Finite Group Databasebeta

← C61×#24402 #29527835

Subgroups — C61×#24402 #29527835

Order 15616.

1358 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#575C211yesmaximal, characteristic, complemented
2C2×C61×#472C211yesmaximal, characteristic, complemented
3C2×C61×#471C211yesmaximal, characteristic, complemented
4C61×#3006C211yesmaximal, characteristic, complemented
5C2×C61×#449C211yesmaximal, characteristic, complemented
6C61×#2880C211yesmaximal, characteristic, complemented
7C61×#2052C211yesmaximal, characteristic, complemented
8C61×#2051C211yesmaximal, characteristic, complemented
9C61×#2019C211yesmaximal, characteristic, complemented
10C61×#2018C211yesmaximal, characteristic, complemented
11C61×#1908C211yesmaximal, characteristic, complemented
12C61×#1907C211yesmaximal, characteristic, complemented
13C61×#1900C211yesmaximal, characteristic, complemented
14C61×#1855C211yesmaximal, characteristic, complemented
15C61×#1785C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×#41×C61C2211yescharacteristic
18C61×#575—24no—
19C61×#575—24no—
20C2×#137×C61—21no—
21C2×#137×C61C2211yescharacteristic
22C2×#137×C61C2211yescharacteristic
23C2×AGL(1,ℤ/8)×C61—21no—
24C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
26C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
28C2×#135×C61—21no—
29C2×#135×C61—21no—
30C22×SD16×C61C2211yescharacteristic, complemented
31C22×D8×C61C2211yescharacteristic, complemented
32C2×#131×C61C2211yescharacteristic
33C2×#131×C61C2211yescharacteristic
34C22×M16×C61C2211yescharacteristic
35C2×#121×C61C2211yescharacteristic
36C61×#472—24no—
37C61×#471—24no—
38C61×#449—21no—
39C61×#449—21no—
40C61×#449—21no—
41C61×#449—21no—
42C61×#449—21no—
43C61×#449—21no—
44C61×#448—21no—
45C61×#447—21no—
46C2×#108×C61C2211yescharacteristic, complemented
47C2×#108×C61C2211yescharacteristic, complemented
48C61×#417C2211yescharacteristic
49C61×#417C2211yescharacteristic
50C2×#103×C61C2211yescharacteristic, complemented
51C2×#102×C61C2211yescharacteristic, complemented
52C2×#101×C61C2211yescharacteristic, complemented
53C2×#101×C61C2211yescharacteristic, complemented
54C2×#100×C61C2211yescharacteristic, complemented
55C2×#100×C61C2211yescharacteristic, complemented
56C2×#100×C61C2211yescharacteristic, complemented
57C2×#100×C61C2211yescharacteristic, complemented
58C61×#408—21no—
59C61×#408—21no—
60C61×#408C2211yescharacteristic
61C61×#408C2211yescharacteristic
62C61×#407—21no—
63C61×#407C2211yescharacteristic
64C61×#407C2211yescharacteristic
65C2×C22⋊C8×C61—21no—
66C2×C22⋊C8×C61C2211yescharacteristic
67C61×#343C2211yescharacteristic, complemented
68C61×#343C2211yescharacteristic, complemented
69C61×#341C2211yescharacteristic, complemented
70C61×#341C2211yescharacteristic, complemented
71C2×#41×C61—21no—
72C2×#41×C61—21no—
73C2×#41×C61—22no—
74C2×#41×C61—22no—
75C2×#41×C61—22no—
76C2×#41×C61—22no—
77C2×#41×C61—21no—
78C2×#41×C61—21no—
79C2×#41×C61—21no—
80C2×#41×C61—21no—
81C2×#41×C61—41no—
82C2×#41×C61—41no—
83C2×#41×C61—41no—
84C2×#41×C61—41no—
85C2×#41×C61D411yescharacteristic
86C2×#41×C61D411yescharacteristic
87C2×#41×C61C2311yescharacteristic
88C2×#41×C61C2311yescharacteristic
