Finite Group Databasebeta

← C61×#11043 #29514476

Subgroups — C61×#11043 #29514476

Order 15616.

1454 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#99×C61C212yesmaximal
2C2×C61×#386C211yesmaximal, characteristic
3C2×C61×#380C211yesmaximal, characteristic, complemented
4C2×C61×#342C212yesmaximal, complemented
5C61×C22⋊#95C211yesmaximal, characteristic, complemented
6C23×D4×C61C2211yescharacteristic
7C24×C4×C61C2211yescharacteristic
8C22×C4⋊C4×C61—21no—
9C22×C22⋊C4×C61C412yescomplemented
10C22×C22⋊C4×C61C2211yescharacteristic
11C22×C22⋊C4×C61C2212yes—
12C22×C22⋊C4×C61C2212yes—
13C2×#99×C61—24no—
14C2×#99×C61—24no—
15C2×#99×C61—24no—
16C61×#386—21no—
17C61×#386—22no—
18C61×#386—21no—
19C61×#380—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—21no—
31C22×D4×C61—21no—
32C22×D4×C61—22no—
33C22×D4×C61—22no—
34C22×D4×C61D412yes—
35C22×D4×C61Q812yes—
36C23×C4×C61—22no—
37C23×C4×C61—22no—
38C23×C4×C61—22no—
39C23×C4×C61—22no—
40C23×C4×C61—44no—
41C23×C4×C61C2×C411yescharacteristic
42C23×C4×C61C2×C412yes—
43C23×C4×C61C2×C412yes—
44C23×C4×C61D411yescharacteristic
45C23×C4×C61D412yes—
46C23×C4×C61D411yescharacteristic
47C2×C4⋊C4×C61—24no—
48C2×C4⋊C4×C61—44no—
49C2×C22⋊C4×C61—22no—
50C2×C22⋊C4×C61—22no—
51C2×C22⋊C4×C61—22no—
52C2×C22⋊C4×C61—22no—
53C2×C22⋊C4×C61—22no—
54C2×C22⋊C4×C61—22no—
55C2×C22⋊C4×C61—22no—
56C2×C22⋊C4×C61—22no—
57C2×C22⋊C4×C61—22no—
58C2×C22⋊C4×C61—22no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—22no—
62C2×C22⋊C4×C61—22no—
63C2×C22⋊C4×C61—22no—
64C2×C22⋊C4×C61—22no—
65C2×C22⋊C4×C61—44no—
66C2×C22⋊C4×C61D414yes—
67C2×C22⋊C4×C61D414yes—
68#99×C61—216no—
69#95×C61—24no—
70#95×C61—22no—
71#95×C61—22no—
72#95×C61—44no—
73C24×C61—21no—
74C24×C61—21no—
75C24×C61—22no—
76C24×C61—22no—
77C24×C61—42no—
78C24×C61—42no—
79C24×C61—42no—
80C24×C61—42no—
81C24×C61C4⋊C412yescomplemented
82C24×C61C22×C411yescharacteristic
83C24×C61C2×D411yescharacteristic
84C24×C61C2×D411yescharacteristic
85C24×C61C2×D411yescharacteristic
86C24×C61C2×D412yes—
87C24×C61C2×D412yes—
88C24×C61C2×Q811yescharacteristic
89C24×C61#4111yescharacteristic
90C24×C61#4111yescharacteristic
91C24×C61#4112yes—
92C24×C61#4112yes—
93C2×D4×C61—24no—
94C2×D4×C61—22no—
95C2×D4×C61—22no—
96C2×D4×C61—22no—
97C2×D4×C61—22no—
98C2×D4×C61—24no—
99C2×D4×C61—24no—
100C2×D4×C61—24no—
101C2×D4×C61—41no—
102C2×D4×C61—42no—
103C2×D4×C61—42no—
104C2×D4×C61—42no—
105C2×D4×C61—41no—
106C2×D4×C61—42no—
107C2×D4×C61—42no—
108C2×D4×C61—41no—
109C2×D4×C61—42no—
110C2×D4×C61—41no—
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—24no—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—24no—
117C22×C4×C61—22no—
118C22×C4×C61—22no—
119C22×C4×C61—21no—
120C22×C4×C61—24no—
121C22×C4×C61—21no—
122C22×C4×C61—24no—
123C22×C4×C61—24no—
124C22×C4×C61—22no—
125C22×C4×C61—24no—
126C22×C4×C61—24no—
127C22×C4×C61—24no—
128C22×C4×C61—42no—
129C22×C4×C61—42no—
130C22×C4×C61—42no—
131C22×C4×C61—48no—
132C22×C4×C61—48no—
133C22×C4×C61—44no—
134C22×C4×C61—44no—
135C22×C4×C61—44no—
136C22×C4×C61—44no—
137C22×C4×C61—42no—
138C22×C4×C61—42no—
139C22×C4×C61—42no—
140C22×C4×C61—42no—
141C22×C4×C61—42no—
142C22×C4×C61—42no—
