Finite Group Databasebeta

← C61×#15310 #29518743

Subgroups — C61×#15310 #29518743

Order 15616.

3562 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#127×C61C211yesmaximal, characteristic, complemented
2C22×#121×C61C211yesmaximal, characteristic, complemented
3C2×C61×#394C211yesmaximal, characteristic, complemented
4C2×C61×#392C212yesmaximal, complemented
5C2×C61×#392C212yesmaximal, complemented
6C2×C61×#392C211yesmaximal, characteristic, complemented
7C2×C61×#386C212yesmaximal, complemented
8C61×#1438C212yesmaximal, complemented
9C61×#1438C211yesmaximal, characteristic, complemented
10C61×#1437C211yesmaximal, characteristic, complemented
11C61×#1436C211yesmaximal, characteristic, complemented
12C23×D4×C61C2211yescharacteristic
13C23×D4×C61C2211yescharacteristic
14C23×D4×C61C2211yescharacteristic
15C23×D4×C61C2212yes—
16C23×D4×C61C2212yes—
17C23×D4×C61C2211yescharacteristic
18C23×D4×C61C2212yes—
19C24×C4×C61C2211yescharacteristic
20C2×#127×C61—28no—
21C2×#127×C61—24no—
22C2×#121×C61—24no—
23C2×#121×C61—24no—
24C2×#121×C61—24no—
25C22×C4⋊C4×C61C2211yescharacteristic
26C22×C22⋊C4×C61C2212yes—
27C22×C22⋊C4×C61C2212yes—
28C22×C22⋊C4×C61C2211yescharacteristic
29C22×C22⋊C4×C61C2212yes—
30C22×C22⋊C4×C61C2212yes—
31C22×C22⋊C4×C61C2212yes—
32C22×C22⋊C4×C61C2211yescharacteristic
33C22×C22⋊C4×C61C2212yes—
34C22×C42×C61C2211yescharacteristic
35C61×#394—24no—
36C61×#392—28no—
37C61×#392—24no—
38C61×#392—28no—
39C61×#386—28no—
40C2×#95×C61C2212yes—
41C2×#95×C61C2211yescharacteristic
42C2×#95×C61C2212yes—
43C2×#95×C61C2211yescharacteristic
44C2×#95×C61C2212yes—
45C25×C61C2312yes—
46C25×C61C2311yescharacteristic
47C25×C61C2311yescharacteristic
48C25×C61C2311yescharacteristic
49C22×D4×C61—24no—
50C22×D4×C61—24no—
51C22×D4×C61—24no—
52C22×D4×C61—24no—
53C22×D4×C61—24no—
54C22×D4×C61—24no—
55C22×D4×C61—22no—
56C22×D4×C61—22no—
57C22×D4×C61—22no—
58C22×D4×C61—22no—
59C22×D4×C61—24no—
60C22×D4×C61—24no—
61C22×D4×C61—24no—
62C22×D4×C61—22no—
63C22×D4×C61—24no—
64C22×D4×C61—24no—
65C22×D4×C61—22no—
66C22×D4×C61—22no—
67C22×D4×C61—22no—
68C22×D4×C61—22no—
69C22×D4×C61—24no—
70C22×D4×C61—22no—
71C22×D4×C61—24no—
72C22×D4×C61—24no—
73C22×D4×C61—22no—
74C22×D4×C61—24no—
75C22×D4×C61—24no—
76C22×D4×C61—42no—
77C22×D4×C61—42no—
78C22×D4×C61—42no—
79C22×D4×C61—42no—
80C22×D4×C61—42no—
81C22×D4×C61—42no—
82C22×D4×C61—42no—
83C22×D4×C61—42no—
84C22×D4×C61—42no—
85C22×D4×C61—42no—
86C22×D4×C61—42no—
87C22×D4×C61—42no—
88C22×D4×C61D418yescomplemented
89C22×D4×C61D414yescomplemented
90C23×C4×C61—22no—
91C23×C4×C61—22no—
92C23×C4×C61—22no—
93C23×C4×C61—24no—
94C23×C4×C61—42no—
95C23×C4×C61C2312yes—
96C23×C4×C61C2311yescharacteristic
97C23×C4×C61C2312yes—
98C23×C4×C61C2311yescharacteristic
