Finite Group Databasebeta

← C61×#10960 #29514393

Subgroups — C61×#10960 #29514393

Order 15616.

1526 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#99×C61C212yesmaximal
2C2×C61×#386C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C61C211yesmaximal, characteristic, complemented
4C2×C61×#342C212yesmaximal, complemented
5C61×C22⋊#95C211yesmaximal, characteristic, complemented
6C23×D4×C61C2211yescharacteristic
7C24×C4×C61C2211yescharacteristic
8C22×C22⋊C4×C61C412yescomplemented
9C22×C22⋊C4×C61C2211yescharacteristic
10C22×C22⋊C4×C61C2212yes—
11C22×C22⋊C4×C61C2212yes—
12C22×C42×C61—21no—
13C2×#99×C61—24no—
14C2×#99×C61—24no—
15C2×#99×C61C418yescomplemented
16C61×#386—21no—
17C61×#386—22no—
18C61×#386—21no—
19C4×C22⋊C4×C61—24no—
20C2×#95×C61—21no—
21C2×#95×C61—22no—
22C2×#95×C61C412yescomplemented
23C61×#342—24no—
24C25×C61C2×C411yescharacteristic
25C25×C61C2311yescharacteristic
26C22×D4×C61—21no—
27C22×D4×C61—21no—
28C22×D4×C61—22no—
29C22×D4×C61—22no—
30C22×D4×C61—22no—
31C22×D4×C61—22no—
32C22×D4×C61—22no—
33C22×D4×C61C2×C414yes—
34C23×C4×C61—22no—
35C23×C4×C61—22no—
36C23×C4×C61—22no—
37C23×C4×C61—22no—
38C23×C4×C61—44no—
39C23×C4×C61C2×C411yescharacteristic
40C23×C4×C61C2×C412yes—
41C23×C4×C61C2×C412yes—
42C23×C4×C61D411yescharacteristic
43C23×C4×C61D412yes—
44C23×C4×C61D411yescharacteristic
45C2×C22⋊C4×C61—22no—
46C2×C22⋊C4×C61—22no—
47C2×C22⋊C4×C61—22no—
48C2×C22⋊C4×C61—22no—
49C2×C22⋊C4×C61—22no—
50C2×C22⋊C4×C61—22no—
51C2×C22⋊C4×C61—22no—
52C2×C22⋊C4×C61—22no—
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61—21no—
55C2×C22⋊C4×C61—22no—
56C2×C22⋊C4×C61—22no—
57C2×C22⋊C4×C61—22no—
58C2×C22⋊C4×C61—22no—
59C2×C22⋊C4×C61—44no—
60C2×C22⋊C4×C61C2×C414yes—
61C2×C22⋊C4×C61C2×C414yes—
62C2×C22⋊C4×C61D414yes—
63C2×C22⋊C4×C61D414yes—
64C2×C42×C61—24no—
65C2×C42×C61—44no—
66#99×C61—216no—
67#95×C61—24no—
68#95×C61—22no—
69#95×C61—22no—
70#95×C61—44no—
71C24×C61—21no—
72C24×C61—21no—
73C24×C61—22no—
74C24×C61—22no—
75C24×C61—42no—
76C24×C61—42no—
77C24×C61—42no—
78C24×C61—42no—
79C24×C61C4212yescomplemented
80C24×C61C22×C411yescharacteristic
81C24×C61C22×C412yes—
82C24×C61C2×D411yescharacteristic
83C24×C61C2×D411yescharacteristic
84C24×C61C2×D412yes—
85C24×C61C2×D412yes—
86C24×C61#4112yes—
87C24×C61#4112yes—
88C24×C61#4112yes—
89C2×D4×C61—24no—
90C2×D4×C61—24no—
91C2×D4×C61—24no—
92C2×D4×C61—24no—
93C2×D4×C61—24no—
94C2×D4×C61—24no—
95C2×D4×C61—41no—
96C2×D4×C61—42no—
97C2×D4×C61—42no—
98C2×D4×C61—42no—
99C2×D4×C61—41no—
100C2×D4×C61—42no—
101C2×D4×C61—42no—
102C2×D4×C61—41no—
103C2×D4×C61—42no—
104C2×D4×C61—41no—
105C22×C4×C61—21no—
106C22×C4×C61—21no—
107C22×C4×C61—24no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—24no—
111C22×C4×C61—24no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—21no—
115C22×C4×C61—24no—
116C22×C4×C61—24no—
117C22×C4×C61—24no—
118C22×C4×C61—21no—
119C22×C4×C61—24no—
120C22×C4×C61—24no—
121C22×C4×C61—22no—
122C22×C4×C61—24no—
123C22×C4×C61—24no—
124C22×C4×C61—42no—
125C22×C4×C61—42no—
126C22×C4×C61—42no—
127C22×C4×C61—48no—
128C22×C4×C61—48no—
