Finite Group Databasebeta

← C61×#22423 #29525856

Subgroups — C61×#22423 #29525856

Order 15616.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C61C211yesmaximal, characteristic
2C2×C61×#435C211yesmaximal, characteristic, complemented
3C2×C61×#418C211yesmaximal, characteristic, complemented
4C22×#102×C61C211yesmaximal, characteristic, complemented
5C61×#2352C211yesmaximal, characteristic, complemented
6C61×#1982C211yesmaximal, characteristic, complemented
7C61×#1961C211yesmaximal, characteristic, complemented
8C61×#1895C211yesmaximal, characteristic, complemented
9C61×#1893C211yesmaximal, characteristic, complemented
10C61×#1875C211yesmaximal, characteristic, complemented
11C61×#1874C211yesmaximal, characteristic, complemented
12C61×#1804C211yesmaximal, characteristic, complemented
13C61×#1786C211yesmaximal, characteristic, complemented
14C61×#1786C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C23×D4×C61—21no—
17C23×D4×C61C2211yescharacteristic
18C23×D4×C61C2211yescharacteristic
19C22×M16×C61C2211yescharacteristic, complemented
20C23×C8×C61C2211yescharacteristic, complemented
21D42×C61—24no—
22D42×C61C418yescomplemented
23C2×#127×C61C2211yescharacteristic
24C2×#121×C61—21no—
25C2×#121×C61C2211yescharacteristic
26C2×#121×C61C2211yescharacteristic
27C2×#120×C61—21no—
28C2×#120×C61—21no—
29C2×C4×D4×C61C2211yescharacteristic
30C2×C4×D4×C61C2211yescharacteristic
31C2×#117×C61C2211yescharacteristic, complemented
32C22×C4⋊C4×C61C2211yescharacteristic, complemented
33C61×#435—24no—
34C2×C4⋊C8×C61C2211yescharacteristic, complemented
35C61×#418—24no—
36C2×#102×C61—24no—
37C2×#102×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic, complemented
42C2×#102×C61C2211yescharacteristic, complemented
43C2×#102×C61C2211yescharacteristic, complemented
44C2×#102×C61C2211yescharacteristic, complemented
45C2×#102×C61C2211yescharacteristic, complemented
46C2×#102×C61C2211yescharacteristic, complemented
47C2×#102×C61C2211yescharacteristic, complemented
48C2×#102×C61C2211yescharacteristic, complemented
49C2×C22⋊C8×C61C2211yescharacteristic, complemented
50C2×C22⋊C8×C61C2211yescharacteristic, complemented
51C2×#97×C61C2211yescharacteristic, complemented
52C61×#388—21no—
53C61×#387—21no—
54C61×#386—21no—
55C61×#382C2211yescharacteristic, complemented
56C61×#380C2211yescharacteristic, complemented
57C61×#380C2211yescharacteristic, complemented
58C4×C4⋊C4×C61C2211yescharacteristic, complemented
59C4×C22⋊C4×C61—21no—
60C61×#340C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C25×C61—21no—
65C25×C61—21no—
66C22×D4×C61—22no—
67C22×D4×C61—22no—
68C22×D4×C61—22no—
69C22×D4×C61—22no—
70C22×D4×C61—21no—
71C22×D4×C61—21no—
72C22×D4×C61—28no—
73C22×D4×C61—21no—
74C22×D4×C61—22no—
75C22×D4×C61—22no—
76C22×D4×C61—21no—
77C22×D4×C61—21no—
78C22×D4×C61—21no—
79C22×D4×C61—41no—
80C22×D4×C61—41no—
81C22×D4×C61—41no—
82C22×D4×C61—41no—
83C22×D4×C61—44no—
84C22×D4×C61—44no—
85C22×D4×C61C2×C414yes—
86C22×D4×C61C2×C414yescomplemented
87C22×D4×C61D411yescharacteristic
88C22×D4×C61C2311yescharacteristic
89C22×D4×C61C2311yescharacteristic
90C22×D4×C61C2311yescharacteristic
91C23×C4×C61—21no—
92C23×C4×C61—21no—
93C23×C4×C61C2311yescharacteristic
94C23×C4×C61C2311yescharacteristic
95C2×M16×C61—22no—
96C2×M16×C61—22no—
97C2×M16×C61—41no—
98C22×C8×C61—22no—
99C22×C8×C61—22no—
100C22×C8×C61—41no—
101C22×C8×C61C2311yescharacteristic
102C22×C8×C61C2311yescharacteristic
103C22×C8×C61C2311yescharacteristic
