Finite Group Databasebeta

← C61×#14718 #29518151

Subgroups — C61×#14718 #29518151

Order 15616.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C61C211yesmaximal, characteristic
2C23×C22⋊C4×C61C211yesmaximal, characteristic, complemented
3C2×C61×#394C212yesmaximal, complemented
4C2×C61×#386C211yesmaximal, characteristic, complemented
5C2×C61×#386C211yesmaximal, characteristic, complemented
6C2×C61×#385C211yesmaximal, characteristic, complemented
7C2×C61×#379C211yesmaximal, characteristic, complemented
8C61×#1440C212yesmaximal, complemented
9C61×#1439C212yesmaximal, complemented
10C61×#1438C212yesmaximal, complemented
11C61×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C61C2211yescharacteristic
13C23×D4×C61C2211yescharacteristic
14C23×D4×C61C2211yescharacteristic
15C23×D4×C61C2211yescharacteristic
16C24×C4×C61C2211yescharacteristic
17C24×C4×C61C2211yescharacteristic
18C2×#120×C61—24no—
19C2×#120×C61—24no—
20C2×#120×C61—24no—
21C22×C4⋊C4×C61C2212yescomplemented
22C22×C22⋊C4×C61—24no—
23C22×C22⋊C4×C61—28no—
24C22×C22⋊C4×C61C2211yescharacteristic
25C22×C22⋊C4×C61C2212yes—
26C22×C22⋊C4×C61C2211yescharacteristic
27C22×C22⋊C4×C61C2211yescharacteristic
28C22×C22⋊C4×C61C2212yes—
29C22×C22⋊C4×C61C2212yes—
30C22×C22⋊C4×C61C2211yescharacteristic
31C22×C22⋊C4×C61C2211yescharacteristic
32C22×C22⋊C4×C61C2212yes—
33C22×C22⋊C4×C61C2212yescomplemented
34C22×C22⋊C4×C61C2212yescomplemented
35C61×#394—28no—
36C61×#386—24no—
37C61×#386—24no—
38C61×#385—24no—
39C61×#379—24no—
40C2×#95×C61C2212yescomplemented
41C2×#95×C61C2212yescomplemented
42C2×#95×C61C2212yescomplemented
43C2×#95×C61C2212yescomplemented
44C2×#95×C61C2212yescomplemented
45C25×C61—24no—
46C25×C61—24no—
47C25×C61—22no—
48C25×C61—22no—
49C25×C61—22no—
50C25×C61—22no—
51C25×C61—22no—
52C25×C61—22no—
53C25×C61—42no—
54C25×C61—42no—
55C25×C61D414yes—
56C25×C61C2311yescharacteristic
57C25×C61C2311yescharacteristic
58C25×C61C2311yescharacteristic
59C25×C61C2311yescharacteristic
60C22×D4×C61—22no—
61C22×D4×C61—22no—
62C22×D4×C61—22no—
63C22×D4×C61—22no—
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—22no—
73C22×D4×C61—22no—
74C22×D4×C61—42no—
75C22×D4×C61—42no—
76C22×D4×C61D414yes—
77C23×C4×C61—22no—
78C23×C4×C61—22no—
79C23×C4×C61—24no—
80C23×C4×C61—24no—
81C23×C4×C61—22no—
82C23×C4×C61—22no—
83C23×C4×C61—22no—
84C23×C4×C61—22no—
85C23×C4×C61—42no—
86C23×C4×C61—42no—
87C23×C4×C61C2312yes—
88C23×C4×C61C2312yes—
89C23×C4×C61C2312yes—
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C23×C4×C61C2311yescharacteristic
93C23×C4×C61C2312yes—
94#120×C61—232no—
95C2×C4⋊C4×C61—24no—
96C2×C4⋊C4×C61—24no—
97C2×C4⋊C4×C61—42no—
98C2×C22⋊C4×C61—232no—
99C2×C22⋊C4×C61—22no—
100C2×C22⋊C4×C61—24no—
101C2×C22⋊C4×C61—24no—
102C2×C22⋊C4×C61—24no—
103C2×C22⋊C4×C61—22no—
104C2×C22⋊C4×C61—22no—
105C2×C22⋊C4×C61—22no—
106C2×C22⋊C4×C61—22no—
