Finite Group Databasebeta

← C61×#24382 #29527815

Subgroups — C61×#24382 #29527815

Order 15616.

1678 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#525C211yesmaximal, characteristic, complemented
2C2×C61×#466C211yesmaximal, characteristic, complemented
3C2×C61×#465C211yesmaximal, characteristic, complemented
4C2×C61×#449C211yesmaximal, characteristic, complemented
5C22×C22⋊C8×C61C211yesmaximal, characteristic, complemented
6C61×#2847C211yesmaximal, characteristic, complemented
7C61×#2036C211yesmaximal, characteristic, complemented
8C61×#2034C211yesmaximal, characteristic, complemented
9C61×#2000C211yesmaximal, characteristic, complemented
10C61×#1999C211yesmaximal, characteristic, complemented
11C61×#1893C211yesmaximal, characteristic, complemented
12C61×#1892C211yesmaximal, characteristic, complemented
13C61×#1875C211yesmaximal, characteristic, complemented
14C61×#1854C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C24×C4×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic, complemented
19C22×D8×C61C2211yescharacteristic, complemented
20C23×C8×C61C2211yescharacteristic
21C23×C8×C61C2211yescharacteristic
22C61×#525—24no—
23C61×#525—24no—
24C2×#123×C61—21no—
25C2×C22⋊Q8×C61C2211yescharacteristic
26C2×C22⋊Q8×C61C2211yescharacteristic
27C2×#121×C61C2211yescharacteristic
28C2×#121×C61C2211yescharacteristic
29C2×#121×C61C2211yescharacteristic
30C2×#121×C61C2211yescharacteristic
31C2×#121×C61C2211yescharacteristic
32C2×#120×C61—21no—
33C2×#120×C61—21no—
34C2×C4×D4×C61—21no—
35C2×C4×D4×C61—21no—
36C2×#117×C61C2211yescharacteristic
37C61×#466—24no—
38C61×#465—24no—
39C61×#449—24no—
40C2×#107×C61C2211yescharacteristic, complemented
41C2×#106×C61C2211yescharacteristic, complemented
42C2×#103×C61C2211yescharacteristic, complemented
43C2×#103×C61C2211yescharacteristic, complemented
44C2×#103×C61C2211yescharacteristic, complemented
45C2×#102×C61C2211yescharacteristic, complemented
46C2×#102×C61C2211yescharacteristic, complemented
47C2×#102×C61C2211yescharacteristic, complemented
48C2×#102×C61C2211yescharacteristic, complemented
49C2×#102×C61C2211yescharacteristic, complemented
50C2×C22⋊C8×C61—24no—
51C2×C22⋊C8×C61C2211yescharacteristic
52C2×C22⋊C8×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C61×#386—21no—
56C61×#386—21no—
57C61×#386—21no—
58C61×#380C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#380C2211yescharacteristic
61C61×#340C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C61×#340C2211yescharacteristic, complemented
65C25×C61D411yescharacteristic
66C2×#41×C61—22no—
67C2×#41×C61—22no—
68C2×#41×C61—22no—
69C2×#41×C61—22no—
70C2×#41×C61—41no—
71C2×#41×C61—41no—
72C22×Q8×C61C2311yescharacteristic
73C22×D4×C61—21no—
74C22×D4×C61—21no—
75C22×D4×C61—21no—
76C22×D4×C61—21no—
77C22×D4×C61—21no—
78C22×D4×C61—21no—
79C22×D4×C61C2311yescharacteristic
80C22×D4×C61C2311yescharacteristic
81C23×C4×C61—22no—
82C23×C4×C61—22no—
83C23×C4×C61—22no—
84C23×C4×C61—21no—
85C23×C4×C61—22no—
86C23×C4×C61—41no—
87C23×C4×C61—41no—
88C23×C4×C61D411yescharacteristic
89C23×C4×C61D411yescharacteristic
90C23×C4×C61D411yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2311yescharacteristic
93C23×C4×C61C2311yescharacteristic
94C2×SD16×C61—22no—
95C2×SD16×C61—22no—
