Finite Group Databasebeta

← C61×#23975 #29527408

Subgroups — C61×#23975 #29527408

Order 15616.

1326 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#553C211yesmaximal, characteristic, complemented
2C2×C61×#449C211yesmaximal, characteristic, complemented
3C2×C61×#417C211yesmaximal, characteristic, complemented
4C61×#2407C211yesmaximal, characteristic, complemented
5C61×#2026C211yesmaximal, characteristic, complemented
6C61×#2025C211yesmaximal, characteristic, complemented
7C61×#2000C211yesmaximal, characteristic, complemented
8C61×#1999C211yesmaximal, characteristic, complemented
9C61×#1895C211yesmaximal, characteristic, complemented
10C61×#1879C211yesmaximal, characteristic, complemented
11C61×#1877C211yesmaximal, characteristic, complemented
12C61×#1875C211yesmaximal, characteristic, complemented
13C61×#1873C211yesmaximal, characteristic, complemented
14C61×#1870C211yesmaximal, characteristic, complemented
15C61×#1823C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C22×D8×C61C2211yescharacteristic
19C22×M16×C61C2211yescharacteristic
20C61×#553—24no—
21C61×#553—24no—
22C2×#126×C61—21no—
23C2×#125×C61C2211yescharacteristic
24C2×#123×C61—21no—
25C2×C22⋊Q8×C61C2211yescharacteristic
26C2×#121×C61—21no—
27C2×#121×C61C2211yescharacteristic
28C2×#121×C61C2211yescharacteristic
29C2×#121×C61C2211yescharacteristic
30C2×C4×D4×C61—21no—
31C2×C4×D4×C61C2211yescharacteristic
32C2×C4×D4×C61C2211yescharacteristic
33C2×#117×C61C2211yescharacteristic
34C22×C4⋊C4×C61C2211yescharacteristic
35C61×#449—24no—
36C61×#417—24no—
37C2×#103×C61C2211yescharacteristic
38C2×#103×C61C2211yescharacteristic
39C2×#103×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×#102×C61C2211yescharacteristic
44C2×#102×C61C2211yescharacteristic
45C2×C22⋊C8×C61C2211yescharacteristic
46C2×C22⋊C8×C61C2211yescharacteristic
47C2×C22⋊C8×C61C2211yescharacteristic
48C61×#394—21no—
49C61×#392—21no—
50C61×#391C2211yescharacteristic
51C61×#390C2211yescharacteristic
52C61×#386—21no—
53C61×#385—21no—
54C61×#380C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C2×#41×C61—22no—
64C2×#41×C61—22no—
65C2×#41×C61—22no—
66C2×#41×C61—22no—
67C2×#41×C61—41no—
68C2×#41×C61—41no—
69C22×Q8×C61C2311yescharacteristic
70C22×D4×C61—21no—
71C22×D4×C61—21no—
72C22×D4×C61—21no—
73C22×D4×C61—21no—
74C22×D4×C61D411yescharacteristic
75C22×D4×C61C2311yescharacteristic
76C22×D4×C61C2311yescharacteristic
77C23×C4×C61—21no—
78C23×C4×C61—21no—
79C23×C4×C61—21no—
80C23×C4×C61C2311yescharacteristic
81C23×C4×C61C2311yescharacteristic
82C2×SD16×C61—22no—
83C2×SD16×C61—22no—
84C2×SD16×C61—41no—
85C2×D8×C61—22no—
86C2×D8×C61—22no—
87C2×D8×C61—41no—
88C2×M16×C61—22no—
89C2×M16×C61—41no—
90C2×M16×C61—41no—
91C22×C8×C61C2311yescharacteristic
92C22×C8×C61C2311yescharacteristic
93C22×C8×C61C2311yescharacteristic
94C22×C8×C61C2311yescharacteristic
95#126×C61—28no—
96#125×C61—22no—
97#125×C61—22no—
98#123×C61—28no—
99C22⋊Q8×C61—22no—
100C22⋊Q8×C61—41no—
101#121×C61—28no—
102#121×C61—22no—
103#121×C61—22no—
104#121×C61—22no—
105#121×C61—22no—
106#121×C61—41no—
107#121×C61D414yescomplemented
