Finite Group Databasebeta

← C61×#24474 #29527907

Subgroups — C61×#24474 #29527907

Order 15616.

1298 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3586C211yesmaximal, characteristic
2C61×#3069C211yesmaximal, characteristic, complemented
3C61×#3039C211yesmaximal, characteristic, complemented
4C61×#3022C211yesmaximal, characteristic, complemented
5C2×C61×#456C211yesmaximal, characteristic, complemented
6C61×#2901C211yesmaximal, characteristic, complemented
7C61×#2050C211yesmaximal, characteristic, complemented
8C61×#2049C211yesmaximal, characteristic, complemented
9C61×#2009C211yesmaximal, characteristic, complemented
10C61×#2005C211yesmaximal, characteristic, complemented
11C61×#1906C211yesmaximal, characteristic, complemented
12C61×#1902C211yesmaximal, characteristic, complemented
13C61×#1902C211yesmaximal, characteristic, complemented
14C61×#1861C211yesmaximal, characteristic, complemented
15C61×#1796C211yesmaximal, characteristic, complemented
16C61×#585C2211yescharacteristic
17C2×2−1+4×C61C2211yescharacteristic
18C61×#578—22no—
19C61×#578—22no—
20C61×#577—22no—
21C61×#577—22no—
22C61×#575—22no—
23C61×#575C2211yescharacteristic
24C61×#575C2211yescharacteristic
25C2×#137×C61—22no—
26C2×#137×C61C2211yescharacteristic
27C2×#137×C61C2211yescharacteristic
28C2×#137×C61C2211yescharacteristic
29C2×#137×C61C2211yescharacteristic
30C2×#137×C61C2211yescharacteristic, complemented
31C61×#568C2211yescharacteristic
32C61×#568C2211yescharacteristic
33C61×#536C2211yescharacteristic
34C2×C4⋊Q8×C61C2211yescharacteristic, complemented
35C4×#41×C61C2211yescharacteristic
36C61×#473—22no—
37C61×#471—22no—
38C61×#462—22no—
39C61×#461—22no—
40C61×#456—22no—
41C61×#456—22no—
42C61×#456—22no—
43C61×#455—22no—
44C61×#430C2211yescharacteristic, complemented
45C61×#423C2211yescharacteristic, complemented
46C61×#421—22no—
47C61×#421C2211yescharacteristic
48C61×#421C2211yescharacteristic
49C61×#421C2211yescharacteristic
50C61×#421C2211yescharacteristic
51C2×#104×C61—22no—
52C2×#104×C61C2211yescharacteristic
53C2×#104×C61C2211yescharacteristic
54C2×#104×C61C2211yescharacteristic, complemented
55C61×#419C2211yescharacteristic, complemented
56C61×#419C2211yescharacteristic, complemented
57C61×#419C2211yescharacteristic, complemented
58C61×#413C2211yescharacteristic
59C61×#413C2211yescharacteristic, complemented
60C2×#101×C61C2211yescharacteristic, complemented
61C2×#101×C61C2211yescharacteristic, complemented
62C61×#410C2211yescharacteristic, complemented
63C61×#344C2211yescharacteristic, complemented
64C61×#344C2211yescharacteristic, complemented
65C61×#339C2211yescharacteristic, complemented
66C61×#338C2211yescharacteristic, complemented
672−1+4×C61—22no—
682−1+4×C61—22no—
692−1+4×C61—21no—
702−1+4×C61—21no—
712−1+4×C61—22no—
722−1+4×C61—41no—
732−1+4×C61D412yes—
74H(5,𝔽2)×C61—21no—
75H(5,𝔽2)×C61—21no—
