Finite Group Databasebeta

← C61×#19068 #29522501

Subgroups — C61×#19068 #29522501

Order 15616.

920 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3545C211yesmaximal, characteristic, complemented
2C61×#3219C211yesmaximal, characteristic, complemented
3C61×#3213C211yesmaximal, characteristic, complemented
4C61×#3171C211yesmaximal, characteristic, complemented
5C61×#1664C211yesmaximal, characteristic, complemented
6C61×#1662C211yesmaximal, characteristic, complemented
7C61×#1661C211yesmaximal, characteristic, complemented
8C61×#1659C211yesmaximal, characteristic, complemented
9C61×#1657C211yesmaximal, characteristic, complemented
10C61×#1656C211yesmaximal, characteristic, complemented
11C61×#1656C211yesmaximal, characteristic, complemented
12C61×#1655C211yesmaximal, characteristic, complemented
13C61×#1535C211yesmaximal, characteristic, complemented
14C61×#1529C211yesmaximal, characteristic, complemented
15C61×#1527C211yesmaximal, characteristic, complemented
16C61×#563C2211yescharacteristic
17C61×#562C2211yescharacteristic
18C61×#562C2211yescharacteristic
19C61×H(3,𝔽4)C2211yescharacteristic
20C61×#555—21no—
21C61×#551—21no—
22C61×#551—21no—
23C61×#551—21no—
24C61×#546—21no—
25C61×#546—21no—
26C61×#542—21no—
27C61×#542—21no—
28C61×#538—21no—
29C61×#538—21no—
30C61×#536—21no—
31C61×#534—21no—
32C61×#532C2211yescharacteristic, complemented
33C61×#529C2211yescharacteristic
34C61×#529C2211yescharacteristic
35C2×#124×C61C2211yescharacteristic
36C61×#501C2211yescharacteristic, complemented
37C61×#497C2211yescharacteristic, complemented
38C61×#496C2211yescharacteristic
39C61×#496C2211yescharacteristic, complemented
40C61×#496C2211yescharacteristic, complemented
41C61×#496C2211yescharacteristic, complemented
42C61×#491C2211yescharacteristic, complemented
43C61×#490C2211yescharacteristic, complemented
44C61×#490C2211yescharacteristic, complemented
45C61×#489C2211yescharacteristic
46C61×#489C2211yescharacteristic, complemented
47C61×#489C2211yescharacteristic, complemented
48C61×#469—21no—
49C61×#468—21no—
50C61×#464—21no—
51C61×#463—21no—
52C61×#463—21no—
53C61×#463—21no—
54C61×#452—21no—
55C61×#449—21no—
56C61×#448—21no—
57C61×#447—21no—
58C4×SD16×C61—21no—
59C4×D8×C61—21no—
60C61×#432C2211yescharacteristic, complemented
61C61×#432C2211yescharacteristic, complemented
62C4×M16×C61C2211yescharacteristic, complemented
63C61×#330C2211yescharacteristic, complemented
64C61×#330C2211yescharacteristic, complemented
65C61×#330C2211yescharacteristic, complemented
66C61×#330C2211yescharacteristic, complemented
67C61×#329C2211yescharacteristic
68C61×#329C2211yescharacteristic
69C61×#329C2211yescharacteristic, complemented
70C61×#329C2211yescharacteristic, complemented
71C61×#329C2211yescharacteristic, complemented
72C61×#329C2211yescharacteristic, complemented
73C61×#329C2211yescharacteristic, complemented
74C61×#329C2211yescharacteristic, complemented
75C2×#41×C61—21no—
76C2×#41×C61—21no—
77C22×Q8×C61D411yescharacteristic
78C22×D4×C61—21no—
79C22×D4×C61D411yescharacteristic
80C2×Q16×C61—21no—
81C2×SD16×C61—21no—
82C2×SD16×C61—21no—
83C2×SD16×C61—21no—
84C2×SD16×C61—21no—
85C2×SD16×C61—21no—
86C2×D8×C61—21no—
87C2×D8×C61—21no—
