Finite Group Databasebeta

← C61×#19814 #29523247

Subgroups — C61×#19814 #29523247

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3384C211yesmaximal, characteristic
2C61×#3380C211yesmaximal, characteristic
3C61×#3338C211yesmaximal, characteristic, complemented
4C61×#3299C211yesmaximal, characteristic, complemented
5C61×#1723C211yesmaximal, characteristic, complemented
6C61×#1696C211yesmaximal, characteristic, complemented
7C61×#1683C211yesmaximal, characteristic, complemented
8C61×#1675C211yesmaximal, characteristic, complemented
9C61×#1672C211yesmaximal, characteristic, complemented
10C61×#1644C211yesmaximal, characteristic, complemented
11C61×#1637C211yesmaximal, characteristic, complemented
12C61×#1632C211yesmaximal, characteristic, complemented
13C61×#1632C211yesmaximal, characteristic, complemented
14C61×#1584C211yesmaximal, characteristic, complemented
15C61×#1580C211yesmaximal, characteristic
16C61×#554C2211yescharacteristic
17C61×#554C2211yescharacteristic
18C61×#554C2211yescharacteristic
19D4×Q8×C61C2211yescharacteristic
20C61×#501—21no—
21C61×#500C2211yescharacteristic
22C61×#500C2211yescharacteristic
23C61×#499—21no—
24C61×#498C2211yescharacteristic
25C61×#494C2211yescharacteristic
26C61×#487C2211yescharacteristic
27C61×#487C2211yescharacteristic
28C61×#484—21no—
29C61×#484—21no—
30C61×#484—21no—
31C61×#478—21no—
32C61×#478—21no—
33C61×#478—21no—
34C61×#477C2211yescharacteristic
35C61×#477C2211yescharacteristic
36C61×#477C2211yescharacteristic
37C61×#476—21no—
38C61×#476C2211yescharacteristic
39C61×#476C2211yescharacteristic
40C61×#476C2211yescharacteristic
41C61×#474C2211yescharacteristic
42C61×#467—21no—
43C61×#467—21no—
44C61×#462C2211yescharacteristic
45C61×#451—21no—
46C61×#446C2211yescharacteristic
47C8×Q8×C61C2211yescharacteristic
48C61×#442—21no—
49C4×Q16×C61C2211yescharacteristic
50C4×D8×C61—21no—
51C4×D8×C61C2211yescharacteristic
52C8×D4×C61C2211yescharacteristic
53C8×D4×C61C2211yescharacteristic
54C2×#107×C61—21no—
55C2×#103×C61—21no—
56C61×#335C2211yescharacteristic
57C61×#334C2211yescharacteristic
58C61×#333C2211yescharacteristic
59C61×#333C2211yescharacteristic
60C61×#333C2211yescharacteristic
61C61×#332C2211yescharacteristic
62C61×Q8⋊C8C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic
64C61×D4⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C22×Q8×C61—21no—
68C2×Q16×C61—21no—
69C2×Q16×C61—41no—
70C2×Q16×C61D411yescharacteristic
71C2×D8×C61D411yescharacteristic
72C22×C8×C61—21no—
73C22×C8×C61—21no—
74C4⋊Q8×C61—21no—
75C4⋊Q8×C61C2311yescharacteristic
76C4⋊Q8×C61C2311yescharacteristic
77C4⋊Q8×C61C2311yescharacteristic
78C4⋊Q8×C61C2311yescharacteristic
79#125×C61—21no—
80#125×C61—21no—
81#125×C61—21no—
82C22⋊Q8×C61—21no—
83C22⋊Q8×C61—21no—
84C22⋊Q8×C61—21no—
85C22⋊Q8×C61—21no—
86C22⋊Q8×C61—41no—
87C22⋊Q8×C61—41no—
88C22⋊Q8×C61—41no—
89C22⋊Q8×C61—41no—
90C4×Q8×C61C2311yescharacteristic
91C4×Q8×C61C2311yescharacteristic
92C4×D4×C61—21no—
93C4×D4×C61—21no—
94C4×D4×C61—21no—
95C4×D4×C61—21no—
96C4×D4×C61C2311yescharacteristic
97C4×D4×C61C2311yescharacteristic
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101#107×C61—21no—
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#107×C61—21no—
