Finite Group Databasebeta

← C61×#19010 #29522443

Subgroups — C61×#19010 #29522443

Order 15616.

920 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3529C211yesmaximal, characteristic, complemented
2C61×#3219C211yesmaximal, characteristic, complemented
3C61×#3214C211yesmaximal, characteristic, complemented
4C61×#3180C211yesmaximal, 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×#1532C211yesmaximal, characteristic, complemented
15C61×#1530C211yesmaximal, characteristic, complemented
16C61×#563—21no—
17C61×#563C2211yescharacteristic
18C61×#562—21no—
19C61×#562—21no—
20C61×#562C2211yescharacteristic
21C61×#562C2211yescharacteristic
22C61×H(3,𝔽4)C2211yescharacteristic
23C61×#560—21no—
24C61×#560—21no—
25C61×#560—21no—
26C61×#532—21no—
27C61×#532C2211yescharacteristic
28C61×#532C2211yescharacteristic, complemented
29C61×#529—21no—
30C61×#529—21no—
31C61×#529C2211yescharacteristic
32C61×#529C2211yescharacteristic
33C61×#525—21no—
34C61×#525—21no—
35C61×#525—21no—
36C61×#501C2211yescharacteristic, complemented
37C61×#497C2211yescharacteristic
38C61×#496C2211yescharacteristic
39C61×#496C2211yescharacteristic
40C61×#496C2211yescharacteristic
41C61×#496C2211yescharacteristic, complemented
42C61×#491C2211yescharacteristic, complemented
43C61×#490C2211yescharacteristic, complemented
44C61×#490C2211yescharacteristic, complemented
45C61×#489C2211yescharacteristic
46C61×#489C2211yescharacteristic
47C61×#489C2211yescharacteristic, complemented
48C61×#466—21no—
49C61×#465—21no—
50C61×#464—21no—
51C61×#463—21no—
52C61×#461—21no—
53C61×#459—21no—
54C61×#452—21no—
55C61×#449—21no—
56C61×#449—21no—
57C61×#449—21no—
58C61×#442—21no—
59C61×#440—21no—
60C61×#432C2211yescharacteristic, complemented
61C61×#432C2211yescharacteristic, complemented
62C2×#97×C61C2211yescharacteristic, complemented
63C61×#330C2211yescharacteristic, complemented
64C61×#330C2211yescharacteristic, complemented
65C61×#330C2211yescharacteristic, complemented
66C61×#330C2211yescharacteristic, complemented
67C61×#329C2211yescharacteristic
68C61×#329C2211yescharacteristic
69C61×#329C2211yescharacteristic
70C61×#329C2211yescharacteristic
71C61×#329C2211yescharacteristic
72C61×#329C2211yescharacteristic
73C61×#329C2211yescharacteristic, complemented
74C61×#329C2211yescharacteristic, complemented
75C2×#41×C61—21no—
76C2×#41×C61—21no—
77C2×#41×C61D411yescharacteristic
78C2×#41×C61D411yescharacteristic
79C23×C4×C61—21no—
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—
90C22×C8×C61—21no—
91C4⋊Q8×C61—21no—
92C4⋊Q8×C61D411yescharacteristic
93C4⋊Q8×C61C2311yescharacteristic
94#127×C61—21no—
95#127×C61D411yescharacteristic
96#127×C61C2311yescharacteristic
97#126×C61—21no—
98#126×C61—21no—
99#126×C61—21no—
100#126×C61—21no—
101#126×C61—21no—
102#126×C61—21no—
103#125×C61—21no—
104#125×C61—21no—
105#125×C61C2311yescharacteristic
106#125×C61C2311yescharacteristic
107#124×C61—21no—
108#124×C61—21no—
109#124×C61—21no—
110#124×C61—21no—
111#124×C61—21no—
112#124×C61C2311yescharacteristic
113#124×C61C2311yescharacteristic
114#124×C61C2311yescharacteristic
115#124×C61C2311yescharacteristic
116#123×C61—21no—
117#123×C61—21no—
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—
128C22⋊Q8×C61—21no—
129C22⋊Q8×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×C61D411yescharacteristic
137C22⋊Q8×C61D411yescharacteristic
138#121×C61—21no—
139#121×C61—21no—
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×C61—21no—
151#121×C61—21no—
152#121×C61—21no—
153#121×C61—21no—
154#121×C61D411yescharacteristic
155#121×C61D411yescharacteristic
156#120×C61—21no—
157#120×C61—21no—
158#120×C61—21no—
159#120×C61—21no—
160#120×C61—21no—
161#120×C61—21no—
162C4×Q8×C61D411yescharacteristic
163C4×Q8×C61D411yescharacteristic
164C4×D4×C61—21no—
165C4×D4×C61—21no—
166C4×D4×C61—21no—
167C4×D4×C61—21no—
168C4×D4×C61—21no—
