Finite Group Databasebeta

← C61×#25575 #29529008

Subgroups — C61×#25575 #29529008

Order 15616.

1238 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#553C211yesmaximal, characteristic, complemented
2C2×C61×#488C211yesmaximal, characteristic, complemented
3C2×C61×#463C211yesmaximal, characteristic, complemented
4C61×#2540C211yesmaximal, characteristic, complemented
5C61×#2000C211yesmaximal, characteristic, complemented
6C61×#2000C211yesmaximal, characteristic, complemented
7C61×#1999C211yesmaximal, characteristic, complemented
8C61×#1999C211yesmaximal, characteristic, complemented
9C61×#1989C211yesmaximal, characteristic, complemented
10C61×#1954C211yesmaximal, characteristic, complemented
11C61×#1875C211yesmaximal, characteristic, complemented
12C61×#1874C211yesmaximal, characteristic, complemented
13C61×#1873C211yesmaximal, characteristic, complemented
14C61×#1872C211yesmaximal, characteristic, complemented
15C4×#102×C61C211yesmaximal, characteristic, complemented
16C22×SD16×C61C2211yescharacteristic
17C22×D8×C61C2211yescharacteristic
18C61×#553—24no—
19C61×#553—24no—
20C2×#126×C61—21no—
21C2×#125×C61C2211yescharacteristic
22C2×#124×C61C2211yescharacteristic
23C2×#123×C61—21no—
24C2×C22⋊Q8×C61C2211yescharacteristic
25C2×C22⋊Q8×C61C2211yescharacteristic
26C2×#121×C61—21no—
27C2×#121×C61C2211yescharacteristic
28C2×#121×C61C2211yescharacteristic
29C2×#121×C61C2211yescharacteristic
30C2×#121×C61C2211yescharacteristic
31C2×C4×D4×C61—21no—
32C2×C4×D4×C61C2211yescharacteristic
33C2×C4×D4×C61C2211yescharacteristic
34C2×#117×C61C2211yescharacteristic
35C22×C4⋊C4×C61C2211yescharacteristic
36C61×#488—24no—
37C61×#463—24no—
38C2×C4⋊C8×C61C2211yescharacteristic
39C2×#103×C61C2211yescharacteristic
40C2×#103×C61C2211yescharacteristic
41C2×#103×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×#102×C61C2211yescharacteristic
44C2×#102×C61C2211yescharacteristic
45C2×#102×C61C2211yescharacteristic
46C2×#102×C61C2211yescharacteristic
47C2×C22⋊C8×C61C2211yescharacteristic
48C2×C22⋊C8×C61C2211yescharacteristic
49C2×C22⋊C8×C61C2211yescharacteristic
50C2×C22⋊C8×C61C2211yescharacteristic
51C2×C4×C8×C61C2211yescharacteristic
52C61×#399—21no—
53C61×#392—21no—
54C61×#390—21no—
55C61×#390—21no—
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C22×Q8×C61C2311yescharacteristic
64C22×D4×C61—21no—
65C22×D4×C61—21no—
66C22×D4×C61—21no—
67C22×D4×C61—21no—
68C22×D4×C61D411yescharacteristic
69C22×D4×C61C2311yescharacteristic
70C22×D4×C61C2311yescharacteristic
71C23×C4×C61—21no—
72C23×C4×C61—21no—
73C23×C4×C61C2311yescharacteristic
74C23×C4×C61C2311yescharacteristic
75C2×SD16×C61—22no—
76C2×SD16×C61—41no—
77C2×SD16×C61—41no—
78C2×D8×C61—22no—
79C2×D8×C61—41no—
80C2×D8×C61—41no—
81C22×C8×C61C2311yescharacteristic
82C22×C8×C61C2311yescharacteristic
83C22×C8×C61C2311yescharacteristic
84C22×C8×C61C2311yescharacteristic
85#126×C61—28no—
86#125×C61—22no—
87#125×C61D414yescomplemented
88#124×C61—22no—
89#124×C61—22no—
90#123×C61—28no—
91C22⋊Q8×C61—22no—
92C22⋊Q8×C61—22no—
93C22⋊Q8×C61—41no—
94C22⋊Q8×C61—41no—
95#121×C61—28no—
96#121×C61—22no—
97#121×C61—22no—
98#121×C61—22no—
99#121×C61—22no—
100#121×C61—22no—
101#121×C61—22no—
102#121×C61—41no—
103#121×C61—41no—
104C4×D4×C61—28no—
105C4×D4×C61—22no—
106C4×D4×C61—22no—
107C4×D4×C61—22no—
108C4×D4×C61D414yescomplemented
109#117×C61—22no—
110#117×C61—22no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61—22no—
115C2×C4⋊C4×C61—22no—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61D411yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61D411yescharacteristic
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C42×C61—21no—
137C2×C42×C61—21no—
138C2×C42×C61C2311yescharacteristic
139C4⋊C8×C61—22no—
140#103×C61—22no—
141#103×C61—22no—
142#103×C61—22no—
143#102×C61—22no—
144#102×C61—22no—
145#102×C61—22no—
146#102×C61—22no—
