Finite Group Databasebeta

← C61×#24140 #29527573

Subgroups — C61×#24140 #29527573

Order 15616.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3505C211yesmaximal, characteristic, complemented
2C61×#2848C211yesmaximal, characteristic, complemented
3C61×#2847C211yesmaximal, characteristic, complemented
4C4×#120×C61C211yesmaximal, characteristic, complemented
5C61×#2044C212yesmaximal, complemented
6C61×#2021C212yesmaximal, complemented
7C61×#1996C211yesmaximal, characteristic, complemented
8C61×#1964C211yesmaximal, characteristic, complemented
9C61×#1889C212yesmaximal, complemented
10C61×#1867C212yesmaximal, complemented
11C61×#1799C211yesmaximal, characteristic, complemented
12C24×C4×C61C2211yescharacteristic
13C61×#553—21no—
14C61×#553—22no—
15C61×#552—21no—
16C61×#551—22no—
17C61×#548—21no—
18C61×#546—21no—
19C61×#539—21no—
20C61×#538—21no—
21C61×#534C2212yes—
22C61×#529—21no—
23C61×#525—21no—
24C2×C22⋊Q8×C61—21no—
25C2×C22⋊Q8×C61C2211yescharacteristic
26C2×#121×C61—21no—
27C2×#121×C61C2211yescharacteristic
28C2×#120×C61C2211yescharacteristic
29C2×#120×C61C2212yes—
30C61×#518C2212yes—
31C2×C4×D4×C61—21no—
32C2×C4×D4×C61C2211yescharacteristic
33C2×#99×C61C2212yes—
34C2×#99×C61C2212yes—
35C2×#99×C61C2212yes—
36C61×#386—21no—
37C61×#386—22no—
38C61×#386C2211yescharacteristic
39C61×#386C2212yes—
40C61×#385—21no—
41C61×#385—22no—
42C61×#385C2211yescharacteristic
43C61×#385C2212yes—
44C61×#380—21no—
45C61×#380—21no—
46C61×#380C2211yescharacteristic
47C61×#380C2211yescharacteristic
48C61×#379C2212yes—
49C61×#379C2211yescharacteristic
50C4×C22⋊C4×C61—21no—
51C4×C22⋊C4×C61C2211yescharacteristic
52C61×#342C2212yes—
53C61×#342C2212yes—
54C61×#342C2212yes—
55C25×C61C2311yescharacteristic
56C2×#41×C61—21no—
57C22×Q8×C61D411yescharacteristic, complemented
58C22×D4×C61—21no—
59C22×D4×C61—22no—
60C22×D4×C61D411yescharacteristic, complemented
61C22×D4×C61C2311yescharacteristic
62C22×D4×C61C2312yes—
63C23×C4×C61—21no—
64C23×C4×C61—21no—
65C23×C4×C61—21no—
66C23×C4×C61—21no—
67C23×C4×C61—21no—
68C23×C4×C61—21no—
69C23×C4×C61—44no—
70C23×C4×C61D411yescharacteristic, complemented
71C23×C4×C61C2311yescharacteristic
72C23×C4×C61C2311yescharacteristic
73#126×C61—22no—
74#126×C61—22no—
75#126×C61—22no—
76#125×C61—22no—
77#125×C61—21no—
78#124×C61—22no—
79#124×C61—21no—
80#123×C61—22no—
81#123×C61—22no—
82#123×C61—22no—
83#123×C61—22no—
84#123×C61—22no—
85C22⋊Q8×C61—22no—
86C22⋊Q8×C61—21no—
87C22⋊Q8×C61—21no—
88C22⋊Q8×C61—21no—
89C22⋊Q8×C61—21no—
90C22⋊Q8×C61—21no—
91C22⋊Q8×C61—44no—
92#121×C61—22no—
93#121×C61—21no—
94#121×C61—22no—
95#121×C61—22no—
96#121×C61—21no—
97#121×C61—21no—
98#121×C61—21no—
99#121×C61—21no—
100#121×C61—44no—
101#120×C61—22no—
102#120×C61—22no—
103#120×C61—22no—
104#120×C61—22no—
105#120×C61—24no—
106#120×C61—42no—
107C4×Q8×C61—21no—
108C4×D4×C61—21no—
109C4×D4×C61—22no—
110C4×D4×C61—22no—
111C4×D4×C61—22no—
112C4×D4×C61—21no—
113C4×D4×C61—21no—
114C4×D4×C61—22no—
115C4×D4×C61—21no—
116C4×D4×C61—21no—
117C4×D4×C61—22no—
118C4×D4×C61—44no—
119#117×C61—22no—
120#117×C61—21no—
121#117×C61—22no—
122C2×C4⋊C4×C61—21no—
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61—22no—
126C2×C4⋊C4×C61D411yescharacteristic, complemented
127C2×C4⋊C4×C61D411yescharacteristic, complemented
128C2×C4⋊C4×C61D411yescharacteristic, complemented
129C2×C4⋊C4×C61D412yescomplemented
130C2×C22⋊C4×C61—22no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—22no—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—22no—
