Finite Group Databasebeta

← C61×#14725 #29518158

Subgroups — C61×#14725 #29518158

Order 15616.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 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×#380C211yesmaximal, 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×C61C2212yes—
15C24×C4×C61C2211yescharacteristic
16C24×C4×C61C2211yescharacteristic
17C2×#120×C61—24no—
18C2×#120×C61—24no—
19C2×#120×C61—24no—
20C22×C4⋊C4×C61C2212yescomplemented
21C22×C22⋊C4×C61—24no—
22C22×C22⋊C4×C61—28no—
23C22×C22⋊C4×C61C2211yescharacteristic
24C22×C22⋊C4×C61C2211yescharacteristic
25C22×C22⋊C4×C61C2212yes—
26C22×C22⋊C4×C61C2212yes—
27C22×C22⋊C4×C61C2212yes—
28C22×C22⋊C4×C61C2211yescharacteristic
29C22×C22⋊C4×C61C2212yes—
30C22×C22⋊C4×C61C2212yes—
31C22×C22⋊C4×C61C2211yescharacteristic, complemented
32C22×C22⋊C4×C61C2212yescomplemented
33C22×C22⋊C4×C61C2211yescharacteristic, complemented
34C61×#394—28no—
35C61×#386—24no—
36C61×#386—24no—
37C61×#380—24no—
38C61×#379—24no—
39C2×#95×C61C2212yescomplemented
40C2×#95×C61C2211yescharacteristic, complemented
41C2×#95×C61C2212yescomplemented
42C2×#95×C61C2211yescharacteristic, complemented
43C2×#95×C61C2212yescomplemented
44C2×#95×C61C2212yescomplemented
45C25×C61—24no—
46C25×C61—22no—
47C25×C61—24no—
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×C61C2312yes—
58C25×C61C2311yescharacteristic
59C22×D4×C61—22no—
60C22×D4×C61—24no—
61C22×D4×C61—24no—
62C22×D4×C61—22no—
63C22×D4×C61—22no—
64C22×D4×C61—22no—
65C22×D4×C61—22no—
66C22×D4×C61—22no—
67C22×D4×C61—24no—
68C22×D4×C61—24no—
69C22×D4×C61—24no—
70C22×D4×C61—42no—
71C22×D4×C61—42no—
72C22×D4×C61D414yes—
73C23×C4×C61—22no—
74C23×C4×C61—22no—
75C23×C4×C61—22no—
76C23×C4×C61—24no—
77C23×C4×C61—24no—
78C23×C4×C61—22no—
79C23×C4×C61—22no—
80C23×C4×C61—42no—
81C23×C4×C61—42no—
82C23×C4×C61D414yescomplemented
83C23×C4×C61C2311yescharacteristic
84C23×C4×C61C2311yescharacteristic
85C23×C4×C61C2312yes—
86C23×C4×C61C2311yescharacteristic
87C23×C4×C61C2312yes—
88C23×C4×C61C2311yescharacteristic
89C23×C4×C61C2312yes—
90C23×C4×C61C2311yescharacteristic
91#120×C61—232no—
92C2×C4⋊C4×C61—24no—
93C2×C4⋊C4×C61—24no—
94C2×C4⋊C4×C61—42no—
95C2×C22⋊C4×C61—232no—
96C2×C22⋊C4×C61—24no—
97C2×C22⋊C4×C61—24no—
98C2×C22⋊C4×C61—22no—
99C2×C22⋊C4×C61—22no—
100C2×C22⋊C4×C61—24no—
101C2×C22⋊C4×C61—24no—
102C2×C22⋊C4×C61—24no—
103C2×C22⋊C4×C61—24no—
104C2×C22⋊C4×C61—24no—
105C2×C22⋊C4×C61—24no—
106C2×C22⋊C4×C61—24no—
107C2×C22⋊C4×C61—22no—
108C2×C22⋊C4×C61—24no—
109C2×C22⋊C4×C61—22no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—22no—
113C2×C22⋊C4×C61—24no—
114C2×C22⋊C4×C61—24no—
115C2×C22⋊C4×C61—24no—
116C2×C22⋊C4×C61—22no—
117C2×C22⋊C4×C61—22no—
118C2×C22⋊C4×C61—22no—
119C2×C22⋊C4×C61—24no—
120C2×C22⋊C4×C61—24no—
121C2×C22⋊C4×C61—42no—
122C2×C22⋊C4×C61—42no—
123C2×C22⋊C4×C61—42no—
124C2×C22⋊C4×C61—42no—
125C2×C22⋊C4×C61D414yes—
126C2×C22⋊C4×C61D418yescomplemented
127#95×C61—24no—
128#95×C61—22no—
129#95×C61—22no—
130#95×C61—24no—
131#95×C61—24no—
132#95×C61—42no—
133C24×C61—22no—
134C24×C61—22no—
135C24×C61—22no—
136C24×C61—22no—
137C24×C61—28no—