104C22×C8×C61C2311yescharacteristic
105#127×C61—22no—
106#127×C61C2×C414yescomplemented
107#121×C61—22no—
108#121×C61—22no—
109#121×C61—28no—
110#121×C61C2×C414yes—
111#121×C61C2×C414yescomplemented
112#120×C61—28no—
113#120×C61—28no—
114C4×D4×C61—22no—
115C4×D4×C61C2×C414yes—
116C4×D4×C61C2×C414yescomplemented
117C4×D4×C61D414yes—
118#117×C61—22no—
119#117×C61—41no—
120C2×C4⋊C4×C61—22no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61—41no—
123C2×C4⋊C4×C61D411yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C22⋊C4×C61D411yescharacteristic
137C2×C42×C61—21no—
138C2×C42×C61—21no—
139C2×C42×C61C2311yescharacteristic
140C4⋊C8×C61—22no—
141#102×C61—22no—
142#102×C61—22no—
143#102×C61—22no—
144#102×C61—22no—
145#102×C61—22no—
146#102×C61—22no—
147#102×C61—22no—
148#102×C61—41no—
149#102×C61—41no—
150#102×C61—41no—
151#102×C61—41no—
152#102×C61D414yescomplemented
153C22⋊C8×C61—22no—
154C22⋊C8×C61—22no—
155#97×C61—22no—
156#95×C61—21no—
157#95×C61—21no—
158#95×C61—21no—
159#95×C61—21no—
160#95×C61—21no—
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—21no—
164C24×C61—24no—
165C24×C61—24no—
166C24×C61—42no—
167C24×C61—42no—
168C24×C61—42no—
169C24×C61—42no—
170C24×C61—42no—
171C24×C61—42no—
172C24×C61—42no—
173C24×C61—42no—
174C24×C61—81no—
175C24×C61—81no—
176C24×C61—81no—
177C24×C61—81no—
178C24×C61C2×D411yescharacteristic
179C24×C61C2×D411yescharacteristic
180C2×D4×C61—22no—
181C2×D4×C61—22no—
182C2×D4×C61—28no—
183C2×D4×C61—28no—
184C2×D4×C61—24no—
185C2×D4×C61—24no—
186C2×D4×C61—24no—
187C2×D4×C61—24no—
188C2×D4×C61—24no—
189C2×D4×C61—24no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—44no—
204C2×D4×C61—44no—
205C2×D4×C61—44no—
206C2×D4×C61—44no—
207C2×D4×C61—44no—
208C2×D4×C61—44no—
209C2×D4×C61—42no—
210C2×D4×C61—42no—
211C2×D4×C61—42no—
212C2×D4×C61—42no—
213C2×D4×C61—42no—
214C2×D4×C61—42no—
215C2×D4×C61—432no—
216C2×D4×C61—42no—
217C2×D4×C61—42no—
218C2×D4×C61—42no—
219C2×D4×C61—42no—
220C2×D4×C61—81no—
221C2×D4×C61—81no—
222C2×D4×C61C22⋊C414yes—
223C2×D4×C61C22×C412yes—
224C2×D4×C61C22×C412yes—
225C2×D4×C61C22×C412yes—
226C2×D4×C61C2×D412yes—
227C2×D4×C61#4112yes—
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—21no—
237C22×C4×C61—21no—
238C22×C4×C61—24no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—42no—
243C22×C4×C61—42no—
244C22×C4×C61—42no—
245C22×C4×C61—42no—
246C22×C4×C61—81no—
247C22×C4×C61C22×C412yes—
248C22×C4×C61C22×C412yes—
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D412yes—
254C22×C4×C61C2×D412yes—
255C22×C4×C61C2411yescharacteristic
256M16×C61—44no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—44no—
269C2×C8×C61C2×D412yescomplemented
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—42no—
279C4⋊C4×C61C22⋊C414yes—
280C4⋊C4×C61C22×C412yes—
281C4⋊C4×C61C2×D412yescomplemented
282C22⋊C4×C61—24no—
283C22⋊C4×C61—24no—
284C22⋊C4×C61—24no—
285C22⋊C4×C61—42no—
286C22⋊C4×C61—42no—
287C22⋊C4×C61—81no—
288C22⋊C4×C61C22⋊C414yes—
289C22⋊C4×C61C22⋊C414yes—
290C42×C61—42no—
291C42×C61—81no—
292C42×C61C22×C412yes—
293C42×C61C2×D412yes—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—22no—
299C23×C61—21no—
300C23×C61—22no—
301C23×C61—21no—
302C23×C61—22no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—48no—
310C23×C61—48no—
311C23×C61—48no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61—48no—
329C23×C61—84no—
330C23×C61—84no—
331C23×C61—84no—
332C23×C61—84no—
333C23×C61—84no—
334C23×C61—84no—
335C23×C61—84no—
