Finite Group Databasebeta

← C61×#18005 #29521438

Subgroups — C61×#18005 #29521438

Order 15616.

608 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3102C211yesmaximal, characteristic
2C61×#2971C211yesmaximal, characteristic, complemented
3C61×#2969C211yesmaximal, characteristic, complemented
4C61×#1594C211yesmaximal, characteristic, complemented
5C61×#1592C211yesmaximal, characteristic, complemented
6C61×#1588C211yesmaximal, characteristic, complemented
7C61×#1588C211yesmaximal, characteristic, complemented
8C61×#1587C211yesmaximal, characteristic, complemented
9C61×#1586C211yesmaximal, characteristic, complemented
10C61×#1579C211yesmaximal, characteristic, complemented
11C61×SD16⋊C8C211yesmaximal, characteristic, complemented
12C61×#1572C211yesmaximal, characteristic, complemented
13C61×#1494C211yesmaximal, characteristic, complemented
14C61×#1476C211yesmaximal, characteristic, complemented
15C61×#1451C211yesmaximal, characteristic, complemented
16C61×#529C2211yescharacteristic
17C4×#41×C61C2211yescharacteristic
18C61×#485C411yescharacteristic
19C61×#482C411yescharacteristic
20C61×#479C411yescharacteristic
21C61×#478C411yescharacteristic
22C61×#464C411yescharacteristic
23C61×#463C411yescharacteristic
24C61×#452C411yescharacteristic
25C61×#449C411yescharacteristic
26C61×#446C2211yescharacteristic
27C8×Q8×C61C2211yescharacteristic
28C8×Q8×C61C2211yescharacteristic
29C8×Q8×C61C2211yescharacteristic
30C4×Q16×C61C2211yescharacteristic
31C4×SD16×C61C2211yescharacteristic
32C4×SD16×C61C2211yescharacteristic
33C4×D8×C61C2211yescharacteristic
34C61×#436—21no—
35C61×#436—21no—
36C61×#436—21no—
37C61×#436C2211yescharacteristic
38C61×#436C2211yescharacteristic
39C61×#436C2211yescharacteristic
40C61×#435—21no—
41C8×D4×C61C2211yescharacteristic
42C61×#433—21no—
43C61×#432—21no—
44C61×#432C2211yescharacteristic
45C61×#431C2211yescharacteristic
46C61×#431C2211yescharacteristic
47C61×#405—21no—
48C4×M16×C61—21no—
49C4×M16×C61C2211yescharacteristic
50C2×C4×C8×C61C2211yescharacteristic
51C61×#335C2211yescharacteristic
52C61×#335C2211yescharacteristic
53C61×#334C2211yescharacteristic
54C61×#334C2211yescharacteristic
55C61×Q8⋊C8C2211yescharacteristic
56C61×Q8⋊C8C2211yescharacteristic
57C61×Q8⋊C8C2211yescharacteristic
58C61×Q8⋊C8C2211yescharacteristic
59C61×D4⋊C8C2211yescharacteristic
60C61×D4⋊C8C2211yescharacteristic
61C61×D4⋊C8C2211yescharacteristic
62C61×D4⋊C8C2211yescharacteristic
63C61×#322C2211yescharacteristic
64C61×#322C2211yescharacteristic
65C61×#322C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#41×C61C2×C411yescharacteristic
68C2×Q16×C61C2×C411yescharacteristic
69C2×SD16×C61C2×C411yescharacteristic
70C2×SD16×C61C2×C411yescharacteristic
71C2×D8×C61C2×C411yescharacteristic
72C2×M16×C61—21no—
73C2×M16×C61—21no—
74C2×M16×C61—21no—
75C2×M16×C61D411yescharacteristic
76C2×M16×C61D411yescharacteristic
77C22×C8×C61—21no—
78C22×C8×C61—21no—
79#126×C61—21no—
80#125×C61C2×C411yescharacteristic
81#124×C61C2×C411yescharacteristic
82#123×C61—21no—
83C22⋊Q8×C61C2×C411yescharacteristic
84#121×C61C2×C411yescharacteristic
