Finite Group Databasebeta

← C61×#10991 #29514424

Subgroups — C61×#10991 #29514424

Order 15616.

3122 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C61C211yesmaximal, characteristic
2C22×#99×C61C211yesmaximal, characteristic, complemented
3C61×#2308C211yesmaximal, characteristic, complemented
4C2×C61×#379C212yesmaximal, complemented
5C2×C61×#342C212yesmaximal, complemented
6C26×C61C2211yescharacteristic
7C23×D4×C61—21no—
8C23×D4×C61C2211yescharacteristic
9C2×#120×C61—24no—
10C2×#120×C61—22no—
11C2×#120×C61—24no—
12C2×#120×C61C414yescomplemented
13C22×C22⋊C4×C61—21no—
14C22×C22⋊C4×C61—24no—
15C22×C22⋊C4×C61C2212yes—
16C22×C22⋊C4×C61C2212yes—
17C22×C22⋊C4×C61C2211yescharacteristic
18C2×#99×C61—22no—
19C2×#99×C61—24no—
20C61×#386—24no—
21C61×#381—21no—
22C61×#379—24no—
23C61×#379—21no—
24C61×#379—24no—
25C61×#342—24no—
26C25×C61—21no—
27C25×C61—22no—
28C25×C61—22no—
29C25×C61—21no—
30C25×C61—22no—
31C25×C61—22no—
32C25×C61—22no—
33C25×C61—48no—
34C25×C61C2×C412yes—
35C25×C61D411yescharacteristic
36C25×C61D414yes—
37C25×C61C2311yescharacteristic
38C22×D4×C61—28no—
39C22×D4×C61—24no—
40C22×D4×C61—22no—
41C22×D4×C61—22no—
42C22×D4×C61—22no—
43C22×D4×C61—22no—
44C22×D4×C61—22no—
45C22×D4×C61—22no—
46C22×D4×C61—48no—
47C22×D4×C61C2×C412yes—
48C22×D4×C61D412yes—
49C23×C4×C61—21no—
50C23×C4×C61—22no—
51C23×C4×C61D411yescharacteristic
52C23×C4×C61D414yescomplemented
53#120×C61—216no—
54#120×C61—28no—
55#120×C61—28no—
56C2×C22⋊C4×C61—28no—
57C2×C22⋊C4×C61—22no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—24no—
60C2×C22⋊C4×C61—22no—
61C2×C22⋊C4×C61—22no—
62C2×C22⋊C4×C61—22no—
63C2×C22⋊C4×C61—22no—
64C2×C22⋊C4×C61—216no—
65C2×C22⋊C4×C61—22no—
66C2×C22⋊C4×C61—22no—
67C2×C22⋊C4×C61—22no—
68C2×C22⋊C4×C61—22no—
69C2×C22⋊C4×C61—22no—
70C2×C22⋊C4×C61—22no—
71C2×C22⋊C4×C61—22no—
72C2×C22⋊C4×C61—24no—
73C2×C22⋊C4×C61—416no—
74C2×C22⋊C4×C61C2×C412yes—
75C2×C22⋊C4×C61D414yes—
76C2×C22⋊C4×C61D414yescomplemented
77#99×C61—28no—
78#95×C61—24no—
79C24×C61—216no—
80C24×C61—28no—
81C24×C61—22no—
82C24×C61—24no—
83C24×C61—24no—
84C24×C61—24no—
85C24×C61—24no—
86C24×C61—22no—
87C24×C61—24no—
88C24×C61—24no—
89C24×C61—22no—
90C24×C61—21no—
91C24×C61—24no—
92C24×C61—24no—
93C24×C61—22no—
94C24×C61—21no—
95C24×C61—48no—
96C24×C61—416no—
97C24×C61—44no—
98C24×C61—48no—
99C24×C61—44no—
100C24×C61—416no—
101C24×C61—48no—
102C24×C61—416no—
103C24×C61—416no—
104C24×C61—416no—
105C24×C61—44no—
106C24×C61—41no—
107C24×C61—41no—
108C24×C61—42no—
109C24×C61—42no—
110C24×C61—42no—
111C24×C61—42no—
112C24×C61—41no—
113C24×C61—41no—
114C24×C61—42no—
115C24×C61—42no—
116C24×C61C22⋊C414yescomplemented
117C24×C61C22⋊C412yescomplemented
118C24×C61C22×C411yescharacteristic