108C4×D4×C61—28no—
109C4×D4×C61—22no—
110C4×D4×C61—22no—
111C4×D4×C61—22no—
112C4×D4×C61—22no—
113#117×C61—22no—
114#117×C61—22no—
115C2×C4⋊C4×C61—22no—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61D411yescharacteristic
121C2×C4⋊C4×C61D414yescomplemented
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61D411yescharacteristic
137C2×C22⋊C4×C61D411yescharacteristic
138C2×C42×C61—21no—
139C2×C42×C61C2311yescharacteristic
140#103×C61—22no—
141#103×C61—22no—
142#103×C61—22no—
143#102×C61—22no—
144#102×C61—22no—
145#102×C61—22no—
146#102×C61—41no—
147#102×C61—41no—
148C22⋊C8×C61—22no—
149C22⋊C8×C61—41no—
150C22⋊C8×C61—41no—
151#95×C61—21no—
152#95×C61—21no—
153#95×C61—21no—
154C24×C61—21no—
155C24×C61—21no—
156C24×C61C2×D411yescharacteristic
157C24×C61C2×D411yescharacteristic
158#41×C61—28no—
159#41×C61—44no—
160#41×C61—44no—
161#41×C61—44no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61#4112yes—
168C2×D4×C61—22no—
169C2×D4×C61—24no—
170C2×D4×C61—24no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—41no—
182C2×D4×C61—41no—
183C2×D4×C61—42no—
184C2×D4×C61—42no—
185C2×D4×C61—42no—
186C2×D4×C61—42no—
187C2×D4×C61—42no—
188C2×D4×C61—42no—
189C2×D4×C61—42no—
190C2×D4×C61—81no—
191C2×D4×C61—81no—
192C2×D4×C61—81no—
193C2×D4×C61C2×D412yes—
194C2×D4×C61#4112yes—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—24no—
204C22×C4×C61—24no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—42no—
214C22×C4×C61—42no—
215C22×C4×C61—42no—
216C22×C4×C61—81no—
217C22×C4×C61—81no—
218C22×C4×C61—81no—
219C22×C4×C61—81no—
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D412yes—
225C22×C4×C61C2×D412yes—
226C22×C4×C61C2411yescharacteristic
227SD16×C61—44no—
228D8×C61—44no—
229M16×C61—44no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C4⋊C4×C61—24no—
243C4⋊C4×C61—24no—
244C4⋊C4×C61—24no—
245C4⋊C4×C61—22no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—42no—
254C4⋊C4×C61C2×D412yes—
255C4⋊C4×C61C2×D412yes—
256C4⋊C4×C61C2×D412yes—
257C22⋊C4×C61—24no—
258C22⋊C4×C61—24no—
259C22⋊C4×C61—24no—
260C22⋊C4×C61—22no—
261C22⋊C4×C61—24no—
262C22⋊C4×C61—22no—
263C22⋊C4×C61—42no—
264C22⋊C4×C61—42no—
265C22⋊C4×C61—42no—
266C22⋊C4×C61—81no—
267C22⋊C4×C61—81no—
268C42×C61—24no—
269C42×C61—21no—
270C42×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—22no—
279C23×C61—21no—
280C23×C61—22no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61#12012yes—
299C23×C61C22×D411yescharacteristic
300Q8×C61—22no—
301Q8×C61—22no—
302Q8×C61—41no—
303Q8×C61—41no—
304D4×C61—22no—
305D4×C61—22no—
306D4×C61—22no—
307D4×C61—22no—
308D4×C61—44no—
309D4×C61—48no—
310D4×C61—48no—
311D4×C61—41no—
312D4×C61—41no—
313D4×C61—41no—
314D4×C61—41no—
315D4×C61—84no—
316D4×C61—84no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—22no—
326C2×C4×C61—21no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—21no—
330C2×C4×C61—22no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—48no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—84no—
356C2×C4×C61—84no—
357C2×C4×C61#12012yes—
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C2×#4111yescharacteristic
