Finite Group Databasebeta

← C61×#15257 #29518690

Subgroups — C61×#15257 #29518690

Order 15616.

4462 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C61C211yesmaximal, characteristic, complemented
2C22×#120×C61C211yesmaximal, characteristic, complemented
3C22×#120×C61C211yesmaximal, characteristic, complemented
4C2×C61×#392C212yesmaximal, complemented
5C2×C61×#386C212yesmaximal, complemented
6C2×C61×#379C211yesmaximal, characteristic, complemented
7C61×#1440C211yesmaximal, characteristic, complemented
8C61×#1439C212yesmaximal, complemented
9C61×#1438C212yesmaximal, complemented
10C61×#1438C211yesmaximal, characteristic, complemented
11C61×#1438C211yesmaximal, characteristic, complemented
12C26×C61C2211yescharacteristic
13C23×D4×C61C2212yes—
14C23×D4×C61C2212yes—
15C23×D4×C61C2211yescharacteristic
16C23×D4×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic, complemented
18C24×C4×C61C2211yescharacteristic, complemented
19C2×#121×C61—24no—
20C2×#121×C61—24no—
21C2×#121×C61—24no—
22C2×#120×C61—28no—
23C2×#120×C61—24no—
24C2×#120×C61—24no—
25C2×#120×C61—28no—
26C22×C4⋊C4×C61C2211yescharacteristic, complemented
27C22×C22⋊C4×C61C2212yes—
28C22×C22⋊C4×C61C2211yescharacteristic
29C22×C22⋊C4×C61C2211yescharacteristic
30C22×C22⋊C4×C61C2212yes—
31C22×C22⋊C4×C61C2212yes—
32C22×C22⋊C4×C61C2211yescharacteristic
33C22×C22⋊C4×C61C2212yes—
34C22×C22⋊C4×C61C2211yescharacteristic
35C22×C22⋊C4×C61C2211yescharacteristic, complemented
36C22×C22⋊C4×C61C2212yescomplemented
37C22×C22⋊C4×C61C2212yescomplemented
38C61×#392—28no—
39C61×#386—28no—
40C61×#379—24no—
41C2×#95×C61C2212yescomplemented
42C2×#95×C61C2212yescomplemented
43C2×#95×C61C2212yescomplemented
44C2×#95×C61C2212yescomplemented
45C25×C61—22no—
46C25×C61—22no—
47C25×C61—22no—
48C25×C61—24no—
49C25×C61—24no—
50C25×C61—24no—
51C25×C61—42no—
52C25×C61—42no—
53C25×C61—42no—
54C25×C61C2311yescharacteristic
55C25×C61C2311yescharacteristic
56C25×C61C2311yescharacteristic
57C25×C61C2312yes—
58C22×D4×C61—24no—
59C22×D4×C61—24no—
60C22×D4×C61—24no—
61C22×D4×C61—24no—
62C22×D4×C61—24no—
63C22×D4×C61—24no—
64C22×D4×C61—22no—
65C22×D4×C61—22no—
66C22×D4×C61—22no—
67C22×D4×C61—22no—
68C22×D4×C61—22no—
69C22×D4×C61—22no—
70C22×D4×C61—24no—
71C22×D4×C61—24no—
72C22×D4×C61—24no—
73C22×D4×C61—24no—
74C22×D4×C61—24no—
75C22×D4×C61—24no—
76C22×D4×C61—22no—
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×C61D418yescomplemented
85C22×D4×C61D414yescomplemented
86C22×D4×C61D414yescomplemented
87C23×C4×C61—22no—
88C23×C4×C61—22no—
89C23×C4×C61—22no—
90C23×C4×C61—24no—
91C23×C4×C61—42no—
92C23×C4×C61C2312yes—
93C23×C4×C61C2311yescharacteristic
94C23×C4×C61C2312yes—
95C23×C4×C61C2312yes—
96C23×C4×C61C2311yescharacteristic
97C23×C4×C61C2311yescharacteristic
98C23×C4×C61C2311yescharacteristic
99#121×C61—232no—
100#120×C61—232no—
101#120×C61—232no—
102C2×C4⋊C4×C61—22no—
103C2×C4⋊C4×C61—22no—