76H(5,𝔽2)×C61—41no—
77H(5,𝔽2)×C61D412yes—
78C2×#41×C61—22no—
79C2×#41×C61—22no—
80C2×#41×C61—21no—
81C2×#41×C61—21no—
82C2×#41×C61—41no—
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×Q8×C61C2311yescharacteristic
92#137×C61—24no—
93#137×C61—24no—
94#137×C61—24no—
95#137×C61—22no—
96#137×C61—22no—
97#137×C61—21no—
98#137×C61—22no—
99#137×C61—21no—
100#137×C61—21no—
101#137×C61—22no—
102#137×C61—22no—
103#137×C61—22no—
104#137×C61—22no—
105#137×C61—22no—
106#137×C61—22no—
107#137×C61—41no—
108#137×C61D412yes—
109AGL(1,ℤ/8)×C61—24no—
110AGL(1,ℤ/8)×C61—21no—
111AGL(1,ℤ/8)×C61—21no—
112AGL(1,ℤ/8)×C61—21no—
113AGL(1,ℤ/8)×C61D412yes—
114#135×C61—24no—
115#135×C61—24no—
116#135×C61—22no—
117#135×C61—22no—
118C2×Q16×C61—24no—
119C2×Q16×C61—21no—
120C2×Q16×C61—21no—
121C2×Q16×C61—21no—
122C2×Q16×C61—21no—
123C2×Q16×C61D412yes—
124C2×SD16×C61—24no—
125C2×SD16×C61—21no—
126C2×SD16×C61—21no—
127C2×SD16×C61—21no—
128C2×SD16×C61—21no—
129C2×SD16×C61D412yes—
130#131×C61—22no—
131#131×C61—22no—
132#131×C61—22no—
133#131×C61—41no—
134C2×M16×C61—22no—
135C2×M16×C61—22no—
136C2×M16×C61C2311yescharacteristic
137C2×M16×C61C2311yescharacteristic
138C2×M16×C61C2311yescharacteristic
139C2×M16×C61C2311yescharacteristic
140C2×M16×C61C2311yescharacteristic
141C2×M16×C61C2311yescharacteristic
142C4⋊Q8×C61—22no—
143C4⋊Q8×C61—21no—
144C4⋊Q8×C61—21no—
145C4⋊Q8×C61—21no—
146#124×C61—21no—
147#123×C61—41no—
148C22⋊Q8×C61—41no—
149C4×Q8×C61—21no—
150C4×D4×C61—21no—
151C4×D4×C61—41no—
152#117×C61—21no—
153#117×C61C2311yescharacteristic
154#117×C61C2311yescharacteristic
155C2×C4⋊C4×C61—41no—
156C2×C42×C61—21no—
157C2×C42×C61C2311yescharacteristic
158#108×C61—22no—
159C4⋊C8×C61—22no—
160#104×C61—22no—
161#104×C61—22no—
162#104×C61—22no—
163#104×C61—22no—
164#104×C61—21no—
165#104×C61—21no—
166#104×C61—21no—
167#104×C61—21no—
168#104×C61D412yes—
169#104×C61D412yes—
170#103×C61—22no—
171#103×C61—22no—
172#103×C61—41no—
173#101×C61—21no—
174#101×C61—21no—
175#101×C61—22no—
176#101×C61—22no—
177#100×C61—21no—
178#100×C61—21no—
179#99×C61—41no—
180#41×C61—21no—
181#41×C61—21no—
182#41×C61—21no—
183#41×C61—21no—
184#41×C61—24no—
185#41×C61—22no—
186#41×C61—22no—
187#41×C61—22no—
188#41×C61—22no—
189#41×C61—21no—
190#41×C61—21no—
191#41×C61—21no—
192#41×C61—21no—
193#41×C61—21no—
194#41×C61—21no—
195#41×C61—21no—
196#41×C61—21no—
197#41×C61—42no—
198#41×C61—42no—
199#41×C61—42no—
200#41×C61—42no—
201#41×C61—42no—
202#41×C61—44no—
203#41×C61—42no—
204#41×C61—41no—
205#41×C61—41no—
206#41×C61—44no—
207#41×C61—42no—
208#41×C61C2×D412yes—
209#41×C61C2×D412yes—
210#41×C61C2×D412yes—
211#41×C61C2×D412yes—
212C2×Q8×C61—21no—
213C2×Q8×C61—24no—
214C2×Q8×C61—22no—
215C2×Q8×C61—22no—
216C2×Q8×C61—21no—
217C2×Q8×C61—21no—
218C2×Q8×C61—21no—
219C2×Q8×C61—21no—
220C2×Q8×C61—21no—
221C2×Q8×C61—21no—
222C2×Q8×C61—21no—
