Finite Group Databasebeta

← C61×#24432 #29527865

Subgroups — C61×#24432 #29527865

Order 15616.

1922 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C61C211yesmaximal, characteristic
2C2×C61×#465C211yesmaximal, characteristic, complemented
3C2×C61×#450C211yesmaximal, characteristic, complemented
4C2×C61×#450C211yesmaximal, characteristic, complemented
5C22×#102×C61C211yesmaximal, characteristic, complemented
6C61×#2417C211yesmaximal, characteristic, complemented
7C61×#2041C211yesmaximal, characteristic, complemented
8C61×#2034C211yesmaximal, characteristic, complemented
9C61×#2014C211yesmaximal, characteristic, complemented
10C61×#2000C211yesmaximal, characteristic, complemented
11C61×#1877C211yesmaximal, characteristic, complemented
12C61×#1874C211yesmaximal, characteristic, complemented
13C61×#1869C211yesmaximal, characteristic, complemented
14C61×#1864C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C61—21no—
17C23×D4×C61C2211yescharacteristic
18C23×D4×C61C2211yescharacteristic
19C22×SD16×C61C2211yescharacteristic
20C22×SD16×C61C2211yescharacteristic, complemented
21C22×SD16×C61C2211yescharacteristic, complemented
22C23×C8×C61C2211yescharacteristic, complemented
23D42×C61—24no—
24D42×C61—24no—
25C2×#127×C61C2211yescharacteristic
26C2×C22⋊Q8×C61C2211yescharacteristic, complemented
27C2×C22⋊Q8×C61C2211yescharacteristic, complemented
28C2×#121×C61—21no—
29C2×#121×C61C2211yescharacteristic
30C2×#121×C61C2211yescharacteristic
31C2×#120×C61—21no—
32C2×#120×C61—21no—
33C2×C4×D4×C61C2211yescharacteristic
34C2×C4×D4×C61C2211yescharacteristic
35C22×C4⋊C4×C61C2211yescharacteristic, complemented
36C61×#465—24no—
37C61×#450—24no—
38C61×#450—24no—
39C2×#106×C61C2211yescharacteristic, complemented
40C2×#103×C61C2211yescharacteristic, complemented
41C2×#102×C61—24no—
42C2×#102×C61C2211yescharacteristic
43C2×#102×C61C2211yescharacteristic
44C2×#102×C61C2211yescharacteristic
45C2×#102×C61C2211yescharacteristic, complemented
46C2×#102×C61C2211yescharacteristic, complemented
47C2×#102×C61C2211yescharacteristic, complemented
48C2×#102×C61C2211yescharacteristic, complemented
49C2×#102×C61C2211yescharacteristic, complemented
50C2×#102×C61C2211yescharacteristic, complemented
51C2×C22⋊C8×C61C2211yescharacteristic, complemented
52C2×C22⋊C8×C61C2211yescharacteristic, complemented
53C2×C22⋊C8×C61C2211yescharacteristic, complemented
54C61×#398—21no—
55C61×#396—21no—
56C61×#391C2211yescharacteristic, complemented
57C61×#389C2211yescharacteristic, complemented
58C61×#386—21no—
59C61×#380—21no—
60C61×#380C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#336C2211yescharacteristic, complemented
64C61×#336C2211yescharacteristic, complemented
65C25×C61—21no—
66C25×C61—21no—
67C22×Q8×C61C2311yescharacteristic
68C22×D4×C61—22no—
69C22×D4×C61—22no—
70C22×D4×C61—28no—
71C22×D4×C61—21no—
72C22×D4×C61—21no—
73C22×D4×C61—22no—
74C22×D4×C61—22no—
75C22×D4×C61—22no—
76C22×D4×C61—22no—
77C22×D4×C61—21no—
78C22×D4×C61—22no—
79C22×D4×C61—21no—
80C22×D4×C61—21no—
81C22×D4×C61—21no—
82C22×D4×C61—41no—
83C22×D4×C61—41no—
84C22×D4×C61—41no—
