Finite Group Databasebeta

← C61×#11094 #29514527

Subgroups — C61×#11094 #29514527

Order 15616.

868 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2905C211yesmaximal, characteristic, complemented
2C2×C61×#421C211yesmaximal, characteristic
3C2×C61×#421C211yesmaximal, characteristic
4C2×C61×#410C211yesmaximal, characteristic
5C61×#1740C211yesmaximal, characteristic, complemented
6C61×#1733C211yesmaximal, characteristic, complemented
7C61×#1733C211yesmaximal, characteristic, complemented
8C22×#41×C61C2211yescharacteristic
9C22×M16×C61C2211yescharacteristic
10C22×M16×C61C2211yescharacteristic
11C2×#117×C61C2211yescharacteristic
12C2×#117×C61C2211yescharacteristic
13C2×#117×C61C2211yescharacteristic
14C2×#117×C61C2211yescharacteristic
15C61×#424—22no—
16C61×#424—22no—
17C61×#423—22no—
18C61×#421—22no—
19C61×#421—22no—
20C61×#421—22no—
21C61×#421—22no—
22C2×#104×C61—22no—
23C2×#104×C61—22no—
24C61×#410—22no—
25C61×#410C414yescomplemented
26C2×#99×C61—22no—
27C61×#342—22no—
28C61×#339—22no—
29C61×#339—22no—
30C2×#41×C61—21no—
31C2×#41×C61—21no—
32C2×#41×C61—21no—
33C2×#41×C61—21no—
34C2×#41×C61—21no—
35C2×#41×C61—21no—
36C2×#41×C61—21no—
37C2×#41×C61—21no—
38C2×#41×C61—21no—
39C2×#41×C61—21no—
40C2×#41×C61C2×C412yes—
41C2×#41×C61D412yes—
42C22×Q8×C61Q811yescharacteristic
43C22×D4×C61—21no—
44C22×D4×C61Q811yescharacteristic
45C23×C4×C61—21no—
46C23×C4×C61C2311yescharacteristic
47C2×M16×C61—21no—
48C2×M16×C61—21no—
49C2×M16×C61—21no—
50C2×M16×C61—21no—
51C2×M16×C61—21no—
52C2×M16×C61—21no—
53C2×M16×C61—21no—
54C2×M16×C61—21no—
55C2×M16×C61—21no—
56C2×M16×C61—21no—
57C2×M16×C61D412yes—
58C2×M16×C61D412yes—
59C22×C8×C61—21no—
60C22×C8×C61—21no—
61#117×C61—21no—
62#117×C61—21no—
63#117×C61—21no—
64#117×C61—21no—
65#117×C61—21no—
66#117×C61—21no—
67#117×C61—21no—
68#117×C61—21no—
69#117×C61—21no—
70#117×C61—21no—
71#117×C61—21no—
72#117×C61—21no—
73#117×C61C2×C412yes—
74#117×C61C2×C412yes—
75#117×C61D412yes—
76#117×C61D412yes—
77C2×C4⋊C4×C61—21no—
78C2×C4⋊C4×C61—21no—
79C2×C4⋊C4×C61—21no—
80C2×C4⋊C4×C61—21no—
81C2×C22⋊C4×C61—21no—
82C2×C22⋊C4×C61—21no—
83C2×C22⋊C4×C61—21no—
84C2×C22⋊C4×C61D412yes—
85C2×C42×C61—21no—
86C2×C42×C61—21no—
87C2×C42×C61—21no—
88C2×C42×C61D412yes—
89C4⋊C8×C61—28no—
90#104×C61—28no—
91#104×C61—28no—
92#99×C61—28no—
93C24×C61—21no—
94C24×C61C2×D411yescharacteristic
95#41×C61—22no—
96#41×C61—22no—
97#41×C61—22no—
98#41×C61—22no—
99#41×C61—22no—
100#41×C61—22no—
101#41×C61—22no—
102#41×C61—22no—
103#41×C61—41no—
104#41×C61—41no—
105#41×C61—41no—
106#41×C61—41no—
107#41×C61—41no—
108#41×C61—41no—
109#41×C61—41no—
110#41×C61—41no—
111C2×Q8×C61—21no—
112C2×Q8×C61—21no—
113C2×Q8×C61—21no—
114C2×Q8×C61—21no—
115C2×Q8×C61—21no—
116C2×Q8×C61C4⋊C412yes—
117C2×D4×C61—22no—
118C2×D4×C61—22no—
119C2×D4×C61—21no—
120C2×D4×C61—21no—
121C2×D4×C61—21no—
122C2×D4×C61—21no—
123C2×D4×C61—21no—
124C2×D4×C61—41no—
125C2×D4×C61—41no—
126C2×D4×C61—41no—
127C2×D4×C61—41no—
128C2×D4×C61C4⋊C412yes—
129C22×C4×C61—21no—
130C22×C4×C61—22no—
131C22×C4×C61—22no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
134C22×C4×C61—41no—
135C22×C4×C61—41no—
136C22×C4×C61—41no—
137C22×C4×C61—41no—
138C22×C4×C61—41no—
139C22×C4×C61—41no—
