Finite Group Databasebeta

← C61×#19311 #29522744

Subgroups — C61×#19311 #29522744

Order 15616.

578 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3185C211yesmaximal, characteristic
2C61×#3113C211yesmaximal, characteristic
3C61×#3078C211yesmaximal, characteristic
4Q8×M16×C61C211yesmaximal, characteristic
5C61×#1704C211yesmaximal, characteristic, complemented
6C61×#1700C211yesmaximal, characteristic, complemented
7C61×#1692C211yesmaximal, characteristic, complemented
8C61×#1690C211yesmaximal, characteristic, complemented
9C61×#1684C211yesmaximal, characteristic, complemented
10C61×#1680C211yesmaximal, characteristic, complemented
11C61×#1672C211yesmaximal, characteristic, complemented
12C61×#1670C211yesmaximal, characteristic, complemented
13C61×#1569C211yesmaximal, characteristic
14C61×#1561C211yesmaximal, characteristic
15C61×#1559C211yesmaximal, characteristic
16C61×#533C2211yescharacteristic
17C61×#533C2211yescharacteristic
18C2×C4×Q8×C61C2211yescharacteristic
19C61×#498C2211yescharacteristic
20C61×#494C2211yescharacteristic
21C61×#487C2211yescharacteristic
22C61×#487C2211yescharacteristic
23C61×#483—21no—
24C61×#479—21no—
25C61×#479—21no—
26C61×#477C2211yescharacteristic
27C61×#477C2211yescharacteristic
28C61×#475C2211yescharacteristic
29C61×#475C2211yescharacteristic
30C61×#475C2211yescharacteristic
31C61×#475C2211yescharacteristic
32C61×#470—21no—
33C61×#470—21no—
34C61×#462C2211yescharacteristic
35C61×#462C2211yescharacteristic
36C61×#451—21no—
37C61×#446—21no—
38C61×#446—21no—
39C61×#446C2211yescharacteristic
40C61×#446C2211yescharacteristic
41C8×Q8×C61C2211yescharacteristic
42C8×Q8×C61C2211yescharacteristic
43C61×#441—21no—
44C61×#441—21no—
45C61×#441—21no—
46C61×#441—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×#332C2211yescharacteristic
62C61×#332C2211yescharacteristic
63C61×#332C2211yescharacteristic
64C61×#332C2211yescharacteristic
65C61×#332C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C22×Q8×C61D411yescharacteristic
68C2×Q16×C61—21no—
69C2×Q16×C61—21no—
70C2×Q16×C61—21no—
71C2×Q16×C61—21no—
72C2×M16×C61—21no—
73C2×M16×C61—21no—
74C2×M16×C61D411yescharacteristic
75C2×M16×C61D411yescharacteristic
76C4⋊Q8×C61C2311yescharacteristic
77C4⋊Q8×C61C2311yescharacteristic
78C4⋊Q8×C61C2311yescharacteristic
79C4⋊Q8×C61C2311yescharacteristic
80#125×C61—21no—
81#125×C61—21no—
82C22⋊Q8×C61—21no—
83C22⋊Q8×C61—21no—
84C22⋊Q8×C61—21no—
85C22⋊Q8×C61—21no—
86C4×Q8×C61—21no—
87C4×Q8×C61—21no—
88C4×Q8×C61—21no—
89C4×Q8×C61—21no—
90C4×Q8×C61—21no—
91C4×Q8×C61—21no—
92C4×Q8×C61D411yescharacteristic
93C4×Q8×C61D411yescharacteristic
94C4×Q8×C61C2311yescharacteristic
95C4×Q8×C61C2311yescharacteristic
96#117×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#106×C61—21no—
105#106×C61—21no—
106#106×C61—21no—
107#106×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#103×C61—21no—
131#103×C61—21no—
132#103×C61—21no—
133#103×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
144C2×Q8×C61—21no—
145C2×Q8×C61—22no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—41no—
151C2×Q8×C61C2×D411yescharacteristic
152C2×Q8×C61C2×D411yescharacteristic
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61#4111yescharacteristic
158Q16×C61—42no—
159Q16×C61—42no—
160Q16×C61—42no—
161Q16×C61—42no—
162M16×C61—22no—
163M16×C61—41no—
164M16×C61—42no—
165M16×C61—42no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
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—21no—
187C4⋊C4×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—41no—
190C4⋊C4×C61—41no—
191C4⋊C4×C61—41no—
192C4⋊C4×C61—41no—
193C4⋊C4×C61C2×D411yescharacteristic
194C4⋊C4×C61C2×D411yescharacteristic
195C22⋊C4×C61—41no—
196C22⋊C4×C61—41no—
197C42×C61—21no—
198C42×C61—21no—
199C42×C61—21no—
200C42×C61—21no—
201C42×C61—41no—
202C42×C61—41no—
203C42×C61C2×D411yescharacteristic
204C42×C61C2×D411yescharacteristic