147#102×C61—22no—
148C22⋊C8×C61—41no—
149C22⋊C8×C61—41no—
150C22⋊C8×C61—41no—
151C22⋊C8×C61—41no—
152C4×C8×C61—22no—
153#95×C61—21no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61C2×D411yescharacteristic
157C24×C61C2×D411yescharacteristic
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×D4×C61—24no—
165C2×D4×C61—22no—
166C2×D4×C61—24no—
167C2×D4×C61—22no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—41no—
180C2×D4×C61—42no—
181C2×D4×C61—42no—
182C2×D4×C61—42no—
183C2×D4×C61—42no—
184C2×D4×C61—42no—
185C2×D4×C61—42no—
186C2×D4×C61—81no—
187C2×D4×C61—81no—
188C2×D4×C61—81no—
189C2×D4×C61—81no—
190C2×D4×C61C2×D412yes—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—24no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—24no—
210C22×C4×C61—21no—
211C22×C4×C61—81no—
212C22×C4×C61—81no—
213C22×C4×C61—81no—
214C22×C4×C61—81no—
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2411yescharacteristic
220SD16×C61—44no—
221D8×C61—44no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C4⋊C4×C61—24no—
235C4⋊C4×C61—24no—
236C4⋊C4×C61—24no—
237C4⋊C4×C61—22no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—42no—
244C4⋊C4×C61—42no—
245C4⋊C4×C61C2×D412yes—
246C4⋊C4×C61C2×D412yes—
247C4⋊C4×C61C2×D412yes—
248C4⋊C4×C61#4112yes—
249C4⋊C4×C61#4112yes—
250C22⋊C4×C61—24no—
251C22⋊C4×C61—24no—
252C22⋊C4×C61—24no—
253C22⋊C4×C61—24no—
254C22⋊C4×C61—22no—
255C22⋊C4×C61—22no—
256C22⋊C4×C61—42no—
257C22⋊C4×C61—42no—
258C22⋊C4×C61—42no—
259C22⋊C4×C61—42no—
260C22⋊C4×C61—42no—
261C22⋊C4×C61—42no—
262C42×C61—24no—
263C42×C61—81no—
264C42×C61C2×D412yes—
265C42×C61C2×D412yes—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—22no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61#13512yes—
294C23×C61C22×D411yescharacteristic
295Q8×C61—41no—
296Q8×C61—41no—
297Q8×C61—41no—
298Q8×C61—41no—
299D4×C61—22no—
300D4×C61—22no—
301D4×C61—44no—
302D4×C61—48no—
303D4×C61—41no—
304D4×C61—41no—
305D4×C61—41no—
306D4×C61—41no—
307D4×C61—41no—
308D4×C61—41no—
309D4×C61—84no—
310D4×C61—84no—
311D4×C61—84no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—21no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—84no—
349C2×C4×C61—84no—
350C2×C4×C61#12012yes—
351C2×C4×C61#12012yes—
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C2×#4111yescharacteristic
355C2×C4×C61C2×#4111yescharacteristic
356C2×C4×C61H(5,𝔽2)11yescharacteristic
357C2×C4×C61H(5,𝔽2)11yescharacteristic
358C8×C61—41no—
359C8×C61—41no—
360C8×C61—41no—
361C8×C61—41no—
362#25575C6111yesmaximal, characteristic, direct product factor, Sylow
363C22×C61—22no—
364C22×C61—22no—
365C22×C61—22no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—42no—
372C22×C61—41no—
373C22×C61—42no—
374C22×C61—42no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—81no—
381C22×C61—81no—
382C22×C61—81no—
383C22×C61—81no—
384C22×C61—81no—
385C22×C61—81no—
386C22×C61—81no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61—81no—
391C22×C61C2×#12011yescharacteristic
392C22×C61#54611yescharacteristic
393C22×C61#54611yescharacteristic
394C22×C61C2×#13511yescharacteristic
395C22×C61#57511yescharacteristic
396C22×C61#57611yescharacteristic
397C22×C61#57711yescharacteristic
398C4×C61—22no—
399C4×C61—22no—
400C4×C61—41no—
401C4×C61—41no—
402C4×C61—42no—
403C4×C61—42no—
404C4×C61—42no—
405C4×C61—42no—
406C4×C61—42no—
407C4×C61—81no—
408C4×C61#53211yescharacteristic
409C4×C61#53511yescharacteristic
410C4×C61#55011yescharacteristic
411C4×C61#55011yescharacteristic
412C2×#553C2×C6111yescharacteristic, complemented
413C2×#488C2×C6111yescharacteristic, complemented
414C2×#463C2×C6111yescharacteristic, complemented
415#2540C2×C6111yescharacteristic, complemented
416#2000C2×C6111yescharacteristic, complemented
417#2000C2×C6111yescharacteristic, complemented
418#1999C2×C6111yescharacteristic, complemented
419#1999C2×C6111yescharacteristic, complemented
