Finite Group Databasebeta

← C2×C61×#2200 #29536981

Subgroups — C2×C61×#2200 #29536981

Order 15616.

1328 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#560C211yesmaximal, characteristic, complemented
2C2×C61×#458C211yesmaximal, characteristic, complemented
3C2×C61×B(4,𝔽2)C211yesmaximal, characteristic, complemented
4C2×C61×#453C211yesmaximal, characteristic, complemented
5C61×#2200C218yesmaximal, direct product factor
6C2×C61×#353C211yesmaximal, characteristic, complemented
7C2×C61×#352C211yesmaximal, characteristic, complemented
8C2×C61×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C61C2211yescharacteristic
10C2×AGL(1,ℤ/8)×C61—21no—
11C61×#560—22no—
12C61×#560—22no—
13C61×#560—22no—
14C61×#560C2214yescomplemented
15C2×#127×C61C2211yescharacteristic
16C2×#126×C61—21no—
17C2×#123×C61—21no—
18C2×#123×C61—21no—
19C2×#123×C61C2211yescharacteristic
20C2×#121×C61—21no—
21C2×#121×C61—21no—
22C2×#121×C61—21no—
23C2×#120×C61—21no—
24C2×#120×C61—21no—
25C2×#120×C61C2211yescharacteristic
26C61×#458—22no—
27C61×#458C2214yescomplemented
28C61×B(4,𝔽2)—22no—
29C61×B(4,𝔽2)C2214yescomplemented
30C61×#453—22no—
31C61×#453C2214yescomplemented
32C2×#104×C61—21no—
33C2×#100×C61C2211yescharacteristic
34C2×#99×C61—21no—
35C2×#99×C61—21no—
36C2×#99×C61C2211yescharacteristic
37C2×#99×C61C2211yescharacteristic
38C61×#353C2214yescomplemented
39C61×#352C2214yescomplemented
40C61×AΣL(1,𝔽16)C2214yescomplemented
41C25×C61D411yescharacteristic
42H(5,𝔽2)×C61—21no—
43H(5,𝔽2)×C61—21no—
44H(5,𝔽2)×C61—21no—
45H(5,𝔽2)×C61—42no—
46H(5,𝔽2)×C61C2312yes—
47C2×#41×C61—21no—
48C2×#41×C61—41no—
49C22×D4×C61—21no—
50C22×D4×C61—21no—
51C22×D4×C61—21no—
52C22×D4×C61—21no—
53C22×D4×C61—21no—
54C22×D4×C61—21no—
55C22×D4×C61—21no—
56C22×D4×C61—41no—
57C22×D4×C61—41no—
58C22×D4×C61D411yescharacteristic, complemented
59C22×D4×C61C2311yescharacteristic
60C23×C4×C61—21no—
61C23×C4×C61D411yescharacteristic, complemented
62AGL(1,ℤ/8)×C61—24no—
63AGL(1,ℤ/8)×C61—42no—
64C2×SD16×C61—41no—
65C2×D8×C61—41no—
66C2×M16×C61—21no—
67#127×C61—21no—
68#127×C61—21no—
69#127×C61D412yescomplemented
70#127×C61C2312yes—
71#126×C61—24no—
72#126×C61—24no—
73#123×C61—24no—
74#123×C61—21no—
75#123×C61—21no—
76#123×C61—24no—
77#123×C61—24no—
78#123×C61—42no—
79#123×C61D412yescomplemented
80#123×C61C2312yes—
81#121×C61—24no—
82#121×C61—24no—
83#121×C61—24no—
84#121×C61—24no—
85#121×C61—24no—
86#121×C61—24no—
87#120×C61—24no—
88#120×C61—24no—
89#120×C61—21no—
90#120×C61—21no—
91#120×C61—24no—
92#120×C61—42no—
93#120×C61D412yes—
94#120×C61C2312yes—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61—41no—
99C2×C22⋊C4×C61—21no—
100C2×C22⋊C4×C61—21no—
101C2×C22⋊C4×C61—21no—
102C2×C22⋊C4×C61—21no—
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61—41no—
107C2×C22⋊C4×C61—41no—
108C2×C22⋊C4×C61D411yescharacteristic
109C2×C22⋊C4×C61D411yescharacteristic, complemented
110C2×C42×C61D411yescharacteristic, complemented
111#104×C61—24no—
112#100×C61—21no—
113#100×C61C2312yes—
114#99×C61—21no—
115#99×C61—21no—
116#99×C61—24no—
117#99×C61—24no—
118#99×C61C2312yes—