88C2×D8×C61—21no—
89C2×D8×C61—21no—
90C2×M16×C61—21no—
91C4⋊Q8×C61—21no—
92C4⋊Q8×C61—21no—
93C4⋊Q8×C61C2311yescharacteristic
94#127×C61C2311yescharacteristic
95#126×C61—21no—
96#126×C61—21no—
97#126×C61—21no—
98#126×C61—21no—
99#126×C61—21no—
100#126×C61—21no—
101#125×C61C2311yescharacteristic
102#125×C61C2311yescharacteristic
103#124×C61—21no—
104#124×C61—21no—
105#124×C61—21no—
106#124×C61—21no—
107#124×C61—21no—
108#124×C61—21no—
109#124×C61—21no—
110#124×C61—21no—
111#124×C61—21no—
112#124×C61D411yescharacteristic
113#124×C61D411yescharacteristic
114#124×C61C2311yescharacteristic
115#124×C61C2311yescharacteristic
116#124×C61C2311yescharacteristic
117#124×C61C2311yescharacteristic
118#123×C61—21no—
119#123×C61—21no—
120#123×C61—21no—
121#123×C61—21no—
122#123×C61—21no—
123#123×C61—21no—
124#123×C61—21no—
125#123×C61—21no—
126#123×C61—21no—
127#123×C61—21no—
128#123×C61—21no—
129#123×C61—21no—
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61—21no—
133C22⋊Q8×C61—21no—
134C22⋊Q8×C61—21no—
135C22⋊Q8×C61—21no—
136C22⋊Q8×C61—21no—
137C22⋊Q8×C61—21no—
138C22⋊Q8×C61D411yescharacteristic
139C22⋊Q8×C61D411yescharacteristic
140#121×C61—21no—
141#121×C61—21no—
142#121×C61—21no—
143#121×C61—21no—
144#121×C61—21no—
145#121×C61—21no—
146#121×C61—21no—
147#121×C61—21no—
148#121×C61—21no—
149#121×C61—21no—
150#121×C61D411yescharacteristic
151#121×C61D411yescharacteristic
152#120×C61—21no—
153#120×C61—21no—
154#120×C61—21no—
155#120×C61—21no—
156#120×C61—21no—
157#120×C61—21no—
158C4×Q8×C61D411yescharacteristic
159C4×Q8×C61D411yescharacteristic
160C4×D4×C61—21no—
161C4×D4×C61—21no—
162C4×D4×C61—21no—
163C4×D4×C61—21no—
164C4×D4×C61—21no—
165C4×D4×C61—21no—
166C4×D4×C61—21no—
167C4×D4×C61—21no—
168C4×D4×C61D411yescharacteristic
169C4×D4×C61D411yescharacteristic
170#117×C61—21no—
171#117×C61—21no—
172#117×C61—21no—
173#117×C61—21no—
174#117×C61—21no—
175C2×C22⋊C4×C61—21no—
176C2×C22⋊C4×C61—21no—
177C2×C22⋊C4×C61—21no—
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—21no—
180C2×C42×C61C2311yescharacteristic
181#107×C61—21no—
182#106×C61—21no—
183C4⋊C8×C61—21no—
184C4⋊C8×C61—21no—
185#103×C61—21no—
186#103×C61—21no—
187#103×C61—21no—
188#103×C61—21no—
189#103×C61—21no—
190#102×C61—21no—
191#102×C61—21no—
192#102×C61—21no—
193#102×C61—21no—
194#102×C61—21no—
195#102×C61—21no—
196#102×C61—21no—
197C22⋊C8×C61—21no—
198C22⋊C8×C61—21no—
199#97×C61C2311yescharacteristic
200#97×C61C2311yescharacteristic
201#97×C61C2311yescharacteristic
202#97×C61C2311yescharacteristic
203#97×C61C2311yescharacteristic
204#97×C61C2311yescharacteristic
205C4×C8×C61—21no—
206C24×C61—21no—
207C24×C61—21no—
208#41×C61—82no—
209#41×C61—81no—
210#41×C61—81no—
211C2×Q8×C61—21no—
212C2×Q8×C61—21no—
213C2×Q8×C61—21no—
214C2×Q8×C61—81no—
215C2×Q8×C61C2×D411yescharacteristic
216C2×Q8×C61C2×D411yescharacteristic
217C2×Q8×C61C2×D411yescharacteristic
218C2×Q8×C61C2×D411yescharacteristic
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61—21no—
228C2×D4×C61—21no—
229C2×D4×C61—21no—
230C2×D4×C61—21no—
231C2×D4×C61—21no—
232C2×D4×C61—41no—
233C2×D4×C61—81no—
234C2×D4×C61—82no—
235C2×D4×C61C2×D411yescharacteristic
236C2×D4×C61C2×D411yescharacteristic