89C22×Q8×C61D411yescharacteristic
90C22×Q8×C61C2311yescharacteristic
91C22×D4×C61—21no—
92C22×D4×C61—21no—
93C22×D4×C61—21no—
94C22×D4×C61D411yescharacteristic
95C22×D4×C61C2311yescharacteristic
96C22×D4×C61C2311yescharacteristic
97C23×C4×C61—21no—
98C23×C4×C61—21no—
99C23×C4×C61C2311yescharacteristic
100#137×C61—28no—
101#137×C61—22no—
102#137×C61—22no—
103#137×C61—22no—
104#137×C61D414yescomplemented
105AGL(1,ℤ/8)×C61—28no—
106AGL(1,ℤ/8)×C61—22no—
107AGL(1,ℤ/8)×C61—22no—
108AGL(1,ℤ/8)×C61—22no—
109AGL(1,ℤ/8)×C61—22no—
110AGL(1,ℤ/8)×C61—22no—
111AGL(1,ℤ/8)×C61—41no—
112AGL(1,ℤ/8)×C61—41no—
113AGL(1,ℤ/8)×C61D414yescomplemented
114#135×C61—28no—
115#135×C61—28no—
116C2×Q16×C61—21no—
117C2×Q16×C61—21no—
118C2×SD16×C61—21no—
119C2×SD16×C61—21no—
120C2×SD16×C61—21no—
121C2×SD16×C61—21no—
122C2×SD16×C61—22no—
123C2×SD16×C61—21no—
124C2×SD16×C61—21no—
125C2×SD16×C61—21no—
126C2×SD16×C61—21no—
127C2×SD16×C61—41no—
128C2×D8×C61—21no—
129C2×D8×C61—21no—
130C2×D8×C61—22no—
131C2×D8×C61—21no—
132C2×D8×C61—21no—
133C2×D8×C61—21no—
134C2×D8×C61—21no—
135C2×D8×C61—41no—
136#131×C61—22no—
137#131×C61—22no—
138#131×C61—41no—
139#131×C61—41no—
140C2×M16×C61—21no—
141C2×M16×C61—22no—
142C2×M16×C61—22no—
143C2×M16×C61—21no—
144C2×M16×C61—21no—
145C2×M16×C61C2311yescharacteristic
146C2×M16×C61C2311yescharacteristic
147C2×M16×C61C2311yescharacteristic
148C2×M16×C61C2311yescharacteristic
149C2×M16×C61C2311yescharacteristic
150C2×M16×C61C2311yescharacteristic
151C22×C8×C61—21no—
152C22×C8×C61—21no—
153C22×C8×C61—21no—
154C22×C8×C61C2311yescharacteristic
155C22×C8×C61C2311yescharacteristic
156#121×C61—21no—
157#121×C61—21no—
158#121×C61—21no—
159#121×C61—21no—
160C2×C4⋊C4×C61C2311yescharacteristic
161C2×C22⋊C4×C61—21no—
162#108×C61—22no—
163#108×C61—22no—
164#103×C61—21no—
165#103×C61—21no—
166#103×C61—21no—
167#103×C61—21no—
168#102×C61—21no—
169#102×C61—21no—
170#102×C61—21no—
171#102×C61—21no—
172#101×C61—22no—
173#101×C61—41no—
174#100×C61—22no—
175#100×C61—22no—
176#100×C61—22no—
177#100×C61—41no—
178C22⋊C8×C61—21no—
179C22⋊C8×C61—21no—
180C22⋊C8×C61—21no—
181C22⋊C8×C61—21no—
182C22⋊C8×C61—21no—
183C22⋊C8×C61—21no—
184C22⋊C8×C61—21no—
185C22⋊C8×C61—21no—
186C22⋊C8×C61D411yescharacteristic
187C22⋊C8×C61D411yescharacteristic
188C22⋊C8×C61D411yescharacteristic
189C22⋊C8×C61D411yescharacteristic
190C24×C61—21no—
191C24×C61—21no—
192C24×C61—21no—
193C24×C61#4111yescharacteristic
194#41×C61—21no—
195#41×C61—21no—
196#41×C61—24no—
197#41×C61—24no—
198#41×C61—22no—
199#41×C61—22no—
200#41×C61—21no—
201#41×C61—21no—
202#41×C61—21no—
203#41×C61—21no—
204#41×C61—42no—
205#41×C61—42no—
206#41×C61—41no—
207#41×C61—41no—
208#41×C61—42no—
209#41×C61—42no—
210#41×C61—42no—
211#41×C61—42no—
212#41×C61—42no—
213#41×C61—42no—
214#41×C61—42no—
215#41×C61—42no—
216#41×C61C2×D412yes—
217#41×C61C2×D412yes—
218C2×Q8×C61—21no—
219C2×Q8×C61—21no—
220C2×Q8×C61—22no—
221C2×Q8×C61—21no—
222C2×Q8×C61—21no—
223C2×Q8×C61—21no—
224C2×Q8×C61—21no—
225C2×Q8×C61—41no—
226C2×Q8×C61C2×D412yes—
227C2×Q8×C61C2×D411yescharacteristic
228C2×Q8×C61C2×D411yescharacteristic
229C2×D4×C61—21no—
230C2×D4×C61—22no—
231C2×D4×C61—21no—
232C2×D4×C61—21no—
233C2×D4×C61—21no—