169C4×D4×C61—21no—
170C4×D4×C61—21no—
171C4×D4×C61—21no—
172C4×D4×C61—21no—
173C4×D4×C61—21no—
174C4×D4×C61D411yescharacteristic
175C4×D4×C61D411yescharacteristic
176#117×C61—21no—
177#117×C61—21no—
178#117×C61—21no—
179C2×C42×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×C61—21no—
200#97×C61C2311yescharacteristic
201#97×C61C2311yescharacteristic
202#97×C61C2311yescharacteristic
203#97×C61C2311yescharacteristic
204#97×C61C2311yescharacteristic
205#97×C61C2311yescharacteristic
206C24×C61—21no—
207#41×C61—81no—
208#41×C61—81no—
209#41×C61—82no—
210#41×C61—81no—
211#41×C61—81no—
212C2×Q8×C61—21no—
213C2×Q8×C61—21no—
214C2×Q8×C61C2×D411yescharacteristic
215C2×Q8×C61C2×D411yescharacteristic
216C2×Q8×C61C2×D411yescharacteristic
217C2×Q8×C61C2×D411yescharacteristic
218C2×D4×C61—21no—
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—21no—
233C2×D4×C61—21no—
234C2×D4×C61—41no—
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—21no—
248C22×C4×C61—41no—
249C22×C4×C61—82no—
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253Q16×C61—81no—
254SD16×C61—42no—
255SD16×C61—81no—
256SD16×C61—81no—
257SD16×C61—81no—
258SD16×C61—81no—
259D8×C61—42no—
260D8×C61—81no—
261D8×C61—81no—
262D8×C61—81no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61—42no—
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×C61—21no—
285C4⋊C4×C61—21no—
286C4⋊C4×C61—21no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61C2×D411yescharacteristic
289C4⋊C4×C61C2×D411yescharacteristic
290C4⋊C4×C61C2×D411yescharacteristic
291C4⋊C4×C61C2×D411yescharacteristic
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—41no—
331C23×C61—81no—
332C23×C61—81no—
333C23×C61—81no—
334C23×C61#12011yescharacteristic
335Q8×C61—41no—
336Q8×C61—41no—
337Q8×C61—41no—
338Q8×C61—41no—
339Q8×C61—41no—
340Q8×C61—41no—
341Q8×C61—81no—
342D4×C61—41no—
343D4×C61—41no—
344D4×C61—41no—
345D4×C61—41no—
346D4×C61—41no—
347D4×C61—41no—
348D4×C61—41no—
349D4×C61—41no—
350D4×C61—41no—
351D4×C61—41no—
352D4×C61—81no—
353D4×C61—81no—
354D4×C61—81no—
355D4×C61—81no—
356D4×C61—81no—
357D4×C61—81no—
358D4×C61—81no—
359D4×C61—81no—
360D4×C61—81no—
361D4×C61—81no—
362D4×C61—81no—
363D4×C61—81no—
364D4×C61—81no—
365D4×C61—82no—
366C2×C4×C61—21no—
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—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—42no—
378C2×C4×C61—42no—
379C2×C4×C61—42no—
380C2×C4×C61—42no—
381C2×C4×C61—41no—
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#19010C6111yesmaximal, 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—84no—
417C22×C61—81no—
418C22×C61—81no—
419C22×C61—81no—
420C22×C61C2×#12011yescharacteristic
421C4×C61—21no—
422C4×C61—21no—
423C4×C61—21no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—41no—
428C4×C61—41no—
429C4×C61—41no—
430C4×C61—41no—
431C4×C61—41no—
432C4×C61—41no—
433C4×C61—41no—
434C4×C61—41no—
435C4×C61—81no—
436#3529C2×C6111yescharacteristic, complemented
437#3219C2×C6111yescharacteristic, complemented
438#3214C2×C6111yescharacteristic, complemented
439#3180C2×C6111yescharacteristic, complemented
440#1664C2×C6111yescharacteristic, complemented
441#1662C2×C6111yescharacteristic, complemented
442#1661C2×C6111yescharacteristic, complemented
443#1659C2×C6111yescharacteristic, complemented
444#1657C2×C6111yescharacteristic, complemented
445#1656C2×C6111yescharacteristic, complemented
446#1656C2×C6111yescharacteristic, complemented
447#1655C2×C6111yescharacteristic, complemented
448#1535C2×C6111yescharacteristic, complemented
449#1532C2×C6111yescharacteristic, complemented
450#1530C2×C6111yescharacteristic, complemented
451C2×C61—41no—
452C2×C61—81no—
453C2×C61—81no—
454C2×C61—81no—
455C2×C61—81no—
456C2×C61—161no—
457C2×C61#301811yescharacteristic
458C2×C61#301911yescharacteristic
459C2×C61#302111yescharacteristic
460#563—21no—
461#563C22×C6111yescharacteristic