336C23×C61—84no—
337C23×C61—84no—
338C23×C61—84no—
339C23×C61C2×C22⋊C412yes—
340C23×C61C2×C22⋊C412yes—
341C23×C61AGL(1,ℤ/8)12yes—
342C23×C61AGL(1,ℤ/8)12yes—
343C23×C61C22×D411yescharacteristic
344D4×C61—28no—
345D4×C61—22no—
346D4×C61—22no—
347D4×C61—22no—
348D4×C61—22no—
349D4×C61—22no—
350D4×C61—22no—
351D4×C61—22no—
352D4×C61—48no—
353D4×C61—48no—
354D4×C61—48no—
355D4×C61—48no—
356D4×C61—48no—
357D4×C61—41no—
358D4×C61—41no—
359D4×C61—41no—
360D4×C61—41no—
361D4×C61—84no—
362D4×C61C4×D414yes—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—22no—
372C2×C4×C61—22no—
373C2×C4×C61—22no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—22no—
377C2×C4×C61—22no—
378C2×C4×C61—22no—
379C2×C4×C61—22no—
380C2×C4×C61—22no—
381C2×C4×C61—48no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—84no—
396C2×C4×C61C2×C22⋊C412yes—
397C2×C4×C61C2×C22⋊C412yes—
398C2×C4×C61C2×C22⋊C412yes—
399C2×C4×C61C2×C22⋊C412yes—
400C2×C4×C61C23×C411yescharacteristic
401C2×C4×C61C22×D411yescharacteristic
402C2×C4×C61C22×D411yescharacteristic
403C2×C4×C61C2×#4111yescharacteristic
404C2×C4×C61H(5,𝔽2)11yescharacteristic
405C2×C4×C61H(5,𝔽2)11yescharacteristic
406C8×C61—22no—
407C8×C61—41no—
408C8×C61—41no—
409C8×C61—41no—
410#22423C6111yesmaximal, characteristic, direct product factor, Sylow
411C22×C61—22no—
412C22×C61—22no—
413C22×C61—22no—
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—22no—
417C22×C61—22no—
418C22×C61—24no—
419C22×C61—22no—
420C22×C61—22no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61—41no—
424C22×C61—42no—
425C22×C61—41no—
426C22×C61—42no—
427C22×C61—41no—
428C22×C61—42no—
429C22×C61—41no—
430C22×C61—42no—
431C22×C61—42no—
432C22×C61—42no—
433C22×C61—42no—
434C22×C61—42no—
435C22×C61—42no—
436C22×C61—42no—
437C22×C61—816no—
438C22×C61—816no—
439C22×C61—81no—
440C22×C61—81no—
441C22×C61—81no—
442C22×C61—81no—
443C22×C61—81no—
444C22×C61—81no—
445C22×C61—81no—
446C22×C61—81no—
447C22×C61#41814yescomplemented
448C22×C61C22×C22⋊C411yescharacteristic
449C22×C61D4211yescharacteristic
450C22×C61#54611yescharacteristic
451C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
452C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
453C22×C61#57611yescharacteristic
454C22×C61#57711yescharacteristic
455C4×C61—22no—
456C4×C61—22no—
457C4×C61—22no—
458C4×C61—22no—
459C4×C61—42no—
460C4×C61—42no—
461C4×C61—81no—
462C4×C61—81no—
463C4×C61—81no—
464C4×C61C2×C4×D411yescharacteristic
465C4×C61#51811yescharacteristic
466C4×C61D4211yescharacteristic
467C4×C61#54611yescharacteristic
468C2×D42C2×C6111yescharacteristic
469C2×#435C2×C6111yescharacteristic, complemented
470C2×#418C2×C6111yescharacteristic, complemented
471C22×#102C2×C6111yescharacteristic, complemented
472#2352C2×C6111yescharacteristic, complemented
473#1982C2×C6111yescharacteristic, complemented
474#1961C2×C6111yescharacteristic, complemented
475#1895C2×C6111yescharacteristic, complemented
476#1893C2×C6111yescharacteristic, complemented
477#1875C2×C6111yescharacteristic, complemented
478#1874C2×C6111yescharacteristic, complemented
479#1804C2×C6111yescharacteristic, complemented
480#1786C2×C6111yescharacteristic, complemented
481#1786C2×C6111yescharacteristic, complemented
482#1762C2×C6111yescharacteristic, complemented
483C2×C61—24no—
484C2×C61—42no—
485C2×C61—44no—
486C2×C61—82no—
487C2×C61—82no—
488C2×C61D4×C22⋊C411yescharacteristic
489C2×C61C2×#41811yescharacteristic
490C2×C61#289711yescharacteristic
491C2×C61#326411yescharacteristic