234C2×D4×C61—21no—
235C2×D4×C61—21no—
236C2×D4×C61—21no—
237C2×D4×C61—21no—
238C2×D4×C61—21no—
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—41no—
247C2×D4×C61—42no—
248C2×D4×C61—42no—
249C2×D4×C61—42no—
250C2×D4×C61—42no—
251C2×D4×C61—41no—
252C2×D4×C61—41no—
253C2×D4×C61—41no—
254C2×D4×C61—41no—
255C2×D4×C61—82no—
256C2×D4×C61C2×D412yes—
257C2×D4×C61C2×D411yescharacteristic
258C2×D4×C61C2×D411yescharacteristic
259C22×C4×C61—21no—
260C22×C4×C61—21no—
261C22×C4×C61—21no—
262C22×C4×C61—21no—
263C22×C4×C61—21no—
264C22×C4×C61—21no—
265C22×C4×C61—21no—
266C22×C4×C61—21no—
267C22×C4×C61—21no—
268C22×C4×C61—21no—
269C22×C4×C61—21no—
270C22×C4×C61—42no—
271C22×C4×C61—42no—
272C22×C4×C61—42no—
273C22×C4×C61—42no—
274C22×C4×C61—41no—
275C22×C4×C61—41no—
276C22×C4×C61C2×D411yescharacteristic
277C22×C4×C61C2×D411yescharacteristic
278C22×C4×C61C2×D411yescharacteristic
279C22×C4×C61C2×D411yescharacteristic
280C22×C4×C61#4111yescharacteristic
281C22×C4×C61C2411yescharacteristic
282Q16×C61—24no—
283Q16×C61—24no—
284SD16×C61—24no—
285SD16×C61—24no—
286SD16×C61—24no—
287SD16×C61—24no—
288SD16×C61—42no—
289SD16×C61—42no—
290SD16×C61—42no—
291SD16×C61—42no—
292D8×C61—24no—
293D8×C61—24no—
294D8×C61—42no—
295D8×C61—42no—
296D8×C61—42no—
297D8×C61—42no—
298M16×C61—24no—
299M16×C61—21no—
300M16×C61—21no—
301M16×C61—21no—
302M16×C61—21no—
303M16×C61—21no—
304M16×C61—21no—
305M16×C61—21no—
306M16×C61—21no—
307M16×C61—21no—
308M16×C61—21no—
309M16×C61—42no—
310M16×C61—42no—
311M16×C61C2×D412yes—
312M16×C61C2×D412yes—
313C2×C8×C61—24no—
314C2×C8×C61—21no—
315C2×C8×C61—21no—
316C2×C8×C61—21no—
317C2×C8×C61—21no—
318C2×C8×C61—21no—
319C2×C8×C61—21no—
320C2×C8×C61—21no—
321C2×C8×C61—21no—
322C2×C8×C61—21no—
323C2×C8×C61—21no—
324C2×C8×C61—42no—
325C2×C8×C61—42no—
326C2×C8×C61C2×D411yescharacteristic
327C2×C8×C61C2×D411yescharacteristic
328C2×C8×C61C2×D411yescharacteristic
329C2×C8×C61C2×D411yescharacteristic
330C4⋊C4×C61—21no—
331C4⋊C4×C61—21no—
332C22⋊C4×C61—41no—
333C22⋊C4×C61—41no—
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—22no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—42no—
342C23×C61—42no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61—81no—
349C23×C61—81no—
350C23×C61—81no—
351C23×C61—81no—
352C23×C61—81no—
353C23×C61#12111yescharacteristic
354C23×C61#12111yescharacteristic
355C23×C61C2×#4111yescharacteristic
356Q8×C61—21no—
357Q8×C61—21no—
358Q8×C61—22no—
359Q8×C61—21no—
360Q8×C61—22no—
361Q8×C61—42no—
362Q8×C61—41no—
363Q8×C61—41no—
364Q8×C61#12012yes—
365D4×C61—22no—
366D4×C61—22no—
367D4×C61—21no—
368D4×C61—22no—
369D4×C61—21no—
370D4×C61—21no—
371D4×C61—22no—
372D4×C61—42no—
373D4×C61—42no—
374D4×C61—42no—
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—82no—
386D4×C61—82no—
387D4×C61#12012yes—
388C2×C4×C61—21no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—22no—
396C2×C4×C61—22no—
397C2×C4×C61—21no—
398C2×C4×C61—21no—
399C2×C4×C61—21no—
400C2×C4×C61—21no—
401C2×C4×C61—21no—
402C2×C4×C61—22no—
403C2×C4×C61—42no—
404C2×C4×C61—42no—
405C2×C4×C61—42no—
406C2×C4×C61—44no—
407C2×C4×C61—44no—
408C2×C4×C61—41no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—81no—
