Finite Group Databasebeta

← C61×#24008 #29527441

Subgroups — C61×#24008 #29527441

Order 15616.

1448 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#525C211yesmaximal, characteristic
2C2×C61×#485C211yesmaximal, characteristic, complemented
3C2×C61×#482C211yesmaximal, characteristic, complemented
4C61×#2280C211yesmaximal, characteristic, complemented
5C61×#2036C211yesmaximal, characteristic, complemented
6C61×#2035C211yesmaximal, characteristic, complemented
7C61×#2034C211yesmaximal, characteristic, complemented
8C61×#2033C211yesmaximal, characteristic, complemented
9C61×#1875C211yesmaximal, characteristic, complemented
10C61×#1873C211yesmaximal, characteristic, complemented
11C61×#1854C211yesmaximal, characteristic, complemented
12C61×#1854C211yesmaximal, characteristic, complemented
13C61×#1788C211yesmaximal, characteristic, complemented
14C61×#1788C211yesmaximal, characteristic, complemented
15C61×#1779C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C24×C4×C61C2211yescharacteristic
18C61×#525—24no—
19C61×#525—24no—
20C2×#123×C61—21no—
21C2×C22⋊Q8×C61C2211yescharacteristic
22C2×C22⋊Q8×C61C2211yescharacteristic
23C2×#121×C61C2211yescharacteristic
24C2×#121×C61C2211yescharacteristic
25C2×#120×C61—21no—
26C2×C4×D4×C61—21no—
27C2×C4×D4×C61—21no—
28C2×#117×C61C2211yescharacteristic
29C2×#117×C61C2211yescharacteristic
30C2×#117×C61C2211yescharacteristic
31C61×#485—24no—
32C61×#482—24no—
33C2×#107×C61C2211yescharacteristic, complemented
34C2×#107×C61C2211yescharacteristic, complemented
35C2×#106×C61C2211yescharacteristic, complemented
36C2×#106×C61C2211yescharacteristic, complemented
37C2×#103×C61C2211yescharacteristic, complemented
38C2×#103×C61C2211yescharacteristic, complemented
39C2×#103×C61C2211yescharacteristic, complemented
40C2×#103×C61C2211yescharacteristic, complemented
41C2×#102×C61C2211yescharacteristic, complemented
42C2×#102×C61C2211yescharacteristic, complemented
43C2×#102×C61C2211yescharacteristic, complemented
44C2×#102×C61C2211yescharacteristic, complemented
45C2×C22⋊C8×C61C2211yescharacteristic
46C2×C22⋊C8×C61C2211yescharacteristic
47C2×C22⋊C8×C61C2211yescharacteristic
48C2×C22⋊C8×C61C2211yescharacteristic
49C2×C22⋊C8×C61C2211yescharacteristic
50C2×C22⋊C8×C61C2211yescharacteristic
51C61×#381—21no—
52C61×#380C2211yescharacteristic
53C61×#380C2211yescharacteristic
54C61×#380C2211yescharacteristic
55C61×#380C2211yescharacteristic
56C61×#379—21no—
57C4×C22⋊C4×C61—21no—
58C4×C22⋊C4×C61—21no—
59C61×#340C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C25×C61D411yescharacteristic
64C2×#41×C61—22no—
65C2×#41×C61—22no—
66C2×#41×C61—22no—
67C2×#41×C61—22no—
68C2×#41×C61—41no—
69C2×#41×C61—41no—
70C22×Q8×C61C2311yescharacteristic
71C22×D4×C61—21no—
72C22×D4×C61—21no—
73C22×D4×C61—21no—
74C22×D4×C61C2311yescharacteristic
75C23×C4×C61—22no—
76C23×C4×C61—22no—
77C23×C4×C61—21no—
78C23×C4×C61—22no—
79C23×C4×C61—22no—
80C23×C4×C61—41no—
81C23×C4×C61—41no—
82C23×C4×C61D411yescharacteristic
83C23×C4×C61D411yescharacteristic
84C23×C4×C61D411yescharacteristic
85C23×C4×C61C2311yescharacteristic
86C23×C4×C61C2311yescharacteristic
87C23×C4×C61C2311yescharacteristic
88C22×C8×C61C2311yescharacteristic
89C22×C8×C61C2311yescharacteristic
90C22×C8×C61C2311yescharacteristic
91C22×C8×C61C2311yescharacteristic
92#123×C61—28no—
93C22⋊Q8×C61—22no—