119C24×C61C2×D411yescharacteristic
120C24×C61C2×D412yes—
121C24×C61C2×D412yes—
122C24×C61C2×D411yescharacteristic
123C24×C61C2×D412yes—
124C24×C61C2×D412yes—
125C24×C61#4112yes—
126C24×C61#4112yes—
127C2×D4×C61—216no—
128C2×D4×C61—22no—
129C2×D4×C61—22no—
130C2×D4×C61—24no—
131C2×D4×C61—24no—
132C2×D4×C61—22no—
133C2×D4×C61—24no—
134C2×D4×C61—24no—
135C2×D4×C61—22no—
136C2×D4×C61—416no—
137C2×D4×C61—432no—
138C2×D4×C61—42no—
139C2×D4×C61—42no—
140C2×D4×C61—42no—
141C2×D4×C61—42no—
142C2×D4×C61—42no—
143C2×D4×C61—42no—
144C2×D4×C61—42no—
145C2×D4×C61—42no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—24no—
149C22×C4×C61—21no—
150C22×C4×C61—22no—
151C22×C4×C61—21no—
152C22×C4×C61—24no—
153C22×C4×C61—24no—
154C22×C4×C61—24no—
155C22×C4×C61—24no—
156C22×C4×C61—44no—
157C22×C4×C61—48no—
158C22×C4×C61—48no—
159C22×C4×C61—42no—
160C22×C4×C61—42no—
161C22×C4×C61C22⋊C412yescomplemented
162C22⋊C4×C61—216no—
163C22⋊C4×C61—22no—
164C22⋊C4×C61—24no—
165C22⋊C4×C61—24no—
166C22⋊C4×C61—24no—
167C22⋊C4×C61—432no—
168C22⋊C4×C61—42no—
169C22⋊C4×C61—42no—
170C22⋊C4×C61—42no—
171C22⋊C4×C61—42no—
172C22⋊C4×C61—42no—
173C22⋊C4×C61—42no—
174C22⋊C4×C61—84no—
175C22⋊C4×C61C22⋊C414yescomplemented
176C23×C61—28no—
177C23×C61—24no—
178C23×C61—216no—
179C23×C61—28no—
180C23×C61—216no—
181C23×C61—216no—
182C23×C61—216no—
183C23×C61—24no—
184C23×C61—28no—
185C23×C61—22no—
186C23×C61—22no—
187C23×C61—22no—
188C23×C61—48no—
189C23×C61—42no—
190C23×C61—42no—
191C23×C61—44no—
192C23×C61—44no—
193C23×C61—44no—
194C23×C61—44no—
195C23×C61—44no—
196C23×C61—44no—
197C23×C61—416no—
198C23×C61—48no—
199C23×C61—48no—
200C23×C61—48no—
201C23×C61—48no—
202C23×C61—416no—
203C23×C61—416no—
204C23×C61—48no—
205C23×C61—416no—
206C23×C61—48no—
207C23×C61—416no—
208C23×C61—416no—
209C23×C61—416no—
210C23×C61—416no—
211C23×C61—44no—
212C23×C61—48no—
213C23×C61—48no—
214C23×C61—416no—
215C23×C61—48no—
216C23×C61—416no—
217C23×C61—42no—
218C23×C61—42no—
219C23×C61—44no—
220C23×C61—44no—
221C23×C61—44no—
222C23×C61—44no—
223C23×C61—44no—
224C23×C61—48no—
225C23×C61—42no—
226C23×C61—42no—
227C23×C61—44no—
228C23×C61—82no—
229C23×C61—84no—
230C23×C61C2×C22⋊C411yescharacteristic
231C23×C61C2×C22⋊C411yescharacteristic
232C23×C61C2×C22⋊C411yescharacteristic
233C23×C61C4×D412yes—
234C23×C61C4×D412yes—
235C23×C61#12012yes—
236C23×C61#12012yes—
237C23×C61#12012yes—
238C23×C61#12011yescharacteristic
239C23×C61#12011yescharacteristic
240C23×C61#12112yes—
241C23×C61#12112yes—
242C23×C61#12112yes—
243C23×C61#12112yes—
244C23×C61#12112yes—
245C23×C61#12112yes—
246C23×C61#12311yescharacteristic
247C23×C61#12311yescharacteristic
248C23×C61#12312yes—
249C23×C61#12412yes—
250C23×C61#12712yes—
