Finite Group Databasebeta

← C61×#23889 #29527322

Subgroups — C61×#23889 #29527322

Order 15616.

1648 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#578C211yesmaximal, characteristic, complemented
2C2×C61×#577C211yesmaximal, characteristic, complemented
3C2×C61×#454C211yesmaximal, characteristic, complemented
4C2×C61×#455C211yesmaximal, characteristic, complemented
5C61×#3013C211yesmaximal, characteristic, complemented
6C61×#3012C211yesmaximal, characteristic, complemented
7C61×#2020C211yesmaximal, characteristic, complemented
8C61×#2019C211yesmaximal, characteristic, complemented
9C61×#2015C211yesmaximal, characteristic, complemented
10C61×#2007C211yesmaximal, characteristic, complemented
11C61×#1908C211yesmaximal, characteristic, complemented
12C61×#1907C211yesmaximal, characteristic, complemented
13C61×#1876C211yesmaximal, characteristic, complemented
14C61×#1876C211yesmaximal, characteristic, complemented
15C61×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C61C2211yescharacteristic
17C2×2−1+4×C61C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C61C2211yescharacteristic
19C61×#578—24no—
20C61×#578—24no—
21C61×#577—24no—
22C61×#577—24no—
23C2×#137×C61—21no—
24C2×#137×C61—21no—
25C2×#137×C61—21no—
26C2×#137×C61C2211yescharacteristic
27C2×#137×C61C2211yescharacteristic
28C2×#137×C61C2211yescharacteristic
29C2×#137×C61C2211yescharacteristic, complemented
30C2×AGL(1,ℤ/8)×C61—21no—
31C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
32C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
33C2×#135×C61—21no—
34C2×#135×C61—21no—
35C2×#135×C61C2211yescharacteristic
36C2×#135×C61C2211yescharacteristic
37C22×Q16×C61—21no—
38C22×Q16×C61C2211yescharacteristic, complemented
39C22×SD16×C61—21no—
40C22×SD16×C61C2211yescharacteristic
41C2×#131×C61C2211yescharacteristic
42C2×#131×C61C2211yescharacteristic, complemented
43C61×#537C2211yescharacteristic
44C2×#124×C61C2211yescharacteristic
45C61×#455—24no—
46C61×#454—24no—
47C61×#452—21no—
48C61×#452—21no—
49C61×#451—21no—
50C61×#450—21no—
51C61×#449—21no—
52C61×#449—21no—
53C61×#448—21no—
54C61×#447—21no—
55C2×#104×C61C2211yescharacteristic
56C2×#104×C61C2211yescharacteristic
57C2×#104×C61C2211yescharacteristic, complemented
58C2×#104×C61C2211yescharacteristic, complemented
59C61×#417C2211yescharacteristic
60C61×#417C2211yescharacteristic, complemented
61C2×#103×C61C2211yescharacteristic, complemented
62C2×#102×C61C2211yescharacteristic
63C2×#101×C61C2211yescharacteristic, complemented
64C2×#101×C61C2211yescharacteristic, complemented
65C2×#100×C61C2211yescharacteristic
66C61×#408C2211yescharacteristic
67C61×#408C2211yescharacteristic, complemented
68C61×#391C2211yescharacteristic, complemented
69C61×#343C2211yescharacteristic, complemented
70C61×#341C2211yescharacteristic, complemented
71C61×#341C2211yescharacteristic, complemented
72C61×#336C2211yescharacteristic, complemented