129C22×C4×C61—44no—
130C22×C4×C61—44no—
131C22×C4×C61—44no—
132C22×C4×C61—44no—
133C22×C4×C61—42no—
134C22×C4×C61—42no—
135C22×C4×C61—42no—
136C22×C4×C61—42no—
137C22×C4×C61C4212yescomplemented
138C22×C4×C61C22⋊C412yes—
139C22×C4×C61C22⋊C412yes—
140C22⋊C4×C61—24no—
141C22⋊C4×C61—24no—
142C22⋊C4×C61—24no—
143C22⋊C4×C61—24no—
144C22⋊C4×C61—24no—
145C22⋊C4×C61—44no—
146C22⋊C4×C61—42no—
147C22⋊C4×C61—42no—
148C22⋊C4×C61—42no—
149C22⋊C4×C61—41no—
150C22⋊C4×C61—41no—
151C22⋊C4×C61—44no—
152C22⋊C4×C61C22⋊C418yescomplemented
153C42×C61—48no—
154C23×C61—22no—
155C23×C61—22no—
156C23×C61—22no—
157C23×C61—22no—
158C23×C61—22no—
159C23×C61—22no—
160C23×C61—22no—
161C23×C61—24no—
162C23×C61—42no—
163C23×C61—42no—
164C23×C61—44no—
165C23×C61—42no—
166C23×C61—44no—
167C23×C61—42no—
168C23×C61—44no—
169C23×C61—44no—
170C23×C61—44no—
171C23×C61—44no—
172C23×C61—41no—
173C23×C61—42no—
174C23×C61—41no—
175C23×C61—42no—
176C23×C61—42no—
177C23×C61—82no—
178C23×C61—82no—
179C23×C61—84no—
180C23×C61C2×C4211yescharacteristic
181C23×C61C2×C22⋊C412yes—
182C23×C61C2×C22⋊C411yescharacteristic
183C23×C61#11711yescharacteristic
184C23×C61#11712yes—
185C23×C61C4×D412yes—
186C23×C61C4×D412yes—
187C23×C61C4×D412yes—
188C23×C61C4×D412yes—
189C23×C61C4×D412yes—
190C23×C61C4×D412yes—
191C23×C61#12011yescharacteristic
192C23×C61#12112yes—
193C23×C61#12112yes—
194C23×C61#12112yes—
195C23×C61#12311yescharacteristic
196C23×C61#12312yes—
197C23×C61#12411yescharacteristic
198C23×C61#12412yes—
199C23×C61#12612yes—
200C23×C61#12711yescharacteristic
201D4×C61—44no—
202D4×C61—44no—
203D4×C61—44no—
204D4×C61—44no—
205C2×C4×C61—24no—
206C2×C4×C61—24no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—24no—
210C2×C4×C61—22no—
211C2×C4×C61—28no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61—48no—
216C2×C4×C61—48no—
217C2×C4×C61—44no—
218C2×C4×C61—44no—
219C2×C4×C61—48no—
220C2×C4×C61—48no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61—41no—
224C2×C4×C61—42no—
225C2×C4×C61—41no—
226C2×C4×C61—48no—
227C2×C4×C61—44no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—82no—
232C2×C4×C61—82no—
233C2×C4×C61—84no—
234C2×C4×C61—84no—
235C2×C4×C61#9914yescomplemented
236#10960C6111yesmaximal, characteristic, direct product factor, Sylow
237C22×C61—21no—
238C22×C61—21no—
239C22×C61—22no—
240C22×C61—22no—
241C22×C61—21no—
242C22×C61—22no—
243C22×C61—22no—
244C22×C61—21no—
245C22×C61—24no—
246C22×C61—22no—
247C22×C61—24no—
248C22×C61—22no—
249C22×C61—24no—
250C22×C61—24no—
251C22×C61—22no—
252C22×C61—22no—
253C22×C61—42no—
254C22×C61—42no—
255C22×C61—42no—
256C22×C61—42no—
257C22×C61—42no—
258C22×C61—42no—
259C22×C61—42no—
260C22×C61—42no—
261C22×C61—42no—
262C22×C61—44no—
263C22×C61—84no—
264C22×C61—84no—
265C22×C61—81no—
266C22×C61—81no—
267C22×C61—82no—
268C22×C61C4×C22⋊C412yes—
269C22×C61C4×C22⋊C411yescharacteristic
270C22×C61#38612yes—
271C22×C61#38611yescharacteristic
272C22×C61#38812yes—
273C22×C61#38812yes—
274C22×C61#38812yes—
275C22×C61#39012yes—
276C22×C61#39011yescharacteristic
277C22×C61C2×#9912yes—
278C22×C61#41012yes—
279C4×C61—24no—
