Finite Group Databasebeta

← C61×#25762 #29529195

Subgroups — C61×#25762 #29529195

Order 15616.

1722 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#546C211yesmaximal, characteristic, complemented
2C2×C61×#495C211yesmaximal, characteristic, complemented
3C2×C61×#463C211yesmaximal, characteristic, complemented
4C2×C61×#452C211yesmaximal, characteristic, complemented
5C2×C61×#449C211yesmaximal, characteristic, complemented
6C2×C61×#450C211yesmaximal, characteristic, complemented
7C2×C61×#447C211yesmaximal, characteristic, complemented
8C61×#2540C211yesmaximal, characteristic, complemented
9C61×#2001C211yesmaximal, characteristic, complemented
10C61×#2000C211yesmaximal, characteristic, complemented
11C61×#2000C211yesmaximal, characteristic, complemented
12C61×#1999C211yesmaximal, characteristic, complemented
13C61×#1983C211yesmaximal, characteristic, complemented
14C61×#1954C211yesmaximal, characteristic, complemented
15C4×#102×C61C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C22×Q16×C61C2211yescharacteristic, complemented
19C22×SD16×C61C2211yescharacteristic
20C22×SD16×C61C2211yescharacteristic
21C22×SD16×C61C2211yescharacteristic, complemented
22C22×D8×C61C2211yescharacteristic
23C22×D8×C61C2211yescharacteristic
24C61×#546—24no—
25C61×#546—24no—
26C2×#124×C61C2211yescharacteristic
27C2×#124×C61C2211yescharacteristic, complemented
28C2×#123×C61—21no—
29C2×C22⋊Q8×C61C2211yescharacteristic
30C2×C22⋊Q8×C61C2211yescharacteristic
31C2×C22⋊Q8×C61C2211yescharacteristic, complemented
32C2×#121×C61—21no—
33C2×#121×C61C2211yescharacteristic
34C2×#121×C61C2211yescharacteristic
35C2×#121×C61C2211yescharacteristic, complemented
36C2×#120×C61—21no—
37C2×C4×D4×C61C2211yescharacteristic
38C2×C4×D4×C61C2211yescharacteristic
39C22×C22⋊C4×C61—21no—
40C61×#495—24no—
41C61×#463—24no—
42C61×#452—24no—
43C61×#450—24no—
44C61×#449—24no—
45C61×#447—24no—
46C2×C4⋊C8×C61C2211yescharacteristic, complemented
47C2×#103×C61C2211yescharacteristic, complemented
48C2×#103×C61C2211yescharacteristic, complemented
49C2×#103×C61C2211yescharacteristic, complemented
50C2×#102×C61C2211yescharacteristic
51C2×#102×C61C2211yescharacteristic
52C2×#102×C61C2211yescharacteristic
53C2×#102×C61C2211yescharacteristic
54C2×#102×C61C2211yescharacteristic, complemented
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×C22⋊C8×C61C2211yescharacteristic, complemented
58C2×C22⋊C8×C61C2211yescharacteristic, complemented
59C2×C4×C8×C61C2211yescharacteristic, complemented
60C61×#399—21no—
61C61×#392—21no—
62C61×#390—21no—
63C61×#390—21no—
64C4×C4⋊C4×C61C2211yescharacteristic, complemented
65C61×#340C2211yescharacteristic, complemented
66C61×#340C2211yescharacteristic, complemented
67C25×C61—21no—
68C2×#41×C61—22no—
69C2×#41×C61—22no—
70C2×#41×C61—22no—
71C2×#41×C61—22no—