107C2×C22⋊C4×C61—22no—
108C2×C22⋊C4×C61—24no—
109C2×C22⋊C4×C61—24no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—22no—
113C2×C22⋊C4×C61—22no—
114C2×C22⋊C4×C61—22no—
115C2×C22⋊C4×C61—22no—
116C2×C22⋊C4×C61—24no—
117C2×C22⋊C4×C61—24no—
118C2×C22⋊C4×C61—24no—
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—42no—
126C2×C22⋊C4×C61—42no—
127C2×C22⋊C4×C61—42no—
128C2×C22⋊C4×C61—42no—
129C2×C22⋊C4×C61D414yes—
130C2×C22⋊C4×C61D414yescomplemented
131C2×C22⋊C4×C61D418yescomplemented
132#95×C61—24no—
133#95×C61—24no—
134#95×C61—24no—
135#95×C61—24no—
136#95×C61—42no—
137C24×C61—22no—
138C24×C61—22no—
139C24×C61—22no—
140C24×C61—22no—
141C24×C61—216no—
142C24×C61—216no—
143C24×C61—28no—
144C24×C61—28no—
145C24×C61—28no—
146C24×C61—22no—
147C24×C61—21no—
148C24×C61—21no—
149C24×C61—21no—
150C24×C61—21no—
151C24×C61—21no—
152C24×C61—21no—
153C24×C61—21no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61—21no—
157C24×C61—22no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—22no—
161C24×C61—22no—
162C24×C61—22no—
163C24×C61—22no—
164C24×C61—28no—
165C24×C61—28no—
166C24×C61—21no—
167C24×C61—22no—
168C24×C61—21no—
169C24×C61—21no—
170C24×C61—21no—
171C24×C61—21no—
172C24×C61—21no—
173C24×C61—22no—
174C24×C61—22no—
175C24×C61—22no—
176C24×C61—44no—
177C24×C61—44no—
178C24×C61—48no—
179C24×C61—48no—
180C24×C61—48no—
181C24×C61—48no—
182C24×C61—48no—
183C24×C61—48no—
184C24×C61—48no—
185C24×C61—48no—
186C24×C61—48no—
187C24×C61—48no—
188C24×C61—44no—
189C24×C61—44no—
190C24×C61—44no—
191C24×C61—44no—
192C24×C61C2×D412yes—
193C24×C61C2×D412yes—
194C24×C61C2×D414yes—
195C24×C61C2×D412yes—
196C24×C61C2×D412yes—
197C24×C61C2×D412yes—
198C24×C61C2×D412yes—
199C24×C61C2×D412yes—
200C24×C61#4114yes—
201C24×C61#4112yes—
202C24×C61#4112yes—
203C24×C61#4112yes—
204C24×C61C2411yescharacteristic
205C2×D4×C61—28no—
206C2×D4×C61—28no—
207C2×D4×C61—28no—
208C2×D4×C61—28no—
209C2×D4×C61—28no—
210C2×D4×C61—48no—
211C2×D4×C61—48no—
212C2×D4×C61—48no—
213C2×D4×C61—48no—
214C2×D4×C61—44no—
215C2×D4×C61—44no—
216C2×D4×C61—44no—
217C2×D4×C61—44no—
218C2×D4×C61—44no—
219C2×D4×C61—44no—
220C2×D4×C61—44no—
221C2×D4×C61—44no—
222C22×C4×C61—28no—
223C22×C4×C61—28no—
224C22×C4×C61—21no—
225C22×C4×C61—22no—
226C22×C4×C61—22no—
227C22×C4×C61—22no—
228C22×C4×C61—22no—
229C22×C4×C61—22no—
230C22×C4×C61—22no—
231C22×C4×C61—22no—
232C22×C4×C61—22no—
233C22×C4×C61—22no—
234C22×C4×C61—22no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—22no—
242C22×C4×C61—22no—
243C22×C4×C61—22no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
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—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—48no—
264C22×C4×C61—48no—
265C22×C4×C61—48no—
266C22×C4×C61—48no—
267C22×C4×C61—44no—
268C22×C4×C61—44no—
269C22×C4×C61—44no—
270C22×C4×C61—44no—
271C22×C4×C61C2×D412yes—
272C22×C4×C61C2×D412yes—
