Finite Group Databasebeta

← C61×#14722 #29518155

Subgroups — C61×#14722 #29518155

Order 15616.

3246 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C61C211yesmaximal, characteristic, complemented
2C22×C4×D4×C61C211yesmaximal, characteristic, complemented
3C2×C61×#394C211yesmaximal, characteristic, complemented
4C2×C61×#392C212yesmaximal, complemented
5C2×C61×#392C211yesmaximal, characteristic, complemented
6C2×C61×#386C212yesmaximal, complemented
7C61×#1441C211yesmaximal, characteristic, complemented
8C61×#1439C211yesmaximal, characteristic, complemented
9C61×#1438C212yesmaximal, complemented
10C61×#1437C212yesmaximal, complemented
11C61×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C61C2211yescharacteristic
13C23×D4×C61C2212yes—
14C23×D4×C61C2211yescharacteristic
15C23×D4×C61C2212yes—
16C24×C4×C61C2211yescharacteristic
17C24×C4×C61C2211yescharacteristic
18C2×#121×C61—24no—
19C2×#121×C61—28no—
20C2×C4×D4×C61—24no—
21C2×C4×D4×C61—24no—
22C2×C4×D4×C61—24no—
23C22×C4⋊C4×C61C2211yescharacteristic
24C22×C4⋊C4×C61C2211yescharacteristic
25C22×C22⋊C4×C61C2212yes—
26C22×C22⋊C4×C61C2211yescharacteristic
27C22×C22⋊C4×C61C2212yes—
28C22×C22⋊C4×C61C2212yes—
29C22×C22⋊C4×C61C2212yes—
30C22×C22⋊C4×C61C2212yes—
31C22×C22⋊C4×C61C2212yes—
32C22×C22⋊C4×C61C2211yescharacteristic
33C22×C42×C61C2211yescharacteristic
34C61×#394—24no—
35C61×#392—28no—
36C61×#392—24no—
37C61×#386—28no—
38C2×#95×C61C2212yes—
39C2×#95×C61C2212yes—
40C2×#95×C61C2211yescharacteristic
41C2×#95×C61C2212yes—
42C2×#95×C61C2211yescharacteristic
43C2×#95×C61C2212yes—
44C25×C61C2312yes—
45C25×C61C2311yescharacteristic
46C25×C61C2311yescharacteristic
47C22×D4×C61—22no—
48C22×D4×C61—22no—
49C22×D4×C61—22no—
50C22×D4×C61—22no—
51C22×D4×C61—24no—
52C22×D4×C61—24no—
53C22×D4×C61—24no—
54C22×D4×C61—24no—
55C22×D4×C61—24no—
56C22×D4×C61—24no—
57C22×D4×C61—24no—
58C22×D4×C61—24no—
59C22×D4×C61—24no—
60C22×D4×C61—22no—
61C22×D4×C61—24no—
62C22×D4×C61—22no—
63C22×D4×C61—22no—
64C22×D4×C61—22no—
65C22×D4×C61—22no—
66C22×D4×C61—24no—
67C22×D4×C61—42no—
68C22×D4×C61—42no—
69C22×D4×C61—42no—
70C22×D4×C61—42no—
71C22×D4×C61—42no—
72C22×D4×C61D414yescomplemented
73C23×C4×C61—22no—
74C23×C4×C61—22no—
75C23×C4×C61—22no—
76C23×C4×C61—22no—
77C23×C4×C61—22no—
78C23×C4×C61—24no—
79C23×C4×C61—24no—
80C23×C4×C61—42no—
81C23×C4×C61—42no—
82C23×C4×C61D414yescomplemented
83C23×C4×C61C2312yes—
84C23×C4×C61C2311yescharacteristic
85C23×C4×C61C2312yes—
86C23×C4×C61C2311yescharacteristic
87C23×C4×C61C2312yes—
88C23×C4×C61C2311yescharacteristic
89C23×C4×C61C2311yescharacteristic
90C23×C4×C61C2311yescharacteristic
91#121×C61—232no—
92C4×D4×C61—232no—
93C2×C4⋊C4×C61—22no—
94C2×C4⋊C4×C61—22no—
95C2×C4⋊C4×C61—24no—
96C2×C4⋊C4×C61—22no—
97C2×C4⋊C4×C61D414yescomplemented
98C2×C22⋊C4×C61—22no—
99C2×C22⋊C4×C61—22no—
100C2×C22⋊C4×C61—22no—
101C2×C22⋊C4×C61—22no—