237C2×D4×C61C2×D411yescharacteristic
238C2×D4×C61C2×D411yescharacteristic
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—41no—
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D411yescharacteristic
251Q16×C61—81no—
252SD16×C61—42no—
253SD16×C61—81no—
254SD16×C61—81no—
255SD16×C61—81no—
256SD16×C61—81no—
257D8×C61—42no—
258D8×C61—81no—
259D8×C61—81no—
260D8×C61—81no—
261M16×C61—42no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61—21no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61C2×D411yescharacteristic
285C4⋊C4×C61C2×D411yescharacteristic
286C4⋊C4×C61C2×D411yescharacteristic
287C4⋊C4×C61C2×D411yescharacteristic
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C22⋊C4×C61—21no—
292C22⋊C4×C61—21no—
293C22⋊C4×C61—21no—
294C22⋊C4×C61—21no—
295C22⋊C4×C61—21no—
296C22⋊C4×C61—21no—
297C22⋊C4×C61—21no—
298C22⋊C4×C61—21no—
299C22⋊C4×C61—21no—
300C22⋊C4×C61—21no—
301C22⋊C4×C61—21no—
302C22⋊C4×C61—21no—
303C22⋊C4×C61—21no—
304C22⋊C4×C61—21no—
305C22⋊C4×C61—21no—
306C22⋊C4×C61—21no—
307C22⋊C4×C61—21no—
308C22⋊C4×C61—21no—
309C22⋊C4×C61—21no—
310C22⋊C4×C61—21no—
311C22⋊C4×C61—21no—
312C22⋊C4×C61—21no—
313C22⋊C4×C61—21no—
314C22⋊C4×C61—21no—
315C22⋊C4×C61—21no—
316C22⋊C4×C61—41no—
317C22⋊C4×C61—41no—
318C42×C61—21no—
319C42×C61—21no—
320C42×C61—21no—
321C42×C61—21no—
322C42×C61C2×D411yescharacteristic
323C42×C61C2×D411yescharacteristic
324C42×C61C2×D411yescharacteristic
325C42×C61C2411yescharacteristic
326C23×C61—21no—
327C23×C61—21no—
328C23×C61—21no—
329C23×C61—21no—
330C23×C61—42no—
331C23×C61—41no—
332C23×C61—81no—
333C23×C61—81no—
334C23×C61—81no—
335C23×C61—81no—
336C23×C61—81no—
337C23×C61#12011yescharacteristic
338Q8×C61—41no—
339Q8×C61—41no—
340Q8×C61—41no—
341Q8×C61—41no—
342Q8×C61—41no—
343Q8×C61—41no—
344Q8×C61—81no—
345Q8×C61—81no—
346D4×C61—41no—
347D4×C61—41no—
348D4×C61—41no—
349D4×C61—41no—
350D4×C61—41no—
351D4×C61—41no—
352D4×C61—41no—
353D4×C61—41no—
354D4×C61—41no—
355D4×C61—41no—
356D4×C61—42no—
357D4×C61—42no—
358D4×C61—81no—
359D4×C61—81no—
360D4×C61—81no—
361D4×C61—81no—
362D4×C61—81no—
363D4×C61—81no—
364D4×C61—81no—
365D4×C61—81no—
366D4×C61—82no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—42no—
379C2×C4×C61—41no—
380C2×C4×C61—81no—
381C2×C4×C61—81no—
382C2×C4×C61—82no—
383C2×C4×C61—81no—
384C2×C4×C61—81no—
385C2×C4×C61—81no—
386C2×C4×C61—81no—
387C2×C4×C61—81no—
388C2×C4×C61#12011yescharacteristic
389C2×C4×C61#12011yescharacteristic
390C2×C4×C61#12011yescharacteristic
391C2×C4×C61C22×D411yescharacteristic
392C2×C4×C61C22×D411yescharacteristic
393C2×C4×C61C22×D411yescharacteristic
394C8×C61—22no—
395C8×C61—41no—
396C8×C61—41no—
397C8×C61—41no—
398C8×C61—41no—
399C8×C61—41no—
400#19068C6111yesmaximal, characteristic, direct product factor, Sylow
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—41no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61—41no—
415C22×C61—41no—
416C22×C61—81no—
417C22×C61—81no—
418C22×C61—81no—
419C22×C61—162no—
420C22×C61—162no—
421C22×C61C2×#12011yescharacteristic
422C4×C61—21no—
423C4×C61—21no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—21no—
428C4×C61—41no—
429C4×C61—41no—
430C4×C61—41no—
431C4×C61—41no—
