Finite Group Databasebeta

← C61×#25563 #29528996

Subgroups — C61×#25563 #29528996

Order 15616.

1608 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3490C211yesmaximal, characteristic, complemented
2C61×#2410C212yesmaximal, complemented
3C61×#2405C211yesmaximal, characteristic, complemented
4C61×#2062C211yesmaximal, characteristic, complemented
5C61×#2044C211yesmaximal, characteristic, complemented
6C61×#2029C211yesmaximal, characteristic, complemented
7C61×#2021C211yesmaximal, characteristic, complemented
8C61×#1898C212yesmaximal, complemented
9C61×#1889C212yesmaximal, complemented
10C61×#1867C212yesmaximal, complemented
11C2×C61×#342C211yesmaximal, characteristic, complemented
12C23×D4×C61C2211yescharacteristic
13C61×#551—22no—
14C61×#551—22no—
15C61×#546—22no—
16C61×#546—22no—
17C61×#543C2211yescharacteristic
18C61×#538—21no—
19C61×#538—21no—
20C61×#534C2211yescharacteristic
21C61×#525—21no—
22C61×#525—21no—
23C2×#123×C61—21no—
24C2×#121×C61—22no—
25C2×#120×C61C2212yes—
26C2×#120×C61C2212yes—
27C61×#518C2212yes—
28C22×C22⋊C4×C61C2211yescharacteristic
29C22×C22⋊C4×C61C2212yes—
30C2×#99×C61C2212yes—
31C2×#99×C61C2212yes—
32C61×#394—21no—
33C61×#394—21no—
34C61×#394—22no—
35C61×#392—22no—
36C61×#386—21no—
37C61×#386—22no—
38C61×#386C2212yes—
39C61×#385C2211yescharacteristic
40C61×#385C2212yes—
41C61×#385C2211yescharacteristic
42C61×#379C2211yescharacteristic
43C61×#379C2212yes—
44C61×#379C2211yescharacteristic
45C61×#379C2211yescharacteristic
46C61×#342C2211yescharacteristic
47C61×#342C2211yescharacteristic
48C61×#342C2212yes—
49C61×#342C2212yes—
50C61×#342C2212yes—
51C25×C61C2311yescharacteristic
52C25×C61C2311yescharacteristic
53C2×#41×C61—21no—
54C2×#41×C61—21no—
55C22×D4×C61—22no—
56C22×D4×C61—21no—
57C22×D4×C61—22no—
58C22×D4×C61—21no—
59C22×D4×C61—22no—
60C22×D4×C61—44no—
61C22×D4×C61D412yescomplemented
62C22×D4×C61D412yescomplemented
63C22×D4×C61C2312yes—
64C23×C4×C61—22no—
65C23×C4×C61D411yescharacteristic, complemented
66C23×C4×C61D411yescharacteristic, complemented
67C23×C4×C61C2311yescharacteristic
68#126×C61—22no—
69#126×C61—22no—
70#124×C61—22no—
71#124×C61—22no—
72#123×C61—22no—
73#123×C61—22no—
74#123×C61—22no—
75#123×C61—22no—
76#123×C61—22no—
77#123×C61—44no—
78C22⋊Q8×C61—21no—
79C22⋊Q8×C61—21no—
80C22⋊Q8×C61—21no—
81C22⋊Q8×C61—21no—
82C22⋊Q8×C61—22no—
83C22⋊Q8×C61—22no—
84#121×C61—22no—
85#121×C61—22no—
86#121×C61—21no—
87#121×C61—21no—
88#121×C61—21no—
89#121×C61—21no—
90#121×C61—48no—
91#120×C61—22no—
92#120×C61—22no—
93#120×C61—22no—
94#120×C61—22no—
95#120×C61—22no—
96#120×C61—24no—
97#120×C61—42no—
98C4×D4×C61—22no—
99C4×D4×C61—22no—
100C4×D4×C61—22no—
101C4×D4×C61—22no—
102C4×D4×C61—22no—
103C4×D4×C61—22no—
104#117×C61—21no—
105#117×C61—21no—
106#117×C61—22no—
107C2×C4⋊C4×C61—22no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61—21no—
110C2×C22⋊C4×C61—22no—
111C2×C22⋊C4×C61—22no—
112C2×C22⋊C4×C61—22no—
113C2×C22⋊C4×C61—24no—
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—22no—
116C2×C22⋊C4×C61—22no—
117C2×C22⋊C4×C61—22no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—22no—
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—22no—