732−1+4×C61—22no—
742−1+4×C61—22no—
752−1+4×C61—22no—
762−1+4×C61—22no—
772−1+4×C61—22no—
782−1+4×C61—41no—
792−1+4×C61—41no—
802−1+4×C61D414yescomplemented
81H(5,𝔽2)×C61—22no—
82H(5,𝔽2)×C61—22no—
83H(5,𝔽2)×C61—22no—
84H(5,𝔽2)×C61—41no—
85C2×#41×C61—21no—
86C2×#41×C61—21no—
87C2×#41×C61—21no—
88C2×#41×C61—21no—
89C2×#41×C61—21no—
90C2×#41×C61—21no—
91C2×#41×C61—41no—
92C2×#41×C61—41no—
93C2×#41×C61C2311yescharacteristic
94C2×#41×C61C2311yescharacteristic
95C2×#41×C61C2311yescharacteristic
96C2×#41×C61C2311yescharacteristic
97C22×Q8×C61—21no—
98C22×Q8×C61—21no—
99C22×Q8×C61—21no—
100C22×Q8×C61—21no—
101C22×Q8×C61C2311yescharacteristic
102C22×Q8×C61C2311yescharacteristic
103C22×D4×C61—21no—
104C22×D4×C61—21no—
105C22×D4×C61—41no—
106C22×D4×C61C2311yescharacteristic
107#137×C61—28no—
108#137×C61—28no—
109#137×C61—28no—
110#137×C61—22no—
111#137×C61—22no—
112#137×C61—22no—
113#137×C61—22no—
114#137×C61—22no—
115#137×C61—22no—
116#137×C61—41no—
117#137×C61D414yescomplemented
118AGL(1,ℤ/8)×C61—28no—
119AGL(1,ℤ/8)×C61—22no—
120AGL(1,ℤ/8)×C61—22no—
121AGL(1,ℤ/8)×C61—41no—
122AGL(1,ℤ/8)×C61D414yescomplemented
123#135×C61—28no—
124#135×C61—28no—
125#135×C61—22no—
126#135×C61—22no—
127#135×C61—22no—
128#135×C61—22no—
129C2×Q16×C61—28no—
130C2×Q16×C61—21no—
131C2×Q16×C61—21no—
132C2×Q16×C61—22no—
133C2×Q16×C61—22no—
134C2×Q16×C61—21no—
135C2×Q16×C61—21no—
136C2×Q16×C61—21no—
137C2×Q16×C61—21no—
138C2×Q16×C61D411yescharacteristic
139C2×Q16×C61D411yescharacteristic
140C2×SD16×C61—28no—
141C2×SD16×C61—21no—
142C2×SD16×C61—22no—
143C2×SD16×C61—21no—
144C2×SD16×C61—22no—
145C2×SD16×C61—21no—
146C2×SD16×C61—21no—
147C2×SD16×C61—21no—
148C2×SD16×C61—21no—
149C2×SD16×C61—21no—
150C2×SD16×C61—21no—
151C2×SD16×C61D411yescharacteristic
152C2×SD16×C61D411yescharacteristic
153C2×SD16×C61D411yescharacteristic
154C2×SD16×C61D411yescharacteristic
155C2×D8×C61—21no—
156C2×D8×C61—21no—
157C2×D8×C61D411yescharacteristic
158C2×D8×C61D411yescharacteristic
159#131×C61—22no—
160#131×C61—22no—
161#131×C61—22no—
162#131×C61—22no—
163C2×M16×C61—21no—
164C2×M16×C61—21no—
165C2×M16×C61C2311yescharacteristic
166C2×M16×C61C2311yescharacteristic
167C2×M16×C61C2311yescharacteristic
168C2×M16×C61C2311yescharacteristic
169C22×C8×C61—21no—
170C22×C8×C61—21no—
171C22×C8×C61C2311yescharacteristic
172C22×C8×C61C2311yescharacteristic
173#124×C61—22no—
174#124×C61—22no—
175C22⋊Q8×C61—21no—
176C22⋊Q8×C61—21no—
177#121×C61—21no—
178#121×C61—21no—
179#121×C61—41no—
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61—41no—
182C2×C42×C61C2311yescharacteristic
183#104×C61—22no—
184#104×C61—22no—
185#104×C61—22no—
186#104×C61—22no—
187#103×C61—21no—
188#103×C61—21no—
189#103×C61—21no—
190#103×C61—21no—
191#102×C61—21no—
192#102×C61—21no—
193#102×C61—21no—
194#102×C61—21no—
195#101×C61—22no—
196#101×C61—41no—
197#100×C61—22no—
198C22⋊C8×C61—21no—
199C22⋊C8×C61—21no—
