Finite Group Databasebeta

← C61×#33560 #29536993

Subgroups — C61×#33560 #29536993

Order 15616.

1132 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3551C211yesmaximal, characteristic, complemented
2C61×#3028C211yesmaximal, characteristic, complemented
3C61×#3027C211yesmaximal, characteristic, complemented
4C61×#3018C211yesmaximal, characteristic, complemented
5C61×#2200C214yesmaximal, complemented
6C61×#2197C214yesmaximal, complemented
7C61×#2126C211yesmaximal, characteristic, complemented
8C61×#2123C211yesmaximal, characteristic, complemented
9C61×#2122C211yesmaximal, characteristic, complemented
10C61×#585C2211yescharacteristic
11C61×#575—21no—
12C61×#563—21no—
13C61×#560C2212yescomplemented
14C61×#555—21no—
15C61×#553—21no—
16C61×#552—21no—
17C61×#551C2212yescomplemented
18C61×#548—21no—
19C61×#546—21no—
20C61×#540—22no—
21C61×#538—22no—
22C61×#537—21no—
23C61×#536—21no—
24C61×#536C2211yescharacteristic
25C61×#535—21no—
26C61×#535C2211yescharacteristic
27C61×#532C2211yescharacteristic
28C61×#529—21no—
29C61×#458—22no—
30C61×#458C2214yes—
31C61×B(4,𝔽2)—22no—
32C61×B(4,𝔽2)C2214yes—
33C61×#456—21no—
34C61×#455C2212yes—
35C61×#454—21no—
36C61×#453C2212yes—
37C2×#104×C61—21no—
38C61×#413C2211yescharacteristic
39C61×#410—21no—
40C61×#410—21no—
41C61×#410C2211yescharacteristic
42C61×#410C2211yescharacteristic
43C61×#354C2212yescomplemented
44C61×#353C2212yescomplemented
45C61×#352C2214yescomplemented
46C61×AΣL(1,𝔽16)C2214yescomplemented
472−1+4×C61—21no—
482−1+4×C61—41no—
49H(5,𝔽2)×C61—21no—
50H(5,𝔽2)×C61—21no—
51H(5,𝔽2)×C61—41no—
52H(5,𝔽2)×C61C2312yes—
53C2×#41×C61—21no—
54C2×#41×C61—21no—
55C2×#41×C61—21no—
56C2×#41×C61—21no—
57C2×#41×C61—42no—
58C2×#41×C61D411yescharacteristic, complemented
59C2×#41×C61C2311yescharacteristic
60C22×Q8×C61D411yescharacteristic, complemented
61C22×D4×C61D411yescharacteristic
62#137×C61—22no—
63#137×C61—41no—
64AGL(1,ℤ/8)×C61—22no—
65AGL(1,ℤ/8)×C61—41no—
66#135×C61—42no—
67C2×M16×C61—21no—
68C4⋊Q8×C61—21no—
69C4⋊Q8×C61—41no—
70C4⋊Q8×C61D411yescharacteristic, complemented
71#127×C61—21no—
72#127×C61—41no—
73#127×C61C2311yescharacteristic
74#126×C61—22no—
75#126×C61—22no—
76#126×C61—22no—
77#125×C61—22no—
78#125×C61—21no—
79#124×C61—22no—
80#124×C61—21no—
81#124×C61—21no—
82#124×C61—21no—
83#124×C61—41no—
84#124×C61—41no—
85#124×C61D411yescharacteristic, complemented
86#124×C61C2311yescharacteristic
87#123×C61—22no—
88#123×C61—22no—
89#123×C61—22no—
90#123×C61—22no—
91#123×C61—24no—
92#123×C61D412yescomplemented
93#123×C61C2312yes—
94C22⋊Q8×C61—21no—
95C22⋊Q8×C61—22no—
96C22⋊Q8×C61—22no—
97C22⋊Q8×C61—21no—
98C22⋊Q8×C61—21no—
99C22⋊Q8×C61—42no—
100#121×C61—22no—
101#121×C61—22no—
102#121×C61—21no—
103#121×C61—22no—
104#121×C61—21no—
105#121×C61—21no—
106#121×C61—22no—
107#121×C61—21no—
108#121×C61—21no—
109#121×C61—22no—
110#121×C61—22no—
111#121×C61—42no—
112#120×C61—22no—
113#120×C61—24no—
114#120×C61D412yes—
115#120×C61C2312yes—
116C4×Q8×C61—21no—
117C4×D4×C61—22no—
118C4×D4×C61—22no—
119C4×D4×C61—21no—
120C4×D4×C61—21no—
