Finite Group Databasebeta

← C61×#24295 #29527728

Subgroups — C61×#24295 #29527728

Order 15616.

1302 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#577C211yesmaximal, characteristic, complemented
2C61×#3067C211yesmaximal, characteristic, complemented
3C61×#3057C211yesmaximal, characteristic, complemented
4C61×#3020C211yesmaximal, characteristic, complemented
5C61×#3019C211yesmaximal, characteristic, complemented
6C61×#2955C211yesmaximal, characteristic, complemented
7C61×#2049C211yesmaximal, characteristic, complemented
8C61×#2048C211yesmaximal, characteristic, complemented
9C61×#2009C211yesmaximal, characteristic, complemented
10C61×#2008C211yesmaximal, characteristic, complemented
11C61×#1977C211yesmaximal, characteristic, complemented
12C61×#1976C211yesmaximal, characteristic, complemented
13C61×#1814C211yesmaximal, characteristic, complemented
14C61×#1796C211yesmaximal, characteristic, complemented
15C61×#1795C211yesmaximal, characteristic, complemented
16C2×2−1+4×C61C2211yescharacteristic
17C2×H(5,𝔽2)×C61C2211yescharacteristic
18C61×#577—22no—
19C61×#577—22no—
20C61×#577—22no—
21C61×#577—22no—
22C61×#575C2211yescharacteristic
23C61×#575C2211yescharacteristic
24C61×#575C2211yescharacteristic, complemented
25C2×#137×C61—21no—
26C2×#137×C61C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C61—21no—
28C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
29C2×#135×C61—21no—
30C2×#135×C61C2211yescharacteristic
31C22×SD16×C61—21no—
32C22×SD16×C61C2211yescharacteristic
33C2×#131×C61C2211yescharacteristic
34C2×#131×C61C2211yescharacteristic, complemented
35C61×#536C2211yescharacteristic, complemented
36C61×#535C2211yescharacteristic
37C61×#473—21no—
38C61×#472—21no—
39C61×#471—21no—
40C61×#471—21no—
41C61×#468—22no—
42C61×#465—22no—
43C61×#456—22no—
44C61×#455—22no—
45C61×#454—22no—
46C61×#453—22no—
47C61×#444—22no—
48C61×#443—22no—
49C61×#430C2211yescharacteristic, complemented
50C2×#108×C61C2211yescharacteristic, complemented
51C61×#427C2211yescharacteristic, complemented
52C61×#421C2211yescharacteristic
53C61×#421C2211yescharacteristic
54C61×#421C2211yescharacteristic
55C61×#421C2211yescharacteristic
56C61×#421C2211yescharacteristic, complemented
57C61×#421C2211yescharacteristic, complemented
58C61×#419C2211yescharacteristic, complemented
59C61×#419C2211yescharacteristic, complemented
60C61×#418C2211yescharacteristic
61C61×#418C2211yescharacteristic
62C61×#413C2211yescharacteristic
63C61×#413C2211yescharacteristic, complemented
64C2×#101×C61C2211yescharacteristic, complemented
65C2×#100×C61C2211yescharacteristic
66C61×#410C2211yescharacteristic
67C61×#410C2211yescharacteristic, complemented
68C61×#405C2211yescharacteristic, complemented
69C61×#344C2211yescharacteristic, complemented