492C2×C61#326511yescharacteristic
493C2×C61#331011yescharacteristic
494C2×C61#331811yescharacteristic
495C23×D4—21no—
496C23×D4C22×C6111yescharacteristic
497C23×D4C22×C6111yescharacteristic
498C22×M16C22×C6111yescharacteristic, complemented
499C23×C8C22×C6111yescharacteristic, complemented
500D42—24no—
501D42C4×C6118yescomplemented
502C2×#127C22×C6111yescharacteristic
503C2×#121—21no—
504C2×#121C22×C6111yescharacteristic
505C2×#121C22×C6111yescharacteristic
506C2×#120—21no—
507C2×#120—21no—
508C2×C4×D4C22×C6111yescharacteristic
509C2×C4×D4C22×C6111yescharacteristic
510C2×#117C22×C6111yescharacteristic, complemented
511C22×C4⋊C4C22×C6111yescharacteristic, complemented
512#435—24no—
513C2×C4⋊C8C22×C6111yescharacteristic, complemented
514#418—24no—
515C2×#102—24no—
516C2×#102C22×C6111yescharacteristic
517C2×#102C22×C6111yescharacteristic
518C2×#102C22×C6111yescharacteristic
519C2×#102C22×C6111yescharacteristic
520C2×#102C22×C6111yescharacteristic, complemented
521C2×#102C22×C6111yescharacteristic, complemented
522C2×#102C22×C6111yescharacteristic, complemented
523C2×#102C22×C6111yescharacteristic, complemented
524C2×#102C22×C6111yescharacteristic, complemented
525C2×#102C22×C6111yescharacteristic, complemented
526C2×#102C22×C6111yescharacteristic, complemented
527C2×#102C22×C6111yescharacteristic, complemented
528C2×C22⋊C8C22×C6111yescharacteristic, complemented
529C2×C22⋊C8C22×C6111yescharacteristic, complemented
530C2×#97C22×C6111yescharacteristic, complemented
531#388—21no—
532#387—21no—
533#386—21no—
534#382C22×C6111yescharacteristic, complemented
535#380C22×C6111yescharacteristic, complemented
536#380C22×C6111yescharacteristic, complemented
537C4×C4⋊C4C22×C6111yescharacteristic, complemented
538C4×C22⋊C4—21no—
539#340C22×C6111yescharacteristic, complemented
540#340C22×C6111yescharacteristic, complemented
541#340C22×C6111yescharacteristic, complemented
542#340C22×C6111yescharacteristic, complemented
543C61#2242311yescharacteristic, direct product factor, Sylow
544C25—21no—
545C25—21no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—28no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—21no—
559C22×D4—41no—
560C22×D4—41no—
561C22×D4—41no—
562C22×D4—41no—
563C22×D4—44no—
564C22×D4—44no—
565C22×D4C2×C4×C6114yes—
566C22×D4C2×C4×C6114yescomplemented
567C22×D4D4×C6111yescharacteristic
568C22×D4C23×C6111yescharacteristic
569C22×D4C23×C6111yescharacteristic
570C22×D4C23×C6111yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4C23×C6111yescharacteristic
574C23×C4C23×C6111yescharacteristic
575C2×M16—22no—
576C2×M16—22no—
577C2×M16—41no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8C23×C6111yescharacteristic
582C22×C8C23×C6111yescharacteristic
583C22×C8C23×C6111yescharacteristic
584C22×C8C23×C6111yescharacteristic
585#127—22no—
586#127C2×C4×C6114yescomplemented
587#121—22no—
588#121—22no—
589#121—28no—
590#121C2×C4×C6114yes—
591#121C2×C4×C6114yescomplemented
592#120—28no—
593#120—28no—
594C4×D4—22no—
595C4×D4C2×C4×C6114yes—
596C4×D4C2×C4×C6114yescomplemented
597C4×D4D4×C6114yes—
598#117—22no—
599#117—41no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4D4×C6111yescharacteristic
604C2×C4⋊C4C23×C6111yescharacteristic
605C2×C4⋊C4C23×C6111yescharacteristic
606C2×C4⋊C4C23×C6111yescharacteristic
607C2×C4⋊C4C23×C6111yescharacteristic
608C2×C4⋊C4C23×C6111yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4D4×C6111yescharacteristic
616C2×C22⋊C4D4×C6111yescharacteristic
