61—42no—
217C23×C61—42no—
218C23×C61—41no—
219C23×C61—41no—
220C23×C61—42no—
221C23×C61—42no—
222C23×C61—41no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61—42no—
228C23×C61—42no—
229C23×C61—42no—
230C23×C61—41no—
231C23×C61—42no—
232C23×C61—41no—
233C23×C61—42no—
234C23×C61—41no—
235C23×C61—42no—
236C23×C61—42no—
237C23×C61—42no—
238C23×C61—42no—
239C23×C61—42no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61#12314yes—
243C23×C61C22×D411yescharacteristic
244C23×C61C22×D412yes—
245C23×C61C2×#4112yes—
246C23×C61C2×#4111yescharacteristic
247C23×C61C2×#4111yescharacteristic
248C23×C61C2×#4111yescharacteristic
249C23×C61C2×#4111yescharacteristic
250C23×C61C2×#4112yes—
251C23×C61H(5,𝔽2)11yescharacteristic
252C23×C61H(5,𝔽2)12yes—
253C23×C612−1+411yescharacteristic
254D4×C61—416no—
255C2×C4×C61—232no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—24no—
261C2×C4×C61—24no—
262C2×C4×C61—24no—
263C2×C4×C61—24no—
264C2×C4×C61—24no—
265C2×C4×C61—24no—
266C2×C4×C61—24no—
267C2×C4×C61—24no—
268C2×C4×C61—22no—
269C2×C4×C61—24no—
270C2×C4×C61—24no—
271C2×C4×C61—24no—
272C2×C4×C61—24no—
273C2×C4×C61—24no—
274C2×C4×C61—24no—
275C2×C4×C61—41no—
276C2×C4×C61—42no—
277C2×C4×C61—42no—
278C2×C4×C61—42no—
279C2×C4×C61—42no—
280C2×C4×C61—42no—
281C2×C4×C61—42no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—41no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—42no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—41no—
295C2×C4×C61—42no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61—41no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—42no—
304C2×C4×C61—42no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61#12014yes—
308C2×C4×C61#12314yes—
309#15113C6111yesmaximal, characteristic, direct product factor, Sylow
310C22×C61—24no—
311C22×C61—24no—
312C22×C61—24no—
313C22×C61—44no—
314C22×C61—44no—
315C22×C61—44no—
316C22×C61—44no—
317C22×C61—42no—
318C22×C61—42no—
319C22×C61—42no—
320C22×C61—42no—
321C22×C61—44no—
322C22×C61—44no—
323C22×C61—42no—
324C22×C61—42no—
325C22×C61—42no—
326C22×C61—81no—
327C22×C61—82no—
328C22×C61—82no—
329C22×C61—81no—
330C22×C61—81no—
331C22×C61—81no—
332C22×C61C2×#12011yescharacteristic
333C22×C61C2×#12311yescharacteristic
334C22×C61C2×#12311yescharacteristic
335C22×C61#52512yes—
336C22×C61#52512yes—
337C22×C61#52512yes—
338C22×C61#52511yescharacteristic
339C22×C61#53212yes—
340C22×C61#53211yescharacteristic
341C22×C61#53512yes—
342C22×C61#53511yescharacteristic
343C22×C61#53712yes—
344C22×C61#53711yescharacteristic
345C22×C61#55112yes—
346C22×C61#55112yes—
347C22×C61#55112yes—
348C22×C61#55212yes—
349C22×C61#55211yescharacteristic
350C22×C61#55311yescharacteristic
351C22×C61#55312yes—
352C22×C61#55512yes—
353C22×C61#55511yescharacteristic
354C22×C61#55611yescharacteristic
355C4×C61—24no—
356C4×C61—24no—
357C4×C61—44no—
358C4×C61—44no—
359C4×C61—44no—
360C4×C61—42no—
361C4×C61—82no—
362C4×C61—81no—
363C4×C61—81no—
364C22×#117C2×C6111yescharacteristic, complemented
365C2×#388C2×C6112yescomplemented
366C2×#386C2×C6111yescharacteristic
367#1444C2×C6111yescharacteristic, complemented
368#1442C2×C6111yescharacteristic, complemented
369#1439C2×C6112yescomplemented
370#1439C2×C6111yescharacteristic, complemented
