Finite Group Databasebeta

← C61×#33555 #29536988

Subgroups — C61×#33555 #29536988

Order 15616.

1146 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3540C211yesmaximal, characteristic, complemented
2C61×#3027C211yesmaximal, characteristic, complemented
3C61×#3025C211yesmaximal, characteristic, complemented
4C61×#3022C211yesmaximal, characteristic, complemented
5C61×#2199C214yesmaximal, complemented
6C61×#2197C214yesmaximal, complemented
7C61×#2129C211yesmaximal, characteristic, complemented
8C61×#2122C211yesmaximal, characteristic, complemented
9C61×#2120C211yesmaximal, characteristic, complemented
10C61×#585C2211yescharacteristic
11C2×#137×C61—21no—
12C61×H(3,𝔽4)C2212yescomplemented
13C61×#560—21no—
14C61×#559—21no—
15C61×#556—21no—
16C61×#555—21no—
17C61×#551C2212yescomplemented
18C61×#548—21no—
19C61×#546—21no—
20C61×#542—22no—
21C61×#542—21no—
22C61×#538—22no—
23C61×#536C2211yescharacteristic
24C61×#535—21no—
25C61×#535C2211yescharacteristic
26C61×#525—21no—
27C61×#525—21no—
28C61×#525C2211yescharacteristic
29C61×#458—21no—
30C61×#458C2212yes—
31C61×B(4,𝔽2)—21no—
32C61×B(4,𝔽2)—22no—
33C61×B(4,𝔽2)C2214yes—
34C61×B(4,𝔽2)C2212yes—
35C61×#456—22no—
36C61×#455C2214yes—
37C61×#421—21no—
38C61×#413C2211yescharacteristic
39C61×#410—21no—
40C61×#410—21no—
41C61×#410C2211yescharacteristic
42C61×#410C2211yescharacteristic
43C61×#354C2214yescomplemented
44C61×#352C2212yescomplemented
45C61×AΣL(1,𝔽16)C2212yescomplemented
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×C61C2311yescharacteristic
59C22×Q8×C61D411yescharacteristic, complemented
60C22×D4×C61D411yescharacteristic, complemented
61C23×C4×C61D411yescharacteristic, complemented
62#137×C61—24no—
63#137×C61—42no—
64C2×Q16×C61—41no—
65C2×SD16×C61—41no—
66C2×M16×C61—21no—
67C4⋊Q8×C61—21no—
68C4⋊Q8×C61D412yescomplemented
69#127×C61—21no—
70#127×C61—41no—
71#126×C61—22no—
72#126×C61—22no—
73#126×C61—22no—
74#124×C61—22no—
75#124×C61—21no—
76#124×C61—21no—
77#124×C61—22no—
78#124×C61—22no—
79#124×C61—22no—
80#124×C61—22no—
81#124×C61—41no—
82#124×C61C2312yes—
83#123×C61—22no—
84#123×C61—22no—
85#123×C61—21no—
86#123×C61—21no—
87#123×C61—22no—
88#123×C61—22no—
89#123×C61D411yescharacteristic, complemented
90#123×C61C2311yescharacteristic
91C22⋊Q8×C61—22no—
92C22⋊Q8×C61—21no—
93C22⋊Q8×C61—21no—
94C22⋊Q8×C61—22no—
95C22⋊Q8×C61—21no—
96C22⋊Q8×C61—21no—
97C22⋊Q8×C61—41no—
98#121×C61—22no—
99#121×C61—22no—
100#121×C61—22no—
101#121×C61—21no—
102#121×C61—21no—
103#121×C61—21no—
104#121×C61—21no—
105#121×C61—42no—
106#121×C61—41no—
107#120×C61—22no—
108#120×C61—22no—
109#120×C61—24no—
110#120×C61—22no—
111#120×C61D412yescomplemented
112#120×C61D411yescharacteristic, complemented
113#120×C61C2312yes—
114#120×C61C2311yescharacteristic
115C4×Q8×C61—21no—
116C4×Q8×C61—22no—
117C4×D4×C61—22no—
118C4×D4×C61—22no—
119C4×D4×C61—21no—
120C4×D4×C61—21no—
121C4×D4×C61—21no—
122C4×D4×C61—22no—
123C4×D4×C61—42no—
124#117×C61—21no—
125#117×C61—22no—
126#117×C61—21no—
127#117×C61—21no—