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—42no—
126C2×C22⋊C4×C61D411yescharacteristic, complemented
127C2×C22⋊C4×C61D411yescharacteristic, complemented
128C2×C22⋊C4×C61D412yescomplemented
129C2×C22⋊C4×C61D412yescomplemented
130C2×C22⋊C4×C61C2312yes—
131C2×C22⋊C4×C61C2311yescharacteristic
132C2×C22⋊C4×C61C2311yescharacteristic
133C2×C22⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61C2312yes—
135C2×C22⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61C2312yes—
137#99×C61—24no—
138#99×C61—42no—
139#95×C61—22no—
140#95×C61—21no—
141#95×C61—21no—
142#95×C61—22no—
143C24×C61—22no—
144C24×C61—21no—
145C24×C61—21no—
146C24×C61—21no—
147C24×C61—22no—
148C24×C61—22no—
149C24×C61—21no—
150C24×C61—21no—
151C24×C61—42no—
152C24×C61—42no—
153C24×C61—81no—
154C24×C61—81no—
155C24×C61C2×D412yes—
156C24×C61C2×D411yescharacteristic
157C24×C61C2×D412yes—
158C24×C61C2×D412yes—
159C24×C61C2×D411yescharacteristic
160C24×C61C2411yescharacteristic
161#41×C61—82no—
162#41×C61—82no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×D4×C61—28no—
166C2×D4×C61—24no—
167C2×D4×C61—22no—
168C2×D4×C61—22no—
169C2×D4×C61—22no—
170C2×D4×C61—22no—
171C2×D4×C61—22no—
172C2×D4×C61—22no—
173C2×D4×C61—22no—
174C2×D4×C61—22no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—22no—
178C2×D4×C61—22no—
179C2×D4×C61—44no—
180C2×D4×C61—42no—
181C2×D4×C61—44no—
182C2×D4×C61—42no—
183C2×D4×C61—44no—
184C2×D4×C61—42no—
185C2×D4×C61—44no—
186C2×D4×C61—42no—
187C2×D4×C61—41no—
188C2×D4×C61—41no—
189C2×D4×C61—44no—
190C2×D4×C61—44no—
191C2×D4×C61—82no—
192C2×D4×C61—82no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—22no—
196C22×C4×C61—21no—
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—21no—
204C22×C4×C61—22no—
205C22×C4×C61—42no—
206C22×C4×C61—44no—
207C22×C4×C61—42no—
208C22×C4×C61—44no—
209C22×C4×C61—81no—
210C22×C4×C61—82no—
211C22×C4×C61C2×D412yes—
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D412yes—
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D412yes—
217C22×C4×C61C2×D411yescharacteristic
218C4⋊C4×C61—22no—
219C4⋊C4×C61—22no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—22no—
225C4⋊C4×C61—22no—
226C4⋊C4×C61—44no—
227C4⋊C4×C61—42no—
228C4⋊C4×C61—42no—
229C22⋊C4×C61—22no—
230C22⋊C4×C61—22no—
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—22no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—22no—
241C22⋊C4×C61—22no—
242C22⋊C4×C61—22no—
243C22⋊C4×C61—22no—
244C22⋊C4×C61—22no—
245C22⋊C4×C61—22no—
246C22⋊C4×C61—21no—
247C22⋊C4×C61—22no—
248C22⋊C4×C61—21no—
249C22⋊C4×C61—44no—
250C22⋊C4×C61—44no—
251C22⋊C4×C61—44no—
252C22⋊C4×C61—44no—
253C22⋊C4×C61—42no—
254C22⋊C4×C61—42no—
255C22⋊C4×C61—42no—
256C22⋊C4×C61—81no—
257C22⋊C4×C61—81no—
258C22⋊C4×C61—82no—
259C22⋊C4×C61—81no—
260C22⋊C4×C61#4114yescomplemented
261C42×C61—22no—
262C42×C61—22no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—22no—
266C23×C61—22no—
267C23×C61—22no—
268C23×C61—24no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—24no—
275C23×C61—22no—
276C23×C61—22no—