104C2×C4⋊C4×C61—22no—
105C2×C22⋊C4×C61—22no—
106C2×C22⋊C4×C61—22no—
107C2×C22⋊C4×C61—24no—
108C2×C22⋊C4×C61—22no—
109C2×C22⋊C4×C61—22no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—24no—
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—22no—
118C2×C22⋊C4×C61—22no—
119C2×C22⋊C4×C61—22no—
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—24no—
126C2×C22⋊C4×C61—24no—
127C2×C22⋊C4×C61—42no—
128C2×C22⋊C4×C61—42no—
129C2×C22⋊C4×C61—42no—
130C2×C22⋊C4×C61—42no—
131C2×C22⋊C4×C61—42no—
132C2×C22⋊C4×C61—42no—
133C2×C22⋊C4×C61D414yescomplemented
134C2×C22⋊C4×C61D418yescomplemented
135#95×C61—24no—
136#95×C61—24no—
137#95×C61—24no—
138#95×C61—42no—
139C24×C61—22no—
140C24×C61—22no—
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—22no—
150C24×C61—22no—
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—28no—
165C24×C61—28no—
166C24×C61—28no—
167C24×C61—21no—
168C24×C61—21no—
169C24×C61—22no—
170C24×C61—22no—
171C24×C61—22no—
172C24×C61—22no—
173C24×C61—22no—
174C24×C61—22no—
175C24×C61—48no—
176C24×C61—48no—
177C24×C61—48no—
178C24×C61—48no—
179C24×C61—48no—
180C24×C61—48no—
181C24×C61—48no—
182C24×C61—48no—
183C24×C61—48no—
184C24×C61—44no—
185C24×C61—44no—
186C24×C61—48no—
187C24×C61—44no—
188C24×C61—48no—
189C24×C61—48no—
190C24×C61—48no—
191C24×C61—44no—
192C24×C61—48no—
193C24×C61C2×D412yes—
194C24×C61C2×D412yes—
195C24×C61C2×D412yes—
196C24×C61C2×D412yes—
197C24×C61C2×D414yes—
198C24×C61C2×D412yes—
199C24×C61C2×D414yes—
200C24×C61C2×D414yes—
201C24×C61#4114yes—
202C24×C61C2411yescharacteristic
203C2×D4×C61—216no—
204C2×D4×C61—28no—
205C2×D4×C61—28no—
206C2×D4×C61—28no—
207C2×D4×C61—216no—
208C2×D4×C61—28no—
209C2×D4×C61—216no—
210C2×D4×C61—28no—
211C2×D4×C61—44no—
212C2×D4×C61—48no—
213C2×D4×C61—44no—
214C2×D4×C61—48no—
215C2×D4×C61—48no—
216C2×D4×C61—48no—
217C2×D4×C61—48no—
218C2×D4×C61—48no—
219C2×D4×C61—48no—
220C2×D4×C61—48no—
221C2×D4×C61—48no—
222C2×D4×C61—48no—
223C2×D4×C61—48no—
224C2×D4×C61—48no—
225C2×D4×C61—48no—
226C2×D4×C61—48no—
227C2×D4×C61—48no—
228C2×D4×C61—44no—
229C2×D4×C61—48no—
230C2×D4×C61—44no—
231C2×D4×C61—48no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—22no—
235C22×C4×C61—28no—
236C22×C4×C61—22no—
237C22×C4×C61—22no—
238C22×C4×C61—22no—
239C22×C4×C61—22no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—22no—
243C22×C4×C61—22no—
244C22×C4×C61—22no—
245C22×C4×C61—22no—
246C22×C4×C61—22no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—22no—
252C22×C4×C61—22no—
253C22×C4×C61—22no—
254C22×C4×C61—22no—
255C22×C4×C61—22no—
256C22×C4×C61—22no—
257C22×C4×C61—22no—
258C22×C4×C61—22no—
259C22×C4×C61—22no—
260C22×C4×C61—22no—
261C22×C4×C61—22no—
262C22×C4×C61—22no—
263C22×C4×C61—22no—
264C22×C4×C61—22no—
265C22×C4×C61—22no—
266C22×C4×C61—22no—
267C22×C4×C61—48no—
268C22×C4×C61—48no—
269C22×C4×C61—44no—
270C22×C4×C61—44no—
271C22×C4×C61C2×D414yes—
272C22×C4×C61C2×D414yes—