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—22no—
138C2×C22⋊C4×C61—22no—
139C2×C22⋊C4×C61D411yescharacteristic, complemented
140C2×C22⋊C4×C61D412yescomplemented
141C2×C22⋊C4×C61C2312yes—
142C2×C22⋊C4×C61C2311yescharacteristic
143C2×C22⋊C4×C61C2312yes—
144C2×C22⋊C4×C61C2312yes—
145C2×C22⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61C2311yescharacteristic
147C2×C42×C61—21no—
148C2×C42×C61D411yescharacteristic, complemented
149#99×C61—24no—
150#99×C61—42no—
151#99×C61—42no—
152#95×C61—21no—
153#95×C61—21no—
154#95×C61—21no—
155#95×C61—22no—
156#95×C61—22no—
157#95×C61—21no—
158#95×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—21no—
164C24×C61—21no—
165C24×C61—42no—
166C24×C61—42no—
167C24×C61C2×D412yes—
168C24×C61C2×D411yescharacteristic
169C24×C61#4112yescomplemented
170C24×C61C2411yescharacteristic
171#41×C61—82no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—42no—
175C2×D4×C61—24no—
176C2×D4×C61—21no—
177C2×D4×C61—22no—
178C2×D4×C61—21no—
179C2×D4×C61—22no—
180C2×D4×C61—22no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—22no—
184C2×D4×C61—21no—
185C2×D4×C61—22no—
186C2×D4×C61—21no—
187C2×D4×C61—22no—
188C2×D4×C61—22no—
189C2×D4×C61—22no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—42no—
193C2×D4×C61—42no—
194C2×D4×C61—42no—
195C2×D4×C61—44no—
196C2×D4×C61—44no—
197C2×D4×C61—44no—
198C22×C4×C61—24no—
199C22×C4×C61—24no—
200C22×C4×C61—24no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—22no—
206C22×C4×C61—22no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—22no—
211C22×C4×C61—22no—
212C22×C4×C61—42no—
213C22×C4×C61—42no—
214C22×C4×C61—42no—
215C22×C4×C61—42no—
216C22×C4×C61—42no—
217C22×C4×C61—42no—
218C22×C4×C61—42no—
219C22×C4×C61—42no—
220C22×C4×C61—42no—
221C22×C4×C61—42no—
222C22×C4×C61—42no—
223C22×C4×C61—42no—
224C22×C4×C61—41no—
225C22×C4×C61—41no—
226C22×C4×C61—41no—
227C22×C4×C61—41no—
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D412yes—
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D412yes—
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D412yes—
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D411yescharacteristic
240C4⋊C4×C61—22no—
241C4⋊C4×C61—22no—
242C4⋊C4×C61—22no—
243C4⋊C4×C61—22no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—22no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—22no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—42no—
253C4⋊C4×C61—42no—
254C4⋊C4×C61—42no—
255C4⋊C4×C61—44no—
256C22⋊C4×C61—22no—
257C22⋊C4×C61—22no—
258C22⋊C4×C61—24no—
259C22⋊C4×C61—22no—
260C22⋊C4×C61—22no—
261C22⋊C4×C61—22no—
262C22⋊C4×C61—22no—
263C22⋊C4×C61—21no—
264C22⋊C4×C61—22no—
265C22⋊C4×C61—21no—
266C22⋊C4×C61—22no—
267C22⋊C4×C61—21no—
268C22⋊C4×C61—22no—
269C22⋊C4×C61—21no—
270C22⋊C4×C61—21no—
271C22⋊C4×C61—22no—
272C22⋊C4×C61—22no—
273C22⋊C4×C61—22no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—22no—
276C22⋊C4×C61—22no—
277C22⋊C4×C61—21no—
278C22⋊C4×C61—44no—
279C22⋊C4×C61—42no—
280C22⋊C4×C61—44no—
281C22⋊C4×C61—44no—
282C22⋊C4×C61—42no—
283C22⋊C4×C61—42no—
284C22⋊C4×C61—44no—
285C22⋊C4×C61#4112yescomplemented
286C42×C61—22no—
287C42×C61—22no—
288C42×C61—21no—
289C42×C61—21no—
290C42×C61—42no—
291C23×C61—22no—
292C23×C61—22no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—22no—
300C23×C61—21no—
301C23×C61—22no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—22no—
305C23×C61—22no—
306C23×C61—41no—
307C23×C61—44no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—44no—