109#107×C61D411yescharacteristic
110#107×C61D411yescharacteristic
111#106×C61—21no—
112#106×C61—21no—
113#106×C61—21no—
114#106×C61—21no—
115#106×C61—21no—
116C4⋊C8×C61—21no—
117C4⋊C8×C61—21no—
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—41no—
129#103×C61D411yescharacteristic
130#103×C61D411yescharacteristic
131#102×C61—21no—
132#102×C61—21no—
133#102×C61—21no—
134#102×C61—21no—
135#102×C61D411yescharacteristic
136#102×C61D411yescharacteristic
137C22⋊C8×C61—21no—
138C22⋊C8×C61—21no—
139#97×C61—21no—
140C4×C8×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—41no—
149C2×Q8×C61—42no—
150C2×Q8×C61—81no—
151C2×Q8×C61C2×D411yescharacteristic
152C2×Q8×C61C2×D411yescharacteristic
153C2×D4×C61C2×D411yescharacteristic
154C2×D4×C61C2×D411yescharacteristic
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—41no—
158C22×C4×C61—41no—
159C22×C4×C61—41no—
160C22×C4×C61—41no—
161Q16×C61—41no—
162Q16×C61—81no—
163Q16×C61—82no—
164D8×C61Q1614yescomplemented
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—42no—
171C2×C8×C61—81no—
172C2×C8×C61C2×D411yescharacteristic
173C2×C8×C61C2×D411yescharacteristic
174C2×C8×C61C2×D411yescharacteristic
175C2×C8×C61C2×D411yescharacteristic
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—41no—
187C4⋊C4×C61—41no—
188C4⋊C4×C61—41no—
189C4⋊C4×C61—41no—
190C4⋊C4×C61—41no—
191C4⋊C4×C61—41no—
192C4⋊C4×C61—41no—
193C4⋊C4×C61C2×D411yescharacteristic
194C4⋊C4×C61C2×D411yescharacteristic
195C4⋊C4×C61C2×D411yescharacteristic
196C4⋊C4×C61C2×D411yescharacteristic
197C22⋊C4×C61—21no—
198C22⋊C4×C61—21no—
199C22⋊C4×C61—41no—
200C22⋊C4×C61—41no—
201C22⋊C4×C61—41no—
202C22⋊C4×C61—41no—
203C42×C61—21no—
204C42×C61—21no—
205C42×C61C2411yescharacteristic
206C23×C61—21no—
207C23×C61—21no—
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—41no—
213Q8×C61—41no—
214Q8×C61—81no—
215Q8×C61—81no—
216Q8×C61—81no—
217Q8×C61—82no—
218D4×C61—21no—
219D4×C61—21no—
220D4×C61C2×Q1612yes—
221D4×C61C2×Q1612yes—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—82no—
237C2×C4×C61—161no—
238C2×C4×C61—161no—
239C2×C4×C61—161no—
240C2×C4×C61C22×D411yescharacteristic
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61H(5,𝔽2)11yescharacteristic
243C8×C61—21no—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—41no—
247C8×C61—41no—
248C8×C61—41no—
249C8×C61—41no—
250C8×C61—41no—
251C8×C61C2×Q1612yes—
252#19814C6111yesmaximal, characteristic, direct product factor, Sylow
253C22×C61—22no—
254C22×C61—22no—
255C22×C61—41no—
256C22×C61—41no—
257C22×C61—41no—
258C22×C61—41no—
259C22×C61D4211yescharacteristic
260C4×C61—21no—
261C4×C61—41no—
262C4×C61—41no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61—81no—
268C4×C61—81no—
269C4×C61—81no—
270C4×C61—81no—
271C4×C61C22×Q1611yescharacteristic
272C4×C61#57511yescharacteristic
273C4×C61#57711yescharacteristic
274C4×C61#57811yescharacteristic
275#3384C2×C6111yescharacteristic
276#3380C2×C6111yescharacteristic
277#3338C2×C6111yescharacteristic, complemented
278#3299C2×C6111yescharacteristic, complemented
279#1723C2×C6111yescharacteristic, complemented
280#1696C2×C6111yescharacteristic, complemented
