Finite Group Databasebeta

← C61×#19309 #29522742

Subgroups — C61×#19309 #29522742

Order 15616.

600 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3182C211yesmaximal, characteristic
2C61×#3112C211yesmaximal, characteristic
3C61×#3078C211yesmaximal, characteristic, complemented
4Q8×M16×C61C211yesmaximal, characteristic, complemented
5C61×#1704C211yesmaximal, characteristic, complemented
6C61×#1698C211yesmaximal, characteristic, complemented
7C61×#1696C211yesmaximal, characteristic, complemented
8C61×#1686C211yesmaximal, characteristic, complemented
9C61×#1684C211yesmaximal, characteristic, complemented
10C61×#1678C211yesmaximal, characteristic, complemented
11C61×#1676C211yesmaximal, characteristic, complemented
12C61×#1666C211yesmaximal, characteristic, complemented
13C61×#1569C211yesmaximal, characteristic, complemented
14C61×#1560C211yesmaximal, characteristic
15C61×#1559C211yesmaximal, characteristic, complemented
16C61×#533C2211yescharacteristic
17C61×#532C2211yescharacteristic
18C2×C4×Q8×C61C2211yescharacteristic
19C61×#500C2211yescharacteristic
20C61×#492C2211yescharacteristic
21C61×#487C2211yescharacteristic
22C61×#486C2211yescharacteristic
23C61×#480—21no—
24C61×#479—21no—
25C61×#479—21no—
26C61×#477C2211yescharacteristic
27C61×#477C2211yescharacteristic
28C61×#477C2211yescharacteristic
29C61×#477C2211yescharacteristic
30C61×#475C2211yescharacteristic
31C61×#475C2211yescharacteristic
32C61×#468—21no—
33C61×#468—21no—
34C61×#460C2211yescharacteristic
35C61×#460C2211yescharacteristic
36C61×#448—21no—
37C61×#446—21no—
38C61×#446—21no—
39C61×#446C2211yescharacteristic
40C61×#446C2211yescharacteristic
41C8×Q8×C61C2211yescharacteristic
42C8×Q8×C61C2211yescharacteristic
43C61×#440—21no—
44C61×#440—21no—
45C61×#440—21no—
46C61×#440—21no—
47C61×#432C2211yescharacteristic
48C61×#428—21no—
49C61×#423—21no—
50C61×#423C2211yescharacteristic
51C61×#423C2211yescharacteristic
52C61×#419—21no—
53C4×M16×C61—21no—
54C4×M16×C61C2211yescharacteristic
55C61×#335C2211yescharacteristic
56C61×#335C2211yescharacteristic
57C61×#334C2211yescharacteristic
58C61×#334C2211yescharacteristic
59C61×#333C2211yescharacteristic
60C61×#333C2211yescharacteristic
61C61×#333C2211yescharacteristic
62C61×#333C2211yescharacteristic
63C61×#332C2211yescharacteristic
64C61×#332C2211yescharacteristic
65C61×#331C2211yescharacteristic
66C61×#331C2211yescharacteristic
67C2×#41×C61—21no—
68C22×Q8×C61D411yescharacteristic
69C2×SD16×C61—21no—
70C2×SD16×C61—21no—
71C2×SD16×C61—21no—
72C2×SD16×C61—21no—
73C2×M16×C61—21no—
74C2×M16×C61—21no—
75C2×M16×C61D411yescharacteristic
76C2×M16×C61D411yescharacteristic
77C4⋊Q8×C61C2311yescharacteristic
78C4⋊Q8×C61C2311yescharacteristic
79C4⋊Q8×C61C2311yescharacteristic
80#127×C61C2311yescharacteristic
81#125×C61—21no—
82#124×C61—21no—
83C22⋊Q8×C61—21no—
84C22⋊Q8×C61—21no—
85#121×C61—21no—
86#121×C61—21no—
87C4×Q8×C61—21no—
88C4×Q8×C61—21no—
89C4×Q8×C61—21no—
90C4×Q8×C61—21no—
91C4×Q8×C61D411yescharacteristic
92C4×Q8×C61D411yescharacteristic
93C4×Q8×C61C2311yescharacteristic
94C4×Q8×C61C2311yescharacteristic
95C4×D4×C61—21no—
96C4×D4×C61—21no—
97#117×C61—21no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61D411yescharacteristic
100C2×C42×C61—21no—
101C2×C42×C61C2311yescharacteristic
102#107×C61—21no—
103#107×C61—21no—
104#107×C61—21no—
105#107×C61—21no—
106#107×C61—21no—