138C24×C61—28no—
139C24×C61—216no—
140C24×C61—216no—
141C24×C61—28no—
142C24×C61—22no—
143C24×C61—22no—
144C24×C61—22no—
145C24×C61—22no—
146C24×C61—22no—
147C24×C61—22no—
148C24×C61—22no—
149C24×C61—22no—
150C24×C61—22no—
151C24×C61—22no—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—28no—
155C24×C61—28no—
156C24×C61—21no—
157C24×C61—22no—
158C24×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—21no—
162C24×C61—21no—
163C24×C61—22no—
164C24×C61—22no—
165C24×C61—22no—
166C24×C61—48no—
167C24×C61—48no—
168C24×C61—48no—
169C24×C61—48no—
170C24×C61—48no—
171C24×C61—48no—
172C24×C61—48no—
173C24×C61—48no—
174C24×C61—48no—
175C24×C61—44no—
176C24×C61—44no—
177C24×C61—48no—
178C24×C61—44no—
179C24×C61—44no—
180C24×C61—44no—
181C24×C61—44no—
182C24×C61C2×D412yes—
183C24×C61C2×D414yes—
184C24×C61C2×D414yes—
185C24×C61C2×D412yes—
186C24×C61C2×D412yes—
187C24×C61C2×D412yes—
188C24×C61C2×D412yes—
189C24×C61#4114yes—
190C24×C61#4112yes—
191C24×C61#4112yes—
192C24×C61#4112yes—
193C24×C61C2411yescharacteristic
194C2×D4×C61—216no—
195C2×D4×C61—28no—
196C2×D4×C61—28no—
197C2×D4×C61—28no—
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—44no—
205C2×D4×C61—44no—
206C2×D4×C61—44no—
207C2×D4×C61—44no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—22no—
211C22×C4×C61—28no—
212C22×C4×C61—28no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—22no—
216C22×C4×C61—22no—
217C22×C4×C61—22no—
218C22×C4×C61—22no—
219C22×C4×C61—22no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—22no—
223C22×C4×C61—22no—
224C22×C4×C61—21no—
225C22×C4×C61—22no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
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—28no—
236C22×C4×C61—21no—
237C22×C4×C61—22no—
238C22×C4×C61—22no—
239C22×C4×C61—21no—
240C22×C4×C61—22no—
241C22×C4×C61—22no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—22no—
245C22×C4×C61—21no—
246C22×C4×C61—22no—
247C22×C4×C61—21no—
248C22×C4×C61—22no—
249C22×C4×C61—22no—
250C22×C4×C61—22no—
251C22×C4×C61—22no—
252C22×C4×C61—22no—
253C22×C4×C61—44no—
254C22×C4×C61—48no—
255C22×C4×C61—48no—
256C22×C4×C61—48no—
257C22×C4×C61—48no—
258C22×C4×C61—44no—
259C22×C4×C61—44no—
260C22×C4×C61C2×D412yes—
261C22×C4×C61C2×D412yes—
262C22×C4×C61C2×D414yes—
263C22×C4×C61C2×D414yes—
264C22×C4×C61C2×D412yes—
265C22×C4×C61C2×D414yes—
266C4⋊C4×C61—48no—
267C22⋊C4×C61—216no—
268C22⋊C4×C61—216no—
269C22⋊C4×C61—28no—
270C22⋊C4×C61—216no—
271C22⋊C4×C61—48no—
272C22⋊C4×C61—44no—
273C22⋊C4×C61—48no—
274C22⋊C4×C61—44no—
275C22⋊C4×C61—48no—
276C22⋊C4×C61—44no—
277C22⋊C4×C61—44no—
278C23×C61—22no—
279C23×C61—24no—
280C23×C61—22no—
281C23×C61—24no—
282C23×C61—22no—
283C23×C61—24no—
284C23×C61—22no—
285C23×C61—24no—
286C23×C61—24no—
287C23×C61—24no—
288C23×C61—24no—
289C23×C61—24no—
290C23×C61—24no—
291C23×C61—24no—
292C23×C61—24no—
293C23×C61—24no—
294C23×C61—232no—
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—24no—
306C23×C61—24no—
307C23×C61—24no—
308C23×C61—24no—
309C23×C61—24no—
310C23×C61—24no—
311C23×C61—24no—
312C23×C61—24no—
313C23×C61—22no—
314C23×C61—22no—