432C4×C61—41no—
433C4×C61—41no—
434C4×C61—41no—
435C4×C61—41no—
436C4×C61—81no—
437#3545C2×C6111yescharacteristic, complemented
438#3219C2×C6111yescharacteristic, complemented
439#3213C2×C6111yescharacteristic, complemented
440#3171C2×C6111yescharacteristic, complemented
441#1664C2×C6111yescharacteristic, complemented
442#1662C2×C6111yescharacteristic, complemented
443#1661C2×C6111yescharacteristic, complemented
444#1659C2×C6111yescharacteristic, complemented
445#1657C2×C6111yescharacteristic, complemented
446#1656C2×C6111yescharacteristic, complemented
447#1656C2×C6111yescharacteristic, complemented
448#1655C2×C6111yescharacteristic, complemented
449#1535C2×C6111yescharacteristic, complemented
450#1529C2×C6111yescharacteristic, complemented
451#1527C2×C6111yescharacteristic, complemented
452C2×C61—41no—
453C2×C61—81no—
454C2×C61—81no—
455C2×C61—81no—
456C2×C61—81no—
457C2×C61—161no—
458C2×C61#301811yescharacteristic
459C2×C61#301911yescharacteristic
460C2×C61#302111yescharacteristic
461#563C22×C6111yescharacteristic
462#562C22×C6111yescharacteristic
463#562C22×C6111yescharacteristic
464H(3,𝔽4)C22×C6111yescharacteristic
465#555—21no—
466#551—21no—
467#551—21no—
468#551—21no—
469#546—21no—
470#546—21no—
471#542—21no—
472#542—21no—
473#538—21no—
474#538—21no—
475#536—21no—
476#534—21no—
477#532C22×C6111yescharacteristic, complemented
478#529C22×C6111yescharacteristic
479#529C22×C6111yescharacteristic
480C2×#124C22×C6111yescharacteristic
481#501C22×C6111yescharacteristic, complemented
482#497C22×C6111yescharacteristic, complemented
483#496C22×C6111yescharacteristic
484#496C22×C6111yescharacteristic, complemented
485#496C22×C6111yescharacteristic, complemented
486#496C22×C6111yescharacteristic, complemented
487#491C22×C6111yescharacteristic, complemented
488#490C22×C6111yescharacteristic, complemented
489#490C22×C6111yescharacteristic, complemented
490#489C22×C6111yescharacteristic
491#489C22×C6111yescharacteristic, complemented
492#489C22×C6111yescharacteristic, complemented
493#469—21no—
494#468—21no—
495#464—21no—
496#463—21no—
497#463—21no—
498#463—21no—
499#452—21no—
500#449—21no—
501#448—21no—
502#447—21no—
503C4×SD16—21no—
504C4×D8—21no—
505#432C22×C6111yescharacteristic, complemented
506#432C22×C6111yescharacteristic, complemented
507C4×M16C22×C6111yescharacteristic, complemented
508#330C22×C6111yescharacteristic, complemented
509#330C22×C6111yescharacteristic, complemented
510#330C22×C6111yescharacteristic, complemented
511#330C22×C6111yescharacteristic, complemented
512#329C22×C6111yescharacteristic
513#329C22×C6111yescharacteristic
514#329C22×C6111yescharacteristic, complemented
515#329C22×C6111yescharacteristic, complemented
516#329C22×C6111yescharacteristic, complemented
517#329C22×C6111yescharacteristic, complemented
518#329C22×C6111yescharacteristic, complemented
519#329C22×C6111yescharacteristic, complemented
520C61#1906811yescharacteristic, direct product factor, Sylow
521C2×#41—21no—
522C2×#41—21no—
523C22×Q8D4×C6111yescharacteristic
524C22×D4—21no—
525C22×D4D4×C6111yescharacteristic
526C2×Q16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×SD16—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C2×D8—21no—
