Finite Group Databasebeta

← C61×#24450 #29527883

Subgroups — C61×#24450 #29527883

Order 15616.

1620 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#546C211yesmaximal, characteristic, complemented
2C2×C61×#468C211yesmaximal, characteristic, complemented
3C2×C61×#449C211yesmaximal, characteristic, complemented
4C2×C61×#447C211yesmaximal, characteristic, complemented
5C2×C61×#418C211yesmaximal, characteristic, complemented
6C61×#2414C211yesmaximal, characteristic, complemented
7C61×#2042C211yesmaximal, characteristic, complemented
8C61×#2033C211yesmaximal, characteristic, complemented
9C61×#2012C211yesmaximal, characteristic, complemented
10C61×#1999C211yesmaximal, characteristic, complemented
11C61×#1879C211yesmaximal, characteristic, complemented
12C61×#1873C211yesmaximal, characteristic, complemented
13C61×#1870C211yesmaximal, characteristic, complemented
14C61×#1862C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic, complemented
19C22×D8×C61C2211yescharacteristic
20C22×D8×C61C2211yescharacteristic
21C22×M16×C61C2211yescharacteristic
22C61×#546—24no—
23C61×#546—24no—
24C2×#124×C61C2211yescharacteristic
25C2×#123×C61—21no—
26C2×C22⋊Q8×C61C2211yescharacteristic
27C2×#121×C61—21no—
28C2×#121×C61C2211yescharacteristic
29C2×#121×C61C2211yescharacteristic
30C2×#121×C61C2211yescharacteristic, complemented
31C2×#120×C61—21no—
32C2×C4×D4×C61C2211yescharacteristic
33C2×C4×D4×C61C2211yescharacteristic
34C2×#117×C61C2211yescharacteristic
35C22×C22⋊C4×C61—21no—
36C61×#468—24no—
37C61×#449—24no—
38C61×#447—24no—
39C2×#107×C61C2211yescharacteristic, complemented
40C61×#418—24no—
41C2×#103×C61C2211yescharacteristic, complemented
42C2×#103×C61C2211yescharacteristic, complemented
43C2×#103×C61C2211yescharacteristic, complemented
44C2×#102×C61C2211yescharacteristic
45C2×#102×C61C2211yescharacteristic
46C2×#102×C61C2211yescharacteristic
47C2×#102×C61C2211yescharacteristic
48C2×#102×C61C2211yescharacteristic
49C2×#102×C61C2211yescharacteristic
50C2×#102×C61C2211yescharacteristic, complemented
51C2×C22⋊C8×C61C2211yescharacteristic
52C2×C22⋊C8×C61C2211yescharacteristic, complemented
53C2×C22⋊C8×C61C2211yescharacteristic, complemented
54C61×#394—21no—
55C61×#392—21no—
56C61×#390—21no—
57C61×#390C2211yescharacteristic, complemented
58C61×#389C2211yescharacteristic, complemented
59C61×#388—21no—
60C61×#380C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#336C2211yescharacteristic, complemented
64C61×#336C2211yescharacteristic, complemented
65C25×C61—21no—
66C2×#41×C61—22no—
67C2×#41×C61—22no—
68C2×#41×C61—22no—
69C2×#41×C61—22no—
70C2×#41×C61—41no—
71C2×#41×C61—41no—
72C22×Q8×C61C2311yescharacteristic
73C22×D4×C61—22no—
74C22×D4×C61—22no—
75C22×D4×C61—21no—
76C22×D4×C61—21no—
77C22×D4×C61—21no—
78C22×D4×C61—21no—
79C22×D4×C61—22no—
80C22×D4×C61—21no—
81C22×D4×C61—41no—
82C22×D4×C61—41no—
83C22×D4×C61D411yescharacteristic
84C22×D4×C61D414yescomplemented
85C22×D4×C61C2311yescharacteristic
86C22×D4×C61C2311yescharacteristic
87C22×D4×C61C2311yescharacteristic
88C23×C4×C61—21no—
89C23×C4×C61—21no—
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C2×SD16×C61—22no—
93C2×SD16×C61—22no—
94C2×SD16×C61—41no—