315C23×C61—22no—
316C23×C61—24no—
317C23×C61—24no—
318C23×C61—432no—
319C23×C61—432no—
320C23×C61—416no—
321C23×C61—416no—
322C23×C61—416no—
323C23×C61—416no—
324C23×C61—432no—
325C23×C61—432no—
326C23×C61—416no—
327C23×C61—42no—
328C23×C61—42no—
329C23×C61—42no—
330C23×C61—42no—
331C23×C61—42no—
332C23×C61—42no—
333C23×C61—42no—
334C23×C61—42no—
335C23×C61—42no—
336C23×C61—42no—
337C23×C61—42no—
338C23×C61—42no—
339C23×C61—42no—
340C23×C61—42no—
341C23×C61—42no—
342C23×C61—42no—
343C23×C61—416no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—42no—
348C23×C61—41no—
349C23×C61—42no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—41no—
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#12014yes—
363C23×C61#12118yes—
364C23×C61#12114yes—
365C23×C61#12114yes—
366C23×C61#12114yes—
367C23×C61#12314yes—
368C23×C61#12314yes—
369C23×C61#12414yes—
370C23×C61C22×D411yescharacteristic
371C23×C61C22×D411yescharacteristic
372C23×C61C22×D411yescharacteristic
373C23×C61C22×D412yes—
374C23×C61C22×D411yescharacteristic
375C23×C61C2×#4111yescharacteristic
376C23×C61C2×#4111yescharacteristic
377C23×C61C2×#4111yescharacteristic
378C23×C61C2×#4112yes—
379C23×C61H(5,𝔽2)12yes—
380C23×C61H(5,𝔽2)12yes—
381D4×C61—432no—
382D4×C61—416no—
383C2×C4×C61—22no—
384C2×C4×C61—22no—
385C2×C4×C61—24no—
386C2×C4×C61—24no—
387C2×C4×C61—24no—
388C2×C4×C61—22no—
389C2×C4×C61—22no—
390C2×C4×C61—24no—
391C2×C4×C61—22no—
392C2×C4×C61—22no—
393C2×C4×C61—22no—
394C2×C4×C61—22no—
395C2×C4×C61—24no—
396C2×C4×C61—24no—
397C2×C4×C61—24no—
398C2×C4×C61—24no—
399C2×C4×C61—416no—
400C2×C4×C61—416no—
401C2×C4×C61—42no—
402C2×C4×C61—41no—
403C2×C4×C61—41no—
404C2×C4×C61—42no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—42no—
408C2×C4×C61—42no—
409C2×C4×C61—42no—
410C2×C4×C61—42no—
411C2×C4×C61—42no—
412C2×C4×C61—42no—
413C2×C4×C61—42no—
414C2×C4×C61—42no—
415C2×C4×C61—41no—
416C2×C4×C61—42no—
417C2×C4×C61—41no—
418C2×C4×C61—42no—
419C2×C4×C61—41no—
420C2×C4×C61—42no—
421C2×C4×C61—41no—
422C2×C4×C61—42no—
423C2×C4×C61—42no—
424C2×C4×C61—41no—
425C2×C4×C61—42no—
426C2×C4×C61—41no—
427C2×C4×C61—42no—
428C2×C4×C61—42no—
429C2×C4×C61—42no—
430C2×C4×C61—42no—
431C2×C4×C61—42no—
432C2×C4×C61#12014yescomplemented
433#14725C6111yesmaximal, characteristic, direct product factor, Sylow
434C22×C61—24no—
435C22×C61—24no—
436C22×C61—24no—
437C22×C61—24no—
438C22×C61—28no—
439C22×C61—24no—
440C22×C61—28no—
441C22×C61—28no—
442C22×C61—28no—
443C22×C61—24no—
444C22×C61—28no—
445C22×C61—28no—
446C22×C61—28no—
447C22×C61—464no—
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—44no—
457C22×C61—44no—
458C22×C61—44no—
459C22×C61—44no—
460C22×C61—42no—
461C22×C61—42no—
462C22×C61—44no—
463C22×C61—44no—
464C22×C61—42no—
465C22×C61—81no—
466C22×C61—81no—
467C22×C61—81no—
468C22×C61—81no—
469C22×C61—82no—
470C22×C61—82no—
471C22×C61#39418yescomplemented
472C22×C61C2×#12011yescharacteristic
473C22×C61C2×#12011yescharacteristic
474C22×C61C2×#12111yescharacteristic
475C22×C61C2×#12112yes—
476C22×C61C2×#12111yescharacteristic
477C22×C61C2×#12111yescharacteristic