85C4×Q8×C61C2×C411yescharacteristic
86C4×Q8×C61C2311yescharacteristic
87C4×Q8×C61C2311yescharacteristic
88C4×D4×C61—21no—
89C4×D4×C61—21no—
90C4×D4×C61—21no—
91C4×D4×C61C2×C411yescharacteristic
92C4×D4×C61C2311yescharacteristic
93C4×D4×C61C2311yescharacteristic
94#117×C61—21no—
95#117×C61—21no—
96#117×C61C2×C411yescharacteristic
97C2×C42×C61—21no—
98C2×C42×C61C2311yescharacteristic
99#107×C61C2×C411yescharacteristic
100#107×C61C2×C411yescharacteristic
101#106×C61C2×C411yescharacteristic
102#106×C61C2×C411yescharacteristic
103C4⋊C8×C61—21no—
104C4⋊C8×C61—21no—
105C4⋊C8×C61—21no—
106C4⋊C8×C61—21no—
107C4⋊C8×C61C2×C411yescharacteristic
108C4⋊C8×C61C2×C411yescharacteristic
109C4⋊C8×C61C2311yescharacteristic
110C4⋊C8×C61C2311yescharacteristic
111C4⋊C8×C61C2311yescharacteristic
112C4⋊C8×C61C2311yescharacteristic
113#103×C61C2×C411yescharacteristic
114#103×C61C2×C411yescharacteristic
115#103×C61C2×C411yescharacteristic
116#103×C61C2×C411yescharacteristic
117#102×C61C2×C411yescharacteristic
118#102×C61C2×C411yescharacteristic
119#102×C61C2×C411yescharacteristic
120#102×C61C2×C411yescharacteristic
121C22⋊C8×C61—21no—
122C22⋊C8×C61—21no—
123C22⋊C8×C61—21no—
124C22⋊C8×C61—21no—
125C22⋊C8×C61—21no—
126C22⋊C8×C61—21no—
127C22⋊C8×C61C2×C411yescharacteristic
128C22⋊C8×C61C2×C411yescharacteristic
129#97×C61—21no—
130#97×C61—21no—
131#97×C61D411yescharacteristic
132#97×C61D411yescharacteristic
133C4×C8×C61—21no—
134C4×C8×C61—21no—
135C4×C8×C61—21no—
136C4×C8×C61—21no—
137C4×C8×C61—21no—
138C4×C8×C61C2311yescharacteristic
139C4×C8×C61C2311yescharacteristic
140C4×C8×C61C2311yescharacteristic
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—22no—
145#41×C61—41no—
146C2×Q8×C61C22×C411yescharacteristic
147C2×Q8×C61C22×C411yescharacteristic
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61C22×C411yescharacteristic
151C2×D4×C61C22×C411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61#4111yescharacteristic
159Q16×C61—22no—
160SD16×C61—22no—
161SD16×C61—41no—
162D8×C61—41no—
163M16×C61—41no—
164M16×C61—41no—
165M16×C61—42no—
166M16×C61—42no—
167M16×C61—42no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—42no—
175C2×C8×C61—42no—
176C2×C8×C61C22×C411yescharacteristic
177C2×C8×C61C22×C411yescharacteristic
178C2×C8×C61C22×C411yescharacteristic
179C2×C8×C61C22×C411yescharacteristic
180C2×C8×C61C2×D411yescharacteristic
181C2×C8×C61C2×D411yescharacteristic
182C2×C8×C61C2×D411yescharacteristic
183C2×C8×C61C2×D411yescharacteristic
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×C61C22×C411yescharacteristic
191C4⋊C4×C61C22×C411yescharacteristic
192C4⋊C4×C61C22×C411yescharacteristic
193C4⋊C4×C61C22×C411yescharacteristic
194C22⋊C4×C61—21no—
195C22⋊C4×C61—21no—
196C22⋊C4×C61—21no—
197C22⋊C4×C61—21no—
198C22⋊C4×C61—21no—
199C22⋊C4×C61—21no—
200C22⋊C4×C61—21no—
201C22⋊C4×C61—21no—
202C42×C61—21no—
203C42×C61—21no—
204C42×C61—21no—
205C42×C61—21no—
206C42×C61C22×C411yescharacteristic
207C42×C61C2×D411yescharacteristic
208C42×C61#4111yescharacteristic
209C42×C61C2411yescharacteristic
210C23×C61—21no—