251D4×C61—432no—
252D4×C61—44no—
253D4×C61—44no—
254D4×C61—44no—
255D4×C61—44no—
256C2×C4×C61—22no—
257C2×C4×C61—24no—
258C2×C4×C61—22no—
259C2×C4×C61—22no—
260C2×C4×C61—44no—
261C2×C4×C61—48no—
262C2×C4×C61—42no—
263C2×C4×C61—42no—
264C2×C4×C61—48no—
265C2×C4×C61—48no—
266C2×C4×C61—44no—
267C2×C4×C61—44no—
268C2×C4×C61—48no—
269C2×C4×C61—84no—
270C2×C4×C61—84no—
271C2×C4×C61—84no—
272#10991C6111yesmaximal, characteristic, direct product factor, Sylow
273C22×C61—22no—
274C22×C61—24no—
275C22×C61—24no—
276C22×C61—22no—
277C22×C61—24no—
278C22×C61—24no—
279C22×C61—24no—
280C22×C61—24no—
281C22×C61—24no—
282C22×C61—24no—
283C22×C61—28no—
284C22×C61—216no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61—42no—
288C22×C61—42no—
289C22×C61—41no—
290C22×C61—42no—
291C22×C61—42no—
292C22×C61—42no—
293C22×C61—41no—
294C22×C61—42no—
295C22×C61—44no—
296C22×C61—416no—
297C22×C61—48no—
298C22×C61—48no—
299C22×C61—416no—
300C22×C61—416no—
301C22×C61—416no—
302C22×C61—44no—
303C22×C61—48no—
304C22×C61—44no—
305C22×C61—416no—
306C22×C61—44no—
307C22×C61—42no—
308C22×C61—82no—
309C22×C61—84no—
310C22×C61—84no—
311C22×C61#37911yescharacteristic
312C22×C61#38611yescharacteristic
313C22×C61#38612yes—
314C22×C61#38611yescharacteristic
315C22×C61#39012yes—
316C22×C61#39212yes—
317C22×C61#39212yes—
318C22×C61#39412yes—
319C22×C61#39412yes—
320C22×C61B(4,𝔽2)14yes—
321C4×C61—44no—
322C4×C61—42no—
323C4×C61—84no—
324C4×C61—84no—
325C22×#120C2×C6111yescharacteristic
326C22×#99C2×C6111yescharacteristic, complemented
327#2308C2×C6111yescharacteristic, complemented
328C2×#379C2×C6112yescomplemented
329C2×#342C2×C6112yescomplemented
330C2×C61—21no—
331C2×C61—22no—
332C2×C61—22no—
333C2×C61—21no—
334C2×C61—22no—
335C2×C61—22no—
336C2×C61—22no—
337C2×C61—48no—
338C2×C61—82no—
339C2×C61#143811yescharacteristic
340C2×C61#188912yes—
341C2×C61#202114yes—
342C26C22×C6111yescharacteristic
343C23×D4—21no—
344C23×D4C22×C6111yescharacteristic
345C2×#120—24no—
346C2×#120—22no—
347C2×#120—24no—
348C2×#120C4×C6114yescomplemented
349C22×C22⋊C4—21no—
350C22×C22⋊C4—24no—
351C22×C22⋊C4C22×C6112yes—
352C22×C22⋊C4C22×C6112yes—
353C22×C22⋊C4C22×C6111yescharacteristic
354C2×#99—22no—
355C2×#99—24no—
356#386—24no—
357#381—21no—
358#379—21no—
359#379—24no—
360#379—24no—
361#342—24no—
362C61#1099111yescharacteristic, direct product factor, Sylow
363C25—22no—
364C25—21no—
365C25—21no—
366C25—22no—
367C25—22no—
368C25—22no—
369C25—22no—
370C25—48no—
371C25C2×C4×C6112yes—
372C25D4×C6114yes—
373C25D4×C6111yescharacteristic
374C25C23×C6111yescharacteristic
375C22×D4—28no—
376C22×D4—24no—
377C22×D4—22no—
378C22×D4—22no—
379C22×D4—22no—
380C22×D4—22no—
381C22×D4—22no—
382C22×D4—22no—