70C61×#344C2211yescharacteristic, complemented
712−1+4×C61—22no—
722−1+4×C61—22no—
732−1+4×C61—22no—
742−1+4×C61—41no—
75H(5,𝔽2)×C61—22no—
76H(5,𝔽2)×C61—22no—
77H(5,𝔽2)×C61—22no—
78H(5,𝔽2)×C61—41no—
79C2×#41×C61—21no—
80C2×#41×C61—21no—
81C2×#41×C61—21no—
82C2×#41×C61—21no—
83C2×#41×C61—41no—
84C2×#41×C61C2311yescharacteristic
85C2×#41×C61C2311yescharacteristic
86C2×#41×C61C2311yescharacteristic
87C2×#41×C61C2311yescharacteristic
88C22×Q8×C61—21no—
89C22×Q8×C61—21no—
90C22×Q8×C61C2311yescharacteristic
91C22×D4×C61—21no—
92C22×D4×C61—21no—
93C22×D4×C61—41no—
94C22×D4×C61C2311yescharacteristic
95#137×C61—24no—
96#137×C61—24no—
97#137×C61—22no—
98#137×C61—21no—
99#137×C61—21no—
100#137×C61—21no—
101#137×C61—21no—
102#137×C61—21no—
103#137×C61—22no—
104#137×C61D412yes—
105AGL(1,ℤ/8)×C61—24no—
106AGL(1,ℤ/8)×C61—24no—
107AGL(1,ℤ/8)×C61—22no—
108AGL(1,ℤ/8)×C61—21no—
109AGL(1,ℤ/8)×C61—21no—
110AGL(1,ℤ/8)×C61—21no—
111AGL(1,ℤ/8)×C61—21no—
112AGL(1,ℤ/8)×C61—21no—
113AGL(1,ℤ/8)×C61—22no—
114AGL(1,ℤ/8)×C61D412yes—
115#135×C61—24no—
116#135×C61—24no—
117#135×C61—22no—
118#135×C61—21no—
119#135×C61—21no—
120#135×C61—21no—
121#135×C61—21no—
122#135×C61—41no—
123#135×C61—41no—
124C2×Q16×C61—21no—
125C2×Q16×C61D411yescharacteristic, complemented
126C2×SD16×C61—24no—
127C2×SD16×C61—24no—
128C2×SD16×C61—21no—
129C2×SD16×C61—21no—
130C2×SD16×C61—21no—
131C2×SD16×C61—21no—
132C2×SD16×C61—21no—
133C2×SD16×C61—21no—
134C2×SD16×C61D412yes—
135C2×SD16×C61D412yes—
136C2×SD16×C61D411yescharacteristic, complemented
137C2×SD16×C61D411yescharacteristic, complemented
138C2×D8×C61—21no—
139C2×D8×C61D411yescharacteristic, complemented
140#131×C61—21no—
141#131×C61—21no—
142#131×C61—21no—
143#131×C61—21no—
144#131×C61—21no—
145#131×C61—21no—
146#131×C61D412yescomplemented
147#131×C61D412yescomplemented
148C2×M16×C61—21no—
149C2×M16×C61—21no—
150C2×M16×C61C2311yescharacteristic
151C2×M16×C61C2311yescharacteristic
152C2×M16×C61C2311yescharacteristic
153C2×M16×C61C2311yescharacteristic
154C2×M16×C61C2311yescharacteristic
155C22×C8×C61—21no—
156C22×C8×C61—21no—
157C22×C8×C61C2311yescharacteristic
158C4⋊Q8×C61—21no—
159#127×C61—21no—
160#124×C61—21no—
161#124×C61—21no—
162#123×C61—41no—
163C22⋊Q8×C61—22no—
164#121×C61—22no—
165#120×C61—41no—
166#117×C61C2311yescharacteristic
167#117×C61C2311yescharacteristic
168#117×C61C2311yescharacteristic
169#108×C61—22no—
170#108×C61—21no—
171#108×C61—21no—
172#107×C61—21no—
173#106×C61—21no—
174#104×C61—22no—
175#104×C61—22no—
176#104×C61—22no—
177#104×C61—22no—
178#104×C61—22no—
179#104×C61—22no—
180#103×C61—22no—
181#103×C61—41no—
182#102×C61—22no—
183#102×C61—41no—
184#101×C61—21no—
185#101×C61—21no—
186#101×C61—22no—
187#100×C61—21no—
188#100×C61—21no—
189#100×C61—22no—
190#99×C61—41no—
191#99×C61—41no—
192#97×C61—21no—
193C4×C8×C61—21no—