121C4×D4×C61—21no—
122C4×D4×C61—22no—
123#117×C61—22no—
124#117×C61—22no—
125#117×C61—21no—
126#117×C61—21no—
127#117×C61D411yescharacteristic
128#117×C61D411yescharacteristic, complemented
129C2×C4⋊C4×C61—21no—
130C2×C22⋊C4×C61—22no—
131C2×C42×C61D411yescharacteristic, complemented
132#104×C61—22no—
133#104×C61—22no—
134#101×C61—21no—
135#100×C61C2312yes—
136#99×C61—21no—
137#99×C61—21no—
138#99×C61—24no—
139#99×C61—24no—
140#99×C61C2312yes—
141#99×C61C2312yes—
142C24×C61C2×D412yes—
143#41×C61—22no—
144#41×C61—22no—
145#41×C61—41no—
146#41×C61—41no—
147#41×C61—42no—
148#41×C61—41no—
149#41×C61—41no—
150#41×C61—41no—
151#41×C61—41no—
152#41×C61—41no—
153#41×C61—42no—
154#41×C61—42no—
155#41×C61—41no—
156#41×C61—41no—
157#41×C61—42no—
158#41×C61—41no—
159#41×C61—41no—
160#41×C61—41no—
161#41×C61—81no—
162#41×C61—81no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×Q8×C61—41no—
169C2×Q8×C61—41no—
170C2×Q8×C61—42no—
171C2×Q8×C61C2×D411yescharacteristic
172C2×Q8×C61C2×D411yescharacteristic
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—22no—
177C2×D4×C61—22no—
178C2×D4×C61—22no—
179C2×D4×C61—22no—
180C2×D4×C61—22no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—22no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—41no—
188C2×D4×C61—41no—
189C2×D4×C61—42no—
190C2×D4×C61—42no—
191C2×D4×C61—42no—
192C2×D4×C61—41no—
193C2×D4×C61—44no—
194C2×D4×C61C2×D411yescharacteristic
195C2×D4×C61C2×D411yescharacteristic
196C2×D4×C61C2×D411yescharacteristic
197C2×D4×C61C2411yescharacteristic
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—22no—
201C22×C4×C61—22no—
202C22×C4×C61—22no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—41no—
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D412yes—
210Q16×C61—42no—
211SD16×C61—42no—
212SD16×C61—42no—
213D8×C61—42no—
214M16×C61—22no—
215M16×C61—41no—
216C2×C8×C61—41no—
217C4⋊C4×C61—22no—
218C4⋊C4×C61—22no—
219C4⋊C4×C61—22no—
220C4⋊C4×C61—22no—
221C4⋊C4×C61—22no—
222C4⋊C4×C61—22no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—22no—
228C4⋊C4×C61—41no—
229C4⋊C4×C61—41no—
230C4⋊C4×C61—44no—
231C22⋊C4×C61—22no—
232C22⋊C4×C61—22no—
233C22⋊C4×C61—22no—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—22no—
236C22⋊C4×C61—22no—
237C22⋊C4×C61—21no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—21no—
240C22⋊C4×C61—21no—
241C22⋊C4×C61—21no—
242C22⋊C4×C61—22no—
243C22⋊C4×C61—22no—
244C22⋊C4×C61—22no—
245C22⋊C4×C61—22no—
246C22⋊C4×C61—44no—
247C22⋊C4×C61—44no—
248C22⋊C4×C61C2×D412yes—
249C22⋊C4×C61C2×D412yes—
250C42×C61—22no—
251C42×C61—21no—
252C42×C61—21no—
253C42×C61—21no—
254C42×C61—41no—
255C42×C61—41no—
256C42×C61C2×D411yescharacteristic
257C42×C61C2×D411yescharacteristic
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—21no—
262C23×C61—41no—
263C23×C61—42no—
264C23×C61—82no—
265C23×C61#12011yescharacteristic
266C23×C61C22×D411yescharacteristic
267C23×C61C22×D411yescharacteristic
268Q8×C61—22no—
269Q8×C61—41no—
270Q8×C61—41no—
271Q8×C61—41no—
272Q8×C61—41no—
273Q8×C61—41no—
274Q8×C61—41no—
275Q8×C61—41no—