95C2×D8×C61—22no—
96C2×D8×C61—22no—
97C2×D8×C61—22no—
98C2×D8×C61—22no—
99C2×D8×C61—41no—
100C2×D8×C61—41no—
101C2×M16×C61—22no—
102C2×M16×C61—22no—
103C2×M16×C61—41no—
104C22×C8×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108#124×C61—22no—
109#124×C61—22no—
110#123×C61—28no—
111C22⋊Q8×C61—22no—
112C22⋊Q8×C61D414yescomplemented
113#121×C61—28no—
114#121×C61—22no—
115#121×C61—22no—
116#121×C61—22no—
117#121×C61—22no—
118#121×C61—22no—
119#121×C61—41no—
120#120×C61—28no—
121C4×D4×C61—22no—
122C4×D4×C61—22no—
123C4×D4×C61—22no—
124C4×D4×C61—22no—
125#117×C61—22no—
126#117×C61—41no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61D411yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—28no—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61—21no—
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C22⋊C4×C61—21no—
145C2×C22⋊C4×C61—21no—
146C2×C22⋊C4×C61D411yescharacteristic
147C2×C22⋊C4×C61D411yescharacteristic
148C2×C42×C61—21no—
149C2×C42×C61C2311yescharacteristic
150#107×C61—22no—
151#103×C61—22no—
152#103×C61—22no—
153#103×C61—41no—
154#102×C61—22no—
155#102×C61—22no—
156#102×C61—22no—
157#102×C61—22no—
158#102×C61—22no—
159#102×C61—22no—
160#102×C61D414yescomplemented
161C22⋊C8×C61—22no—
162C22⋊C8×C61—22no—
163C22⋊C8×C61—41no—
164#95×C61—21no—
165#95×C61—21no—
166C24×C61—21no—
167C24×C61—21no—
168C24×C61—24no—
169C24×C61—21no—
170C24×C61—42no—
171C24×C61—42no—
172C24×C61—42no—
173C24×C61—42no—
174C24×C61—81no—
175C24×C61—81no—
176C24×C61C2×D411yescharacteristic
177C24×C61C2×D411yescharacteristic
178#41×C61—44no—
179#41×C61—44no—
180#41×C61—44no—
181#41×C61—44no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61C2×D412yes—
188C2×D4×C61—28no—
189C2×D4×C61—24no—
190C2×D4×C61—22no—
191C2×D4×C61—24no—
192C2×D4×C61—24no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—44no—
208C2×D4×C61—44no—
209C2×D4×C61—44no—
210C2×D4×C61—41no—
211C2×D4×C61—41no—
212C2×D4×C61—42no—
213C2×D4×C61—42no—
214C2×D4×C61—42no—
215C2×D4×C61—42no—
216C2×D4×C61—42no—
217C2×D4×C61—42no—
218C2×D4×C61—42no—
219C2×D4×C61—81no—
220C2×D4×C61—81no—
221C2×D4×C61—81no—
222C2×D4×C61—81no—
223C2×D4×C61—81no—
224C2×D4×C61C2×D412yes—
225C2×D4×C61C2×D412yes—
226C2×D4×C61C2×D412yes—
227C2×D4×C61#4112yes—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—24no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—24no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—42no—
246C22×C4×C61—42no—
247C22×C4×C61—81no—
248C22×C4×C61—81no—
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D412yes—
254C22×C4×C61C2×D412yes—
255C22×C4×C61C2411yescharacteristic
256SD16×C61—44no—
257D8×C61—44no—
258D8×C61—44no—
259M16×C61—44no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61—21no—
270C2×C8×C61—21no—
271C2×C8×C61C2×D412yes—
272C4⋊C4×C61—24no—
273C4⋊C4×C61—22no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—81no—
281C4⋊C4×C61C2×D412yes—
282C4⋊C4×C61C2×D412yes—
283C22⋊C4×C61—24no—
284C22⋊C4×C61—24no—
285C22⋊C4×C61—24no—
286C22⋊C4×C61—24no—
287C22⋊C4×C61—22no—
288C22⋊C4×C61—24no—
289C22⋊C4×C61—22no—
290C22⋊C4×C61—42no—
291C22⋊C4×C61—42no—
292C22⋊C4×C61—42no—
293C22⋊C4×C61—42no—
294C22⋊C4×C61—81no—
295C22⋊C4×C61—81no—