194C24×C61—21no—
195C24×C61—41no—
196#41×C61—21no—
197#41×C61—21no—
198#41×C61—24no—
199#41×C61—24no—
200#41×C61—21no—
201#41×C61—21no—
202#41×C61—21no—
203#41×C61—21no—
204#41×C61—21no—
205#41×C61—21no—
206#41×C61—21no—
207#41×C61—21no—
208#41×C61—21no—
209#41×C61—21no—
210#41×C61—21no—
211#41×C61—21no—
212#41×C61—42no—
213#41×C61—44no—
214#41×C61—42no—
215#41×C61—42no—
216#41×C61—42no—
217#41×C61—44no—
218#41×C61—42no—
219#41×C61—42no—
220#41×C61C2×D412yes—
221#41×C61C2×D412yes—
222C2×Q8×C61—21no—
223C2×Q8×C61—24no—
224C2×Q8×C61—21no—
225C2×Q8×C61—21no—
226C2×Q8×C61—21no—
227C2×Q8×C61—21no—
228C2×Q8×C61—41no—
229C2×Q8×C61—42no—
230C2×Q8×C61—42no—
231C2×Q8×C61—42no—
232C2×Q8×C61C2×D411yescharacteristic
233C2×Q8×C61C2×D411yescharacteristic
234C2×Q8×C61C2×D412yes—
235C2×Q8×C61C2×D411yescharacteristic
236C2×Q8×C61#4111yescharacteristic
237C2×D4×C61—21no—
238C2×D4×C61—24no—
239C2×D4×C61—21no—
240C2×D4×C61—21no—
241C2×D4×C61—21no—
242C2×D4×C61—21no—
243C2×D4×C61—21no—
244C2×D4×C61—21no—
245C2×D4×C61—21no—
246C2×D4×C61—21no—
247C2×D4×C61—42no—
248C2×D4×C61—41no—
249C2×D4×C61—41no—
250C2×D4×C61—42no—
251C2×D4×C61—44no—
252C2×D4×C61—44no—
253C2×D4×C61—41no—
254C2×D4×C61—42no—
255C2×D4×C61—42no—
256C2×D4×C61C2×D411yescharacteristic
257C2×D4×C61C2×D411yescharacteristic
258C2×D4×C61C2×D412yes—
259C2×D4×C61C2×D411yescharacteristic
260C2×D4×C61#4111yescharacteristic
261C22×C4×C61—21no—
262C22×C4×C61—21no—
263C22×C4×C61—21no—
264C22×C4×C61—21no—
265C22×C4×C61—21no—
266C22×C4×C61—41no—
267C22×C4×C61—41no—
268C22×C4×C61—41no—
269C22×C4×C61C2411yescharacteristic
270Q16×C61—24no—
271Q16×C61—22no—
272Q16×C61—21no—
273Q16×C61—21no—
274Q16×C61—41no—
275Q16×C61—41no—
276SD16×C61—24no—
277SD16×C61—24no—
278SD16×C61—22no—
279SD16×C61—22no—
280SD16×C61—22no—
281SD16×C61—22no—
282SD16×C61—21no—
283SD16×C61—21no—
284SD16×C61—22no—
285SD16×C61—22no—
286SD16×C61—21no—
287SD16×C61—21no—
288SD16×C61—41no—
289SD16×C61—41no—
290SD16×C61—41no—
291SD16×C61—41no—
292D8×C61—24no—
293D8×C61—22no—
294D8×C61—21no—
295D8×C61—21no—
296D8×C61—41no—
297D8×C61—41no—
298M16×C61—21no—
299M16×C61—21no—
300M16×C61—22no—
301M16×C61—22no—
302M16×C61—21no—
303M16×C61—21no—
304M16×C61—21no—
305M16×C61—21no—
306M16×C61—21no—
307M16×C61—21no—
308M16×C61—41no—
309M16×C61—41no—
310M16×C61C2×D412yes—
311M16×C61C2×D412yes—
312C2×C8×C61—21no—
313C2×C8×C61—21no—
314C2×C8×C61—22no—
315C2×C8×C61—22no—
316C2×C8×C61—21no—
317C2×C8×C61—21no—
318C2×C8×C61—21no—
319C2×C8×C61—41no—
320C2×C8×C61—41no—
321C2×C8×C61C2×D411yescharacteristic
322C2×C8×C61C2×D411yescharacteristic
323C2×C8×C61C2×D411yescharacteristic
324C2×C8×C61C2×D411yescharacteristic
325C2×C8×C61C2×D411yescharacteristic
326C2×C8×C61C2×D411yescharacteristic
327C4⋊C4×C61—21no—
328C4⋊C4×C61—21no—
329C4⋊C4×C61—21no—