361C2×C4×C61C2×#4111yescharacteristic
362C2×C4×C61H(5,𝔽2)11yescharacteristic
363C2×C4×C61H(5,𝔽2)11yescharacteristic
364C8×C61—41no—
365C8×C61—41no—
366C8×C61—41no—
367C8×C61—41no—
368#23975C6111yesmaximal, characteristic, direct product factor, Sylow
369C22×C61—22no—
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—42no—
377C22×C61—41no—
378C22×C61—42no—
379C22×C61—41no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—41no—
383C22×C61—41no—
384C22×C61—42no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—42no—
388C22×C61—41no—
389C22×C61—81no—
390C22×C61—81no—
391C22×C61—81no—
392C22×C61—81no—
393C22×C61—81no—
394C22×C61—81no—
395C22×C61—81no—
396C22×C61—81no—
397C22×C61C2×#12011yescharacteristic
398C22×C61#54611yescharacteristic
399C22×C61#54611yescharacteristic
400C22×C61#57511yescharacteristic
401C22×C61#57511yescharacteristic
402C22×C61#57611yescharacteristic
403C22×C61#57711yescharacteristic
404C4×C61—22no—
405C4×C61—41no—
406C4×C61—42no—
407C4×C61—41no—
408C4×C61—42no—
409C4×C61—41no—
410C4×C61—42no—
411C4×C61—42no—
412C4×C61—81no—
413C4×C61—81no—
414C4×C61#52511yescharacteristic
415C4×C61#53511yescharacteristic
416C4×C61#54611yescharacteristic
417C4×C61#54611yescharacteristic
418C2×#553C2×C6111yescharacteristic, complemented
419C2×#449C2×C6111yescharacteristic, complemented
420C2×#417C2×C6111yescharacteristic, complemented
421#2407C2×C6111yescharacteristic, complemented
422#2026C2×C6111yescharacteristic, complemented
423#2025C2×C6111yescharacteristic, complemented
424#2000C2×C6111yescharacteristic, complemented
425#1999C2×C6111yescharacteristic, complemented
426#1895C2×C6111yescharacteristic, complemented
427#1879C2×C6111yescharacteristic, complemented
428#1877C2×C6111yescharacteristic, complemented
429#1875C2×C6111yescharacteristic, complemented
430#1873C2×C6111yescharacteristic, complemented
431#1870C2×C6111yescharacteristic, complemented
432#1823C2×C6111yescharacteristic, complemented
433C2×C61—42no—
434C2×C61—81no—
435C2×C61—82no—
436C2×C61—82no—
437C2×C61#240411yescharacteristic
438C2×C61#300511yescharacteristic
439C2×C61#301211yescharacteristic
440C2×C61#330711yescharacteristic
441C2×C61#330911yescharacteristic
442C2×C61#332211yescharacteristic
443C2×C61#332611yescharacteristic
444C22×#41C22×C6111yescharacteristic
445C22×SD16C22×C6111yescharacteristic
446C22×D8C22×C6111yescharacteristic
447C22×M16C22×C6111yescharacteristic
448#553—24no—
449#553—24no—
450C2×#126—21no—
451C2×#125C22×C6111yescharacteristic
452C2×#123—21no—
453C2×C22⋊Q8C22×C6111yescharacteristic
454C2×#121—21no—
455C2×#121C22×C6111yescharacteristic
456C2×#121C22×C6111yescharacteristic
457C2×#121C22×C6111yescharacteristic
458C2×C4×D4—21no—
459C2×C4×D4C22×C6111yescharacteristic
460C2×C4×D4C22×C6111yescharacteristic
461C2×#117C22×C6111yescharacteristic
462C22×C4⋊C4C22×C6111yescharacteristic
463#449—24no—
464#417—24no—
465C2×#103C22×C6111yescharacteristic
466C2×#103C22×C6111yescharacteristic
467C2×#103C22×C6111yescharacteristic
468C2×#102C22×C6111yescharacteristic
469C2×#102C22×C6111yescharacteristic
470C2×#102C22×C6111yescharacteristic
