Finite Group Databasebeta

← C61×#10745 #29514178

Subgroups — C61×#10745 #29514178

Order 15616.

1794 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#518C211yesmaximal, characteristic
2C22×#99×C61C211yesmaximal, characteristic
3C2×C61×#386C211yesmaximal, characteristic
4C2×C61×#342C212yesmaximal, complemented
5C61×C22⋊#95C212yesmaximal, complemented
6C23×D4×C61C2211yescharacteristic
7C24×C4×C61C2211yescharacteristic
8C61×#518—22no—
9C61×#518—24no—
10C61×#518C414yescomplemented
11C2×C4×D4×C61—24no—
12C2×#117×C61—21no—
13C22×C22⋊C4×C61—21no—
14C22×C22⋊C4×C61—21no—
15C22×C22⋊C4×C61C2211yescharacteristic
16C22×C22⋊C4×C61C2212yes—
17C22×C22⋊C4×C61C2212yes—
18C2×#99×C61—22no—
19C2×#99×C61—22no—
20C2×#99×C61C414yescomplemented
21C61×#386—22no—
22C61×#386C414yescomplemented
23C2×#95×C61—21no—
24C2×#95×C61—24no—
25C61×#342—24no—
26C25×C61D411yescharacteristic
27C25×C61C2311yescharacteristic
28C22×D4×C61—22no—
29C22×D4×C61—22no—
30C22×D4×C61—22no—
31C22×D4×C61—22no—
32C22×D4×C61C2×C412yes—
33C22×D4×C61C2×C412yes—
34C22×D4×C61C2×C412yes—
35C22×D4×C61D412yes—
36C22×D4×C61D412yes—
37C22×D4×C61Q812yes—
38C23×C4×C61—22no—
39C23×C4×C61—21no—
40C23×C4×C61—22no—
41C23×C4×C61—21no—
42C23×C4×C61—22no—
43C23×C4×C61—21no—
44C23×C4×C61—22no—
45C23×C4×C61—44no—
46C23×C4×C61C2×C412yescomplemented
47C23×C4×C61D411yescharacteristic
48C23×C4×C61D414yes—
49C4×D4×C61—216no—
50C4×D4×C61—216no—
51#117×C61—24no—
52#117×C61—24no—
53C2×C4⋊C4×C61—22no—
54C2×C22⋊C4×C61—22no—
55C2×C22⋊C4×C61—24no—
56C2×C22⋊C4×C61—24no—
57C2×C22⋊C4×C61—22no—
58C2×C22⋊C4×C61—22no—
59C2×C22⋊C4×C61—22no—
60C2×C22⋊C4×C61—22no—
61C2×C22⋊C4×C61—22no—
62C2×C22⋊C4×C61—22no—
63C2×C22⋊C4×C61—22no—
64C2×C22⋊C4×C61—22no—
65C2×C22⋊C4×C61—22no—
66C2×C22⋊C4×C61—22no—
67C2×C22⋊C4×C61—24no—
68C2×C22⋊C4×C61—21no—
69C2×C22⋊C4×C61—22no—
70C2×C22⋊C4×C61—44no—
71C2×C22⋊C4×C61C2×C414yes—
72C2×C22⋊C4×C61C2×C412yescomplemented
73C2×C22⋊C4×C61C2×C414yescomplemented
74C2×C22⋊C4×C61D414yes—
75C2×C42×C61—22no—
76#99×C61—28no—
77#95×C61—24no—
78#95×C61—48no—
79C24×C61—21no—
80C24×C61—21no—
81C24×C61—21no—
82C24×C61—21no—
83C24×C61—42no—
84C24×C61—42no—
85C24×C61—42no—
86C24×C61—42no—
87C24×C61C22⋊C412yes—
88C24×C61C22⋊C412yes—
89C24×C61C4⋊C412yes—
90C24×C61C22×C411yescharacteristic
91C24×C61C22×C411yescharacteristic
92C24×C61C22×C411yescharacteristic
93C24×C61C2×D411yescharacteristic
94C24×C61C2×D412yes—
95C24×C61C2×D411yescharacteristic
96C24×C61C2×D411yescharacteristic
97C24×C61C2×D412yes—
98C24×C61C2×Q811yescharacteristic
99C24×C61#4112yes—
100C24×C61#4112yes—
101C2×D4×C61—24no—
102C2×D4×C61—24no—
103C2×D4×C61—24no—
104C2×D4×C61—24no—
105C2×D4×C61—24no—
106C2×D4×C61—24no—
107C2×D4×C61—24no—
108C2×D4×C61—24no—
109C2×D4×C61—24no—
110C2×D4×C61—24no—
111C2×D4×C61—24no—