273C22×C4×C61C2×D412yes—
274C22×C4×C61C2×D412yes—
275C22×C4×C61C2×D412yes—
276C22×C4×C61C2×D414yes—
277C22×C4×C61C2×D412yes—
278C4⋊C4×C61—28no—
279C22⋊C4×C61—216no—
280C22⋊C4×C61—28no—
281C22⋊C4×C61—28no—
282C22⋊C4×C61—28no—
283C22⋊C4×C61—28no—
284C22⋊C4×C61—216no—
285C22⋊C4×C61—48no—
286C22⋊C4×C61—48no—
287C22⋊C4×C61—48no—
288C22⋊C4×C61—48no—
289C22⋊C4×C61—44no—
290C23×C61—22no—
291C23×C61—22no—
292C23×C61—24no—
293C23×C61—24no—
294C23×C61—22no—
295C23×C61—24no—
296C23×C61—22no—
297C23×C61—24no—
298C23×C61—22no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61—24no—
302C23×C61—24no—
303C23×C61—22no—
304C23×C61—24no—
305C23×C61—24no—
306C23×C61—24no—
307C23×C61—24no—
308C23×C61—24no—
309C23×C61—24no—
310C23×C61—24no—
311C23×C61—24no—
312C23×C61—24no—
313C23×C61—24no—
314C23×C61—24no—
315C23×C61—24no—
316C23×C61—24no—
317C23×C61—24no—
318C23×C61—24no—
319C23×C61—24no—
320C23×C61—24no—
321C23×C61—24no—
322C23×C61—24no—
323C23×C61—24no—
324C23×C61—24no—
325C23×C61—24no—
326C23×C61—24no—
327C23×C61—24no—
328C23×C61—24no—
329C23×C61—24no—
330C23×C61—22no—
331C23×C61—22no—
332C23×C61—22no—
333C23×C61—24no—
334C23×C61—24no—
335C23×C61—416no—
336C23×C61—416no—
337C23×C61—416no—
338C23×C61—432no—
339C23×C61—432no—
340C23×C61—432no—
341C23×C61—432no—
342C23×C61—432no—
343C23×C61—432no—
344C23×C61—41no—
345C23×C61—42no—
346C23×C61—42no—
347C23×C61—42no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—42no—
351C23×C61—42no—
352C23×C61—42no—
353C23×C61—42no—
354C23×C61—41no—
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—42no—
376C23×C61—42no—
377C23×C61—42no—
378C23×C61—41no—
379C23×C61—42no—
380C23×C61—41no—
381C23×C61—42no—
382C23×C61—41no—
383C23×C61—42no—
384C23×C61—41no—
385C23×C61—42no—
386C23×C61—42no—
387C23×C61—42no—
388C23×C61—42no—
389C23×C61—42no—
390C23×C61—42no—
391C23×C61—42no—
392C23×C61—42no—
393C23×C61—42no—
394C23×C61#12014yes—
395C23×C61#12014yescomplemented
396C23×C61#12118yescomplemented
397C23×C61C22×D411yescharacteristic
398C23×C61C22×D411yescharacteristic
399C23×C61C22×D412yes—
400C23×C61C22×D412yes—
401C23×C61C22×D411yescharacteristic
402C23×C61C2×#4112yes—
403C23×C61H(5,𝔽2)12yes—
404C23×C61H(5,𝔽2)12yes—
405C23×C61H(5,𝔽2)12yes—
406D4×C61—416no—
407D4×C61—416no—
408D4×C61—432no—
409D4×C61—416no—
410D4×C61—432no—
411C2×C4×C61—22no—
412C2×C4×C61—22no—
413C2×C4×C61—24no—
414C2×C4×C61—24no—
415C2×C4×C61—22no—
416C2×C4×C61—22no—
417C2×C4×C61—24no—
418C2×C4×C61—24no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—24no—
422C2×C4×C61—24no—
423C2×C4×C61—22no—
424C2×C4×C61—24no—
425C2×C4×C61—24no—
426C2×C4×C61—24no—
427C2×C4×C61—24no—
428C2×C4×C61—416no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—42no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—42no—
435C2×C4×C61—42no—
436C2×C4×C61—42no—
437C2×C4×C61—42no—
438C2×C4×C61—42no—
439C2×C4×C61—42no—
440C2×C4×C61—42no—