471C2×#102C22×C6111yescharacteristic
472C2×#102C22×C6111yescharacteristic
473C2×C22⋊C8C22×C6111yescharacteristic
474C2×C22⋊C8C22×C6111yescharacteristic
475C2×C22⋊C8C22×C6111yescharacteristic
476#394—21no—
477#392—21no—
478#391C22×C6111yescharacteristic
479#390C22×C6111yescharacteristic
480#386—21no—
481#385—21no—
482#380C22×C6111yescharacteristic
483#340C22×C6111yescharacteristic
484#340C22×C6111yescharacteristic
485#340C22×C6111yescharacteristic
486#340C22×C6111yescharacteristic
487#340C22×C6111yescharacteristic
488#340C22×C6111yescharacteristic
489#336C22×C6111yescharacteristic
490#336C22×C6111yescharacteristic
491C61#2397511yescharacteristic, direct product factor, Sylow
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C22×Q8C23×C6111yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4D4×C6111yescharacteristic
504C22×D4C23×C6111yescharacteristic
505C22×D4C23×C6111yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C23×C6111yescharacteristic
510C23×C4C23×C6111yescharacteristic
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—41no—
517C2×M16—22no—
518C2×M16—41no—
519C2×M16—41no—
520C22×C8C23×C6111yescharacteristic
521C22×C8C23×C6111yescharacteristic
522C22×C8C23×C6111yescharacteristic
523C22×C8C23×C6111yescharacteristic
524#126—28no—
525#125—22no—
526#125—22no—
527#123—28no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530#121—28no—
531#121—22no—
532#121—22no—
533#121—22no—
534#121—22no—
535#121—41no—
536#121D4×C6114yescomplemented
537C4×D4—28no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4D4×C6111yescharacteristic
550C2×C4⋊C4D4×C6114yescomplemented
551C2×C4⋊C4C23×C6111yescharacteristic
552C2×C4⋊C4C23×C6111yescharacteristic
553C2×C4⋊C4C23×C6111yescharacteristic
554C2×C4⋊C4C23×C6111yescharacteristic
555C2×C4⋊C4C23×C6111yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4D4×C6111yescharacteristic
566C2×C22⋊C4D4×C6111yescharacteristic
567C2×C42—21no—
568C2×C42C23×C6111yescharacteristic
569#103—22no—
570#103—22no—
571#103—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—41no—
576#102—41no—
577C22⋊C8—22no—
578C22⋊C8—41no—
579C22⋊C8—41no—
580#95—21no—
581#95—21no—
582#95—21no—
583C24—21no—
584C24—21no—
585C24C2×D4×C6111yescharacteristic
586C24C2×D4×C6111yescharacteristic
587#41—28no—
588#41—44no—
589#41—44no—
590#41—44no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8#41×C6112yes—
597C2×D4—22no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4C2×D4×C6112yes—
623C2×D4#41×C6112yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4—81no—
649C22×C4C2×D4×C6111yescharacteristic
650C22×C4C2×D4×C6111yescharacteristic
651C22×C4C2×D4×C6111yescharacteristic
652C22×C4C2×D4×C6111yescharacteristic
653C22×C4C2×D4×C6112yes—
654C22×C4C2×D4×C6112yes—
655C22×C4C24×C6111yescharacteristic
656SD16—44no—
657D8—44no—
658M16—44no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—22no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—42no—
683C4⋊C4C2×D4×C6112yes—
684C4⋊C4C2×D4×C6112yes—
685C4⋊C4C2×D4×C6112yes—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—24no—