72C2×#41×C61—41no—
73C2×#41×C61—41no—
74C22×Q8×C61C2311yescharacteristic
75C22×Q8×C61C2311yescharacteristic
76C22×D4×C61—21no—
77C22×D4×C61—21no—
78C22×D4×C61—22no—
79C22×D4×C61—22no—
80C22×D4×C61—22no—
81C22×D4×C61—22no—
82C22×D4×C61—21no—
83C22×D4×C61—21no—
84C22×D4×C61—21no—
85C22×D4×C61—41no—
86C22×D4×C61—41no—
87C22×D4×C61D411yescharacteristic
88C22×D4×C61C2311yescharacteristic
89C22×D4×C61C2311yescharacteristic
90C22×D4×C61C2311yescharacteristic
91C23×C4×C61—21no—
92C23×C4×C61—21no—
93C23×C4×C61C2311yescharacteristic
94C23×C4×C61C2311yescharacteristic
95C2×Q16×C61—22no—
96C2×Q16×C61—22no—
97C2×Q16×C61—41no—
98C2×SD16×C61—22no—
99C2×SD16×C61—22no—
100C2×SD16×C61—22no—
101C2×SD16×C61—22no—
102C2×SD16×C61—22no—
103C2×SD16×C61—22no—
104C2×SD16×C61—22no—
105C2×SD16×C61—41no—
106C2×SD16×C61—41no—
107C2×D8×C61—22no—
108C2×D8×C61—22no—
109C2×D8×C61—22no—
110C2×D8×C61—22no—
111C2×D8×C61—22no—
112C2×D8×C61—41no—
113C22×C8×C61C2311yescharacteristic
114C22×C8×C61C2311yescharacteristic
115C22×C8×C61C2311yescharacteristic
116C22×C8×C61C2311yescharacteristic
117#124×C61—22no—
118#124×C61—22no—
119#124×C61—22no—
120#124×C61D414yescomplemented
121#123×C61—28no—
122C22⋊Q8×C61—22no—
123C22⋊Q8×C61—22no—
124C22⋊Q8×C61—22no—
125C22⋊Q8×C61—22no—
126C22⋊Q8×C61—41no—
127C22⋊Q8×C61—41no—
128#121×C61—28no—
129#121×C61—22no—
130#121×C61—22no—
131#121×C61—22no—
132#121×C61—22no—
133#121×C61—41no—
134#121×C61—41no—
135#120×C61—28no—
136C4×D4×C61—22no—
137C4×D4×C61—22no—
138C4×D4×C61—22no—
139C4×D4×C61D414yescomplemented
140C2×C4⋊C4×C61—21no—
141C2×C4⋊C4×C61—21no—
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61D411yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C22⋊C4×C61—28no—
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61—21no—
150C2×C22⋊C4×C61—21no—
151C2×C22⋊C4×C61—21no—
152C2×C22⋊C4×C61—21no—
153C2×C22⋊C4×C61—21no—
154C2×C22⋊C4×C61—21no—
155C2×C22⋊C4×C61—21no—
156C2×C22⋊C4×C61—21no—
157C2×C22⋊C4×C61—21no—
158C2×C22⋊C4×C61—21no—
159C2×C22⋊C4×C61D411yescharacteristic
160C2×C22⋊C4×C61D411yescharacteristic
161C2×C42×C61—21no—
162C2×C42×C61C2311yescharacteristic
163C4⋊C8×C61—22no—
164#103×C61—22no—
165#103×C61—22no—
166#103×C61—22no—
167#102×C61—22no—
168#102×C61—22no—
169#102×C61—22no—
170#102×C61D414yescomplemented
171#102×C61D414yescomplemented
172C22⋊C8×C61—22no—
173C22⋊C8×C61—22no—
174C22⋊C8×C61—22no—
175C22⋊C8×C61—22no—
176C4×C8×C61—22no—
177#95×C61—21no—
178C24×C61—21no—
179C24×C61—24no—
180C24×C61—21no—
181C24×C61—21no—
182C24×C61—42no—
183C24×C61—42no—
184C24×C61—42no—
185C24×C61—42no—
186C24×C61—81no—
187C24×C61—81no—
188C24×C61C2×D411yescharacteristic
189C24×C61C2×D411yescharacteristic
190#41×C61—44no—
191#41×C61—44no—
192#41×C61—44no—
193#41×C61—44no—
194C2×Q8×C61—21no—
195C2×Q8×C61—21no—
196C2×Q8×C61—21no—