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×Q811yescharacteristic
148C22×C4×C61#4111yescharacteristic
149C22×C4×C61#4111yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C22×C4×C61#4111yescharacteristic
152C22×C4×C61#4111yescharacteristic
153C22×C4×C61#4111yescharacteristic
154M16×C61—22no—
155M16×C61—22no—
156M16×C61—22no—
157M16×C61—22no—
158M16×C61—41no—
159M16×C61—41no—
160M16×C61—41no—
161M16×C61—41no—
162C2×C8×C61—22no—
163C2×C8×C61—22no—
164C2×C8×C61—41no—
165C2×C8×C61—41no—
166C2×C8×C61—41no—
167C2×C8×C61—41no—
168C4⋊C4×C61—22no—
169C4⋊C4×C61—22no—
170C4⋊C4×C61—22no—
171C4⋊C4×C61—22no—
172C4⋊C4×C61—41no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C22⋊C4×C61—22no—
177C22⋊C4×C61—22no—
178C22⋊C4×C61—22no—
179C22⋊C4×C61—41no—
180C22⋊C4×C61—41no—
181C22⋊C4×C61—41no—
182C22⋊C4×C61—41no—
183C22⋊C4×C61C22⋊C414yes—
184C42×C61—22no—
185C42×C61—22no—
186C42×C61—22no—
187C42×C61—22no—
188C42×C61—22no—
189C42×C61—22no—
190C42×C61—41no—
191C42×C61—41no—
192C23×C61—22no—
193C23×C61—41no—
194C23×C61—41no—
195C23×C61—81no—
196C23×C61—82no—
197C23×C61C2×C22⋊C411yescharacteristic
198C23×C61#12111yescharacteristic
199C23×C61#12111yescharacteristic
200C23×C61#12111yescharacteristic
201C23×C61#12111yescharacteristic
202C23×C61#12111yescharacteristic
203C23×C61C22⋊Q811yescharacteristic
204Q8×C61—22no—
205Q8×C61—22no—
206Q8×C61—41no—
207Q8×C61—41no—
208D4×C61—22no—
209D4×C61—22no—
210D4×C61—42no—
211D4×C61—42no—
212D4×C61—42no—
213D4×C61—42no—
214D4×C61—41no—
215D4×C61—41no—
216C2×C4×C61—22no—
217C2×C4×C61—24no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—42no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61—82no—
228C2×C4×C61—82no—
229C2×C4×C61—82no—
230C2×C4×C61—82no—
231C2×C4×C61C2×C4⋊C411yescharacteristic
232C2×C4×C61#11711yescharacteristic
233C2×C4×C61C4×D411yescharacteristic
234C2×C4×C61C4×D411yescharacteristic
235C2×C4×C61C4×D411yescharacteristic
236C2×C4×C61C4×D411yescharacteristic
237C2×C4×C61#12011yescharacteristic
238C2×C4×C61#12011yescharacteristic
239C2×C4×C61#12011yescharacteristic
240C2×C4×C61#12111yescharacteristic
241C2×C4×C61#12111yescharacteristic
242C2×C4×C61#12111yescharacteristic
243C2×C4×C61C22⋊Q811yescharacteristic
244C2×C4×C61C22⋊Q811yescharacteristic
245C2×C4×C61C22⋊Q811yescharacteristic
246C2×C4×C61C22⋊Q811yescharacteristic
247C2×C4×C61C22⋊Q811yescharacteristic
248C2×C4×C61#12311yescharacteristic
249C2×C4×C61#12311yescharacteristic
250C2×C4×C61#12311yescharacteristic
251C2×C4×C61#12311yescharacteristic
252C2×C4×C61#12311yescharacteristic
253C2×C4×C61#12411yescharacteristic
254C2×C4×C61#12411yescharacteristic
255C2×C4×C61#12411yescharacteristic
256C2×C4×C61#12611yescharacteristic
257C2×C4×C61#12611yescharacteristic
258C2×C4×C61#12711yescharacteristic
259C8×C61—42no—
260C8×C61—42no—
261#11094C6111yesmaximal, characteristic, direct product factor, Sylow
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—42no—
270C22×C61—82no—
271C22×C61—82no—
272C22×C61—82no—
273C22×C61#38011yescharacteristic
274C22×C61#38611yescharacteristic
275C22×C61#39011yescharacteristic
276C22×C61#39411yescharacteristic
277C22×C61#39411yescharacteristic
278C22×C61#39611yescharacteristic
279C22×C61#39611yescharacteristic
280C4×C61—44no—
281C4×C61—42no—