277C23×C61—22no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—42no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—42no—
285C23×C61—42no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—42no—
289C23×C61—41no—
290C23×C61—42no—
291C23×C61—42no—
292C23×C61—42no—
293C23×C61—42no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—42no—
298C23×C61—42no—
299C23×C61—84no—
300C23×C61—84no—
301C23×C61—82no—
302C23×C61—82no—
303C23×C61—82no—
304C23×C61—82no—
305C23×C61#12012yes—
306C23×C61#12011yescharacteristic
307C23×C61#12011yescharacteristic
308C23×C61C22×D411yescharacteristic
309C23×C61C22×D412yes—
310C23×C61C2×#4112yes—
311C23×C61H(5,𝔽2)11yescharacteristic
312C23×C612−1+411yescharacteristic
313Q8×C61—81no—
314Q8×C61—81no—
315D4×C61—44no—
316D4×C61—48no—
317D4×C61—44no—
318D4×C61—42no—
319D4×C61—42no—
320D4×C61—42no—
321D4×C61—42no—
322D4×C61—44no—
323D4×C61—44no—
324D4×C61—82no—
325D4×C61—82no—
326D4×C61—81no—
327D4×C61—81no—
328D4×C61—88no—
329C2×C4×C61—24no—
330C2×C4×C61—22no—
331C2×C4×C61—22no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—24no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—42no—
342C2×C4×C61—41no—
343C2×C4×C61—42no—
344C2×C4×C61—42no—
345C2×C4×C61—42no—
346C2×C4×C61—41no—
347C2×C4×C61—42no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—42no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—42no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—42no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—42no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—42no—
363C2×C4×C61—81no—
364C2×C4×C61—81no—
365C2×C4×C61—82no—
366C2×C4×C61—82no—
367C2×C4×C61—88no—
368#25563C6111yesmaximal, characteristic, direct product factor, Sylow
369C22×C61—21no—
370C22×C61—21no—
371C22×C61—22no—
372C22×C61—21no—
373C22×C61—22no—
374C22×C61—21no—
375C22×C61—21no—
376C22×C61—22no—
377C22×C61—21no—
378C22×C61—22no—
379C22×C61—21no—
380C22×C61—22no—
381C22×C61—42no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—44no—
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—44no—
388C22×C61—44no—
389C22×C61—42no—
390C22×C61—42no—
391C22×C61—44no—
392C22×C61—42no—
393C22×C61—42no—
394C22×C61—42no—
395C22×C61—42no—
396C22×C61—82no—
397C22×C61—81no—
398C22×C61—81no—
399C22×C61—82no—
400C22×C61—82no—
401C22×C61—82no—
402C22×C61—82no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61—82no—
406C22×C61—81no—
407C22×C61—81no—
408C22×C61B(4,𝔽2)12yes—
409C22×C61C2×#12011yescharacteristic
410C22×C61#53211yescharacteristic
411C22×C61#53711yescharacteristic
412C22×C61#54612yes—
413C22×C61#54712yes—
414C4×C61—44no—
415C4×C61—42no—
416C4×C61—42no—
417C4×C61—41no—
418C4×C61—41no—
419C4×C61—42no—
420C4×C61—41no—
421C4×C61—41no—
422C4×C61—42no—
423C4×C61—81no—
424C4×C61—81no—
425C4×C61—82no—
426#3490C2×C6111yescharacteristic, complemented
427#2410C2×C6112yescomplemented
428#2405C2×C6111yescharacteristic, complemented
429#2062C2×C6111yescharacteristic, complemented
430#2044C2×C6111yescharacteristic, complemented
431#2029C2×C6111yescharacteristic, complemented
432#2021C2×C6111yescharacteristic, complemented
433#1898C2×C6112yescomplemented
434#1889C2×C6112yescomplemented
435#1867C2×C6112yescomplemented