197C2×Q8×C61—21no—
198C2×Q8×C61—21no—
199C2×Q8×C61—21no—
200C2×Q8×C61—21no—
201C2×Q8×C61—21no—
202C2×Q8×C61—21no—
203C2×Q8×C61—21no—
204C2×Q8×C61—21no—
205C2×Q8×C61C2×D412yes—
206C2×D4×C61—24no—
207C2×D4×C61—24no—
208C2×D4×C61—22no—
209C2×D4×C61—24no—
210C2×D4×C61—22no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—41no—
226C2×D4×C61—42no—
227C2×D4×C61—42no—
228C2×D4×C61—42no—
229C2×D4×C61—42no—
230C2×D4×C61—44no—
231C2×D4×C61—44no—
232C2×D4×C61—44no—
233C2×D4×C61—42no—
234C2×D4×C61—42no—
235C2×D4×C61—44no—
236C2×D4×C61—42no—
237C2×D4×C61—42no—
238C2×D4×C61—81no—
239C2×D4×C61—81no—
240C2×D4×C61—81no—
241C2×D4×C61—81no—
242C2×D4×C61C2×D412yes—
243C2×D4×C61C2×D412yes—
244C2×D4×C61C2×D412yes—
245C2×D4×C61C2×D412yes—
246C22×C4×C61—24no—
247C22×C4×C61—21no—
248C22×C4×C61—21no—
249C22×C4×C61—21no—
250C22×C4×C61—21no—
251C22×C4×C61—21no—
252C22×C4×C61—21no—
253C22×C4×C61—21no—
254C22×C4×C61—21no—
255C22×C4×C61—21no—
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61—21no—
261C22×C4×C61—21no—
262C22×C4×C61—21no—
263C22×C4×C61—24no—
264C22×C4×C61—21no—
265C22×C4×C61—42no—
266C22×C4×C61—42no—
267C22×C4×C61—81no—
268C22×C4×C61—81no—
269C22×C4×C61C2×D411yescharacteristic
270C22×C4×C61C2×D411yescharacteristic
271C22×C4×C61C2×D411yescharacteristic
272C22×C4×C61C2×D411yescharacteristic
273C22×C4×C61C2411yescharacteristic
274Q16×C61—44no—
275SD16×C61—44no—
276SD16×C61—44no—
277SD16×C61—44no—
278D8×C61—44no—
279D8×C61—44no—
280C2×C8×C61—21no—
281C2×C8×C61—21no—
282C2×C8×C61—21no—
283C2×C8×C61—21no—
284C2×C8×C61—21no—
285C2×C8×C61—21no—
286C2×C8×C61—21no—
287C2×C8×C61—21no—
288C2×C8×C61—21no—
289C2×C8×C61—21no—
290C2×C8×C61C2×D412yes—
291C2×C8×C61C2×D412yes—
292C4⋊C4×C61—24no—
293C4⋊C4×C61—22no—
294C4⋊C4×C61—21no—
295C4⋊C4×C61—21no—
296C4⋊C4×C61—21no—
297C4⋊C4×C61—42no—
298C4⋊C4×C61—42no—
299C4⋊C4×C61C2×D412yes—
300C4⋊C4×C61C2×D412yes—
301C4⋊C4×C61C2×D412yes—
302C22⋊C4×C61—24no—
303C22⋊C4×C61—24no—
304C22⋊C4×C61—22no—
305C22⋊C4×C61—24no—
306C22⋊C4×C61—24no—
307C22⋊C4×C61—24no—
308C22⋊C4×C61—22no—
309C22⋊C4×C61—42no—
310C22⋊C4×C61—42no—
311C22⋊C4×C61—42no—
312C22⋊C4×C61—42no—
313C22⋊C4×C61—42no—
314C22⋊C4×C61—42no—
315C42×C61—81no—
316C42×C61C2×D412yes—
317C42×C61C2×D412yes—
318C23×C61—21no—
319C23×C61—22no—
320C23×C61—21no—
321C23×C61—21no—
322C23×C61—22no—
323C23×C61—22no—
324C23×C61—21no—
325C23×C61—21no—
326C23×C61—21no—
327C23×C61—22no—
328C23×C61—21no—
329C23×C61—21no—
330C23×C61—21no—
331C23×C61—21no—
332C23×C61—21no—
333C23×C61—21no—
334C23×C61—21no—
335C23×C61—48no—
336C23×C61—48no—
337C23×C61—41no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—41no—
352C23×C61—41no—
353C23×C61—41no—
354C23×C61—84no—
355C23×C61—84no—
356C23×C61—84no—
357C23×C61—84no—
358C23×C61—84no—
359C23×C61#13512yes—
360C23×C61C22×D411yescharacteristic