273C22×C4×C61C2×D414yes—
274C22×C4×C61C2×D414yes—
275C22×C4×C61C2×D414yes—
276C22×C4×C61C2×D412yes—
277C4⋊C4×C61—48no—
278C22⋊C4×C61—216no—
279C22⋊C4×C61—28no—
280C22⋊C4×C61—28no—
281C22⋊C4×C61—216no—
282C22⋊C4×C61—28no—
283C22⋊C4×C61—28no—
284C22⋊C4×C61—48no—
285C22⋊C4×C61—48no—
286C22⋊C4×C61—48no—
287C22⋊C4×C61—48no—
288C22⋊C4×C61—44no—
289C23×C61—22no—
290C23×C61—22no—
291C23×C61—24no—
292C23×C61—24no—
293C23×C61—22no—
294C23×C61—22no—
295C23×C61—24no—
296C23×C61—24no—
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—232no—
306C23×C61—22no—
307C23×C61—22no—
308C23×C61—22no—
309C23×C61—22no—
310C23×C61—22no—
311C23×C61—22no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—24no—
315C23×C61—24no—
316C23×C61—24no—
317C23×C61—24no—
318C23×C61—22no—
319C23×C61—22no—
320C23×C61—22no—
321C23×C61—22no—
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—416no—
339C23×C61—416no—
340C23×C61—432no—
341C23×C61—432no—
342C23×C61—432no—
343C23×C61—432no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—41no—
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—416no—
365C23×C61—41no—
366C23×C61—41no—
367C23×C61—41no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—42no—
371C23×C61—42no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—41no—
375C23×C61—42no—
376C23×C61—42no—
377C23×C61—42no—
378C23×C61—42no—
379C23×C61—42no—
380C23×C61—42no—
381C23×C61—42no—
382C23×C61—42no—
383C23×C61#12014yes—
384C23×C61#12014yes—
385C23×C61#12114yes—
386C23×C61#12114yes—
387C23×C61#12114yes—
388C23×C61#12314yes—
389C23×C61#12314yes—
390C23×C61#12314yes—
391C23×C61#12414yes—
392C23×C61C22×D411yescharacteristic
393C23×C61C22×D411yescharacteristic
394C23×C61C22×D411yescharacteristic
395C23×C61C22×D412yes—
396C23×C61C22×D411yescharacteristic
397C23×C61C2×#4111yescharacteristic
398C23×C61C2×#4111yescharacteristic
399C23×C61C2×#4111yescharacteristic
400C23×C61C2×#4112yes—
401C23×C61H(5,𝔽2)12yes—
402C23×C61H(5,𝔽2)12yes—
403D4×C61—416no—
404D4×C61—416no—
405D4×C61—416no—
406C2×C4×C61—24no—
407C2×C4×C61—24no—
408C2×C4×C61—22no—
409C2×C4×C61—22no—
410C2×C4×C61—22no—
411C2×C4×C61—24no—
412C2×C4×C61—22no—
413C2×C4×C61—22no—
414C2×C4×C61—24no—
415C2×C4×C61—24no—
416C2×C4×C61—24no—
417C2×C4×C61—24no—
418C2×C4×C61—24no—
419C2×C4×C61—24no—
420C2×C4×C61—24no—
421C2×C4×C61—24no—
422C2×C4×C61—416no—
423C2×C4×C61—416no—
424C2×C4×C61—42no—
425C2×C4×C61—41no—
426C2×C4×C61—42no—
427C2×C4×C61—41no—
428C2×C4×C61—41no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—42no—
432C2×C4×C61—41no—
433C2×C4×C61—42no—
434C2×C4×C61—42no—
435C2×C4×C61—41no—
436C2×C4×C61—41no—
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—42no—
453#14718C6111yesmaximal, characteristic, direct product factor, Sylow
454C22×C61—24no—
455C22×C61—24no—
456C22×C61—24no—
457C22×C61—24no—
458C22×C61—24no—
459C22×C61—24no—
460C22×C61—28no—