85C22×D4×C61—41no—
86C22×D4×C61—44no—
87C22×D4×C61—44no—
88C22×D4×C61D411yescharacteristic
89C22×D4×C61D414yes—
90C22×D4×C61C2311yescharacteristic
91C22×D4×C61C2311yescharacteristic
92C22×D4×C61C2311yescharacteristic
93C23×C4×C61—21no—
94C23×C4×C61—21no—
95C23×C4×C61C2311yescharacteristic
96C23×C4×C61C2311yescharacteristic
97C2×SD16×C61—22no—
98C2×SD16×C61—22no—
99C2×SD16×C61—22no—
100C2×SD16×C61—22no—
101C2×SD16×C61—22no—
102C2×SD16×C61—22no—
103C2×SD16×C61—41no—
104C2×SD16×C61—41no—
105C2×SD16×C61—41no—
106C22×C8×C61—22no—
107C22×C8×C61—22no—
108C22×C8×C61—41no—
109C22×C8×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113#127×C61—22no—
114#127×C61—22no—
115C22⋊Q8×C61—22no—
116C22⋊Q8×C61—22no—
117C22⋊Q8×C61—22no—
118C22⋊Q8×C61—41no—
119#121×C61—28no—
120#121×C61—22no—
121#121×C61—22no—
122#121×C61—22no—
123#121×C61D414yes—
124#120×C61—28no—
125#120×C61—28no—
126C4×D4×C61—22no—
127C4×D4×C61—22no—
128C4×D4×C61—22no—
129C4×D4×C61—22no—
130C2×C4⋊C4×C61—22no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61—21no—
135C2×C4⋊C4×C61—41no—
136C2×C4⋊C4×C61D411yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61C2311yescharacteristic
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×C61D411yescharacteristic
148C2×C22⋊C4×C61D411yescharacteristic
149C2×C42×C61C2311yescharacteristic
150#106×C61—22no—
151#103×C61—22no—
152#102×C61—22no—
153#102×C61—22no—
154#102×C61—22no—
155#102×C61—22no—
156#102×C61—22no—
157#102×C61—22no—
158#102×C61—22no—
159#102×C61—41no—
160#102×C61D414yescomplemented
161C22⋊C8×C61—22no—
162C22⋊C8×C61—22no—
163C22⋊C8×C61—41no—
164#95×C61—21no—
165#95×C61—21no—
166#95×C61—21no—
167#95×C61—21no—
168C24×C61—21no—
169C24×C61—24no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—24no—
173C24×C61—42no—
174C24×C61—42no—
175C24×C61—42no—
176C24×C61—42no—
177C24×C61—42no—
178C24×C61—42no—
179C24×C61—42no—
180C24×C61—42no—
181C24×C61—81no—
182C24×C61—81no—
183C24×C61—81no—
184C24×C61—81no—
185C24×C61C2×D411yescharacteristic
186C24×C61C2×D411yescharacteristic
187C2×Q8×C61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—21no—
191C2×Q8×C61—21no—
192C2×Q8×C61—21no—
193C2×D4×C61—22no—
194C2×D4×C61—22no—
195C2×D4×C61—28no—
196C2×D4×C61—24no—
197C2×D4×C61—24no—
198C2×D4×C61—24no—
199C2×D4×C61—24no—
200C2×D4×C61—24no—
201C2×D4×C61—24no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—21no—
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—44no—
216C2×D4×C61—44no—
217C2×D4×C61—44no—
218C2×D4×C61—42no—
219C2×D4×C61—42no—
220C2×D4×C61—42no—
221C2×D4×C61—42no—
222C2×D4×C61—42no—
223C2×D4×C61—44no—
224C2×D4×C61—44no—
225C2×D4×C61—432no—
226C2×D4×C61—44no—
227C2×D4×C61—42no—
228C2×D4×C61—42no—
229C2×D4×C61—42no—
230C2×D4×C61—42no—
231C2×D4×C61—44no—
232C2×D4×C61—42no—
233C2×D4×C61—81no—
234C2×D4×C61—81no—
235C2×D4×C61SD1614yescomplemented
236C2×D4×C61C2×D412yes—
237C2×D4×C61C2×D412yes—
238C2×D4×C61C2×D412yes—
239C2×D4×C61C2×D412yes—
240C2×D4×C61#4112yes—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—24no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—42no—
258C22×C4×C61—42no—
