Finite Group Databasebeta

← C61×#25164 #29528597

Subgroups — C61×#25164 #29528597

Order 15616.

1296 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#463C211yesmaximal, characteristic, complemented
2C2×C61×#450C211yesmaximal, characteristic, complemented
3C2×C61×#447C211yesmaximal, characteristic
4C2×C61×#440C211yesmaximal, characteristic, complemented
5C61×#2426C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
7C61×#2067C211yesmaximal, characteristic, complemented
8C61×#2035C211yesmaximal, characteristic, complemented
9C61×#2033C211yesmaximal, characteristic, complemented
10C61×#2012C211yesmaximal, characteristic, complemented
11C61×#1972C211yesmaximal, characteristic, complemented
12C61×#1924C211yesmaximal, characteristic, complemented
13C61×#1880C211yesmaximal, characteristic, complemented
14C61×#1879C211yesmaximal, characteristic, complemented
15C61×#1864C211yesmaximal, characteristic, complemented
16C23×D4×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic
19C22×D8×C61C2211yescharacteristic
20C22×D8×C61C2211yescharacteristic
21C2×#124×C61C2211yescharacteristic, complemented
22C2×C22⋊Q8×C61C2211yescharacteristic
23C2×#121×C61C2211yescharacteristic
24C2×C4×Q8×C61C2211yescharacteristic, complemented
25C2×C4×D4×C61C2211yescharacteristic
26C2×C4×D4×C61C2211yescharacteristic
27C22×C22⋊C4×C61—21no—
28C61×#463—24no—
29C61×#450—24no—
30C61×#447—24no—
31C61×#440—24no—
32C2×#107×C61C2211yescharacteristic, complemented
33C2×#106×C61C2211yescharacteristic, complemented
34C2×C4⋊C8×C61C2211yescharacteristic, complemented
35C2×#103×C61C2211yescharacteristic, complemented
36C2×#103×C61C2211yescharacteristic, complemented
37C2×#102×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic, complemented
42C2×#102×C61C2211yescharacteristic, complemented
43C2×C22⋊C8×C61C2211yescharacteristic
44C2×C22⋊C8×C61C2211yescharacteristic
45C2×#97×C61C2211yescharacteristic, complemented
46C61×#396—21no—
47C61×#394—21no—
48C61×#390—21no—
49C61×#390C2211yescharacteristic
50C61×#390C2211yescharacteristic
51C61×#390C2211yescharacteristic, complemented
52C61×#389C2211yescharacteristic, complemented
53C61×#388—21no—
54C61×#386—21no—
55C61×#386—21no—
56C61×#380C2211yescharacteristic
57C61×#379—21no—
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#340C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C61×#336C2211yescharacteristic, complemented
62C61×#336C2211yescharacteristic, complemented
63C25×C61—21no—
64C22×Q8×C61C2311yescharacteristic
65C22×D4×C61—22no—
66C22×D4×C61—22no—
67C22×D4×C61—22no—
68C22×D4×C61—22no—
69C22×D4×C61—21no—
70C22×D4×C61—21no—
71C22×D4×C61—41no—
72C22×D4×C61—41no—
73C22×D4×C61C2311yescharacteristic
74C22×D4×C61C2311yescharacteristic
75C22×D4×C61C2311yescharacteristic
76C23×C4×C61—21no—
77C23×C4×C61—21no—
78C23×C4×C61C2311yescharacteristic
79C2×SD16×C61—22no—
80C2×SD16×C61—22no—
81C2×SD16×C61—22no—
82C2×SD16×C61—22no—
83C2×SD16×C61—41no—
84C2×SD16×C61D414yescomplemented
85C2×D8×C61—22no—
86C2×D8×C61—22no—
87C2×D8×C61—22no—
88C2×D8×C61—22no—
89C2×D8×C61—22no—
90C2×D8×C61—41no—
91C22×C8×C61C2311yescharacteristic
92C22×C8×C61C2311yescharacteristic
93C22×C8×C61C2311yescharacteristic
94C22×C8×C61C2311yescharacteristic
95#124×C61—22no—
96#124×C61—41no—
97C22⋊Q8×C61—22no—
98C22⋊Q8×C61—41no—
99#121×C61—22no—
100#121×C61—41no—