200C22⋊C8×C61—21no—
201C22⋊C8×C61—21no—
202#95×C61—41no—
203C24×C61—21no—
204C24×C61—41no—
205#41×C61—21no—
206#41×C61—21no—
207#41×C61—21no—
208#41×C61—21no—
209#41×C61—24no—
210#41×C61—24no—
211#41×C61—24no—
212#41×C61—24no—
213#41×C61—21no—
214#41×C61—21no—
215#41×C61—21no—
216#41×C61—21no—
217#41×C61—21no—
218#41×C61—21no—
219#41×C61—21no—
220#41×C61—21no—
221#41×C61—44no—
222#41×C61—42no—
223#41×C61—42no—
224#41×C61—42no—
225#41×C61—44no—
226#41×C61—42no—
227#41×C61—44no—
228#41×C61—42no—
229#41×C61—42no—
230#41×C61—44no—
231#41×C61—42no—
232#41×C61—42no—
233#41×C61C2×D412yes—
234#41×C61C2×D412yes—
235#41×C61C2×D412yes—
236#41×C61C2×D412yes—
237C2×Q8×C61—21no—
238C2×Q8×C61—21no—
239C2×Q8×C61—24no—
240C2×Q8×C61—24no—
241C2×Q8×C61—24no—
242C2×Q8×C61—21no—
243C2×Q8×C61—21no—
244C2×Q8×C61—21no—
245C2×Q8×C61—21no—
246C2×Q8×C61—21no—
247C2×Q8×C61—21no—
248C2×Q8×C61—21no—
249C2×Q8×C61—21no—
250C2×Q8×C61—41no—
251C2×Q8×C61—41no—
252C2×Q8×C61—42no—
253C2×Q8×C61—42no—
254C2×Q8×C61—42no—
255C2×Q8×C61—42no—
256C2×Q8×C61—42no—
257C2×Q8×C61C2×D411yescharacteristic
258C2×Q8×C61C2×D411yescharacteristic
259C2×Q8×C61C2×D412yes—
260C2×Q8×C61C2×D412yes—
261C2×Q8×C61C2×D411yescharacteristic
262C2×Q8×C61C2×D411yescharacteristic
263C2×D4×C61—21no—
264C2×D4×C61—21no—
265C2×D4×C61—24no—
266C2×D4×C61—21no—
267C2×D4×C61—21no—
268C2×D4×C61—21no—
269C2×D4×C61—21no—
270C2×D4×C61—21no—
271C2×D4×C61—21no—
272C2×D4×C61—21no—
273C2×D4×C61—42no—
274C2×D4×C61—41no—
275C2×D4×C61—41no—
276C2×D4×C61—42no—
277C2×D4×C61—44no—
278C2×D4×C61—44no—
279C2×D4×C61—41no—
280C2×D4×C61—41no—
281C2×D4×C61—42no—
282C2×D4×C61—41no—
283C2×D4×C61C2×D411yescharacteristic
284C2×D4×C61C2×D411yescharacteristic
285C2×D4×C61C2×D412yes—
286C2×D4×C61C2×D411yescharacteristic
287C2×D4×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—41no—
297C22×C4×C61—41no—
298C22×C4×C61—41no—
299C22×C4×C61—41no—
300C22×C4×C61—41no—
301C22×C4×C61C2411yescharacteristic
302Q16×C61—24no—
303Q16×C61—24no—
304Q16×C61—24no—
305Q16×C61—24no—
306Q16×C61—22no—
307Q16×C61—24no—
308Q16×C61—22no—
309Q16×C61—42no—
310SD16×C61—24no—
311SD16×C61—24no—
312SD16×C61—24no—
313SD16×C61—24no—
314SD16×C61—22no—
315SD16×C61—24no—
316SD16×C61—22no—
317SD16×C61—24no—
318SD16×C61—22no—
319SD16×C61—22no—
320SD16×C61—42no—
321SD16×C61—42no—
322D8×C61—24no—
323D8×C61—22no—
324D8×C61—22no—
325D8×C61—42no—
326M16×C61—24no—
327M16×C61—24no—
328M16×C61—21no—
329M16×C61—21no—
330M16×C61—21no—
331M16×C61—21no—
332M16×C61—21no—
333M16×C61—21no—
334M16×C61C2×D412yes—
335M16×C61C2×D412yes—
336C2×C8×C61—24no—
337C2×C8×C61—24no—
338C2×C8×C61—21no—
339C2×C8×C61—21no—
340C2×C8×C61—21no—
341C2×C8×C61—21no—
342C2×C8×C61—21no—
343C2×C8×C61—21no—
344C2×C8×C61—21no—
345C2×C8×C61—21no—
346C2×C8×C61C2×D411yescharacteristic
347C2×C8×C61C2×D411yescharacteristic
348C2×C8×C61C2×D411yescharacteristic
349C2×C8×C61C2×D411yescharacteristic
350C4⋊C4×C61—21no—