99C23×C4×C61C2311yescharacteristic
100C23×C4×C61C2311yescharacteristic
101C23×C4×C61C2312yes—
102#127×C61—232no—
103#121×C61—232no—
104C2×C4⋊C4×C61—22no—
105C2×C4⋊C4×C61—22no—
106C2×C4⋊C4×C61D414yescomplemented
107C2×C22⋊C4×C61—22no—
108C2×C22⋊C4×C61—22no—
109C2×C22⋊C4×C61—22no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—24no—
113C2×C22⋊C4×C61—24no—
114C2×C22⋊C4×C61—24no—
115C2×C22⋊C4×C61—24no—
116C2×C22⋊C4×C61—24no—
117C2×C22⋊C4×C61—24no—
118C2×C22⋊C4×C61—24no—
119C2×C22⋊C4×C61—24no—
120C2×C22⋊C4×C61—24no—
121C2×C22⋊C4×C61—24no—
122C2×C22⋊C4×C61—24no—
123C2×C22⋊C4×C61—24no—
124C2×C22⋊C4×C61—24no—
125C2×C22⋊C4×C61—42no—
126C2×C22⋊C4×C61—42no—
127C2×C22⋊C4×C61—42no—
128C2×C22⋊C4×C61—42no—
129C2×C22⋊C4×C61—42no—
130C2×C22⋊C4×C61D414yescomplemented
131C2×C42×C61—22no—
132C2×C42×C61—24no—
133#95×C61—24no—
134#95×C61—22no—
135#95×C61—24no—
136#95×C61—22no—
137#95×C61D418yescomplemented
138C24×C61—22no—
139C24×C61—21no—
140C24×C61—21no—
141C24×C61—22no—
142C24×C61—22no—
143C24×C61—22no—
144C24×C61—22no—
145C24×C61—22no—
146C24×C61—22no—
147C24×C61—21no—
148C24×C61—21no—
149C24×C61—21no—
150C24×C61—21no—
151C24×C61—22no—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61—22no—
157C24×C61—22no—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61—22no—
163C24×C61—22no—
164C24×C61—22no—
165C24×C61—22no—
166C24×C61—22no—
167C24×C61—22no—
168C24×C61—22no—
169C24×C61—22no—
170C24×C61—22no—
171C24×C61—22no—
172C24×C61—22no—
173C24×C61—22no—
174C24×C61—22no—
175C24×C61C2×D412yes—
176C24×C61C2×D414yes—
177C24×C61C2×D412yes—
178C24×C61C2×D414yes—
179C24×C61C2×D412yes—
180C24×C61C2411yescharacteristic
181C2×D4×C61—28no—
182C2×D4×C61—28no—
183C2×D4×C61—28no—
184C2×D4×C61—216no—
185C2×D4×C61—216no—
186C2×D4×C61—28no—
187C2×D4×C61—28no—
188C2×D4×C61—216no—
189C2×D4×C61—44no—
190C2×D4×C61—48no—
191C2×D4×C61—48no—
192C2×D4×C61—48no—
193C2×D4×C61—48no—
194C2×D4×C61—48no—
195C2×D4×C61—48no—
196C2×D4×C61—48no—
197C2×D4×C61—48no—
198C2×D4×C61—48no—
199C2×D4×C61—48no—
200C2×D4×C61—48no—
201C2×D4×C61—48no—
202C2×D4×C61—48no—
203C2×D4×C61—48no—
204C2×D4×C61—48no—
205C2×D4×C61—48no—
206C2×D4×C61—48no—
207C2×D4×C61—48no—
208C2×D4×C61—44no—
209C2×D4×C61—48no—
210C2×D4×C61—44no—
211C2×D4×C61—48no—
212C2×D4×C61—48no—
213C2×D4×C61—48no—
214C2×D4×C61—44no—
215C2×D4×C61—48no—
216C2×D4×C61—48no—
217C2×D4×C61—48no—
218C2×D4×C61—44no—
219C2×D4×C61—44no—
220C2×D4×C61—48no—
221C2×D4×C61—44no—
222C22×C4×C61—22no—
223C22×C4×C61—22no—
224C22×C4×C61—22no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—22no—
228C22×C4×C61—22no—
229C22×C4×C61—22no—
230C22×C4×C61—22no—
231C22×C4×C61—28no—
232C22×C4×C61—22no—
233C22×C4×C61—22no—
234C22×C4×C61—22no—
235C22×C4×C61—22no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—22no—