461C22×C61—28no—
462C22×C61—28no—
463C22×C61—28no—
464C22×C61—24no—
465C22×C61—24no—
466C22×C61—24no—
467C22×C61—24no—
468C22×C61—24no—
469C22×C61—24no—
470C22×C61—464no—
471C22×C61—42no—
472C22×C61—42no—
473C22×C61—42no—
474C22×C61—42no—
475C22×C61—42no—
476C22×C61—42no—
477C22×C61—42no—
478C22×C61—42no—
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—42no—
488C22×C61—42no—
489C22×C61—42no—
490C22×C61—44no—
491C22×C61—44no—
492C22×C61—81no—
493C22×C61—81no—
494C22×C61—81no—
495C22×C61—81no—
496C22×C61—82no—
497C22×C61—82no—
498C22×C61#39418yescomplemented
499C22×C61C2×#12011yescharacteristic
500C22×C61C2×#12011yescharacteristic
501C22×C61C2×#12111yescharacteristic
502C22×C61C2×#12111yescharacteristic
503C22×C61C2×#12111yescharacteristic
504C22×C61C2×#12311yescharacteristic
505C22×C61C2×#12311yescharacteristic
506C22×C61C2×#12311yescharacteristic
507C22×C61#52512yes—
508C22×C61#52512yes—
509C22×C61C2×#12411yescharacteristic
510C22×C61#53411yescharacteristic
511C22×C61#53411yescharacteristic
512C22×C61#53812yes—
513C22×C61#53812yes—
514C22×C61D4212yes—
515C22×C61D4212yes—
516C22×C61D4212yes—
517C22×C61#54612yes—
518C22×C61#54612yes—
519C22×C61#54612yes—
520C22×C61#54612yes—
521C22×C61#55112yes—
522C4×C61—42no—
523C4×C61—44no—
524C4×C61—42no—
525C4×C61—42no—
526C4×C61—44no—
527C4×C61—44no—
528C4×C61—82no—
529C22×#120C2×C6111yescharacteristic
530C23×C22⋊C4C2×C6111yescharacteristic, complemented
531C2×#394C2×C6112yescomplemented
532C2×#386C2×C6111yescharacteristic, complemented
533C2×#386C2×C6111yescharacteristic, complemented
534C2×#385C2×C6111yescharacteristic, complemented
535C2×#379C2×C6111yescharacteristic, complemented
536#1440C2×C6112yescomplemented
537#1439C2×C6112yescomplemented
538#1438C2×C6112yescomplemented
539C22⋊#95C2×C6111yescharacteristic, complemented
540C2×C61—28no—
541C2×C61—44no—
542C2×C61—44no—
543C2×C61—82no—
544C2×C61C2×#39411yescharacteristic
545C2×C61#240311yescharacteristic
546C2×C61#240511yescharacteristic
547C2×C61#241011yescharacteristic
548C2×C61#241211yescharacteristic
549C2×C61#241812yes—
550C2×C61#242412yes—
551C2×C61#242412yes—
552C2×C61#247212yes—
553C2×C61#262211yescharacteristic
554C2×C61#284911yescharacteristic
555C26C22×C6111yescharacteristic
556C23×D4C22×C6111yescharacteristic
557C23×D4C22×C6111yescharacteristic
558C23×D4C22×C6111yescharacteristic
559C24×C4C22×C6111yescharacteristic
560C24×C4C22×C6111yescharacteristic
561C2×#120—24no—
562C2×#120—24no—
563C2×#120—24no—
564C22×C4⋊C4C22×C6112yescomplemented
565C22×C22⋊C4—24no—
566C22×C22⋊C4—28no—
567C22×C22⋊C4C22×C6112yes—
568C22×C22⋊C4C22×C6111yescharacteristic
569C22×C22⋊C4C22×C6111yescharacteristic
570C22×C22⋊C4C22×C6111yescharacteristic
571C22×C22⋊C4C22×C6112yes—
572C22×C22⋊C4C22×C6112yes—
573C22×C22⋊C4C22×C6111yescharacteristic
574C22×C22⋊C4C22×C6112yes—
575C22×C22⋊C4C22×C6111yescharacteristic