414C2×C4×C61#12111yescharacteristic
415C2×C4×C61#12111yescharacteristic
416C2×C4×C61C22×D411yescharacteristic
417C2×C4×C61C22×D411yescharacteristic
418C2×C4×C61C22×D411yescharacteristic
419C2×C4×C61C22×D411yescharacteristic
420C2×C4×C61H(5,𝔽2)11yescharacteristic
421C2×C4×C61H(5,𝔽2)11yescharacteristic
422C8×C61—22no—
423C8×C61—22no—
424C8×C61—21no—
425C8×C61—21no—
426C8×C61—21no—
427C8×C61—21no—
428C8×C61—41no—
429C8×C61—41no—
430C8×C61—41no—
431C8×C61—41no—
432#24402C6111yesmaximal, characteristic, direct product factor, Sylow
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—22no—
438C22×C61—21no—
439C22×C61—21no—
440C22×C61—21no—
441C22×C61—21no—
442C22×C61—41no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—42no—
446C22×C61—41no—
447C22×C61—41no—
448C22×C61—81no—
449C22×C61—81no—
450C22×C61—82no—
451C22×C61—82no—
452C22×C61—84no—
453C22×C61—81no—
454C22×C61—81no—
455C22×C61—81no—
456C22×C61—81no—
457C22×C61—81no—
458C22×C61—161no—
459C22×C61—161no—
460C22×C61C2×#12111yescharacteristic
461C22×C61#54611yescharacteristic
462C22×C61#54611yescharacteristic
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—22no—
466C4×C61—41no—
467C4×C61—42no—
468C4×C61—81no—
469C4×C61C2×#12011yescharacteristic
470C4×C61#53411yescharacteristic
471C4×C61D4211yescharacteristic
472C4×C61D4211yescharacteristic
473C2×#575C2×C6111yescharacteristic, complemented
474C2×#472C2×C6111yescharacteristic, complemented
475C2×#471C2×C6111yescharacteristic, complemented
476#3006C2×C6111yescharacteristic, complemented
477C2×#449C2×C6111yescharacteristic, complemented
478#2880C2×C6111yescharacteristic, complemented
479#2052C2×C6111yescharacteristic, complemented
480#2051C2×C6111yescharacteristic, complemented
481#2019C2×C6111yescharacteristic, complemented
482#2018C2×C6111yescharacteristic, complemented
483#1908C2×C6111yescharacteristic, complemented
484#1907C2×C6111yescharacteristic, complemented
485#1900C2×C6111yescharacteristic, complemented
486#1855C2×C6111yescharacteristic, complemented
487#1785C2×C6111yescharacteristic, complemented
488C2×C61—21no—
489C2×C61—21no—
490C2×C61—41no—
491C2×C61—41no—
492C2×C61—42no—
493C2×C61—81no—
494C2×C61—82no—
495C2×C61—161no—
496C2×C61#241011yescharacteristic
497C2×C61#306711yescharacteristic
498C2×C61#306811yescharacteristic
499C22×#41C22×C6111yescharacteristic
500C22×#41C22×C6111yescharacteristic
501#575—24no—
502#575—24no—
503C2×#137—21no—
504C2×#137C22×C6111yescharacteristic
505C2×#137C22×C6111yescharacteristic
506C2×AGL(1,ℤ/8)—21no—
507C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
508C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
509C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
510C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
511C2×#135—21no—
512C2×#135—21no—
513C22×SD16C22×C6111yescharacteristic, complemented
514C22×D8C22×C6111yescharacteristic, complemented
515C2×#131C22×C6111yescharacteristic
516C2×#131C22×C6111yescharacteristic
517C22×M16C22×C6111yescharacteristic
518C2×#121C22×C6111yescharacteristic
519#472—24no—
520#471—24no—
521#449—21no—
522#449—21no—
523#449—21no—
524#449—21no—
525#449—21no—
526#449—21no—
527#448—21no—
528#447—21no—