361Q8×C61—22no—
362Q8×C61—22no—
363Q8×C61—41no—
364Q8×C61—41no—
365Q8×C61—41no—
366Q8×C61—41no—
367Q8×C61—41no—
368Q8×C61—41no—
369D4×C61—22no—
370D4×C61—22no—
371D4×C61—22no—
372D4×C61—22no—
373D4×C61—22no—
374D4×C61—44no—
375D4×C61—48no—
376D4×C61—48no—
377D4×C61—41no—
378D4×C61—41no—
379D4×C61—41no—
380D4×C61—41no—
381D4×C61—41no—
382D4×C61—41no—
383D4×C61—84no—
384D4×C61—84no—
385D4×C61—84no—
386D4×C61#12714yes—
387C2×C4×C61—21no—
388C2×C4×C61—21no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—22no—
392C2×C4×C61—21no—
393C2×C4×C61—22no—
394C2×C4×C61—21no—
395C2×C4×C61—22no—
396C2×C4×C61—22no—
397C2×C4×C61—21no—
398C2×C4×C61—21no—
399C2×C4×C61—21no—
400C2×C4×C61—21no—
401C2×C4×C61—48no—
402C2×C4×C61—41no—
403C2×C4×C61—41no—
404C2×C4×C61—41no—
405C2×C4×C61—41no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61—41no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61—41no—
417C2×C4×C61—41no—
418C2×C4×C61—41no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—84no—
422C2×C4×C61#12012yes—
423C2×C4×C61#12012yes—
424C2×C4×C61C22×D411yescharacteristic
425C2×C4×C61C22×D411yescharacteristic
426C2×C4×C61C22×D411yescharacteristic
427C2×C4×C61C22×D411yescharacteristic
428C2×C4×C61H(5,𝔽2)11yescharacteristic
429C2×C4×C61H(5,𝔽2)11yescharacteristic
430C8×C61—22no—
431C8×C61—22no—
432C8×C61—41no—
433C8×C61—41no—
434#25762C6111yesmaximal, characteristic, direct product factor, Sylow
435C22×C61—24no—
436C22×C61—22no—
437C22×C61—22no—
438C22×C61—22no—
439C22×C61—41no—
440C22×C61—42no—
441C22×C61—42no—
442C22×C61—41no—
443C22×C61—41no—
444C22×C61—42no—
445C22×C61—41no—
446C22×C61—42no—
447C22×C61—42no—
448C22×C61—42no—
449C22×C61—41no—
450C22×C61—42no—
451C22×C61—41no—
452C22×C61—42no—
453C22×C61—41no—
454C22×C61—42no—
455C22×C61—41no—
456C22×C61—41no—
457C22×C61—41no—
458C22×C61—41no—
459C22×C61—816no—
460C22×C61—81no—
461C22×C61—81no—
462C22×C61—81no—
463C22×C61—81no—
464C22×C61—81no—
465C22×C61—81no—
466C22×C61—81no—
467C22×C61—81no—
468C22×C61—81no—
469C22×C61—81no—
470C22×C61—81no—
471C22×C61C2×#12011yescharacteristic
472C22×C61D4211yescharacteristic
473C22×C61D4211yescharacteristic
474C22×C61C2×#13511yescharacteristic
475C22×C61#57511yescharacteristic
476C22×C61#57611yescharacteristic
477C22×C61#57711yescharacteristic
478C4×C61—22no—
479C4×C61—22no—
480C4×C61—41no—
481C4×C61—41no—
482C4×C61—42no—
483C4×C61—42no—
484C4×C61—42no—
485C4×C61—42no—
486C4×C61—81no—
487C4×C61C2×#12711yescharacteristic
488C4×C61#53511yescharacteristic
489C4×C61D4211yescharacteristic
490C4×C61D4211yescharacteristic
491C2×#546C2×C6111yescharacteristic, complemented
492C2×#495C2×C6111yescharacteristic, complemented
493C2×#463C2×C6111yescharacteristic, complemented
494C2×#452C2×C6111yescharacteristic, complemented