576C22×C22⋊C4C22×C6112yescomplemented
577C22×C22⋊C4C22×C6112yescomplemented
578#394—28no—
579#386—24no—
580#386—24no—
581#385—24no—
582#379—24no—
583C2×#95C22×C6112yescomplemented
584C2×#95C22×C6112yescomplemented
585C2×#95C22×C6112yescomplemented
586C2×#95C22×C6112yescomplemented
587C2×#95C22×C6112yescomplemented
588C61#1471811yescharacteristic, direct product factor, Sylow
589C25—24no—
590C25—24no—
591C25—22no—
592C25—22no—
593C25—22no—
594C25—22no—
595C25—22no—
596C25—22no—
597C25—42no—
598C25—42no—
599C25D4×C6114yes—
600C25C23×C6111yescharacteristic
601C25C23×C6111yescharacteristic
602C25C23×C6111yescharacteristic
603C25C23×C6111yescharacteristic
604C22×D4—22no—
605C22×D4—22no—
606C22×D4—22no—
607C22×D4—22no—
608C22×D4—22no—
609C22×D4—22no—
610C22×D4—22no—
611C22×D4—22no—
612C22×D4—22no—
613C22×D4—22no—
614C22×D4—24no—
615C22×D4—24no—
616C22×D4—22no—
617C22×D4—22no—
618C22×D4—42no—
619C22×D4—42no—
620C22×D4D4×C6114yes—
621C23×C4—22no—
622C23×C4—22no—
623C23×C4—24no—
624C23×C4—24no—
625C23×C4—22no—
626C23×C4—22no—
627C23×C4—22no—
628C23×C4—22no—
629C23×C4—42no—
630C23×C4—42no—
631C23×C4C23×C6112yes—
632C23×C4C23×C6112yes—
633C23×C4C23×C6112yes—
634C23×C4C23×C6112yes—
635C23×C4C23×C6111yescharacteristic
636C23×C4C23×C6111yescharacteristic
637C23×C4C23×C6111yescharacteristic
638#120—232no—
639C2×C4⋊C4—24no—
640C2×C4⋊C4—24no—
641C2×C4⋊C4—42no—
642C2×C22⋊C4—232no—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—24no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—24no—
661C2×C22⋊C4—24no—
662C2×C22⋊C4—24no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—24no—
665C2×C22⋊C4—24no—
666C2×C22⋊C4—24no—
667C2×C22⋊C4—24no—
668C2×C22⋊C4—24no—
669C2×C22⋊C4—42no—
670C2×C22⋊C4—42no—
671C2×C22⋊C4—42no—
672C2×C22⋊C4—42no—
673C2×C22⋊C4D4×C6114yes—
674C2×C22⋊C4D4×C6118yescomplemented
675C2×C22⋊C4D4×C6114yescomplemented
676#95—24no—
677#95—24no—
678#95—24no—
679#95—24no—
680#95—42no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—216no—
686C24—216no—
687C24—28no—
688C24—28no—
689C24—28no—
690C24—21no—
691C24—21no—
692C24—22no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—21no—
701C24—22no—
702C24—21no—
703C24—21no—
704C24—22no—
705C24—22no—
706C24—22no—
707C24—22no—
708C24—28no—
709C24—28no—
710C24—22no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—22no—
715C24—21no—
716C24—21no—
717C24—21no—
718C24—22no—
719C24—22no—
720C24—44no—
721C24—44no—
722C24—48no—
723C24—48no—
724C24—48no—
725C24—48no—
726C24—48no—
727C24—48no—
728C24—48no—
729C24—48no—
730C24—48no—
731C24—48no—
732C24—44no—
733C24—44no—
734C24—44no—
735C24—44no—
736C24C2×D4×C6112yes—
737C24C2×D4×C6112yes—
738C24C2×D4×C6114yes—
739C24C2×D4×C6112yes—
740C24C2×D4×C6112yes—
741C24C2×D4×C6112yes—
742C24C2×D4×C6112yes—
743C24C2×D4×C6112yes—
744C24#41×C6114yes—
745C24#41×C6112yes—
746C24#41×C6112yes—
