Finite Group Databasebeta

← C61×#18469 #29521902

Subgroups — C61×#18469 #29521902

Order 15616.

814 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3563C211yesmaximal, characteristic
2C61×#3236C211yesmaximal, characteristic, complemented
3C61×#3232C211yesmaximal, characteristic
4C61×#2822C211yesmaximal, characteristic, complemented
5C61×#1617C212yesmaximal, complemented
6C61×#1615C212yesmaximal
7C61×#1611C212yesmaximal, complemented
8C61×#1609C212yesmaximal
9C61×#1518C211yesmaximal, characteristic, complemented
10C61×#1512C211yesmaximal, characteristic
11C61×#1470C211yesmaximal, characteristic, complemented
12C61×#564—21no—
13C61×#563—21no—
14C61×#557—21no—
15C61×#554—21no—
16C61×#552—21no—
17C61×#552—22no—
18C61×#552—21no—
19C61×#544—21no—
20C61×#544C2212yes—
21C61×#541—21no—
22C61×#541—22no—
23C61×#539C2212yes—
24C61×#533C2211yescharacteristic
25C61×#529C2211yescharacteristic
26C2×#125×C61C2211yescharacteristic
27C2×#125×C61C2211yescharacteristic
28C61×#501—21no—
29C61×#499—21no—
30C61×#491—21no—
31C61×#488—21no—
32C61×#484C2212yes—
33C61×#484C2211yescharacteristic
34C61×#483C2212yes—
35C61×#483C2211yescharacteristic
36C61×#481C2211yescharacteristic
37C61×#480C2211yescharacteristic
38C61×#479—21no—
39C61×#479—22no—
40C61×#478—21no—
41C61×#432C2211yescharacteristic
42C61×#431C2211yescharacteristic
43C61×#400—21no—
44C61×#400C2212yes—
45C61×#398—21no—
46C61×#398—22no—
47C61×#398C2212yes—
48C61×#382C2211yescharacteristic
49C61×#328C2212yes—
50C61×#328C2212yes—
51C61×#328C2212yes—
52C61×#327C2212yes—
53C61×#324C2212yes—
54C61×#324C2212yes—
55C4⋊Q8×C61—21no—
56C4⋊Q8×C61—22no—
57C4⋊Q8×C61—22no—
58C4⋊Q8×C61D411yescharacteristic
59C4⋊Q8×C61D411yescharacteristic
60#126×C61—22no—
61#126×C61—22no—
62#126×C61—22no—
63#126×C61—22no—
64#126×C61—21no—
65#125×C61—22no—
66#125×C61—22no—
67#125×C61—22no—
68#125×C61—22no—
69#125×C61—21no—
70#125×C61—22no—
71#125×C61—22no—
72#125×C61—22no—
73#125×C61—22no—
74#125×C61—21no—
75#125×C61—21no—
76#125×C61—21no—
77#125×C61—21no—
78#125×C61—21no—
79#125×C61—21no—
80#125×C61—21no—
81#125×C61—21no—
82#125×C61—21no—
83#125×C61D411yescharacteristic
84#124×C61D411yescharacteristic
85#123×C61—22no—
86#123×C61—22no—
87#123×C61—21no—
88C22⋊Q8×C61—21no—
89C22⋊Q8×C61—21no—
90C22⋊Q8×C61—22no—
91C22⋊Q8×C61—22no—
92C22⋊Q8×C61—22no—
93C22⋊Q8×C61—21no—
94C22⋊Q8×C61—22no—
95C22⋊Q8×C61C2312yes—
96C22⋊Q8×C61C2311yescharacteristic
97#121×C61C2311yescharacteristic
98C4×Q8×C61—21no—
99C4×Q8×C61—22no—
100C4×Q8×C61—21no—
101C4×Q8×C61—21no—
102C4×Q8×C61D412yes—
103C4×Q8×C61D411yescharacteristic
104C4×D4×C61—22no—
105C4×D4×C61—21no—
106C4×D4×C61D411yescharacteristic
107#117×C61—22no—
108#117×C61—21no—
109#117×C61—21no—
110#117×C61—22no—
111#117×C61—21no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61—22no—
117C2×C4⋊C4×C61D411yescharacteristic
118C2×C4⋊C4×C61D412yes—
119C2×C4⋊C4×C61D411yescharacteristic
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2312yes—
123C2×C42×C61C2311yescharacteristic