383C22×D4—48no—
384C22×D4C2×C4×C6112yes—
385C22×D4D4×C6112yes—
386C23×C4—21no—
387C23×C4—22no—
388C23×C4D4×C6111yescharacteristic
389C23×C4D4×C6114yescomplemented
390#120—216no—
391#120—28no—
392#120—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—216no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—416no—
411C2×C22⋊C4C2×C4×C6112yes—
412C2×C22⋊C4D4×C6114yes—
413C2×C22⋊C4D4×C6114yescomplemented
414#99—28no—
415#95—24no—
416C24—216no—
417C24—28no—
418C24—22no—
419C24—24no—
420C24—24no—
421C24—24no—
422C24—24no—
423C24—22no—
424C24—24no—
425C24—21no—
426C24—24no—
427C24—22no—
428C24—24no—
429C24—24no—
430C24—22no—
431C24—21no—
432C24—48no—
433C24—416no—
434C24—44no—
435C24—48no—
436C24—44no—
437C24—416no—
438C24—416no—
439C24—48no—
440C24—416no—
441C24—416no—
442C24—44no—
443C24—41no—
444C24—41no—
445C24—42no—
446C24—42no—
447C24—42no—
448C24—42no—
449C24—41no—
450C24—41no—
451C24—42no—
452C24—42no—
453C24C22⋊C4×C6114yescomplemented
454C24C22⋊C4×C6112yescomplemented
455C24C22×C4×C6111yescharacteristic
456C24C2×D4×C6111yescharacteristic
457C24C2×D4×C6112yes—
458C24C2×D4×C6112yes—
459C24C2×D4×C6111yescharacteristic
460C24C2×D4×C6112yes—
461C24C2×D4×C6112yes—
462C24#41×C6112yes—
463C24#41×C6112yes—
464C2×D4—216no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—24no—
468C2×D4—24no—
469C2×D4—22no—
470C2×D4—24no—
471C2×D4—24no—
472C2×D4—22no—
473C2×D4—416no—
474C2×D4—432no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—42no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—44no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4C22⋊C4×C6112yescomplemented
499C22⋊C4—216no—
500C22⋊C4—22no—
501C22⋊C4—24no—
502C22⋊C4—24no—
503C22⋊C4—24no—
504C22⋊C4—432no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—84no—
512C22⋊C4C22⋊C4×C6114yescomplemented
513C23—28no—
514C23—24no—
515C23—216no—
516C23—216no—
517C23—28no—
518C23—216no—
519C23—216no—
520C23—24no—
521C23—28no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—48no—
526C23—42no—
527C23—44no—
528C23—44no—
529C23—44no—
530C23—42no—
531C23—44no—
532C23—44no—
533C23—48no—
534C23—48no—
535C23—416no—
536C23—416no—
537C23—48no—
538C23—416no—
539C23—44no—
540C23—416no—
541C23—48no—
542C23—48no—
543C23—48no—
544C23—416no—
545C23—416no—
546C23—416no—
547C23—416no—
548C23—44no—
549C23—48no—
550C23—48no—
551C23—416no—
552C23—48no—
553C23—416no—
554C23—42no—
555C23—42no—
556C23—44no—
557C23—44no—
558C23—44no—
559C23—44no—
560C23—44no—
561C23—48no—
562C23—42no—
563C23—42no—
564C23—44no—
565C23—82no—
566C23—84no—
567C23C2×C22⋊C4×C6111yescharacteristic
568C23C2×C22⋊C4×C6111yescharacteristic
569C23C2×C22⋊C4×C6111yescharacteristic
570C23C4×D4×C6112yes—
571C23C4×D4×C6112yes—
572C23#120×C6112yes—