128#117×C61D411yescharacteristic, complemented
129#117×C61D411yescharacteristic, complemented
130#117×C61D411yescharacteristic, complemented
131C2×C22⋊C4×C61—22no—
132#104×C61—24no—
133#101×C61—21no—
134#100×C61C2312yes—
135#99×C61—21no—
136#99×C61—21no—
137#99×C61—24no—
138#99×C61—22no—
139#99×C61—22no—
140#99×C61C2312yes—
141#99×C61C2312yes—
142C24×C61C2×D412yes—
143C24×C61C2×D411yescharacteristic
144#41×C61—22no—
145#41×C61—22no—
146#41×C61—41no—
147#41×C61—41no—
148#41×C61—42no—
149#41×C61—41no—
150#41×C61—41no—
151#41×C61—41no—
152#41×C61—41no—
153#41×C61—41no—
154#41×C61—42no—
155#41×C61—42no—
156#41×C61—42no—
157#41×C61—41no—
158#41×C61—41no—
159#41×C61—41no—
160#41×C61—81no—
161#41×C61—81no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—22no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—41no—
168C2×Q8×C61—41no—
169C2×Q8×C61—42no—
170C2×Q8×C61C2×D412yes—
171C2×Q8×C61C2×D411yescharacteristic
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—22no—
176C2×D4×C61—22no—
177C2×D4×C61—22no—
178C2×D4×C61—22no—
179C2×D4×C61—21no—
180C2×D4×C61—22no—
181C2×D4×C61—21no—
182C2×D4×C61—22no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—41no—
186C2×D4×C61—41no—
187C2×D4×C61—42no—
188C2×D4×C61—42no—
189C2×D4×C61—42no—
190C2×D4×C61—41no—
191C2×D4×C61—42no—
192C2×D4×C61—44no—
193C2×D4×C61C2×D411yescharacteristic
194C2×D4×C61C2×D411yescharacteristic
195C2×D4×C61C2411yescharacteristic
196C22×C4×C61—22no—
197C22×C4×C61—22no—
198C22×C4×C61—22no—
199C22×C4×C61—22no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—41no—
204C22×C4×C61—41no—
205C22×C4×C61—41no—
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210Q16×C61—44no—
211SD16×C61—44no—
212M16×C61—22no—
213M16×C61—41no—
214C2×C8×C61—41no—
215C4⋊C4×C61—22no—
216C4⋊C4×C61—22no—
217C4⋊C4×C61—22no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—22no—
221C4⋊C4×C61—22no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—41no—
226C4⋊C4×C61—41no—
227C4⋊C4×C61—42no—
228C22⋊C4×C61—22no—
229C22⋊C4×C61—22no—
230C22⋊C4×C61—22no—
231C22⋊C4×C61—22no—
232C22⋊C4×C61—22no—
233C22⋊C4×C61—22no—
234C22⋊C4×C61—21no—
235C22⋊C4×C61—21no—
236C22⋊C4×C61—21no—
237C22⋊C4×C61—22no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—21no—
240C22⋊C4×C61—22no—
241C22⋊C4×C61—22no—
242C22⋊C4×C61—21no—
243C22⋊C4×C61—22no—
244C22⋊C4×C61—22no—
245C22⋊C4×C61—42no—
246C22⋊C4×C61—44no—
247C22⋊C4×C61—42no—
248C22⋊C4×C61C2×D412yes—
249C22⋊C4×C61C2×D411yescharacteristic
250C22⋊C4×C61C2×D411yescharacteristic
251C42×C61—22no—
252C42×C61—22no—
253C42×C61—21no—
254C42×C61—21no—
255C42×C61—41no—
256C42×C61—41no—
257C42×C61C2×D412yes—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—21no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—42no—
265C23×C61—81no—
266C23×C61—82no—
267C23×C61#12011yescharacteristic
268C23×C61C22×D411yescharacteristic
269C23×C61C22×D411yescharacteristic
270Q8×C61—22no—
271Q8×C61—41no—
272Q8×C61—41no—
273Q8×C61—41no—
274Q8×C61—42no—
275Q8×C61—41no—