441C2×C4×C61—42no—
442C2×C4×C61—42no—
443C2×C4×C61—42no—
444C2×C4×C61—42no—
445C2×C4×C61—42no—
446C2×C4×C61—42no—
447C2×C4×C61—42no—
448C2×C4×C61—42no—
449C2×C4×C61—42no—
450C2×C4×C61—42no—
451C2×C4×C61—42no—
452C2×C4×C61#12014yescomplemented
453#15257C6111yesmaximal, characteristic, direct product factor, Sylow
454C22×C61—24no—
455C22×C61—24no—
456C22×C61—24no—
457C22×C61—24no—
458C22×C61—28no—
459C22×C61—28no—
460C22×C61—28no—
461C22×C61—28no—
462C22×C61—464no—
463C22×C61—42no—
464C22×C61—44no—
465C22×C61—44no—
466C22×C61—42no—
467C22×C61—44no—
468C22×C61—44no—
469C22×C61—44no—
470C22×C61—44no—
471C22×C61—44no—
472C22×C61—44no—
473C22×C61—44no—
474C22×C61—44no—
475C22×C61—44no—
476C22×C61—44no—
477C22×C61—44no—
478C22×C61—44no—
479C22×C61—44no—
480C22×C61—44no—
481C22×C61—44no—
482C22×C61—44no—
483C22×C61—44no—
484C22×C61—44no—
485C22×C61—44no—
486C22×C61—44no—
487C22×C61—44no—
488C22×C61—42no—
489C22×C61—42no—
490C22×C61—42no—
491C22×C61—44no—
492C22×C61—44no—
493C22×C61—82no—
494C22×C61—82no—
495C22×C61—82no—
496C22×C61—82no—
497C22×C61C2×#12011yescharacteristic
498C22×C61C2×#12011yescharacteristic
499C22×C61C2×#12011yescharacteristic
500C22×C61C2×#12112yes—
501C22×C61#52511yescharacteristic
502C22×C61#53411yescharacteristic
503C22×C61#53411yescharacteristic
504C22×C61#53412yes—
505C22×C61#53511yescharacteristic
506C22×C61#53512yes—
507C22×C61#53812yes—
508C22×C61D4212yes—
509C22×C61D4212yes—
510C22×C61D4212yes—
511C22×C61D4212yes—
512C22×C61D4212yes—
513C22×C61#54612yes—
514C22×C61#54612yes—
515C22×C61#54612yes—
516C22×C61#54612yes—
517C22×C61#56012yes—
518C4×C61—24no—
519C4×C61—42no—
520C4×C61—42no—
521C4×C61—42no—
522C4×C61—44no—
523C4×C61—44no—
524C4×C61—82no—
525C22×#121C2×C6111yescharacteristic, complemented
526C22×#120C2×C6111yescharacteristic, complemented
527C22×#120C2×C6111yescharacteristic, complemented
528C2×#392C2×C6112yescomplemented
529C2×#386C2×C6112yescomplemented
530C2×#379C2×C6111yescharacteristic, complemented
531#1440C2×C6111yescharacteristic, complemented
532#1439C2×C6112yescomplemented
533#1438C2×C6112yescomplemented
534#1438C2×C6111yescharacteristic, complemented
535#1438C2×C6111yescharacteristic, complemented
536C2×C61—44no—
537C2×C61—44no—
538C2×C61—48no—
539C2×C61—82no—
540C2×C61#240311yescharacteristic
541C2×C61#240311yescharacteristic
542C2×C61#240411yescharacteristic
543C2×C61#240812yes—
544C2×C61#241012yes—
545C2×C61#242412yes—
546C2×C61#266812yes—
547C2×C61#266912yes—
548C2×C61#267812yes—
549C26C22×C6111yescharacteristic
550C23×D4C22×C6112yes—
551C23×D4C22×C6112yes—
552C23×D4C22×C6111yescharacteristic
553C23×D4C22×C6111yescharacteristic
554C23×D4C22×C6111yescharacteristic, complemented
555C24×C4C22×C6111yescharacteristic, complemented
556C2×#121—24no—
557C2×#121—24no—
558C2×#121—24no—
559C2×#120—24no—
560C2×#120—24no—
561C2×#120—28no—
562C2×#120—28no—
563C22×C4⋊C4C22×C6111yescharacteristic, complemented