281#1683C2×C6111yescharacteristic, complemented
282#1675C2×C6111yescharacteristic, complemented
283#1672C2×C6111yescharacteristic, complemented
284#1644C2×C6111yescharacteristic, complemented
285#1637C2×C6111yescharacteristic, complemented
286#1632C2×C6111yescharacteristic, complemented
287#1632C2×C6111yescharacteristic, complemented
288#1584C2×C6111yescharacteristic, complemented
289#1580C2×C6111yescharacteristic
290C2×C61—42no—
291C2×C61—42no—
292C2×C61#326711yescharacteristic
293C2×C61D4×Q1611yescharacteristic
294C2×C61#328811yescharacteristic
295#554C22×C6111yescharacteristic
296#554C22×C6111yescharacteristic
297#554C22×C6111yescharacteristic
298D4×Q8C22×C6111yescharacteristic
299#501—21no—
300#500C22×C6111yescharacteristic
301#500C22×C6111yescharacteristic
302#499—21no—
303#498C22×C6111yescharacteristic
304#494C22×C6111yescharacteristic
305#487C22×C6111yescharacteristic
306#487C22×C6111yescharacteristic
307#484—21no—
308#484—21no—
309#484—21no—
310#478—21no—
311#478—21no—
312#478—21no—
313#477C22×C6111yescharacteristic
314#477C22×C6111yescharacteristic
315#477C22×C6111yescharacteristic
316#476—21no—
317#476C22×C6111yescharacteristic
318#476C22×C6111yescharacteristic
319#476C22×C6111yescharacteristic
320#474C22×C6111yescharacteristic
321#467—21no—
322#467—21no—
323#462C22×C6111yescharacteristic
324#451—21no—
325#446C22×C6111yescharacteristic
326C8×Q8C22×C6111yescharacteristic
327#442—21no—
328C4×Q16C22×C6111yescharacteristic
329C4×D8—21no—
330C4×D8C22×C6111yescharacteristic
331C8×D4C22×C6111yescharacteristic
332C8×D4C22×C6111yescharacteristic
333C2×#107—21no—
334C2×#103—21no—
335#335C22×C6111yescharacteristic
336#334C22×C6111yescharacteristic
337#333C22×C6111yescharacteristic
338#333C22×C6111yescharacteristic
339#333C22×C6111yescharacteristic
340#332C22×C6111yescharacteristic
341Q8⋊C8C22×C6111yescharacteristic
342Q8⋊C8C22×C6111yescharacteristic
343D4⋊C8C22×C6111yescharacteristic
344D4⋊C8C22×C6111yescharacteristic
345#322C22×C6111yescharacteristic
346C61#1981411yescharacteristic, direct product factor, Sylow
347C22×Q8—21no—
348C2×Q16—21no—
349C2×Q16—41no—
350C2×Q16D4×C6111yescharacteristic
351C2×D8D4×C6111yescharacteristic
352C22×C8—21no—
353C22×C8—21no—
354C4⋊Q8—21no—
355C4⋊Q8C23×C6111yescharacteristic
356C4⋊Q8C23×C6111yescharacteristic
357C4⋊Q8C23×C6111yescharacteristic
358C4⋊Q8C23×C6111yescharacteristic
359#125—21no—
360#125—21no—
361#125—21no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—41no—
367C22⋊Q8—41no—
368C22⋊Q8—41no—
369C22⋊Q8—41no—
370C4×Q8C23×C6111yescharacteristic
371C4×Q8C23×C6111yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4C23×C6111yescharacteristic
377C4×D4C23×C6111yescharacteristic
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#107—21no—
389#107D4×C6111yescharacteristic
390#107D4×C6111yescharacteristic
391#106—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395#106—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8C23×C6111yescharacteristic
399C4⋊C8C23×C6111yescharacteristic
400C4⋊C8C23×C6111yescharacteristic
401C4⋊C8C23×C6111yescharacteristic
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—41no—
409#103D4×C6111yescharacteristic
410#103D4×C6111yescharacteristic