462#562—21no—
463#562—21no—
464#562C22×C6111yescharacteristic
465#562C22×C6111yescharacteristic
466H(3,𝔽4)C22×C6111yescharacteristic
467#560—21no—
468#560—21no—
469#560—21no—
470#532—21no—
471#532C22×C6111yescharacteristic
472#532C22×C6111yescharacteristic, complemented
473#529—21no—
474#529—21no—
475#529C22×C6111yescharacteristic
476#529C22×C6111yescharacteristic
477#525—21no—
478#525—21no—
479#525—21no—
480#501C22×C6111yescharacteristic, complemented
481#497C22×C6111yescharacteristic
482#496C22×C6111yescharacteristic
483#496C22×C6111yescharacteristic
484#496C22×C6111yescharacteristic
485#496C22×C6111yescharacteristic, complemented
486#491C22×C6111yescharacteristic, complemented
487#490C22×C6111yescharacteristic, complemented
488#490C22×C6111yescharacteristic, complemented
489#489C22×C6111yescharacteristic
490#489C22×C6111yescharacteristic
491#489C22×C6111yescharacteristic, complemented
492#466—21no—
493#465—21no—
494#464—21no—
495#463—21no—
496#461—21no—
497#459—21no—
498#452—21no—
499#449—21no—
500#449—21no—
501#449—21no—
502#442—21no—
503#440—21no—
504#432C22×C6111yescharacteristic, complemented
505#432C22×C6111yescharacteristic, complemented
506C2×#97C22×C6111yescharacteristic, complemented
507#330C22×C6111yescharacteristic, complemented
508#330C22×C6111yescharacteristic, complemented
509#330C22×C6111yescharacteristic, complemented
510#330C22×C6111yescharacteristic, complemented
511#329C22×C6111yescharacteristic
512#329C22×C6111yescharacteristic
513#329C22×C6111yescharacteristic
514#329C22×C6111yescharacteristic
515#329C22×C6111yescharacteristic
516#329C22×C6111yescharacteristic
517#329C22×C6111yescharacteristic, complemented
518#329C22×C6111yescharacteristic, complemented
519C61#1901011yescharacteristic, direct product factor, Sylow
520C2×#41—21no—
521C2×#41—21no—
522C2×#41D4×C6111yescharacteristic
523C2×#41D4×C6111yescharacteristic
524C23×C4—21no—
525C2×Q16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×D8—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C22×C8—21no—
536C4⋊Q8—21no—
537C4⋊Q8D4×C6111yescharacteristic
538C4⋊Q8C23×C6111yescharacteristic
539#127—21no—
540#127D4×C6111yescharacteristic
541#127C23×C6111yescharacteristic
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#126—21no—
548#125—21no—
549#125—21no—
550#125C23×C6111yescharacteristic
551#125C23×C6111yescharacteristic
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124C23×C6111yescharacteristic
558#124C23×C6111yescharacteristic
559#124C23×C6111yescharacteristic
560#124C23×C6111yescharacteristic
561#123—21no—
562#123—21no—
563#123—21no—
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—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8D4×C6111yescharacteristic
582C22⋊Q8D4×C6111yescharacteristic
583#121—21no—
584#121—21no—
585#121—21no—
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#121—21no—
597#121—21no—
598#121—21no—
599#121D4×C6111yescharacteristic
600#121D4×C6111yescharacteristic
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607C4×Q8D4×C6111yescharacteristic
608C4×Q8D4×C6111yescharacteristic
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4D4×C6111yescharacteristic
620C4×D4D4×C6111yescharacteristic
621#117—21no—
622#117—21no—
623#117—21no—
624C2×C42—21no—
625C2×C42C23×C6111yescharacteristic
626#107—21no—
627#106—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630#103—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644#97—21no—
645#97C23×C6111yescharacteristic
646#97C23×C6111yescharacteristic
647#97C23×C6111yescharacteristic
648#97C23×C6111yescharacteristic
649#97C23×C6111yescharacteristic
650#97C23×C6111yescharacteristic
651C24—21no—
652#41—81no—
653#41—81no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8C2×D4×C6111yescharacteristic
660C2×Q8C2×D4×C6111yescharacteristic
661C2×Q8C2×D4×C6111yescharacteristic