241C22×C4×C61—22no—
242C22×C4×C61—22no—
243C22×C4×C61—22no—
244C22×C4×C61—22no—
245C22×C4×C61—22no—
246C22×C4×C61—22no—
247C22×C4×C61—22no—
248C22×C4×C61—22no—
249C22×C4×C61—22no—
250C22×C4×C61—22no—
251C22×C4×C61—22no—
252C22×C4×C61—22no—
253C22×C4×C61—48no—
254C22×C4×C61—48no—
255C22×C4×C61—44no—
256C22×C4×C61—44no—
257C22×C4×C61C2×D414yes—
258C22×C4×C61C2×D412yes—
259C22×C4×C61C2×D412yes—
260C22×C4×C61C2×D412yes—
261C22×C4×C61C2×D412yes—
262C22×C4×C61C2×D412yes—
263C22×C4×C61C2×D414yes—
264C22×C4×C61C2×D414yes—
265C22×C4×C61C2×D414yes—
266C22×C4×C61C2×D412yes—
267C22×C4×C61#4114yes—
268C4⋊C4×C61—28no—
269C22⋊C4×C61—28no—
270C22⋊C4×C61—28no—
271C22⋊C4×C61—48no—
272C22⋊C4×C61—48no—
273C22⋊C4×C61—48no—
274C22⋊C4×C61—48no—
275C22⋊C4×C61—48no—
276C22⋊C4×C61—48no—
277C42×C61—28no—
278C23×C61—22no—
279C23×C61—24no—
280C23×C61—22no—
281C23×C61—24no—
282C23×C61—24no—
283C23×C61—24no—
284C23×C61—24no—
285C23×C61—24no—
286C23×C61—24no—
287C23×C61—24no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—24no—
292C23×C61—24no—
293C23×C61—22no—
294C23×C61—24no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—24no—
298C23×C61—24no—
299C23×C61—24no—
300C23×C61—24no—
301C23×C61—24no—
302C23×C61—24no—
303C23×C61—24no—
304C23×C61—24no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—42no—
310C23×C61—42no—
311C23×C61—42no—
312C23×C61—42no—
313C23×C61—42no—
314C23×C61—42no—
315C23×C61—41no—
316C23×C61—42no—
317C23×C61—42no—
318C23×C61—42no—
319C23×C61—42no—
320C23×C61—42no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—42no—
324C23×C61—41no—
325C23×C61—42no—
326C23×C61—41no—
327C23×C61—42no—
328C23×C61—42no—
329C23×C61—42no—
330C23×C61—42no—
331C23×C61—42no—
332C23×C61—42no—
333C23×C61—42no—
334C23×C61—41no—
335C23×C61—41no—
336C23×C61—42no—
337C23×C61—41no—
338C23×C61—42no—
339C23×C61—42no—
340C23×C61—42no—
341C23×C61—42no—
342C23×C61—42no—
343C23×C61—42no—
344C23×C61—42no—
345C23×C61—42no—
346C23×C61—42no—
347C23×C61—42no—
348C23×C61—42no—
349C23×C61—42no—
350C23×C61—42no—
351C23×C61—42no—
352C23×C61—42no—
353C23×C61—42no—
354C23×C61—42no—
355C23×C61—42no—
356C23×C61—42no—
357C23×C61—42no—
358C23×C61—42no—
359C23×C61—42no—
360C23×C61—42no—
361C23×C61—42no—
362C23×C61—42no—
363C23×C61—42no—
364C23×C61—42no—
365C23×C61—42no—
366C23×C61—42no—
367C23×C61—42no—
368C23×C61—42no—
369C23×C61—42no—
370C23×C61—42no—
371C23×C61—42no—
372C23×C61—42no—
373C23×C61—42no—
374C23×C61—42no—
375C23×C61#12014yes—
376C23×C61C22×D411yescharacteristic
377C23×C61C22×D412yes—
378C23×C61C22×D411yescharacteristic
379C23×C61C22×D411yescharacteristic
380C23×C61C22×D412yes—
381C23×C61C2×#4112yes—
382C23×C61H(5,𝔽2)12yes—
383C23×C61H(5,𝔽2)12yes—