276Q8×C61—81no—
277D4×C61—22no—
278D4×C61—41no—
279D4×C61—41no—
280D4×C61—41no—
281D4×C61—41no—
282D4×C61—41no—
283D4×C61—41no—
284D4×C61—42no—
285D4×C61—42no—
286D4×C61—42no—
287D4×C61—42no—
288D4×C61—41no—
289D4×C61—41no—
290D4×C61—41no—
291D4×C61—81no—
292D4×C61—81no—
293D4×C61—82no—
294D4×C61—82no—
295D4×C61—82no—
296D4×C61—81no—
297D4×C61—81no—
298D4×C61—82no—
299D4×C61—164no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—21no—
309C2×C4×C61—22no—
310C2×C4×C61—21no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—21no—
314C2×C4×C61—42no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—41no—
318C2×C4×C61—42no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—42no—
322C2×C4×C61—42no—
323C2×C4×C61—42no—
324C2×C4×C61—82no—
325C2×C4×C61—81no—
326C2×C4×C61—82no—
327C2×C4×C61—82no—
328C2×C4×C61#12011yescharacteristic
329C2×C4×C61#12011yescharacteristic
330C2×C4×C61#12011yescharacteristic
331C2×C4×C61C22×D411yescharacteristic
332C8×C61—42no—
333#33560C6111yesmaximal, characteristic, direct product factor, Sylow
334C22×C61—21no—
335C22×C61—21no—
336C22×C61—21no—
337C22×C61—41no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—42no—
342C22×C61—41no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—41no—
346C22×C61—42no—
347C22×C61—82no—
348C22×C61—84no—
349C22×C61—82no—
350C22×C61—161no—
351C22×C61C2×#12011yescharacteristic
352C4×C61—21no—
353C4×C61—21no—
354C4×C61—21no—
355C4×C61—41no—
356C4×C61—42no—
357C4×C61—42no—
358C4×C61—41no—
359C4×C61—42no—
360C4×C61—41no—
361C4×C61—42no—
362C4×C61—82no—
363C4×C61—82no—
364C4×C61B(4,𝔽2)11yescharacteristic
365C4×C61B(4,𝔽2)11yescharacteristic
366#3551C2×C6111yescharacteristic, complemented
367#3028C2×C6111yescharacteristic, complemented
368#3027C2×C6111yescharacteristic, complemented
369#3018C2×C6111yescharacteristic, complemented
370#2200C2×C6114yescomplemented
371#2197C2×C6114yescomplemented
372#2126C2×C6111yescharacteristic, complemented
373#2123C2×C6111yescharacteristic, complemented
374#2122C2×C6111yescharacteristic, complemented
375C2×C61—21no—
376C2×C61—41no—
377C2×C61—41no—
378C2×C61—41no—
379C2×C61—81no—
380C2×C61—82no—
381C2×C61—82no—
382C2×C61C2×B(4,𝔽2)11yescharacteristic
383#585C22×C6111yescharacteristic
384#575—21no—
385#563—21no—
386#560C22×C6112yescomplemented
387#555—21no—
388#553—21no—
389#552—21no—
390#551C22×C6112yescomplemented
391#548—21no—
392#546—21no—
393#540—22no—
394#538—22no—
395#537—21no—
396#536—21no—
397#536C22×C6111yescharacteristic
398#535—21no—
399#535C22×C6111yescharacteristic
400#532C22×C6111yescharacteristic
401#529—21no—
402#458—22no—
403#458C22×C6114yes—
404B(4,𝔽2)—22no—
405B(4,𝔽2)C22×C6114yes—
406#456—21no—
407#455C22×C6112yes—
408#454—21no—
409#453C22×C6112yes—
410C2×#104—21no—
411#413C22×C6111yescharacteristic
412#410—21no—
413#410—21no—
414#410C22×C6111yescharacteristic
415#410C22×C6111yescharacteristic
416#354C22×C6112yescomplemented
417#353C22×C6112yescomplemented
418#352C22×C6114yescomplemented
419AΣL(1,𝔽16)C22×C6114yescomplemented