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102D4×C6111yescharacteristic
416#102D4×C6111yescharacteristic
417C22⋊C8—21no—
418C22⋊C8—21no—
419#97—21no—
420C4×C8—21no—
421C4×C8C23×C6111yescharacteristic
422C4×C8C23×C6111yescharacteristic
423C4×C8C23×C6111yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—41no—
429C2×Q8—42no—
430C2×Q8—81no—
431C2×Q8C2×D4×C6111yescharacteristic
432C2×Q8C2×D4×C6111yescharacteristic
433C2×D4C2×D4×C6111yescharacteristic
434C2×D4C2×D4×C6111yescharacteristic
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441Q16—41no—
442Q16—81no—
443Q16—82no—
444D8Q16×C6114yescomplemented
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—42no—
451C2×C8—81no—
452C2×C8C2×D4×C6111yescharacteristic
453C2×C8C2×D4×C6111yescharacteristic
454C2×C8C2×D4×C6111yescharacteristic
455C2×C8C2×D4×C6111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4C2×D4×C6111yescharacteristic
474C4⋊C4C2×D4×C6111yescharacteristic
475C4⋊C4C2×D4×C6111yescharacteristic
476C4⋊C4C2×D4×C6111yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C42—21no—
484C42—21no—
485C42C24×C6111yescharacteristic
486C23—21no—
487C23—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8—81no—
496Q8—81no—
497Q8—82no—
498D4—21no—
499D4—21no—
500D4C2×Q16×C6112yes—
501D4C2×Q16×C6112yes—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—82no—
517C2×C4—161no—
518C2×C4—161no—
519C2×C4—161no—
520C2×C4C22×D4×C6111yescharacteristic
521C2×C4C22×D4×C6111yescharacteristic
522C2×C4H(5,𝔽2)×C6111yescharacteristic
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8C2×Q16×C6112yes—
532C22—22no—
533C22—22no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22D42×C6111yescharacteristic
539C4—21no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—81no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4C22×Q16×C6111yescharacteristic
551C4C61×#57511yescharacteristic
552C4C61×#57711yescharacteristic
553C4C61×#57811yescharacteristic
554C2—42no—
555C2—42no—
556C2C61×#326711yescharacteristic
557C2D4×Q16×C6111yescharacteristic
558C2C61×#328811yescharacteristic
subgroupG/H
center, socleC22×C61D42
commutator, Frattini, cosocleC42C24×C61
prime radicalC2×D8×C61D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
3. C61×#3338C2semidirect
4. C61×#3299C2semidirect
5. C61×#1723C2semidirect
6. C61×#1696C2semidirect
7. C61×#1683C2semidirect
8. C61×#1675C2semidirect
9. C61×#1672C2semidirect
10. C61×#1644C2semidirect
11. C61×#1637C2semidirect
12. C61×#1632C2semidirect
13. C61×#1632C2semidirect
14. C61×#1584C2semidirect
164. D8×C61Q16semidirect
252. #19814C61direct (N × H)
277. #3338C2×C61semidirect
278. #3299C2×C61semidirect
279. #1723C2×C61semidirect
280. #1696C2×C61semidirect
281. #1683C2×C61semidirect
282. #1675C2×C61semidirect
283. #1672C2×C61semidirect
284. #1644C2×C61semidirect
285. #1637C2×C61semidirect
286. #1632C2×C61semidirect
287. #1632C2×C61semidirect
288. #1584C2×C61semidirect
346. C61#19814direct (N × H)
444. D8Q16×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#33842
C61×#33802
C61×#33382
C61×#32992
C61×#17232
C61×#16962
C61×#16832
C61×#16752
C61×#16722
C61×#16442
C61×#16372
C61×#16322
C61×#15842
C61×#15802
#1981461