Finite Group Databasebeta

← C61×#26403 #29529836

Subgroups — C61×#26403 #29529836

Order 15616.

706 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3084C211yesmaximal, characteristic
2C61×#3082C211yesmaximal, characteristic, complemented
3C61×#2947C211yesmaximal, characteristic
4C61×#2913C211yesmaximal, characteristic
5C61×#2097C211yesmaximal, characteristic, complemented
6C61×#2089C211yesmaximal, characteristic, complemented
7C61×#2064C211yesmaximal, characteristic, complemented
8C61×#2061C211yesmaximal, characteristic, complemented
9C61×#1951C211yesmaximal, characteristic, complemented
10C61×#1922C211yesmaximal, characteristic, complemented
11C61×#1908C211yesmaximal, characteristic
12C61×#1882C211yesmaximal, characteristic
13C61×#1866C211yesmaximal, characteristic
14C61×#1860C211yesmaximal, characteristic
15C61×#1857C211yesmaximal, characteristic, complemented
16C2×#137×C61C2211yescharacteristic
17C2×#131×C61C2211yescharacteristic
18C61×#544C2211yescharacteristic
19C61×#520C2211yescharacteristic
20C61×#520C2211yescharacteristic
21C61×#519C2211yescharacteristic
22C61×#479—21no—
23C61×#479—21no—
24C61×#479—21no—
25C61×#478—21no—
26C61×#477—21no—
27C61×#476—21no—
28C61×#475—21no—
29C61×#475—21no—
30C61×#441—21no—
31C61×#440—21no—
32C4×Q16×C61—21no—
33C4×SD16×C61—21no—
34C2×#108×C61C2211yescharacteristic
35C61×#428—21no—
36C61×#428—21no—
37C61×#428C2211yescharacteristic
38C61×#428C2211yescharacteristic
39C61×#428C2211yescharacteristic
40C61×#428C2211yescharacteristic
41C61×#428C2211yescharacteristic
42C61×#427—21no—
43C61×#427C2211yescharacteristic
44C2×#107×C61—21no—
45C2×#107×C61C2211yescharacteristic
46C2×#106×C61C2211yescharacteristic
47C61×#424C2211yescharacteristic
48C61×#424C2211yescharacteristic
49C2×#104×C61C2211yescharacteristic
50C61×#419C2211yescharacteristic
51C61×#417C2211yescharacteristic
52C61×#416C2211yescharacteristic
53C2×#103×C61C2211yescharacteristic
54C2×#103×C61C2211yescharacteristic
55C2×#101×C61C2211yescharacteristic
56C61×#405C2211yescharacteristic
57C61×#391C2211yescharacteristic
58C61×#382C2211yescharacteristic
59C61×#343C2211yescharacteristic
60C61×#343C2211yescharacteristic
61C61×#343C2211yescharacteristic
62C61×#341C2211yescharacteristic
63C61×#339C2211yescharacteristic
64C61×#339C2211yescharacteristic
65C61×#339C2211yescharacteristic
66C61×#336C2211yescharacteristic
67C2×#41×C61C2311yescharacteristic
68C22×Q8×C61C2311yescharacteristic
69#137×C61—22no—
70#137×C61Q814yescomplemented
71C2×Q16×C61—21no—
72C2×SD16×C61—21no—
73#131×C61—22no—
74#131×C61—22no—
75C2×M16×C61—21no—
76C2×M16×C61C2311yescharacteristic
77C2×M16×C61C2311yescharacteristic
78C2×M16×C61C2311yescharacteristic
79C2×M16×C61C2311yescharacteristic
80C22×C8×C61—21no—
81C22×C8×C61C2311yescharacteristic
82C22×C8×C61C2311yescharacteristic
83C4⋊Q8×C61—21no—
84C4⋊Q8×C61—21no—
85#125×C61—21no—
86#125×C61—21no—
87C22⋊Q8×C61—41no—
88C4×Q8×C61—21no—
89C4×Q8×C61—21no—
90C4×Q8×C61—21no—
91C4×Q8×C61—21no—
92C4×Q8×C61—21no—
93C4×Q8×C61—21no—
94C4×D4×C61—21no—
95C4×D4×C61—21no—
96C4×D4×C61—41no—
97C4×D4×C61—41no—
98#117×C61—21no—
99#117×C61—21no—
100#117×C61—41no—
101#117×C61C2311yescharacteristic
102#117×C61C2311yescharacteristic
103#117×C61C2311yescharacteristic
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C4⋊C4×C61C2311yescharacteristic
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C42×C61C2311yescharacteristic
110#108×C61—22no—
111#107×C61—21no—
112#107×C61—21no—
113#107×C61—21no—
114#107×C61—21no—
115#107×C61—21no—
116#107×C61—21no—
117#107×C61—21no—
118#107×C61D411yescharacteristic
119#107×C61D411yescharacteristic