211C23×C61—21no—
212C23×C61C4×D411yescharacteristic
213Q8×C61—21no—
214Q8×C61—21no—
215Q8×C61—21no—
216Q8×C61#13112yes—
217D4×C61—21no—
218D4×C61—21no—
219D4×C61—21no—
220D4×C61—21no—
221D4×C61—42no—
222D4×C61—81no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
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—41no—
239C2×C4×C61—81no—
240C2×C4×C61C4×D411yescharacteristic
241C2×C4×C61C4×D411yescharacteristic
242C2×C4×C61C4×D411yescharacteristic
243C2×C4×C61C23×C411yescharacteristic
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C8×C61—22no—
247C8×C61—21no—
248C8×C61—21no—
249C8×C61—21no—
250C8×C61—21no—
251C8×C61—21no—
252C8×C61—21no—
253C8×C61—21no—
254C8×C61—21no—
255C8×C61—41no—
256C8×C61—41no—
257C8×C61—41no—
258C8×C61—41no—
259C8×C61—41no—
260#18005C6111yesmaximal, characteristic, direct product factor, Sylow
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61C2×C4×D411yescharacteristic
271C4×C61—21no—
272C4×C61—22no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—21no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61C2×#13111yescharacteristic
282C4×C61#56811yescharacteristic
283C4×C61#57511yescharacteristic
284C4×C61#57511yescharacteristic
285#3102C2×C6111yescharacteristic
286#2971C2×C6111yescharacteristic, complemented
287#2969C2×C6111yescharacteristic, complemented
288#1594C2×C6111yescharacteristic, complemented
289#1592C2×C6111yescharacteristic, complemented
290#1588C2×C6111yescharacteristic, complemented
291#1588C2×C6111yescharacteristic, complemented
292#1587C2×C6111yescharacteristic, complemented
293#1586C2×C6111yescharacteristic, complemented
294#1579C2×C6111yescharacteristic, complemented
295SD16⋊C8C2×C6111yescharacteristic, complemented
296#1572C2×C6111yescharacteristic, complemented
297#1494C2×C6111yescharacteristic, complemented
298#1476C2×C6111yescharacteristic, complemented
299#1451C2×C6111yescharacteristic, complemented
300C2×C61—41no—
301C2×C61—81no—
302C2×C61—81no—
303C2×C61#293311yescharacteristic
304C2×C61#294311yescharacteristic
305C2×C61#295611yescharacteristic
306#529C22×C6111yescharacteristic
307C4×#41C22×C6111yescharacteristic
308#485C4×C6111yescharacteristic
309#482C4×C6111yescharacteristic
310#479C4×C6111yescharacteristic
311#478C4×C6111yescharacteristic
312#464C4×C6111yescharacteristic
313#463C4×C6111yescharacteristic
314#452C4×C6111yescharacteristic
315#449C4×C6111yescharacteristic
316#446C22×C6111yescharacteristic
317C8×Q8C22×C6111yescharacteristic
318C8×Q8C22×C6111yescharacteristic
319C8×Q8C22×C6111yescharacteristic
320C4×Q16C22×C6111yescharacteristic
321C4×SD16C22×C6111yescharacteristic
322C4×SD16C22×C6111yescharacteristic
323C4×D8C22×C6111yescharacteristic
324#436—21no—
325#436—21no—
326#436—21no—
327#436C22×C6111yescharacteristic
328#436C22×C6111yescharacteristic
329#436C22×C6111yescharacteristic
330#435—21no—
331C8×D4C22×C6111yescharacteristic
332#433—21no—
333#432—21no—
334#432C22×C6111yescharacteristic
335#431C22×C6111yescharacteristic
336#431C22×C6111yescharacteristic
337#405—21no—
338C4×M16—21no—
339C4×M16C22×C6111yescharacteristic