223C2×Q8×C61—21no—
224C2×Q8×C61—21no—
225C2×Q8×C61—21no—
226C2×Q8×C61—41no—
227C2×Q8×C61—42no—
228C2×Q8×C61—42no—
229C2×Q8×C61—41no—
230C2×Q8×C61—42no—
231C2×Q8×C61C2×D411yescharacteristic
232C2×Q8×C61C2×D411yescharacteristic
233C2×Q8×C61C2×D412yes—
234C2×Q8×C61C2×D411yescharacteristic
235C2×Q8×C61#4111yescharacteristic
236C2×D4×C61—21no—
237C2×D4×C61—21no—
238C2×D4×C61—22no—
239C2×D4×C61—22no—
240C2×D4×C61—21no—
241C2×D4×C61—21no—
242C2×D4×C61—42no—
243C2×D4×C61—41no—
244C2×D4×C61—42no—
245C2×D4×C61—42no—
246C2×D4×C61—41no—
247C2×D4×C61C2×D411yescharacteristic
248C2×D4×C61C2×D411yescharacteristic
249C2×D4×C61C2×D411yescharacteristic
250C2×D4×C61#4111yescharacteristic
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—42no—
259C22×C4×C61—41no—
260C22×C4×C61—41no—
261C22×C4×C61—41no—
262C22×C4×C61C2411yescharacteristic
263Q16×C61—24no—
264Q16×C61—22no—
265Q16×C61—22no—
266Q16×C61—24no—
267Q16×C61—42no—
268Q16×C61—42no—
269Q16×C61—42no—
270SD16×C61—24no—
271SD16×C61—22no—
272SD16×C61—22no—
273SD16×C61—22no—
274SD16×C61—22no—
275SD16×C61—24no—
276SD16×C61—42no—
277SD16×C61—42no—
278SD16×C61—42no—
279D8×C61—22no—
280D8×C61—22no—
281M16×C61—24no—
282M16×C61—21no—
283M16×C61—21no—
284M16×C61—21no—
285M16×C61—21no—
286M16×C61—21no—
287M16×C61—21no—
288M16×C61—21no—
289M16×C61—21no—
290M16×C61—21no—
291M16×C61—21no—
292M16×C61—42no—
293M16×C61C2×D412yes—
294M16×C61C2×D412yes—
295C2×C8×C61—24no—
296C2×C8×C61—21no—
297C2×C8×C61—21no—
298C2×C8×C61—21no—
299C2×C8×C61—21no—
300C2×C8×C61—21no—
301C2×C8×C61—42no—
302C2×C8×C61C2×D412yes—
303C4⋊C4×C61—21no—
304C4⋊C4×C61—21no—
305C4⋊C4×C61—42no—
306C4⋊C4×C61—42no—
307C4⋊C4×C61—41no—
308C4⋊C4×C61—42no—
309C22⋊C4×C61—21no—
310C22⋊C4×C61—21no—
311C22⋊C4×C61—41no—
312C22⋊C4×C61—42no—
313C42×C61—21no—
314C42×C61—21no—
315C42×C61—21no—
316C42×C61—41no—
317C42×C61C2×D411yescharacteristic
318C42×C61C2×D411yescharacteristic
319C23×C61—21no—
320C23×C61—21no—
321C23×C61—21no—
322C23×C61—21no—
323C23×C61—42no—
324C23×C61H(5,𝔽2)11yescharacteristic
325Q8×C61—21no—
326Q8×C61—21no—
327Q8×C61—21no—
328Q8×C61—22no—
329Q8×C61—21no—
330Q8×C61—21no—
331Q8×C61—21no—
332Q8×C61—22no—
333Q8×C61—42no—
334Q8×C61—44no—
335Q8×C61—41no—
336Q8×C61—41no—
337Q8×C61—41no—
338Q8×C61—41no—
339Q8×C61—41no—
340Q8×C61—41no—
341Q8×C61#12012yes—
342Q8×C61#12112yes—
343D4×C61—22no—
344D4×C61—22no—
345D4×C61—22no—
346D4×C61—22no—
347D4×C61—21no—
348D4×C61—21no—
349D4×C61—21no—
350D4×C61—21no—
351D4×C61—21no—
352D4×C61—21no—
353D4×C61—42no—
354D4×C61—42no—
355D4×C61—42no—
356D4×C61—44no—
357D4×C61—41no—
358D4×C61—41no—
359D4×C61—41no—
360D4×C61—41no—
361D4×C61#12012yes—
362D4×C61#12112yes—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—22no—
373C2×C4×C61—21no—
374C2×C4×C61—42no—
375C2×C4×C61—42no—
376C2×C4×C61—42no—
377C2×C4×C61—42no—
378C2×C4×C61—44no—