276Q8×C61—41no—
277Q8×C61—41no—
278Q8×C61—82no—
279D4×C61—22no—
280D4×C61—41no—
281D4×C61—41no—
282D4×C61—41no—
283D4×C61—41no—
284D4×C61—41no—
285D4×C61—42no—
286D4×C61—42no—
287D4×C61—42no—
288D4×C61—42no—
289D4×C61—41no—
290D4×C61—41no—
291D4×C61—41no—
292D4×C61—81no—
293D4×C61—81no—
294D4×C61—82no—
295D4×C61—82no—
296D4×C61—82no—
297D4×C61—81no—
298D4×C61—82no—
299D4×C61—84no—
300D4×C61—164no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—21no—
310C2×C4×C61—22no—
311C2×C4×C61—21no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—21no—
315C2×C4×C61—42no—
316C2×C4×C61—42no—
317C2×C4×C61—42no—
318C2×C4×C61—41no—
319C2×C4×C61—42no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—42no—
324C2×C4×C61—42no—
325C2×C4×C61—81no—
326C2×C4×C61—81no—
327C2×C4×C61—82no—
328C2×C4×C61—82no—
329C2×C4×C61#12011yescharacteristic
330C2×C4×C61#12011yescharacteristic
331C2×C4×C61#12011yescharacteristic
332C2×C4×C61C22×D411yescharacteristic
333C8×C61—42no—
334#33555C6111yesmaximal, characteristic, direct product factor, Sylow
335C22×C61—21no—
336C22×C61—21no—
337C22×C61—21no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—42no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—41no—
348C22×C61—42no—
349C22×C61—82no—
350C22×C61—82no—
351C22×C61—84no—
352C22×C61—81no—
353C22×C61—161no—
354C22×C61C2×#12011yescharacteristic
355C4×C61—21no—
356C4×C61—21no—
357C4×C61—21no—
358C4×C61—41no—
359C4×C61—42no—
360C4×C61—42no—
361C4×C61—41no—
362C4×C61—42no—
363C4×C61—41no—
364C4×C61—42no—
365C4×C61—82no—
366C4×C61—82no—
367C4×C61B(4,𝔽2)11yescharacteristic
368C4×C61B(4,𝔽2)11yescharacteristic
369#3540C2×C6111yescharacteristic, complemented
370#3027C2×C6111yescharacteristic, complemented
371#3025C2×C6111yescharacteristic, complemented
372#3022C2×C6111yescharacteristic, complemented
373#2199C2×C6114yescomplemented
374#2197C2×C6114yescomplemented
375#2129C2×C6111yescharacteristic, complemented
376#2122C2×C6111yescharacteristic, complemented
377#2120C2×C6111yescharacteristic, complemented
378C2×C61—21no—
379C2×C61—41no—
380C2×C61—41no—
381C2×C61—41no—
382C2×C61—81no—
383C2×C61—82no—
384C2×C61—82no—
385C2×C61C2×B(4,𝔽2)11yescharacteristic
386#585C22×C6111yescharacteristic
387C2×#137—21no—
388H(3,𝔽4)C22×C6112yescomplemented
389#560—21no—
390#559—21no—
391#556—21no—
392#555—21no—
393#551C22×C6112yescomplemented
394#548—21no—
395#546—21no—
396#542—22no—
397#542—21no—
398#538—22no—
399#536C22×C6111yescharacteristic
400#535—21no—
401#535C22×C6111yescharacteristic
402#525—21no—
403#525—21no—
404#525C22×C6111yescharacteristic
405#458—21no—
406#458C22×C6112yes—
407B(4,𝔽2)—21no—
408B(4,𝔽2)—22no—
409B(4,𝔽2)C22×C6114yes—
410B(4,𝔽2)C22×C6112yes—
411#456—22no—
412#455C22×C6114yes—
413#421—21no—
414#413C22×C6111yescharacteristic
415#410—21no—
416#410—21no—
417#410C22×C6111yescharacteristic
418#410C22×C6111yescharacteristic
419#354C22×C6114yescomplemented
420#352C22×C6112yescomplemented
421AΣL(1,𝔽16)C22×C6112yescomplemented
422AΣL(1,𝔽16)C22×C6114yescomplemented