316C23×C61—44no—
317C23×C61—44no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—42no—
321C23×C61—42no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61C22×D411yescharacteristic
327C23×C61C22×D411yescharacteristic
328C23×C61C22×D411yescharacteristic
329C23×C61C2×#4111yescharacteristic
330C23×C61C2×#4111yescharacteristic
331C23×C61H(5,𝔽2)11yescharacteristic
332C23×C612−1+411yescharacteristic
333Q8×C61—42no—
334Q8×C61—81no—
335D4×C61—48no—
336D4×C61—42no—
337D4×C61—42no—
338D4×C61—41no—
339D4×C61—41no—
340D4×C61—41no—
341D4×C61—42no—
342D4×C61—42no—
343D4×C61—41no—
344D4×C61—42no—
345D4×C61—81no—
346D4×C61—82no—
347D4×C61—82no—
348D4×C61—88no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—21no—
356C2×C4×C61—22no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—21no—
362C2×C4×C61—22no—
363C2×C4×C61—21no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—44no—
370C2×C4×C61—44no—
371C2×C4×C61—44no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—44no—
379C2×C4×C61—42no—
380C2×C4×C61—41no—
381C2×C4×C61—42no—
382C2×C4×C61—41no—
383C2×C4×C61—42no—
384C2×C4×C61—41no—
385C2×C4×C61—42no—
386C2×C4×C61—42no—
387C2×C4×C61—42no—
388C2×C4×C61—41no—
389C2×C4×C61—42no—
390C2×C4×C61—41no—
391C2×C4×C61—42no—
392C2×C4×C61—42no—
393C2×C4×C61—81no—
394C2×C4×C61—82no—
395C2×C4×C61—82no—
396C2×C4×C61#12011yescharacteristic
397C2×C4×C61#12011yescharacteristic
398C2×C4×C61#12011yescharacteristic
399C2×C4×C61#12011yescharacteristic
400#24140C6111yesmaximal, characteristic, direct product factor, Sylow
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—21no—
405C22×C61—21no—
406C22×C61—21no—
407C22×C61—24no—
408C22×C61—24no—
409C22×C61—24no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61—42no—
415C22×C61—42no—
416C22×C61—42no—
417C22×C61—42no—
418C22×C61—42no—
419C22×C61—42no—
420C22×C61—42no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61—42no—
424C22×C61—42no—
425C22×C61—42no—
426C22×C61—42no—
427C22×C61—41no—
428C22×C61—42no—
429C22×C61—41no—
430C22×C61—42no—
431C22×C61—42no—
432C22×C61—41no—
433C22×C61—82no—
434C22×C61—81no—
435C22×C61—82no—
436C22×C61C2×#12011yescharacteristic
437C22×C61#52511yescharacteristic
438C22×C61#53711yescharacteristic
439C22×C61#54611yescharacteristic
440C22×C61#54711yescharacteristic
441C22×C61#54811yescharacteristic
442C22×C61#55011yescharacteristic
443C4×C61—21no—
444C4×C61—21no—
445C4×C61—21no—
446C4×C61—42no—
447C4×C61—41no—
448C4×C61—42no—
449C4×C61—42no—
450C4×C61—41no—
451C4×C61—42no—
452C4×C61—41no—
453C4×C61—42no—
454C4×C61—82no—
455C4×C61—81no—
456C4×C61—82no—
457C4×C61B(4,𝔽2)12yes—
458#3505C2×C6111yescharacteristic, complemented
459#2848C2×C6111yescharacteristic, complemented
460#2847C2×C6111yescharacteristic, complemented
461C4×#120C2×C6111yescharacteristic, complemented
462#2044C2×C6112yescomplemented
463#2021C2×C6112yescomplemented
464#1996C2×C6111yescharacteristic, complemented
465#1964C2×C6111yescharacteristic, complemented
466#1889C2×C6112yescomplemented
467#1867C2×C6112yescomplemented
468#1799C2×C6111yescharacteristic, complemented
469C2×C61—21no—
470C2×C61—21no—
471C2×C61—21no—
472C2×C61—21no—
473C2×C61—21no—
474C2×C61—21no—
475C2×C61—44no—
476C2×C61—81no—
477C2×C61—82no—
478C2×C61#240711yescharacteristic
479C2×C61C2×B(4,𝔽2)11yescharacteristic
480C2×C61#302511yescharacteristic
481C24×C4C22×C6111yescharacteristic
482#553—21no—
483#553—22no—
484#552—21no—
485#551—22no—
486#548—21no—
487#546—21no—
488#539—21no—
489#538—21no—
490#534C22×C6112yes—