340C2×C4×C8C22×C6111yescharacteristic
341#335C22×C6111yescharacteristic
342#335C22×C6111yescharacteristic
343#334C22×C6111yescharacteristic
344#334C22×C6111yescharacteristic
345Q8⋊C8C22×C6111yescharacteristic
346Q8⋊C8C22×C6111yescharacteristic
347Q8⋊C8C22×C6111yescharacteristic
348Q8⋊C8C22×C6111yescharacteristic
349D4⋊C8C22×C6111yescharacteristic
350D4⋊C8C22×C6111yescharacteristic
351D4⋊C8C22×C6111yescharacteristic
352D4⋊C8C22×C6111yescharacteristic
353#322C22×C6111yescharacteristic
354#322C22×C6111yescharacteristic
355#322C22×C6111yescharacteristic
356#322C22×C6111yescharacteristic
357C61#1800511yescharacteristic, direct product factor, Sylow
358C2×#41C2×C4×C6111yescharacteristic
359C2×Q16C2×C4×C6111yescharacteristic
360C2×SD16C2×C4×C6111yescharacteristic
361C2×SD16C2×C4×C6111yescharacteristic
362C2×D8C2×C4×C6111yescharacteristic
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16D4×C6111yescharacteristic
367C2×M16D4×C6111yescharacteristic
368C22×C8—21no—
369C22×C8—21no—
370#126—21no—
371#125C2×C4×C6111yescharacteristic
372#124C2×C4×C6111yescharacteristic
373#123—21no—
374C22⋊Q8C2×C4×C6111yescharacteristic
375#121C2×C4×C6111yescharacteristic
376C4×Q8C2×C4×C6111yescharacteristic
377C4×Q8C23×C6111yescharacteristic
378C4×Q8C23×C6111yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4C2×C4×C6111yescharacteristic
383C4×D4C23×C6111yescharacteristic
384C4×D4C23×C6111yescharacteristic
385#117—21no—
386#117—21no—
387#117C2×C4×C6111yescharacteristic
388C2×C42—21no—
389C2×C42C23×C6111yescharacteristic
390#107C2×C4×C6111yescharacteristic
391#107C2×C4×C6111yescharacteristic
392#106C2×C4×C6111yescharacteristic
393#106C2×C4×C6111yescharacteristic
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8C2×C4×C6111yescharacteristic
399C4⋊C8C2×C4×C6111yescharacteristic
400C4⋊C8C23×C6111yescharacteristic
401C4⋊C8C23×C6111yescharacteristic
402C4⋊C8C23×C6111yescharacteristic
403C4⋊C8C23×C6111yescharacteristic
404#103C2×C4×C6111yescharacteristic
405#103C2×C4×C6111yescharacteristic
406#103C2×C4×C6111yescharacteristic
407#103C2×C4×C6111yescharacteristic
408#102C2×C4×C6111yescharacteristic
409#102C2×C4×C6111yescharacteristic
410#102C2×C4×C6111yescharacteristic
411#102C2×C4×C6111yescharacteristic
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8C2×C4×C6111yescharacteristic
419C22⋊C8C2×C4×C6111yescharacteristic
420#97—21no—
421#97—21no—
422#97D4×C6111yescharacteristic
423#97D4×C6111yescharacteristic
424C4×C8—21no—
425C4×C8—21no—
426C4×C8—21no—
427C4×C8—21no—
428C4×C8—21no—
429C4×C8C23×C6111yescharacteristic
430C4×C8C23×C6111yescharacteristic
431C4×C8C23×C6111yescharacteristic
432C4×C8C23×C6111yescharacteristic
433C4×C8C23×C6111yescharacteristic
434C4×C8C23×C6111yescharacteristic
435#41—22no—
436#41—41no—
437C2×Q8C22×C4×C6111yescharacteristic
438C2×Q8C22×C4×C6111yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4C22×C4×C6111yescharacteristic
442C2×D4C22×C4×C6111yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4C22×C4×C6111yescharacteristic
448C22×C4C2×D4×C6111yescharacteristic
449C22×C4#41×C6111yescharacteristic