96C2×SD16×C61—41no—
97C2×D8×C61—22no—
98C2×D8×C61—22no—
99C2×D8×C61—41no—
100C22×C8×C61—22no—
101C22×C8×C61—22no—
102C22×C8×C61—22no—
103C22×C8×C61—22no—
104C22×C8×C61—41no—
105C22×C8×C61—41no—
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110#123×C61—28no—
111C22⋊Q8×C61—22no—
112C22⋊Q8×C61—22no—
113C22⋊Q8×C61—22no—
114C22⋊Q8×C61D414yescomplemented
115#121×C61—22no—
116#121×C61—22no—
117#121×C61—22no—
118#121×C61—22no—
119#121×C61—22no—
120#121×C61—22no—
121#121×C61—22no—
122#121×C61—41no—
123#121×C61—41no—
124#121×C61D414yescomplemented
125#120×C61—28no—
126#120×C61—44no—
127C4×D4×C61—28no—
128C4×D4×C61—28no—
129#117×C61—22no—
130#117×C61—22no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61—21no—
149C2×C42×C61—21no—
150#107×C61—22no—
151#106×C61—22no—
152#103×C61—22no—
153#103×C61—22no—
154#103×C61—41no—
155#102×C61—22no—
156#102×C61—22no—
157#102×C61—22no—
158#102×C61—22no—
159#102×C61—41no—
160C22⋊C8×C61—22no—
161C22⋊C8×C61—22no—
162C22⋊C8×C61—22no—
163C22⋊C8×C61D414yescomplemented
164#95×C61—21no—
165#95×C61—21no—
166#95×C61—21no—
167C24×C61—22no—
168C24×C61—22no—
169C24×C61—22no—
170C24×C61—22no—
171C24×C61—22no—
172C24×C61—21no—
173C24×C61—21no—
174C24×C61—41no—
175C24×C61—41no—
176C24×C61C2×D411yescharacteristic
177C24×C61C2×D411yescharacteristic
178C24×C61C2×D411yescharacteristic
179#41×C61—44no—
180#41×C61—44no—
181#41×C61—44no—
182#41×C61—44no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61C2×D412yes—
189C2×D4×C61—24no—
190C2×D4×C61—24no—
191C2×D4×C61—24no—
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—42no—
204C2×D4×C61—42no—
205C2×D4×C61—42no—
206C2×D4×C61—42no—
207C2×D4×C61—42no—
208C2×D4×C61—42no—
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—42no—
216C2×D4×C61—42no—
217C2×D4×C61—42no—
218C2×D4×C61C2×D412yes—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—24no—
228C22×C4×C61—22no—
229C22×C4×C61—22no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—22no—
234C22×C4×C61—22no—
235C22×C4×C61—22no—
236C22×C4×C61—22no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—41no—
247C22×C4×C61—41no—
248C22×C4×C61—41no—
249C22×C4×C61—44no—
250C22×C4×C61—44no—
251C22×C4×C61—44no—
252C22×C4×C61—44no—
253C22×C4×C61—42no—
254C22×C4×C61—42no—
255C22×C4×C61C2×D411yescharacteristic
256C22×C4×C61C2×D411yescharacteristic
257C22×C4×C61C2×D412yes—
258C22×C4×C61C2×D412yes—
259C22×C4×C61C2×D411yescharacteristic
260C22×C4×C61C2×D412yes—
261C22×C4×C61#4112yes—
262C22×C4×C61C2411yescharacteristic
263SD16×C61—44no—
264D8×C61—44no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61—21no—
270C2×C8×C61—21no—
271C2×C8×C61—21no—
272C2×C8×C61—21no—
273C2×C8×C61—21no—
274C2×C8×C61—21no—
275C2×C8×C61—44no—
276C2×C8×C61—44no—
277C2×C8×C61C2×D412yes—
278C2×C8×C61C2×D412yes—
279C4⋊C4×C61—24no—
280C4⋊C4×C61—24no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61—21no—
285C4⋊C4×C61—21no—
286C4⋊C4×C61—21no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61—21no—
289C4⋊C4×C61C2×D412yes—
290C4⋊C4×C61C2×D412yes—
291C22⋊C4×C61—24no—
292C22⋊C4×C61—24no—
293C22⋊C4×C61—24no—
294C22⋊C4×C61—24no—
295C22⋊C4×C61—24no—
296C22⋊C4×C61—42no—
297C22⋊C4×C61—42no—
298C22⋊C4×C61—42no—
299C22⋊C4×C61—42no—
300C22⋊C4×C61—42no—
301C22⋊C4×C61—42no—