617C2×C42—21no—
618C2×C42—21no—
619C2×C42C23×C6111yescharacteristic
620C4⋊C8—22no—
621#102—22no—
622#102—22no—
623#102—22no—
624#102—22no—
625#102—22no—
626#102—22no—
627#102—22no—
628#102—41no—
629#102—41no—
630#102—41no—
631#102—41no—
632#102D4×C6114yescomplemented
633C22⋊C8—22no—
634C22⋊C8—22no—
635#97—22no—
636#95—21no—
637#95—21no—
638#95—21no—
639#95—21no—
640#95—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—24no—
645C24—24no—
646C24—42no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24C2×D4×C6111yescharacteristic
659C24C2×D4×C6111yescharacteristic
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—432no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C22⋊C4×C6114yes—
703C2×D4C22×C4×C6112yes—
704C2×D4C22×C4×C6112yes—
705C2×D4C22×C4×C6112yes—
706C2×D4C2×D4×C6112yes—
707C2×D4#41×C6112yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—24no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—81no—
727C22×C4C22×C4×C6112yes—
728C22×C4C22×C4×C6112yes—
729C22×C4C2×D4×C6111yescharacteristic
730C22×C4C2×D4×C6111yescharacteristic
731C22×C4C2×D4×C6111yescharacteristic
732C22×C4C2×D4×C6111yescharacteristic
733C22×C4C2×D4×C6112yes—
734C22×C4C2×D4×C6112yes—
735C22×C4C24×C6111yescharacteristic
736M16—44no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—44no—
749C2×C8C2×D4×C6112yescomplemented
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—42no—
759C4⋊C4C22⋊C4×C6114yes—
760C4⋊C4C22×C4×C6112yes—
761C4⋊C4C2×D4×C6112yescomplemented
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—81no—
768C22⋊C4C22⋊C4×C6114yes—
769C22⋊C4C22⋊C4×C6114yes—
770C42—42no—
771C42—81no—
772C42C22×C4×C6112yes—
773C42C2×D4×C6112yes—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—21no—
781C23—22no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—48no—
790C23—48no—
791C23—48no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—48no—
809C23—84no—
810C23—84no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23C2×C22⋊C4×C6112yes—
820C23C2×C22⋊C4×C6112yes—
821C23AGL(1,ℤ/8)×C6112yes—
822C23AGL(1,ℤ/8)×C6112yes—
823C23C22×D4×C6111yescharacteristic
824D4—28no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—48no—
833D4—48no—
834D4—48no—
835D4—48no—
836D4—48no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—84no—
842D4C4×D4×C6114yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—84no—
876C2×C4C2×C22⋊C4×C6112yes—
877C2×C4C2×C22⋊C4×C6112yes—
878C2×C4C2×C22⋊C4×C6112yes—
879C2×C4C2×C22⋊C4×C6112yes—
880C2×C4C23×C4×C6111yescharacteristic
881C2×C4C22×D4×C6111yescharacteristic
882C2×C4C22×D4×C6111yescharacteristic
883C2×C4C2×#41×C6111yescharacteristic
884C2×C4H(5,𝔽2)×C6111yescharacteristic
885C2×C4H(5,𝔽2)×C6111yescharacteristic
886C8—22no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—24no—
898C22—22no—
899C22—22no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—816no—
917C22—816no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22C61×#41814yescomplemented
927C22C22×C22⋊C4×C6111yescharacteristic
928C22D42×C6111yescharacteristic
929C22C61×#54611yescharacteristic
930C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
931C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
932C22C61×#57611yescharacteristic
933C22C61×#57711yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—42no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4C2×C4×D4×C6111yescharacteristic
944C4C61×#51811yescharacteristic
945C4D42×C6111yescharacteristic
946C4C61×#54611yescharacteristic