495C2×#449C2×C6111yescharacteristic, complemented
496C2×#450C2×C6111yescharacteristic, complemented
497C2×#447C2×C6111yescharacteristic, complemented
498#2540C2×C6111yescharacteristic, complemented
499#2001C2×C6111yescharacteristic, complemented
500#2000C2×C6111yescharacteristic, complemented
501#2000C2×C6111yescharacteristic, complemented
502#1999C2×C6111yescharacteristic, complemented
503#1983C2×C6111yescharacteristic, complemented
504#1954C2×C6111yescharacteristic, complemented
505C4×#102C2×C6111yescharacteristic, complemented
506C2×C61—42no—
507C2×C61—44no—
508C2×C61—81no—
509C2×C61—82no—
510C2×C61—161no—
511C2×C61#243311yescharacteristic
512C2×C61#300211yescharacteristic
513C2×C61#301211yescharacteristic
514C2×C61#327311yescharacteristic
515C2×C61#327511yescharacteristic
516C2×C61#328011yescharacteristic
517C2×C61#328211yescharacteristic
518C22×#41C22×C6111yescharacteristic
519C23×D4C22×C6111yescharacteristic
520C22×Q16C22×C6111yescharacteristic, complemented
521C22×SD16C22×C6111yescharacteristic
522C22×SD16C22×C6111yescharacteristic
523C22×SD16C22×C6111yescharacteristic, complemented
524C22×D8C22×C6111yescharacteristic
525C22×D8C22×C6111yescharacteristic
526#546—24no—
527#546—24no—
528C2×#124C22×C6111yescharacteristic
529C2×#124C22×C6111yescharacteristic, complemented
530C2×#123—21no—
531C2×C22⋊Q8C22×C6111yescharacteristic
532C2×C22⋊Q8C22×C6111yescharacteristic
533C2×C22⋊Q8C22×C6111yescharacteristic, complemented
534C2×#121—21no—
535C2×#121C22×C6111yescharacteristic
536C2×#121C22×C6111yescharacteristic
537C2×#121C22×C6111yescharacteristic, complemented
538C2×#120—21no—
539C2×C4×D4C22×C6111yescharacteristic
540C2×C4×D4C22×C6111yescharacteristic
541C22×C22⋊C4—21no—
542#495—24no—
543#463—24no—
544#452—24no—
545#450—24no—
546#449—24no—
547#447—24no—
548C2×C4⋊C8C22×C6111yescharacteristic, complemented
549C2×#103C22×C6111yescharacteristic, complemented
550C2×#103C22×C6111yescharacteristic, complemented
551C2×#103C22×C6111yescharacteristic, complemented
552C2×#102C22×C6111yescharacteristic
553C2×#102C22×C6111yescharacteristic
554C2×#102C22×C6111yescharacteristic
555C2×#102C22×C6111yescharacteristic
556C2×#102C22×C6111yescharacteristic, complemented
557C2×C22⋊C8C22×C6111yescharacteristic
558C2×C22⋊C8C22×C6111yescharacteristic
559C2×C22⋊C8C22×C6111yescharacteristic, complemented
560C2×C22⋊C8C22×C6111yescharacteristic, complemented
561C2×C4×C8C22×C6111yescharacteristic, complemented
562#399—21no—
563#392—21no—
564#390—21no—
565#390—21no—
566C4×C4⋊C4C22×C6111yescharacteristic, complemented
567#340C22×C6111yescharacteristic, complemented
568#340C22×C6111yescharacteristic, complemented
569C61#2576211yescharacteristic, direct product factor, Sylow
570C25—21no—
571C2×#41—22no—
572C2×#41—22no—
573C2×#41—22no—
574C2×#41—22no—
575C2×#41—41no—
576C2×#41—41no—