662C2×Q8C2×D4×C6111yescharacteristic
663C2×D4—21no—
664C2×D4—21no—
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—21no—
679C2×D4—41no—
680C2×D4C2×D4×C6111yescharacteristic
681C2×D4C2×D4×C6111yescharacteristic
682C2×D4C2×D4×C6111yescharacteristic
683C2×D4C2×D4×C6111yescharacteristic
684C22×C4—21no—
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×C4—82no—
695C22×C4C2×D4×C6111yescharacteristic
696C22×C4C2×D4×C6111yescharacteristic
697C22×C4C2×D4×C6111yescharacteristic
698Q16—81no—
699SD16—42no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703SD16—81no—
704D8—42no—
705D8—81no—
706D8—81no—
707D8—81no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—42no—
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⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4C2×D4×C6111yescharacteristic
734C4⋊C4C2×D4×C6111yescharacteristic
735C4⋊C4C2×D4×C6111yescharacteristic
736C4⋊C4C2×D4×C6111yescharacteristic
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—41no—
762C22⋊C4—41no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42C2×D4×C6111yescharacteristic
768C42C2×D4×C6111yescharacteristic
769C42C2×D4×C6111yescharacteristic
770C42C24×C6111yescharacteristic
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—81no—
777C23—81no—
778C23—81no—
779C23#120×C6111yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—81no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—82no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—82no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4#120×C6111yescharacteristic
834C2×C4#120×C6111yescharacteristic
835C2×C4#120×C6111yescharacteristic
836C2×C4C22×D4×C6111yescharacteristic
837C2×C4C22×D4×C6111yescharacteristic
838C2×C4C22×D4×C6111yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—84no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22C2×#120×C6111yescharacteristic
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C2—41no—
881C2—81no—
882C2—81no—
883C2—81no—
884C2—81no—
885C2—161no—
886C2C61×#301811yescharacteristic
887C2C61×#301911yescharacteristic
888C2C61×#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×#3529C2semidirect
2. C61×#3219C2semidirect
3. C61×#3214C2semidirect
4. C61×#3180C2semidirect
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×#1532C2semidirect
15. C61×#1530C2semidirect
28. C61×#532C22semidirect
36. C61×#501C22semidirect
41. C61×#496C22semidirect
42. C61×#491C22semidirect
43. C61×#490C22semidirect
44. C61×#490C22semidirect
47. C61×#489C22semidirect
60. C61×#432C22semidirect
61. C61×#432C22semidirect
62. C2×#97×C61C22semidirect
63. C61×#330C22semidirect
64. C61×#330C22semidirect
65. C61×#330C22semidirect
66. C61×#330C22semidirect
73. C61×#329C22semidirect
74. C61×#329C22semidirect
400. #19010C61direct (N × H)
436. #3529C2×C61semidirect
437. #3219C2×C61semidirect
438. #3214C2×C61semidirect
439. #3180C2×C61semidirect
440. #1664C2×C61semidirect
441. #1662C2×C61semidirect
442. #1661C2×C61semidirect
443. #1659C2×C61semidirect
444. #1657C2×C61semidirect
445. #1656C2×C61semidirect
446. #1656C2×C61semidirect
447. #1655C2×C61semidirect
448. #1535C2×C61semidirect
449. #1532C2×C61semidirect
450. #1530C2×C61semidirect
472. #532C22×C61semidirect
480. #501C22×C61semidirect
485. #496C22×C61semidirect
486. #491C22×C61semidirect
487. #490C22×C61semidirect
488. #490C22×C61semidirect
491. #489C22×C61semidirect
504. #432C22×C61semidirect
505. #432C22×C61semidirect
506. C2×#97C22×C61semidirect
507. #330C22×C61semidirect
508. #330C22×C61semidirect
509. #330C22×C61semidirect
510. #330C22×C61semidirect
517. #329C22×C61semidirect
518. #329C22×C61semidirect
519. C61#19010direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35292
C61×#32192
C61×#32142
C61×#31802
C61×#16642
C61×#16622
C61×#16612
C61×#16592
C61×#16572
C61×#16562
C61×#16552
C61×#15352
C61×#15322
C61×#15302
#1901061