107#107×C61—21no—
108#106×C61—21no—
109#106×C61—21no—
110C4⋊C8×C61—21no—
111C4⋊C8×C61—21no—
112C4⋊C8×C61—21no—
113C4⋊C8×C61—21no—
114C4⋊C8×C61—21no—
115C4⋊C8×C61—21no—
116C4⋊C8×C61C2311yescharacteristic
117C4⋊C8×C61C2311yescharacteristic
118C4⋊C8×C61C2311yescharacteristic
119C4⋊C8×C61C2311yescharacteristic
120C4⋊C8×C61C2311yescharacteristic
121C4⋊C8×C61C2311yescharacteristic
122#103×C61—21no—
123#103×C61—21no—
124#103×C61—21no—
125#103×C61—21no—
126#103×C61—21no—
127#103×C61—21no—
128#103×C61—21no—
129#103×C61—21no—
130#102×C61—21no—
131#102×C61—21no—
132#102×C61—21no—
133#102×C61—21no—
134C22⋊C8×C61—21no—
135#97×C61—21no—
136#97×C61—21no—
137#97×C61—21no—
138#97×C61D411yescharacteristic
139#97×C61D411yescharacteristic
140C4×C8×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—82no—
145C2×Q8×C61—21no—
146C2×Q8×C61—22no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—41no—
151C2×Q8×C61C2×D411yescharacteristic
152C2×Q8×C61C2×D411yescharacteristic
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—41no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—41no—
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61#4111yescharacteristic
163SD16×C61—42no—
164SD16×C61—42no—
165SD16×C61—42no—
166SD16×C61—42no—
167M16×C61—22no—
168M16×C61—41no—
169M16×C61—42no—
170M16×C61—42no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61C2×D411yescharacteristic
178C2×C8×C61C2×D411yescharacteristic
179C2×C8×C61C2×D411yescharacteristic
180C2×C8×C61C2×D411yescharacteristic
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—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—41no—
193C4⋊C4×C61—41no—
194C4⋊C4×C61C2×D411yescharacteristic
195C4⋊C4×C61C2×D411yescharacteristic
196C22⋊C4×C61—41no—
197C22⋊C4×C61—41no—
198C22⋊C4×C61—41no—
199C42×C61—21no—
200C42×C61—21no—
201C42×C61—21no—
202C42×C61—21no—
203C42×C61—41no—
204C42×C61C2×D411yescharacteristic
205C42×C61C2×D411yescharacteristic
206C42×C61#4111yescharacteristic
207C42×C61C2411yescharacteristic
208C23×C61—41no—
209C23×C61#12111yescharacteristic
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—42no—
214Q8×C61—41no—
215Q8×C61—41no—
216Q8×C61—81no—
217Q8×C61—81no—
218Q8×C61#13712yes—
219D4×C61—41no—
220D4×C61—41no—
221D4×C61—41no—
222D4×C61—41no—
223D4×C61—81no—
224D4×C61—82no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—41no—
234C2×C4×C61—42no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—82no—
239C2×C4×C61—81no—
240C2×C4×C61#12111yescharacteristic
241C2×C4×C61#12111yescharacteristic
242C2×C4×C61#12111yescharacteristic
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C8×C61—21no—
247C8×C61—21no—
248C8×C61—21no—
249C8×C61—41no—
250C8×C61—41no—
251C8×C61—41no—
252C8×C61—41no—
253C8×C61—41no—
254C8×C61—41no—
255C8×C61#13712yes—
256#19309C6111yesmaximal, characteristic, direct product factor, Sylow
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—81no—
261C22×C61—81no—
262C22×C61—81no—
263C22×C61C2×#12111yescharacteristic
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—22no—
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61—81no—
273C4×C61—81no—
274C4×C61—81no—
275C4×C61C2×#13711yescharacteristic
276C4×C61C2×#13711yescharacteristic
277C4×C61#57511yescharacteristic
278C4×C61#57511yescharacteristic
279#3182C2×C6111yescharacteristic
280#3112C2×C6111yescharacteristic
281#3078C2×C6111yescharacteristic, complemented