564C22×C22⋊C4C22×C6112yes—
565C22×C22⋊C4C22×C6111yescharacteristic
566C22×C22⋊C4C22×C6111yescharacteristic
567C22×C22⋊C4C22×C6112yes—
568C22×C22⋊C4C22×C6112yes—
569C22×C22⋊C4C22×C6112yes—
570C22×C22⋊C4C22×C6111yescharacteristic
571C22×C22⋊C4C22×C6111yescharacteristic
572C22×C22⋊C4C22×C6111yescharacteristic, complemented
573C22×C22⋊C4C22×C6112yescomplemented
574C22×C22⋊C4C22×C6112yescomplemented
575#392—28no—
576#386—28no—
577#379—24no—
578C2×#95C22×C6112yescomplemented
579C2×#95C22×C6112yescomplemented
580C2×#95C22×C6112yescomplemented
581C2×#95C22×C6112yescomplemented
582C61#1525711yescharacteristic, direct product factor, Sylow
583C25—22no—
584C25—22no—
585C25—24no—
586C25—24no—
587C25—22no—
588C25—24no—
589C25—42no—
590C25—42no—
591C25—42no—
592C25C23×C6111yescharacteristic
593C25C23×C6111yescharacteristic
594C25C23×C6111yescharacteristic
595C25C23×C6112yes—
596C22×D4—24no—
597C22×D4—24no—
598C22×D4—24no—
599C22×D4—24no—
600C22×D4—24no—
601C22×D4—22no—
602C22×D4—22no—
603C22×D4—22no—
604C22×D4—22no—
605C22×D4—22no—
606C22×D4—22no—
607C22×D4—24no—
608C22×D4—24no—
609C22×D4—24no—
610C22×D4—24no—
611C22×D4—24no—
612C22×D4—24no—
613C22×D4—24no—
614C22×D4—22no—
615C22×D4—42no—
616C22×D4—42no—
617C22×D4—42no—
618C22×D4—42no—
619C22×D4—42no—
620C22×D4—42no—
621C22×D4—42no—
622C22×D4D4×C6114yescomplemented
623C22×D4D4×C6114yescomplemented
624C22×D4D4×C6118yescomplemented
625C23×C4—22no—
626C23×C4—22no—
627C23×C4—22no—
628C23×C4—24no—
629C23×C4—42no—
630C23×C4C23×C6112yes—
631C23×C4C23×C6111yescharacteristic
632C23×C4C23×C6111yescharacteristic
633C23×C4C23×C6111yescharacteristic
634C23×C4C23×C6112yes—
635C23×C4C23×C6112yes—
636C23×C4C23×C6111yescharacteristic
637#121—232no—
638#120—232no—
639#120—232no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—24no—
650C2×C22⋊C4—24no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—24no—
654C2×C22⋊C4—24no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—24no—
659C2×C22⋊C4—24no—
660C2×C22⋊C4—24no—
661C2×C22⋊C4—24no—
662C2×C22⋊C4—24no—
663C2×C22⋊C4—24no—
664C2×C22⋊C4—24no—
665C2×C22⋊C4—42no—
666C2×C22⋊C4—42no—
667C2×C22⋊C4—42no—
668C2×C22⋊C4—42no—
669C2×C22⋊C4—42no—
670C2×C22⋊C4—42no—
671C2×C22⋊C4D4×C6118yescomplemented
672C2×C22⋊C4D4×C6114yescomplemented
673#95—24no—
674#95—24no—
675#95—24no—
676#95—42no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—22no—
702C24—28no—
703C24—28no—
704C24—28no—
705C24—22no—
706C24—21no—
707C24—21no—
708C24—22no—
709C24—22no—
710C24—22no—
711C24—22no—
712C24—22no—
713C24—48no—
714C24—48no—
715C24—48no—
716C24—48no—
717C24—48no—
718C24—48no—
719C24—48no—
720C24—48no—
721C24—48no—
722C24—44no—
723C24—44no—
724C24—48no—
725C24—44no—
726C24—48no—
727C24—48no—
728C24—48no—
729C24—44no—
730C24—48no—
731C24C2×D4×C6112yes—
732C24C2×D4×C6112yes—
733C24C2×D4×C6112yes—
734C24C2×D4×C6112yes—
735C24C2×D4×C6114yes—