119#99×C61C2312yes—
120C24×C61—21no—
121C24×C61—21no—
122C24×C61—21no—
123C24×C61—21no—
124C24×C61—21no—
125C24×C61—41no—
126C24×C61—41no—
127C24×C61—82no—
128C24×C61C2×D411yescharacteristic
129C24×C61C2×D411yescharacteristic
130C24×C61C2×D412yes—
131#41×C61—22no—
132#41×C61—22no—
133#41×C61—42no—
134#41×C61—41no—
135#41×C61—42no—
136#41×C61—42no—
137#41×C61—42no—
138#41×C61—41no—
139C2×Q8×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—22no—
142C2×D4×C61—22no—
143C2×D4×C61—22no—
144C2×D4×C61—22no—
145C2×D4×C61—24no—
146C2×D4×C61—24no—
147C2×D4×C61—22no—
148C2×D4×C61—22no—
149C2×D4×C61—22no—
150C2×D4×C61—22no—
151C2×D4×C61—22no—
152C2×D4×C61—22no—
153C2×D4×C61—21no—
154C2×D4×C61—41no—
155C2×D4×C61—41no—
156C2×D4×C61—41no—
157C2×D4×C61—41no—
158C2×D4×C61—42no—
159C2×D4×C61—42no—
160C2×D4×C61—41no—
161C2×D4×C61—41no—
162C2×D4×C61—41no—
163C2×D4×C61—41no—
164C2×D4×C61—42no—
165C2×D4×C61—42no—
166C2×D4×C61—41no—
167C2×D4×C61—41no—
168C2×D4×C61—41no—
169C2×D4×C61—44no—
170C2×D4×C61—82no—
171C2×D4×C61—82no—
172C2×D4×C61—82no—
173C2×D4×C61—82no—
174C2×D4×C61—81no—
175C2×D4×C61—81no—
176C2×D4×C61—84no—
177C2×D4×C61C2×D411yescharacteristic
178C2×D4×C61C2×D411yescharacteristic
179C2×D4×C61C2×D411yescharacteristic
180C2×D4×C61C2×D412yescomplemented
181C2×D4×C61C2411yescharacteristic
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—24no—
189C22×C4×C61—21no—
190C22×C4×C61—41no—
191C22×C4×C61—41no—
192C22×C4×C61—41no—
193C22×C4×C61—41no—
194C22×C4×C61—41no—
195C22×C4×C61—82no—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D412yescomplemented
198SD16×C61—44no—
199D8×C61—44no—
200M16×C61—22no—
201M16×C61—41no—
202C2×C8×C61—41no—
203C4⋊C4×C61—24no—
204C4⋊C4×C61—24no—
205C4⋊C4×C61—22no—
206C4⋊C4×C61—22no—
207C4⋊C4×C61—44no—
208C22⋊C4×C61—24no—
209C22⋊C4×C61—24no—
210C22⋊C4×C61—24no—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—21no—
213C22⋊C4×C61—21no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—22no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—22no—
219C22⋊C4×C61—44no—
220C22⋊C4×C61—41no—
221C22⋊C4×C61—41no—
222C22⋊C4×C61—44no—
223C22⋊C4×C61C2×D412yes—
224C22⋊C4×C61C2×D412yescomplemented
225C42×C61—21no—
226C42×C61C2×D412yescomplemented
227C23×C61—21no—
228C23×C61—21no—
229C23×C61—21no—
230C23×C61—21no—
231C23×C61—22no—
232C23×C61—22no—
233C23×C61—22no—
234C23×C61—22no—
235C23×C61—42no—
236C23×C61—42no—
237C23×C61—42no—
238C23×C61—42no—
239C23×C61—42no—
240C23×C61—42no—
241C23×C61—42no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—44no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—81no—
251C23×C61—82no—
252C23×C61—82no—
253C23×C61—84no—
254C23×C61—82no—
255C23×C61—82no—
256C23×C61—82no—
257C23×C61#12011yescharacteristic
258C23×C61#12011yescharacteristic
259C23×C61#12011yescharacteristic
260C23×C61C22×D411yescharacteristic
261C23×C61C22×D411yescharacteristic
262Q8×C61—22no—
263Q8×C61—41no—
264D4×C61—22no—
265D4×C61—41no—
266D4×C61—41no—
267D4×C61—41no—
268D4×C61—41no—
269D4×C61—42no—
270D4×C61—41no—
271D4×C61—42no—
272D4×C61—42no—
273D4×C61—42no—
274D4×C61—42no—
275D4×C61—42no—