302C42×C61—24no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—28no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—21no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—21no—
318C23×C61—21no—
319C23×C61—21no—
320C23×C61—22no—
321C23×C61—44no—
322C23×C61—44no—
323C23×C61—44no—
324C23×C61—44no—
325C23×C61—44no—
326C23×C61—44no—
327C23×C61—41no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61—41no—
336C23×C61—41no—
337C23×C61—41no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61#12012yes—
341C23×C61#12112yes—
342C23×C61#13512yes—
343C23×C61#13512yes—
344C23×C61AGL(1,ℤ/8)12yes—
345C23×C61C22×D411yescharacteristic
346Q8×C61—22no—
347Q8×C61—22no—
348Q8×C61—41no—
349Q8×C61—41no—
350D4×C61—22no—
351D4×C61—22no—
352D4×C61—48no—
353D4×C61—48no—
354D4×C61—48no—
355D4×C61—41no—
356D4×C61—41no—
357D4×C61—41no—
358D4×C61—41no—
359D4×C61—41no—
360D4×C61—41no—
361D4×C61—84no—
362D4×C61—84no—
363D4×C61—84no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—22no—
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—21no—
379C2×C4×C61—22no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—44no—
383C2×C4×C61—44no—
384C2×C4×C61—44no—
385C2×C4×C61—48no—
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—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61—41no—
402C2×C4×C61—41no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61#12012yes—
406C2×C4×C61#12112yes—
407C2×C4×C61C22×D411yescharacteristic
408C2×C4×C61C22×D411yescharacteristic
409C2×C4×C61C22×D411yescharacteristic
410C2×C4×C61C2×#4111yescharacteristic
411C2×C4×C61H(5,𝔽2)11yescharacteristic
412C2×C4×C61H(5,𝔽2)11yescharacteristic
413C8×C61—22no—
414C8×C61—22no—
415C8×C61—41no—
416C8×C61—41no—
417#24382C6111yesmaximal, characteristic, direct product factor, Sylow
418C22×C61—22no—
419C22×C61—22no—
420C22×C61—22no—
421C22×C61—22no—
422C22×C61—22no—
423C22×C61—22no—
424C22×C61—22no—
425C22×C61—22no—
426C22×C61—22no—
427C22×C61—22no—
428C22×C61—22no—
429C22×C61—22no—
430C22×C61—416no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—42no—
440C22×C61—42no—
441C22×C61—42no—
442C22×C61—81no—
443C22×C61—81no—
444C22×C61—81no—
445C22×C61—81no—
446C22×C61—81no—
447C22×C61—81no—
448C22×C61—81no—
449C22×C61—81no—
450C22×C61—81no—
451C22×C61—81no—
452C22×C61—81no—
453C22×C61#44914yescomplemented
454C22×C61C2×#12011yescharacteristic
455C22×C61C2×#12111yescharacteristic
456C22×C61#53411yescharacteristic
457C22×C61C2×#13511yescharacteristic
458C22×C61C2×#13511yescharacteristic
459C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
460C22×C61#57511yescharacteristic
461C4×C61—22no—
462C4×C61—22no—
463C4×C61—41no—
464C4×C61—42no—
465C4×C61—42no—
466C4×C61—42no—
467C4×C61—81no—
468C4×C61—81no—
469C4×C61—81no—
470C4×C61D4211yescharacteristic
471C4×C61D4211yescharacteristic
472C4×C61#54611yescharacteristic
473C4×C61#54611yescharacteristic
474C2×#525C2×C6111yescharacteristic, complemented
475C2×#466C2×C6111yescharacteristic, complemented
476C2×#465C2×C6111yescharacteristic, complemented
477C2×#449C2×C6111yescharacteristic, complemented
478C22×C22⋊C8C2×C6111yescharacteristic, complemented
479#2847C2×C6111yescharacteristic, complemented
480#2036C2×C6111yescharacteristic, complemented
481#2034C2×C6111yescharacteristic, complemented