112C2×D4×C61—24no—
113C2×D4×C61C4214yes—
114C2×D4×C61C22⋊C414yes—
115C2×D4×C61C4⋊C414yes—
116C2×D4×C61C4⋊C414yes—
117C22×C4×C61—21no—
118C22×C4×C61—21no—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—28no—
122C22×C4×C61—24no—
123C22×C4×C61—22no—
124C22×C4×C61—24no—
125C22×C4×C61—24no—
126C22×C4×C61—28no—
127C22×C4×C61—24no—
128C22×C4×C61—22no—
129C22×C4×C61—24no—
130C22×C4×C61—44no—
131C22×C4×C61—44no—
132C22×C4×C61—48no—
133C22×C4×C61—44no—
134C22×C4×C61—42no—
135C22×C4×C61—41no—
136C22×C4×C61—42no—
137C22×C4×C61—41no—
138C22×C4×C61—44no—
139C22×C4×C61—44no—
140C22×C4×C61—44no—
141C22×C4×C61—42no—
142C22×C4×C61—44no—
143C22×C4×C61—42no—
144C22×C4×C61—41no—
145C22×C4×C61—42no—
146C22×C4×C61—42no—
147C22×C4×C61—41no—
148C22×C4×C61—82no—
149C22×C4×C61—82no—
150C22×C4×C61C22⋊C412yes—
151C22×C4×C61C22⋊C412yes—
152C22×C4×C61C22⋊C418yescomplemented
153C22×C4×C61C4⋊C412yes—
154C4⋊C4×C61—28no—
155C22⋊C4×C61—28no—
156C22⋊C4×C61—24no—
157C22⋊C4×C61—24no—
158C22⋊C4×C61—24no—
159C22⋊C4×C61—24no—
160C22⋊C4×C61—24no—
161C22⋊C4×C61—24no—
162C22⋊C4×C61—24no—
163C22⋊C4×C61—48no—
164C22⋊C4×C61—42no—
165C22⋊C4×C61—42no—
166C22⋊C4×C61—42no—
167C42×C61—28no—
168C23×C61—24no—
169C23×C61—22no—
170C23×C61—24no—
171C23×C61—22no—
172C23×C61—22no—
173C23×C61—22no—
174C23×C61—22no—
175C23×C61—22no—
176C23×C61—22no—
177C23×C61—22no—
178C23×C61—41no—
179C23×C61—41no—
180C23×C61—42no—
181C23×C61—42no—
182C23×C61—41no—
183C23×C61—42no—
184C23×C61—41no—
185C23×C61—44no—
186C23×C61—42no—
187C23×C61—42no—
188C23×C61—44no—
189C23×C61—42no—
190C23×C61—42no—
191C23×C61—42no—
192C23×C61—44no—
193C23×C61—44no—
194C23×C61—42no—
195C23×C61—42no—
196C23×C61—82no—
197C23×C61—81no—
198C23×C61—81no—
199C23×C61—82no—
200C23×C61#9514yescomplemented
201C23×C61C2×C4211yescharacteristic
202C23×C61C2×C22⋊C411yescharacteristic
203C23×C61C2×C22⋊C411yescharacteristic
204C23×C61C2×C22⋊C412yes—
205C23×C61C2×C22⋊C411yescharacteristic
206C23×C61C2×C4⋊C411yescharacteristic
207C23×C61C2×C4⋊C411yescharacteristic
208C23×C61C2×C4⋊C411yescharacteristic
209C23×C61#11712yes—
210C23×C61C4×D412yes—
211C23×C61C4×D412yes—
212C23×C61C4×D412yes—
213C23×C61C4×D412yes—
214C23×C61#12011yescharacteristic
215C23×C61#12012yes—
216C23×C61#12011yescharacteristic
217C23×C61#12112yes—
218C23×C61#12112yes—
219C23×C61C22⋊Q812yes—
220C23×C61C22⋊Q812yes—
221C23×C61#12311yescharacteristic
222C23×C61#12311yescharacteristic
223C23×C61#12312yes—
224D4×C61—28no—
225D4×C61—28no—
226D4×C61—28no—
227D4×C61—28no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—24no—
235C2×C4×C61—28no—
236C2×C4×C61—28no—
237C2×C4×C61—42no—
238C2×C4×C61—44no—
239C2×C4×C61—48no—
240C2×C4×C61—44no—
241C2×C4×C61—42no—
242C2×C4×C61—44no—
243C2×C4×C61—44no—
244C2×C4×C61—44no—
245C2×C4×C61—48no—
246C2×C4×C61—42no—