143C22×C4×C61C22⋊C412yes—
144C22×C4×C61C22⋊C412yes—
145C22×C4×C61C4⋊C412yescomplemented
146C4⋊C4×C61—48no—
147C22⋊C4×C61—24no—
148C22⋊C4×C61—24no—
149C22⋊C4×C61—24no—
150C22⋊C4×C61—24no—
151C22⋊C4×C61—44no—
152C22⋊C4×C61—42no—
153C22⋊C4×C61—42no—
154C22⋊C4×C61—42no—
155C22⋊C4×C61—42no—
156C22⋊C4×C61—41no—
157C22⋊C4×C61—42no—
158C22⋊C4×C61—41no—
159C22⋊C4×C61—44no—
160C23×C61—22no—
161C23×C61—22no—
162C23×C61—22no—
163C23×C61—22no—
164C23×C61—22no—
165C23×C61—22no—
166C23×C61—22no—
167C23×C61—24no—
168C23×C61—42no—
169C23×C61—42no—
170C23×C61—42no—
171C23×C61—42no—
172C23×C61—44no—
173C23×C61—42no—
174C23×C61—42no—
175C23×C61—42no—
176C23×C61—42no—
177C23×C61—44no—
178C23×C61—44no—
179C23×C61—44no—
180C23×C61—41no—
181C23×C61—42no—
182C23×C61—41no—
183C23×C61—42no—
184C23×C61—42no—
185C23×C61—82no—
186C23×C61—82no—
187C23×C61—84no—
188C23×C61C2×C22⋊C411yescharacteristic
189C23×C61C2×C4⋊C411yescharacteristic
190C23×C61#11711yescharacteristic
191C23×C61C4×D412yes—
192C23×C61C4×D412yes—
193C23×C61#12011yescharacteristic
194C23×C61#12012yes—
195C23×C61#12111yescharacteristic
196C23×C61#12111yescharacteristic
197C23×C61#12112yes—
198C23×C61#12112yes—
199C23×C61#12112yes—
200C23×C61C22⋊Q811yescharacteristic
201C23×C61C22⋊Q811yescharacteristic
202C23×C61C22⋊Q812yes—
203C23×C61C22⋊Q812yes—
204C23×C61#12311yescharacteristic
205C23×C61#12312yes—
206C23×C61#12312yes—
207C23×C61#12411yescharacteristic
208C23×C61#12412yes—
209C23×C61#12612yes—
210C23×C61#12711yescharacteristic
211D4×C61—42no—
212D4×C61—42no—
213D4×C61—44no—
214D4×C61—44no—
215D4×C61—42no—
216D4×C61—42no—
217C2×C4×C61—24no—
218C2×C4×C61—24no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—24no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—48no—
227C2×C4×C61—48no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—41no—
231C2×C4×C61—42no—
232C2×C4×C61—41no—
233C2×C4×C61—44no—
234C2×C4×C61—44no—
235C2×C4×C61—48no—
236C2×C4×C61—42no—
237C2×C4×C61—44no—
238C2×C4×C61—44no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—84no—
242C2×C4×C61—84no—
243C2×C4×C61—82no—
244C2×C4×C61—82no—
245C2×C4×C61—84no—
246C2×C4×C61—84no—
247C2×C4×C61#9914yescomplemented
248#11043C6111yesmaximal, characteristic, direct product factor, Sylow
249C22×C61—22no—
250C22×C61—22no—
251C22×C61—22no—
252C22×C61—22no—
253C22×C61—22no—
254C22×C61—22no—
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—22no—
258C22×C61—22no—
259C22×C61—21no—
260C22×C61—22no—
261C22×C61—22no—
262C22×C61—21no—
263C22×C61—24no—
264C22×C61—22no—
265C22×C61—24no—
266C22×C61—22no—
267C22×C61—42no—
268C22×C61—42no—
269C22×C61—42no—
270C22×C61—42no—
271C22×C61—42no—
272C22×C61—42no—
273C22×C61—42no—
274C22×C61—42no—
275C22×C61—44no—
276C22×C61—42no—
277C22×C61—84no—
278C22×C61—84no—
279C22×C61—81no—
280C22×C61—81no—
281C22×C61—82no—
282C22×C61#38011yescharacteristic
283C22×C61#38512yes—
284C22×C61#38611yescharacteristic
285C22×C61#38812yes—
286C22×C61#39011yescharacteristic
287C22×C61#39211yescharacteristic
288C22×C61#39311yescharacteristic
289C22×C61#39412yes—
290C22×C61#39612yes—
291C22×C61#39711yescharacteristic
292C22×C61#39911yescharacteristic