120#106×C61—21no—
121#106×C61—21no—
122#106×C61—21no—
123#106×C61—21no—
124#106×C61—21no—
125#106×C61—21no—
126#106×C61—21no—
127#106×C61D411yescharacteristic
128#106×C61D411yescharacteristic
129C4⋊C8×C61—21no—
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61—21no—
133#104×C61—22no—
134#103×C61—21no—
135#103×C61—21no—
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#103×C61—21no—
140#103×C61—21no—
141#103×C61D411yescharacteristic
142#103×C61D411yescharacteristic
143#102×C61—21no—
144#102×C61D411yescharacteristic
145#102×C61D411yescharacteristic
146#101×C61—22no—
147#97×C61—21no—
148C4×C8×C61—21no—
149#95×C61—41no—
150#95×C61—41no—
151#41×C61—21no—
152#41×C61—21no—
153#41×C61C2×Q812yes—
154#41×C61#4112yes—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—41no—
161C2×Q8×C61C2×D411yescharacteristic
162C2×Q8×C61C2×Q812yes—
163C2×D4×C61—21no—
164C2×D4×C61C2×D411yescharacteristic
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—41no—
172C22×C4×C61—41no—
173C22×C4×C61C2411yescharacteristic
174Q16×C61—24no—
175SD16×C61—24no—
176M16×C61—24no—
177M16×C61—21no—
178M16×C61—21no—
179M16×C61—21no—
180M16×C61—21no—
181M16×C61—21no—
182M16×C61—21no—
183M16×C61C2×Q812yes—
184M16×C61#4112yes—
185C2×C8×C61—24no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61C2×D411yescharacteristic
195C2×C8×C61C2×D411yescharacteristic
196C2×C8×C61C2×D411yescharacteristic
197C2×C8×C61C2×D411yescharacteristic
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×C61—41no—
205C4⋊C4×C61—41no—
206C4⋊C4×C61—41no—
207C4⋊C4×C61—41no—
208C4⋊C4×C61—41no—
209C4⋊C4×C61—41no—
210C4⋊C4×C61—41no—
211C4⋊C4×C61C2×D411yescharacteristic
212C4⋊C4×C61C2×D411yescharacteristic
213C4⋊C4×C61C2×D411yescharacteristic
214C4⋊C4×C61C2×D411yescharacteristic
215C4⋊C4×C61C2×D411yescharacteristic
216C4⋊C4×C61C2×D411yescharacteristic
217C22⋊C4×C61—21no—
218C22⋊C4×C61—21no—
219C22⋊C4×C61—21no—
220C22⋊C4×C61—41no—
221C22⋊C4×C61—41no—
222C42×C61—21no—
223C42×C61—21no—
224C42×C61—21no—
225C42×C61—21no—
226C42×C61—21no—
227C42×C61—41no—
228C42×C61—41no—
229C42×C61—41no—
230C42×C61—41no—
231C23×C61—21no—
232C23×C61H(5,𝔽2)11yescharacteristic
233Q8×C61—21no—
234Q8×C61—22no—
235Q8×C61—22no—
236Q8×C61—41no—
237Q8×C61—41no—
238Q8×C61—161no—
239Q8×C61C22⋊Q812yes—
240D4×C61—22no—
241D4×C61—22no—
242D4×C61—21no—
243D4×C61C22⋊Q812yes—
244C2×C4×C61—21no—
245C2×C4×C61—22no—
246C2×C4×C61—22no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—22no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—81no—
263C2×C4×C61—81no—
264C2×C4×C61—81no—
265C2×C4×C61—161no—
266C2×C4×C61—161no—
267C2×C4×C61C22×D411yescharacteristic
268C2×C4×C61C22×D411yescharacteristic
269C2×C4×C61C22×Q811yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61C2×#4111yescharacteristic
272C2×C4×C612−1+411yescharacteristic
273C8×C61—22no—
274C8×C61—21no—
275C8×C61—22no—
276C8×C61—21no—
277C8×C61—21no—
278C8×C61—21no—
279C8×C61—41no—
280C8×C61—41no—
281#26403C6111yesmaximal, characteristic, direct product factor, Sylow
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—22no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61#53911yescharacteristic
288C22×C61D4211yescharacteristic
289C22×C61#55411yescharacteristic
290C4×C61—22no—
291C4×C61—42no—
292C4×C61—41no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61—41no—
296C4×C61—41no—
297C4×C61—41no—
298C4×C61—81no—
299C4×C61—81no—
300C4×C61—81no—
301C4×C61—81no—
302C4×C61C2×C22⋊Q811yescharacteristic
303C4×C61#52511yescharacteristic
304C4×C61#54711yescharacteristic
305C4×C61D4×Q811yescharacteristic
306#3084C2×C6111yescharacteristic