351C4⋊C4×C61—21no—
352C4⋊C4×C61—41no—
353C22⋊C4×C61—44no—
354C22⋊C4×C61—41no—
355C22⋊C4×C61—41no—
356C42×C61—21no—
357C42×C61—21no—
358C23×C61—21no—
359C23×C61—21no—
360C23×C61—21no—
361C23×C61—21no—
362C23×C61—22no—
363C23×C61—44no—
364C23×C61—41no—
365C23×C61—41no—
366C23×C61—81no—
367C23×C61—81no—
368C23×C61—161no—
369C23×C61—161no—
370C23×C61H(5,𝔽2)11yescharacteristic
371Q8×C61—21no—
372Q8×C61—21no—
373Q8×C61—22no—
374Q8×C61—22no—
375Q8×C61—22no—
376Q8×C61—21no—
377Q8×C61—21no—
378Q8×C61—21no—
379Q8×C61—22no—
380Q8×C61—21no—
381Q8×C61—44no—
382Q8×C61—44no—
383Q8×C61—41no—
384Q8×C61—41no—
385Q8×C61—41no—
386Q8×C61—41no—
387Q8×C61#12012yes—
388Q8×C61#12012yes—
389D4×C61—22no—
390D4×C61—22no—
391D4×C61—22no—
392D4×C61—22no—
393D4×C61—22no—
394D4×C61—21no—
395D4×C61—21no—
396D4×C61—21no—
397D4×C61—21no—
398D4×C61—21no—
399D4×C61—22no—
400D4×C61—21no—
401D4×C61—44no—
402D4×C61—44no—
403D4×C61—44no—
404D4×C61—44no—
405D4×C61—41no—
406D4×C61—41no—
407D4×C61—41no—
408D4×C61—41no—
409D4×C61—41no—
410D4×C61—41no—
411D4×C61—161no—
412D4×C61#12012yes—
413D4×C61#12012yes—
414C2×C4×C61—21no—
415C2×C4×C61—21no—
416C2×C4×C61—22no—
417C2×C4×C61—22no—
418C2×C4×C61—22no—
419C2×C4×C61—22no—
420C2×C4×C61—22no—
421C2×C4×C61—22no—
422C2×C4×C61—21no—
423C2×C4×C61—21no—
424C2×C4×C61—44no—
425C2×C4×C61—44no—
426C2×C4×C61—44no—
427C2×C4×C61—44no—
428C2×C4×C61—44no—
429C2×C4×C61—41no—
430C2×C4×C61—41no—
431C2×C4×C61—41no—
432C2×C4×C61—41no—
433C2×C4×C61—41no—
434C2×C4×C61—41no—
435C2×C4×C61—41no—
436C2×C4×C61—41no—
437C2×C4×C61—41no—
438C2×C4×C61—41no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
441C2×C4×C61—81no—
442C2×C4×C61C22×D411yescharacteristic
443C2×C4×C61C22×D411yescharacteristic
444C2×C4×C61C22×D411yescharacteristic
445C2×C4×C61C22×D411yescharacteristic
446C2×C4×C61C22×D411yescharacteristic
447C2×C4×C61H(5,𝔽2)11yescharacteristic
448C8×C61—21no—
449C8×C61—21no—
450C8×C61—22no—
451C8×C61—22no—
452C8×C61—21no—
453C8×C61—21no—
454C8×C61—41no—
455C8×C61—41no—
456#23889C6111yesmaximal, characteristic, direct product factor, Sylow
457C22×C61—21no—
458C22×C61—21no—
459C22×C61—22no—
460C22×C61—22no—
461C22×C61—41no—
462C22×C61—41no—
463C22×C61—41no—
464C22×C61—41no—
465C22×C61—41no—
466C22×C61—41no—
467C22×C61—42no—
468C22×C61—41no—
469C22×C61—41no—
470C22×C61—41no—
471C22×C61—41no—
472C22×C61—82no—
473C22×C61—81no—
474C22×C61—81no—
475C22×C61—161no—
476C22×C61—164no—
477C22×C61#53411yescharacteristic
478C22×C61D4211yescharacteristic
479C22×C61D4211yescharacteristic
480C4×C61—22no—
481C4×C61—22no—
482C4×C61—41no—
483C4×C61—42no—
484C4×C61—42no—
485C4×C61—41no—
486C4×C61—81no—
487C4×C61—81no—
488C4×C61C2×#12011yescharacteristic
489C4×C61C2×#12011yescharacteristic
490C4×C61D4211yescharacteristic
491C4×C61D4211yescharacteristic
492C2×#578C2×C6111yescharacteristic, complemented
493C2×#577C2×C6111yescharacteristic, complemented
494C2×#454C2×C6111yescharacteristic, complemented