101C4×Q8×C61—22no—
102C4×Q8×C61—41no—
103C4×D4×C61—22no—
104C4×D4×C61—22no—
105C4×D4×C61—41no—
106C4×D4×C61—41no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—44no—
128C2×C22⋊C4×C61D411yescharacteristic
129C2×C22⋊C4×C61D411yescharacteristic
130C2×C42×C61—21no—
131C2×C42×C61C2311yescharacteristic
132C2×C42×C61C2311yescharacteristic
133#107×C61—22no—
134#106×C61—41no—
135C4⋊C8×C61—22no—
136#103×C61—22no—
137#103×C61—22no—
138#102×C61—22no—
139#102×C61—22no—
140#102×C61—22no—
141#102×C61—22no—
142#102×C61—41no—
143#102×C61D414yes—
144C22⋊C8×C61—22no—
145C22⋊C8×C61—22no—
146#97×C61—22no—
147#95×C61—21no—
148#95×C61—21no—
149#95×C61D411yescharacteristic
150#95×C61D411yescharacteristic
151C24×C61—21no—
152C24×C61—24no—
153C24×C61—21no—
154C24×C61—21no—
155C24×C61—42no—
156C24×C61—42no—
157C24×C61—42no—
158C24×C61—42no—
159C24×C61—81no—
160C24×C61—81no—
161C24×C61C2×D411yescharacteristic
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61C2×D412yes—
168C2×D4×C61—24no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—42no—
184C2×D4×C61—42no—
185C2×D4×C61—42no—
186C2×D4×C61—44no—
187C2×D4×C61—44no—
188C2×D4×C61—44no—
189C2×D4×C61—44no—
190C2×D4×C61—42no—
191C2×D4×C61—81no—
192C2×D4×C61C2×D412yes—
193C2×D4×C61C2×D412yes—
194C2×D4×C61#4112yes—
195C2×D4×C61#4112yes—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—42no—
208C22×C4×C61—42no—
209C22×C4×C61—42no—
210C22×C4×C61—42no—
211C22×C4×C61—81no—
212C22×C4×C61—81no—
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2411yescharacteristic
219SD16×C61—28no—
220SD16×C61—44no—
221D8×C61—44no—
222D8×C61—44no—
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×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61C2×D412yes—
234C2×C8×C61C2×D412yes—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—42no—
243C4⋊C4×C61—42no—
244C4⋊C4×C61—81no—
245C4⋊C4×C61C2×D412yes—
246C22⋊C4×C61—22no—
247C22⋊C4×C61—41no—
248C22⋊C4×C61—42no—
249C22⋊C4×C61—42no—
250C22⋊C4×C61—42no—
251C22⋊C4×C61—42no—
252C22⋊C4×C61—42no—
253C22⋊C4×C61—42no—
254C22⋊C4×C61—42no—
255C22⋊C4×C61—42no—
256C22⋊C4×C61—42no—
257C22⋊C4×C61—42no—
258C22⋊C4×C61—81no—
259C22⋊C4×C61—81no—
260C22⋊C4×C61—81no—
261C42×C61—21no—
262C42×C61—21no—
263C42×C61—21no—
264C42×C61—21no—
265C42×C61—42no—
266C23×C61—21no—
267C23×C61—22no—
268C23×C61—21no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—22no—
276C23×C61—48no—
277C23×C61—48no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—84no—
296C23×C61—84no—
297C23×C61—84no—
298C23×C61—84no—
299C23×C61—84no—
300C23×C61AGL(1,ℤ/8)12yes—
301C23×C61C22×D411yescharacteristic
302Q8×C61—22no—
303Q8×C61—22no—
304Q8×C61—41no—
305Q8×C61—41no—
306D4×C61—22no—
307D4×C61—22no—
308D4×C61—22no—
309D4×C61—22no—
310D4×C61—22no—
311D4×C61—48no—
312D4×C61—41no—
313D4×C61—41no—
314D4×C61—41no—
315D4×C61—41no—
316D4×C61—41no—
317D4×C61—41no—
318D4×C61—84no—
319D4×C61#12114yes—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—84no—
355C2×C4×C61—84no—
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C2×#4111yescharacteristic
359C2×C4×C61C2×#4111yescharacteristic
360C2×C4×C61H(5,𝔽2)11yescharacteristic
361C2×C4×C61H(5,𝔽2)11yescharacteristic
362C8×C61—22no—
363C8×C61—22no—
364C8×C61—41no—
365C8×C61—41no—
366#25164C6111yesmaximal, characteristic, direct product factor, Sylow
367C22×C61—22no—