102C2×C22⋊C4×C61—22no—
103C2×C22⋊C4×C61—24no—
104C2×C22⋊C4×C61—24no—
105C2×C22⋊C4×C61—24no—
106C2×C22⋊C4×C61—24no—
107C2×C22⋊C4×C61—24no—
108C2×C22⋊C4×C61—24no—
109C2×C22⋊C4×C61—24no—
110C2×C22⋊C4×C61—24no—
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—42no—
117C2×C22⋊C4×C61—42no—
118C2×C22⋊C4×C61—42no—
119C2×C22⋊C4×C61—42no—
120C2×C22⋊C4×C61D418yescomplemented
121C2×C22⋊C4×C61D414yescomplemented
122C2×C42×C61—22no—
123C2×C42×C61—22no—
124C2×C42×C61—22no—
125#95×C61—24no—
126#95×C61—24no—
127#95×C61—22no—
128#95×C61—24no—
129#95×C61—22no—
130#95×C61—42no—
131C24×C61—21no—
132C24×C61—21no—
133C24×C61—21no—
134C24×C61—21no—
135C24×C61—22no—
136C24×C61—22no—
137C24×C61—22no—
138C24×C61—21no—
139C24×C61—21no—
140C24×C61—21no—
141C24×C61—21no—
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—22no—
155C24×C61—22no—
156C24×C61—22no—
157C24×C61—22no—
158C24×C61—22no—
159C24×C61—22no—
160C24×C61—22no—
161C24×C61C2×D414yes—
162C24×C61C2×D412yes—
163C24×C61C2×D412yes—
164C24×C61C2×D412yes—
165C24×C61C2×D412yes—
166C24×C61#4112yes—
167C24×C61#4112yes—
168C24×C61C2411yescharacteristic
169C2×D4×C61—28no—
170C2×D4×C61—28no—
171C2×D4×C61—28no—
172C2×D4×C61—28no—
173C2×D4×C61—28no—
174C2×D4×C61—28no—
175C2×D4×C61—28no—
176C2×D4×C61—216no—
177C2×D4×C61—216no—
178C2×D4×C61—28no—
179C2×D4×C61—48no—
180C2×D4×C61—48no—
181C2×D4×C61—48no—
182C2×D4×C61—48no—
183C2×D4×C61—48no—
184C2×D4×C61—48no—
185C2×D4×C61—44no—
186C2×D4×C61—48no—
187C2×D4×C61—48no—
188C2×D4×C61—48no—
189C2×D4×C61—48no—
190C2×D4×C61—48no—
191C2×D4×C61—48no—
192C2×D4×C61—48no—
193C2×D4×C61—48no—
194C2×D4×C61—44no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—22no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—22no—
203C22×C4×C61—22no—
204C22×C4×C61—28no—
205C22×C4×C61—22no—
206C22×C4×C61—22no—
207C22×C4×C61—22no—
208C22×C4×C61—22no—
209C22×C4×C61—22no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—22no—
215C22×C4×C61—22no—
216C22×C4×C61—22no—
217C22×C4×C61—22no—
218C22×C4×C61—22no—
219C22×C4×C61—22no—
220C22×C4×C61—22no—
221C22×C4×C61—22no—
222C22×C4×C61—22no—
223C22×C4×C61—22no—
224C22×C4×C61—22no—
225C22×C4×C61—28no—
226C22×C4×C61—28no—
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—44no—
235C22×C4×C61—48no—
236C22×C4×C61—48no—
237C22×C4×C61—48no—
238C22×C4×C61—48no—
239C22×C4×C61—44no—
240C22×C4×C61—44no—
241C22×C4×C61C2×D414yes—
242C22×C4×C61C2×D412yes—
243C22×C4×C61C2×D412yes—
244C22×C4×C61C2×D414yes—
245C22×C4×C61C2×D412yes—
246C22×C4×C61C2×D412yes—
247C22×C4×C61C2×D412yes—
248C22×C4×C61C2×D412yes—
249C22×C4×C61C2×D412yes—
250C22×C4×C61C2×D412yes—
251C22×C4×C61#4114yes—
252C22×C4×C61#4112yes—
253C4⋊C4×C61—28no—
254C4⋊C4×C61—28no—
255C22⋊C4×C61—28no—
256C22⋊C4×C61—28no—
257C22⋊C4×C61—216no—
258C22⋊C4×C61—48no—
259C22⋊C4×C61—48no—
260C22⋊C4×C61—48no—
261C22⋊C4×C61—48no—
262C22⋊C4×C61—48no—