450Q16—22no—
451SD16—22no—
452SD16—41no—
453D8—41no—
454M16—41no—
455M16—41no—
456M16—42no—
457M16—42no—
458M16—42no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—42no—
466C2×C8—42no—
467C2×C8C22×C4×C6111yescharacteristic
468C2×C8C22×C4×C6111yescharacteristic
469C2×C8C22×C4×C6111yescharacteristic
470C2×C8C22×C4×C6111yescharacteristic
471C2×C8C2×D4×C6111yescharacteristic
472C2×C8C2×D4×C6111yescharacteristic
473C2×C8C2×D4×C6111yescharacteristic
474C2×C8C2×D4×C6111yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4C22×C4×C6111yescharacteristic
482C4⋊C4C22×C4×C6111yescharacteristic
483C4⋊C4C22×C4×C6111yescharacteristic
484C4⋊C4C22×C4×C6111yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42C22×C4×C6111yescharacteristic
498C42C2×D4×C6111yescharacteristic
499C42#41×C6111yescharacteristic
500C42C24×C6111yescharacteristic
501C23—21no—
502C23—21no—
503C23C4×D4×C6111yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8#131×C6112yes—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—21no—
512D4—42no—
513D4—81no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—81no—
531C2×C4C4×D4×C6111yescharacteristic
532C2×C4C4×D4×C6111yescharacteristic
533C2×C4C4×D4×C6111yescharacteristic
534C2×C4C23×C4×C6111yescharacteristic
535C2×C4C22×D4×C6111yescharacteristic
536C2×C4C2×#41×C6111yescharacteristic
537C8—22no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—21no—
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22C2×C4×D4×C6111yescharacteristic
561C4—21no—
562C4—22no—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4C2×#131×C6111yescharacteristic
572C4C61×#56811yescharacteristic
573C4C61×#57511yescharacteristic
574C4C61×#57511yescharacteristic
575C2—41no—
576C2—81no—
577C2—81no—
578C2C61×#293311yescharacteristic
579C2C61×#294311yescharacteristic
580C2C61×#295611yescharacteristic
subgroupG/H
centerC2×C4×C61C22×D4
commutatorC2×C4C23×C4×C61
Frattini, cosocleC42C24×C61
socleC22×C61C2×C4×D4
prime radicalC61×#449C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C61 ◁ C4×M16×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2971C2semidirect
3. C61×#2969C2semidirect
4. C61×#1594C2semidirect
5. C61×#1592C2semidirect
6. C61×#1588C2semidirect
7. C61×#1588C2semidirect
8. C61×#1587C2semidirect
9. C61×#1586C2semidirect
10. C61×#1579C2semidirect
11. C61×SD16⋊C8C2semidirect
12. C61×#1572C2semidirect
13. C61×#1494C2semidirect
14. C61×#1476C2semidirect
15. C61×#1451C2semidirect
260. #18005C61direct (N × H)
286. #2971C2×C61semidirect
287. #2969C2×C61semidirect
288. #1594C2×C61semidirect
289. #1592C2×C61semidirect
290. #1588C2×C61semidirect
291. #1588C2×C61semidirect
292. #1587C2×C61semidirect
293. #1586C2×C61semidirect
294. #1579C2×C61semidirect
295. SD16⋊C8C2×C61semidirect
296. #1572C2×C61semidirect
297. #1494C2×C61semidirect
298. #1476C2×C61semidirect
299. #1451C2×C61semidirect
357. C61#18005direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#31022
C61×#29712
C61×#29692
C61×#15942
C61×#15922
C61×#15882
C61×#15872
C61×#15862
C61×#15792
C61×SD16⋊C82
C61×#15722
C61×#14942
C61×#14762
C61×#14512
#1800561