747C24#41×C6112yes—
748C24C24×C6111yescharacteristic
749C2×D4—28no—
750C2×D4—28no—
751C2×D4—28no—
752C2×D4—28no—
753C2×D4—28no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
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—22no—
806C22×C4—22no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—48no—
810C22×C4—48no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4C2×D4×C6112yes—
816C22×C4C2×D4×C6112yes—
817C22×C4C2×D4×C6114yes—
818C22×C4C2×D4×C6114yes—
819C22×C4C2×D4×C6114yes—
820C22×C4C2×D4×C6112yes—
821C4⋊C4—48no—
822C22⋊C4—216no—
823C22⋊C4—28no—
824C22⋊C4—28no—
825C22⋊C4—216no—
826C22⋊C4—28no—
827C22⋊C4—28no—
828C22⋊C4—48no—
829C22⋊C4—48no—
830C22⋊C4—48no—
831C22⋊C4—48no—
832C22⋊C4—44no—
833C23—22no—
834C23—22no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—24no—
840C23—24no—
841C23—24no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—22no—
846C23—22no—
847C23—24no—
848C23—24no—
849C23—232no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—24no—
871C23—24no—
872C23—24no—
873C23—24no—
874C23—24no—
875C23—24no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—416no—
880C23—416no—
881C23—416no—
882C23—416no—
883C23—416no—
884C23—432no—
885C23—432no—
886C23—432no—
887C23—432no—
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—416no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—42no—
915C23—42no—
916C23—42no—
917C23—42no—
918C23—42no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—42no—
925C23—42no—
926C23—41no—
927C23#120×C6114yes—
928C23#120×C6114yes—
929C23#121×C6114yes—
930C23#121×C6114yes—
931C23#121×C6114yes—
932C23#123×C6114yes—
933C23#123×C6114yes—
934C23#123×C6114yes—
935C23#124×C6114yes—
936C23C22×D4×C6111yescharacteristic
937C23C22×D4×C6112yes—
938C23C22×D4×C6111yescharacteristic
939C23C22×D4×C6111yescharacteristic
940C23C22×D4×C6111yescharacteristic
941C23C2×#41×C6111yescharacteristic
942C23C2×#41×C6111yescharacteristic
943C23C2×#41×C6112yes—
944C23C2×#41×C6111yescharacteristic
945C23H(5,𝔽2)×C6112yes—
946C23H(5,𝔽2)×C6112yes—
947D4—416no—
948D4—416no—
949D4—416no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—24no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—416no—
967C2×C4—416no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—41no—
971C2×C4—41no—
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—42no—
981C2×C4—42no—
982C2×C4—41no—
983C2×C4—42no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—42no—
989C2×C4—41no—
990C2×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22—28no—
1004C22—28no—
1005C22—28no—
1006C22—28no—
1007C22—24no—
1008C22—24no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—464no—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22—44no—
1026C22—44no—
1027C22—44no—
1028C22—44no—
1029C22—44no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—44no—
1034C22—44no—
1035C22—81no—