330C4⋊C4×C61—42no—
331C22⋊C4×C61—21no—
332C22⋊C4×C61—21no—
333C22⋊C4×C61—21no—
334C22⋊C4×C61—42no—
335C22⋊C4×C61—42no—
336C42×C61—21no—
337C42×C61—21no—
338C42×C61—21no—
339C23×C61—21no—
340C23×C61—21no—
341C23×C61—22no—
342C23×C61—21no—
343C23×C61—21no—
344C23×C61—44no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—161no—
348C23×C61—162no—
349C23×C61H(5,𝔽2)11yescharacteristic
350Q8×C61—21no—
351Q8×C61—21no—
352Q8×C61—22no—
353Q8×C61—21no—
354Q8×C61—21no—
355Q8×C61—21no—
356Q8×C61—21no—
357Q8×C61—21no—
358Q8×C61—22no—
359Q8×C61—44no—
360Q8×C61—41no—
361Q8×C61—41no—
362Q8×C61#12112yes—
363D4×C61—22no—
364D4×C61—22no—
365D4×C61—21no—
366D4×C61—22no—
367D4×C61—21no—
368D4×C61—21no—
369D4×C61—21no—
370D4×C61—21no—
371D4×C61—21no—
372D4×C61—21no—
373D4×C61—22no—
374D4×C61—44no—
375D4×C61—44no—
376D4×C61—44no—
377D4×C61—41no—
378D4×C61—41no—
379D4×C61—41no—
380D4×C61—41no—
381D4×C61—41no—
382D4×C61—41no—
383D4×C61—41no—
384D4×C61—41no—
385D4×C61—162no—
386D4×C61#12112yes—
387C2×C4×C61—21no—
388C2×C4×C61—22no—
389C2×C4×C61—22no—
390C2×C4×C61—21no—
391C2×C4×C61—22no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—44no—
395C2×C4×C61—44no—
396C2×C4×C61—44no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61—41no—
402C2×C4×C61—41no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61C22×D411yescharacteristic
409C2×C4×C61C22×D411yescharacteristic
410C2×C4×C61C22×D411yescharacteristic
411C2×C4×C61C22×D411yescharacteristic
412C2×C4×C61C2×#4111yescharacteristic
413C2×C4×C61H(5,𝔽2)11yescharacteristic
414C8×C61—22no—
415C8×C61—22no—
416C8×C61—41no—
417C8×C61—41no—
418C8×C61—41no—
419C8×C61#12011yescharacteristic
420C8×C61#12011yescharacteristic
421C8×C61#12011yescharacteristic
422C8×C61#12011yescharacteristic
423#24295C6111yesmaximal, characteristic, direct product factor, Sylow
424C22×C61—22no—
425C22×C61—41no—
426C22×C61—42no—
427C22×C61—42no—
428C22×C61—41no—
429C22×C61—42no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—82no—
433C22×C61—81no—
434C22×C61—81no—
435C22×C61—82no—
436C22×C61—161no—
437C22×C61—164no—
438C22×C61#53511yescharacteristic
439C22×C61D4211yescharacteristic
440C22×C61#54611yescharacteristic
441C4×C61—22no—
442C4×C61—41no—
443C4×C61—42no—
444C4×C61—41no—
445C4×C61—41no—
446C4×C61—81no—
447C4×C61—81no—
448C4×C61—81no—
449C4×C61C2×#12011yescharacteristic
450C4×C61C2×#12111yescharacteristic
451C4×C61D4211yescharacteristic
452C4×C61#54611yescharacteristic
453C2×#577C2×C6111yescharacteristic, complemented
454#3067C2×C6111yescharacteristic, complemented
455#3057C2×C6111yescharacteristic, complemented
456#3020C2×C6111yescharacteristic, complemented
457#3019C2×C6111yescharacteristic, complemented
458#2955C2×C6111yescharacteristic, complemented
459#2049C2×C6111yescharacteristic, complemented