478C22×C61C2×#12311yescharacteristic
479C22×C61C2×#12311yescharacteristic
480C22×C61#52511yescharacteristic
481C22×C61#52512yes—
482C22×C61C2×#12411yescharacteristic
483C22×C61#53412yes—
484C22×C61#53411yescharacteristic
485C22×C61#53511yescharacteristic
486C22×C61#53812yes—
487C22×C61D4212yes—
488C22×C61D4212yes—
489C22×C61#54612yes—
490C22×C61#54612yes—
491C22×C61#54612yes—
492C22×C61#54612yes—
493C22×C61#55112yes—
494C22×C61#55112yes—
495C4×C61—24no—
496C4×C61—42no—
497C4×C61—44no—
498C4×C61—42no—
499C4×C61—44no—
500C4×C61—81no—
501C4×C61—81no—
502C4×C61—82no—
503C22×#120C2×C6111yescharacteristic
504C23×C22⋊C4C2×C6111yescharacteristic, complemented
505C2×#394C2×C6112yescomplemented
506C2×#386C2×C6111yescharacteristic, complemented
507C2×#386C2×C6111yescharacteristic, complemented
508C2×#380C2×C6111yescharacteristic, complemented
509C2×#379C2×C6111yescharacteristic, complemented
510#1440C2×C6112yescomplemented
511#1439C2×C6112yescomplemented
512#1438C2×C6112yescomplemented
513C22⋊#95C2×C6111yescharacteristic, complemented
514C2×C61—28no—
515C2×C61—48no—
516C2×C61—82no—
517C2×C61C2×#39411yescharacteristic
518C2×C61#240811yescharacteristic
519C2×C61#241011yescharacteristic
520C2×C61#241012yes—
521C2×C61#241111yescharacteristic
522C2×C61#241212yes—
523C2×C61#241812yes—
524C2×C61#247212yes—
525C2×C61#253411yescharacteristic
526C2×C61#261711yescharacteristic
527C2×C61#284711yescharacteristic
528C26C22×C6111yescharacteristic
529C23×D4C22×C6111yescharacteristic
530C23×D4C22×C6112yes—
531C24×C4C22×C6111yescharacteristic
532C24×C4C22×C6111yescharacteristic
533C2×#120—24no—
534C2×#120—24no—
535C2×#120—24no—
536C22×C4⋊C4C22×C6112yescomplemented
537C22×C22⋊C4—24no—
538C22×C22⋊C4—28no—
539C22×C22⋊C4C22×C6112yes—
540C22×C22⋊C4C22×C6112yes—
541C22×C22⋊C4C22×C6112yes—
542C22×C22⋊C4C22×C6111yescharacteristic
543C22×C22⋊C4C22×C6111yescharacteristic
544C22×C22⋊C4C22×C6111yescharacteristic
545C22×C22⋊C4C22×C6112yes—
546C22×C22⋊C4C22×C6112yes—
547C22×C22⋊C4C22×C6111yescharacteristic, complemented
548C22×C22⋊C4C22×C6112yescomplemented
549C22×C22⋊C4C22×C6111yescharacteristic, complemented
550#394—28no—
551#386—24no—
552#386—24no—
553#380—24no—
554#379—24no—
555C2×#95C22×C6112yescomplemented
556C2×#95C22×C6112yescomplemented
557C2×#95C22×C6111yescharacteristic, complemented
558C2×#95C22×C6112yescomplemented
559C2×#95C22×C6111yescharacteristic, complemented
560C2×#95C22×C6112yescomplemented
561C61#1472511yescharacteristic, direct product factor, Sylow
562C25—24no—
563C25—22no—
564C25—24no—
565C25—22no—
566C25—22no—
567C25—22no—
568C25—22no—
569C25—22no—
570C25—42no—
571C25—42no—
572C25D4×C6114yes—
573C25C23×C6111yescharacteristic
574C25C23×C6112yes—
575C25C23×C6111yescharacteristic
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—22no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—42no—
588C22×D4—42no—
589C22×D4D4×C6114yes—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—24no—
594C23×C4—24no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—42no—
598C23×C4—42no—
599C23×C4D4×C6114yescomplemented
600C23×C4C23×C6112yes—