420#1989C2×C6111yescharacteristic, complemented
421#1954C2×C6111yescharacteristic, complemented
422#1875C2×C6111yescharacteristic, complemented
423#1874C2×C6111yescharacteristic, complemented
424#1873C2×C6111yescharacteristic, complemented
425#1872C2×C6111yescharacteristic, complemented
426C4×#102C2×C6111yescharacteristic, complemented
427C2×C61—42no—
428C2×C61—81no—
429C2×C61—82no—
430C2×C61—161no—
431C2×C61#243111yescharacteristic
432C2×C61#300211yescharacteristic
433C2×C61#301211yescharacteristic
434C2×C61#329711yescharacteristic
435C2×C61#330111yescharacteristic
436C2×C61#332211yescharacteristic
437C2×C61#332611yescharacteristic
438C22×SD16C22×C6111yescharacteristic
439C22×D8C22×C6111yescharacteristic
440#553—24no—
441#553—24no—
442C2×#126—21no—
443C2×#125C22×C6111yescharacteristic
444C2×#124C22×C6111yescharacteristic
445C2×#123—21no—
446C2×C22⋊Q8C22×C6111yescharacteristic
447C2×C22⋊Q8C22×C6111yescharacteristic
448C2×#121—21no—
449C2×#121C22×C6111yescharacteristic
450C2×#121C22×C6111yescharacteristic
451C2×#121C22×C6111yescharacteristic
452C2×#121C22×C6111yescharacteristic
453C2×C4×D4—21no—
454C2×C4×D4C22×C6111yescharacteristic
455C2×C4×D4C22×C6111yescharacteristic
456C2×#117C22×C6111yescharacteristic
457C22×C4⋊C4C22×C6111yescharacteristic
458#488—24no—
459#463—24no—
460C2×C4⋊C8C22×C6111yescharacteristic
461C2×#103C22×C6111yescharacteristic
462C2×#103C22×C6111yescharacteristic
463C2×#103C22×C6111yescharacteristic
464C2×#102C22×C6111yescharacteristic
465C2×#102C22×C6111yescharacteristic
466C2×#102C22×C6111yescharacteristic
467C2×#102C22×C6111yescharacteristic
468C2×#102C22×C6111yescharacteristic
469C2×C22⋊C8C22×C6111yescharacteristic
470C2×C22⋊C8C22×C6111yescharacteristic
471C2×C22⋊C8C22×C6111yescharacteristic
472C2×C22⋊C8C22×C6111yescharacteristic
473C2×C4×C8C22×C6111yescharacteristic
474#399—21no—
475#392—21no—
476#390—21no—
477#390—21no—
478C4×C4⋊C4C22×C6111yescharacteristic
479#340C22×C6111yescharacteristic
480#340C22×C6111yescharacteristic
481#340C22×C6111yescharacteristic
482#340C22×C6111yescharacteristic
483#340C22×C6111yescharacteristic
484#340C22×C6111yescharacteristic
485C61#2557511yescharacteristic, direct product factor, Sylow
486C22×Q8C23×C6111yescharacteristic
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4D4×C6111yescharacteristic
492C22×D4C23×C6111yescharacteristic
493C22×D4C23×C6111yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C23×C6111yescharacteristic
497C23×C4C23×C6111yescharacteristic
498C2×SD16—22no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×D8—22no—
502C2×D8—41no—
503C2×D8—41no—
504C22×C8C23×C6111yescharacteristic
505C22×C8C23×C6111yescharacteristic
506C22×C8C23×C6111yescharacteristic
507C22×C8C23×C6111yescharacteristic
508#126—28no—
509#125—22no—
510#125D4×C6114yescomplemented
511#124—22no—
512#124—22no—
513#123—28no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—41no—
517C22⋊Q8—41no—
518#121—28no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—22no—
523#121—22no—
524#121—22no—
525#121—41no—
526#121—41no—
527C4×D4—28no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4D4×C6114yescomplemented
532#117—22no—
533#117—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4D4×C6111yescharacteristic
542C2×C4⋊C4C23×C6111yescharacteristic
543C2×C4⋊C4C23×C6111yescharacteristic
544C2×C4⋊C4C23×C6111yescharacteristic
545C2×C4⋊C4C23×C6111yescharacteristic
546C2×C4⋊C4C23×C6111yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4D4×C6111yescharacteristic
558C2×C22⋊C4D4×C6111yescharacteristic
559C2×C42—21no—
560C2×C42—21no—
561C2×C42C23×C6111yescharacteristic
562C4⋊C8—22no—
563#103—22no—
564#103—22no—
565#103—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571C22⋊C8—41no—
572C22⋊C8—41no—
573C22⋊C8—41no—
574C22⋊C8—41no—
575C4×C8—22no—
576#95—21no—
577C24—21no—
578C24—21no—