368C22×C61—24no—
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—42no—
372C22×C61—41no—
373C22×C61—42no—
374C22×C61—41no—
375C22×C61—42no—
376C22×C61—42no—
377C22×C61—41no—
378C22×C61—42no—
379C22×C61—41no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—816no—
385C22×C61—81no—
386C22×C61—81no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61—81no—
391C22×C61—81no—
392C22×C61—81no—
393C22×C61—81no—
394C22×C61—81no—
395C22×C61—81no—
396C22×C61#52511yescharacteristic
397C22×C61D4211yescharacteristic
398C22×C61D4211yescharacteristic
399C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C61#57511yescharacteristic
401C22×C61#57611yescharacteristic
402C22×C61#57711yescharacteristic
403C4×C61—41no—
404C4×C61—42no—
405C4×C61—41no—
406C4×C61—42no—
407C4×C61—41no—
408C4×C61—41no—
409C4×C61—41no—
410C4×C61—81no—
411C4×C61—81no—
412C4×C61—81no—
413C4×C61C2×#12111yescharacteristic
414C4×C61#53811yescharacteristic
415C4×C61#54611yescharacteristic
416C4×C61#54611yescharacteristic
417C2×#463C2×C6111yescharacteristic, complemented
418C2×#450C2×C6111yescharacteristic, complemented
419C2×#447C2×C6111yescharacteristic
420C2×#440C2×C6111yescharacteristic, complemented
421#2426C2×C6111yescharacteristic, complemented
422D4×C22⋊C4C2×C6111yescharacteristic, complemented
423#2067C2×C6111yescharacteristic, complemented
424#2035C2×C6111yescharacteristic, complemented
425#2033C2×C6111yescharacteristic, complemented
426#2012C2×C6111yescharacteristic, complemented
427#1972C2×C6111yescharacteristic, complemented
428#1924C2×C6111yescharacteristic, complemented
429#1880C2×C6111yescharacteristic, complemented
430#1879C2×C6111yescharacteristic, complemented
431#1864C2×C6111yescharacteristic, complemented
432C2×C61—42no—
433C2×C61—44no—
434C2×C61—82no—
435C2×C61—161no—
436C2×C61#242411yescharacteristic
437C2×C61#311411yescharacteristic
438C2×C61#311811yescharacteristic
439C2×C61#326411yescharacteristic
440C2×C61#326511yescharacteristic
441C2×C61#326811yescharacteristic
442C2×C61#327511yescharacteristic
443C23×D4C22×C6111yescharacteristic
444C22×SD16C22×C6111yescharacteristic
445C22×SD16C22×C6111yescharacteristic
446C22×D8C22×C6111yescharacteristic
447C22×D8C22×C6111yescharacteristic
448C2×#124C22×C6111yescharacteristic, complemented
449C2×C22⋊Q8C22×C6111yescharacteristic
450C2×#121C22×C6111yescharacteristic
451C2×C4×Q8C22×C6111yescharacteristic, complemented
452C2×C4×D4C22×C6111yescharacteristic
453C2×C4×D4C22×C6111yescharacteristic
454C22×C22⋊C4—21no—
455#463—24no—
456#450—24no—
457#447—24no—
458#440—24no—
459C2×#107C22×C6111yescharacteristic, complemented
460C2×#106C22×C6111yescharacteristic, complemented
461C2×C4⋊C8C22×C6111yescharacteristic, complemented
462C2×#103C22×C6111yescharacteristic, complemented
463C2×#103C22×C6111yescharacteristic, complemented
464C2×#102C22×C6111yescharacteristic
465C2×#102C22×C6111yescharacteristic
466C2×#102C22×C6111yescharacteristic
467C2×#102C22×C6111yescharacteristic
468C2×#102C22×C6111yescharacteristic, complemented
469C2×#102C22×C6111yescharacteristic, complemented
470C2×C22⋊C8C22×C6111yescharacteristic
471C2×C22⋊C8C22×C6111yescharacteristic
472C2×#97C22×C6111yescharacteristic, complemented
473#396—21no—
474#394—21no—
475#390—21no—
476#390C22×C6111yescharacteristic
477#390C22×C6111yescharacteristic
478#390C22×C6111yescharacteristic, complemented