529C2×#108C22×C6111yescharacteristic, complemented
530C2×#108C22×C6111yescharacteristic, complemented
531#417C22×C6111yescharacteristic
532#417C22×C6111yescharacteristic
533C2×#103C22×C6111yescharacteristic, complemented
534C2×#102C22×C6111yescharacteristic, complemented
535C2×#101C22×C6111yescharacteristic, complemented
536C2×#101C22×C6111yescharacteristic, complemented
537C2×#100C22×C6111yescharacteristic, complemented
538C2×#100C22×C6111yescharacteristic, complemented
539C2×#100C22×C6111yescharacteristic, complemented
540C2×#100C22×C6111yescharacteristic, complemented
541#408—21no—
542#408—21no—
543#408C22×C6111yescharacteristic
544#408C22×C6111yescharacteristic
545#407—21no—
546#407C22×C6111yescharacteristic
547#407C22×C6111yescharacteristic
548C2×C22⋊C8—21no—
549C2×C22⋊C8C22×C6111yescharacteristic
550#343C22×C6111yescharacteristic, complemented
551#343C22×C6111yescharacteristic, complemented
552#341C22×C6111yescharacteristic, complemented
553#341C22×C6111yescharacteristic, complemented
554C61#2440211yescharacteristic, direct product factor, Sylow
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—22no—
560C2×#41—22no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—41no—
566C2×#41—41no—
567C2×#41—41no—
568C2×#41—41no—
569C2×#41D4×C6111yescharacteristic
570C2×#41D4×C6111yescharacteristic
571C2×#41C23×C6111yescharacteristic
572C2×#41C23×C6111yescharacteristic
573C22×Q8D4×C6111yescharacteristic
574C22×Q8C23×C6111yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4D4×C6111yescharacteristic
579C22×D4C23×C6111yescharacteristic
580C22×D4C23×C6111yescharacteristic
581C23×C4—21no—
582C23×C4—21no—
583C23×C4C23×C6111yescharacteristic
584#137—28no—
585#137—22no—
586#137—22no—
587#137—22no—
588#137D4×C6114yescomplemented
589AGL(1,ℤ/8)—28no—
590AGL(1,ℤ/8)—22no—
591AGL(1,ℤ/8)—22no—
592AGL(1,ℤ/8)—22no—
593AGL(1,ℤ/8)—22no—
594AGL(1,ℤ/8)—22no—
595AGL(1,ℤ/8)—41no—
596AGL(1,ℤ/8)—41no—
597AGL(1,ℤ/8)D4×C6114yescomplemented
598#135—28no—
599#135—28no—
600C2×Q16—21no—
601C2×Q16—21no—
602C2×SD16—21no—
603C2×SD16—21no—
604C2×SD16—21no—
605C2×SD16—21no—
606C2×SD16—22no—
607C2×SD16—21no—
608C2×SD16—21no—
609C2×SD16—21no—
610C2×SD16—21no—
611C2×SD16—41no—
612C2×D8—21no—
613C2×D8—21no—
614C2×D8—22no—
615C2×D8—21no—
616C2×D8—21no—
617C2×D8—21no—
618C2×D8—21no—
619C2×D8—41no—
620#131—22no—
621#131—22no—
622#131—41no—
623#131—41no—
624C2×M16—21no—
625C2×M16—22no—
626C2×M16—22no—
627C2×M16—21no—
628C2×M16—21no—
629C2×M16C23×C6111yescharacteristic
630C2×M16C23×C6111yescharacteristic
631C2×M16C23×C6111yescharacteristic
632C2×M16C23×C6111yescharacteristic
633C2×M16C23×C6111yescharacteristic
634C2×M16C23×C6111yescharacteristic
635C22×C8—21no—
636C22×C8—21no—
637C22×C8—21no—
638C22×C8C23×C6111yescharacteristic
639C22×C8C23×C6111yescharacteristic
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644C2×C4⋊C4C23×C6111yescharacteristic
645C2×C22⋊C4—21no—
646#108—22no—
647#108—22no—
648#103—21no—
649#103—21no—
650#103—21no—
651#103—21no—
652#102—21no—
653#102—21no—
654#102—21no—
655#102—21no—
656#101—22no—
657#101—41no—
658#100—22no—
659#100—22no—
660#100—22no—
661#100—41no—
662C22⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—21no—