495C2×#455C2×C6111yescharacteristic, complemented
496#3013C2×C6111yescharacteristic, complemented
497#3012C2×C6111yescharacteristic, complemented
498#2020C2×C6111yescharacteristic, complemented
499#2019C2×C6111yescharacteristic, complemented
500#2015C2×C6111yescharacteristic, complemented
501#2007C2×C6111yescharacteristic, complemented
502#1908C2×C6111yescharacteristic, complemented
503#1907C2×C6111yescharacteristic, complemented
504#1876C2×C6111yescharacteristic, complemented
505#1876C2×C6111yescharacteristic, complemented
506#1793C2×C6111yescharacteristic, complemented
507C2×C61—21no—
508C2×C61—21no—
509C2×C61—42no—
510C2×C61—42no—
511C2×C61—81no—
512C2×C61—81no—
513C2×C61—82no—
514C2×C61#240311yescharacteristic
515C2×C61#328911yescharacteristic
516C2×C61#329011yescharacteristic
517C2×2−1+4C22×C6111yescharacteristic
518C2×2−1+4C22×C6111yescharacteristic, complemented
519C2×H(5,𝔽2)C22×C6111yescharacteristic
520#578—24no—
521#578—24no—
522#577—24no—
523#577—24no—
524C2×#137—21no—
525C2×#137—21no—
526C2×#137—21no—
527C2×#137C22×C6111yescharacteristic
528C2×#137C22×C6111yescharacteristic
529C2×#137C22×C6111yescharacteristic
530C2×#137C22×C6111yescharacteristic, complemented
531C2×AGL(1,ℤ/8)—21no—
532C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
533C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
534C2×#135—21no—
535C2×#135—21no—
536C2×#135C22×C6111yescharacteristic
537C2×#135C22×C6111yescharacteristic
538C22×Q16—21no—
539C22×Q16C22×C6111yescharacteristic, complemented
540C22×SD16—21no—
541C22×SD16C22×C6111yescharacteristic
542C2×#131C22×C6111yescharacteristic
543C2×#131C22×C6111yescharacteristic, complemented
544#537C22×C6111yescharacteristic
545C2×#124C22×C6111yescharacteristic
546#455—24no—
547#454—24no—
548#452—21no—
549#452—21no—
550#451—21no—
551#450—21no—
552#449—21no—
553#449—21no—
554#448—21no—
555#447—21no—
556C2×#104C22×C6111yescharacteristic
557C2×#104C22×C6111yescharacteristic
558C2×#104C22×C6111yescharacteristic, complemented
559C2×#104C22×C6111yescharacteristic, complemented
560#417C22×C6111yescharacteristic
561#417C22×C6111yescharacteristic, complemented
562C2×#103C22×C6111yescharacteristic, complemented
563C2×#102C22×C6111yescharacteristic
564C2×#101C22×C6111yescharacteristic, complemented
565C2×#101C22×C6111yescharacteristic, complemented
566C2×#100C22×C6111yescharacteristic
567#408C22×C6111yescharacteristic
568#408C22×C6111yescharacteristic, complemented
569#391C22×C6111yescharacteristic, complemented
570#343C22×C6111yescharacteristic, complemented
571#341C22×C6111yescharacteristic, complemented
572#341C22×C6111yescharacteristic, complemented
573#336C22×C6111yescharacteristic, complemented
574C61#2388911yescharacteristic, direct product factor, Sylow
5752−1+4—22no—
5762−1+4—22no—
5772−1+4—22no—
5782−1+4—22no—
5792−1+4—22no—
5802−1+4—41no—
5812−1+4—41no—
5822−1+4D4×C6114yescomplemented