601C23×C4C23×C6111yescharacteristic
602C23×C4C23×C6111yescharacteristic
603C23×C4C23×C6111yescharacteristic
604C23×C4C23×C6112yes—
605C23×C4C23×C6112yes—
606C23×C4C23×C6111yescharacteristic
607C23×C4C23×C6111yescharacteristic
608#120—232no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—42no—
612C2×C22⋊C4—232no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—24no—
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—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4D4×C6114yes—
643C2×C22⋊C4D4×C6118yescomplemented
644#95—24no—
645#95—22no—
646#95—22no—
647#95—24no—
648#95—24no—
649#95—42no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—216no—
657C24—216no—
658C24—28no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—22no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—22no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—22no—
682C24—22no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24C2×D4×C6112yes—
700C24C2×D4×C6114yes—
701C24C2×D4×C6114yes—
702C24C2×D4×C6112yes—
703C24C2×D4×C6112yes—
704C24C2×D4×C6112yes—
705C24C2×D4×C6112yes—
706C24#41×C6114yes—
707C24#41×C6112yes—
708C24#41×C6112yes—
709C24#41×C6112yes—
710C24C24×C6111yescharacteristic
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—22no—
742C22×C4—21no—
743C22×C4—22no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—21no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×D4×C6112yes—
778C22×C4C2×D4×C6112yes—
779C22×C4C2×D4×C6114yes—
780C22×C4C2×D4×C6114yes—
781C22×C4C2×D4×C6112yes—
782C22×C4C2×D4×C6114yes—
783C4⋊C4—48no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—28no—
787C22⋊C4—216no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—22no—
808C23—24no—
809C23—22no—
810C23—24no—
811C23—232no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—432no—
836C23—432no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—416no—
842C23—432no—
843C23—432no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—416no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—41no—
862C23—42no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—42no—
870C23—42no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—42no—
875C23—41no—
876C23—41no—
877C23—42no—
878C23—41no—
879C23#120×C6114yes—
880C23#121×C6118yes—
881C23#121×C6114yes—
882C23#121×C6114yes—
883C23#121×C6114yes—
884C23#123×C6114yes—
885C23#123×C6114yes—
886C23#124×C6114yes—
887C23C22×D4×C6111yescharacteristic
888C23C22×D4×C6111yescharacteristic
889C23C22×D4×C6111yescharacteristic
890C23C22×D4×C6112yes—
891C23C22×D4×C6111yescharacteristic
892C23C2×#41×C6111yescharacteristic
893C23C2×#41×C6111yescharacteristic
894C23C2×#41×C6111yescharacteristic
895C23C2×#41×C6112yes—
896C23H(5,𝔽2)×C6112yes—
897C23H(5,𝔽2)×C6112yes—
898D4—432no—
899D4—416no—
900C2×C4—22no—
901C2×C4—24no—
902C2×C4—24no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—416no—
917C2×C4—416no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—42no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—42no—
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—41no—
944C2×C4—42no—