736C24C2×D4×C6112yes—
737C24C2×D4×C6114yes—
738C24C2×D4×C6114yes—
739C24#41×C6114yes—
740C24C24×C6111yescharacteristic
741C2×D4—216no—
742C2×D4—28no—
743C2×D4—28no—
744C2×D4—28no—
745C2×D4—28no—
746C2×D4—216no—
747C2×D4—216no—
748C2×D4—28no—
749C2×D4—44no—
750C2×D4—48no—
751C2×D4—44no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—44no—
767C2×D4—48no—
768C2×D4—44no—
769C2×D4—48no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—28no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4C2×D4×C6114yes—
810C22×C4C2×D4×C6114yes—
811C22×C4C2×D4×C6112yes—
812C22×C4C2×D4×C6112yes—
813C22×C4C2×D4×C6112yes—
814C22×C4C2×D4×C6114yes—
815C22×C4C2×D4×C6112yes—
816C4⋊C4—28no—
817C22⋊C4—216no—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—216no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—48no—
827C22⋊C4—44no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—24no—
832C23—24no—
833C23—22no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—24no—
840C23—24no—
841C23—24no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—24no—
851C23—24no—
852C23—24no—
853C23—24no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—22no—
861C23—22no—
862C23—24no—
863C23—24no—
864C23—22no—
865C23—24no—
866C23—22no—
867C23—24no—
868C23—22no—
869C23—24no—
870C23—24no—
871C23—22no—
872C23—22no—
873C23—416no—
874C23—416no—
875C23—416no—
876C23—432no—
877C23—432no—
878C23—432no—
879C23—432no—
880C23—432no—
881C23—432no—
882C23—41no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23—41no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—42no—
905C23—42no—
906C23—42no—
907C23—42no—
908C23—42no—
909C23—42no—
910C23—42no—
911C23—41no—
912C23—42no—
913C23—42no—
914C23—42no—
915C23—41no—
916C23—42no—
917C23—41no—
918C23—42no—
919C23—41no—
920C23—42no—
921C23—42no—
922C23—42no—
923C23—42no—
924C23—42no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—41no—
930C23—42no—
931C23—41no—
932C23#120×C6114yes—
933C23#120×C6114yescomplemented
934C23#121×C6118yescomplemented
935C23C22×D4×C6112yes—
936C23C22×D4×C6111yescharacteristic
937C23C22×D4×C6111yescharacteristic
938C23C22×D4×C6111yescharacteristic
939C23C22×D4×C6112yes—
940C23C2×#41×C6112yes—
941C23H(5,𝔽2)×C6112yes—
942C23H(5,𝔽2)×C6112yes—
943C23H(5,𝔽2)×C6112yes—
944D4—416no—
945D4—416no—
946D4—432no—
947D4—416no—
948D4—432no—
949C2×C4—22no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—24no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—24no—
966C2×C4—416no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4#120×C6114yescomplemented
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—28no—
996C22—28no—
997C22—28no—
998C22—28no—
999C22—464no—
1000C22—42no—
1001C22—44no—
1002C22—44no—
1003C22—42no—
1004C22—44no—
1005C22—44no—
1006C22—44no—
1007C22—44no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—44no—
1029C22—44no—
1030C22—82no—
1031C22—82no—
1032C22—82no—