259C22×C4×C61—42no—
260C22×C4×C61—42no—
261C22×C4×C61—81no—
262C22×C4×C61C2×D411yescharacteristic
263C22×C4×C61C2×D411yescharacteristic
264C22×C4×C61C2×D411yescharacteristic
265C22×C4×C61C2×D412yes—
266C22×C4×C61C2×D412yes—
267C22×C4×C61C2×D411yescharacteristic
268C22×C4×C61C2411yescharacteristic
269SD16×C61—44no—
270SD16×C61—44no—
271SD16×C61—44no—
272C2×C8×C61—21no—
273C2×C8×C61—21no—
274C2×C8×C61—21no—
275C2×C8×C61—21no—
276C2×C8×C61—21no—
277C2×C8×C61—21no—
278C2×C8×C61—21no—
279C2×C8×C61—21no—
280C2×C8×C61—21no—
281C2×C8×C61—21no—
282C2×C8×C61—21no—
283C2×C8×C61—44no—
284C2×C8×C61C2×D412yescomplemented
285C4⋊C4×C61—22no—
286C4⋊C4×C61—21no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61—21no—
289C4⋊C4×C61—21no—
290C4⋊C4×C61—21no—
291C4⋊C4×C61—21no—
292C4⋊C4×C61—42no—
293C4⋊C4×C61—42no—
294C4⋊C4×C61—42no—
295C4⋊C4×C61—81no—
296C4⋊C4×C61C2×D412yes—
297C4⋊C4×C61C2×D412yescomplemented
298C22⋊C4×C61—24no—
299C22⋊C4×C61—24no—
300C22⋊C4×C61—22no—
301C22⋊C4×C61—24no—
302C22⋊C4×C61—22no—
303C22⋊C4×C61—42no—
304C22⋊C4×C61—42no—
305C22⋊C4×C61—81no—
306C42×C61—21no—
307C42×C61—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—22no—
314C23×C61—21no—
315C23×C61—22no—
316C23×C61—21no—
317C23×C61—22no—
318C23×C61—21no—
319C23×C61—21no—
320C23×C61—21no—
321C23×C61—22no—
322C23×C61—22no—
323C23×C61—48no—
324C23×C61—48no—
325C23×C61—48no—
326C23×C61—41no—
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—41no—
341C23×C61—41no—
342C23×C61—48no—
343C23×C61—84no—
344C23×C61—84no—
345C23×C61—84no—
346C23×C61—84no—
347C23×C61—84no—
348C23×C61—84no—
349C23×C61—84no—
350C23×C61—84no—
351C23×C61—84no—
352C23×C61—84no—
353C23×C61#12012yes—
354C23×C61C2×SD1612yes—
355C23×C61C2×SD1612yes—
356C23×C61AGL(1,ℤ/8)12yes—
357C23×C61C22×D411yescharacteristic
358Q8×C61—41no—
359Q8×C61—41no—
360Q8×C61—41no—
361Q8×C61—41no—
362D4×C61—28no—
363D4×C61—22no—
364D4×C61—22no—
365D4×C61—22no—
366D4×C61—22no—
367D4×C61—22no—
368D4×C61—22no—
369D4×C61—22no—
370D4×C61—48no—
371D4×C61—48no—
372D4×C61—48no—
373D4×C61—48no—
374D4×C61—48no—
375D4×C61—41no—
376D4×C61—41no—
377D4×C61—41no—
378D4×C61—41no—
379D4×C61—84no—
380D4×C61#12114yes—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—21no—
384C2×C4×C61—21no—
385C2×C4×C61—22no—
386C2×C4×C61—22no—
387C2×C4×C61—22no—
388C2×C4×C61—22no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—22no—
392C2×C4×C61—22no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—21no—
396C2×C4×C61—21no—
397C2×C4×C61—48no—
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—41no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61—41no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—84no—
416C2×C4×C61#12012yes—
417C2×C4×C61C2×SD1612yes—
418C2×C4×C61C22×D411yescharacteristic
419C2×C4×C61C22×D411yescharacteristic
420C2×C4×C61C22×D411yescharacteristic
421C2×C4×C61C2×#4111yescharacteristic
422C2×C4×C61H(5,𝔽2)11yescharacteristic
423C2×C4×C61H(5,𝔽2)11yescharacteristic
424C8×C61—22no—
425C8×C61—41no—
426C8×C61—41no—
427C8×C61—41no—
428#24432C6111yesmaximal, characteristic, direct product factor, Sylow