460#2048C2×C6111yescharacteristic, complemented
461#2009C2×C6111yescharacteristic, complemented
462#2008C2×C6111yescharacteristic, complemented
463#1977C2×C6111yescharacteristic, complemented
464#1976C2×C6111yescharacteristic, complemented
465#1814C2×C6111yescharacteristic, complemented
466#1796C2×C6111yescharacteristic, complemented
467#1795C2×C6111yescharacteristic, complemented
468C2×C61—21no—
469C2×C61—21no—
470C2×C61—21no—
471C2×C61—42no—
472C2×C61—81no—
473C2×C61—81no—
474C2×C61—82no—
475C2×C61—81no—
476C2×C61#240811yescharacteristic
477C2×2−1+4C22×C6111yescharacteristic
478C2×H(5,𝔽2)C22×C6111yescharacteristic
479#577—22no—
480#577—22no—
481#577—22no—
482#577—22no—
483#575C22×C6111yescharacteristic
484#575C22×C6111yescharacteristic
485#575C22×C6111yescharacteristic, complemented
486C2×#137—21no—
487C2×#137C22×C6111yescharacteristic
488C2×AGL(1,ℤ/8)—21no—
489C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
490C2×#135—21no—
491C2×#135C22×C6111yescharacteristic
492C22×SD16—21no—
493C22×SD16C22×C6111yescharacteristic
494C2×#131C22×C6111yescharacteristic
495C2×#131C22×C6111yescharacteristic, complemented
496#536C22×C6111yescharacteristic, complemented
497#535C22×C6111yescharacteristic
498#473—21no—
499#472—21no—
500#471—21no—
501#471—21no—
502#468—22no—
503#465—22no—
504#456—22no—
505#455—22no—
506#454—22no—
507#453—22no—
508#444—22no—
509#443—22no—
510#430C22×C6111yescharacteristic, complemented
511C2×#108C22×C6111yescharacteristic, complemented
512#427C22×C6111yescharacteristic, complemented
513#421C22×C6111yescharacteristic
514#421C22×C6111yescharacteristic
515#421C22×C6111yescharacteristic
516#421C22×C6111yescharacteristic
517#421C22×C6111yescharacteristic, complemented
518#421C22×C6111yescharacteristic, complemented
519#419C22×C6111yescharacteristic, complemented
520#419C22×C6111yescharacteristic, complemented
521#418C22×C6111yescharacteristic
522#418C22×C6111yescharacteristic
523#413C22×C6111yescharacteristic
524#413C22×C6111yescharacteristic, complemented
525C2×#101C22×C6111yescharacteristic, complemented
526C2×#100C22×C6111yescharacteristic
527#410C22×C6111yescharacteristic
528#410C22×C6111yescharacteristic, complemented
529#405C22×C6111yescharacteristic, complemented
530#344C22×C6111yescharacteristic, complemented
531#344C22×C6111yescharacteristic, complemented
532C61#2429511yescharacteristic, direct product factor, Sylow
5332−1+4—22no—
5342−1+4—22no—
5352−1+4—22no—
5362−1+4—41no—
537H(5,𝔽2)—22no—
538H(5,𝔽2)—22no—
539H(5,𝔽2)—22no—
540H(5,𝔽2)—41no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—41no—
546C2×#41C23×C6111yescharacteristic
547C2×#41C23×C6111yescharacteristic
548C2×#41C23×C6111yescharacteristic
549C2×#41C23×C6111yescharacteristic
550C22×Q8—21no—
551C22×Q8—21no—