263C42×C61—28no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—22no—
269C23×C61—22no—
270C23×C61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—24no—
278C23×C61—22no—
279C23×C61—22no—
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—24no—
289C23×C61—24no—
290C23×C61—24no—
291C23×C61—24no—
292C23×C61—24no—
293C23×C61—24no—
294C23×C61—24no—
295C23×C61—24no—
296C23×C61—24no—
297C23×C61—41no—
298C23×C61—42no—
299C23×C61—42no—
300C23×C61—42no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—42no—
305C23×C61—42no—
306C23×C61—42no—
307C23×C61—42no—
308C23×C61—42no—
309C23×C61—42no—
310C23×C61—42no—
311C23×C61—42no—
312C23×C61—42no—
313C23×C61—42no—
314C23×C61—42no—
315C23×C61—42no—
316C23×C61—42no—
317C23×C61—42no—
318C23×C61—42no—
319C23×C61—42no—
320C23×C61—42no—
321C23×C61—42no—
322C23×C61—42no—
323C23×C61—42no—
324C23×C61—42no—
325C23×C61—42no—
326C23×C61—42no—
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#12114yes—
344C23×C61#12114yescomplemented
345C23×C61C22×D411yescharacteristic
346C23×C61C22×D411yescharacteristic
347C23×C61C22×D411yescharacteristic
348C23×C61C22×D412yes—
349C23×C61C22×D411yescharacteristic
350C23×C61C2×#4111yescharacteristic
351C23×C61C2×#4111yescharacteristic
352C23×C61C2×#4111yescharacteristic
353C23×C61C2×#4112yes—
354C23×C61H(5,𝔽2)12yes—
355C23×C61H(5,𝔽2)12yes—
356D4×C61—232no—
357D4×C61—416no—
358D4×C61—432no—
359D4×C61—432no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—24no—
371C2×C4×C61—24no—
372C2×C4×C61—24no—
373C2×C4×C61—24no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—24no—
377C2×C4×C61—24no—
378C2×C4×C61—24no—
379C2×C4×C61—24no—
380C2×C4×C61—24no—
381C2×C4×C61—24no—
382C2×C4×C61—24no—
383C2×C4×C61—24no—
384C2×C4×C61—416no—
385C2×C4×C61—416no—
386C2×C4×C61—41no—
387C2×C4×C61—42no—
388C2×C4×C61—42no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—42no—
393C2×C4×C61—42no—
394C2×C4×C61—42no—
395C2×C4×C61—42no—
396C2×C4×C61—42no—
397C2×C4×C61—42no—
398C2×C4×C61—42no—
399C2×C4×C61—42no—
400C2×C4×C61—42no—
401C2×C4×C61—42no—
402C2×C4×C61—42no—
403C2×C4×C61—42no—
404C2×C4×C61—42no—
405C2×C4×C61—42no—
406C2×C4×C61—42no—
407C2×C4×C61#12014yes—
408C2×C4×C61#12014yes—
409C2×C4×C61#12114yescomplemented
410#14722C6111yesmaximal, characteristic, direct product factor, Sylow
411C22×C61—24no—
412C22×C61—24no—
413C22×C61—24no—
414C22×C61—28no—
415C22×C61—24no—
416C22×C61—42no—
417C22×C61—42no—
418C22×C61—42no—
419C22×C61—42no—
420C22×C61—42no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61—44no—
424C22×C61—44no—
425C22×C61—44no—
426C22×C61—42no—
427C22×C61—42no—
428C22×C61—44no—
429C22×C61—44no—
430C22×C61—44no—
431C22×C61—44no—
432C22×C61—42no—
433C22×C61—44no—
434C22×C61—44no—
435C22×C61—44no—
436C22×C61—44no—
437C22×C61—44no—
438C22×C61—44no—
439C22×C61—44no—
440C22×C61—82no—
441C22×C61—82no—
442C22×C61—82no—
443C22×C61—82no—