384C23×C61H(5,𝔽2)12yes—
385D4×C61—416no—
386D4×C61—432no—
387D4×C61—416no—
388D4×C61—432no—
389D4×C61—416no—
390D4×C61—416no—
391D4×C61—432no—
392C2×C4×C61—22no—
393C2×C4×C61—24no—
394C2×C4×C61—22no—
395C2×C4×C61—22no—
396C2×C4×C61—24no—
397C2×C4×C61—22no—
398C2×C4×C61—24no—
399C2×C4×C61—24no—
400C2×C4×C61—24no—
401C2×C4×C61—24no—
402C2×C4×C61—24no—
403C2×C4×C61—24no—
404C2×C4×C61—24no—
405C2×C4×C61—24no—
406C2×C4×C61—22no—
407C2×C4×C61—22no—
408C2×C4×C61—24no—
409C2×C4×C61—24no—
410C2×C4×C61—24no—
411C2×C4×C61—24no—
412C2×C4×C61—24no—
413C2×C4×C61—416no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—42no—
418C2×C4×C61—41no—
419C2×C4×C61—42no—
420C2×C4×C61—42no—
421C2×C4×C61—42no—
422C2×C4×C61—42no—
423C2×C4×C61—42no—
424C2×C4×C61—42no—
425C2×C4×C61—42no—
426C2×C4×C61—42no—
427C2×C4×C61—42no—
428C2×C4×C61—42no—
429C2×C4×C61—42no—
430C2×C4×C61—42no—
431C2×C4×C61#12014yes—
432C2×C4×C61#12118yescomplemented
433C2×C4×C61#12714yescomplemented
434#15310C6111yesmaximal, characteristic, direct product factor, Sylow
435C22×C61—24no—
436C22×C61—28no—
437C22×C61—44no—
438C22×C61—44no—
439C22×C61—44no—
440C22×C61—44no—
441C22×C61—42no—
442C22×C61—42no—
443C22×C61—44no—
444C22×C61—42no—
445C22×C61—44no—
446C22×C61—42no—
447C22×C61—44no—
448C22×C61—44no—
449C22×C61—44no—
450C22×C61—44no—
451C22×C61—44no—
452C22×C61—44no—
453C22×C61—44no—
454C22×C61—44no—
455C22×C61—44no—
456C22×C61—42no—
457C22×C61—42no—
458C22×C61—42no—
459C22×C61—42no—
460C22×C61—44no—
461C22×C61—82no—
462C22×C61—82no—
463C22×C61—82no—
464C22×C61—82no—
465C22×C61—82no—
466C22×C61—82no—
467C22×C61—82no—
468C22×C61—82no—
469C22×C61—82no—
470C22×C61—82no—
471C22×C61—82no—
472C22×C61—82no—
473C22×C61—82no—
474C22×C61—82no—
475C22×C61—82no—
476C22×C61—82no—
477C22×C61C2×#12011yescharacteristic
478C22×C61C2×#12011yescharacteristic
479C22×C61C2×#12112yes—
480C22×C61C2×#12711yescharacteristic
481C22×C61#53211yescharacteristic
482C22×C61#53411yescharacteristic
483C22×C61#53412yes—
484C22×C61#53511yescharacteristic
485C22×C61#53512yes—
486C22×C61#53511yescharacteristic
487C22×C61#54012yes—
488C22×C61D4212yes—
489C22×C61D4212yes—
490C22×C61D4212yes—
491C22×C61D4212yes—
492C22×C61D4212yes—
493C22×C61#54612yes—
494C22×C61#54612yes—
495C22×C61#55012yes—
496C22×C61#55012yes—
497C22×C61#56012yes—
498C4×C61—24no—
499C4×C61—28no—
500C4×C61—24no—
501C4×C61—42no—
502C4×C61—44no—
503C4×C61—42no—
504C4×C61—82no—
505C22×#127C2×C6111yescharacteristic, complemented
506C22×#121C2×C6111yescharacteristic, complemented
507C2×#394C2×C6111yescharacteristic, complemented
508C2×#392C2×C6112yescomplemented
509C2×#392C2×C6112yescomplemented
510C2×#392C2×C6111yescharacteristic, complemented
511C2×#386C2×C6112yescomplemented
512#1438C2×C6112yescomplemented