536C2×M16—21no—
537C4⋊Q8—21no—
538C4⋊Q8—21no—
539C4⋊Q8C23×C6111yescharacteristic
540#127C23×C6111yescharacteristic
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#125C23×C6111yescharacteristic
548#125C23×C6111yescharacteristic
549#124—21no—
550#124—21no—
551#124—21no—
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#124D4×C6111yescharacteristic
559#124D4×C6111yescharacteristic
560#124C23×C6111yescharacteristic
561#124C23×C6111yescharacteristic
562#124C23×C6111yescharacteristic
563#124C23×C6111yescharacteristic
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573#123—21no—
574#123—21no—
575#123—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8D4×C6111yescharacteristic
585C22⋊Q8D4×C6111yescharacteristic
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121D4×C6111yescharacteristic
597#121D4×C6111yescharacteristic
598#120—21no—
599#120—21no—
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604C4×Q8D4×C6111yescharacteristic
605C4×Q8D4×C6111yescharacteristic
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4D4×C6111yescharacteristic
615C4×D4D4×C6111yescharacteristic
616#117—21no—
617#117—21no—
618#117—21no—
619#117—21no—
620#117—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C42C23×C6111yescharacteristic
627#107—21no—
628#106—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#103—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642#102—21no—
643C22⋊C8—21no—
644C22⋊C8—21no—
645#97C23×C6111yescharacteristic
646#97C23×C6111yescharacteristic
647#97C23×C6111yescharacteristic
648#97C23×C6111yescharacteristic
649#97C23×C6111yescharacteristic
650#97C23×C6111yescharacteristic
651C4×C8—21no—
652C24—21no—
653C24—21no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—81no—
661C2×Q8C2×D4×C6111yescharacteristic
662C2×Q8C2×D4×C6111yescharacteristic
663C2×Q8C2×D4×C6111yescharacteristic
664C2×Q8C2×D4×C6111yescharacteristic
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—41no—
679C2×D4—81no—
680C2×D4—82no—
681C2×D4C2×D4×C6111yescharacteristic
682C2×D4C2×D4×C6111yescharacteristic
683C2×D4C2×D4×C6111yescharacteristic
684C2×D4C2×D4×C6111yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—41no—
694C22×C4C2×D4×C6111yescharacteristic
695C22×C4C2×D4×C6111yescharacteristic
696C22×C4C2×D4×C6111yescharacteristic
697Q16—81no—
698SD16—42no—
699SD16—81no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703D8—42no—
704D8—81no—
705D8—81no—
706D8—81no—
707M16—42no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4C2×D4×C6111yescharacteristic
731C4⋊C4C2×D4×C6111yescharacteristic
732C4⋊C4C2×D4×C6111yescharacteristic
733C4⋊C4C2×D4×C6111yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—41no—
763C22⋊C4—41no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42C2×D4×C6111yescharacteristic
769C42C2×D4×C6111yescharacteristic
770C42C2×D4×C6111yescharacteristic
771C42C24×C6111yescharacteristic
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—42no—
777C23—41no—
778C23—81no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23#120×C6111yescharacteristic
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—81no—
791Q8—81no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—42no—