444C22×C61—82no—
445C22×C61—82no—
446C22×C61—82no—
447C22×C61—82no—
448C22×C61C2×#12011yescharacteristic
449C22×C61C2×#12011yescharacteristic
450C22×C61C2×#12111yescharacteristic
451C22×C61C2×#12111yescharacteristic
452C22×C61C2×#12111yescharacteristic
453C22×C61#52511yescharacteristic
454C22×C61#52511yescharacteristic
455C22×C61#52511yescharacteristic
456C22×C61#52512yes—
457C22×C61#53212yes—
458C22×C61#53211yescharacteristic
459C22×C61#53411yescharacteristic
460C22×C61#53511yescharacteristic
461C22×C61#53812yes—
462C22×C61#54012yes—
463C22×C61D4212yes—
464C22×C61D4212yes—
465C22×C61D4212yes—
466C22×C61#54612yes—
467C22×C61#54612yes—
468C22×C61#54612yes—
469C22×C61#55012yes—
470C22×C61#55312yes—
471C4×C61—24no—
472C4×C61—24no—
473C4×C61—24no—
474C4×C61—42no—
475C4×C61—44no—
476C4×C61—44no—
477C4×C61—42no—
478C4×C61—82no—
479C22×#121C2×C6111yescharacteristic, complemented
480C22×C4×D4C2×C6111yescharacteristic, complemented
481C2×#394C2×C6111yescharacteristic, complemented
482C2×#392C2×C6112yescomplemented
483C2×#392C2×C6111yescharacteristic, complemented
484C2×#386C2×C6112yescomplemented
485#1441C2×C6111yescharacteristic, complemented
486#1439C2×C6111yescharacteristic, complemented
487#1438C2×C6112yescomplemented
488#1437C2×C6112yescomplemented
489C22⋊#95C2×C6111yescharacteristic, complemented
490C2×C61—44no—
491C2×C61—44no—
492C2×C61—84no—
493C2×C61#238811yescharacteristic
494C2×C61#240311yescharacteristic
495C2×C61#240811yescharacteristic
496C2×C61#242412yes—
497C2×C61#242812yes—
498C2×C61#243111yescharacteristic
499C2×C61#245612yes—
500C2×C61#246412yes—
501C2×C61#254311yescharacteristic
502C2×C61#263511yescharacteristic
503C2×C61#284711yescharacteristic
504C23×D4C22×C6111yescharacteristic
505C23×D4C22×C6112yes—
506C23×D4C22×C6111yescharacteristic
507C23×D4C22×C6112yes—
508C24×C4C22×C6111yescharacteristic
509C24×C4C22×C6111yescharacteristic
510C2×#121—24no—
511C2×#121—28no—
512C2×C4×D4—24no—
513C2×C4×D4—24no—
514C2×C4×D4—24no—
515C22×C4⋊C4C22×C6111yescharacteristic
516C22×C4⋊C4C22×C6111yescharacteristic
517C22×C22⋊C4C22×C6112yes—
518C22×C22⋊C4C22×C6111yescharacteristic
519C22×C22⋊C4C22×C6112yes—
520C22×C22⋊C4C22×C6112yes—
521C22×C22⋊C4C22×C6112yes—
522C22×C22⋊C4C22×C6112yes—
523C22×C22⋊C4C22×C6111yescharacteristic
524C22×C22⋊C4C22×C6112yes—
525C22×C42C22×C6111yescharacteristic
526#394—24no—
527#392—28no—
528#392—24no—
529#386—28no—
530C2×#95C22×C6111yescharacteristic
531C2×#95C22×C6112yes—
532C2×#95C22×C6111yescharacteristic
533C2×#95C22×C6112yes—
534C2×#95C22×C6112yes—
535C2×#95C22×C6112yes—
536C61#1472211yescharacteristic, direct product factor, Sylow
537C25C23×C6112yes—
538C25C23×C6111yescharacteristic
539C25C23×C6111yescharacteristic
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—24no—
550C22×D4—24no—
551C22×D4—24no—
552C22×D4—24no—
553C22×D4—22no—