296C42×C61—21no—
297C42×C61—21no—
298C42×C61—42no—
299C23×C61—22no—
300C23×C61—21no—
301C23×C61—22no—
302C23×C61—21no—
303C23×C61—22no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—22no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—21no—
314C23×C61—21no—
315C23×C61—21no—
316C23×C61—48no—
317C23×C61—48no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61—41no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61—41no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61—84no—
336C23×C61—84no—
337C23×C61—84no—
338C23×C61—84no—
339C23×C61—84no—
340C23×C61#12012yes—
341C23×C61C22×D411yescharacteristic
342Q8×C61—22no—
343Q8×C61—22no—
344Q8×C61—41no—
345Q8×C61—41no—
346D4×C61—22no—
347D4×C61—22no—
348D4×C61—22no—
349D4×C61—22no—
350D4×C61—22no—
351D4×C61—48no—
352D4×C61—44no—
353D4×C61—48no—
354D4×C61—41no—
355D4×C61—41no—
356D4×C61—41no—
357D4×C61—41no—
358D4×C61—41no—
359D4×C61—41no—
360D4×C61—84no—
361D4×C61—84no—
362D4×C61—84no—
363D4×C61#12114yes—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—22no—
367C2×C4×C61—22no—
368C2×C4×C61—22no—
369C2×C4×C61—22no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—22no—
373C2×C4×C61—21no—
374C2×C4×C61—22no—
375C2×C4×C61—22no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—48no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—84no—
400C2×C4×C61#12012yes—
401C2×C4×C61C22×D411yescharacteristic
402C2×C4×C61C22×D411yescharacteristic
403C2×C4×C61C22×D411yescharacteristic
404C2×C4×C61C2×#4111yescharacteristic
405C2×C4×C61H(5,𝔽2)11yescharacteristic
406C2×C4×C61H(5,𝔽2)11yescharacteristic
407C8×C61—22no—
408C8×C61—41no—
409C8×C61—41no—
410C8×C61—41no—
411#24450C6111yesmaximal, characteristic, direct product factor, Sylow
412C22×C61—22no—
413C22×C61—24no—
414C22×C61—22no—
415C22×C61—22no—
416C22×C61—42no—
417C22×C61—42no—
418C22×C61—41no—
419C22×C61—42no—
420C22×C61—41no—
421C22×C61—42no—
422C22×C61—41no—
423C22×C61—42no—
424C22×C61—41no—
425C22×C61—42no—
426C22×C61—41no—
427C22×C61—42no—
428C22×C61—41no—
429C22×C61—42no—
430C22×C61—41no—
431C22×C61—42no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—816no—
437C22×C61—81no—
438C22×C61—81no—
439C22×C61—81no—
440C22×C61—81no—
441C22×C61—81no—
442C22×C61—81no—
443C22×C61—81no—
444C22×C61—81no—
445C22×C61—81no—
446C22×C61—81no—
447C22×C61—81no—
448C22×C61C2×#12011yescharacteristic
449C22×C61D4211yescharacteristic
450C22×C61#54611yescharacteristic
451C22×C61#57511yescharacteristic
452C22×C61#57511yescharacteristic
453C22×C61#57611yescharacteristic
454C22×C61#57611yescharacteristic
455C4×C61—22no—
456C4×C61—41no—
457C4×C61—42no—
458C4×C61—41no—
459C4×C61—41no—
460C4×C61—42no—
461C4×C61—42no—
462C4×C61—81no—
463C4×C61—81no—
464C4×C61C2×#12111yescharacteristic
465C4×C61#53411yescharacteristic
466C4×C61D4211yescharacteristic
467C4×C61#54611yescharacteristic
468C2×#546C2×C6111yescharacteristic, complemented
469C2×#468C2×C6111yescharacteristic, complemented
470C2×#449C2×C6111yescharacteristic, complemented
471C2×#447C2×C6111yescharacteristic, complemented
472C2×#418C2×C6111yescharacteristic, complemented
473#2414C2×C6111yescharacteristic, complemented
474#2042C2×C6111yescharacteristic, complemented