379C2×C4×C61—44no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—82no—
392C2×C4×C61C22×D411yescharacteristic
393C2×C4×C61C22×D411yescharacteristic
394C2×C4×C61C22×D411yescharacteristic
395C2×C4×C61C22×D411yescharacteristic
396C2×C4×C61C2×#4111yescharacteristic
397C2×C4×C61H(5,𝔽2)11yescharacteristic
398C8×C61—22no—
399C8×C61—22no—
400C8×C61—22no—
401C8×C61—41no—
402C8×C61—41no—
403C8×C61—41no—
404#24474C6111yesmaximal, characteristic, direct product factor, Sylow
405C22×C61—22no—
406C22×C61—22no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61—81no—
411C22×C61—81no—
412C22×C61—81no—
413C22×C61—81no—
414C22×C61—162no—
415C22×C61#53411yescharacteristic
416C22×C61D4211yescharacteristic
417C22×C61#54611yescharacteristic
418C4×C61—22no—
419C4×C61—22no—
420C4×C61—22no—
421C4×C61—41no—
422C4×C61—41no—
423C4×C61—42no—
424C4×C61—41no—
425C4×C61—81no—
426C4×C61—81no—
427C4×C61—81no—
428C4×C61C2×#12011yescharacteristic
429C4×C61C2×#12111yescharacteristic
430C4×C61D4211yescharacteristic
431C4×C61#54611yescharacteristic
432#3586C2×C6111yescharacteristic
433#3069C2×C6111yescharacteristic, complemented
434#3039C2×C6111yescharacteristic, complemented
435#3022C2×C6111yescharacteristic, complemented
436C2×#456C2×C6111yescharacteristic, complemented
437#2901C2×C6111yescharacteristic, complemented
438#2050C2×C6111yescharacteristic, complemented
439#2049C2×C6111yescharacteristic, complemented
440#2009C2×C6111yescharacteristic, complemented
441#2005C2×C6111yescharacteristic, complemented
442#1906C2×C6111yescharacteristic, complemented
443#1902C2×C6111yescharacteristic, complemented
444#1902C2×C6111yescharacteristic, complemented
445#1861C2×C6111yescharacteristic, complemented
446#1796C2×C6111yescharacteristic, complemented
447C2×C61—21no—
448C2×C61—21no—
449C2×C61—21no—
450C2×C61—42no—
451C2×C61—42no—
452C2×C61—81no—
453C2×C61—81no—
454C2×C61#241011yescharacteristic
455#585C22×C6111yescharacteristic
456C2×2−1+4C22×C6111yescharacteristic
457#578—22no—
458#578—22no—
459#577—22no—
460#577—22no—
461#575—22no—
462#575C22×C6111yescharacteristic
463#575C22×C6111yescharacteristic
464C2×#137—22no—
465C2×#137C22×C6111yescharacteristic
466C2×#137C22×C6111yescharacteristic
467C2×#137C22×C6111yescharacteristic
468C2×#137C22×C6111yescharacteristic
469C2×#137C22×C6111yescharacteristic, complemented
470#568C22×C6111yescharacteristic
471#568C22×C6111yescharacteristic
472#536C22×C6111yescharacteristic
473C2×C4⋊Q8C22×C6111yescharacteristic, complemented
474C4×#41C22×C6111yescharacteristic
475#473—22no—
476#471—22no—
477#462—22no—
478#461—22no—
479#456—22no—
480#456—22no—
481#456—22no—
482#455—22no—
483#430C22×C6111yescharacteristic, complemented
484#423C22×C6111yescharacteristic, complemented
485#421—22no—
486#421C22×C6111yescharacteristic
487#421C22×C6111yescharacteristic
488#421C22×C6111yescharacteristic
489#421C22×C6111yescharacteristic