436C2×#342C2×C6111yescharacteristic, complemented
437C2×C61—22no—
438C2×C61—21no—
439C2×C61—21no—
440C2×C61—22no—
441C2×C61—22no—
442C2×C61—41no—
443C2×C61—42no—
444C2×C61—82no—
445C2×C61—82no—
446C2×C61#243011yescharacteristic
447C2×C61C2×B(4,𝔽2)11yescharacteristic
448C2×C61#302611yescharacteristic
449C23×D4C22×C6111yescharacteristic
450#551—22no—
451#551—22no—
452#546—22no—
453#546—22no—
454#543C22×C6111yescharacteristic
455#538—21no—
456#538—21no—
457#534C22×C6111yescharacteristic
458#525—21no—
459#525—21no—
460C2×#123—21no—
461C2×#121—22no—
462C2×#120C22×C6112yes—
463C2×#120C22×C6112yes—
464#518C22×C6112yes—
465C22×C22⋊C4C22×C6111yescharacteristic
466C22×C22⋊C4C22×C6112yes—
467C2×#99C22×C6112yes—
468C2×#99C22×C6112yes—
469#394—21no—
470#394—21no—
471#394—22no—
472#392—22no—
473#386—21no—
474#386—22no—
475#386C22×C6112yes—
476#385C22×C6112yes—
477#385C22×C6111yescharacteristic
478#385C22×C6111yescharacteristic
479#379C22×C6111yescharacteristic
480#379C22×C6112yes—
481#379C22×C6111yescharacteristic
482#379C22×C6111yescharacteristic
483#342C22×C6112yes—
484#342C22×C6111yescharacteristic
485#342C22×C6112yes—
486#342C22×C6112yes—
487#342C22×C6111yescharacteristic
488C61#2556311yescharacteristic, direct product factor, Sylow
489C25C23×C6111yescharacteristic
490C25C23×C6111yescharacteristic
491C2×#41—21no—
492C2×#41—21no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—44no—
499C22×D4D4×C6112yescomplemented
500C22×D4D4×C6112yescomplemented
501C22×D4C23×C6112yes—
502C23×C4—22no—
503C23×C4D4×C6111yescharacteristic, complemented
504C23×C4D4×C6111yescharacteristic, complemented
505C23×C4C23×C6111yescharacteristic
506#126—22no—
507#126—22no—
508#124—22no—
509#124—22no—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—22no—
514#123—22no—
515#123—44no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522#121—21no—
523#121—21no—
524#121—22no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—48no—
529#120—22no—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534#120—24no—
535#120—42no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—21no—
543#117—21no—
544#117—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4D4×C6111yescharacteristic, complemented
565C2×C22⋊C4D4×C6111yescharacteristic, complemented
566C2×C22⋊C4D4×C6112yescomplemented
567C2×C22⋊C4D4×C6112yescomplemented
568C2×C22⋊C4C23×C6112yes—
569C2×C22⋊C4C23×C6111yescharacteristic
570C2×C22⋊C4C23×C6111yescharacteristic
571C2×C22⋊C4C23×C6111yescharacteristic
572C2×C22⋊C4C23×C6111yescharacteristic
573C2×C22⋊C4C23×C6112yes—
574C2×C22⋊C4C23×C6112yes—
575#99—24no—
576#99—42no—
577#95—22no—
578#95—21no—
579#95—21no—
580#95—22no—
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—42no—
590C24—42no—
591C24—81no—
592C24—81no—
593C24C2×D4×C6112yes—
594C24C2×D4×C6111yescharacteristic
595C24C2×D4×C6112yes—
596C24C2×D4×C6112yes—
597C24C2×D4×C6111yescharacteristic
598C24C24×C6111yescharacteristic
599#41—82no—
600#41—82no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—82no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—81no—
648C22×C4—82no—
649C22×C4C2×D4×C6112yes—