371#1439C2×C6111yescharacteristic, complemented
372#1438C2×C6112yes—
373#1434C2×C6112yescomplemented
374C22⋊#95C2×C6111yescharacteristic, complemented
375C2×C61—44no—
376C2×C61—82no—
377C2×C61#238811yescharacteristic
378C2×C61#248211yescharacteristic
379C2×C61#248511yescharacteristic
380C2×C61#249811yescharacteristic
381C2×C61#250011yescharacteristic
382C2×C61#259812yes—
383C2×C61#260112yes—
384C2×C61#260912yes—
385C2×C61#261012yes—
386C2×C61#261511yescharacteristic
387C2×C61#284911yescharacteristic
388C23×D4C22×C6111yescharacteristic
389C24×C4C22×C6111yescharacteristic
390C2×#117—24no—
391C2×#117—28no—
392C22×C4⋊C4C22×C6111yescharacteristic
393C22×C4⋊C4C22×C6111yescharacteristic
394C22×C4⋊C4C22×C6112yes—
395C22×C22⋊C4C22×C6112yes—
396C22×C22⋊C4C22×C6112yes—
397C22×C22⋊C4C22×C6111yescharacteristic
398C22×C22⋊C4C22×C6111yescharacteristic
399C22×C22⋊C4C22×C6112yes—
400C22×C22⋊C4C22×C6112yes—
401C22×C22⋊C4C22×C6111yescharacteristic
402C22×C42C22×C6112yes—
403#388—28no—
404#386—24no—
405C2×#95C22×C6112yes—
406C2×#95C22×C6111yescharacteristic
407C2×#95C22×C6111yescharacteristic
408C2×#95C22×C6111yescharacteristic
409C2×#95C22×C6112yes—
410C2×#95C22×C6112yes—
411C2×#95C22×C6112yes—
412C2×#95C22×C6111yescharacteristic
413C2×#95C22×C6112yes—
414C2×#95C22×C6112yes—
415C61#1511311yescharacteristic, direct product factor, Sylow
416C25C23×C6111yescharacteristic
417C25C23×C6111yescharacteristic
418C22×D4—22no—
419C22×D4—22no—
420C22×D4—24no—
421C22×D4—22no—
422C22×D4—42no—
423C23×C4—24no—
424C23×C4—24no—
425C23×C4—22no—
426C23×C4—22no—
427C23×C4D4×C6114yes—
428C23×C4C23×C6111yescharacteristic
429C23×C4C23×C6112yes—
430C23×C4C23×C6111yescharacteristic
431C23×C4C23×C6112yes—
432C23×C4C23×C6112yes—
433C23×C4C23×C6112yes—
434C23×C4C23×C6111yescharacteristic
435C23×C4C23×C6111yescharacteristic
436C23×C4C23×C6111yescharacteristic
437#117—232no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—42no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4—42no—
463C2×C22⋊C4—42no—
464C2×C42—24no—
465C2×C42—24no—
466C2×C42D4×C6118yescomplemented
467#95—22no—
468#95—22no—
469#95—24no—
470#95—24no—
471#95—22no—
472#95—24no—
473#95—24no—
474#95—22no—
475#95—42no—
476#95—42no—
477C24—22no—
478C24—22no—
479C24—21no—
480C24—21no—
481C24—21no—
482C24—21no—
483C24—21no—
484C24—22no—
485C24—21no—
486C24—22no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—22no—
491C24—22no—
492C24—21no—
493C24—21no—
494C24—22no—
495C24—21no—
496C24C2×D4×C6112yes—
497C24#41×C6112yes—
498C24#41×C6114yes—
499C24C24×C6111yescharacteristic
500C2×D4—28no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—44no—
504C2×D4—44no—
505C22×C4—216no—
506C22×C4—216no—
507C22×C4—28no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4C2×D4×C6114yes—
555C22×C4C2×D4×C6114yes—
556C22×C4C2×D4×C6112yes—
557C22×C4C2×D4×C6114yes—
558C22×C4C2×D4×C6112yes—
559C22×C4#41×C6112yes—
560C22×C4#41×C6114yes—
561C22×C4#41×C6112yes—
562C22×C4#41×C6112yes—
563C4⋊C4—28no—
564C4⋊C4—28no—
565C4⋊C4—48no—
566C22⋊C4—216no—
567C22⋊C4—216no—
568C22⋊C4—48no—
569C22⋊C4—48no—
570C22⋊C4—44no—
571C22⋊C4—44no—
572C22⋊C4—44no—
573C42—216no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—22no—
582C23—22no—
583C23—24no—
584C23—24no—