552C22×Q8C23×C6111yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—41no—
556C22×D4C23×C6111yescharacteristic
557#137—24no—
558#137—24no—
559#137—22no—
560#137—21no—
561#137—21no—
562#137—21no—
563#137—21no—
564#137—21no—
565#137—22no—
566#137D4×C6112yes—
567AGL(1,ℤ/8)—24no—
568AGL(1,ℤ/8)—24no—
569AGL(1,ℤ/8)—22no—
570AGL(1,ℤ/8)—21no—
571AGL(1,ℤ/8)—21no—
572AGL(1,ℤ/8)—21no—
573AGL(1,ℤ/8)—21no—
574AGL(1,ℤ/8)—21no—
575AGL(1,ℤ/8)—22no—
576AGL(1,ℤ/8)D4×C6112yes—
577#135—24no—
578#135—24no—
579#135—22no—
580#135—21no—
581#135—21no—
582#135—21no—
583#135—21no—
584#135—41no—
585#135—41no—
586C2×Q16—21no—
587C2×Q16D4×C6111yescharacteristic, complemented
588C2×SD16—24no—
589C2×SD16—24no—
590C2×SD16—21no—
591C2×SD16—21no—
592C2×SD16—21no—
593C2×SD16—21no—
594C2×SD16—21no—
595C2×SD16—21no—
596C2×SD16D4×C6112yes—
597C2×SD16D4×C6112yes—
598C2×SD16D4×C6111yescharacteristic, complemented
599C2×SD16D4×C6111yescharacteristic, complemented
600C2×D8—21no—
601C2×D8D4×C6111yescharacteristic, complemented
602#131—21no—
603#131—21no—
604#131—21no—
605#131—21no—
606#131—21no—
607#131—21no—
608#131D4×C6112yescomplemented
609#131D4×C6112yescomplemented
610C2×M16—21no—
611C2×M16—21no—
612C2×M16C23×C6111yescharacteristic
613C2×M16C23×C6111yescharacteristic
614C2×M16C23×C6111yescharacteristic
615C2×M16C23×C6111yescharacteristic
616C2×M16C23×C6111yescharacteristic
617C22×C8—21no—
618C22×C8—21no—
619C22×C8C23×C6111yescharacteristic
620C4⋊Q8—21no—
621#127—21no—
622#124—21no—
623#124—21no—
624#123—41no—
625C22⋊Q8—22no—
626#121—22no—
627#120—41no—
628#117C23×C6111yescharacteristic
629#117C23×C6111yescharacteristic
630#117C23×C6111yescharacteristic
631#108—22no—
632#108—21no—
633#108—21no—
634#107—21no—
635#106—21no—
636#104—22no—
637#104—22no—
638#104—22no—
639#104—22no—
640#104—22no—
641#104—22no—
642#103—22no—
643#103—41no—
644#102—22no—
645#102—41no—
646#101—21no—
647#101—21no—
648#101—22no—
649#100—21no—
650#100—21no—
651#100—22no—
652#99—41no—
653#99—41no—
654#97—21no—
655C4×C8—21no—
656C24—21no—
657C24—41no—
658#41—21no—
659#41—21no—
660#41—24no—
661#41—24no—
662#41—21no—
663#41—21no—
664#41—21no—
665#41—21no—
666#41—21no—
667#41—21no—
668#41—21no—
669#41—21no—
670#41—21no—
671#41—21no—
672#41—21no—
673#41—21no—
674#41—42no—
675#41—44no—
676#41—42no—
677#41—42no—
678#41—42no—
679#41—44no—
680#41—42no—
681#41—42no—
682#41C2×D4×C6112yes—
683#41C2×D4×C6112yes—
684C2×Q8—21no—
685C2×Q8—24no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—41no—
691C2×Q8—42no—
692C2×Q8—42no—
693C2×Q8—42no—
694C2×Q8C2×D4×C6111yescharacteristic
695C2×Q8C2×D4×C6111yescharacteristic
696C2×Q8C2×D4×C6112yes—
697C2×Q8C2×D4×C6111yescharacteristic
698C2×Q8#41×C6111yescharacteristic
699C2×D4—21no—