475#2033C2×C6111yescharacteristic, complemented
476#2012C2×C6111yescharacteristic, complemented
477#1999C2×C6111yescharacteristic, complemented
478#1879C2×C6111yescharacteristic, complemented
479#1873C2×C6111yescharacteristic, complemented
480#1870C2×C6111yescharacteristic, complemented
481#1862C2×C6111yescharacteristic, complemented
482#1788C2×C6111yescharacteristic, complemented
483C2×C61—42no—
484C2×C61—44no—
485C2×C61—81no—
486C2×C61—82no—
487C2×C61—161no—
488C2×C61#241011yescharacteristic
489C2×C61#300511yescharacteristic
490C2×C61#300811yescharacteristic
491C2×C61#326811yescharacteristic
492C2×C61#327311yescharacteristic
493C2×C61#331911yescharacteristic
494C2×C61#332211yescharacteristic
495C22×#41C22×C6111yescharacteristic
496C23×D4C22×C6111yescharacteristic
497C22×SD16C22×C6111yescharacteristic, complemented
498C22×D8C22×C6111yescharacteristic
499C22×D8C22×C6111yescharacteristic
500C22×M16C22×C6111yescharacteristic
501#546—24no—
502#546—24no—
503C2×#124C22×C6111yescharacteristic
504C2×#123—21no—
505C2×C22⋊Q8C22×C6111yescharacteristic
506C2×#121—21no—
507C2×#121C22×C6111yescharacteristic
508C2×#121C22×C6111yescharacteristic
509C2×#121C22×C6111yescharacteristic, complemented
510C2×#120—21no—
511C2×C4×D4C22×C6111yescharacteristic
512C2×C4×D4C22×C6111yescharacteristic
513C2×#117C22×C6111yescharacteristic
514C22×C22⋊C4—21no—
515#468—24no—
516#449—24no—
517#447—24no—
518C2×#107C22×C6111yescharacteristic, complemented
519#418—24no—
520C2×#103C22×C6111yescharacteristic, complemented
521C2×#103C22×C6111yescharacteristic, complemented
522C2×#103C22×C6111yescharacteristic, complemented
523C2×#102C22×C6111yescharacteristic
524C2×#102C22×C6111yescharacteristic
525C2×#102C22×C6111yescharacteristic
526C2×#102C22×C6111yescharacteristic
527C2×#102C22×C6111yescharacteristic
528C2×#102C22×C6111yescharacteristic
529C2×#102C22×C6111yescharacteristic, complemented
530C2×C22⋊C8C22×C6111yescharacteristic
531C2×C22⋊C8C22×C6111yescharacteristic, complemented
532C2×C22⋊C8C22×C6111yescharacteristic, complemented
533#394—21no—
534#392—21no—
535#390—21no—
536#390C22×C6111yescharacteristic, complemented
537#389C22×C6111yescharacteristic, complemented
538#388—21no—
539#380C22×C6111yescharacteristic, complemented
540#340C22×C6111yescharacteristic, complemented
541#340C22×C6111yescharacteristic, complemented
542#336C22×C6111yescharacteristic, complemented
543#336C22×C6111yescharacteristic, complemented
544C61#2445011yescharacteristic, direct product factor, Sylow
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C22×Q8C23×C6111yescharacteristic
553C22×D4—22no—
554C22×D4—22no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—22no—
561C22×D4—41no—
562C22×D4—41no—
563C22×D4D4×C6111yescharacteristic
564C22×D4D4×C6114yescomplemented
565C22×D4C23×C6111yescharacteristic
566C22×D4C23×C6111yescharacteristic
567C22×D4C23×C6111yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4C23×C6111yescharacteristic
571C23×C4C23×C6111yescharacteristic
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—41no—
580C2×D8—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16—41no—
584C22×C8C23×C6111yescharacteristic