429C22×C61—22no—
430C22×C61—22no—
431C22×C61—22no—
432C22×C61—22no—
433C22×C61—22no—
434C22×C61—22no—
435C22×C61—24no—
436C22×C61—22no—
437C22×C61—22no—
438C22×C61—22no—
439C22×C61—41no—
440C22×C61—42no—
441C22×C61—41no—
442C22×C61—42no—
443C22×C61—41no—
444C22×C61—42no—
445C22×C61—42no—
446C22×C61—42no—
447C22×C61—41no—
448C22×C61—42no—
449C22×C61—42no—
450C22×C61—42no—
451C22×C61—42no—
452C22×C61—42no—
453C22×C61—42no—
454C22×C61—42no—
455C22×C61—816no—
456C22×C61—816no—
457C22×C61—81no—
458C22×C61—81no—
459C22×C61—81no—
460C22×C61—81no—
461C22×C61—81no—
462C22×C61—81no—
463C22×C61—81no—
464C22×C61—81no—
465C22×C61#45014yescomplemented
466C22×C61C2×#12011yescharacteristic
467C22×C61D4211yescharacteristic
468C22×C61#54611yescharacteristic
469C22×C61C22×SD1611yescharacteristic
470C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
471C22×C61#57611yescharacteristic
472C22×C61#57711yescharacteristic
473C4×C61—22no—
474C4×C61—22no—
475C4×C61—41no—
476C4×C61—42no—
477C4×C61—42no—
478C4×C61—41no—
479C4×C61—81no—
480C4×C61—81no—
481C4×C61—81no—
482C4×C61C2×#12111yescharacteristic
483C4×C61#53411yescharacteristic
484C4×C61D4211yescharacteristic
485C4×C61#54611yescharacteristic
486C2×D42C2×C6111yescharacteristic
487C2×#465C2×C6111yescharacteristic, complemented
488C2×#450C2×C6111yescharacteristic, complemented
489C2×#450C2×C6111yescharacteristic, complemented
490C22×#102C2×C6111yescharacteristic, complemented
491#2417C2×C6111yescharacteristic, complemented
492#2041C2×C6111yescharacteristic, complemented
493#2034C2×C6111yescharacteristic, complemented
494#2014C2×C6111yescharacteristic, complemented
495#2000C2×C6111yescharacteristic, complemented
496#1877C2×C6111yescharacteristic, complemented
497#1874C2×C6111yescharacteristic, complemented
498#1869C2×C6111yescharacteristic, complemented
499#1864C2×C6111yescharacteristic, complemented
500#1786C2×C6111yescharacteristic, complemented
501C2×C61—24no—
502C2×C61—42no—
503C2×C61—44no—
504C2×C61—82no—
505C2×C61—82no—
506C2×C61#241011yescharacteristic
507C2×C61C2×#45011yescharacteristic
508C2×C61#301211yescharacteristic
509C2×C61#326411yescharacteristic
510C2×C61D4×SD1611yescharacteristic
511C2×C61#329511yescharacteristic
512C2×C61#331011yescharacteristic
513C23×D4—21no—
514C23×D4C22×C6111yescharacteristic
515C23×D4C22×C6111yescharacteristic
516C22×SD16C22×C6111yescharacteristic
517C22×SD16C22×C6111yescharacteristic, complemented
518C22×SD16C22×C6111yescharacteristic, complemented
519C23×C8C22×C6111yescharacteristic, complemented
520D42—24no—
521D42—24no—
522C2×#127C22×C6111yescharacteristic
523C2×C22⋊Q8C22×C6111yescharacteristic, complemented
524C2×C22⋊Q8C22×C6111yescharacteristic, complemented
525C2×#121—21no—
526C2×#121C22×C6111yescharacteristic
527C2×#121C22×C6111yescharacteristic
528C2×#120—21no—
529C2×#120—21no—
530C2×C4×D4C22×C6111yescharacteristic
531C2×C4×D4C22×C6111yescharacteristic
532C22×C4⋊C4C22×C6111yescharacteristic, complemented
533#465—24no—
534#450—24no—
535#450—24no—
536C2×#106C22×C6111yescharacteristic, complemented
537C2×#103C22×C6111yescharacteristic, complemented