554C22×D4—24no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—24no—
560C22×D4—42no—
561C22×D4—42no—
562C22×D4—42no—
563C22×D4—42no—
564C22×D4—42no—
565C22×D4D4×C6114yescomplemented
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—24no—
572C23×C4—24no—
573C23×C4—42no—
574C23×C4—42no—
575C23×C4D4×C6114yescomplemented
576C23×C4C23×C6112yes—
577C23×C4C23×C6111yescharacteristic
578C23×C4C23×C6111yescharacteristic
579C23×C4C23×C6112yes—
580C23×C4C23×C6112yes—
581C23×C4C23×C6111yescharacteristic
582C23×C4C23×C6111yescharacteristic
583C23×C4C23×C6111yescharacteristic
584#121—232no—
585C4×D4—232no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4D4×C6114yescomplemented
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—24no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4—42no—
612C2×C22⋊C4—42no—
613C2×C22⋊C4D4×C6114yescomplemented
614C2×C22⋊C4D4×C6118yescomplemented
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618#95—24no—
619#95—24no—
620#95—22no—
621#95—24no—
622#95—22no—
623#95—42no—
624C24—22no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24C2×D4×C6114yes—
655C24C2×D4×C6112yes—
656C24C2×D4×C6112yes—
657C24C2×D4×C6112yes—
658C24C2×D4×C6112yes—
659C24#41×C6112yes—
660C24#41×C6112yes—
661C24C24×C6111yescharacteristic
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—28no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—44no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—44no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—28no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—44no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—48no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4C2×D4×C6114yes—
735C22×C4C2×D4×C6112yes—
736C22×C4C2×D4×C6112yes—
737C22×C4C2×D4×C6114yes—
738C22×C4C2×D4×C6112yes—
739C22×C4C2×D4×C6112yes—
740C22×C4C2×D4×C6112yes—
741C22×C4C2×D4×C6112yes—
742C22×C4C2×D4×C6112yes—
743C22×C4C2×D4×C6112yes—
744C22×C4#41×C6114yes—
745C22×C4#41×C6112yes—
746C4⋊C4—28no—
747C4⋊C4—28no—
748C22⋊C4—28no—
749C22⋊C4—28no—
750C22⋊C4—216no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C42—28no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—24no—
761C23—24no—
762C23—24no—
763C23—24no—
764C23—24no—
765C23—24no—
766C23—24no—
767C23—24no—
768C23—24no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—41no—
791C23—42no—
792C23—42no—
793C23—41no—
794C23—41no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—41no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23#121×C6114yes—
837C23#121×C6114yescomplemented
838C23C22×D4×C6111yescharacteristic
839C23C22×D4×C6112yes—
840C23C22×D4×C6111yescharacteristic
841C23C22×D4×C6111yescharacteristic
842C23C22×D4×C6111yescharacteristic
843C23C2×#41×C6111yescharacteristic
844C23C2×#41×C6112yes—
845C23C2×#41×C6111yescharacteristic
846C23C2×#41×C6111yescharacteristic
847C23H(5,𝔽2)×C6112yes—
848C23H(5,𝔽2)×C6112yes—