585C22×C8C23×C6111yescharacteristic
586C22×C8C23×C6111yescharacteristic
587C22×C8C23×C6111yescharacteristic
588#124—22no—
589#124—22no—
590#123—28no—
591C22⋊Q8—22no—
592C22⋊Q8D4×C6114yescomplemented
593#121—28no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—41no—
600#120—28no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605#117—22no—
606#117—41no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4D4×C6111yescharacteristic
610C2×C4⋊C4C23×C6111yescharacteristic
611C2×C4⋊C4C23×C6111yescharacteristic
612C2×C4⋊C4C23×C6111yescharacteristic
613C2×C4⋊C4C23×C6111yescharacteristic
614C2×C22⋊C4—28no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4D4×C6111yescharacteristic
627C2×C22⋊C4D4×C6111yescharacteristic
628C2×C42—21no—
629C2×C42C23×C6111yescharacteristic
630#107—22no—
631#103—22no—
632#103—22no—
633#103—41no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102D4×C6114yescomplemented
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—41no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—21no—
648C24—24no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24C2×D4×C6111yescharacteristic
657C24C2×D4×C6111yescharacteristic
658#41—44no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×D4×C6112yes—
668C2×D4—28no—
669C2×D4—24no—
670C2×D4—22no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—41no—
691C2×D4—41no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4C2×D4×C6112yes—
705C2×D4C2×D4×C6112yes—
706C2×D4C2×D4×C6112yes—
707C2×D4#41×C6112yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—81no—
728C22×C4—81no—
729C22×C4C2×D4×C6111yescharacteristic
730C22×C4C2×D4×C6111yescharacteristic
731C22×C4C2×D4×C6111yescharacteristic
732C22×C4C2×D4×C6111yescharacteristic
733C22×C4C2×D4×C6112yes—
734C22×C4C2×D4×C6112yes—
735C22×C4C24×C6111yescharacteristic
736SD16—44no—
737D8—44no—
738D8—44no—
739M16—44no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8C2×D4×C6112yes—
752C4⋊C4—24no—
753C4⋊C4—22no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—81no—
761C4⋊C4C2×D4×C6112yes—
762C4⋊C4C2×D4×C6112yes—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—22no—
768C22⋊C4—24no—
769C22⋊C4—22no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42—21no—
777C42—21no—
778C42—42no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—22no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—21no—
796C23—48no—
797C23—48no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23#120×C6112yes—
821C23C22×D4×C6111yescharacteristic
822Q8—22no—
823Q8—22no—
824Q8—41no—
825Q8—41no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—48no—
832D4—44no—
833D4—48no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—84no—
841D4—84no—
842D4—84no—
843D4#121×C6114yes—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—48no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—84no—
880C2×C4#120×C6112yes—
881C2×C4C22×D4×C6111yescharacteristic
882C2×C4C22×D4×C6111yescharacteristic
883C2×C4C22×D4×C6111yescharacteristic
884C2×C4C2×#41×C6111yescharacteristic
885C2×C4H(5,𝔽2)×C6111yescharacteristic
886C2×C4H(5,𝔽2)×C6111yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—22no—
892C22—24no—
893C22—22no—