538C2×#102—24no—
539C2×#102C22×C6111yescharacteristic
540C2×#102C22×C6111yescharacteristic
541C2×#102C22×C6111yescharacteristic
542C2×#102C22×C6111yescharacteristic, complemented
543C2×#102C22×C6111yescharacteristic, complemented
544C2×#102C22×C6111yescharacteristic, complemented
545C2×#102C22×C6111yescharacteristic, complemented
546C2×#102C22×C6111yescharacteristic, complemented
547C2×#102C22×C6111yescharacteristic, complemented
548C2×C22⋊C8C22×C6111yescharacteristic, complemented
549C2×C22⋊C8C22×C6111yescharacteristic, complemented
550C2×C22⋊C8C22×C6111yescharacteristic, complemented
551#398—21no—
552#396—21no—
553#391C22×C6111yescharacteristic, complemented
554#389C22×C6111yescharacteristic, complemented
555#386—21no—
556#380—21no—
557#380C22×C6111yescharacteristic, complemented
558#340C22×C6111yescharacteristic, complemented
559#340C22×C6111yescharacteristic, complemented
560#336C22×C6111yescharacteristic, complemented
561#336C22×C6111yescharacteristic, complemented
562C61#2443211yescharacteristic, direct product factor, Sylow
563C25—21no—
564C25—21no—
565C22×Q8C23×C6111yescharacteristic
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—28no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—22no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—22no—
579C22×D4—21no—
580C22×D4—41no—
581C22×D4—41no—
582C22×D4—41no—
583C22×D4—41no—
584C22×D4—44no—
585C22×D4—44no—
586C22×D4D4×C6111yescharacteristic
587C22×D4D4×C6114yes—
588C22×D4C23×C6111yescharacteristic
589C22×D4C23×C6111yescharacteristic
590C22×D4C23×C6111yescharacteristic
591C23×C4—21no—
592C23×C4—21no—
593C23×C4C23×C6111yescharacteristic
594C23×C4C23×C6111yescharacteristic
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—22no—
601C2×SD16—41no—
602C2×SD16—41no—
603C2×SD16—41no—
604C22×C8—22no—
605C22×C8—22no—
606C22×C8—41no—
607C22×C8C23×C6111yescharacteristic
608C22×C8C23×C6111yescharacteristic
609C22×C8C23×C6111yescharacteristic
610C22×C8C23×C6111yescharacteristic
611#127—22no—
612#127—22no—
613C22⋊Q8—22no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—41no—
617#121—28no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121D4×C6114yes—
622#120—28no—
623#120—28no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4D4×C6111yescharacteristic
635C2×C4⋊C4C23×C6111yescharacteristic
636C2×C4⋊C4C23×C6111yescharacteristic
637C2×C4⋊C4C23×C6111yescharacteristic
638C2×C4⋊C4C23×C6111yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4D4×C6111yescharacteristic
646C2×C22⋊C4D4×C6111yescharacteristic
647C2×C42C23×C6111yescharacteristic
648#106—22no—
649#103—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—41no—
658#102D4×C6114yescomplemented
659C22⋊C8—22no—
660C22⋊C8—22no—
661C22⋊C8—41no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666C24—21no—
667C24—24no—
668C24—21no—
669C24—21no—
670C24—24no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—42no—
677C24—42no—
678C24—42no—
679C24—81no—
680C24—81no—
681C24—81no—
682C24—81no—
683C24C2×D4×C6111yescharacteristic
684C24C2×D4×C6111yescharacteristic