947C2—24no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—82no—
952C2D4×C22⋊C4×C6111yescharacteristic
953C2C2×C61×#41811yescharacteristic
954C2C61×#289711yescharacteristic
955C2C61×#326411yescharacteristic
956C2C61×#326511yescharacteristic
957C2C61×#331011yescharacteristic
958C2C61×#331811yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutatorC2×C4C23×C4×C61
Frattini, cosocleC22×C4C24×C61
prime radicalC2×D42×C61C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C4×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#435C2semidirect
3. C2×C61×#418C2semidirect
4. C22×#102×C61C2semidirect
5. C61×#2352C2semidirect
6. C61×#1982C2semidirect
7. C61×#1961C2semidirect
8. C61×#1895C2semidirect
9. C61×#1893C2semidirect
10. C61×#1875C2semidirect
11. C61×#1874C2semidirect
12. C61×#1804C2semidirect
13. C61×#1786C2semidirect
14. C61×#1786C2semidirect
15. C61×#1762C2semidirect
19. C22×M16×C61C22semidirect
20. C23×C8×C61C22semidirect
22. D42×C61C4semidirect
31. C2×#117×C61C22semidirect
32. C22×C4⋊C4×C61C22semidirect
34. C2×C4⋊C8×C61C22semidirect
41. C2×#102×C61C22semidirect
42. C2×#102×C61C22semidirect
43. C2×#102×C61C22semidirect
44. C2×#102×C61C22semidirect
45. C2×#102×C61C22semidirect
46. C2×#102×C61C22semidirect
47. C2×#102×C61C22semidirect
48. C2×#102×C61C22semidirect
49. C2×C22⋊C8×C61C22semidirect
50. C2×C22⋊C8×C61C22semidirect
51. C2×#97×C61C22semidirect
55. C61×#382C22semidirect
56. C61×#380C22semidirect
57. C61×#380C22semidirect
58. C4×C4⋊C4×C61C22semidirect
60. C61×#340C22semidirect
61. C61×#340C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
86. C22×D4×C61C2×C4semidirect
106. #127×C61C2×C4semidirect
111. #121×C61C2×C4semidirect
116. C4×D4×C61C2×C4semidirect
152. #102×C61D4semidirect
269. C2×C8×C61C2×D4semidirect
281. C4⋊C4×C61C2×D4semidirect
410. #22423C61direct (N × H)
447. C22×C61#418semidirect
469. C2×#435C2×C61semidirect
470. C2×#418C2×C61semidirect
471. C22×#102C2×C61semidirect
472. #2352C2×C61semidirect
473. #1982C2×C61semidirect
474. #1961C2×C61semidirect
475. #1895C2×C61semidirect
476. #1893C2×C61semidirect
477. #1875C2×C61semidirect
478. #1874C2×C61semidirect
479. #1804C2×C61semidirect
480. #1786C2×C61semidirect
481. #1786C2×C61semidirect
482. #1762C2×C61semidirect
498. C22×M16C22×C61semidirect
499. C23×C8C22×C61semidirect
501. D42C4×C61semidirect
510. C2×#117C22×C61semidirect
511. C22×C4⋊C4C22×C61semidirect
513. C2×C4⋊C8C22×C61semidirect
520. C2×#102C22×C61semidirect
521. C2×#102C22×C61semidirect
522. C2×#102C22×C61semidirect
523. C2×#102C22×C61semidirect
524. C2×#102C22×C61semidirect
525. C2×#102C22×C61semidirect
526. C2×#102C22×C61semidirect
527. C2×#102C22×C61semidirect
528. C2×C22⋊C8C22×C61semidirect
529. C2×C22⋊C8C22×C61semidirect
530. C2×#97C22×C61semidirect
534. #382C22×C61semidirect
535. #380C22×C61semidirect
536. #380C22×C61semidirect
537. C4×C4⋊C4C22×C61semidirect
539. #340C22×C61semidirect
540. #340C22×C61semidirect
541. #340C22×C61semidirect
542. #340C22×C61semidirect
543. C61#22423direct (N × H)
566. C22×D4C2×C4×C61semidirect
586. #127C2×C4×C61semidirect
591. #121C2×C4×C61semidirect
596. C4×D4C2×C4×C61semidirect
632. #102D4×C61semidirect
749. C2×C8C2×D4×C61semidirect
761. C4⋊C4C2×D4×C61semidirect
926. C22C61×#418semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C612
C2×C61×#4352
C2×C61×#4182
C22×#102×C612
C61×#23522
C61×#19822
C61×#19612
C61×#18952
C61×#18932
C61×#18752
C61×#18742
C61×#18042
C61×#17862
C61×#17622
#2242361