491#529—21no—
492#525—21no—
493C2×C22⋊Q8—21no—
494C2×C22⋊Q8C22×C6111yescharacteristic
495C2×#121—21no—
496C2×#121C22×C6111yescharacteristic
497C2×#120C22×C6111yescharacteristic
498C2×#120C22×C6112yes—
499#518C22×C6112yes—
500C2×C4×D4—21no—
501C2×C4×D4C22×C6111yescharacteristic
502C2×#99C22×C6112yes—
503C2×#99C22×C6112yes—
504C2×#99C22×C6112yes—
505#386—22no—
506#386—21no—
507#386C22×C6112yes—
508#386C22×C6111yescharacteristic
509#385—22no—
510#385—21no—
511#385C22×C6112yes—
512#385C22×C6111yescharacteristic
513#380—21no—
514#380—21no—
515#380C22×C6111yescharacteristic
516#380C22×C6111yescharacteristic
517#379C22×C6112yes—
518#379C22×C6111yescharacteristic
519C4×C22⋊C4—21no—
520C4×C22⋊C4C22×C6111yescharacteristic
521#342C22×C6112yes—
522#342C22×C6112yes—
523#342C22×C6112yes—
524C61#2414011yescharacteristic, direct product factor, Sylow
525C25C23×C6111yescharacteristic
526C2×#41—21no—
527C22×Q8D4×C6111yescharacteristic, complemented
528C22×D4—21no—
529C22×D4—22no—
530C22×D4D4×C6111yescharacteristic, complemented
531C22×D4C23×C6111yescharacteristic
532C22×D4C23×C6112yes—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—44no—
540C23×C4D4×C6111yescharacteristic, complemented
541C23×C4C23×C6111yescharacteristic
542C23×C4C23×C6111yescharacteristic
543#126—22no—
544#126—22no—
545#126—22no—
546#125—21no—
547#125—22no—
548#124—21no—
549#124—22no—
550#123—22no—
551#123—22no—
552#123—22no—
553#123—22no—
554#123—22no—
555C22⋊Q8—21no—
556C22⋊Q8—22no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—44no—
562#121—21no—
563#121—22no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—44no—
571#120—22no—
572#120—22no—
573#120—22no—
574#120—22no—
575#120—24no—
576#120—42no—
577C4×Q8—21no—
578C4×D4—22no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—44no—
589#117—21no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4D4×C6111yescharacteristic, complemented
597C2×C4⋊C4D4×C6111yescharacteristic, complemented
598C2×C4⋊C4D4×C6111yescharacteristic, complemented
599C2×C4⋊C4D4×C6112yescomplemented
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4D4×C6111yescharacteristic, complemented
610C2×C22⋊C4D4×C6112yescomplemented
611C2×C22⋊C4C23×C6112yes—
612C2×C22⋊C4C23×C6111yescharacteristic
613C2×C22⋊C4C23×C6112yes—
614C2×C22⋊C4C23×C6111yescharacteristic
615C2×C22⋊C4C23×C6112yes—
616C2×C22⋊C4C23×C6111yescharacteristic
617C2×C42—21no—
618C2×C42D4×C6111yescharacteristic, complemented
619#99—24no—
620#99—42no—
621#99—42no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—22no—
626#95—22no—
627#95—21no—
628#95—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—42no—
636C24—42no—
637C24C2×D4×C6112yes—
638C24C2×D4×C6111yescharacteristic
639C24#41×C6112yescomplemented
640C24C24×C6111yescharacteristic
641#41—82no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—42no—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4C2×D4×C6111yescharacteristic
699C22×C4C2×D4×C6112yes—
700C22×C4C2×D4×C6111yescharacteristic
701C22×C4C2×D4×C6111yescharacteristic
702C22×C4C2×D4×C6111yescharacteristic
703C22×C4C2×D4×C6111yescharacteristic
704C22×C4C2×D4×C6112yes—
705C22×C4C2×D4×C6111yescharacteristic
706C22×C4C2×D4×C6112yes—
707C22×C4C2×D4×C6111yescharacteristic
708C22×C4C2×D4×C6111yescharacteristic
709C22×C4C2×D4×C6111yescharacteristic
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—22no—
721C4⋊C4—21no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—44no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—24no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—21no—