482#2000C2×C6111yescharacteristic, complemented
483#1999C2×C6111yescharacteristic, complemented
484#1893C2×C6111yescharacteristic, complemented
485#1892C2×C6111yescharacteristic, complemented
486#1875C2×C6111yescharacteristic, complemented
487#1854C2×C6111yescharacteristic, complemented
488#1788C2×C6111yescharacteristic, complemented
489C2×C61—24no—
490C2×C61—42no—
491C2×C61—42no—
492C2×C61—82no—
493C2×C61—161no—
494C2×C61#241011yescharacteristic
495C2×C61C2×#44911yescharacteristic
496C2×C61#300211yescharacteristic
497C2×C61#305011yescharacteristic
498C2×C61#305511yescharacteristic
499C2×C61#318811yescharacteristic
500C2×C61#319111yescharacteristic
501C22×#41C22×C6111yescharacteristic
502C24×C4C22×C6111yescharacteristic
503C22×SD16C22×C6111yescharacteristic, complemented
504C22×D8C22×C6111yescharacteristic, complemented
505C23×C8C22×C6111yescharacteristic
506C23×C8C22×C6111yescharacteristic
507#525—24no—
508#525—24no—
509C2×#123—21no—
510C2×C22⋊Q8C22×C6111yescharacteristic
511C2×C22⋊Q8C22×C6111yescharacteristic
512C2×#121C22×C6111yescharacteristic
513C2×#121C22×C6111yescharacteristic
514C2×#121C22×C6111yescharacteristic
515C2×#121C22×C6111yescharacteristic
516C2×#121C22×C6111yescharacteristic
517C2×#120—21no—
518C2×#120—21no—
519C2×C4×D4—21no—
520C2×C4×D4—21no—
521C2×#117C22×C6111yescharacteristic
522#466—24no—
523#465—24no—
524#449—24no—
525C2×#107C22×C6111yescharacteristic, complemented
526C2×#106C22×C6111yescharacteristic, complemented
527C2×#103C22×C6111yescharacteristic, complemented
528C2×#103C22×C6111yescharacteristic, complemented
529C2×#103C22×C6111yescharacteristic, complemented
530C2×#102C22×C6111yescharacteristic, complemented
531C2×#102C22×C6111yescharacteristic, complemented
532C2×#102C22×C6111yescharacteristic, complemented
533C2×#102C22×C6111yescharacteristic, complemented
534C2×#102C22×C6111yescharacteristic, complemented
535C2×C22⋊C8—24no—
536C2×C22⋊C8C22×C6111yescharacteristic
537C2×C22⋊C8C22×C6111yescharacteristic
538C2×C22⋊C8C22×C6111yescharacteristic
539C2×C22⋊C8C22×C6111yescharacteristic
540#386—21no—
541#386—21no—
542#386—21no—
543#380C22×C6111yescharacteristic
544#380C22×C6111yescharacteristic
545#380C22×C6111yescharacteristic
546#340C22×C6111yescharacteristic, complemented
547#340C22×C6111yescharacteristic, complemented
548#340C22×C6111yescharacteristic, complemented
549#340C22×C6111yescharacteristic, complemented
550C61#2438211yescharacteristic, direct product factor, Sylow
551C25D4×C6111yescharacteristic
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—41no—
557C2×#41—41no—
558C22×Q8C23×C6111yescharacteristic
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4C23×C6111yescharacteristic
566C22×D4C23×C6111yescharacteristic
567C23×C4—21no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4D4×C6111yescharacteristic
575C23×C4D4×C6111yescharacteristic
576C23×C4D4×C6111yescharacteristic
577C23×C4C23×C6111yescharacteristic
578C23×C4C23×C6111yescharacteristic
579C23×C4C23×C6111yescharacteristic
580C2×SD16—22no—
581C2×SD16—22no—
582C2×SD16—41no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—41no—
586C22×C8—22no—
587C22×C8—22no—
588C22×C8—22no—
589C22×C8—22no—
590C22×C8—41no—
591C22×C8—41no—