577C22×Q8C23×C6111yescharacteristic
578C22×Q8C23×C6111yescharacteristic
579C22×D4—21no—
580C22×D4—21no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—22no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4—41no—
589C22×D4—41no—
590C22×D4D4×C6111yescharacteristic
591C22×D4C23×C6111yescharacteristic
592C22×D4C23×C6111yescharacteristic
593C22×D4C23×C6111yescharacteristic
594C23×C4—21no—
595C23×C4—21no—
596C23×C4C23×C6111yescharacteristic
597C23×C4C23×C6111yescharacteristic
598C2×Q16—22no—
599C2×Q16—22no—
600C2×Q16—41no—
601C2×SD16—22no—
602C2×SD16—22no—
603C2×SD16—22no—
604C2×SD16—22no—
605C2×SD16—22no—
606C2×SD16—22no—
607C2×SD16—22no—
608C2×SD16—41no—
609C2×SD16—41no—
610C2×D8—22no—
611C2×D8—22no—
612C2×D8—22no—
613C2×D8—22no—
614C2×D8—22no—
615C2×D8—41no—
616C22×C8C23×C6111yescharacteristic
617C22×C8C23×C6111yescharacteristic
618C22×C8C23×C6111yescharacteristic
619C22×C8C23×C6111yescharacteristic
620#124—22no—
621#124—22no—
622#124—22no—
623#124D4×C6114yescomplemented
624#123—28no—
625C22⋊Q8—22no—
626C22⋊Q8—22no—
627C22⋊Q8—22no—
628C22⋊Q8—22no—
629C22⋊Q8—41no—
630C22⋊Q8—41no—
631#121—28no—
632#121—22no—
633#121—22no—
634#121—22no—
635#121—22no—
636#121—41no—
637#121—41no—
638#120—28no—
639C4×D4—22no—
640C4×D4—22no—
641C4×D4—22no—
642C4×D4D4×C6114yescomplemented
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4D4×C6111yescharacteristic
647C2×C4⋊C4C23×C6111yescharacteristic
648C2×C4⋊C4C23×C6111yescharacteristic
649C2×C4⋊C4C23×C6111yescharacteristic
650C2×C22⋊C4—28no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4D4×C6111yescharacteristic
663C2×C22⋊C4D4×C6111yescharacteristic
664C2×C42—21no—
665C2×C42C23×C6111yescharacteristic
666C4⋊C8—22no—
667#103—22no—
668#103—22no—
669#103—22no—
670#102—22no—
671#102—22no—
672#102—22no—
673#102D4×C6114yescomplemented
674#102D4×C6114yescomplemented
675C22⋊C8—22no—
676C22⋊C8—22no—
677C22⋊C8—22no—
678C22⋊C8—22no—
679C4×C8—22no—
680#95—21no—
681C24—21no—
682C24—24no—
683C24—21no—
684C24—21no—
685C24—42no—
686C24—42no—
687C24—42no—
688C24—42no—
689C24—81no—
690C24—81no—
691C24C2×D4×C6111yescharacteristic
692C24C2×D4×C6111yescharacteristic
693#41—44no—
694#41—44no—
695#41—44no—
696#41—44no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—21no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8C2×D4×C6112yes—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—22no—
712C2×D4—24no—
713C2×D4—22no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—41no—
729C2×D4—42no—
730C2×D4—42no—
731C2×D4—42no—
732C2×D4—42no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—44no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—81no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4C2×D4×C6112yes—
746C2×D4C2×D4×C6112yes—
747C2×D4C2×D4×C6112yes—
748C2×D4C2×D4×C6112yes—