734C22⋊C4—22no—
735C22⋊C4—21no—
736C22⋊C4—22no—
737C22⋊C4—21no—
738C22⋊C4—22no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—21no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—21no—
748C22⋊C4—44no—
749C22⋊C4—42no—
750C22⋊C4—44no—
751C22⋊C4—42no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—42no—
755C22⋊C4#41×C6112yescomplemented
756C42—22no—
757C42—22no—
758C42—21no—
759C42—21no—
760C42—42no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—44no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C22×D4×C6111yescharacteristic
797C23C22×D4×C6111yescharacteristic
798C23C22×D4×C6111yescharacteristic
799C23C2×#41×C6111yescharacteristic
800C23C2×#41×C6111yescharacteristic
801C23H(5,𝔽2)×C6111yescharacteristic
802C232−1+4×C6111yescharacteristic
803Q8—42no—
804Q8—81no—
805D4—48no—
806D4—42no—
807D4—41no—
808D4—41no—
809D4—41no—
810D4—42no—
811D4—42no—
812D4—41no—
813D4—42no—
814D4—42no—
815D4—81no—
816D4—82no—
817D4—82no—
818D4—88no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—22no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4#120×C6111yescharacteristic
867C2×C4#120×C6111yescharacteristic
868C2×C4#120×C6111yescharacteristic
869C2×C4#120×C6111yescharacteristic
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22C2×#120×C6111yescharacteristic
906C22C61×#52511yescharacteristic
907C22C61×#53711yescharacteristic
908C22C61×#54611yescharacteristic
909C22C61×#54711yescharacteristic
910C22C61×#54811yescharacteristic
911C22C61×#55011yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—41no—
917C4—42no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—82no—
924C4—81no—
925C4—82no—
926C4C61×B(4,𝔽2)12yes—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2C61×#240711yescharacteristic
937C2C2×C61×B(4,𝔽2)11yescharacteristic
938C2C61×#302511yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC24C24×C61
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3505C2semidirect
2. C61×#2848C2semidirect
3. C61×#2847C2semidirect
4. C4×#120×C61C2semidirect
5. C61×#2044C2semidirect
6. C61×#2021C2semidirect
7. C61×#1996C2semidirect
8. C61×#1964C2semidirect
9. C61×#1889C2semidirect
10. C61×#1867C2semidirect
11. C61×#1799C2semidirect
57. C22×Q8×C61D4semidirect
60. C22×D4×C61D4semidirect
70. C23×C4×C61D4semidirect
126. C2×C4⋊C4×C61D4semidirect
127. C2×C4⋊C4×C61D4semidirect
128. C2×C4⋊C4×C61D4semidirect
129. C2×C4⋊C4×C61D4semidirect
139. C2×C22⋊C4×C61D4semidirect
140. C2×C22⋊C4×C61D4semidirect
148. C2×C42×C61D4semidirect
169. C24×C61#41semidirect
285. C22⋊C4×C61#41semidirect
400. #24140C61direct (N × H)
458. #3505C2×C61semidirect
459. #2848C2×C61semidirect
460. #2847C2×C61semidirect
461. C4×#120C2×C61semidirect
462. #2044C2×C61semidirect
463. #2021C2×C61semidirect
464. #1996C2×C61semidirect
465. #1964C2×C61semidirect
466. #1889C2×C61semidirect
467. #1867C2×C61semidirect
468. #1799C2×C61semidirect
524. C61#24140direct (N × H)
527. C22×Q8D4×C61semidirect
530. C22×D4D4×C61semidirect
540. C23×C4D4×C61semidirect
596. C2×C4⋊C4D4×C61semidirect
597. C2×C4⋊C4D4×C61semidirect
598. C2×C4⋊C4D4×C61semidirect
599. C2×C4⋊C4D4×C61semidirect
609. C2×C22⋊C4D4×C61semidirect
610. C2×C22⋊C4D4×C61semidirect
618. C2×C42D4×C61semidirect
639. C24#41×C61semidirect
755. C22⋊C4#41×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#35052
C61×#28482
C61×#28472
C4×#120×C612
C61×#20442
C61×#20212
C61×#19962
C61×#19642
C61×#18892
C61×#18672
C61×#17992
#2414061