583H(5,𝔽2)—22no—
584H(5,𝔽2)—22no—
585H(5,𝔽2)—22no—
586H(5,𝔽2)—41no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—41no—
594C2×#41—41no—
595C2×#41C23×C6111yescharacteristic
596C2×#41C23×C6111yescharacteristic
597C2×#41C23×C6111yescharacteristic
598C2×#41C23×C6111yescharacteristic
599C22×Q8—21no—
600C22×Q8—21no—
601C22×Q8—21no—
602C22×Q8—21no—
603C22×Q8C23×C6111yescharacteristic
604C22×Q8C23×C6111yescharacteristic
605C22×D4—21no—
606C22×D4—21no—
607C22×D4—41no—
608C22×D4C23×C6111yescharacteristic
609#137—28no—
610#137—28no—
611#137—28no—
612#137—22no—
613#137—22no—
614#137—22no—
615#137—22no—
616#137—22no—
617#137—22no—
618#137—41no—
619#137D4×C6114yescomplemented
620AGL(1,ℤ/8)—28no—
621AGL(1,ℤ/8)—22no—
622AGL(1,ℤ/8)—22no—
623AGL(1,ℤ/8)—41no—
624AGL(1,ℤ/8)D4×C6114yescomplemented
625#135—28no—
626#135—28no—
627#135—22no—
628#135—22no—
629#135—22no—
630#135—22no—
631C2×Q16—28no—
632C2×Q16—21no—
633C2×Q16—21no—
634C2×Q16—22no—
635C2×Q16—22no—
636C2×Q16—21no—
637C2×Q16—21no—
638C2×Q16—21no—
639C2×Q16—21no—
640C2×Q16D4×C6111yescharacteristic
641C2×Q16D4×C6111yescharacteristic
642C2×SD16—28no—
643C2×SD16—21no—
644C2×SD16—22no—
645C2×SD16—21no—
646C2×SD16—22no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×SD16—21no—
650C2×SD16—21no—
651C2×SD16—21no—
652C2×SD16—21no—
653C2×SD16D4×C6111yescharacteristic
654C2×SD16D4×C6111yescharacteristic
655C2×SD16D4×C6111yescharacteristic
656C2×SD16D4×C6111yescharacteristic
657C2×D8—21no—
658C2×D8—21no—
659C2×D8D4×C6111yescharacteristic
660C2×D8D4×C6111yescharacteristic
661#131—22no—
662#131—22no—
663#131—22no—
664#131—22no—
665C2×M16—21no—
666C2×M16—21no—
667C2×M16C23×C6111yescharacteristic
668C2×M16C23×C6111yescharacteristic
669C2×M16C23×C6111yescharacteristic
670C2×M16C23×C6111yescharacteristic
671C22×C8—21no—
672C22×C8—21no—
673C22×C8C23×C6111yescharacteristic
674C22×C8C23×C6111yescharacteristic
675#124—22no—
676#124—22no—
677C22⋊Q8—21no—
678C22⋊Q8—21no—
679#121—21no—
680#121—21no—
681#121—41no—
682C2×C4⋊C4C23×C6111yescharacteristic
683C2×C22⋊C4—41no—
684C2×C42C23×C6111yescharacteristic
685#104—22no—
686#104—22no—
687#104—22no—
688#104—22no—
689#103—21no—
690#103—21no—
691#103—21no—
692#103—21no—
693#102—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#101—22no—
698#101—41no—
699#100—22no—
700C22⋊C8—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8—21no—
704#95—41no—
705C24—21no—
706C24—41no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—24no—
712#41—24no—
713#41—24no—
714#41—24no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—21no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—44no—
724#41—42no—
725#41—42no—
726#41—42no—
727#41—44no—
728#41—42no—
729#41—44no—
730#41—42no—
731#41—42no—
732#41—44no—
733#41—42no—
734#41—42no—
735#41C2×D4×C6112yes—
736#41C2×D4×C6112yes—
737#41C2×D4×C6112yes—