293C22×C61C2×#9912yes—
294C22×C61#41012yes—
295C4×C61—24no—
296C4×C61—42no—
297C4×C61—42no—
298C4×C61—84no—
299C4×C61—84no—
300C4×C61—82no—
301C22×#99C2×C6112yes—
302C2×#386C2×C6111yescharacteristic
303C2×#380C2×C6111yescharacteristic, complemented
304C2×#342C2×C6112yescomplemented
305C22⋊#95C2×C6111yescharacteristic, complemented
306C2×C61—21no—
307C2×C61—22no—
308C2×C61—22no—
309C2×C61—22no—
310C2×C61—21no—
311C2×C61—22no—
312C2×C61—21no—
313C2×C61—21no—
314C2×C61—82no—
315C2×C61#143911yescharacteristic
316C2×C61#179912yes—
317C2×C61#189811yescharacteristic
318C2×C61#189911yescharacteristic
319C2×C61#196412yes—
320C23×D4C22×C6111yescharacteristic
321C24×C4C22×C6111yescharacteristic
322C22×C4⋊C4—21no—
323C22×C22⋊C4C4×C6112yescomplemented
324C22×C22⋊C4C22×C6111yescharacteristic
325C22×C22⋊C4C22×C6112yes—
326C22×C22⋊C4C22×C6112yes—
327C2×#99—24no—
328C2×#99—24no—
329C2×#99—24no—
330#386—21no—
331#386—22no—
332#386—21no—
333#380—24no—
334C2×#95—21no—
335C2×#95—22no—
336C2×#95C4×C6112yescomplemented
337#342—24no—
338C61#1104311yescharacteristic, direct product factor, Sylow
339C25C2×C4×C6111yescharacteristic
340C25C23×C6111yescharacteristic
341C22×D4—21no—
342C22×D4—21no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—21no—
346C22×D4—21no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4D4×C6112yes—
350C22×D4Q8×C6112yes—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—44no—
356C23×C4C2×C4×C6111yescharacteristic
357C23×C4C2×C4×C6112yes—
358C23×C4C2×C4×C6112yes—
359C23×C4D4×C6111yescharacteristic
360C23×C4D4×C6112yes—
361C23×C4D4×C6111yescharacteristic
362C2×C4⋊C4—24no—
363C2×C4⋊C4—44no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4D4×C6114yes—
382C2×C22⋊C4D4×C6114yes—
383#99—216no—
384#95—24no—
385#95—22no—
386#95—22no—
387#95—44no—
388C24—21no—
389C24—21no—
390C24—22no—
391C24—22no—
392C24—42no—
393C24—42no—
394C24—42no—
395C24—42no—
396C24C4⋊C4×C6112yescomplemented
397C24C22×C4×C6111yescharacteristic
398C24C2×D4×C6111yescharacteristic
399C24C2×D4×C6111yescharacteristic
400C24C2×D4×C6111yescharacteristic
401C24C2×D4×C6112yes—
402C24C2×D4×C6112yes—
403C24C2×Q8×C6111yescharacteristic
404C24#41×C6111yescharacteristic
405C24#41×C6111yescharacteristic
406C24#41×C6112yes—
407C24#41×C6112yes—
408C2×D4—24no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—24no—
416C2×D4—41no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—41no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—41no—
424C2×D4—42no—
425C2×D4—41no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—24no—
436C22×C4—21no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—48no—
447C22×C4—48no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—44no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4C22⋊C4×C6112yes—
459C22×C4C22⋊C4×C6112yes—
460C22×C4C4⋊C4×C6112yescomplemented
461C4⋊C4—48no—
462C22⋊C4—24no—
463C22⋊C4—24no—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—44no—
467C22⋊C4—42no—
468C22⋊C4—42no—
469C22⋊C4—42no—
470C22⋊C4—42no—
471C22⋊C4—41no—
472C22⋊C4—42no—
473C22⋊C4—41no—
474C22⋊C4—44no—