247C2×C4×C61—48no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61—44no—
251C2×C4×C61—84no—
252C2×C4×C61—88no—
253C2×C4×C61—82no—
254C2×C4×C61—82no—
255C2×C4×C61—82no—
256C2×C4×C61—84no—
257C2×C4×C61—82no—
258C2×C4×C61#9514yescomplemented
259#10745C6111yesmaximal, characteristic, direct product factor, Sylow
260C22×C61—24no—
261C22×C61—22no—
262C22×C61—22no—
263C22×C61—24no—
264C22×C61—21no—
265C22×C61—22no—
266C22×C61—22no—
267C22×C61—21no—
268C22×C61—21no—
269C22×C61—22no—
270C22×C61—21no—
271C22×C61—22no—
272C22×C61—24no—
273C22×C61—24no—
274C22×C61—22no—
275C22×C61—22no—
276C22×C61—24no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61—41no—
281C22×C61—42no—
282C22×C61—42no—
283C22×C61—42no—
284C22×C61—42no—
285C22×C61—42no—
286C22×C61—42no—
287C22×C61—44no—
288C22×C61—44no—
289C22×C61—42no—
290C22×C61—42no—
291C22×C61—44no—
292C22×C61—82no—
293C22×C61—82no—
294C22×C61—82no—
295C22×C61C2×#9511yescharacteristic
296C22×C61C4×C22⋊C412yes—
297C22×C61#37911yescharacteristic
298C22×C61#38012yes—
299C22×C61#38111yescharacteristic
300C22×C61#38511yescharacteristic
301C22×C61#38512yes—
302C22×C61#38511yescharacteristic
303C22×C61#38611yescharacteristic
304C22×C61#38612yes—
305C22×C61#38611yescharacteristic
306C22×C61B(4,𝔽2)12yes—
307C22×C61#45812yes—
308C4×C61—24no—
309C4×C61—44no—
310C4×C61—48no—
311C4×C61—82no—
312C4×C61—84no—
313C2×#518C2×C6111yescharacteristic
314C22×#99C2×C6111yescharacteristic
315C2×#386C2×C6111yescharacteristic
316C2×#342C2×C6112yescomplemented
317C22⋊#95C2×C6112yescomplemented
318C2×C61—21no—
319C2×C61—22no—
320C2×C61—21no—
321C2×C61—21no—
322C2×C61—21no—
323C2×C61—22no—
324C2×C61—22no—
325C2×C61—22no—
326C2×C61—44no—
327C2×C61C22⋊#9511yescharacteristic
328C2×C61#179012yes—
329C2×C61#186712yes—
330C2×C61#188911yescharacteristic
331C2×C61#189011yescharacteristic
332C23×D4C22×C6111yescharacteristic
333C24×C4C22×C6111yescharacteristic
334#518—22no—
335#518—24no—
336#518C4×C6114yescomplemented
337C2×C4×D4—24no—
338C2×#117—21no—
339C22×C22⋊C4—21no—
340C22×C22⋊C4—21no—
341C22×C22⋊C4C22×C6112yes—
342C22×C22⋊C4C22×C6111yescharacteristic
343C22×C22⋊C4C22×C6112yes—
344C2×#99—22no—
345C2×#99—22no—
346C2×#99C4×C6114yescomplemented
347#386—22no—
348#386C4×C6114yescomplemented
349C2×#95—21no—
350C2×#95—24no—
351#342—24no—
352C61#1074511yescharacteristic, direct product factor, Sylow
353C25D4×C6111yescharacteristic
354C25C23×C6111yescharacteristic
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4C2×C4×C6112yes—
360C22×D4C2×C4×C6112yes—
361C22×D4C2×C4×C6112yes—
362C22×D4D4×C6112yes—
363C22×D4D4×C6112yes—
364C22×D4Q8×C6112yes—
365C23×C4—21no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—21no—
369C23×C4—22no—
370C23×C4—21no—
371C23×C4—22no—
372C23×C4—44no—