307#3082C2×C6111yescharacteristic, complemented
308#2947C2×C6111yescharacteristic
309#2913C2×C6111yescharacteristic
310#2097C2×C6111yescharacteristic, complemented
311#2089C2×C6111yescharacteristic, complemented
312#2064C2×C6111yescharacteristic, complemented
313#2061C2×C6111yescharacteristic, complemented
314#1951C2×C6111yescharacteristic, complemented
315#1922C2×C6111yescharacteristic, complemented
316#1908C2×C6111yescharacteristic
317#1882C2×C6111yescharacteristic
318#1866C2×C6111yescharacteristic
319#1860C2×C6111yescharacteristic
320#1857C2×C6111yescharacteristic, complemented
321C2×C61—21no—
322C2×C61—21no—
323C2×C61—42no—
324C2×C61#244911yescharacteristic
325C2×C61#328911yescharacteristic
326C2×C61#329011yescharacteristic
327C2×#137C22×C6111yescharacteristic
328C2×#131C22×C6111yescharacteristic
329#544C22×C6111yescharacteristic
330#520C22×C6111yescharacteristic
331#520C22×C6111yescharacteristic
332#519C22×C6111yescharacteristic
333#479—21no—
334#479—21no—
335#479—21no—
336#478—21no—
337#477—21no—
338#476—21no—
339#475—21no—
340#475—21no—
341#441—21no—
342#440—21no—
343C4×Q16—21no—
344C4×SD16—21no—
345C2×#108C22×C6111yescharacteristic
346#428—21no—
347#428—21no—
348#428C22×C6111yescharacteristic
349#428C22×C6111yescharacteristic
350#428C22×C6111yescharacteristic
351#428C22×C6111yescharacteristic
352#428C22×C6111yescharacteristic
353#427—21no—
354#427C22×C6111yescharacteristic
355C2×#107—21no—
356C2×#107C22×C6111yescharacteristic
357C2×#106C22×C6111yescharacteristic
358#424C22×C6111yescharacteristic
359#424C22×C6111yescharacteristic
360C2×#104C22×C6111yescharacteristic
361#419C22×C6111yescharacteristic
362#417C22×C6111yescharacteristic
363#416C22×C6111yescharacteristic
364C2×#103C22×C6111yescharacteristic
365C2×#103C22×C6111yescharacteristic
366C2×#101C22×C6111yescharacteristic
367#405C22×C6111yescharacteristic
368#391C22×C6111yescharacteristic
369#382C22×C6111yescharacteristic
370#343C22×C6111yescharacteristic
371#343C22×C6111yescharacteristic
372#343C22×C6111yescharacteristic
373#341C22×C6111yescharacteristic
374#339C22×C6111yescharacteristic
375#339C22×C6111yescharacteristic
376#339C22×C6111yescharacteristic
377#336C22×C6111yescharacteristic
378C61#2640311yescharacteristic, direct product factor, Sylow
379C2×#41C23×C6111yescharacteristic
380C22×Q8C23×C6111yescharacteristic
381#137—22no—
382#137Q8×C6114yescomplemented
383C2×Q16—21no—
384C2×SD16—21no—
385#131—22no—
386#131—22no—
387C2×M16—21no—
388C2×M16C23×C6111yescharacteristic
389C2×M16C23×C6111yescharacteristic
390C2×M16C23×C6111yescharacteristic
391C2×M16C23×C6111yescharacteristic
392C22×C8—21no—
393C22×C8C23×C6111yescharacteristic
394C22×C8C23×C6111yescharacteristic
395C4⋊Q8—21no—
396C4⋊Q8—21no—
397#125—21no—
398#125—21no—
399C22⋊Q8—41no—
400C4×Q8—21no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4—41no—
409C4×D4—41no—
410#117—21no—
411#117—21no—
412#117—41no—
413#117C23×C6111yescharacteristic
414#117C23×C6111yescharacteristic
415#117C23×C6111yescharacteristic
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4C23×C6111yescharacteristic
419C2×C4⋊C4C23×C6111yescharacteristic
420C2×C4⋊C4C23×C6111yescharacteristic
421C2×C42C23×C6111yescharacteristic
422#108—22no—
423#107—21no—
424#107—21no—
425#107—21no—
426#107—21no—
427#107—21no—
428#107—21no—
429#107—21no—
430#107D4×C6111yescharacteristic
431#107D4×C6111yescharacteristic
432#106—21no—
433#106—21no—
434#106—21no—
435#106—21no—
436#106—21no—
437#106—21no—
438#106—21no—
439#106D4×C6111yescharacteristic
440#106D4×C6111yescharacteristic
441C4⋊C8—21no—
442C4⋊C8—21no—
443C4⋊C8—21no—
444C4⋊C8—21no—
445#104—22no—