420C61#3356011yescharacteristic, direct product factor, Sylow
4212−1+4—21no—
4222−1+4—41no—
423H(5,𝔽2)—21no—
424H(5,𝔽2)—21no—
425H(5,𝔽2)—41no—
426H(5,𝔽2)C23×C6112yes—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—42no—
432C2×#41D4×C6111yescharacteristic, complemented
433C2×#41C23×C6111yescharacteristic
434C22×Q8D4×C6111yescharacteristic, complemented
435C22×D4D4×C6111yescharacteristic
436#137—22no—
437#137—41no—
438AGL(1,ℤ/8)—22no—
439AGL(1,ℤ/8)—41no—
440#135—42no—
441C2×M16—21no—
442C4⋊Q8—21no—
443C4⋊Q8—41no—
444C4⋊Q8D4×C6111yescharacteristic, complemented
445#127—21no—
446#127—41no—
447#127C23×C6111yescharacteristic
448#126—22no—
449#126—22no—
450#126—22no—
451#125—21no—
452#125—22no—
453#124—21no—
454#124—22no—
455#124—21no—
456#124—21no—
457#124—41no—
458#124—41no—
459#124D4×C6111yescharacteristic, complemented
460#124C23×C6111yescharacteristic
461#123—22no—
462#123—22no—
463#123—22no—
464#123—22no—
465#123—24no—
466#123D4×C6112yescomplemented
467#123C23×C6112yes—
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—42no—
474#121—22no—
475#121—22no—
476#121—21no—
477#121—22no—
478#121—21no—
479#121—21no—
480#121—22no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—42no—
486#120—22no—
487#120—24no—
488#120D4×C6112yes—
489#120C23×C6112yes—
490C4×Q8—21no—
491C4×D4—22no—
492C4×D4—21no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—22no—
497#117—22no—
498#117—22no—
499#117—21no—
500#117—21no—
501#117D4×C6111yescharacteristic
502#117D4×C6111yescharacteristic, complemented
503C2×C4⋊C4—21no—
504C2×C22⋊C4—22no—
505C2×C42D4×C6111yescharacteristic, complemented
506#104—22no—
507#104—22no—
508#101—21no—
509#100C23×C6112yes—
510#99—21no—
511#99—21no—
512#99—24no—
513#99—24no—
514#99C23×C6112yes—
515#99C23×C6112yes—
516C24C2×D4×C6112yes—
517#41—22no—
518#41—22no—
519#41—41no—
520#41—41no—
521#41—42no—
522#41—41no—
523#41—41no—
524#41—41no—
525#41—41no—
526#41—41no—
527#41—42no—
528#41—42no—
529#41—41no—
530#41—41no—
531#41—42no—
532#41—41no—
533#41—41no—
534#41—41no—
535#41—81no—
536#41—81no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—41no—
543C2×Q8—41no—
544C2×Q8—42no—
545C2×Q8C2×D4×C6111yescharacteristic
546C2×Q8C2×D4×C6111yescharacteristic
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—41no—
567C2×D4—44no—
568C2×D4C2×D4×C6111yescharacteristic
569C2×D4C2×D4×C6111yescharacteristic
570C2×D4C2×D4×C6111yescharacteristic
571C2×D4C24×C6111yescharacteristic
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—41no—
580C22×C4C2×D4×C6111yescharacteristic
581C22×C4C2×D4×C6111yescharacteristic
582C22×C4C2×D4×C6111yescharacteristic
583C22×C4C2×D4×C6112yes—
584Q16—42no—
585SD16—42no—
586SD16—42no—
587D8—42no—
588M16—22no—
589M16—41no—
590C2×C8—41no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—22no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—22no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—44no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—22no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4C2×D4×C6112yes—
623C22⋊C4C2×D4×C6112yes—
