Finite Group Databasebeta

← C61×#22424 #29525857

Subgroups — C61×#22424 #29525857

Order 15616.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#546C211yesmaximal, characteristic
2C2×C61×#435C211yesmaximal, characteristic, complemented
3C2×C61×#418C211yesmaximal, characteristic, complemented
4C2×C61×#416C211yesmaximal, characteristic, complemented
5C61×#2354C211yesmaximal, characteristic, complemented
6C61×#1983C211yesmaximal, characteristic, complemented
7C61×#1959C211yesmaximal, characteristic, complemented
8C61×#1894C211yesmaximal, characteristic, complemented
9C61×#1893C211yesmaximal, characteristic, complemented
10C61×#1875C211yesmaximal, characteristic, complemented
11C61×#1873C211yesmaximal, characteristic, complemented
12C61×#1802C211yesmaximal, characteristic, complemented
13C61×#1788C211yesmaximal, characteristic, complemented
14C61×#1786C211yesmaximal, characteristic, complemented
15C61×#1762C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C22×M16×C61C2211yescharacteristic
19C23×C8×C61C2211yescharacteristic, complemented
20C61×#546—24no—
21C61×#546C418yescomplemented
22C2×#124×C61C2211yescharacteristic
23C2×#123×C61—21no—
24C2×C22⋊Q8×C61C2211yescharacteristic
25C2×#121×C61—21no—
26C2×#121×C61C2211yescharacteristic
27C2×#120×C61—21no—
28C2×C4×D4×C61C2211yescharacteristic
29C2×C4×D4×C61C2211yescharacteristic
30C2×#117×C61C2211yescharacteristic
31C2×#117×C61C2211yescharacteristic, complemented
32C22×C22⋊C4×C61—21no—
33C61×#435—24no—
34C2×C4⋊C8×C61C2211yescharacteristic, complemented
35C61×#418—24no—
36C61×#416—24no—
37C2×#103×C61C2211yescharacteristic, complemented
38C2×#103×C61C2211yescharacteristic, complemented
39C2×#103×C61C2211yescharacteristic, complemented
40C2×#103×C61C2211yescharacteristic, complemented
41C2×#102×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×#102×C61C2211yescharacteristic
44C2×#102×C61C2211yescharacteristic
45C2×#102×C61C2211yescharacteristic
46C2×#102×C61C2211yescharacteristic
47C2×#102×C61C2211yescharacteristic
48C2×#102×C61C2211yescharacteristic
49C2×C22⋊C8×C61C2211yescharacteristic
50C2×C22⋊C8×C61C2211yescharacteristic, complemented
51C2×#97×C61C2211yescharacteristic, complemented
52C61×#390—21no—
53C61×#388—21no—
54C61×#388—21no—
55C61×#384C2211yescharacteristic, complemented
56C61×#380C2211yescharacteristic
57C61×#380C2211yescharacteristic, complemented
58C4×C4⋊C4×C61—21no—
59C4×C4⋊C4×C61C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C25×C61—21no—
65C2×#41×C61—22no—
66C2×#41×C61—22no—
67C2×#41×C61—22no—
68C2×#41×C61—41no—
69C2×#41×C61—41no—
70C2×#41×C61C2×C414yes—
71C22×Q8×C61C2311yescharacteristic
72C22×D4×C61—22no—
73C22×D4×C61—22no—
74C22×D4×C61—21no—
75C22×D4×C61—21no—
76C22×D4×C61—22no—
77C22×D4×C61—21no—
78C22×D4×C61—41no—
79C22×D4×C61—41no—
80C22×D4×C61C2×C414yes—
81C22×D4×C61D411yescharacteristic
82C22×D4×C61C2311yescharacteristic
83C22×D4×C61C2311yescharacteristic
84C23×C4×C61—21no—
85C23×C4×C61—21no—
86C23×C4×C61C2311yescharacteristic
87C23×C4×C61C2311yescharacteristic
88C2×M16×C61—22no—
89C2×M16×C61—22no—
90C2×M16×C61—41no—
91C22×C8×C61—22no—
92C22×C8×C61—22no—
93C22×C8×C61—41no—
94C22×C8×C61C2311yescharacteristic