276D4×C61—42no—
277D4×C61—81no—
278D4×C61—82no—
279D4×C61—82no—
280D4×C61—84no—
281D4×C61—82no—
282D4×C61—82no—
283D4×C61—82no—
284D4×C61—82no—
285D4×C61—84no—
286D4×C61—88no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—42no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—81no—
309C2×C4×C61—84no—
310C2×C4×C61—82no—
311C2×C4×C61—82no—
312C2×C4×C61#12011yescharacteristic
313C2×C4×C61C22×D411yescharacteristic
314C8×C61—42no—
315C2×#2200C6111yesmaximal, characteristic, direct product factor, Sylow
316C22×C61—22no—
317C22×C61—21no—
318C22×C61—21no—
319C22×C61—21no—
320C22×C61—21no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61—42no—
326C22×C61—42no—
327C22×C61—42no—
328C22×C61—42no—
329C22×C61—42no—
330C22×C61—42no—
331C22×C61—44no—
332C22×C61—42no—
333C22×C61—42no—
334C22×C61—42no—
335C22×C61—81no—
336C22×C61—81no—
337C22×C61—82no—
338C22×C61—82no—
339C22×C61—82no—
340C22×C61—82no—
341C22×C61—82no—
342C22×C61—84no—
343C22×C61—82no—
344C22×C61—82no—
345C22×C61—82no—
346C22×C61—161no—
347C22×C61—161no—
348C22×C61B(4,𝔽2)11yescharacteristic
349C22×C61B(4,𝔽2)11yescharacteristic
350C22×C61C2×#12011yescharacteristic
351C4×C61—21no—
352C4×C61—21no—
353C4×C61—42no—
354C4×C61—42no—
355C4×C61—42no—
356C4×C61—42no—
357C4×C61—42no—
358C4×C61—82no—
359C4×C61—82no—
360C2×#560C2×C6111yescharacteristic, complemented
361C2×#458C2×C6111yescharacteristic, complemented
362C2×B(4,𝔽2)C2×C6111yescharacteristic, complemented
363C2×#453C2×C6111yescharacteristic, complemented
364#2200C2×C6118yesdirect product factor
365C2×#353C2×C6111yescharacteristic, complemented
366C2×#352C2×C6111yescharacteristic, complemented
367C2×AΣL(1,𝔽16)C2×C6111yescharacteristic, complemented
368C2×C61—21no—
369C2×C61—21no—
370C2×C61—41no—
371C2×C61—41no—
372C2×C61—41no—
373C2×C61—41no—
374C2×C61—82no—
375C2×C61—82no—
376C2×C61—82no—
377C2×C61#220012yesdirect product factor
378C2×C61C2×B(4,𝔽2)11yescharacteristic
379C2×H(5,𝔽2)C22×C6111yescharacteristic
380C2×AGL(1,ℤ/8)—21no—
381#560—22no—
382#560—22no—
383#560—22no—
384#560C22×C6114yescomplemented
385C2×#127C22×C6111yescharacteristic
386C2×#126—21no—
387C2×#123—21no—
388C2×#123—21no—
389C2×#123C22×C6111yescharacteristic
390C2×#121—21no—
391C2×#121—21no—
392C2×#121—21no—
393C2×#120—21no—
394C2×#120—21no—
395C2×#120C22×C6111yescharacteristic
396#458—22no—
397#458C22×C6114yescomplemented
398B(4,𝔽2)—22no—
399B(4,𝔽2)C22×C6114yescomplemented
400#453—22no—
401#453C22×C6114yescomplemented
402C2×#104—21no—
403C2×#100C22×C6111yescharacteristic
404C2×#99—21no—
405C2×#99—21no—
406C2×#99C22×C6111yescharacteristic
407C2×#99C22×C6111yescharacteristic
408#353C22×C6114yescomplemented
409#352C22×C6114yescomplemented
410AΣL(1,𝔽16)C22×C6114yescomplemented
411C61C2×#220011yescharacteristic, direct product factor, Sylow
412C25D4×C6111yescharacteristic
413H(5,𝔽2)—21no—
414H(5,𝔽2)—21no—
415H(5,𝔽2)—21no—
416H(5,𝔽2)—42no—
417H(5,𝔽2)C23×C6112yes—
418C2×#41—21no—
419C2×#41—41no—
420C22×D4—21no—
421C22×D4—21no—
422C22×D4—21no—
423C22×D4—21no—
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—21no—