490C2×#104—22no—
491C2×#104C22×C6111yescharacteristic
492C2×#104C22×C6111yescharacteristic
493C2×#104C22×C6111yescharacteristic, complemented
494#419C22×C6111yescharacteristic, complemented
495#419C22×C6111yescharacteristic, complemented
496#419C22×C6111yescharacteristic, complemented
497#413C22×C6111yescharacteristic
498#413C22×C6111yescharacteristic, complemented
499C2×#101C22×C6111yescharacteristic, complemented
500C2×#101C22×C6111yescharacteristic, complemented
501#410C22×C6111yescharacteristic, complemented
502#344C22×C6111yescharacteristic, complemented
503#344C22×C6111yescharacteristic, complemented
504#339C22×C6111yescharacteristic, complemented
505#338C22×C6111yescharacteristic, complemented
506C61#2447411yescharacteristic, direct product factor, Sylow
5072−1+4—22no—
5082−1+4—22no—
5092−1+4—21no—
5102−1+4—21no—
5112−1+4—22no—
5122−1+4—41no—
5132−1+4D4×C6112yes—
514H(5,𝔽2)—21no—
515H(5,𝔽2)—21no—
516H(5,𝔽2)—41no—
517H(5,𝔽2)D4×C6112yes—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—21no—
521C2×#41—21no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41C23×C6111yescharacteristic
525C2×#41C23×C6111yescharacteristic
526C2×#41C23×C6111yescharacteristic
527C2×#41C23×C6111yescharacteristic
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8C23×C6111yescharacteristic
531C22×Q8C23×C6111yescharacteristic
532#137—24no—
533#137—24no—
534#137—24no—
535#137—22no—
536#137—22no—
537#137—21no—
538#137—22no—
539#137—21no—
540#137—21no—
541#137—22no—
542#137—22no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—22no—
547#137—41no—
548#137D4×C6112yes—
549AGL(1,ℤ/8)—24no—
550AGL(1,ℤ/8)—21no—
551AGL(1,ℤ/8)—21no—
552AGL(1,ℤ/8)—21no—
553AGL(1,ℤ/8)D4×C6112yes—
554#135—24no—
555#135—24no—
556#135—22no—
557#135—22no—
558C2×Q16—24no—
559C2×Q16—21no—
560C2×Q16—21no—
561C2×Q16—21no—
562C2×Q16—21no—
563C2×Q16D4×C6112yes—
564C2×SD16—24no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×SD16—21no—
569C2×SD16D4×C6112yes—
570#131—22no—
571#131—22no—
572#131—22no—
573#131—41no—
574C2×M16—22no—
575C2×M16—22no—
576C2×M16C23×C6111yescharacteristic
577C2×M16C23×C6111yescharacteristic
578C2×M16C23×C6111yescharacteristic
579C2×M16C23×C6111yescharacteristic
580C2×M16C23×C6111yescharacteristic
581C2×M16C23×C6111yescharacteristic
582C4⋊Q8—22no—
583C4⋊Q8—21no—
584C4⋊Q8—21no—
585C4⋊Q8—21no—
586#124—21no—
587#123—41no—
588C22⋊Q8—41no—
589C4×Q8—21no—
590C4×D4—21no—
591C4×D4—41no—
592#117—21no—
593#117C23×C6111yescharacteristic
594#117C23×C6111yescharacteristic
595C2×C4⋊C4—41no—
596C2×C42—21no—
597C2×C42C23×C6111yescharacteristic
598#108—22no—
599C4⋊C8—22no—
600#104—22no—
601#104—22no—
602#104—22no—
603#104—22no—
604#104—21no—
605#104—21no—
606#104—21no—
607#104—21no—
608#104D4×C6112yes—
609#104D4×C6112yes—
610#103—22no—
611#103—22no—
612#103—41no—
613#101—21no—
614#101—21no—
615#101—22no—