1036C22—81no—
1037C22—81no—
1038C22—81no—
1039C22—82no—
1040C22—82no—
1041C22C61×#39418yescomplemented
1042C22C2×#120×C6111yescharacteristic
1043C22C2×#120×C6111yescharacteristic
1044C22C2×#121×C6111yescharacteristic
1045C22C2×#121×C6111yescharacteristic
1046C22C2×#121×C6111yescharacteristic
1047C22C2×#123×C6111yescharacteristic
1048C22C2×#123×C6111yescharacteristic
1049C22C2×#123×C6111yescharacteristic
1050C22C61×#52512yes—
1051C22C61×#52512yes—
1052C22C2×#124×C6111yescharacteristic
1053C22C61×#53411yescharacteristic
1054C22C61×#53411yescharacteristic
1055C22C61×#53812yes—
1056C22C61×#53812yes—
1057C22D42×C6112yes—
1058C22D42×C6112yes—
1059C22D42×C6112yes—
1060C22C61×#54612yes—
1061C22C61×#54612yes—
1062C22C61×#54612yes—
1063C22C61×#54612yes—
1064C22C61×#55112yes—
1065C4—42no—
1066C4—44no—
1067C4—42no—
1068C4—42no—
1069C4—44no—
1070C4—44no—
1071C4—82no—
1072C2—28no—
1073C2—44no—
1074C2—44no—
1075C2—82no—
1076C2C2×C61×#39411yescharacteristic
1077C2C61×#240311yescharacteristic
1078C2C61×#240511yescharacteristic
1079C2C61×#241011yescharacteristic
1080C2C61×#241211yescharacteristic
1081C2C61×#241812yes—
1082C2C61×#242412yes—
1083C2C61×#242412yes—
1084C2C61×#247212yes—
1085C2C61×#262211yescharacteristic
1086C2C61×#284911yescharacteristic
subgroupG/H
center, socleC24×C61C24
commutator, Frattini, cosocleC24C24×C61
prime radicalC22×#120×C61C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C61C2semidirect
3. C2×C61×#394C2semidirect
4. C2×C61×#386C2semidirect
5. C2×C61×#386C2semidirect
6. C2×C61×#385C2semidirect
7. C2×C61×#379C2semidirect
8. C61×#1440C2semidirect
9. C61×#1439C2semidirect
10. C61×#1438C2semidirect
11. C61×C22⋊#95C2semidirect
21. C22×C4⋊C4×C61C22semidirect
33. C22×C22⋊C4×C61C22semidirect
34. C22×C22⋊C4×C61C22semidirect
40. C2×#95×C61C22semidirect
41. C2×#95×C61C22semidirect
42. C2×#95×C61C22semidirect
43. C2×#95×C61C22semidirect
44. C2×#95×C61C22semidirect
130. C2×C22⋊C4×C61D4semidirect
131. C2×C22⋊C4×C61D4semidirect
453. #14718C61direct (N × H)
498. C22×C61#394semidirect
530. C23×C22⋊C4C2×C61semidirect
531. C2×#394C2×C61semidirect
532. C2×#386C2×C61semidirect
533. C2×#386C2×C61semidirect
534. C2×#385C2×C61semidirect
535. C2×#379C2×C61semidirect
536. #1440C2×C61semidirect
537. #1439C2×C61semidirect
538. #1438C2×C61semidirect
539. C22⋊#95C2×C61semidirect
564. C22×C4⋊C4C22×C61semidirect
576. C22×C22⋊C4C22×C61semidirect
577. C22×C22⋊C4C22×C61semidirect
583. C2×#95C22×C61semidirect
584. C2×#95C22×C61semidirect
585. C2×#95C22×C61semidirect
586. C2×#95C22×C61semidirect
587. C2×#95C22×C61semidirect
588. C61#14718direct (N × H)
674. C2×C22⋊C4D4×C61semidirect
675. C2×C22⋊C4D4×C61semidirect
1041. C22C61×#394semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C612
C23×C22⋊C4×C612
C2×C61×#3942
C2×C61×#3862
C2×C61×#3852
C2×C61×#3792
C61×#14402
C61×#14392
C61×#14382
C61×C22⋊#952
#1471861