427C22×D4—41no—
428C22×D4—41no—
429C22×D4D4×C6111yescharacteristic, complemented
430C22×D4C23×C6111yescharacteristic
431C23×C4—21no—
432C23×C4D4×C6111yescharacteristic, complemented
433AGL(1,ℤ/8)—24no—
434AGL(1,ℤ/8)—42no—
435C2×SD16—41no—
436C2×D8—41no—
437C2×M16—21no—
438#127—21no—
439#127—21no—
440#127D4×C6112yescomplemented
441#127C23×C6112yes—
442#126—24no—
443#126—24no—
444#123—24no—
445#123—21no—
446#123—21no—
447#123—24no—
448#123—24no—
449#123—42no—
450#123D4×C6112yescomplemented
451#123C23×C6112yes—
452#121—24no—
453#121—24no—
454#121—24no—
455#121—24no—
456#121—24no—
457#121—24no—
458#120—24no—
459#120—24no—
460#120—21no—
461#120—21no—
462#120—24no—
463#120—42no—
464#120D4×C6112yes—
465#120C23×C6112yes—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—41no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—41no—
478C2×C22⋊C4—41no—
479C2×C22⋊C4D4×C6111yescharacteristic
480C2×C22⋊C4D4×C6111yescharacteristic, complemented
481C2×C42D4×C6111yescharacteristic, complemented
482#104—24no—
483#100—21no—
484#100C23×C6112yes—
485#99—21no—
486#99—21no—
487#99—24no—
488#99—24no—
489#99C23×C6112yes—
490#99C23×C6112yes—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—41no—
497C24—41no—
498C24—82no—
499C24C2×D4×C6111yescharacteristic
500C24C2×D4×C6111yescharacteristic
501C24C2×D4×C6112yes—
502#41—22no—
503#41—22no—
504#41—42no—
505#41—41no—
506#41—42no—
507#41—42no—
508#41—42no—
509#41—41no—
510C2×Q8—21no—
511C2×D4—21no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—21no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—41no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—41no—
538C2×D4—41no—
539C2×D4—41no—
540C2×D4—44no—
541C2×D4—82no—
542C2×D4—82no—
543C2×D4—82no—
544C2×D4—82no—
545C2×D4—81no—
546C2×D4—81no—
547C2×D4—84no—
548C2×D4C2×D4×C6111yescharacteristic
549C2×D4C2×D4×C6111yescharacteristic
550C2×D4C2×D4×C6111yescharacteristic
551C2×D4C2×D4×C6112yescomplemented
552C2×D4C24×C6111yescharacteristic
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—24no—
560C22×C4—21no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—82no—
567C22×C4C2×D4×C6111yescharacteristic
568C22×C4C2×D4×C6112yescomplemented
569SD16—44no—
570D8—44no—
571M16—22no—
572M16—41no—
573C2×C8—41no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—44no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C22⋊C4—24no—
582C22⋊C4—22no—
583C22⋊C4—21no—
584C22⋊C4—21no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—44no—
591C22⋊C4—41no—
592C22⋊C4—41no—
593C22⋊C4—44no—
594C22⋊C4C2×D4×C6112yes—
595C22⋊C4C2×D4×C6112yescomplemented
596C42—21no—
597C42C2×D4×C6112yescomplemented
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—44no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—81no—
622C23—82no—
623C23—82no—
624C23—82no—
625C23—84no—
626C23—82no—
627C23—82no—
628C23#120×C6111yescharacteristic
629C23#120×C6111yescharacteristic
630C23#120×C6111yescharacteristic
631C23C22×D4×C6111yescharacteristic
632C23C22×D4×C6111yescharacteristic
633Q8—22no—
634Q8—41no—
635D4—22no—
636D4—41no—
637D4—41no—
638D4—41no—
639D4—41no—