616#101—22no—
617#100—21no—
618#100—21no—
619#99—41no—
620#41—21no—
621#41—21no—
622#41—21no—
623#41—21no—
624#41—24no—
625#41—22no—
626#41—22no—
627#41—22no—
628#41—22no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—21no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—42no—
638#41—42no—
639#41—42no—
640#41—42no—
641#41—42no—
642#41—44no—
643#41—42no—
644#41—41no—
645#41—41no—
646#41—44no—
647#41—42no—
648#41C2×D4×C6112yes—
649#41C2×D4×C6112yes—
650#41C2×D4×C6112yes—
651#41C2×D4×C6112yes—
652C2×Q8—21no—
653C2×Q8—24no—
654C2×Q8—22no—
655C2×Q8—22no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—41no—
667C2×Q8—42no—
668C2×Q8—42no—
669C2×Q8—41no—
670C2×Q8—42no—
671C2×Q8C2×D4×C6111yescharacteristic
672C2×Q8C2×D4×C6111yescharacteristic
673C2×Q8C2×D4×C6112yes—
674C2×Q8C2×D4×C6111yescharacteristic
675C2×Q8#41×C6111yescharacteristic
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—42no—
683C2×D4—41no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—41no—
687C2×D4C2×D4×C6111yescharacteristic
688C2×D4C2×D4×C6111yescharacteristic
689C2×D4C2×D4×C6111yescharacteristic
690C2×D4#41×C6111yescharacteristic
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—42no—
699C22×C4—41no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4C24×C6111yescharacteristic
703Q16—24no—
704Q16—22no—
705Q16—22no—
706Q16—24no—
707Q16—42no—
708Q16—42no—
709Q16—42no—
710SD16—24no—
711SD16—22no—
712SD16—22no—
713SD16—22no—
714SD16—22no—
715SD16—24no—
716SD16—42no—
717SD16—42no—
718SD16—42no—
719D8—22no—
720D8—22no—
721M16—24no—
722M16—21no—
723M16—21no—
724M16—21no—
725M16—21no—
726M16—21no—
727M16—21no—
728M16—21no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—42no—
733M16C2×D4×C6112yes—
734M16C2×D4×C6112yes—
735C2×C8—24no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—42no—
742C2×C8C2×D4×C6112yes—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4—41no—
748C4⋊C4—42no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—41no—
752C22⋊C4—42no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42—41no—
757C42C2×D4×C6111yescharacteristic
758C42C2×D4×C6111yescharacteristic
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—42no—
764C23H(5,𝔽2)×C6111yescharacteristic
765Q8—21no—
766Q8—21no—
767Q8—21no—
768Q8—22no—
769Q8—21no—
770Q8—22no—
771Q8—21no—
772Q8—21no—
773Q8—42no—
774Q8—44no—
775Q8—41no—
776Q8—41no—
777Q8—41no—
778Q8—41no—
779Q8—41no—
780Q8—41no—
781Q8#120×C6112yes—
782Q8#121×C6112yes—
783D4—22no—
784D4—22no—
785D4—22no—
786D4—22no—
787D4—21no—
788D4—21no—
789D4—21no—
790D4—21no—
791D4—21no—
792D4—21no—
793D4—42no—
794D4—42no—
795D4—42no—
796D4—44no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4#120×C6112yes—
802D4#121×C6112yes—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—82no—
832C2×C4C22×D4×C6111yescharacteristic
833C2×C4C22×D4×C6111yescharacteristic