475C23—22no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—24no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—44no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—44no—
493C23—44no—
494C23—44no—
495C23—41no—
496C23—42no—
497C23—41no—
498C23—42no—
499C23—42no—
500C23—82no—
501C23—82no—
502C23—84no—
503C23C2×C22⋊C4×C6111yescharacteristic
504C23C2×C4⋊C4×C6111yescharacteristic
505C23#117×C6111yescharacteristic
506C23C4×D4×C6112yes—
507C23C4×D4×C6112yes—
508C23#120×C6111yescharacteristic
509C23#120×C6112yes—
510C23#121×C6111yescharacteristic
511C23#121×C6111yescharacteristic
512C23#121×C6112yes—
513C23#121×C6112yes—
514C23#121×C6112yes—
515C23C22⋊Q8×C6111yescharacteristic
516C23C22⋊Q8×C6111yescharacteristic
517C23C22⋊Q8×C6112yes—
518C23C22⋊Q8×C6112yes—
519C23#123×C6111yescharacteristic
520C23#123×C6112yes—
521C23#123×C6112yes—
522C23#124×C6111yescharacteristic
523C23#124×C6112yes—
524C23#126×C6112yes—
525C23#127×C6111yescharacteristic
526D4—42no—
527D4—42no—
528D4—44no—
529D4—44no—
530D4—42no—
531D4—42no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—48no—
542C2×C4—48no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—44no—
549C2×C4—44no—
550C2×C4—48no—
551C2×C4—42no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—84no—
557C2×C4—84no—
558C2×C4—82no—
559C2×C4—82no—
560C2×C4—84no—
561C2×C4—84no—
562C2×C4#99×C6114yescomplemented
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—21no—
570C22—21no—
571C22—22no—
572C22—22no—
573C22—21no—
574C22—22no—
575C22—22no—
576C22—21no—
577C22—24no—
578C22—22no—
579C22—24no—
580C22—22no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22—44no—
590C22—42no—
591C22—84no—
592C22—84no—
593C22—81no—
594C22—81no—
595C22—82no—
596C22C61×#38011yescharacteristic
597C22C61×#38512yes—
598C22C61×#38611yescharacteristic
599C22C61×#38812yes—
600C22C61×#39011yescharacteristic
601C22C61×#39211yescharacteristic
602C22C61×#39311yescharacteristic
603C22C61×#39412yes—
604C22C61×#39612yes—
605C22C61×#39711yescharacteristic
606C22C61×#39911yescharacteristic
607C22C2×#99×C6112yes—
608C22C61×#41012yes—
609C4—24no—
610C4—42no—
611C4—42no—
612C4—84no—
613C4—84no—
614C4—82no—
615C2—21no—
616C2—22no—
617C2—22no—
618C2—22no—
619C2—21no—
620C2—22no—
621C2—21no—
622C2—21no—
623C2—82no—
624C2C61×#143911yescharacteristic
625C2C61×#179912yes—
626C2C61×#189811yescharacteristic
627C2C61×#189911yescharacteristic
628C2C61×#196412yes—
subgroupG/H
center, socleC23×C61C2×C22⋊C4
commutatorC24C22×C4×C61
Frattini, cosocleC25C23×C61
prime radicalC23×D4×C61C22
LCSG ▷ C24 ▷ 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×C61×#380C2semidirect
4. C2×C61×#342C2semidirect
5. C61×C22⋊#95C2semidirect
9. C22×C22⋊C4×C61C4semidirect
22. C2×#95×C61C4semidirect
81. C24×C61C4⋊C4semidirect
145. C22×C4×C61C4⋊C4semidirect
247. C2×C4×C61#99semidirect
248. #11043C61direct (N × H)
303. C2×#380C2×C61semidirect
304. C2×#342C2×C61semidirect
305. C22⋊#95C2×C61semidirect
323. C22×C22⋊C4C4×C61semidirect
336. C2×#95C4×C61semidirect
338. C61#11043direct (N × H)
396. C24C4⋊C4×C61semidirect
460. C22×C4C4⋊C4×C61semidirect
562. 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×C61×#3802
C2×C61×#3422
C61×C22⋊#952
#1104361