94C22⋊Q8×C61—22no—
95C22⋊Q8×C61—22no—
96C22⋊Q8×C61D414yes—
97#121×C61—22no—
98#121×C61—22no—
99#121×C61—22no—
100#121×C61D414yes—
101#120×C61—28no—
102C4×D4×C61—28no—
103C4×D4×C61—28no—
104#117×C61—22no—
105#117×C61—22no—
106#117×C61—22no—
107#117×C61—22no—
108#117×C61—41no—
109#117×C61—41no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
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—21no—
128C2×C22⋊C4×C61—21no—
129C2×C42×C61—21no—
130C2×C42×C61—21no—
131C2×C42×C61—21no—
132#107×C61—22no—
133#107×C61—22no—
134#106×C61—22no—
135#106×C61—22no—
136#103×C61—22no—
137#103×C61—22no—
138#103×C61—41no—
139#103×C61—41no—
140#102×C61—22no—
141#102×C61—22no—
142#102×C61—41no—
143#102×C61—41no—
144C22⋊C8×C61—22no—
145C22⋊C8×C61—22no—
146C22⋊C8×C61—22no—
147C22⋊C8×C61—22no—
148C22⋊C8×C61—41no—
149C22⋊C8×C61—41no—
150#95×C61—21no—
151#95×C61—21no—
152#95×C61—21no—
153#95×C61—21no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61—22no—
157C24×C61—21no—
158C24×C61—41no—
159C24×C61—41no—
160C24×C61—41no—
161C24×C61—41no—
162C24×C61C2×D411yescharacteristic
163C24×C61C2×D411yescharacteristic
164C24×C61C2×D411yescharacteristic
165#41×C61—44no—
166#41×C61—44no—
167#41×C61—44no—
168#41×C61—44no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61C2×D412yes—
175C2×D4×C61—24no—
176C2×D4×C61—24no—
177C2×D4×C61—24no—
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—42no—
187C2×D4×C61—42no—
188C2×D4×C61—42no—
189C2×D4×C61C2×D412yes—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—24no—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—22no—
205C22×C4×C61—22no—
206C22×C4×C61—22no—
207C22×C4×C61—22no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—41no—
219C22×C4×C61—41no—
220C22×C4×C61—41no—
221C22×C4×C61—44no—
222C22×C4×C61—44no—
223C22×C4×C61—44no—
224C22×C4×C61—44no—
225C22×C4×C61—42no—
226C22×C4×C61—42no—
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D412yes—
230C22×C4×C61C2×D412yes—
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61#4112yes—
233C22×C4×C61#4112yes—
234C22×C4×C61C2411yescharacteristic
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C4⋊C4×C61—24no—
248C4⋊C4×C61—24no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61C2×D412yes—
260C4⋊C4×C61C2×D412yes—
261C22⋊C4×C61—24no—
262C22⋊C4×C61—24no—
263C22⋊C4×C61—24no—
264C22⋊C4×C61—24no—
265C22⋊C4×C61—24no—
266C22⋊C4×C61—42no—
267C22⋊C4×C61—42no—
268C22⋊C4×C61—42no—
269C22⋊C4×C61—42no—
270C22⋊C4×C61—42no—
271C22⋊C4×C61—42no—
272C42×C61—24no—
273C42×C61—42no—
274C42×C61—42no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—22no—
294C23×C61—44no—
295C23×C61—44no—
296C23×C61—44no—
297C23×C61—44no—
298C23×C61—44no—
299C23×C61—44no—
300C23×C61—44no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61#12012yes—
308C23×C61#12312yes—
309C23×C61#13512yes—
310C23×C61C22×D411yescharacteristic
311Q8×C61—22no—
312Q8×C61—22no—
313Q8×C61—41no—
314Q8×C61—41no—
315D4×C61—22no—
316D4×C61—22no—
317D4×C61—48no—
318D4×C61—48no—
319D4×C61—48no—
320D4×C61—41no—
321D4×C61—41no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—21no—
337C2×C4×C61—22no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—44no—
341C2×C4×C61—44no—
342C2×C4×C61—44no—
343C2×C4×C61—48no—
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—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61#12012yes—