282C4×C61—82no—
283C4×C61—82no—
284C4×C61—82no—
285C4×C61#38511yescharacteristic
286C4×C61#38511yescharacteristic
287C4×C61#38811yescharacteristic
288C4×C61#38811yescharacteristic
289C4×C61#39211yescharacteristic
290C4×C61#39311yescharacteristic
291C4×C61#39711yescharacteristic
292C4×C61#39911yescharacteristic
293#2905C2×C6111yescharacteristic, complemented
294C2×#421C2×C6111yescharacteristic
295C2×#421C2×C6111yescharacteristic
296C2×#410C2×C6111yescharacteristic
297#1740C2×C6111yescharacteristic, complemented
298#1733C2×C6111yescharacteristic, complemented
299#1733C2×C6111yescharacteristic, complemented
300C2×C61—21no—
301C2×C61—21no—
302C2×C61—21no—
303C2×C61—21no—
304C2×C61—21no—
305C2×C61—21no—
306C2×C61—21no—
307C2×C61—82no—
308C2×C61#143911yescharacteristic
309C22×#41C22×C6111yescharacteristic
310C22×M16C22×C6111yescharacteristic
311C22×M16C22×C6111yescharacteristic
312C2×#117C22×C6111yescharacteristic
313C2×#117C22×C6111yescharacteristic
314C2×#117C22×C6111yescharacteristic
315C2×#117C22×C6111yescharacteristic
316#424—22no—
317#424—22no—
318#423—22no—
319#421—22no—
320#421—22no—
321#421—22no—
322#421—22no—
323C2×#104—22no—
324C2×#104—22no—
325#410—22no—
326#410C4×C6114yescomplemented
327C2×#99—22no—
328#342—22no—
329#339—22no—
330#339—22no—
331C61#1109411yescharacteristic, direct product factor, Sylow
332C2×#41—21no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41C2×C4×C6112yes—
343C2×#41D4×C6112yes—
344C22×Q8Q8×C6111yescharacteristic
345C22×D4—21no—
346C22×D4Q8×C6111yescharacteristic
347C23×C4—21no—
348C23×C4C23×C6111yescharacteristic
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16D4×C6112yes—
360C2×M16D4×C6112yes—
361C22×C8—21no—
362C22×C8—21no—
363#117—21no—
364#117—21no—
365#117—21no—
366#117—21no—
367#117—21no—
368#117—21no—
369#117—21no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117C2×C4×C6112yes—
376#117C2×C4×C6112yes—
377#117D4×C6112yes—
378#117D4×C6112yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4D4×C6112yes—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42D4×C6112yes—
391C4⋊C8—28no—
392#104—28no—
393#104—28no—
394#99—28no—
395C24—21no—
396C24C2×D4×C6111yescharacteristic
397#41—22no—
398#41—22no—
399#41—22no—
400#41—22no—
401#41—22no—
402#41—22no—
403#41—22no—
404#41—22no—
405#41—41no—
406#41—41no—
407#41—41no—
408#41—41no—
409#41—41no—
410#41—41no—
411#41—41no—
412#41—41no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8C4⋊C4×C6112yes—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4C4⋊C4×C6112yes—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4C22×C4×C6111yescharacteristic
443C22×C4C2×D4×C6111yescharacteristic
444C22×C4C2×D4×C6111yescharacteristic
445C22×C4C2×D4×C6111yescharacteristic
446C22×C4C2×D4×C6111yescharacteristic
447C22×C4C2×D4×C6111yescharacteristic
448C22×C4C2×D4×C6111yescharacteristic
449C22×C4C2×Q8×C6111yescharacteristic
450C22×C4#41×C6111yescharacteristic
451C22×C4#41×C6111yescharacteristic
452C22×C4#41×C6111yescharacteristic
453C22×C4#41×C6111yescharacteristic
454C22×C4#41×C6111yescharacteristic
455C22×C4#41×C6111yescharacteristic
456M16—22no—
457M16—22no—
458M16—22no—
459M16—22no—
460M16—41no—
461M16—41no—
462M16—41no—
463M16—41no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—41no—