124#107×C61—21no—
125#107×C61—21no—
126#107×C61—22no—
127#106×C61—21no—
128#106×C61—21no—
129#106×C61—22no—
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132#103×C61—21no—
133#103×C61—22no—
134#103×C61—21no—
135#103×C61—22no—
136#102×C61—21no—
137#102×C61—21no—
138C22⋊C8×C61C2312yes—
139C22⋊C8×C61C2311yescharacteristic
140C22⋊C8×C61C2311yescharacteristic
141#97×C61—21no—
142C4×C8×C61—21no—
143#95×C61—21no—
144#95×C61—22no—
145#95×C61—22no—
146#95×C61—22no—
147#95×C61C2312yes—
148C2×Q8×C61—22no—
149C2×Q8×C61—21no—
150C2×Q8×C61C2×D412yes—
151C2×Q8×C61C2×D411yescharacteristic
152C2×D4×C61—21no—
153C2×D4×C61C2×D411yescharacteristic
154C22×C4×C61—22no—
155C22×C4×C61—21no—
156C22×C4×C61—22no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61C2×D412yes—
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D412yes—
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2411yescharacteristic
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—22no—
167C4⋊C4×C61—22no—
168C4⋊C4×C61—22no—
169C4⋊C4×C61—22no—
170C4⋊C4×C61—22no—
171C4⋊C4×C61—22no—
172C4⋊C4×C61—22no—
173C4⋊C4×C61—22no—
174C4⋊C4×C61—22no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—22no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—22no—
188C4⋊C4×C61—22no—
189C4⋊C4×C61—22no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—22no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—41no—
197C4⋊C4×C61—41no—
198C4⋊C4×C61—41no—
199C4⋊C4×C61—41no—
200C4⋊C4×C61—81no—
201C4⋊C4×C61—82no—
202C4⋊C4×C61C2×D411yescharacteristic
203C4⋊C4×C61C2×D411yescharacteristic
204C4⋊C4×C61C2×D412yes—
205C22⋊C4×C61—22no—
206C22⋊C4×C61—22no—
207C22⋊C4×C61—22no—
208C22⋊C4×C61—22no—
209C22⋊C4×C61—21no—
210C22⋊C4×C61—21no—
211C22⋊C4×C61—21no—
212C22⋊C4×C61—21no—
213C22⋊C4×C61—21no—
214C42×C61—22no—
215C42×C61—22no—
216C42×C61—22no—
217C42×C61—22no—
218C42×C61—21no—
219C42×C61C2×D411yescharacteristic
220C42×C61C2×D411yescharacteristic
221C42×C61C2×D411yescharacteristic
222C42×C61C2×D411yescharacteristic
223C23×C61—21no—
224C23×C61C22×D411yescharacteristic
225Q8×C61—42no—
226Q8×C61—41no—
227Q8×C61—42no—
228Q8×C61—82no—
229D4×C61—41no—
230D4×C61—41no—
231D4×C61—41no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—22no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—22no—
238C2×C4×C61—21no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—42no—
246C2×C4×C61—42no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—42no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—82no—
256C2×C4×C61#12011yescharacteristic
257C2×C4×C61#12011yescharacteristic
258C2×C4×C61#12011yescharacteristic
259C2×C4×C61#12011yescharacteristic
260C2×C4×C61C22×D411yescharacteristic
261C2×C4×C61C22×D411yescharacteristic
262C8×C61—41no—
263C8×C61—41no—
264C8×C61—42no—
265#18469C6111yesmaximal, characteristic, direct product factor, Sylow
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61C2×#12011yescharacteristic
272C22×C61#57711yescharacteristic
273C22×C61#57811yescharacteristic