700C2×D4—24no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—42no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—41no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4C2×D4×C6111yescharacteristic
719C2×D4C2×D4×C6111yescharacteristic
720C2×D4C2×D4×C6112yes—
721C2×D4C2×D4×C6111yescharacteristic
722C2×D4#41×C6111yescharacteristic
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—41no—
729C22×C4—41no—
730C22×C4—41no—
731C22×C4C24×C6111yescharacteristic
732Q16—24no—
733Q16—22no—
734Q16—21no—
735Q16—21no—
736Q16—41no—
737Q16—41no—
738SD16—24no—
739SD16—24no—
740SD16—22no—
741SD16—22no—
742SD16—22no—
743SD16—22no—
744SD16—21no—
745SD16—21no—
746SD16—22no—
747SD16—22no—
748SD16—21no—
749SD16—21no—
750SD16—41no—
751SD16—41no—
752SD16—41no—
753SD16—41no—
754D8—24no—
755D8—22no—
756D8—21no—
757D8—21no—
758D8—41no—
759D8—41no—
760M16—21no—
761M16—21no—
762M16—22no—
763M16—22no—
764M16—21no—
765M16—21no—
766M16—21no—
767M16—21no—
768M16—21no—
769M16—21no—
770M16—41no—
771M16—41no—
772M16C2×D4×C6112yes—
773M16C2×D4×C6112yes—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—22no—
777C2×C8—22no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—41no—
782C2×C8—41no—
783C2×C8C2×D4×C6111yescharacteristic
784C2×C8C2×D4×C6111yescharacteristic
785C2×C8C2×D4×C6111yescharacteristic
786C2×C8C2×D4×C6111yescharacteristic
787C2×C8C2×D4×C6111yescharacteristic
788C2×C8C2×D4×C6111yescharacteristic
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—42no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C42—21no—
799C42—21no—
800C42—21no—
801C23—21no—
802C23—21no—
803C23—22no—
804C23—21no—
805C23—21no—
806C23—44no—
807C23—41no—
808C23—41no—
809C23—161no—
810C23—162no—
811C23H(5,𝔽2)×C6111yescharacteristic
812Q8—21no—
813Q8—21no—
814Q8—21no—
815Q8—21no—
816Q8—22no—
817Q8—21no—
818Q8—22no—
819Q8—21no—
820Q8—21no—
821Q8—44no—
822Q8—41no—
823Q8—41no—
824Q8#121×C6112yes—
825D4—22no—
826D4—22no—
827D4—21no—
828D4—21no—
829D4—21no—
830D4—21no—
831D4—22no—
832D4—21no—
833D4—22no—
834D4—21no—
835D4—21no—
836D4—44no—
837D4—44no—
838D4—44no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—162no—
848D4#121×C6112yes—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4C22×D4×C6111yescharacteristic
871C2×C4C22×D4×C6111yescharacteristic
872C2×C4C22×D4×C6111yescharacteristic
873C2×C4C22×D4×C6111yescharacteristic
874C2×C4C2×#41×C6111yescharacteristic
875C2×C4H(5,𝔽2)×C6111yescharacteristic
876C8—22no—
877C8—22no—
878C8—41no—
879C8—41no—
880C8—41no—
881C8#120×C6111yescharacteristic
882C8#120×C6111yescharacteristic
883C8#120×C6111yescharacteristic
884C8#120×C6111yescharacteristic
885C22—22no—
886C22—41no—
887C22—42no—
888C22—42no—
889C22—41no—
890C22—42no—
891C22—41no—
892C22—41no—
893C22—82no—
894C22—81no—
895C22—81no—
896C22—82no—
897C22—161no—
898C22—164no—
899C22C61×#53511yescharacteristic
900C22D42×C6111yescharacteristic