205C42×C61#4111yescharacteristic
206C42×C61C2411yescharacteristic
207C23×C61#12111yescharacteristic
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—42no—
212Q8×C61—41no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—81no—
219Q8×C61#13712yes—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
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—42no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—81no—
235C2×C4×C61#12111yescharacteristic
236C2×C4×C61#12111yescharacteristic
237C2×C4×C61#12111yescharacteristic
238C2×C4×C61C22×D411yescharacteristic
239C2×C4×C61C22×D411yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—41no—
245C8×C61—41no—
246C8×C61—41no—
247C8×C61—41no—
248C8×C61—41no—
249C8×C61—41no—
250C8×C61#13712yes—
251#19311C6111yesmaximal, characteristic, direct product factor, Sylow
252C22×C61—21no—
253C22×C61—21no—
254C22×C61—21no—
255C22×C61C2×#12111yescharacteristic
256C4×C61—21no—
257C4×C61—21no—
258C4×C61—22no—
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—41no—
262C4×C61—41no—
263C4×C61—41no—
264C4×C61—81no—
265C4×C61—81no—
266C4×C61—81no—
267C4×C61—81no—
268C4×C61C2×#13711yescharacteristic
269C4×C61C2×#13711yescharacteristic
270C4×C61#57511yescharacteristic
271C4×C61#57511yescharacteristic
272#3185C2×C6111yescharacteristic
273#3113C2×C6111yescharacteristic
274#3078C2×C6111yescharacteristic
275Q8×M16C2×C6111yescharacteristic
276#1704C2×C6111yescharacteristic, complemented
277#1700C2×C6111yescharacteristic, complemented
278#1692C2×C6111yescharacteristic, complemented
279#1690C2×C6111yescharacteristic, complemented
280#1684C2×C6111yescharacteristic, complemented
281#1680C2×C6111yescharacteristic, complemented
282#1672C2×C6111yescharacteristic, complemented
283#1670C2×C6111yescharacteristic, complemented
284#1569C2×C6111yescharacteristic
285#1561C2×C6111yescharacteristic
286#1559C2×C6111yescharacteristic
287C2×C61—41no—
288C2×C61#303711yescharacteristic
289C2×C61#305611yescharacteristic
290C2×C61#306911yescharacteristic
291#533C22×C6111yescharacteristic
292#533C22×C6111yescharacteristic
293C2×C4×Q8C22×C6111yescharacteristic
294#498C22×C6111yescharacteristic
295#494C22×C6111yescharacteristic
296#487C22×C6111yescharacteristic
297#487C22×C6111yescharacteristic
298#483—21no—
299#479—21no—
300#479—21no—
301#477C22×C6111yescharacteristic
302#477C22×C6111yescharacteristic
303#475C22×C6111yescharacteristic
304#475C22×C6111yescharacteristic
305#475C22×C6111yescharacteristic
306#475C22×C6111yescharacteristic
307#470—21no—
308#470—21no—
309#462C22×C6111yescharacteristic
310#462C22×C6111yescharacteristic
311#451—21no—
312#446—21no—
313#446—21no—
314#446C22×C6111yescharacteristic
315#446C22×C6111yescharacteristic
316C8×Q8C22×C6111yescharacteristic
317C8×Q8C22×C6111yescharacteristic
318#441—21no—
319#441—21no—
320#441—21no—
321#441—21no—
322#432C22×C6111yescharacteristic
323#428—21no—
324#423—21no—
325#423C22×C6111yescharacteristic
326#423C22×C6111yescharacteristic
327#419—21no—
328C4×M16—21no—
329C4×M16C22×C6111yescharacteristic
330#335C22×C6111yescharacteristic
331#335C22×C6111yescharacteristic
332#334C22×C6111yescharacteristic
333#334C22×C6111yescharacteristic
334#333C22×C6111yescharacteristic
335#333C22×C6111yescharacteristic
336#332C22×C6111yescharacteristic
337#332C22×C6111yescharacteristic
338#332C22×C6111yescharacteristic
339#332C22×C6111yescharacteristic
340#332C22×C6111yescharacteristic
341#332C22×C6111yescharacteristic
342C61#1931111yescharacteristic, direct product factor, Sylow
343C22×Q8D4×C6111yescharacteristic
344C2×Q16—21no—
345C2×Q16—21no—
346C2×Q16—21no—
347C2×Q16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16D4×C6111yescharacteristic
351C2×M16D4×C6111yescharacteristic
352C4⋊Q8C23×C6111yescharacteristic
353C4⋊Q8C23×C6111yescharacteristic
354C4⋊Q8C23×C6111yescharacteristic
355C4⋊Q8C23×C6111yescharacteristic
356#125—21no—