282Q8×M16C2×C6111yescharacteristic, complemented
283#1704C2×C6111yescharacteristic, complemented
284#1698C2×C6111yescharacteristic, complemented
285#1696C2×C6111yescharacteristic, complemented
286#1686C2×C6111yescharacteristic, complemented
287#1684C2×C6111yescharacteristic, complemented
288#1678C2×C6111yescharacteristic, complemented
289#1676C2×C6111yescharacteristic, complemented
290#1666C2×C6111yescharacteristic, complemented
291#1569C2×C6111yescharacteristic, complemented
292#1560C2×C6111yescharacteristic
293#1559C2×C6111yescharacteristic, complemented
294C2×C61—41no—
295C2×C61—161no—
296C2×C61#303711yescharacteristic
297C2×C61#305611yescharacteristic
298C2×C61#306811yescharacteristic
299#533C22×C6111yescharacteristic
300#532C22×C6111yescharacteristic
301C2×C4×Q8C22×C6111yescharacteristic
302#500C22×C6111yescharacteristic
303#492C22×C6111yescharacteristic
304#487C22×C6111yescharacteristic
305#486C22×C6111yescharacteristic
306#480—21no—
307#479—21no—
308#479—21no—
309#477C22×C6111yescharacteristic
310#477C22×C6111yescharacteristic
311#477C22×C6111yescharacteristic
312#477C22×C6111yescharacteristic
313#475C22×C6111yescharacteristic
314#475C22×C6111yescharacteristic
315#468—21no—
316#468—21no—
317#460C22×C6111yescharacteristic
318#460C22×C6111yescharacteristic
319#448—21no—
320#446—21no—
321#446—21no—
322#446C22×C6111yescharacteristic
323#446C22×C6111yescharacteristic
324C8×Q8C22×C6111yescharacteristic
325C8×Q8C22×C6111yescharacteristic
326#440—21no—
327#440—21no—
328#440—21no—
329#440—21no—
330#432C22×C6111yescharacteristic
331#428—21no—
332#423—21no—
333#423C22×C6111yescharacteristic
334#423C22×C6111yescharacteristic
335#419—21no—
336C4×M16—21no—
337C4×M16C22×C6111yescharacteristic
338#335C22×C6111yescharacteristic
339#335C22×C6111yescharacteristic
340#334C22×C6111yescharacteristic
341#334C22×C6111yescharacteristic
342#333C22×C6111yescharacteristic
343#333C22×C6111yescharacteristic
344#333C22×C6111yescharacteristic
345#333C22×C6111yescharacteristic
346#332C22×C6111yescharacteristic
347#332C22×C6111yescharacteristic
348#331C22×C6111yescharacteristic
349#331C22×C6111yescharacteristic
350C61#1930911yescharacteristic, direct product factor, Sylow
351C2×#41—21no—
352C22×Q8D4×C6111yescharacteristic
353C2×SD16—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16D4×C6111yescharacteristic
360C2×M16D4×C6111yescharacteristic
361C4⋊Q8C23×C6111yescharacteristic
362C4⋊Q8C23×C6111yescharacteristic
363C4⋊Q8C23×C6111yescharacteristic
364#127C23×C6111yescharacteristic
365#125—21no—
366#124—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369#121—21no—
370#121—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8D4×C6111yescharacteristic
376C4×Q8D4×C6111yescharacteristic
377C4×Q8C23×C6111yescharacteristic
378C4×Q8C23×C6111yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381#117—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4D4×C6111yescharacteristic
384C2×C42—21no—
385C2×C42C23×C6111yescharacteristic
386#107—21no—
387#107—21no—
388#107—21no—
389#107—21no—
390#107—21no—
391#107—21no—
392#106—21no—
393#106—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8C23×C6111yescharacteristic
401C4⋊C8C23×C6111yescharacteristic
402C4⋊C8C23×C6111yescharacteristic
403C4⋊C8C23×C6111yescharacteristic
404C4⋊C8C23×C6111yescharacteristic
405C4⋊C8C23×C6111yescharacteristic