280C4×C61—48no—
281C4×C61—42no—
282C4×C61—42no—
283C4×C61—84no—
284C4×C61—82no—
285C22×#99C2×C6112yes—
286C2×#386C2×C6111yescharacteristic
287C2×C4×C22⋊C4C2×C6111yescharacteristic, complemented
288C2×#342C2×C6112yescomplemented
289C22⋊#95C2×C6111yescharacteristic, complemented
290C2×C61—22no—
291C2×C61—22no—
292C2×C61—22no—
293C2×C61—22no—
294C2×C61—22no—
295C2×C61—22no—
296C2×C61—82no—
297C2×C61#143711yescharacteristic
298C2×C61C4×#9912yes—
299C2×C61#189811yescharacteristic
300C2×C61#189911yescharacteristic
301C2×C61#196412yes—
302C23×D4C22×C6111yescharacteristic
303C24×C4C22×C6111yescharacteristic
304C22×C22⋊C4C4×C6112yescomplemented
305C22×C22⋊C4C22×C6111yescharacteristic
306C22×C22⋊C4C22×C6112yes—
307C22×C22⋊C4C22×C6112yes—
308C22×C42—21no—
309C2×#99—24no—
310C2×#99—24no—
311C2×#99C4×C6118yescomplemented
312#386—21no—
313#386—22no—
314#386—21no—
315C4×C22⋊C4—24no—
316C2×#95—21no—
317C2×#95—22no—
318C2×#95C4×C6112yescomplemented
319#342—24no—
320C61#1096011yescharacteristic, direct product factor, Sylow
321C25C2×C4×C6111yescharacteristic
322C25C23×C6111yescharacteristic
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4C2×C4×C6114yes—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—44no—
336C23×C4C2×C4×C6111yescharacteristic
337C23×C4C2×C4×C6112yes—
338C23×C4C2×C4×C6112yes—
339C23×C4D4×C6111yescharacteristic
340C23×C4D4×C6112yes—
341C23×C4D4×C6111yescharacteristic
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4C2×C4×C6114yes—
358C2×C22⋊C4C2×C4×C6114yes—
359C2×C22⋊C4D4×C6114yes—
360C2×C22⋊C4D4×C6114yes—
361C2×C42—24no—
362C2×C42—44no—
363#99—216no—
364#95—24no—
365#95—22no—
366#95—22no—
367#95—44no—
368C24—21no—
369C24—21no—
370C24—22no—
371C24—22no—
372C24—42no—
373C24—42no—
374C24—42no—
375C24—42no—
376C24C42×C6112yescomplemented
377C24C22×C4×C6111yescharacteristic
378C24C22×C4×C6112yes—
379C24C2×D4×C6111yescharacteristic
380C24C2×D4×C6111yescharacteristic
381C24C2×D4×C6112yes—
382C24C2×D4×C6112yes—
383C24#41×C6112yes—
384C24#41×C6112yes—
385C24#41×C6112yes—
386C2×D4—24no—
387C2×D4—24no—
388C2×D4—24no—
389C2×D4—24no—
390C2×D4—24no—
391C2×D4—24no—
392C2×D4—41no—
393C2×D4—42no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—41no—
397C2×D4—42no—
398C2×D4—42no—
399C2×D4—41no—
400C2×D4—42no—
401C2×D4—41no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—24no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—22no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—48no—
425C22×C4—48no—
426C22×C4—44no—
427C22×C4—44no—
428C22×C4—44no—
429C22×C4—44no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4C42×C6112yescomplemented
435C22×C4C22⋊C4×C6112yes—
436C22×C4C22⋊C4×C6112yes—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—44no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—42no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—44no—
449C22⋊C4C22⋊C4×C6118yescomplemented
450C42—48no—
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—22no—
458C23—24no—
459C23—42no—
460C23—42no—
461C23—44no—
462C23—42no—
463C23—44no—
464C23—44no—