668C22⋊C8—21no—
669C22⋊C8—21no—
670C22⋊C8D4×C6111yescharacteristic
671C22⋊C8D4×C6111yescharacteristic
672C22⋊C8D4×C6111yescharacteristic
673C22⋊C8D4×C6111yescharacteristic
674C24—21no—
675C24—21no—
676C24—21no—
677C24#41×C6111yescharacteristic
678#41—21no—
679#41—21no—
680#41—24no—
681#41—24no—
682#41—22no—
683#41—22no—
684#41—21no—
685#41—21no—
686#41—21no—
687#41—21no—
688#41—42no—
689#41—42no—
690#41—41no—
691#41—41no—
692#41—42no—
693#41—42no—
694#41—42no—
695#41—42no—
696#41—42no—
697#41—42no—
698#41—42no—
699#41—42no—
700#41C2×D4×C6112yes—
701#41C2×D4×C6112yes—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—22no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8—41no—
710C2×Q8C2×D4×C6112yes—
711C2×Q8C2×D4×C6111yescharacteristic
712C2×Q8C2×D4×C6111yescharacteristic
713C2×D4—21no—
714C2×D4—22no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—41no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—41no—
736C2×D4—41no—
737C2×D4—41no—
738C2×D4—41no—
739C2×D4—82no—
740C2×D4C2×D4×C6112yes—
741C2×D4C2×D4×C6111yescharacteristic
742C2×D4C2×D4×C6111yescharacteristic
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—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4C2×D4×C6111yescharacteristic
761C22×C4C2×D4×C6111yescharacteristic
762C22×C4C2×D4×C6111yescharacteristic
763C22×C4C2×D4×C6111yescharacteristic
764C22×C4#41×C6111yescharacteristic
765C22×C4C24×C6111yescharacteristic
766Q16—24no—
767Q16—24no—
768SD16—24no—
769SD16—24no—
770SD16—24no—
771SD16—24no—
772SD16—42no—
773SD16—42no—
774SD16—42no—
775SD16—42no—
776D8—24no—
777D8—24no—
778D8—42no—
779D8—42no—
780D8—42no—
781D8—42no—
782M16—24no—
783M16—21no—
784M16—21no—
785M16—21no—
786M16—21no—
787M16—21no—
788M16—21no—
789M16—21no—
790M16—21no—
791M16—21no—
792M16—21no—
793M16—42no—
794M16—42no—
795M16C2×D4×C6112yes—
796M16C2×D4×C6112yes—
797C2×C8—24no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—42no—
809C2×C8—42no—
810C2×C8C2×D4×C6111yescharacteristic
811C2×C8C2×D4×C6111yescharacteristic
812C2×C8C2×D4×C6111yescharacteristic
813C2×C8C2×D4×C6111yescharacteristic
814C4⋊C4—21no—
815C4⋊C4—21no—
816C22⋊C4—41no—
817C22⋊C4—41no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—22no—
823C23—41no—
824C23—41no—
825C23—42no—
826C23—42no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23—81no—
837C23#121×C6111yescharacteristic
838C23#121×C6111yescharacteristic
839C23C2×#41×C6111yescharacteristic
840Q8—21no—
841Q8—21no—
842Q8—22no—
843Q8—21no—
844Q8—22no—
845Q8—42no—
846Q8—41no—
847Q8—41no—
848Q8#120×C6112yes—
849D4—22no—
850D4—22no—
851D4—21no—
852D4—21no—
853D4—22no—
854D4—21no—
855D4—22no—
856D4—42no—
857D4—42no—
858D4—42no—
859D4—44no—
860D4—44no—
861D4—41no—
862D4—41no—
863D4—41no—
864D4—41no—
865D4—41no—
866D4—41no—
867D4—41no—
868D4—41no—
869D4—82no—
870D4—82no—
871D4#120×C6112yes—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—22no—
886C2×C4—21no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—81no—
898C2×C4#121×C6111yescharacteristic
899C2×C4#121×C6111yescharacteristic
900C2×C4C22×D4×C6111yescharacteristic
901C2×C4C22×D4×C6111yescharacteristic
902C2×C4C22×D4×C6111yescharacteristic