579C24C2×D4×C6111yescharacteristic
580C24C2×D4×C6111yescharacteristic
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×D4—24no—
588C2×D4—22no—
589C2×D4—24no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—41no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4C2×D4×C6112yes—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—81no—
635C22×C4—81no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4C2×D4×C6111yescharacteristic
639C22×C4C2×D4×C6111yescharacteristic
640C22×C4C2×D4×C6111yescharacteristic
641C22×C4C2×D4×C6111yescharacteristic
642C22×C4C24×C6111yescharacteristic
643SD16—44no—
644D8—44no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4C2×D4×C6112yes—
669C4⋊C4C2×D4×C6112yes—
670C4⋊C4C2×D4×C6112yes—
671C4⋊C4#41×C6112yes—
672C4⋊C4#41×C6112yes—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—24no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C42—24no—
686C42—81no—
687C42C2×D4×C6112yes—
688C42C2×D4×C6112yes—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—22no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23#135×C6112yes—
717C23C22×D4×C6111yescharacteristic
718Q8—41no—
719Q8—41no—
720Q8—41no—
721Q8—41no—
722D4—22no—
723D4—22no—
724D4—44no—
725D4—48no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—84no—
733D4—84no—
734D4—84no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4#120×C6112yes—
774C2×C4#120×C6112yes—
775C2×C4C22×D4×C6111yescharacteristic
776C2×C4C22×D4×C6111yescharacteristic
777C2×C4C2×#41×C6111yescharacteristic
778C2×C4C2×#41×C6111yescharacteristic
779C2×C4H(5,𝔽2)×C6111yescharacteristic
780C2×C4H(5,𝔽2)×C6111yescharacteristic
781C8—41no—
782C8—41no—
783C8—41no—
784C8—41no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—41no—
799C22—42no—
800C22—42no—
801C22—41no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22C2×#120×C6111yescharacteristic
814C22C61×#54611yescharacteristic
815C22C61×#54611yescharacteristic
816C22C2×#135×C6111yescharacteristic
817C22C61×#57511yescharacteristic
818C22C61×#57611yescharacteristic
819C22C61×#57711yescharacteristic
820C4—22no—
821C4—22no—
822C4—42no—
823C4—42no—
824C4—41no—
825C4—41no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—81no—
830C4C61×#53211yescharacteristic
831C4C61×#53511yescharacteristic
832C4C61×#55011yescharacteristic
833C4C61×#55011yescharacteristic
834C2—42no—
835C2—81no—
836C2—82no—
837C2—161no—
838C2C61×#243111yescharacteristic
839C2C61×#300211yescharacteristic
840C2C61×#301211yescharacteristic
841C2C61×#329711yescharacteristic
842C2C61×#330111yescharacteristic
843C2C61×#332211yescharacteristic
844C2C61×#332611yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C4×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#553C2semidirect
2. C2×C61×#488C2semidirect
3. C2×C61×#463C2semidirect
4. C61×#2540C2semidirect
5. C61×#2000C2semidirect
6. C61×#2000C2semidirect
7. C61×#1999C2semidirect
8. C61×#1999C2semidirect
9. C61×#1989C2semidirect
10. C61×#1954C2semidirect
11. C61×#1875C2semidirect
12. C61×#1874C2semidirect
13. C61×#1873C2semidirect
14. C61×#1872C2semidirect
15. C4×#102×C61C2semidirect
87. #125×C61D4semidirect
108. C4×D4×C61D4semidirect
362. #25575C61direct (N × H)
412. C2×#553C2×C61semidirect
413. C2×#488C2×C61semidirect
414. C2×#463C2×C61semidirect
415. #2540C2×C61semidirect
416. #2000C2×C61semidirect
417. #2000C2×C61semidirect
418. #1999C2×C61semidirect
419. #1999C2×C61semidirect
420. #1989C2×C61semidirect
421. #1954C2×C61semidirect
422. #1875C2×C61semidirect
423. #1874C2×C61semidirect
424. #1873C2×C61semidirect
425. #1872C2×C61semidirect
426. C4×#102C2×C61semidirect
485. C61#25575direct (N × H)
510. #125D4×C61semidirect
531. C4×D4D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5532
C2×C61×#4882
C2×C61×#4632
C61×#25402
C61×#20002
C61×#19992
C61×#19892
C61×#19542
C61×#18752
C61×#18742
C61×#18732
C61×#18722
C4×#102×C612
#2557561