592C22×C8C23×C6111yescharacteristic
593C22×C8C23×C6111yescharacteristic
594C22×C8C23×C6111yescharacteristic
595C22×C8C23×C6111yescharacteristic
596#123—28no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8D4×C6114yescomplemented
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—22no—
608#121—41no—
609#121—41no—
610#121D4×C6114yescomplemented
611#120—28no—
612#120—44no—
613C4×D4—28no—
614C4×D4—28no—
615#117—22no—
616#117—22no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4C23×C6111yescharacteristic
620C2×C4⋊C4C23×C6111yescharacteristic
621C2×C4⋊C4C23×C6111yescharacteristic
622C2×C4⋊C4C23×C6111yescharacteristic
623C2×C4⋊C4C23×C6111yescharacteristic
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C42—21no—
636#107—22no—
637#106—22no—
638#103—22no—
639#103—22no—
640#103—41no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—22no—
645#102—41no—
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—22no—
649C22⋊C8D4×C6114yescomplemented
650#95—21no—
651#95—21no—
652#95—21no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—21no—
659C24—21no—
660C24—41no—
661C24—41no—
662C24C2×D4×C6111yescharacteristic
663C24C2×D4×C6111yescharacteristic
664C24C2×D4×C6111yescharacteristic
665#41—44no—
666#41—44no—
667#41—44no—
668#41—44no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8C2×D4×C6112yes—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4C2×D4×C6112yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—24no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—41no—
733C22×C4—41no—
734C22×C4—41no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4C2×D4×C6111yescharacteristic
742C22×C4C2×D4×C6111yescharacteristic
743C22×C4C2×D4×C6112yes—
744C22×C4C2×D4×C6112yes—
745C22×C4C2×D4×C6111yescharacteristic
746C22×C4C2×D4×C6112yes—
747C22×C4#41×C6112yes—
748C22×C4C24×C6111yescharacteristic
749SD16—44no—
750D8—44no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—44no—
762C2×C8—44no—
763C2×C8C2×D4×C6112yes—
764C2×C8C2×D4×C6112yes—
765C4⋊C4—24no—
766C4⋊C4—24no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4C2×D4×C6112yes—
776C4⋊C4C2×D4×C6112yes—
777C22⋊C4—24no—
778C22⋊C4—24no—
779C22⋊C4—24no—
780C22⋊C4—24no—
781C22⋊C4—24no—
782C22⋊C4—42no—
783C22⋊C4—42no—
784C22⋊C4—42no—
785C22⋊C4—42no—
786C22⋊C4—42no—
787C22⋊C4—42no—
788C42—24no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—28no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—22no—
807C23—44no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23#120×C6112yes—
827C23#121×C6112yes—
828C23#135×C6112yes—
829C23#135×C6112yes—
830C23AGL(1,ℤ/8)×C6112yes—
831C23C22×D4×C6111yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—41no—
835Q8—41no—
836D4—22no—
837D4—22no—
838D4—48no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—21no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—48no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4#120×C6112yes—
892C2×C4#121×C6112yes—
893C2×C4C22×D4×C6111yescharacteristic
894C2×C4C22×D4×C6111yescharacteristic
895C2×C4C22×D4×C6111yescharacteristic
896C2×C4C2×#41×C6111yescharacteristic
897C2×C4H(5,𝔽2)×C6111yescharacteristic
898C2×C4H(5,𝔽2)×C6111yescharacteristic
899C8—22no—
900C8—22no—
901C8—41no—