749C22×C4—24no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—81no—
771C22×C4—81no—
772C22×C4C2×D4×C6111yescharacteristic
773C22×C4C2×D4×C6111yescharacteristic
774C22×C4C2×D4×C6111yescharacteristic
775C22×C4C2×D4×C6111yescharacteristic
776C22×C4C24×C6111yescharacteristic
777Q16—44no—
778SD16—44no—
779SD16—44no—
780SD16—44no—
781D8—44no—
782D8—44no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—21no—
788C2×C8—21no—
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8C2×D4×C6112yes—
794C2×C8C2×D4×C6112yes—
795C4⋊C4—24no—
796C4⋊C4—22no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—42no—
801C4⋊C4—42no—
802C4⋊C4C2×D4×C6112yes—
803C4⋊C4C2×D4×C6112yes—
804C4⋊C4C2×D4×C6112yes—
805C22⋊C4—24no—
806C22⋊C4—24no—
807C22⋊C4—22no—
808C22⋊C4—24no—
809C22⋊C4—24no—
810C22⋊C4—24no—
811C22⋊C4—22no—
812C22⋊C4—42no—
813C22⋊C4—42no—
814C22⋊C4—42no—
815C22⋊C4—42no—
816C22⋊C4—42no—
817C22⋊C4—42no—
818C42—81no—
819C42C2×D4×C6112yes—
820C42C2×D4×C6112yes—
821C23—21no—
822C23—21no—
823C23—22no—
824C23—22no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—22no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—22no—
837C23—21no—
838C23—48no—
839C23—48no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—84no—
858C23—84no—
859C23—84no—
860C23—84no—
861C23—84no—
862C23#135×C6112yes—
863C23C22×D4×C6111yescharacteristic
864Q8—22no—
865Q8—22no—
866Q8—41no—
867Q8—41no—
868Q8—41no—
869Q8—41no—
870Q8—41no—
871Q8—41no—
872D4—22no—
873D4—22no—
874D4—22no—
875D4—22no—
876D4—22no—
877D4—44no—
878D4—48no—
879D4—48no—
880D4—41no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—84no—
887D4—84no—
888D4—84no—
889D4#127×C6114yes—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—22no—
901C2×C4—21no—
902C2×C4—22no—
903C2×C4—21no—
904C2×C4—48no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—84no—
925C2×C4#120×C6112yes—
926C2×C4#120×C6112yes—
927C2×C4C22×D4×C6111yescharacteristic
928C2×C4C22×D4×C6111yescharacteristic
929C2×C4C22×D4×C6111yescharacteristic
930C2×C4C22×D4×C6111yescharacteristic
931C2×C4H(5,𝔽2)×C6111yescharacteristic
932C2×C4H(5,𝔽2)×C6111yescharacteristic
933C8—22no—
934C8—22no—
935C8—41no—
936C8—41no—
937C22—24no—
938C22—22no—
939C22—22no—
940C22—22no—
941C22—41no—
942C22—42no—
943C22—42no—
944C22—41no—
945C22—41no—
946C22—42no—
947C22—41no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—41no—
952C22—42no—
953C22—41no—
954C22—42no—
955C22—41no—
956C22—42no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—816no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22C2×#120×C6111yescharacteristic
974C22D42×C6111yescharacteristic
975C22D42×C6111yescharacteristic
976C22C2×#135×C6111yescharacteristic
977C22C61×#57511yescharacteristic
978C22C61×#57611yescharacteristic
979C22C61×#57711yescharacteristic
980C4—22no—