803D4—42no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—82no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—82no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4#120×C6111yescharacteristic
835C2×C4#120×C6111yescharacteristic
836C2×C4#120×C6111yescharacteristic
837C2×C4C22×D4×C6111yescharacteristic
838C2×C4C22×D4×C6111yescharacteristic
839C2×C4C22×D4×C6111yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—162no—
865C22—162no—
866C22C2×#120×C6111yescharacteristic
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—81no—
882C2—41no—
883C2—81no—
884C2—81no—
885C2—81no—
886C2—81no—
887C2—161no—
888C2C61×#301811yescharacteristic
889C2C61×#301911yescharacteristic
890C2C61×#302111yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC42C24×C61
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
1. C61×#3545C2semidirect
2. C61×#3219C2semidirect
3. C61×#3213C2semidirect
4. C61×#3171C2semidirect
5. C61×#1664C2semidirect
6. C61×#1662C2semidirect
7. C61×#1661C2semidirect
8. C61×#1659C2semidirect
9. C61×#1657C2semidirect
10. C61×#1656C2semidirect
11. C61×#1656C2semidirect
12. C61×#1655C2semidirect
13. C61×#1535C2semidirect
14. C61×#1529C2semidirect
15. C61×#1527C2semidirect
32. C61×#532C22semidirect
36. C61×#501C22semidirect
37. C61×#497C22semidirect
39. C61×#496C22semidirect
40. C61×#496C22semidirect
41. C61×#496C22semidirect
42. C61×#491C22semidirect
43. C61×#490C22semidirect
44. C61×#490C22semidirect
46. C61×#489C22semidirect
47. C61×#489C22semidirect
60. C61×#432C22semidirect
61. C61×#432C22semidirect
62. C4×M16×C61C22semidirect
63. C61×#330C22semidirect
64. C61×#330C22semidirect
65. C61×#330C22semidirect
66. C61×#330C22semidirect
69. C61×#329C22semidirect
70. C61×#329C22semidirect
71. C61×#329C22semidirect
72. C61×#329C22semidirect
73. C61×#329C22semidirect
74. C61×#329C22semidirect
400. #19068C61direct (N × H)
437. #3545C2×C61semidirect
438. #3219C2×C61semidirect
439. #3213C2×C61semidirect
440. #3171C2×C61semidirect
441. #1664C2×C61semidirect
442. #1662C2×C61semidirect
443. #1661C2×C61semidirect
444. #1659C2×C61semidirect
445. #1657C2×C61semidirect
446. #1656C2×C61semidirect
447. #1656C2×C61semidirect
448. #1655C2×C61semidirect
449. #1535C2×C61semidirect
450. #1529C2×C61semidirect
451. #1527C2×C61semidirect
477. #532C22×C61semidirect
481. #501C22×C61semidirect
482. #497C22×C61semidirect
484. #496C22×C61semidirect
485. #496C22×C61semidirect
486. #496C22×C61semidirect
487. #491C22×C61semidirect
488. #490C22×C61semidirect
489. #490C22×C61semidirect
491. #489C22×C61semidirect
492. #489C22×C61semidirect
505. #432C22×C61semidirect
506. #432C22×C61semidirect
507. C4×M16C22×C61semidirect
508. #330C22×C61semidirect
509. #330C22×C61semidirect
510. #330C22×C61semidirect
511. #330C22×C61semidirect
514. #329C22×C61semidirect
515. #329C22×C61semidirect
516. #329C22×C61semidirect
517. #329C22×C61semidirect
518. #329C22×C61semidirect
519. #329C22×C61semidirect
520. C61#19068direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35452
C61×#32192
C61×#32132
C61×#31712
C61×#16642
C61×#16622
C61×#16612
C61×#16592
C61×#16572
C61×#16562
C61×#16552
C61×#15352
C61×#15292
C61×#15272
#1906861