691C22⋊C4—22no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—81no—
696C22⋊C4—81no—
697C42—24no—
698C42—21no—
699C42—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—22no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23#120×C6112yes—
728C23C22×D4×C6111yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—41no—
732Q8—41no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—44no—
738D4—48no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—84no—
745D4—84no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—48no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4#120×C6112yes—
787C2×C4C22×D4×C6111yescharacteristic
788C2×C4C22×D4×C6111yescharacteristic
789C2×C4C2×#41×C6111yescharacteristic
790C2×C4C2×#41×C6111yescharacteristic
791C2×C4H(5,𝔽2)×C6111yescharacteristic
792C2×C4H(5,𝔽2)×C6111yescharacteristic
793C8—41no—
794C8—41no—
795C8—41no—
796C8—41no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—41no—
808C22—42no—
809C22—41no—
810C22—42no—
811C22—41no—
812C22—42no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22C2×#120×C6111yescharacteristic
826C22C61×#54611yescharacteristic
827C22C61×#54611yescharacteristic
828C22C61×#57511yescharacteristic
829C22C61×#57511yescharacteristic
830C22C61×#57611yescharacteristic
831C22C61×#57711yescharacteristic
832C4—22no—
833C4—41no—
834C4—42no—
835C4—41no—
836C4—42no—
837C4—41no—
838C4—42no—
839C4—42no—
840C4—81no—
841C4—81no—
842C4C61×#52511yescharacteristic
843C4C61×#53511yescharacteristic
844C4C61×#54611yescharacteristic
845C4C61×#54611yescharacteristic
846C2—42no—
847C2—81no—
848C2—82no—
849C2—82no—
850C2C61×#240411yescharacteristic
851C2C61×#300511yescharacteristic
852C2C61×#301211yescharacteristic
853C2C61×#330711yescharacteristic
854C2C61×#330911yescharacteristic
855C2C61×#332211yescharacteristic
856C2C61×#332611yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×C4×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#553C2semidirect
2. C2×C61×#449C2semidirect
3. C2×C61×#417C2semidirect
4. C61×#2407C2semidirect
5. C61×#2026C2semidirect
6. C61×#2025C2semidirect
7. C61×#2000C2semidirect
8. C61×#1999C2semidirect
9. C61×#1895C2semidirect
10. C61×#1879C2semidirect
11. C61×#1877C2semidirect
12. C61×#1875C2semidirect
13. C61×#1873C2semidirect
14. C61×#1870C2semidirect
15. C61×#1823C2semidirect
107. #121×C61D4semidirect
121. C2×C4⋊C4×C61D4semidirect
368. #23975C61direct (N × H)
418. C2×#553C2×C61semidirect
419. C2×#449C2×C61semidirect
420. C2×#417C2×C61semidirect
421. #2407C2×C61semidirect
422. #2026C2×C61semidirect
423. #2025C2×C61semidirect
424. #2000C2×C61semidirect
425. #1999C2×C61semidirect
426. #1895C2×C61semidirect
427. #1879C2×C61semidirect
428. #1877C2×C61semidirect
429. #1875C2×C61semidirect
430. #1873C2×C61semidirect
431. #1870C2×C61semidirect
432. #1823C2×C61semidirect
491. C61#23975direct (N × H)
536. #121D4×C61semidirect
550. C2×C4⋊C4D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5532
C2×C61×#4492
C2×C61×#4172
C61×#24072
C61×#20262
C61×#20252
C61×#20002
C61×#19992
C61×#18952
C61×#18792
C61×#18772
C61×#18752
C61×#18732
C61×#18702
C61×#18232
#2397561