373C23×C4C2×C4×C6112yescomplemented
374C23×C4D4×C6111yescharacteristic
375C23×C4D4×C6114yes—
376C4×D4—216no—
377C4×D4—216no—
378#117—24no—
379#117—24no—
380C2×C4⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4C2×C4×C6114yes—
399C2×C22⋊C4C2×C4×C6112yescomplemented
400C2×C22⋊C4C2×C4×C6114yescomplemented
401C2×C22⋊C4D4×C6114yes—
402C2×C42—22no—
403#99—28no—
404#95—24no—
405#95—48no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24C22⋊C4×C6112yes—
415C24C22⋊C4×C6112yes—
416C24C4⋊C4×C6112yes—
417C24C22×C4×C6111yescharacteristic
418C24C22×C4×C6111yescharacteristic
419C24C22×C4×C6111yescharacteristic
420C24C2×D4×C6111yescharacteristic
421C24C2×D4×C6112yes—
422C24C2×D4×C6111yescharacteristic
423C24C2×D4×C6111yescharacteristic
424C24C2×D4×C6112yes—
425C24C2×Q8×C6111yescharacteristic
426C24#41×C6112yes—
427C24#41×C6112yes—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—24no—
431C2×D4—24no—
432C2×D4—24no—
433C2×D4—24no—
434C2×D4—24no—
435C2×D4—24no—
436C2×D4—24no—
437C2×D4—24no—
438C2×D4—24no—
439C2×D4—24no—
440C2×D4C42×C6114yes—
441C2×D4C22⋊C4×C6114yes—
442C2×D4C4⋊C4×C6114yes—
443C2×D4C4⋊C4×C6114yes—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—28no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—28no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—48no—
460C22×C4—44no—
461C22×C4—42no—
462C22×C4—41no—
463C22×C4—42no—
464C22×C4—41no—
465C22×C4—44no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—42no—
469C22×C4—44no—
470C22×C4—42no—
471C22×C4—41no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—41no—
475C22×C4—82no—
476C22×C4—82no—
477C22×C4C22⋊C4×C6112yes—
478C22×C4C22⋊C4×C6112yes—
479C22×C4C22⋊C4×C6118yescomplemented
480C22×C4C4⋊C4×C6112yes—
481C4⋊C4—28no—
482C22⋊C4—28no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—24no—
486C22⋊C4—24no—
487C22⋊C4—24no—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—48no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C22⋊C4—42no—
494C42—28no—
495C23—24no—
496C23—22no—
497C23—24no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—41no—
511C23—44no—
512C23—42no—
513C23—41no—
514C23—42no—
515C23—44no—
516C23—42no—
517C23—42no—
518C23—44no—
519C23—42no—
520C23—44no—
521C23—42no—
522C23—42no—
523C23—82no—
524C23—82no—
525C23—81no—
526C23—81no—
527C23#95×C6114yescomplemented
528C23C2×C42×C6111yescharacteristic
529C23C2×C22⋊C4×C6111yescharacteristic
530C23C2×C22⋊C4×C6111yescharacteristic
531C23C2×C22⋊C4×C6112yes—
532C23C2×C22⋊C4×C6111yescharacteristic
533C23C2×C4⋊C4×C6111yescharacteristic
534C23C2×C4⋊C4×C6111yescharacteristic
535C23C2×C4⋊C4×C6111yescharacteristic
536C23#117×C6112yes—
537C23C4×D4×C6112yes—
538C23C4×D4×C6112yes—
539C23C4×D4×C6112yes—
540C23C4×D4×C6112yes—
541C23#120×C6111yescharacteristic
542C23#120×C6112yes—