901C22C61×#54611yescharacteristic
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—81no—
908C4—81no—
909C4—81no—
910C4C2×#120×C6111yescharacteristic
911C4C2×#121×C6111yescharacteristic
912C4D42×C6111yescharacteristic
913C4C61×#54611yescharacteristic
914C2—21no—
915C2—21no—
916C2—21no—
917C2—42no—
918C2—81no—
919C2—82no—
920C2—81no—
921C2—81no—
922C2C61×#240811yescharacteristic
subgroupG/H
center, socleC2×C61#2408
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C61 ◁ C22×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#577C2semidirect
2. C61×#3067C2semidirect
3. C61×#3057C2semidirect
4. C61×#3020C2semidirect
5. C61×#3019C2semidirect
6. C61×#2955C2semidirect
7. C61×#2049C2semidirect
8. C61×#2048C2semidirect
9. C61×#2009C2semidirect
10. C61×#2008C2semidirect
11. C61×#1977C2semidirect
12. C61×#1976C2semidirect
13. C61×#1814C2semidirect
14. C61×#1796C2semidirect
15. C61×#1795C2semidirect
24. C61×#575C22semidirect
34. C2×#131×C61C22semidirect
35. C61×#536C22semidirect
49. C61×#430C22semidirect
50. C2×#108×C61C22semidirect
51. C61×#427C22semidirect
56. C61×#421C22semidirect
57. C61×#421C22semidirect
58. C61×#419C22semidirect
59. C61×#419C22semidirect
63. C61×#413C22semidirect
64. C2×#101×C61C22semidirect
67. C61×#410C22semidirect
68. C61×#405C22semidirect
69. C61×#344C22semidirect
70. C61×#344C22semidirect
125. C2×Q16×C61D4semidirect
136. C2×SD16×C61D4semidirect
137. C2×SD16×C61D4semidirect
139. C2×D8×C61D4semidirect
146. #131×C61D4semidirect
147. #131×C61D4semidirect
423. #24295C61direct (N × H)
453. C2×#577C2×C61semidirect
454. #3067C2×C61semidirect
455. #3057C2×C61semidirect
456. #3020C2×C61semidirect
457. #3019C2×C61semidirect
458. #2955C2×C61semidirect
459. #2049C2×C61semidirect
460. #2048C2×C61semidirect
461. #2009C2×C61semidirect
462. #2008C2×C61semidirect
463. #1977C2×C61semidirect
464. #1976C2×C61semidirect
465. #1814C2×C61semidirect
466. #1796C2×C61semidirect
467. #1795C2×C61semidirect
485. #575C22×C61semidirect
495. C2×#131C22×C61semidirect
496. #536C22×C61semidirect
510. #430C22×C61semidirect
511. C2×#108C22×C61semidirect
512. #427C22×C61semidirect
517. #421C22×C61semidirect
518. #421C22×C61semidirect
519. #419C22×C61semidirect
520. #419C22×C61semidirect
524. #413C22×C61semidirect
525. C2×#101C22×C61semidirect
528. #410C22×C61semidirect
529. #405C22×C61semidirect
530. #344C22×C61semidirect
531. #344C22×C61semidirect
532. C61#24295direct (N × H)
587. C2×Q16D4×C61semidirect
598. C2×SD16D4×C61semidirect
599. C2×SD16D4×C61semidirect
601. C2×D8D4×C61semidirect
608. #131D4×C61semidirect
609. #131D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5772
C61×#30672
C61×#30572
C61×#30202
C61×#30192
C61×#29552
C61×#20492
C61×#20482
C61×#20092
C61×#20082
C61×#19772
C61×#19762
C61×#18142
C61×#17962
C61×#17952
#2429561