902C8—41no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—416no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22C61×#44914yescomplemented
939C22C2×#120×C6111yescharacteristic
940C22C2×#121×C6111yescharacteristic
941C22C61×#53411yescharacteristic
942C22C2×#135×C6111yescharacteristic
943C22C2×#135×C6111yescharacteristic
944C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
945C22C61×#57511yescharacteristic
946C4—22no—
947C4—22no—
948C4—41no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—81no—
953C4—81no—
954C4—81no—
955C4D42×C6111yescharacteristic
956C4D42×C6111yescharacteristic
957C4C61×#54611yescharacteristic
958C4C61×#54611yescharacteristic
959C2—24no—
960C2—42no—
961C2—42no—
962C2—82no—
963C2—161no—
964C2C61×#241011yescharacteristic
965C2C2×C61×#44911yescharacteristic
966C2C61×#300211yescharacteristic
967C2C61×#305011yescharacteristic
968C2C61×#305511yescharacteristic
969C2C61×#318811yescharacteristic
970C2C61×#319111yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
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
1. C2×C61×#525C2semidirect
2. C2×C61×#466C2semidirect
3. C2×C61×#465C2semidirect
4. C2×C61×#449C2semidirect
5. C22×C22⋊C8×C61C2semidirect
6. C61×#2847C2semidirect
7. C61×#2036C2semidirect
8. C61×#2034C2semidirect
9. C61×#2000C2semidirect
10. C61×#1999C2semidirect
11. C61×#1893C2semidirect
12. C61×#1892C2semidirect
13. C61×#1875C2semidirect
14. C61×#1854C2semidirect
15. C61×#1788C2semidirect
18. C22×SD16×C61C22semidirect
19. C22×D8×C61C22semidirect
40. C2×#107×C61C22semidirect
41. C2×#106×C61C22semidirect
42. C2×#103×C61C22semidirect
43. C2×#103×C61C22semidirect
44. C2×#103×C61C22semidirect
45. C2×#102×C61C22semidirect
46. C2×#102×C61C22semidirect
47. C2×#102×C61C22semidirect
48. C2×#102×C61C22semidirect
49. C2×#102×C61C22semidirect
61. C61×#340C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
64. C61×#340C22semidirect
114. C22⋊Q8×C61D4semidirect
124. #121×C61D4semidirect
163. C22⋊C8×C61D4semidirect
417. #24382C61direct (N × H)
453. C22×C61#449semidirect
474. C2×#525C2×C61semidirect
475. C2×#466C2×C61semidirect
476. C2×#465C2×C61semidirect
477. C2×#449C2×C61semidirect
478. C22×C22⋊C8C2×C61semidirect
479. #2847C2×C61semidirect
480. #2036C2×C61semidirect
481. #2034C2×C61semidirect
482. #2000C2×C61semidirect
483. #1999C2×C61semidirect
484. #1893C2×C61semidirect
485. #1892C2×C61semidirect
486. #1875C2×C61semidirect
487. #1854C2×C61semidirect
488. #1788C2×C61semidirect
503. C22×SD16C22×C61semidirect
504. C22×D8C22×C61semidirect
525. C2×#107C22×C61semidirect
526. C2×#106C22×C61semidirect
527. C2×#103C22×C61semidirect
528. C2×#103C22×C61semidirect
529. C2×#103C22×C61semidirect
530. C2×#102C22×C61semidirect
531. C2×#102C22×C61semidirect
532. C2×#102C22×C61semidirect
533. C2×#102C22×C61semidirect
534. C2×#102C22×C61semidirect
546. #340C22×C61semidirect
547. #340C22×C61semidirect
548. #340C22×C61semidirect
549. #340C22×C61semidirect
550. C61#24382direct (N × H)
600. C22⋊Q8D4×C61semidirect
610. #121D4×C61semidirect
649. C22⋊C8D4×C61semidirect
938. C22C61×#449semidirect

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×#4662
C2×C61×#4652
C2×C61×#4492
C22×C22⋊C8×C612
C61×#28472
C61×#20362
C61×#20342
C61×#20002
C61×#19992
C61×#18932
C61×#18922
C61×#18752
C61×#18542
C61×#17882
#2438261