446#103—21no—
447#103—21no—
448#103—21no—
449#103—21no—
450#103—21no—
451#103—21no—
452#103—21no—
453#103D4×C6111yescharacteristic
454#103D4×C6111yescharacteristic
455#102—21no—
456#102D4×C6111yescharacteristic
457#102D4×C6111yescharacteristic
458#101—22no—
459#97—21no—
460C4×C8—21no—
461#95—41no—
462#95—41no—
463#41—21no—
464#41—21no—
465#41C2×Q8×C6112yes—
466#41#41×C6112yes—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—41no—
473C2×Q8C2×D4×C6111yescharacteristic
474C2×Q8C2×Q8×C6112yes—
475C2×D4—21no—
476C2×D4C2×D4×C6111yescharacteristic
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4C24×C6111yescharacteristic
486Q16—24no—
487SD16—24no—
488M16—24no—
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16C2×Q8×C6112yes—
496M16#41×C6112yes—
497C2×C8—24no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8C2×D4×C6111yescharacteristic
507C2×C8C2×D4×C6111yescharacteristic
508C2×C8C2×D4×C6111yescharacteristic
509C2×C8C2×D4×C6111yescharacteristic
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4C2×D4×C6111yescharacteristic
524C4⋊C4C2×D4×C6111yescharacteristic
525C4⋊C4C2×D4×C6111yescharacteristic
526C4⋊C4C2×D4×C6111yescharacteristic
527C4⋊C4C2×D4×C6111yescharacteristic
528C4⋊C4C2×D4×C6111yescharacteristic
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—41no—
533C22⋊C4—41no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—41no—
540C42—41no—
541C42—41no—
542C42—41no—
543C23—21no—
544C23H(5,𝔽2)×C6111yescharacteristic
545Q8—21no—
546Q8—22no—
547Q8—22no—
548Q8—41no—
549Q8—41no—
550Q8—161no—
551Q8C22⋊Q8×C6112yes—
552D4—22no—
553D4—22no—
554D4—21no—
555D4C22⋊Q8×C6112yes—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—81no—
575C2×C4—81no—
576C2×C4—81no—
577C2×C4—161no—
578C2×C4—161no—
579C2×C4C22×D4×C6111yescharacteristic
580C2×C4C22×D4×C6111yescharacteristic
581C2×C4C22×Q8×C6111yescharacteristic
582C2×C4C2×#41×C6111yescharacteristic
583C2×C4C2×#41×C6111yescharacteristic
584C2×C42−1+4×C6111yescharacteristic
585C8—21no—
586C8—21no—
587C8—22no—
588C8—21no—
589C8—22no—
590C8—21no—
591C8—41no—
592C8—41no—
593C22—21no—
594C22—21no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22C61×#53911yescharacteristic
599C22D42×C6111yescharacteristic
600C22C61×#55411yescharacteristic
601C4—22no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—42no—
609C4—81no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4C2×C22⋊Q8×C6111yescharacteristic
614C4C61×#52511yescharacteristic
615C4C61×#54711yescharacteristic
616C4D4×Q8×C6111yescharacteristic
617C2—21no—
618C2—21no—
619C2—42no—
620C2C61×#244911yescharacteristic
621C2C61×#328911yescharacteristic
622C2C61×#329011yescharacteristic
subgroupG/H
center, socleC22×C61D42
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×#41×C61C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C22×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#3082C2semidirect
5. C61×#2097C2semidirect
6. C61×#2089C2semidirect
7. C61×#2064C2semidirect
8. C61×#2061C2semidirect
9. C61×#1951C2semidirect
10. C61×#1922C2semidirect
15. C61×#1857C2semidirect
70. #137×C61Q8semidirect
281. #26403C61direct (N × H)
307. #3082C2×C61semidirect
310. #2097C2×C61semidirect
311. #2089C2×C61semidirect
312. #2064C2×C61semidirect
313. #2061C2×C61semidirect
314. #1951C2×C61semidirect
315. #1922C2×C61semidirect
320. #1857C2×C61semidirect
378. C61#26403direct (N × H)
382. #137Q8×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#30842
C61×#30822
C61×#29472
C61×#29132
C61×#20972
C61×#20892
C61×#20642
C61×#20612
C61×#19512
C61×#19222
C61×#19082
C61×#18822
C61×#18662
C61×#18602
C61×#18572
#2640361