479#389C22×C6111yescharacteristic, complemented
480#388—21no—
481#386—21no—
482#386—21no—
483#380C22×C6111yescharacteristic
484#379—21no—
485C4×C22⋊C4C22×C6111yescharacteristic
486#340C22×C6111yescharacteristic, complemented
487#340C22×C6111yescharacteristic, complemented
488#336C22×C6111yescharacteristic, complemented
489#336C22×C6111yescharacteristic, complemented
490C61#2516411yescharacteristic, direct product factor, Sylow
491C25—21no—
492C22×Q8C23×C6111yescharacteristic
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C23×C6111yescharacteristic
502C22×D4C23×C6111yescharacteristic
503C22×D4C23×C6111yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C23×C6111yescharacteristic
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—41no—
512C2×SD16D4×C6114yescomplemented
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—41no—
519C22×C8C23×C6111yescharacteristic
520C22×C8C23×C6111yescharacteristic
521C22×C8C23×C6111yescharacteristic
522C22×C8C23×C6111yescharacteristic
523#124—22no—
524#124—41no—
525C22⋊Q8—22no—
526C22⋊Q8—41no—
527#121—22no—
528#121—41no—
529C4×Q8—22no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—41no—
534C4×D4—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C6111yescharacteristic
539C2×C4⋊C4C23×C6111yescharacteristic
540C2×C4⋊C4C23×C6111yescharacteristic
541C2×C4⋊C4C23×C6111yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—44no—
556C2×C22⋊C4D4×C6111yescharacteristic
557C2×C22⋊C4D4×C6111yescharacteristic
558C2×C42—21no—
559C2×C42C23×C6111yescharacteristic
560C2×C42C23×C6111yescharacteristic
561#107—22no—
562#106—41no—
563C4⋊C8—22no—
564#103—22no—
565#103—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—41no—
571#102D4×C6114yes—
572C22⋊C8—22no—
573C22⋊C8—22no—
574#97—22no—
575#95—21no—
576#95—21no—
577#95D4×C6111yescharacteristic
578#95D4×C6111yescharacteristic
579C24—21no—
580C24—24no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24C2×D4×C6111yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8C2×D4×C6112yes—
596C2×D4—24no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C6112yes—
621C2×D4C2×D4×C6112yes—
622C2×D4#41×C6112yes—
623C2×D4#41×C6112yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4C2×D4×C6111yescharacteristic
642C22×C4C2×D4×C6111yescharacteristic
643C22×C4C2×D4×C6111yescharacteristic
644C22×C4C2×D4×C6111yescharacteristic
645C22×C4C2×D4×C6111yescharacteristic
646C22×C4C24×C6111yescharacteristic
647SD16—28no—
648SD16—44no—
649D8—44no—
650D8—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8C2×D4×C6112yes—
662C2×C8C2×D4×C6112yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—81no—
673C4⋊C4C2×D4×C6112yes—
674C22⋊C4—22no—
675C22⋊C4—41no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—42no—
694C23—21no—
695C23—22no—
696C23—22no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—22no—
703C23—22no—
704C23—48no—
705C23—48no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23AGL(1,ℤ/8)×C6112yes—
729C23C22×D4×C6111yescharacteristic
730Q8—22no—
731Q8—22no—
732Q8—41no—
733Q8—41no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4#121×C6114yes—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—84no—
783C2×C4—84no—
784C2×C4C22×D4×C6111yescharacteristic
785C2×C4C22×D4×C6111yescharacteristic
786C2×C4C2×#41×C6111yescharacteristic