903C2×C4C22×D4×C6111yescharacteristic
904C2×C4H(5,𝔽2)×C6111yescharacteristic
905C2×C4H(5,𝔽2)×C6111yescharacteristic
906C8—21no—
907C8—21no—
908C8—21no—
909C8—21no—
910C8—22no—
911C8—22no—
912C8—41no—
913C8—41no—
914C8—41no—
915C8—41no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—22no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—42no—
931C22—81no—
932C22—81no—
933C22—82no—
934C22—82no—
935C22—84no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22—81no—
940C22—81no—
941C22—161no—
942C22—161no—
943C22C2×#121×C6111yescharacteristic
944C22C61×#54611yescharacteristic
945C22C61×#54611yescharacteristic
946C4—21no—
947C4—21no—
948C4—22no—
949C4—42no—
950C4—41no—
951C4—81no—
952C4C2×#120×C6111yescharacteristic
953C4C61×#53411yescharacteristic
954C4D42×C6111yescharacteristic
955C4D42×C6111yescharacteristic
956C2—21no—
957C2—21no—
958C2—41no—
959C2—41no—
960C2—42no—
961C2—81no—
962C2—82no—
963C2—161no—
964C2C61×#241011yescharacteristic
965C2C61×#306711yescharacteristic
966C2C61×#306811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#575C2semidirect
2. C2×C61×#472C2semidirect
3. C2×C61×#471C2semidirect
4. C61×#3006C2semidirect
5. C2×C61×#449C2semidirect
6. C61×#2880C2semidirect
7. C61×#2052C2semidirect
8. C61×#2051C2semidirect
9. C61×#2019C2semidirect
10. C61×#2018C2semidirect
11. C61×#1908C2semidirect
12. C61×#1907C2semidirect
13. C61×#1900C2semidirect
14. C61×#1855C2semidirect
15. C61×#1785C2semidirect
30. C22×SD16×C61C22semidirect
31. C22×D8×C61C22semidirect
46. C2×#108×C61C22semidirect
47. C2×#108×C61C22semidirect
50. C2×#103×C61C22semidirect
51. C2×#102×C61C22semidirect
52. C2×#101×C61C22semidirect
53. C2×#101×C61C22semidirect
54. C2×#100×C61C22semidirect
55. C2×#100×C61C22semidirect
56. C2×#100×C61C22semidirect
57. C2×#100×C61C22semidirect
67. C61×#343C22semidirect
68. C61×#343C22semidirect
69. C61×#341C22semidirect
70. C61×#341C22semidirect
104. #137×C61D4semidirect
113. AGL(1,ℤ/8)×C61D4semidirect
432. #24402C61direct (N × H)
473. C2×#575C2×C61semidirect
474. C2×#472C2×C61semidirect
475. C2×#471C2×C61semidirect
476. #3006C2×C61semidirect
477. C2×#449C2×C61semidirect
478. #2880C2×C61semidirect
479. #2052C2×C61semidirect
480. #2051C2×C61semidirect
481. #2019C2×C61semidirect
482. #2018C2×C61semidirect
483. #1908C2×C61semidirect
484. #1907C2×C61semidirect
485. #1900C2×C61semidirect
486. #1855C2×C61semidirect
487. #1785C2×C61semidirect
513. C22×SD16C22×C61semidirect
514. C22×D8C22×C61semidirect
529. C2×#108C22×C61semidirect
530. C2×#108C22×C61semidirect
533. C2×#103C22×C61semidirect
534. C2×#102C22×C61semidirect
535. C2×#101C22×C61semidirect
536. C2×#101C22×C61semidirect
537. C2×#100C22×C61semidirect
538. C2×#100C22×C61semidirect
539. C2×#100C22×C61semidirect
540. C2×#100C22×C61semidirect
550. #343C22×C61semidirect
551. #343C22×C61semidirect
552. #341C22×C61semidirect
553. #341C22×C61semidirect
554. C61#24402direct (N × H)
588. #137D4×C61semidirect
597. 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×#5752
C2×C61×#4722
C2×C61×#4712
C61×#30062
C2×C61×#4492
C61×#28802
C61×#20522
C61×#20512
C61×#20192
C61×#20182
C61×#19082
C61×#19072
C61×#19002
C61×#18552
C61×#17852
#2440261