274C4×C61—21no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—21no—
278C4×C61—21no—
279C4×C61—21no—
280C4×C61—42no—
281C4×C61—41no—
282C4×C61—41no—
283C4×C61—42no—
284C4×C61—42no—
285C4×C61—42no—
286C4×C61—41no—
287C4×C61—82no—
288C4×C61—81no—
289C4×C61—81no—
290#3563C2×C6111yescharacteristic
291#3236C2×C6111yescharacteristic, complemented
292#3232C2×C6111yescharacteristic
293#2822C2×C6111yescharacteristic, complemented
294#1617C2×C6112yescomplemented
295#1615C2×C6112yes—
296#1611C2×C6112yescomplemented
297#1609C2×C6112yes—
298#1518C2×C6111yescharacteristic, complemented
299#1512C2×C6111yescharacteristic
300#1470C2×C6111yescharacteristic, complemented
301C2×C61—21no—
302C2×C61—21no—
303C2×C61—81no—
304C2×C61#301311yescharacteristic
305C2×C61#302011yescharacteristic
306C2×C61#302811yescharacteristic
307#564—21no—
308#563—21no—
309#557—21no—
310#554—21no—
311#552—21no—
312#552—22no—
313#552—21no—
314#544—21no—
315#544C22×C6112yes—
316#541—21no—
317#541—22no—
318#539C22×C6112yes—
319#533C22×C6111yescharacteristic
320#529C22×C6111yescharacteristic
321C2×#125C22×C6111yescharacteristic
322C2×#125C22×C6111yescharacteristic
323#501—21no—
324#499—21no—
325#491—21no—
326#488—21no—
327#484C22×C6112yes—
328#484C22×C6111yescharacteristic
329#483C22×C6112yes—
330#483C22×C6111yescharacteristic
331#481C22×C6111yescharacteristic
332#480C22×C6111yescharacteristic
333#479—21no—
334#479—22no—
335#478—21no—
336#432C22×C6111yescharacteristic
337#431C22×C6111yescharacteristic
338#400—21no—
339#400C22×C6112yes—
340#398—21no—
341#398—22no—
342#398C22×C6112yes—
343#382C22×C6111yescharacteristic
344#328C22×C6112yes—
345#328C22×C6112yes—
346#328C22×C6112yes—
347#327C22×C6112yes—
348#324C22×C6112yes—
349#324C22×C6112yes—
350C61#1846911yescharacteristic, direct product factor, Sylow
351C4⋊Q8—21no—
352C4⋊Q8—22no—
353C4⋊Q8—22no—
354C4⋊Q8D4×C6111yescharacteristic
355C4⋊Q8D4×C6111yescharacteristic
356#126—22no—
357#126—22no—
358#126—22no—
359#126—22no—
360#126—21no—
361#125—22no—
362#125—22no—
363#125—22no—
364#125—22no—
365#125—21no—
366#125—22no—
367#125—22no—
368#125—22no—
369#125—22no—
370#125—21no—
371#125—21no—
372#125—21no—
373#125—21no—
374#125—21no—
375#125—21no—
376#125—21no—
377#125—21no—
378#125—21no—
379#125D4×C6111yescharacteristic
380#124D4×C6111yescharacteristic
381#123—22no—
382#123—21no—
383#123—22no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—22no—
387C22⋊Q8—22no—
388C22⋊Q8—22no—
389C22⋊Q8—21no—
390C22⋊Q8—22no—
391C22⋊Q8C23×C6111yescharacteristic
392C22⋊Q8C23×C6112yes—
393#121C23×C6111yescharacteristic
394C4×Q8—21no—
395C4×Q8—22no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8D4×C6111yescharacteristic
399C4×Q8D4×C6112yes—
400C4×D4—21no—
401C4×D4—22no—
402C4×D4D4×C6111yescharacteristic
403#117—22no—
404#117—21no—
405#117—21no—
406#117—22no—
407#117—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4D4×C6111yescharacteristic
414C2×C4⋊C4D4×C6112yes—
415C2×C4⋊C4D4×C6111yescharacteristic