640D4—42no—
641D4—41no—
642D4—42no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—42no—
647D4—42no—
648D4—81no—
649D4—82no—
650D4—82no—
651D4—84no—
652D4—82no—
653D4—82no—
654D4—82no—
655D4—82no—
656D4—84no—
657D4—88no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—81no—
680C2×C4—84no—
681C2×C4—82no—
682C2×C4—82no—
683C2×C4#120×C6111yescharacteristic
684C2×C4C22×D4×C6111yescharacteristic
685C8—42no—
686C22—22no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—21no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—44no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—81no—
706C22—81no—
707C22—82no—
708C22—82no—
709C22—82no—
710C22—82no—
711C22—82no—
712C22—84no—
713C22—82no—
714C22—82no—
715C22—82no—
716C22—161no—
717C22—161no—
718C22C61×B(4,𝔽2)11yescharacteristic
719C22C61×B(4,𝔽2)11yescharacteristic
720C22C2×#120×C6111yescharacteristic
721C4—21no—
722C4—21no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—82no—
729C4—82no—
730C2—21no—
731C2—21no—
732C2—41no—
733C2—41no—
734C2—41no—
735C2—41no—
736C2—82no—
737C2—82no—
738C2—82no—
739C2C61×#220012yesdirect product factor
740C2C2×C61×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C61B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C61
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C61 ◁ C22×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#560C2semidirect
2. C2×C61×#458C2semidirect
3. C2×C61×B(4,𝔽2)C2semidirect
4. C2×C61×#453C2semidirect
5. C61×#2200C2direct (N × H)
6. C2×C61×#353C2semidirect
7. C2×C61×#352C2semidirect
8. C2×C61×AΣL(1,𝔽16)C2semidirect
14. C61×#560C22semidirect
27. C61×#458C22semidirect
29. C61×B(4,𝔽2)C22semidirect
31. C61×#453C22semidirect
38. C61×#353C22semidirect
39. C61×#352C22semidirect
40. C61×AΣL(1,𝔽16)C22semidirect
58. C22×D4×C61D4semidirect
61. C23×C4×C61D4semidirect
69. #127×C61D4semidirect
79. #123×C61D4semidirect
109. C2×C22⋊C4×C61D4semidirect
110. C2×C42×C61D4semidirect
180. C2×D4×C61C2×D4semidirect
197. C22×C4×C61C2×D4semidirect
224. C22⋊C4×C61C2×D4semidirect
226. C42×C61C2×D4semidirect
315. C2×#2200C61direct (N × H)
360. C2×#560C2×C61semidirect
361. C2×#458C2×C61semidirect
362. C2×B(4,𝔽2)C2×C61semidirect
363. C2×#453C2×C61semidirect
364. #2200C2×C61direct (N × H)
365. C2×#353C2×C61semidirect
366. C2×#352C2×C61semidirect
367. C2×AΣL(1,𝔽16)C2×C61semidirect
377. C2×C61#2200direct (N × H)
384. #560C22×C61semidirect
397. #458C22×C61semidirect
399. B(4,𝔽2)C22×C61semidirect
401. #453C22×C61semidirect
408. #353C22×C61semidirect
409. #352C22×C61semidirect
410. AΣL(1,𝔽16)C22×C61semidirect
411. C61C2×#2200direct (N × H)
429. C22×D4D4×C61semidirect
432. C23×C4D4×C61semidirect
440. #127D4×C61semidirect
450. #123D4×C61semidirect
480. C2×C22⋊C4D4×C61semidirect
481. C2×C42D4×C61semidirect
551. C2×D4C2×D4×C61semidirect
568. C22×C4C2×D4×C61semidirect
595. C22⋊C4C2×D4×C61semidirect
597. C42C2×D4×C61semidirect
739. C2C61×#2200direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#5602
C2×C61×#4582
C2×C61×B(4,𝔽2)2
C2×C61×#4532
C61×#22002
C2×C61×#3532
C2×C61×#3522
C2×C61×AΣL(1,𝔽16)2
C2×#220061