367C2×C4×C61#12312yes—
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C2×#4111yescharacteristic
371C2×C4×C61C2×#4111yescharacteristic
372C2×C4×C61H(5,𝔽2)11yescharacteristic
373C2×C4×C61H(5,𝔽2)11yescharacteristic
374C8×C61—41no—
375C8×C61—41no—
376C8×C61—41no—
377C8×C61—41no—
378#24008C6111yesmaximal, characteristic, direct product factor, Sylow
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—416no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61—41no—
401C22×C61—42no—
402C22×C61—42no—
403C22×C61—42no—
404C22×C61—81no—
405C22×C61—81no—
406C22×C61—81no—
407C22×C61—81no—
408C22×C61C2×#12011yescharacteristic
409C22×C61C2×#12311yescharacteristic
410C22×C61#53411yescharacteristic
411C22×C61C2×#13511yescharacteristic
412C22×C61#57511yescharacteristic
413C22×C61#57511yescharacteristic
414C22×C61#57511yescharacteristic
415C4×C61—22no—
416C4×C61—22no—
417C4×C61—41no—
418C4×C61—42no—
419C4×C61—42no—
420C4×C61—42no—
421C4×C61—81no—
422C4×C61—81no—
423C4×C61—81no—
424C4×C61—81no—
425C4×C61#54611yescharacteristic
426C4×C61#54611yescharacteristic
427C4×C61#54611yescharacteristic
428C4×C61#54611yescharacteristic
429C2×#525C2×C6111yescharacteristic
430C2×#485C2×C6111yescharacteristic, complemented
431C2×#482C2×C6111yescharacteristic, complemented
432#2280C2×C6111yescharacteristic, complemented
433#2036C2×C6111yescharacteristic, complemented
434#2035C2×C6111yescharacteristic, complemented
435#2034C2×C6111yescharacteristic, complemented
436#2033C2×C6111yescharacteristic, complemented
437#1875C2×C6111yescharacteristic, complemented
438#1873C2×C6111yescharacteristic, complemented
439#1854C2×C6111yescharacteristic, complemented
440#1854C2×C6111yescharacteristic, complemented
441#1788C2×C6111yescharacteristic, complemented
442#1788C2×C6111yescharacteristic, complemented
443#1779C2×C6111yescharacteristic, complemented
444C2×C61—42no—
445C2×C61—42no—
446C2×C61—42no—
447C2×C61—82no—
448C2×C61#240511yescharacteristic
449C2×C61#300211yescharacteristic
450C2×C61#300511yescharacteristic
451C2×C61#309111yescharacteristic
452C2×C61#309311yescharacteristic
453C2×C61#319111yescharacteristic
454C2×C61#319711yescharacteristic
455C22×#41C22×C6111yescharacteristic
456C24×C4C22×C6111yescharacteristic
457#525—24no—
458#525—24no—
459C2×#123—21no—
460C2×C22⋊Q8C22×C6111yescharacteristic
461C2×C22⋊Q8C22×C6111yescharacteristic
462C2×#121C22×C6111yescharacteristic
463C2×#121C22×C6111yescharacteristic
464C2×#120—21no—
465C2×C4×D4—21no—
466C2×C4×D4—21no—
467C2×#117C22×C6111yescharacteristic
468C2×#117C22×C6111yescharacteristic
469C2×#117C22×C6111yescharacteristic
470#485—24no—
471#482—24no—
472C2×#107C22×C6111yescharacteristic, complemented
473C2×#107C22×C6111yescharacteristic, complemented
474C2×#106C22×C6111yescharacteristic, complemented
475C2×#106C22×C6111yescharacteristic, complemented
476C2×#103C22×C6111yescharacteristic, complemented
477C2×#103C22×C6111yescharacteristic, complemented
478C2×#103C22×C6111yescharacteristic, complemented
479C2×#103C22×C6111yescharacteristic, complemented
480C2×#102C22×C6111yescharacteristic, complemented
481C2×#102C22×C6111yescharacteristic, complemented
482C2×#102C22×C6111yescharacteristic, complemented
483C2×#102C22×C6111yescharacteristic, complemented
484C2×C22⋊C8C22×C6111yescharacteristic
485C2×C22⋊C8C22×C6111yescharacteristic