416C2×C4⋊C4C23×C6111yescharacteristic
417C2×C4⋊C4C23×C6111yescharacteristic
418C2×C4⋊C4C23×C6112yes—
419C2×C42C23×C6111yescharacteristic
420#107—21no—
421#107—21no—
422#107—22no—
423#106—21no—
424#106—21no—
425#106—22no—
426C4⋊C8—21no—
427C4⋊C8—21no—
428#103—21no—
429#103—22no—
430#103—21no—
431#103—22no—
432#102—21no—
433#102—21no—
434C22⋊C8C23×C6112yes—
435C22⋊C8C23×C6111yescharacteristic
436C22⋊C8C23×C6111yescharacteristic
437#97—21no—
438C4×C8—21no—
439#95—21no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95C23×C6112yes—
444C2×Q8—22no—
445C2×Q8—21no—
446C2×Q8C2×D4×C6112yes—
447C2×Q8C2×D4×C6111yescharacteristic
448C2×D4—21no—
449C2×D4C2×D4×C6111yescharacteristic
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4C2×D4×C6112yes—
456C22×C4C2×D4×C6111yescharacteristic
457C22×C4C2×D4×C6112yes—
458C22×C4C2×D4×C6111yescharacteristic
459C22×C4C24×C6111yescharacteristic
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—21no—
487C4⋊C4—22no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—81no—
497C4⋊C4—82no—
498C4⋊C4C2×D4×C6111yescharacteristic
499C4⋊C4C2×D4×C6111yescharacteristic
500C4⋊C4C2×D4×C6112yes—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C42—22no—
511C42—22no—
512C42—22no—
513C42—22no—
514C42—21no—
515C42C2×D4×C6111yescharacteristic
516C42C2×D4×C6111yescharacteristic
517C42C2×D4×C6111yescharacteristic
518C42C2×D4×C6111yescharacteristic
519C23—21no—
520C23C22×D4×C6111yescharacteristic
521Q8—41no—
522Q8—42no—
523Q8—42no—
524Q8—82no—
525D4—41no—
526D4—41no—
527D4—41no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—82no—
552C2×C4#120×C6111yescharacteristic
553C2×C4#120×C6111yescharacteristic
554C2×C4#120×C6111yescharacteristic
555C2×C4#120×C6111yescharacteristic
556C2×C4C22×D4×C6111yescharacteristic
557C2×C4C22×D4×C6111yescharacteristic
558C8—41no—
559C8—41no—
560C8—42no—
561C22—21no—
562C22—21no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22C2×#120×C6111yescharacteristic
567C22C61×#57711yescharacteristic
568C22C61×#57811yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—42no—
576C4—41no—
577C4—41no—
578C4—42no—
579C4—42no—
580C4—42no—
581C4—41no—
582C4—82no—
583C4—81no—
584C4—81no—
585C2—21no—
586C2—21no—
587C2—81no—
588C2C61×#301311yescharacteristic
589C2C61×#302011yescharacteristic
590C2C61×#302811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC22×C4C24×C61
prime radical#121×C61C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#3236C2semidirect
4. C61×#2822C2semidirect
5. C61×#1617C2semidirect
7. C61×#1611C2semidirect
9. C61×#1518C2semidirect
11. C61×#1470C2semidirect
265. #18469C61direct (N × H)
291. #3236C2×C61semidirect
293. #2822C2×C61semidirect
294. #1617C2×C61semidirect
296. #1611C2×C61semidirect
298. #1518C2×C61semidirect
300. #1470C2×C61semidirect
350. C61#18469direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35632
C61×#32362
C61×#32322
C61×#28222
C61×#16172
C61×#16152
C61×#16112
C61×#16092
C61×#15182
C61×#15122
C61×#14702
#1846961