894C22—22no—
895C22—41no—
896C22—42no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—42no—
913C22—41no—
914C22—41no—
915C22—816no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×#120×C6111yescharacteristic
928C22D42×C6111yescharacteristic
929C22C61×#54611yescharacteristic
930C22C61×#57511yescharacteristic
931C22C61×#57511yescharacteristic
932C22C61×#57611yescharacteristic
933C22C61×#57611yescharacteristic
934C4—22no—
935C4—41no—
936C4—42no—
937C4—41no—
938C4—41no—
939C4—42no—
940C4—42no—
941C4—81no—
942C4—81no—
943C4C2×#121×C6111yescharacteristic
944C4C61×#53411yescharacteristic
945C4D42×C6111yescharacteristic
946C4C61×#54611yescharacteristic
947C2—42no—
948C2—44no—
949C2—81no—
950C2—82no—
951C2—161no—
952C2C61×#241011yescharacteristic
953C2C61×#300511yescharacteristic
954C2C61×#300811yescharacteristic
955C2C61×#326811yescharacteristic
956C2C61×#327311yescharacteristic
957C2C61×#331911yescharacteristic
958C2C61×#332211yescharacteristic
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×#546C2semidirect
2. C2×C61×#468C2semidirect
3. C2×C61×#449C2semidirect
4. C2×C61×#447C2semidirect
5. C2×C61×#418C2semidirect
6. C61×#2414C2semidirect
7. C61×#2042C2semidirect
8. C61×#2033C2semidirect
9. C61×#2012C2semidirect
10. C61×#1999C2semidirect
11. C61×#1879C2semidirect
12. C61×#1873C2semidirect
13. C61×#1870C2semidirect
14. C61×#1862C2semidirect
15. C61×#1788C2semidirect
18. C22×SD16×C61C22semidirect
30. C2×#121×C61C22semidirect
39. C2×#107×C61C22semidirect
41. C2×#103×C61C22semidirect
42. C2×#103×C61C22semidirect
43. C2×#103×C61C22semidirect
50. C2×#102×C61C22semidirect
52. C2×C22⋊C8×C61C22semidirect
53. C2×C22⋊C8×C61C22semidirect
57. C61×#390C22semidirect
58. C61×#389C22semidirect
60. C61×#380C22semidirect
61. C61×#340C22semidirect
62. C61×#340C22semidirect
63. C61×#336C22semidirect
64. C61×#336C22semidirect
84. C22×D4×C61D4semidirect
112. C22⋊Q8×C61D4semidirect
160. #102×C61D4semidirect
411. #24450C61direct (N × H)
468. C2×#546C2×C61semidirect
469. C2×#468C2×C61semidirect
470. C2×#449C2×C61semidirect
471. C2×#447C2×C61semidirect
472. C2×#418C2×C61semidirect
473. #2414C2×C61semidirect
474. #2042C2×C61semidirect
475. #2033C2×C61semidirect
476. #2012C2×C61semidirect
477. #1999C2×C61semidirect
478. #1879C2×C61semidirect
479. #1873C2×C61semidirect
480. #1870C2×C61semidirect
481. #1862C2×C61semidirect
482. #1788C2×C61semidirect
497. C22×SD16C22×C61semidirect
509. C2×#121C22×C61semidirect
518. C2×#107C22×C61semidirect
520. C2×#103C22×C61semidirect
521. C2×#103C22×C61semidirect
522. C2×#103C22×C61semidirect
529. C2×#102C22×C61semidirect
531. C2×C22⋊C8C22×C61semidirect
532. C2×C22⋊C8C22×C61semidirect
536. #390C22×C61semidirect
537. #389C22×C61semidirect
539. #380C22×C61semidirect
540. #340C22×C61semidirect
541. #340C22×C61semidirect
542. #336C22×C61semidirect
543. #336C22×C61semidirect
544. C61#24450direct (N × H)
564. C22×D4D4×C61semidirect
592. C22⋊Q8D4×C61semidirect
640. #102D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5462
C2×C61×#4682
C2×C61×#4492
C2×C61×#4472
C2×C61×#4182
C61×#24142
C61×#20422
C61×#20332
C61×#20122
C61×#19992
C61×#18792
C61×#18732
C61×#18702
C61×#18622
C61×#17882
#2445061