486C2×C22⋊C8C22×C6111yescharacteristic
487C2×C22⋊C8C22×C6111yescharacteristic
488C2×C22⋊C8C22×C6111yescharacteristic
489C2×C22⋊C8C22×C6111yescharacteristic
490#381—21no—
491#380C22×C6111yescharacteristic
492#380C22×C6111yescharacteristic
493#380C22×C6111yescharacteristic
494#380C22×C6111yescharacteristic
495#379—21no—
496C4×C22⋊C4—21no—
497C4×C22⋊C4—21no—
498#340C22×C6111yescharacteristic, complemented
499#340C22×C6111yescharacteristic, complemented
500#340C22×C6111yescharacteristic, complemented
501#340C22×C6111yescharacteristic, complemented
502C61#2400811yescharacteristic, direct product factor, Sylow
503C25D4×C6111yescharacteristic
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8C23×C6111yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4C23×C6111yescharacteristic
515C23×C4—21no—
516C23×C4—22no—
517C23×C4—22no—
518C23×C4—22no—
519C23×C4—22no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4D4×C6111yescharacteristic
523C23×C4D4×C6111yescharacteristic
524C23×C4D4×C6111yescharacteristic
525C23×C4C23×C6111yescharacteristic
526C23×C4C23×C6111yescharacteristic
527C23×C4C23×C6111yescharacteristic
528C22×C8C23×C6111yescharacteristic
529C22×C8C23×C6111yescharacteristic
530C22×C8C23×C6111yescharacteristic
531C22×C8C23×C6111yescharacteristic
532#123—28no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536C22⋊Q8D4×C6114yes—
537#121—22no—
538#121—22no—
539#121—22no—
540#121D4×C6114yes—
541#120—28no—
542C4×D4—28no—
543C4×D4—28no—
544#117—22no—
545#117—22no—
546#117—22no—
547#117—22no—
548#117—41no—
549#117—41no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4C23×C6111yescharacteristic
553C2×C4⋊C4C23×C6111yescharacteristic
554C2×C4⋊C4C23×C6111yescharacteristic
555C2×C4⋊C4C23×C6111yescharacteristic
556C2×C4⋊C4C23×C6111yescharacteristic
557C2×C4⋊C4C23×C6111yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42—21no—
572#107—22no—
573#107—22no—
574#106—22no—
575#106—22no—
576#103—22no—
577#103—22no—
578#103—41no—
579#103—41no—
580#102—22no—
581#102—22no—
582#102—41no—
583#102—41no—
584C22⋊C8—22no—
585C22⋊C8—22no—
586C22⋊C8—22no—
587C22⋊C8—22no—
588C22⋊C8—41no—
589C22⋊C8—41no—
590#95—21no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—21no—
598C24—41no—
599C24—41no—
600C24—41no—
601C24—41no—
602C24C2×D4×C6111yescharacteristic
603C24C2×D4×C6111yescharacteristic
604C24C2×D4×C6111yescharacteristic
605#41—44no—
606#41—44no—
607#41—44no—
608#41—44no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8C2×D4×C6112yes—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4C2×D4×C6112yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C6111yescharacteristic
668C22×C4C2×D4×C6111yescharacteristic
669C22×C4C2×D4×C6112yes—
670C22×C4C2×D4×C6112yes—
671C22×C4C2×D4×C6111yescharacteristic
672C22×C4#41×C6112yes—
673C22×C4#41×C6112yes—
674C22×C4C24×C6111yescharacteristic
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4C2×D4×C6112yes—
700C4⋊C4C2×D4×C6112yes—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C42—24no—
713C42—42no—
714C42—42no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23#120×C6112yes—
748C23#123×C6112yes—
749C23#135×C6112yes—
750C23C22×D4×C6111yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—41no—
754Q8—41no—
755D4—22no—
756D4—22no—
757D4—48no—
758D4—48no—
759D4—48no—
760D4—41no—