423C61#3355511yescharacteristic, direct product factor, Sylow
4242−1+4—21no—
4252−1+4—41no—
426H(5,𝔽2)—21no—
427H(5,𝔽2)—21no—
428H(5,𝔽2)—41no—
429H(5,𝔽2)C23×C6112yes—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—42no—
435C2×#41C23×C6111yescharacteristic
436C22×Q8D4×C6111yescharacteristic, complemented
437C22×D4D4×C6111yescharacteristic, complemented
438C23×C4D4×C6111yescharacteristic, complemented
439#137—24no—
440#137—42no—
441C2×Q16—41no—
442C2×SD16—41no—
443C2×M16—21no—
444C4⋊Q8—21no—
445C4⋊Q8D4×C6112yescomplemented
446#127—21no—
447#127—41no—
448#126—22no—
449#126—22no—
450#126—22no—
451#124—22no—
452#124—21no—
453#124—21no—
454#124—22no—
455#124—22no—
456#124—22no—
457#124—22no—
458#124—41no—
459#124C23×C6112yes—
460#123—22no—
461#123—22no—
462#123—21no—
463#123—21no—
464#123—22no—
465#123—22no—
466#123D4×C6111yescharacteristic, complemented
467#123C23×C6111yescharacteristic
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—22no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—41no—
475#121—21no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—42no—
483#121—41no—
484#120—22no—
485#120—22no—
486#120—22no—
487#120—24no—
488#120D4×C6111yescharacteristic, complemented
489#120D4×C6112yescomplemented
490#120C23×C6111yescharacteristic
491#120C23×C6112yes—
492C4×Q8—21no—
493C4×Q8—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—21no—
497C4×D4—22no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4—42no—
501#117—21no—
502#117—22no—
503#117—21no—
504#117—21no—
505#117D4×C6111yescharacteristic, complemented
506#117D4×C6111yescharacteristic, complemented
507#117D4×C6111yescharacteristic, complemented
508C2×C22⋊C4—22no—
509#104—24no—
510#101—21no—
511#100C23×C6112yes—
512#99—21no—
513#99—21no—
514#99—24no—
515#99—22no—
516#99—22no—
517#99C23×C6112yes—
518#99C23×C6112yes—
519C24C2×D4×C6112yes—
520C24C2×D4×C6111yescharacteristic
521#41—22no—
522#41—22no—
523#41—41no—
524#41—41no—
525#41—42no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—42no—
532#41—42no—
533#41—42no—
534#41—41no—
535#41—41no—
536#41—41no—
537#41—81no—
538#41—81no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—22no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—42no—
547C2×Q8C2×D4×C6112yes—
548C2×Q8C2×D4×C6111yescharacteristic
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—41no—
568C2×D4—42no—
569C2×D4—44no—
570C2×D4C2×D4×C6111yescharacteristic
571C2×D4C2×D4×C6111yescharacteristic
572C2×D4C24×C6111yescharacteristic
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4C2×D4×C6111yescharacteristic
584C22×C4C2×D4×C6111yescharacteristic
585C22×C4C2×D4×C6111yescharacteristic
586C22×C4C2×D4×C6111yescharacteristic
587Q16—44no—
588SD16—44no—
589M16—22no—
590M16—41no—
591C2×C8—41no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—42no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—21no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4—42no—
625C22⋊C4C2×D4×C6112yes—
626C22⋊C4C2×D4×C6111yescharacteristic