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418C22⋊C8—21no—
419#97—21no—
420#97—21no—
421#97—21no—
422#97D4×C6111yescharacteristic
423#97D4×C6111yescharacteristic
424C4×C8—21no—
425C4×C8—21no—
426C4×C8C23×C6111yescharacteristic
427C4×C8C23×C6111yescharacteristic
428#41—82no—
429C2×Q8—21no—
430C2×Q8—22no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—41no—
435C2×Q8C2×D4×C6111yescharacteristic
436C2×Q8C2×D4×C6111yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—41no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—41no—
444C22×C4C2×D4×C6111yescharacteristic
445C22×C4C2×D4×C6111yescharacteristic
446C22×C4#41×C6111yescharacteristic
447SD16—42no—
448SD16—42no—
449SD16—42no—
450SD16—42no—
451M16—22no—
452M16—41no—
453M16—42no—
454M16—42no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8C2×D4×C6111yescharacteristic
462C2×C8C2×D4×C6111yescharacteristic
463C2×C8C2×D4×C6111yescharacteristic
464C2×C8C2×D4×C6111yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4C2×D4×C6111yescharacteristic
479C4⋊C4C2×D4×C6111yescharacteristic
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—41no—
488C42C2×D4×C6111yescharacteristic
489C42C2×D4×C6111yescharacteristic
490C42#41×C6111yescharacteristic
491C42C24×C6111yescharacteristic
492C23—41no—
493C23#121×C6111yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—42no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—81no—
502Q8#137×C6112yes—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—81no—
508D4—82no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—82no—
523C2×C4—81no—
524C2×C4#121×C6111yescharacteristic
525C2×C4#121×C6111yescharacteristic
526C2×C4#121×C6111yescharacteristic
527C2×C4C22×D4×C6111yescharacteristic
528C2×C4C22×D4×C6111yescharacteristic
529C2×C4C2×#41×C6111yescharacteristic
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8#137×C6112yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22C2×#121×C6111yescharacteristic
547C4—21no—
548C4—21no—
549C4—22no—
550C4—21no—
551C4—21no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4C2×#137×C6111yescharacteristic
559C4C2×#137×C6111yescharacteristic
560C4C61×#57511yescharacteristic
561C4C61×#57511yescharacteristic
562C2—41no—
563C2—161no—
564C2C61×#303711yescharacteristic
565C2C61×#305611yescharacteristic
566C2C61×#306811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC42C24×C61
prime radicalC61×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C61×#3078C2semidirect
4. Q8×M16×C61C2semidirect
5. C61×#1704C2semidirect
6. C61×#1698C2semidirect
7. C61×#1696C2semidirect
8. C61×#1686C2semidirect
9. C61×#1684C2semidirect
10. C61×#1678C2semidirect
11. C61×#1676C2semidirect
12. C61×#1666C2semidirect
13. C61×#1569C2semidirect
15. C61×#1559C2semidirect
256. #19309C61direct (N × H)
281. #3078C2×C61semidirect
282. Q8×M16C2×C61semidirect
283. #1704C2×C61semidirect
284. #1698C2×C61semidirect
285. #1696C2×C61semidirect
286. #1686C2×C61semidirect
287. #1684C2×C61semidirect
288. #1678C2×C61semidirect
289. #1676C2×C61semidirect
290. #1666C2×C61semidirect
291. #1569C2×C61semidirect
293. #1559C2×C61semidirect
350. C61#19309direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#31822
C61×#31122
C61×#30782
Q8×M16×C612
C61×#17042
C61×#16982
C61×#16962
C61×#16862
C61×#16842
C61×#16782
C61×#16762
C61×#16662
C61×#15692
C61×#15602
C61×#15592
#1930961