650C22×C4C2×D4×C6111yescharacteristic
651C22×C4C2×D4×C6112yes—
652C22×C4C2×D4×C6111yescharacteristic
653C22×C4C2×D4×C6111yescharacteristic
654C22×C4C2×D4×C6112yes—
655C22×C4C2×D4×C6111yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C22⋊C4—81no—
698C22⋊C4#41×C6114yescomplemented
699C42—22no—
700C42—22no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—41no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23#120×C6112yes—
744C23#120×C6111yescharacteristic
745C23#120×C6111yescharacteristic
746C23C22×D4×C6111yescharacteristic
747C23C22×D4×C6112yes—
748C23C2×#41×C6112yes—
749C23H(5,𝔽2)×C6111yescharacteristic
750C232−1+4×C6111yescharacteristic
751Q8—81no—
752Q8—81no—
753D4—44no—
754D4—48no—
755D4—44no—
756D4—42no—
757D4—42no—
758D4—42no—
759D4—42no—
760D4—44no—
761D4—44no—
762D4—82no—
763D4—82no—
764D4—81no—
765D4—81no—
766D4—88no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—88no—
806C22—21no—
807C22—21no—
808C22—22no—
809C22—21no—
810C22—22no—
811C22—21no—
812C22—21no—
813C22—22no—
814C22—21no—
815C22—22no—
816C22—21no—
817C22—22no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C61×B(4,𝔽2)12yes—
846C22C2×#120×C6111yescharacteristic
847C22C61×#53211yescharacteristic
848C22C61×#53711yescharacteristic
849C22C61×#54612yes—
850C22C61×#54712yes—
851C4—44no—
852C4—42no—
853C4—42no—
854C4—41no—
855C4—41no—
856C4—42no—
857C4—41no—
858C4—41no—
859C4—42no—
860C4—81no—
861C4—81no—
862C4—82no—
863C2—22no—
864C2—21no—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—41no—
869C2—42no—
870C2—82no—
871C2—82no—
872C2C61×#243011yescharacteristic
873C2C2×C61×B(4,𝔽2)11yescharacteristic
874C2C61×#302611yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC24C24×C61
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C25×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3490C2semidirect
2. C61×#2410C2semidirect
3. C61×#2405C2semidirect
4. C61×#2062C2semidirect
5. C61×#2044C2semidirect
6. C61×#2029C2semidirect
7. C61×#2021C2semidirect
8. C61×#1898C2semidirect
9. C61×#1889C2semidirect
10. C61×#1867C2semidirect
11. C2×C61×#342C2semidirect
61. C22×D4×C61D4semidirect
62. C22×D4×C61D4semidirect
65. C23×C4×C61D4semidirect
66. C23×C4×C61D4semidirect
126. C2×C22⋊C4×C61D4semidirect
127. C2×C22⋊C4×C61D4semidirect
128. C2×C22⋊C4×C61D4semidirect
129. C2×C22⋊C4×C61D4semidirect
260. C22⋊C4×C61#41semidirect
368. #25563C61direct (N × H)
426. #3490C2×C61semidirect
427. #2410C2×C61semidirect
428. #2405C2×C61semidirect
429. #2062C2×C61semidirect
430. #2044C2×C61semidirect
431. #2029C2×C61semidirect
432. #2021C2×C61semidirect
433. #1898C2×C61semidirect
434. #1889C2×C61semidirect
435. #1867C2×C61semidirect
436. C2×#342C2×C61semidirect
488. C61#25563direct (N × H)
499. C22×D4D4×C61semidirect
500. C22×D4D4×C61semidirect
503. C23×C4D4×C61semidirect
504. C23×C4D4×C61semidirect
564. C2×C22⋊C4D4×C61semidirect
565. C2×C22⋊C4D4×C61semidirect
566. C2×C22⋊C4D4×C61semidirect
567. C2×C22⋊C4D4×C61semidirect
698. C22⋊C4#41×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#34902
C61×#24102
C61×#24052
C61×#20622
C61×#20442
C61×#20292
C61×#20212
C61×#18982
C61×#18892
C61×#18672
C2×C61×#3422
#2556361