738#41C2×D4×C6112yes—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—24no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—41no—
753C2×Q8—41no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—42no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8C2×D4×C6111yescharacteristic
760C2×Q8C2×D4×C6111yescharacteristic
761C2×Q8C2×D4×C6112yes—
762C2×Q8C2×D4×C6112yes—
763C2×Q8C2×D4×C6111yescharacteristic
764C2×Q8C2×D4×C6111yescharacteristic
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—24no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—42no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—41no—
782C2×D4—41no—
783C2×D4—42no—
784C2×D4—41no—
785C2×D4C2×D4×C6111yescharacteristic
786C2×D4C2×D4×C6111yescharacteristic
787C2×D4C2×D4×C6112yes—
788C2×D4C2×D4×C6111yescharacteristic
789C2×D4C2×D4×C6111yescharacteristic
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4C24×C6111yescharacteristic
804Q16—24no—
805Q16—24no—
806Q16—24no—
807Q16—24no—
808Q16—22no—
809Q16—24no—
810Q16—22no—
811Q16—42no—
812SD16—24no—
813SD16—24no—
814SD16—24no—
815SD16—24no—
816SD16—22no—
817SD16—24no—
818SD16—22no—
819SD16—24no—
820SD16—22no—
821SD16—22no—
822SD16—42no—
823SD16—42no—
824D8—24no—
825D8—22no—
826D8—22no—
827D8—42no—
828M16—24no—
829M16—24no—
830M16—21no—
831M16—21no—
832M16—21no—
833M16—21no—
834M16—21no—
835M16—21no—
836M16C2×D4×C6112yes—
837M16C2×D4×C6112yes—
838C2×C8—24no—
839C2×C8—24no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8C2×D4×C6111yescharacteristic
849C2×C8C2×D4×C6111yescharacteristic
850C2×C8C2×D4×C6111yescharacteristic
851C2×C8C2×D4×C6111yescharacteristic
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—41no—
855C22⋊C4—44no—
856C22⋊C4—41no—
857C22⋊C4—41no—
858C42—21no—
859C42—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—22no—
865C23—44no—
866C23—41no—
867C23—41no—
868C23—81no—
869C23—81no—
870C23—161no—
871C23—161no—
872C23H(5,𝔽2)×C6111yescharacteristic
873Q8—21no—
874Q8—21no—
875Q8—21no—
876Q8—22no—
877Q8—21no—
878Q8—22no—
879Q8—22no—
880Q8—22no—
881Q8—21no—
882Q8—21no—
883Q8—44no—
884Q8—44no—
885Q8—41no—
886Q8—41no—
887Q8—41no—
888Q8—41no—
889Q8#120×C6112yes—
890Q8#120×C6112yes—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—21no—
896D4—21no—
897D4—21no—
898D4—22no—
899D4—21no—
900D4—22no—
901D4—21no—
902D4—21no—
903D4—44no—
904D4—44no—
905D4—44no—
906D4—44no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—41no—
912D4—41no—
913D4—161no—
914D4#120×C6112yes—
915D4#120×C6112yes—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—81no—
944C2×C4C22×D4×C6111yescharacteristic
945C2×C4C22×D4×C6111yescharacteristic
946C2×C4C22×D4×C6111yescharacteristic
947C2×C4C22×D4×C6111yescharacteristic
948C2×C4C22×D4×C6111yescharacteristic
949C2×C4H(5,𝔽2)×C6111yescharacteristic
950C8—21no—
951C8—21no—
952C8—22no—
953C8—22no—
954C8—21no—
955C8—21no—
956C8—41no—
957C8—41no—
958C22—21no—
959C22—21no—
960C22—22no—
961C22—22no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—42no—