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—432no—
724C2×D4—44no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—44no—
730C2×D4—42no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4SD16×C6114yescomplemented
734C2×D4C2×D4×C6112yes—
735C2×D4C2×D4×C6112yes—
736C2×D4C2×D4×C6112yes—
737C2×D4C2×D4×C6112yes—
738C2×D4#41×C6112yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—81no—
760C22×C4C2×D4×C6111yescharacteristic
761C22×C4C2×D4×C6111yescharacteristic
762C22×C4C2×D4×C6111yescharacteristic
763C22×C4C2×D4×C6112yes—
764C22×C4C2×D4×C6112yes—
765C22×C4C2×D4×C6111yescharacteristic
766C22×C4C24×C6111yescharacteristic
767SD16—44no—
768SD16—44no—
769SD16—44no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—44no—
782C2×C8C2×D4×C6112yescomplemented
783C4⋊C4—22no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—81no—
794C4⋊C4C2×D4×C6112yes—
795C4⋊C4C2×D4×C6112yescomplemented
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—22no—
799C22⋊C4—24no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—81no—
804C42—21no—
805C42—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—21no—
813C23—22no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—48no—
822C23—48no—
823C23—48no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—48no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23#120×C6112yes—
852C23C2×SD16×C6112yes—
853C23C2×SD16×C6112yes—
854C23AGL(1,ℤ/8)×C6112yes—
855C23C22×D4×C6111yescharacteristic
856Q8—41no—
857Q8—41no—
858Q8—41no—
859Q8—41no—
860D4—28no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—22no—
865D4—22no—
866D4—22no—
867D4—22no—
868D4—48no—
869D4—48no—
870D4—48no—
871D4—48no—
872D4—48no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—84no—
878D4#121×C6114yes—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—22no—
895C2×C4—48no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—84no—
914C2×C4#120×C6112yes—
915C2×C4C2×SD16×C6112yes—
916C2×C4C22×D4×C6111yescharacteristic
917C2×C4C22×D4×C6111yescharacteristic
918C2×C4C22×D4×C6111yescharacteristic
919C2×C4C2×#41×C6111yescharacteristic
920C2×C4H(5,𝔽2)×C6111yescharacteristic
921C2×C4H(5,𝔽2)×C6111yescharacteristic
922C8—22no—
923C8—41no—
924C8—41no—
925C8—41no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—24no—
934C22—22no—
935C22—22no—
936C22—42no—
937C22—41no—
938C22—42no—
939C22—41no—
940C22—42no—
941C22—41no—
942C22—42no—
943C22—41no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—816no—
953C22—816no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22C61×#45014yescomplemented
963C22C2×#120×C6111yescharacteristic
964C22D42×C6111yescharacteristic
965C22C61×#54611yescharacteristic
966C22C22×SD16×C6111yescharacteristic
967C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
968C22C61×#57611yescharacteristic
969C22C61×#57711yescharacteristic
970C4—22no—
971C4—22no—
972C4—41no—
973C4—42no—
974C4—42no—
975C4—41no—
976C4—81no—
977C4—81no—
978C4—81no—
979C4C2×#121×C6111yescharacteristic
980C4C61×#53411yescharacteristic
981C4D42×C6111yescharacteristic
982C4C61×#54611yescharacteristic
983C2—24no—
984C2—42no—
985C2—44no—