513#1438C2×C6111yescharacteristic, complemented
514#1437C2×C6111yescharacteristic, complemented
515#1436C2×C6111yescharacteristic, complemented
516C2×C61—44no—
517C2×C61—84no—
518C2×C61—82no—
519C2×C61—82no—
520C2×C61#240311yescharacteristic
521C2×C61#241012yes—
522C2×C61#242812yes—
523C2×C61#243111yescharacteristic
524C2×C61#243311yescharacteristic
525C2×C61#254112yes—
526C2×C61#266912yes—
527C2×C61#267312yes—
528C2×C61#267312yes—
529C23×D4C22×C6111yescharacteristic
530C23×D4C22×C6111yescharacteristic
531C23×D4C22×C6111yescharacteristic
532C23×D4C22×C6112yes—
533C23×D4C22×C6112yes—
534C23×D4C22×C6111yescharacteristic
535C23×D4C22×C6112yes—
536C24×C4C22×C6111yescharacteristic
537C2×#127—24no—
538C2×#127—28no—
539C2×#121—24no—
540C2×#121—24no—
541C2×#121—24no—
542C22×C4⋊C4C22×C6111yescharacteristic
543C22×C22⋊C4C22×C6112yes—
544C22×C22⋊C4C22×C6112yes—
545C22×C22⋊C4C22×C6111yescharacteristic
546C22×C22⋊C4C22×C6112yes—
547C22×C22⋊C4C22×C6112yes—
548C22×C22⋊C4C22×C6112yes—
549C22×C22⋊C4C22×C6111yescharacteristic
550C22×C22⋊C4C22×C6112yes—
551C22×C42C22×C6111yescharacteristic
552#394—24no—
553#392—28no—
554#392—24no—
555#392—28no—
556#386—28no—
557C2×#95C22×C6112yes—
558C2×#95C22×C6111yescharacteristic
559C2×#95C22×C6111yescharacteristic
560C2×#95C22×C6112yes—
561C2×#95C22×C6112yes—
562C61#1531011yescharacteristic, direct product factor, Sylow
563C25C23×C6112yes—
564C25C23×C6111yescharacteristic
565C25C23×C6111yescharacteristic
566C25C23×C6111yescharacteristic
567C22×D4—22no—
568C22×D4—22no—
569C22×D4—22no—
570C22×D4—22no—
571C22×D4—24no—
572C22×D4—24no—
573C22×D4—24no—
574C22×D4—24no—
575C22×D4—24no—
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—24no—
579C22×D4—24no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—22no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—24no—
588C22×D4—22no—
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—22no—
592C22×D4—24no—
593C22×D4—24no—
594C22×D4—42no—
595C22×D4—42no—
596C22×D4—42no—
597C22×D4—42no—
598C22×D4—42no—
599C22×D4—42no—
600C22×D4—42no—
601C22×D4—42no—
602C22×D4—42no—
603C22×D4—42no—
604C22×D4—42no—
605C22×D4—42no—
606C22×D4D4×C6114yescomplemented
607C22×D4D4×C6118yescomplemented
608C23×C4—22no—
609C23×C4—22no—
610C23×C4—22no—
611C23×C4—24no—
612C23×C4—42no—
613C23×C4C23×C6112yes—
614C23×C4C23×C6111yescharacteristic
615C23×C4C23×C6111yescharacteristic
616C23×C4C23×C6112yes—
617C23×C4C23×C6111yescharacteristic
618C23×C4C23×C6111yescharacteristic
619C23×C4C23×C6112yes—
620#127—232no—
621#121—232no—
622C2×C4⋊C4—22no—
623C2×C4⋊C4—22no—
624C2×C4⋊C4D4×C6114yescomplemented
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—24no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—42no—