627C22⋊C4C2×D4×C6111yescharacteristic
628C42—22no—
629C42—22no—
630C42—21no—
631C42—21no—
632C42—41no—
633C42—41no—
634C42C2×D4×C6112yes—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—21no—
639C23—41no—
640C23—41no—
641C23—42no—
642C23—81no—
643C23—82no—
644C23#120×C6111yescharacteristic
645C23C22×D4×C6111yescharacteristic
646C23C22×D4×C6111yescharacteristic
647Q8—22no—
648Q8—41no—
649Q8—42no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—82no—
656D4—22no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—81no—
670D4—81no—
671D4—82no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—82no—
676D4—84no—
677D4—164no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4#120×C6111yescharacteristic
707C2×C4#120×C6111yescharacteristic
708C2×C4#120×C6111yescharacteristic
709C2×C4C22×D4×C6111yescharacteristic
710C8—42no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—42no—
718C22—41no—
719C22—41no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—82no—
726C22—82no—
727C22—84no—
728C22—81no—
729C22—161no—
730C22C2×#120×C6111yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—41no—
735C4—42no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—42no—
741C4—82no—
742C4—82no—
743C4C61×B(4,𝔽2)11yescharacteristic
744C4C61×B(4,𝔽2)11yescharacteristic
745C2—21no—
746C2—41no—
747C2—41no—
748C2—41no—
749C2—81no—
750C2—82no—
751C2—82no—
752C2C2×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×#3540C2semidirect
2. C61×#3027C2semidirect
3. C61×#3025C2semidirect
4. C61×#3022C2semidirect
5. C61×#2199C2semidirect
6. C61×#2197C2semidirect
7. C61×#2129C2semidirect
8. C61×#2122C2semidirect
9. C61×#2120C2semidirect
12. C61×H(3,𝔽4)C22semidirect
17. C61×#551C22semidirect
43. C61×#354C22semidirect
44. C61×#352C22semidirect
45. C61×AΣL(1,𝔽16)C22semidirect
46. C61×AΣL(1,𝔽16)C22semidirect
59. C22×Q8×C61D4semidirect
60. C22×D4×C61D4semidirect
61. C23×C4×C61D4semidirect
68. C4⋊Q8×C61D4semidirect
89. #123×C61D4semidirect
111. #120×C61D4semidirect
112. #120×C61D4semidirect
128. #117×C61D4semidirect
129. #117×C61D4semidirect
130. #117×C61D4semidirect
334. #33555C61direct (N × H)
369. #3540C2×C61semidirect
370. #3027C2×C61semidirect
371. #3025C2×C61semidirect
372. #3022C2×C61semidirect
373. #2199C2×C61semidirect
374. #2197C2×C61semidirect
375. #2129C2×C61semidirect
376. #2122C2×C61semidirect
377. #2120C2×C61semidirect
388. H(3,𝔽4)C22×C61semidirect
393. #551C22×C61semidirect
419. #354C22×C61semidirect
420. #352C22×C61semidirect
421. AΣL(1,𝔽16)C22×C61semidirect
422. AΣL(1,𝔽16)C22×C61semidirect
423. C61#33555direct (N × H)
436. C22×Q8D4×C61semidirect
437. C22×D4D4×C61semidirect
438. C23×C4D4×C61semidirect
445. C4⋊Q8D4×C61semidirect
466. #123D4×C61semidirect
488. #120D4×C61semidirect
489. #120D4×C61semidirect
505. #117D4×C61semidirect
506. #117D4×C61semidirect
507. #117D4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#35402
C61×#30272
C61×#30252
C61×#30222
C61×#21992
C61×#21972
C61×#21292
C61×#21222
C61×#21202
#3355561