465C23—42no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—41no—
470C23—42no—
471C23—41no—
472C23—42no—
473C23—42no—
474C23—82no—
475C23—82no—
476C23—84no—
477C23C2×C42×C6111yescharacteristic
478C23C2×C22⋊C4×C6112yes—
479C23C2×C22⋊C4×C6111yescharacteristic
480C23#117×C6111yescharacteristic
481C23#117×C6112yes—
482C23C4×D4×C6112yes—
483C23C4×D4×C6112yes—
484C23C4×D4×C6112yes—
485C23C4×D4×C6112yes—
486C23C4×D4×C6112yes—
487C23C4×D4×C6112yes—
488C23#120×C6111yescharacteristic
489C23#121×C6112yes—
490C23#121×C6112yes—
491C23#121×C6112yes—
492C23#123×C6111yescharacteristic
493C23#123×C6112yes—
494C23#124×C6111yescharacteristic
495C23#124×C6112yes—
496C23#126×C6112yes—
497C23#127×C6111yescharacteristic
498D4—44no—
499D4—44no—
500D4—44no—
501D4—44no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—28no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—48no—
513C2×C4—48no—
514C2×C4—44no—
515C2×C4—48no—
516C2×C4—44no—
517C2×C4—48no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—48no—
524C2×C4—44no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—84no—
531C2×C4—84no—
532C2×C4#99×C6114yescomplemented
533C22—24no—
534C22—24no—
535C22—22no—
536C22—22no—
537C22—21no—
538C22—21no—
539C22—22no—
540C22—22no—
541C22—21no—
542C22—22no—
543C22—22no—
544C22—21no—
545C22—24no—
546C22—22no—
547C22—24no—
548C22—22no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—44no—
558C22—42no—
559C22—84no—
560C22—84no—
561C22—81no—
562C22—81no—
563C22—82no—
564C22C4×C22⋊C4×C6112yes—
565C22C4×C22⋊C4×C6111yescharacteristic
566C22C61×#38612yes—
567C22C61×#38611yescharacteristic
568C22C61×#38812yes—
569C22C61×#38812yes—
570C22C61×#38812yes—
571C22C61×#39012yes—
572C22C61×#39011yescharacteristic
573C22C2×#99×C6112yes—
574C22C61×#41012yes—
575C4—24no—
576C4—48no—
577C4—42no—
578C4—42no—
579C4—84no—
580C4—82no—
581C2—22no—
582C2—22no—
583C2—22no—
584C2—22no—
585C2—22no—
586C2—22no—
587C2—82no—
588C2C61×#143711yescharacteristic
589C2C4×#99×C6112yes—
590C2C61×#189811yescharacteristic
591C2C61×#189911yescharacteristic
592C2C61×#196412yes—
subgroupG/H
center, socleC23×C61C2×C22⋊C4
commutatorC23C2×C42×C61
Frattini, cosocleC25C23×C61
prime radicalC23×D4×C61C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C24×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊C4×C61C2semidirect
4. C2×C61×#342C2semidirect
5. C61×C22⋊#95C2semidirect
8. C22×C22⋊C4×C61C4semidirect
15. C2×#99×C61C4semidirect
22. C2×#95×C61C4semidirect
79. C24×C61C42semidirect
137. C22×C4×C61C42semidirect
152. C22⋊C4×C61C22⋊C4semidirect
235. C2×C4×C61#99semidirect
236. #10960C61direct (N × H)
287. C2×C4×C22⋊C4C2×C61semidirect
288. C2×#342C2×C61semidirect
289. C22⋊#95C2×C61semidirect
304. C22×C22⋊C4C4×C61semidirect
311. C2×#99C4×C61semidirect
318. C2×#95C4×C61semidirect
320. C61#10960direct (N × H)
376. C24C42×C61semidirect
434. C22×C4C42×C61semidirect
449. C22⋊C4C22⋊C4×C61semidirect
532. C2×C4#99×C61semidirect

Maximal subgroups

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

subgroupindex
C22×#99×C612
C2×C61×#3862
C2×C4×C22⋊C4×C612
C2×C61×#3422
C61×C22⋊#952
#1096061