834C2×C4C22×D4×C6111yescharacteristic
835C2×C4C22×D4×C6111yescharacteristic
836C2×C4C2×#41×C6111yescharacteristic
837C2×C4H(5,𝔽2)×C6111yescharacteristic
838C8—22no—
839C8—22no—
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C22—22no—
845C22—22no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—162no—
854C22C61×#53411yescharacteristic
855C22D42×C6111yescharacteristic
856C22C61×#54611yescharacteristic
857C4—22no—
858C4—22no—
859C4—22no—
860C4—41no—
861C4—41no—
862C4—42no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4C2×#120×C6111yescharacteristic
868C4C2×#121×C6111yescharacteristic
869C4D42×C6111yescharacteristic
870C4C61×#54611yescharacteristic
871C2—21no—
872C2—21no—
873C2—21no—
874C2—42no—
875C2—42no—
876C2—81no—
877C2—81no—
878C2C61×#241011yescharacteristic
subgroupG/H
center, socleC2×C61#2410
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#3586C2
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
2. C61×#3069C2semidirect
3. C61×#3039C2semidirect
4. C61×#3022C2semidirect
5. C2×C61×#456C2semidirect
6. C61×#2901C2semidirect
7. C61×#2050C2semidirect
8. C61×#2049C2semidirect
9. C61×#2009C2semidirect
10. C61×#2005C2semidirect
11. C61×#1906C2semidirect
12. C61×#1902C2semidirect
13. C61×#1902C2semidirect
14. C61×#1861C2semidirect
15. C61×#1796C2semidirect
30. C2×#137×C61C22semidirect
34. C2×C4⋊Q8×C61C22semidirect
44. C61×#430C22semidirect
45. C61×#423C22semidirect
54. C2×#104×C61C22semidirect
55. C61×#419C22semidirect
56. C61×#419C22semidirect
57. C61×#419C22semidirect
59. C61×#413C22semidirect
60. C2×#101×C61C22semidirect
61. C2×#101×C61C22semidirect
62. C61×#410C22semidirect
63. C61×#344C22semidirect
64. C61×#344C22semidirect
65. C61×#339C22semidirect
66. C61×#338C22semidirect
404. #24474C61direct (N × H)
433. #3069C2×C61semidirect
434. #3039C2×C61semidirect
435. #3022C2×C61semidirect
436. C2×#456C2×C61semidirect
437. #2901C2×C61semidirect
438. #2050C2×C61semidirect
439. #2049C2×C61semidirect
440. #2009C2×C61semidirect
441. #2005C2×C61semidirect
442. #1906C2×C61semidirect
443. #1902C2×C61semidirect
444. #1902C2×C61semidirect
445. #1861C2×C61semidirect
446. #1796C2×C61semidirect
469. C2×#137C22×C61semidirect
473. C2×C4⋊Q8C22×C61semidirect
483. #430C22×C61semidirect
484. #423C22×C61semidirect
493. C2×#104C22×C61semidirect
494. #419C22×C61semidirect
495. #419C22×C61semidirect
496. #419C22×C61semidirect
498. #413C22×C61semidirect
499. C2×#101C22×C61semidirect
500. C2×#101C22×C61semidirect
501. #410C22×C61semidirect
502. #344C22×C61semidirect
503. #344C22×C61semidirect
504. #339C22×C61semidirect
505. #338C22×C61semidirect
506. C61#24474direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35862
C61×#30692
C61×#30392
C61×#30222
C2×C61×#4562
C61×#29012
C61×#20502
C61×#20492
C61×#20092
C61×#20052
C61×#19062
C61×#19022
C61×#18612
C61×#17962
#2447461