573C23#120×C6112yes—
574C23#120×C6112yes—
575C23#120×C6111yescharacteristic
576C23#120×C6111yescharacteristic
577C23#121×C6112yes—
578C23#121×C6112yes—
579C23#121×C6112yes—
580C23#121×C6112yes—
581C23#121×C6112yes—
582C23#121×C6112yes—
583C23#123×C6111yescharacteristic
584C23#123×C6111yescharacteristic
585C23#123×C6112yes—
586C23#124×C6112yes—
587C23#127×C6112yes—
588D4—432no—
589D4—44no—
590D4—44no—
591D4—44no—
592D4—44no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—48no—
598C2×C4—44no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—48no—
602C2×C4—48no—
603C2×C4—44no—
604C2×C4—44no—
605C2×C4—48no—
606C2×C4—84no—
607C2×C4—84no—
608C2×C4—84no—
609C22—24no—
610C22—24no—
611C22—24no—
612C22—24no—
613C22—24no—
614C22—24no—
615C22—22no—
616C22—24no—
617C22—24no—
618C22—22no—
619C22—28no—
620C22—216no—
621C22—41no—
622C22—41no—
623C22—42no—
624C22—42no—
625C22—41no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—41no—
630C22—42no—
631C22—44no—
632C22—416no—
633C22—48no—
634C22—48no—
635C22—416no—
636C22—416no—
637C22—416no—
638C22—44no—
639C22—416no—
640C22—48no—
641C22—44no—
642C22—44no—
643C22—42no—
644C22—82no—
645C22—84no—
646C22—84no—
647C22C61×#37911yescharacteristic
648C22C61×#38611yescharacteristic
649C22C61×#38612yes—
650C22C61×#38611yescharacteristic
651C22C61×#39012yes—
652C22C61×#39212yes—
653C22C61×#39212yes—
654C22C61×#39412yes—
655C22C61×#39412yes—
656C22C61×B(4,𝔽2)14yes—
657C4—44no—
658C4—42no—
659C4—84no—
660C4—84no—
661C2—21no—
662C2—22no—
663C2—22no—
664C2—21no—
665C2—22no—
666C2—22no—
667C2—22no—
668C2—48no—
669C2—82no—
670C2C61×#143811yescharacteristic
671C2C61×#188912yes—
672C2C61×#202114yes—
subgroupG/H
center, socleC23×C61#120
commutatorC24C22×C4×C61
Frattini, cosocleC25C23×C61
prime radicalC22×#120×C61C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C25×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#99×C61C2semidirect
3. C61×#2308C2semidirect
4. C2×C61×#379C2semidirect
5. C2×C61×#342C2semidirect
12. C2×#120×C61C4semidirect
52. C23×C4×C61D4semidirect
76. C2×C22⋊C4×C61D4semidirect
116. C24×C61C22⋊C4semidirect
117. C24×C61C22⋊C4semidirect
161. C22×C4×C61C22⋊C4semidirect
175. C22⋊C4×C61C22⋊C4semidirect
272. #10991C61direct (N × H)
326. C22×#99C2×C61semidirect
327. #2308C2×C61semidirect
328. C2×#379C2×C61semidirect
329. C2×#342C2×C61semidirect
348. C2×#120C4×C61semidirect
362. C61#10991direct (N × H)
389. C23×C4D4×C61semidirect
413. C2×C22⋊C4D4×C61semidirect
453. C24C22⋊C4×C61semidirect
454. C24C22⋊C4×C61semidirect
498. C22×C4C22⋊C4×C61semidirect
512. C22⋊C4C22⋊C4×C61semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C612
C22×#99×C612
C61×#23082
C2×C61×#3792
C2×C61×#3422
#1099161