787C2×C4C2×#41×C6111yescharacteristic
788C2×C4H(5,𝔽2)×C6111yescharacteristic
789C2×C4H(5,𝔽2)×C6111yescharacteristic
790C8—22no—
791C8—22no—
792C8—41no—
793C8—41no—
794C22—22no—
795C22—24no—
796C22—22no—
797C22—22no—
798C22—42no—
799C22—41no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—816no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22C61×#52511yescharacteristic
824C22D42×C6111yescharacteristic
825C22D42×C6111yescharacteristic
826C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
827C22C61×#57511yescharacteristic
828C22C61×#57611yescharacteristic
829C22C61×#57711yescharacteristic
830C4—41no—
831C4—42no—
832C4—41no—
833C4—42no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—81no—
838C4—81no—
839C4—81no—
840C4C2×#121×C6111yescharacteristic
841C4C61×#53811yescharacteristic
842C4C61×#54611yescharacteristic
843C4C61×#54611yescharacteristic
844C2—42no—
845C2—44no—
846C2—82no—
847C2—161no—
848C2C61×#242411yescharacteristic
849C2C61×#311411yescharacteristic
850C2C61×#311811yescharacteristic
851C2C61×#326411yescharacteristic
852C2C61×#326511yescharacteristic
853C2C61×#326811yescharacteristic
854C2C61×#327511yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×C61×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C4×C22⋊C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#463C2semidirect
2. C2×C61×#450C2semidirect
4. C2×C61×#440C2semidirect
5. C61×#2426C2semidirect
6. D4×C22⋊C4×C61C2semidirect
7. C61×#2067C2semidirect
8. C61×#2035C2semidirect
9. C61×#2033C2semidirect
10. C61×#2012C2semidirect
11. C61×#1972C2semidirect
12. C61×#1924C2semidirect
13. C61×#1880C2semidirect
14. C61×#1879C2semidirect
15. C61×#1864C2semidirect
21. C2×#124×C61C22semidirect
24. C2×C4×Q8×C61C22semidirect
32. C2×#107×C61C22semidirect
33. C2×#106×C61C22semidirect
34. C2×C4⋊C8×C61C22semidirect
35. C2×#103×C61C22semidirect
36. C2×#103×C61C22semidirect
41. C2×#102×C61C22semidirect
42. C2×#102×C61C22semidirect
45. C2×#97×C61C22semidirect
51. C61×#390C22semidirect
52. C61×#389C22semidirect
59. C61×#340C22semidirect
60. C61×#340C22semidirect
61. C61×#336C22semidirect
62. C61×#336C22semidirect
84. C2×SD16×C61D4semidirect
366. #25164C61direct (N × H)
417. C2×#463C2×C61semidirect
418. C2×#450C2×C61semidirect
420. C2×#440C2×C61semidirect
421. #2426C2×C61semidirect
422. D4×C22⋊C4C2×C61semidirect
423. #2067C2×C61semidirect
424. #2035C2×C61semidirect
425. #2033C2×C61semidirect
426. #2012C2×C61semidirect
427. #1972C2×C61semidirect
428. #1924C2×C61semidirect
429. #1880C2×C61semidirect
430. #1879C2×C61semidirect
431. #1864C2×C61semidirect
448. C2×#124C22×C61semidirect
451. C2×C4×Q8C22×C61semidirect
459. C2×#107C22×C61semidirect
460. C2×#106C22×C61semidirect
461. C2×C4⋊C8C22×C61semidirect
462. C2×#103C22×C61semidirect
463. C2×#103C22×C61semidirect
468. C2×#102C22×C61semidirect
469. C2×#102C22×C61semidirect
472. C2×#97C22×C61semidirect
478. #390C22×C61semidirect
479. #389C22×C61semidirect
486. #340C22×C61semidirect
487. #340C22×C61semidirect
488. #336C22×C61semidirect
489. #336C22×C61semidirect
490. C61#25164direct (N × H)
512. C2×SD16D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4632
C2×C61×#4502
C2×C61×#4472
C2×C61×#4402
C61×#24262
D4×C22⋊C4×C612
C61×#20672
C61×#20352
C61×#20332
C61×#20122
C61×#19722
C61×#19242
C61×#18802
C61×#18792
C61×#18642
#2516461