973C22—82no—
974C22—81no—
975C22—81no—
976C22—161no—
977C22—164no—
978C22C61×#53411yescharacteristic
979C22D42×C6111yescharacteristic
980C22D42×C6111yescharacteristic
981C4—22no—
982C4—22no—
983C4—41no—
984C4—42no—
985C4—42no—
986C4—41no—
987C4—81no—
988C4—81no—
989C4C2×#120×C6111yescharacteristic
990C4C2×#120×C6111yescharacteristic
991C4D42×C6111yescharacteristic
992C4D42×C6111yescharacteristic
993C2—21no—
994C2—21no—
995C2—42no—
996C2—42no—
997C2—81no—
998C2—81no—
999C2—82no—
1000C2C61×#240311yescharacteristic
1001C2C61×#328911yescharacteristic
1002C2C61×#329011yescharacteristic
subgroupG/H
center, socleC22×C61D42
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C22×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#578C2semidirect
2. C2×C61×#577C2semidirect
3. C2×C61×#454C2semidirect
4. C2×C61×#455C2semidirect
5. C61×#3013C2semidirect
6. C61×#3012C2semidirect
7. C61×#2020C2semidirect
8. C61×#2019C2semidirect
9. C61×#2015C2semidirect
10. C61×#2007C2semidirect
11. C61×#1908C2semidirect
12. C61×#1907C2semidirect
13. C61×#1876C2semidirect
14. C61×#1876C2semidirect
15. C61×#1793C2semidirect
17. C2×2−1+4×C61C22semidirect
29. C2×#137×C61C22semidirect
38. C22×Q16×C61C22semidirect
42. C2×#131×C61C22semidirect
57. C2×#104×C61C22semidirect
58. C2×#104×C61C22semidirect
60. C61×#417C22semidirect
61. C2×#103×C61C22semidirect
63. C2×#101×C61C22semidirect
64. C2×#101×C61C22semidirect
67. C61×#408C22semidirect
68. C61×#391C22semidirect
69. C61×#343C22semidirect
70. C61×#341C22semidirect
71. C61×#341C22semidirect
72. C61×#336C22semidirect
80. 2−1+4×C61D4semidirect
117. #137×C61D4semidirect
122. AGL(1,ℤ/8)×C61D4semidirect
456. #23889C61direct (N × H)
492. C2×#578C2×C61semidirect
493. C2×#577C2×C61semidirect
494. C2×#454C2×C61semidirect
495. C2×#455C2×C61semidirect
496. #3013C2×C61semidirect
497. #3012C2×C61semidirect
498. #2020C2×C61semidirect
499. #2019C2×C61semidirect
500. #2015C2×C61semidirect
501. #2007C2×C61semidirect
502. #1908C2×C61semidirect
503. #1907C2×C61semidirect
504. #1876C2×C61semidirect
505. #1876C2×C61semidirect
506. #1793C2×C61semidirect
518. C2×2−1+4C22×C61semidirect
530. C2×#137C22×C61semidirect
539. C22×Q16C22×C61semidirect
543. C2×#131C22×C61semidirect
558. C2×#104C22×C61semidirect
559. C2×#104C22×C61semidirect
561. #417C22×C61semidirect
562. C2×#103C22×C61semidirect
564. C2×#101C22×C61semidirect
565. C2×#101C22×C61semidirect
568. #408C22×C61semidirect
569. #391C22×C61semidirect
570. #343C22×C61semidirect
571. #341C22×C61semidirect
572. #341C22×C61semidirect
573. #336C22×C61semidirect
574. C61#23889direct (N × H)
582. 2−1+4D4×C61semidirect
619. #137D4×C61semidirect
624. AGL(1,ℤ/8)D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5782
C2×C61×#5772
C2×C61×#4542
C2×C61×#4552
C61×#30132
C61×#30122
C61×#20202
C61×#20192
C61×#20152
C61×#20072
C61×#19082
C61×#19072
C61×#18762
C61×#17932
#2388961