981C4—22no—
982C4—41no—
983C4—41no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—81no—
989C4C2×#127×C6111yescharacteristic
990C4C61×#53511yescharacteristic
991C4D42×C6111yescharacteristic
992C4D42×C6111yescharacteristic
993C2—42no—
994C2—44no—
995C2—81no—
996C2—82no—
997C2—161no—
998C2C61×#243311yescharacteristic
999C2C61×#300211yescharacteristic
1000C2C61×#301211yescharacteristic
1001C2C61×#327311yescharacteristic
1002C2C61×#327511yescharacteristic
1003C2C61×#328011yescharacteristic
1004C2C61×#328211yescharacteristic
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×#495C2semidirect
3. C2×C61×#463C2semidirect
4. C2×C61×#452C2semidirect
5. C2×C61×#449C2semidirect
6. C2×C61×#450C2semidirect
7. C2×C61×#447C2semidirect
8. C61×#2540C2semidirect
9. C61×#2001C2semidirect
10. C61×#2000C2semidirect
11. C61×#2000C2semidirect
12. C61×#1999C2semidirect
13. C61×#1983C2semidirect
14. C61×#1954C2semidirect
15. C4×#102×C61C2semidirect
18. C22×Q16×C61C22semidirect
21. C22×SD16×C61C22semidirect
27. C2×#124×C61C22semidirect
31. C2×C22⋊Q8×C61C22semidirect
35. C2×#121×C61C22semidirect
46. C2×C4⋊C8×C61C22semidirect
47. C2×#103×C61C22semidirect
48. C2×#103×C61C22semidirect
49. C2×#103×C61C22semidirect
54. C2×#102×C61C22semidirect
57. C2×C22⋊C8×C61C22semidirect
58. C2×C22⋊C8×C61C22semidirect
59. C2×C4×C8×C61C22semidirect
64. C4×C4⋊C4×C61C22semidirect
65. C61×#340C22semidirect
66. C61×#340C22semidirect
120. #124×C61D4semidirect
139. C4×D4×C61D4semidirect
170. #102×C61D4semidirect
171. #102×C61D4semidirect
434. #25762C61direct (N × H)
491. C2×#546C2×C61semidirect
492. C2×#495C2×C61semidirect
493. C2×#463C2×C61semidirect
494. C2×#452C2×C61semidirect
495. C2×#449C2×C61semidirect
496. C2×#450C2×C61semidirect
497. C2×#447C2×C61semidirect
498. #2540C2×C61semidirect
499. #2001C2×C61semidirect
500. #2000C2×C61semidirect
501. #2000C2×C61semidirect
502. #1999C2×C61semidirect
503. #1983C2×C61semidirect
504. #1954C2×C61semidirect
505. C4×#102C2×C61semidirect
520. C22×Q16C22×C61semidirect
523. C22×SD16C22×C61semidirect
529. C2×#124C22×C61semidirect
533. C2×C22⋊Q8C22×C61semidirect
537. C2×#121C22×C61semidirect
548. C2×C4⋊C8C22×C61semidirect
549. C2×#103C22×C61semidirect
550. C2×#103C22×C61semidirect
551. C2×#103C22×C61semidirect
556. C2×#102C22×C61semidirect
559. C2×C22⋊C8C22×C61semidirect
560. C2×C22⋊C8C22×C61semidirect
561. C2×C4×C8C22×C61semidirect
566. C4×C4⋊C4C22×C61semidirect
567. #340C22×C61semidirect
568. #340C22×C61semidirect
569. C61#25762direct (N × H)
623. #124D4×C61semidirect
642. C4×D4D4×C61semidirect
673. #102D4×C61semidirect
674. #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×#4952
C2×C61×#4632
C2×C61×#4522
C2×C61×#4492
C2×C61×#4502
C2×C61×#4472
C61×#25402
C61×#20012
C61×#20002
C61×#19992
C61×#19832
C61×#19542
C4×#102×C612
#2576261