761D4—41no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—48no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4#120×C6112yes—
807C2×C4#123×C6112yes—
808C2×C4C22×D4×C6111yescharacteristic
809C2×C4C22×D4×C6111yescharacteristic
810C2×C4C2×#41×C6111yescharacteristic
811C2×C4C2×#41×C6111yescharacteristic
812C2×C4H(5,𝔽2)×C6111yescharacteristic
813C2×C4H(5,𝔽2)×C6111yescharacteristic
814C8—41no—
815C8—41no—
816C8—41no—
817C8—41no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—416no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22C2×#120×C6111yescharacteristic
848C22C2×#123×C6111yescharacteristic
849C22C61×#53411yescharacteristic
850C22C2×#135×C6111yescharacteristic
851C22C61×#57511yescharacteristic
852C22C61×#57511yescharacteristic
853C22C61×#57511yescharacteristic
854C4—22no—
855C4—22no—
856C4—41no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4C61×#54611yescharacteristic
865C4C61×#54611yescharacteristic
866C4C61×#54611yescharacteristic
867C4C61×#54611yescharacteristic
868C2—42no—
869C2—42no—
870C2—42no—
871C2—82no—
872C2C61×#240511yescharacteristic
873C2C61×#300211yescharacteristic
874C2C61×#300511yescharacteristic
875C2C61×#309111yescharacteristic
876C2C61×#309311yescharacteristic
877C2C61×#319111yescharacteristic
878C2C61×#319711yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×C61×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C24×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#485C2semidirect
3. C2×C61×#482C2semidirect
4. C61×#2280C2semidirect
5. C61×#2036C2semidirect
6. C61×#2035C2semidirect
7. C61×#2034C2semidirect
8. C61×#2033C2semidirect
9. C61×#1875C2semidirect
10. C61×#1873C2semidirect
11. C61×#1854C2semidirect
12. C61×#1854C2semidirect
13. C61×#1788C2semidirect
14. C61×#1788C2semidirect
15. C61×#1779C2semidirect
33. C2×#107×C61C22semidirect
34. C2×#107×C61C22semidirect
35. C2×#106×C61C22semidirect
36. C2×#106×C61C22semidirect
37. C2×#103×C61C22semidirect
38. C2×#103×C61C22semidirect
39. C2×#103×C61C22semidirect
40. C2×#103×C61C22semidirect
41. C2×#102×C61C22semidirect
42. C2×#102×C61C22semidirect
43. C2×#102×C61C22semidirect
44. C2×#102×C61C22semidirect
59. C61×#340C22semidirect
60. C61×#340C22semidirect
61. C61×#340C22semidirect
62. C61×#340C22semidirect
378. #24008C61direct (N × H)
430. C2×#485C2×C61semidirect
431. C2×#482C2×C61semidirect
432. #2280C2×C61semidirect
433. #2036C2×C61semidirect
434. #2035C2×C61semidirect
435. #2034C2×C61semidirect
436. #2033C2×C61semidirect
437. #1875C2×C61semidirect
438. #1873C2×C61semidirect
439. #1854C2×C61semidirect
440. #1854C2×C61semidirect
441. #1788C2×C61semidirect
442. #1788C2×C61semidirect
443. #1779C2×C61semidirect
472. C2×#107C22×C61semidirect
473. C2×#107C22×C61semidirect
474. C2×#106C22×C61semidirect
475. C2×#106C22×C61semidirect
476. C2×#103C22×C61semidirect
477. C2×#103C22×C61semidirect
478. C2×#103C22×C61semidirect
479. C2×#103C22×C61semidirect
480. C2×#102C22×C61semidirect
481. C2×#102C22×C61semidirect
482. C2×#102C22×C61semidirect
483. C2×#102C22×C61semidirect
498. #340C22×C61semidirect
499. #340C22×C61semidirect
500. #340C22×C61semidirect
501. #340C22×C61semidirect
502. C61#24008direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#5252
C2×C61×#4852
C2×C61×#4822
C61×#22802
C61×#20362
C61×#20352
C61×#20342
C61×#20332
C61×#18752
C61×#18732
C61×#18542
C61×#17882
C61×#17792
#2400861