467C2×C8—41no—
468C2×C8—41no—
469C2×C8—41no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4C22⋊C4×C6114yes—
486C42—22no—
487C42—22no—
488C42—22no—
489C42—22no—
490C42—22no—
491C42—22no—
492C42—41no—
493C42—41no—
494C23—22no—
495C23—41no—
496C23—41no—
497C23—81no—
498C23—82no—
499C23C2×C22⋊C4×C6111yescharacteristic
500C23#121×C6111yescharacteristic
501C23#121×C6111yescharacteristic
502C23#121×C6111yescharacteristic
503C23#121×C6111yescharacteristic
504C23#121×C6111yescharacteristic
505C23C22⋊Q8×C6111yescharacteristic
506Q8—22no—
507Q8—22no—
508Q8—41no—
509Q8—41no—
510D4—22no—
511D4—22no—
512D4—42no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—41no—
517D4—41no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—82no—
530C2×C4—82no—
531C2×C4—82no—
532C2×C4—82no—
533C2×C4C2×C4⋊C4×C6111yescharacteristic
534C2×C4#117×C6111yescharacteristic
535C2×C4C4×D4×C6111yescharacteristic
536C2×C4C4×D4×C6111yescharacteristic
537C2×C4C4×D4×C6111yescharacteristic
538C2×C4C4×D4×C6111yescharacteristic
539C2×C4#120×C6111yescharacteristic
540C2×C4#120×C6111yescharacteristic
541C2×C4#120×C6111yescharacteristic
542C2×C4#121×C6111yescharacteristic
543C2×C4#121×C6111yescharacteristic
544C2×C4#121×C6111yescharacteristic
545C2×C4C22⋊Q8×C6111yescharacteristic
546C2×C4C22⋊Q8×C6111yescharacteristic
547C2×C4C22⋊Q8×C6111yescharacteristic
548C2×C4C22⋊Q8×C6111yescharacteristic
549C2×C4C22⋊Q8×C6111yescharacteristic
550C2×C4#123×C6111yescharacteristic
551C2×C4#123×C6111yescharacteristic
552C2×C4#123×C6111yescharacteristic
553C2×C4#123×C6111yescharacteristic
554C2×C4#123×C6111yescharacteristic
555C2×C4#124×C6111yescharacteristic
556C2×C4#124×C6111yescharacteristic
557C2×C4#124×C6111yescharacteristic
558C2×C4#126×C6111yescharacteristic
559C2×C4#126×C6111yescharacteristic
560C2×C4#127×C6111yescharacteristic
561C8—42no—
562C8—42no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—42no—
571C22—82no—
572C22—82no—
573C22—82no—
574C22C61×#38011yescharacteristic
575C22C61×#38611yescharacteristic
576C22C61×#39011yescharacteristic
577C22C61×#39411yescharacteristic
578C22C61×#39411yescharacteristic
579C22C61×#39611yescharacteristic
580C22C61×#39611yescharacteristic
581C4—44no—
582C4—42no—
583C4—82no—
584C4—82no—
585C4—82no—
586C4C61×#38511yescharacteristic
587C4C61×#38511yescharacteristic
588C4C61×#38811yescharacteristic
589C4C61×#38811yescharacteristic
590C4C61×#39211yescharacteristic
591C4C61×#39311yescharacteristic
592C4C61×#39711yescharacteristic
593C4C61×#39911yescharacteristic
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—82no—
602C2C61×#143911yescharacteristic
subgroupG/H
centerC4×C61#392
commutatorC22×C4C22×C4×C61
Frattini, cosocleC23×C4C23×C61
socleC2×C61#1439
prime radicalC22×#41×C61C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#2905C2semidirect
5. C61×#1740C2semidirect
6. C61×#1733C2semidirect
7. C61×#1733C2semidirect
25. C61×#410C4semidirect
261. #11094C61direct (N × H)
293. #2905C2×C61semidirect
297. #1740C2×C61semidirect
298. #1733C2×C61semidirect
299. #1733C2×C61semidirect
326. #410C4×C61semidirect
331. C61#11094direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#29052
C2×C61×#4212
C2×C61×#4102
C61×#17402
C61×#17332
#1109461