357#125—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8D4×C6111yescharacteristic
369C4×Q8D4×C6111yescharacteristic
370C4×Q8C23×C6111yescharacteristic
371C4×Q8C23×C6111yescharacteristic
372#117—21no—
373#117—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4D4×C6111yescharacteristic
376C2×C42—21no—
377C2×C42C23×C6111yescharacteristic
378#107—21no—
379#107—21no—
380#106—21no—
381#106—21no—
382#106—21no—
383#106—21no—
384#106—21no—
385#106—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8C23×C6111yescharacteristic
393C4⋊C8C23×C6111yescharacteristic
394C4⋊C8C23×C6111yescharacteristic
395C4⋊C8C23×C6111yescharacteristic
396C4⋊C8C23×C6111yescharacteristic
397C4⋊C8C23×C6111yescharacteristic
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410C22⋊C8—21no—
411#97—21no—
412#97—21no—
413#97—21no—
414#97D4×C6111yescharacteristic
415#97D4×C6111yescharacteristic
416C4×C8—21no—
417C4×C8—21no—
418C4×C8C23×C6111yescharacteristic
419C4×C8C23×C6111yescharacteristic
420C2×Q8—21no—
421C2×Q8—22no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—41no—
427C2×Q8C2×D4×C6111yescharacteristic
428C2×Q8C2×D4×C6111yescharacteristic
429C22×C4—21no—
430C22×C4—21no—
431C22×C4C2×D4×C6111yescharacteristic
432C22×C4C2×D4×C6111yescharacteristic
433C22×C4#41×C6111yescharacteristic
434Q16—42no—
435Q16—42no—
436Q16—42no—
437Q16—42no—
438M16—22no—
439M16—41no—
440M16—42no—
441M16—42no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8C2×D4×C6111yescharacteristic
449C2×C8C2×D4×C6111yescharacteristic
450C2×C8C2×D4×C6111yescharacteristic
451C2×C8C2×D4×C6111yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
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—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4C2×D4×C6111yescharacteristic
470C4⋊C4C2×D4×C6111yescharacteristic
471C22⋊C4—41no—
472C22⋊C4—41no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—41no—
478C42—41no—
479C42C2×D4×C6111yescharacteristic
480C42C2×D4×C6111yescharacteristic
481C42#41×C6111yescharacteristic
482C42C24×C6111yescharacteristic
483C23#121×C6111yescharacteristic
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—42no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—41no—
494Q8—81no—
495Q8#137×C6112yes—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—81no—
511C2×C4#121×C6111yescharacteristic
512C2×C4#121×C6111yescharacteristic
513C2×C4#121×C6111yescharacteristic
514C2×C4C22×D4×C6111yescharacteristic
515C2×C4C22×D4×C6111yescharacteristic
516C2×C4C2×#41×C6111yescharacteristic
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8#137×C6112yes—
527C22—21no—
528C22—21no—
529C22—21no—
530C22C2×#121×C6111yescharacteristic
531C4—21no—
532C4—21no—
533C4—22no—
534C4—21no—
535C4—21no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—81no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4C2×#137×C6111yescharacteristic
544C4C2×#137×C6111yescharacteristic
545C4C61×#57511yescharacteristic
546C4C61×#57511yescharacteristic
547C2—41no—
548C2C61×#303711yescharacteristic
549C2C61×#305611yescharacteristic
550C2C61×#306911yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC42C24×C61
prime radicalC23×C61#121
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
5. C61×#1704C2semidirect
6. C61×#1700C2semidirect
7. C61×#1692C2semidirect
8. C61×#1690C2semidirect
9. C61×#1684C2semidirect
10. C61×#1680C2semidirect
11. C61×#1672C2semidirect
12. C61×#1670C2semidirect
251. #19311C61direct (N × H)
276. #1704C2×C61semidirect
277. #1700C2×C61semidirect
278. #1692C2×C61semidirect
279. #1690C2×C61semidirect
280. #1684C2×C61semidirect
281. #1680C2×C61semidirect
282. #1672C2×C61semidirect
283. #1670C2×C61semidirect
342. C61#19311direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#31852
C61×#31132
C61×#30782
Q8×M16×C612
C61×#17042
C61×#17002
C61×#16922
C61×#16902
C61×#16842
C61×#16802
C61×#16722
C61×#16702
C61×#15692
C61×#15612
C61×#15592
#1931161