543C23#120×C6111yescharacteristic
544C23#121×C6112yes—
545C23#121×C6112yes—
546C23C22⋊Q8×C6112yes—
547C23C22⋊Q8×C6112yes—
548C23#123×C6111yescharacteristic
549C23#123×C6111yescharacteristic
550C23#123×C6112yes—
551D4—28no—
552D4—28no—
553D4—28no—
554D4—28no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—28no—
563C2×C4—28no—
564C2×C4—42no—
565C2×C4—44no—
566C2×C4—48no—
567C2×C4—44no—
568C2×C4—42no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—44no—
572C2×C4—48no—
573C2×C4—42no—
574C2×C4—48no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—44no—
578C2×C4—84no—
579C2×C4—88no—
580C2×C4—84no—
581C2×C4—82no—
582C2×C4—82no—
583C2×C4—82no—
584C2×C4—82no—
585C2×C4#95×C6114yescomplemented
586C22—24no—
587C22—24no—
588C22—22no—
589C22—22no—
590C22—24no—
591C22—22no—
592C22—22no—
593C22—24no—
594C22—21no—
595C22—22no—
596C22—22no—
597C22—21no—
598C22—21no—
599C22—22no—
600C22—21no—
601C22—22no—
602C22—24no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—42no—
617C22—42no—
618C22—82no—
619C22—82no—
620C22—82no—
621C22C2×#95×C6111yescharacteristic
622C22C4×C22⋊C4×C6112yes—
623C22C61×#37911yescharacteristic
624C22C61×#38012yes—
625C22C61×#38111yescharacteristic
626C22C61×#38511yescharacteristic
627C22C61×#38512yes—
628C22C61×#38511yescharacteristic
629C22C61×#38611yescharacteristic
630C22C61×#38612yes—
631C22C61×#38611yescharacteristic
632C22C61×B(4,𝔽2)12yes—
633C22C61×#45812yes—
634C4—24no—
635C4—48no—
636C4—44no—
637C4—82no—
638C4—84no—
639C2—21no—
640C2—22no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—22no—
645C2—22no—
646C2—22no—
647C2—44no—
648C2C61×C22⋊#9511yescharacteristic
649C2C61×#179012yes—
650C2C61×#186712yes—
651C2C61×#188911yescharacteristic
652C2C61×#189011yescharacteristic
subgroupG/H
center, socleC23×C61#120
commutatorC23C2×C42×C61
Frattini, cosocleC25C23×C61
prime radicalC23×D4×C61C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C25×C61 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C61×#342C2semidirect
5. C61×C22⋊#95C2semidirect
10. C61×#518C4semidirect
20. C2×#99×C61C4semidirect
22. C61×#386C4semidirect
46. C23×C4×C61C2×C4semidirect
72. C2×C22⋊C4×C61C2×C4semidirect
73. C2×C22⋊C4×C61C2×C4semidirect
152. C22×C4×C61C22⋊C4semidirect
200. C23×C61#95semidirect
258. C2×C4×C61#95semidirect
259. #10745C61direct (N × H)
316. C2×#342C2×C61semidirect
317. C22⋊#95C2×C61semidirect
336. #518C4×C61semidirect
346. C2×#99C4×C61semidirect
348. #386C4×C61semidirect
352. C61#10745direct (N × H)
373. C23×C4C2×C4×C61semidirect
399. C2×C22⋊C4C2×C4×C61semidirect
400. C2×C22⋊C4C2×C4×C61semidirect
479. C22×C4C22⋊C4×C61semidirect
527. C23#95×C61semidirect
585. C2×C4#95×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5182
C22×#99×C612
C2×C61×#3862
C2×C61×#3422
C61×C22⋊#952
#1074561