849D4—232no—
850D4—416no—
851D4—432no—
852D4—432no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—416no—
878C2×C4—416no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—41no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4#120×C6114yes—
901C2×C4#120×C6114yes—
902C2×C4#121×C6114yescomplemented
903C22—24no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—28no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—42no—
920C22—42no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C2×#120×C6111yescharacteristic
941C22C2×#120×C6111yescharacteristic
942C22C2×#121×C6111yescharacteristic
943C22C2×#121×C6111yescharacteristic
944C22C2×#121×C6111yescharacteristic
945C22C61×#52511yescharacteristic
946C22C61×#52511yescharacteristic
947C22C61×#52511yescharacteristic
948C22C61×#52512yes—
949C22C61×#53211yescharacteristic
950C22C61×#53212yes—
951C22C61×#53411yescharacteristic
952C22C61×#53511yescharacteristic
953C22C61×#53812yes—
954C22C61×#54012yes—
955C22D42×C6112yes—
956C22D42×C6112yes—
957C22D42×C6112yes—
958C22C61×#54612yes—
959C22C61×#54612yes—
960C22C61×#54612yes—
961C22C61×#55012yes—
962C22C61×#55312yes—
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—44no—
968C4—44no—
969C4—42no—
970C4—82no—
971C2—44no—
972C2—44no—
973C2—84no—
974C2C61×#238811yescharacteristic
975C2C61×#240311yescharacteristic
976C2C61×#240811yescharacteristic
977C2C61×#242412yes—
978C2C61×#242812yes—
979C2C61×#243111yescharacteristic
980C2C61×#245612yes—
981C2C61×#246412yes—
982C2C61×#254311yescharacteristic
983C2C61×#263511yescharacteristic
984C2C61×#284711yescharacteristic
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×C4×D4×C61C2semidirect
3. C2×C61×#394C2semidirect
4. C2×C61×#392C2semidirect
5. C2×C61×#392C2semidirect
6. C2×C61×#386C2semidirect
7. C61×#1441C2semidirect
8. C61×#1439C2semidirect
9. C61×#1438C2semidirect
10. C61×#1437C2semidirect
11. C61×C22⋊#95C2semidirect
72. C22×D4×C61D4semidirect
82. C23×C4×C61D4semidirect
97. C2×C4⋊C4×C61D4semidirect
120. C2×C22⋊C4×C61D4semidirect
121. C2×C22⋊C4×C61D4semidirect
344. C23×C61#121semidirect
409. C2×C4×C61#121semidirect
410. #14722C61direct (N × H)
479. C22×#121C2×C61semidirect
480. C22×C4×D4C2×C61semidirect
481. C2×#394C2×C61semidirect
482. C2×#392C2×C61semidirect
483. C2×#392C2×C61semidirect
484. C2×#386C2×C61semidirect
485. #1441C2×C61semidirect
486. #1439C2×C61semidirect
487. #1438C2×C61semidirect
488. #1437C2×C61semidirect
489. C22⋊#95C2×C61semidirect
536. C61#14722direct (N × H)
565. C22×D4D4×C61semidirect
575. C23×C4D4×C61semidirect
590. C2×C4⋊C4D4×C61semidirect
613. C2×C22⋊C4D4×C61semidirect
614. C2×C22⋊C4D4×C61semidirect
837. C23#121×C61semidirect
902. C2×C4#121×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×C4×D4×C612
C2×C61×#3942
C2×C61×#3922
C2×C61×#3862
C61×#14412
C61×#14392
C61×#14382
C61×#14372
C61×C22⋊#952
#1472261