1033C22—82no—
1034C22C2×#120×C6111yescharacteristic
1035C22C2×#120×C6111yescharacteristic
1036C22C2×#120×C6111yescharacteristic
1037C22C2×#121×C6112yes—
1038C22C61×#52511yescharacteristic
1039C22C61×#53411yescharacteristic
1040C22C61×#53411yescharacteristic
1041C22C61×#53412yes—
1042C22C61×#53511yescharacteristic
1043C22C61×#53512yes—
1044C22C61×#53812yes—
1045C22D42×C6112yes—
1046C22D42×C6112yes—
1047C22D42×C6112yes—
1048C22D42×C6112yes—
1049C22D42×C6112yes—
1050C22C61×#54612yes—
1051C22C61×#54612yes—
1052C22C61×#54612yes—
1053C22C61×#54612yes—
1054C22C61×#56012yes—
1055C4—24no—
1056C4—42no—
1057C4—42no—
1058C4—42no—
1059C4—44no—
1060C4—44no—
1061C4—82no—
1062C2—44no—
1063C2—48no—
1064C2—44no—
1065C2—82no—
1066C2C61×#240311yescharacteristic
1067C2C61×#240311yescharacteristic
1068C2C61×#240411yescharacteristic
1069C2C61×#240812yes—
1070C2C61×#241012yes—
1071C2C61×#242412yes—
1072C2C61×#266812yes—
1073C2C61×#266912yes—
1074C2C61×#267812yes—
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×#121×C61C2semidirect
2. C22×#120×C61C2semidirect
3. C22×#120×C61C2semidirect
4. C2×C61×#392C2semidirect
5. C2×C61×#386C2semidirect
6. C2×C61×#379C2semidirect
7. C61×#1440C2semidirect
8. C61×#1439C2semidirect
9. C61×#1438C2semidirect
10. C61×#1438C2semidirect
11. C61×#1438C2semidirect
17. C23×D4×C61C22semidirect
18. C24×C4×C61C22semidirect
26. C22×C4⋊C4×C61C22semidirect
35. C22×C22⋊C4×C61C22semidirect
36. C22×C22⋊C4×C61C22semidirect
37. C22×C22⋊C4×C61C22semidirect
41. C2×#95×C61C22semidirect
42. C2×#95×C61C22semidirect
43. C2×#95×C61C22semidirect
44. C2×#95×C61C22semidirect
84. C22×D4×C61D4semidirect
85. C22×D4×C61D4semidirect
86. C22×D4×C61D4semidirect
133. C2×C22⋊C4×C61D4semidirect
134. C2×C22⋊C4×C61D4semidirect
395. C23×C61#120semidirect
396. C23×C61#121semidirect
452. C2×C4×C61#120semidirect
453. #15257C61direct (N × H)
525. C22×#121C2×C61semidirect
526. C22×#120C2×C61semidirect
527. C22×#120C2×C61semidirect
528. C2×#392C2×C61semidirect
529. C2×#386C2×C61semidirect
530. C2×#379C2×C61semidirect
531. #1440C2×C61semidirect
532. #1439C2×C61semidirect
533. #1438C2×C61semidirect
534. #1438C2×C61semidirect
535. #1438C2×C61semidirect
554. C23×D4C22×C61semidirect
555. C24×C4C22×C61semidirect
563. C22×C4⋊C4C22×C61semidirect
572. C22×C22⋊C4C22×C61semidirect
573. C22×C22⋊C4C22×C61semidirect
574. C22×C22⋊C4C22×C61semidirect
578. C2×#95C22×C61semidirect
579. C2×#95C22×C61semidirect
580. C2×#95C22×C61semidirect
581. C2×#95C22×C61semidirect
582. C61#15257direct (N × H)
622. C22×D4D4×C61semidirect
623. C22×D4D4×C61semidirect
624. C22×D4D4×C61semidirect
671. C2×C22⋊C4D4×C61semidirect
672. C2×C22⋊C4D4×C61semidirect
933. C23#120×C61semidirect
934. C23#121×C61semidirect
990. C2×C4#120×C61semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C612
C22×#120×C612
C2×C61×#3922
C2×C61×#3862
C2×C61×#3792
C61×#14402
C61×#14392
C61×#14382
#1525761