945C2×C4—41no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4#120×C6114yescomplemented
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—28no—
956C22—24no—
957C22—28no—
958C22—28no—
959C22—28no—
960C22—28no—
961C22—28no—
962C22—28no—
963C22—464no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—44no—
980C22—44no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—82no—
986C22—82no—
987C22C61×#39418yescomplemented
988C22C2×#120×C6111yescharacteristic
989C22C2×#120×C6111yescharacteristic
990C22C2×#121×C6111yescharacteristic
991C22C2×#121×C6111yescharacteristic
992C22C2×#121×C6112yes—
993C22C2×#121×C6111yescharacteristic
994C22C2×#123×C6111yescharacteristic
995C22C2×#123×C6111yescharacteristic
996C22C61×#52511yescharacteristic
997C22C61×#52512yes—
998C22C2×#124×C6111yescharacteristic
999C22C61×#53411yescharacteristic
1000C22C61×#53412yes—
1001C22C61×#53511yescharacteristic
1002C22C61×#53812yes—
1003C22D42×C6112yes—
1004C22D42×C6112yes—
1005C22C61×#54612yes—
1006C22C61×#54612yes—
1007C22C61×#54612yes—
1008C22C61×#54612yes—
1009C22C61×#55112yes—
1010C22C61×#55112yes—
1011C4—24no—
1012C4—42no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—81no—
1017C4—81no—
1018C4—82no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×C61×#39411yescharacteristic
1023C2C61×#240811yescharacteristic
1024C2C61×#241011yescharacteristic
1025C2C61×#241012yes—
1026C2C61×#241111yescharacteristic
1027C2C61×#241212yes—
1028C2C61×#241812yes—
1029C2C61×#247212yes—
1030C2C61×#253411yescharacteristic
1031C2C61×#261711yescharacteristic
1032C2C61×#284711yescharacteristic
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×#380C2semidirect
7. C2×C61×#379C2semidirect
8. C61×#1440C2semidirect
9. C61×#1439C2semidirect
10. C61×#1438C2semidirect
11. C61×C22⋊#95C2semidirect
20. C22×C4⋊C4×C61C22semidirect
31. C22×C22⋊C4×C61C22semidirect
32. C22×C22⋊C4×C61C22semidirect
33. C22×C22⋊C4×C61C22semidirect
39. C2×#95×C61C22semidirect
40. C2×#95×C61C22semidirect
41. C2×#95×C61C22semidirect
42. C2×#95×C61C22semidirect
43. C2×#95×C61C22semidirect
44. C2×#95×C61C22semidirect
82. C23×C4×C61D4semidirect
126. C2×C22⋊C4×C61D4semidirect
432. C2×C4×C61#120semidirect
433. #14725C61direct (N × H)
471. C22×C61#394semidirect
504. C23×C22⋊C4C2×C61semidirect
505. C2×#394C2×C61semidirect
506. C2×#386C2×C61semidirect
507. C2×#386C2×C61semidirect
508. C2×#380C2×C61semidirect
509. C2×#379C2×C61semidirect
510. #1440C2×C61semidirect
511. #1439C2×C61semidirect
512. #1438C2×C61semidirect
513. C22⋊#95C2×C61semidirect
536. C22×C4⋊C4C22×C61semidirect
547. C22×C22⋊C4C22×C61semidirect
548. C22×C22⋊C4C22×C61semidirect
549. C22×C22⋊C4C22×C61semidirect
555. C2×#95C22×C61semidirect
556. C2×#95C22×C61semidirect
557. C2×#95C22×C61semidirect
558. C2×#95C22×C61semidirect
559. C2×#95C22×C61semidirect
560. C2×#95C22×C61semidirect
561. C61#14725direct (N × H)
599. C23×C4D4×C61semidirect
643. C2×C22⋊C4D4×C61semidirect
949. C2×C4#120×C61semidirect
987. 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×#3802
C2×C61×#3792
C61×#14402
C61×#14392
C61×#14382
C61×C22⋊#952
#1472561