986C2—82no—
987C2—82no—
988C2C61×#241011yescharacteristic
989C2C2×C61×#45011yescharacteristic
990C2C61×#301211yescharacteristic
991C2C61×#326411yescharacteristic
992C2D4×SD16×C6111yescharacteristic
993C2C61×#329511yescharacteristic
994C2C61×#331011yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×D42×C61C2
LCSG ▷ C22×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×#465C2semidirect
3. C2×C61×#450C2semidirect
4. C2×C61×#450C2semidirect
5. C22×#102×C61C2semidirect
6. C61×#2417C2semidirect
7. C61×#2041C2semidirect
8. C61×#2034C2semidirect
9. C61×#2014C2semidirect
10. C61×#2000C2semidirect
11. C61×#1877C2semidirect
12. C61×#1874C2semidirect
13. C61×#1869C2semidirect
14. C61×#1864C2semidirect
15. C61×#1786C2semidirect
20. C22×SD16×C61C22semidirect
21. C22×SD16×C61C22semidirect
22. C23×C8×C61C22semidirect
26. C2×C22⋊Q8×C61C22semidirect
27. C2×C22⋊Q8×C61C22semidirect
35. C22×C4⋊C4×C61C22semidirect
39. C2×#106×C61C22semidirect
40. C2×#103×C61C22semidirect
45. C2×#102×C61C22semidirect
46. C2×#102×C61C22semidirect
47. C2×#102×C61C22semidirect
48. C2×#102×C61C22semidirect
49. C2×#102×C61C22semidirect
50. C2×#102×C61C22semidirect
51. C2×C22⋊C8×C61C22semidirect
52. C2×C22⋊C8×C61C22semidirect
53. C2×C22⋊C8×C61C22semidirect
56. C61×#391C22semidirect
57. C61×#389C22semidirect
60. C61×#380C22semidirect
61. C61×#340C22semidirect
62. C61×#340C22semidirect
63. C61×#336C22semidirect
64. C61×#336C22semidirect
160. #102×C61D4semidirect
235. C2×D4×C61SD16semidirect
284. C2×C8×C61C2×D4semidirect
297. C4⋊C4×C61C2×D4semidirect
428. #24432C61direct (N × H)
465. C22×C61#450semidirect
487. C2×#465C2×C61semidirect
488. C2×#450C2×C61semidirect
489. C2×#450C2×C61semidirect
490. C22×#102C2×C61semidirect
491. #2417C2×C61semidirect
492. #2041C2×C61semidirect
493. #2034C2×C61semidirect
494. #2014C2×C61semidirect
495. #2000C2×C61semidirect
496. #1877C2×C61semidirect
497. #1874C2×C61semidirect
498. #1869C2×C61semidirect
499. #1864C2×C61semidirect
500. #1786C2×C61semidirect
517. C22×SD16C22×C61semidirect
518. C22×SD16C22×C61semidirect
519. C23×C8C22×C61semidirect
523. C2×C22⋊Q8C22×C61semidirect
524. C2×C22⋊Q8C22×C61semidirect
532. C22×C4⋊C4C22×C61semidirect
536. C2×#106C22×C61semidirect
537. C2×#103C22×C61semidirect
542. C2×#102C22×C61semidirect
543. C2×#102C22×C61semidirect
544. C2×#102C22×C61semidirect
545. C2×#102C22×C61semidirect
546. C2×#102C22×C61semidirect
547. C2×#102C22×C61semidirect
548. C2×C22⋊C8C22×C61semidirect
549. C2×C22⋊C8C22×C61semidirect
550. C2×C22⋊C8C22×C61semidirect
553. #391C22×C61semidirect
554. #389C22×C61semidirect
557. #380C22×C61semidirect
558. #340C22×C61semidirect
559. #340C22×C61semidirect
560. #336C22×C61semidirect
561. #336C22×C61semidirect
562. C61#24432direct (N × H)
658. #102D4×C61semidirect
733. C2×D4SD16×C61semidirect
782. C2×C8C2×D4×C61semidirect
795. C4⋊C4C2×D4×C61semidirect
962. C22C61×#450semidirect

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×#4652
C2×C61×#4502
C22×#102×C612
C61×#24172
C61×#20412
C61×#20342
C61×#20142
C61×#20002
C61×#18772
C61×#18742
C61×#18692
C61×#18642
C61×#17862
#2443261