624C42—22no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—41no—
629C42—41no—
630C42C2×D4×C6111yescharacteristic
631C42C2×D4×C6111yescharacteristic
632C23—22no—
633C23—22no—
634C23—22no—
635C23—21no—
636C23—41no—
637C23—42no—
638C23—82no—
639C23#120×C6111yescharacteristic
640C23C22×D4×C6111yescharacteristic
641C23C22×D4×C6111yescharacteristic
642Q8—22no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—81no—
651D4—22no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—42no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4—81no—
667D4—82no—
668D4—82no—
669D4—82no—
670D4—81no—
671D4—81no—
672D4—82no—
673D4—164no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—82no—
699C2×C4—81no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4#120×C6111yescharacteristic
703C2×C4#120×C6111yescharacteristic
704C2×C4#120×C6111yescharacteristic
705C2×C4C22×D4×C6111yescharacteristic
706C8—42no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—42no—
715C22—41no—
716C22—42no—
717C22—42no—
718C22—41no—
719C22—42no—
720C22—82no—
721C22—84no—
722C22—82no—
723C22—161no—
724C22C2×#120×C6111yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—41no—
729C4—42no—
730C4—42no—
731C4—41no—
732C4—42no—
733C4—41no—
734C4—42no—
735C4—82no—
736C4—82no—
737C4C61×B(4,𝔽2)11yescharacteristic
738C4C61×B(4,𝔽2)11yescharacteristic
739C2—21no—
740C2—41no—
741C2—41no—
742C2—41no—
743C2—82no—
744C2—81no—
745C2—82no—
746C2C2×C61×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C61C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C61
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C61 ◁ C2×C4×C61 ◁ C2×#41×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3551C2semidirect
2. C61×#3028C2semidirect
3. C61×#3027C2semidirect
4. C61×#3018C2semidirect
5. C61×#2200C2semidirect
6. C61×#2197C2semidirect
7. C61×#2126C2semidirect
8. C61×#2123C2semidirect
9. C61×#2122C2semidirect
13. C61×#560C22semidirect
17. C61×#551C22semidirect
43. C61×#354C22semidirect
44. C61×#353C22semidirect
45. C61×#352C22semidirect
46. C61×AΣL(1,𝔽16)C22semidirect
58. C2×#41×C61D4semidirect
60. C22×Q8×C61D4semidirect
70. C4⋊Q8×C61D4semidirect
85. #124×C61D4semidirect
92. #123×C61D4semidirect
128. #117×C61D4semidirect
131. C2×C42×C61D4semidirect
333. #33560C61direct (N × H)
366. #3551C2×C61semidirect
367. #3028C2×C61semidirect
368. #3027C2×C61semidirect
369. #3018C2×C61semidirect
370. #2200C2×C61semidirect
371. #2197C2×C61semidirect
372. #2126C2×C61semidirect
373. #2123C2×C61semidirect
374. #2122C2×C61semidirect
386. #560C22×C61semidirect
390. #551C22×C61semidirect
416. #354C22×C61semidirect
417. #353C22×C61semidirect
418. #352C22×C61semidirect
419. AΣL(1,𝔽16)C22×C61semidirect
420. C61#33560direct (N × H)
432. C2×#41D4×C61semidirect
434. C22×Q8D4×C61semidirect
444. C4⋊Q8D4×C61semidirect
459. #124D4×C61semidirect
466. #123D4×C61semidirect
502. #117D4×C61semidirect
505. C2×C42D4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#35512
C61×#30282
C61×#30272
C61×#30182
C61×#22002
C61×#21972
C61×#21262
C61×#21232
C61×#21222
#3356061