644C2×C22⋊C4—42no—
645C2×C22⋊C4—42no—
646C2×C22⋊C4—42no—
647C2×C22⋊C4—42no—
648C2×C22⋊C4D4×C6114yescomplemented
649C2×C42—22no—
650C2×C42—24no—
651#95—24no—
652#95—22no—
653#95—24no—
654#95—22no—
655#95D4×C6118yescomplemented
656C24—22no—
657C24—21no—
658C24—21no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24C2×D4×C6114yes—
694C24C2×D4×C6112yes—
695C24C2×D4×C6112yes—
696C24C2×D4×C6114yes—
697C24C2×D4×C6112yes—
698C24C24×C6111yescharacteristic
699C2×D4—28no—
700C2×D4—28no—
701C2×D4—28no—
702C2×D4—216no—
703C2×D4—28no—
704C2×D4—216no—
705C2×D4—28no—
706C2×D4—216no—
707C2×D4—44no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—44no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—44no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—48no—
739C2×D4—44no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—28no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4C2×D4×C6114yes—
776C22×C4C2×D4×C6112yes—
777C22×C4C2×D4×C6112yes—
778C22×C4C2×D4×C6112yes—
779C22×C4C2×D4×C6112yes—
780C22×C4C2×D4×C6112yes—
781C22×C4C2×D4×C6114yes—
782C22×C4C2×D4×C6114yes—
783C22×C4C2×D4×C6114yes—
784C22×C4C2×D4×C6112yes—
785C22×C4#41×C6114yes—
786C4⋊C4—28no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—48no—
790C22⋊C4—48no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—48no—
794C22⋊C4—48no—
795C42—28no—
796C23—22no—
797C23—24no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—22no—
805C23—24no—
806C23—22no—
807C23—24no—
808C23—22no—
809C23—22no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—24no—
822C23—24no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—42no—
827C23—41no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—41no—
835C23—41no—
836C23—42no—
837C23—41no—
838C23—42no—
839C23—41no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—41no—
848C23—41no—
849C23—42no—
850C23—42no—
851C23—41no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23—42no—
888C23—41no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23#120×C6114yes—
894C23C22×D4×C6112yes—
895C23C22×D4×C6111yescharacteristic
896C23C22×D4×C6111yescharacteristic
897C23C22×D4×C6112yes—
898C23C22×D4×C6111yescharacteristic
899C23C2×#41×C6112yes—
900C23H(5,𝔽2)×C6112yes—
901C23H(5,𝔽2)×C6112yes—
902C23H(5,𝔽2)×C6112yes—
903D4—416no—
904D4—432no—
905D4—416no—
906D4—432no—
907D4—416no—
908D4—416no—
909D4—432no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—22no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—22no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—416no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—41no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C6114yes—
950C2×C4#121×C6118yescomplemented
951C2×C4#127×C6114yescomplemented
952C22—24no—