585C23—22no—
586C23—24no—
587C23—22no—
588C23—22no—
589C23—24no—
590C23—22no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—41no—
595C23—41no—
596C23—42no—
597C23—42no—
598C23—41no—
599C23—41no—
600C23—42no—
601C23—42no—
602C23—41no—
603C23—42no—
604C23—41no—
605C23—42no—
606C23—41no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—42no—
618C23—42no—
619C23#123×C6114yes—
620C23C22×D4×C6111yescharacteristic
621C23C22×D4×C6112yes—
622C23C2×#41×C6111yescharacteristic
623C23C2×#41×C6112yes—
624C23C2×#41×C6112yes—
625C23C2×#41×C6111yescharacteristic
626C23C2×#41×C6111yescharacteristic
627C23C2×#41×C6111yescharacteristic
628C23H(5,𝔽2)×C6111yescharacteristic
629C23H(5,𝔽2)×C6112yes—
630C232−1+4×C6111yescharacteristic
631D4—416no—
632C2×C4—232no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—41no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4#120×C6114yes—
685C2×C4#123×C6114yes—
686C22—24no—
687C22—24no—
688C22—24no—
689C22—44no—
690C22—44no—
691C22—44no—
692C22—44no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—44no—
698C22—44no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—81no—
703C22—82no—
704C22—82no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22C2×#120×C6111yescharacteristic
709C22C2×#123×C6111yescharacteristic
710C22C2×#123×C6111yescharacteristic
711C22C61×#52512yes—
712C22C61×#52512yes—
713C22C61×#52512yes—
714C22C61×#52511yescharacteristic
715C22C61×#53212yes—
716C22C61×#53211yescharacteristic
717C22C61×#53512yes—
718C22C61×#53511yescharacteristic
719C22C61×#53712yes—
720C22C61×#53711yescharacteristic
721C22C61×#55112yes—
722C22C61×#55112yes—
723C22C61×#55112yes—
724C22C61×#55212yes—
725C22C61×#55211yescharacteristic
726C22C61×#55311yescharacteristic
727C22C61×#55312yes—
728C22C61×#55512yes—
729C22C61×#55511yescharacteristic
730C22C61×#55611yescharacteristic
731C4—24no—
732C4—24no—
733C4—44no—
734C4—44no—
735C4—44no—
736C4—42no—
737C4—82no—
738C4—81no—
739C4—81no—
740C2—44no—
741C2—82no—
742C2C61×#238811yescharacteristic
743C2C61×#248211yescharacteristic
744C2C61×#248511yescharacteristic
745C2C61×#249811yescharacteristic
746C2C61×#250011yescharacteristic
747C2C61×#259812yes—
748C2C61×#260112yes—
749C2C61×#260912yes—
750C2C61×#261012yes—
751C2C61×#261511yescharacteristic
752C2C61×#284911yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC24C24×C61
prime radicalC23×D4×C61C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#117×C61C2semidirect
2. C2×C61×#388C2semidirect
4. C61×#1444C2semidirect
5. C61×#1442C2semidirect
6. C61×#1439C2semidirect
7. C61×#1439C2semidirect
8. C61×#1439C2semidirect
10. C61×#1434C2semidirect
11. C61×C22⋊#95C2semidirect
89. C2×C42×C61D4semidirect
309. #15113C61direct (N × H)
364. C22×#117C2×C61semidirect
365. C2×#388C2×C61semidirect
367. #1444C2×C61semidirect
368. #1442C2×C61semidirect
369. #1439C2×C61semidirect
370. #1439C2×C61semidirect
371. #1439C2×C61semidirect
373. #1434C2×C61semidirect
374. C22⋊#95C2×C61semidirect
415. C61#15113direct (N × H)
466. C2×C42D4×C61semidirect

Maximal subgroups

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

subgroupindex
C22×#117×C612
C2×C61×#3882
C2×C61×#3862
C61×#14442
C61×#14422
C61×#14392
C61×#14382
C61×#14342
C61×C22⋊#952
#1511361