953C22—28no—
954C22—44no—
955C22—44no—
956C22—44no—
957C22—44no—
958C22—44no—
959C22—42no—
960C22—42no—
961C22—44no—
962C22—42no—
963C22—44no—
964C22—42no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—82no—
979C22—82no—
980C22—82no—
981C22—82no—
982C22—82no—
983C22—82no—
984C22—82no—
985C22—82no—
986C22—82no—
987C22—82no—
988C22—82no—
989C22—82no—
990C22—82no—
991C22—82no—
992C22—82no—
993C22—82no—
994C22C2×#120×C6111yescharacteristic
995C22C2×#120×C6111yescharacteristic
996C22C2×#121×C6112yes—
997C22C2×#127×C6111yescharacteristic
998C22C61×#53211yescharacteristic
999C22C61×#53411yescharacteristic
1000C22C61×#53412yes—
1001C22C61×#53512yes—
1002C22C61×#53511yescharacteristic
1003C22C61×#53511yescharacteristic
1004C22C61×#54012yes—
1005C22D42×C6112yes—
1006C22D42×C6112yes—
1007C22D42×C6112yes—
1008C22D42×C6112yes—
1009C22D42×C6112yes—
1010C22C61×#54612yes—
1011C22C61×#54612yes—
1012C22C61×#55012yes—
1013C22C61×#55012yes—
1014C22C61×#56012yes—
1015C4—24no—
1016C4—28no—
1017C4—24no—
1018C4—42no—
1019C4—44no—
1020C4—42no—
1021C4—82no—
1022C2—44no—
1023C2—84no—
1024C2—82no—
1025C2—82no—
1026C2C61×#240311yescharacteristic
1027C2C61×#241012yes—
1028C2C61×#242812yes—
1029C2C61×#243111yescharacteristic
1030C2C61×#243311yescharacteristic
1031C2C61×#254112yes—
1032C2C61×#266912yes—
1033C2C61×#267312yes—
1034C2C61×#267312yes—
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC24C24×C61
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#127×C61C2semidirect
2. C22×#121×C61C2semidirect
3. C2×C61×#394C2semidirect
4. C2×C61×#392C2semidirect
5. C2×C61×#392C2semidirect
6. C2×C61×#392C2semidirect
7. C2×C61×#386C2semidirect
8. C61×#1438C2semidirect
9. C61×#1438C2semidirect
10. C61×#1437C2semidirect
11. C61×#1436C2semidirect
88. C22×D4×C61D4semidirect
89. C22×D4×C61D4semidirect
106. C2×C4⋊C4×C61D4semidirect
130. C2×C22⋊C4×C61D4semidirect
137. #95×C61D4semidirect
432. C2×C4×C61#121semidirect
433. C2×C4×C61#127semidirect
434. #15310C61direct (N × H)
505. C22×#127C2×C61semidirect
506. C22×#121C2×C61semidirect
507. C2×#394C2×C61semidirect
508. C2×#392C2×C61semidirect
509. C2×#392C2×C61semidirect
510. C2×#392C2×C61semidirect
511. C2×#386C2×C61semidirect
512. #1438C2×C61semidirect
513. #1438C2×C61semidirect
514. #1437C2×C61semidirect
515. #1436C2×C61semidirect
562. C61#15310direct (N × H)
606. C22×D4D4×C61semidirect
607. C22×D4D4×C61semidirect
624. C2×C4⋊C4D4×C61semidirect
648. C2×C22⋊C4D4×C61semidirect
655. #95D4×C61semidirect
950. C2×C4#121×C61semidirect
951. C2×C4#127×C61semidirect

Maximal subgroups

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

subgroupindex
C22×#127×C612
C22×#121×C612
C2×C61×#3942
C2×C61×#3922
C2×C61×#3862
C61×#14382
C61×#14372
C61×#14362
#1531061