95C22×C8×C61C2311yescharacteristic
96C22×C8×C61C2311yescharacteristic
97C22×C8×C61C2311yescharacteristic
98#124×C61—22no—
99#124×C61C2×C414yes—
100#123×C61—28no—
101C22⋊Q8×C61—22no—
102C22⋊Q8×C61C2×C414yes—
103#121×C61—22no—
104#121×C61—28no—
105#121×C61C2×C414yes—
106#120×C61—28no—
107C4×D4×C61—22no—
108C4×D4×C61C2×C414yes—
109C4×D4×C61C2×C414yes—
110C4×D4×C61D414yes—
111#117×C61—22no—
112#117×C61—22no—
113#117×C61—41no—
114#117×C61—41no—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61D411yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—28no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61D411yescharacteristic
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C42×C61—21no—
137C2×C42×C61—21no—
138C2×C42×C61—21no—
139C2×C42×C61C2311yescharacteristic
140C4⋊C8×C61—22no—
141#103×C61—22no—
142#103×C61—22no—
143#103×C61—41no—
144#103×C61—41no—
145#102×C61—22no—
146#102×C61—22no—
147#102×C61—22no—
148#102×C61—22no—
149#102×C61—22no—
150#102×C61—41no—
151#102×C61—41no—
152#102×C61D414yescomplemented
153C22⋊C8×C61—22no—
154C22⋊C8×C61—22no—
155#97×C61—22no—
156#95×C61—21no—
157#95×C61—21no—
158#95×C61—21no—
159C24×C61—21no—
160C24×C61—21no—
161C24×C61—24no—
162C24×C61—42no—
163C24×C61—42no—
164C24×C61—42no—
165C24×C61—42no—
166C24×C61—81no—
167C24×C61—81no—
168C24×C61C2×D411yescharacteristic
169C24×C61C2×D411yescharacteristic
170#41×C61—28no—
171#41×C61—44no—
172#41×C61—44no—
173#41×C61—44no—
174C2×Q8×C61—21no—
175C2×Q8×C61—21no—
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61C22×C412yes—
180C2×D4×C61—28no—
181C2×D4×C61—24no—
182C2×D4×C61—24no—
183C2×D4×C61—24no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—21no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—44no—
193C2×D4×C61—44no—
194C2×D4×C61—44no—
195C2×D4×C61—41no—
196C2×D4×C61—41no—
197C2×D4×C61—42no—
198C2×D4×C61—42no—
199C2×D4×C61—42no—
200C2×D4×C61—42no—
201C2×D4×C61—81no—
202C2×D4×C61—81no—
203C2×D4×C61C22⋊C414yes—
204C2×D4×C61C22×C412yes—
205C2×D4×C61C22×C412yes—
206C2×D4×C61C2×D412yes—
207C2×D4×C61#4112yes—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—24no—
220C22×C4×C61—24no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—42no—
225C22×C4×C61—42no—
226C22×C4×C61—81no—
227C22×C4×C61—81no—
228C22×C4×C61C22×C412yes—
229C22×C4×C61C22×C412yes—
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D412yes—
235C22×C4×C61C2×D412yes—
236C22×C4×C61C2411yescharacteristic
237M16×C61—44no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—44no—
250C2×C8×C61C2×D412yes—
251C4⋊C4×C61—24no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—42no—
261C4⋊C4×C61—81no—
262C4⋊C4×C61C22⋊C414yes—
263C4⋊C4×C61C22×C412yes—
264C4⋊C4×C61C2×D412yes—
265C22⋊C4×C61—24no—
266C22⋊C4×C61—24no—
267C22⋊C4×C61—24no—
268C22⋊C4×C61—24no—
269C22⋊C4×C61—24no—
270C22⋊C4×C61—42no—
271C22⋊C4×C61—42no—
272C22⋊C4×C61—81no—
273C22⋊C4×C61—81no—
274C22⋊C4×C61C22⋊C414yes—
275C22⋊C4×C61C22⋊C414yes—
276C42×C61—42no—
277C42×C61—42no—
278C42×C61—42no—
279C42×C61C22×C412yes—
280C42×C61C2×D412yes—
281C23×C61—22no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—22no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—22no—
288C23×C61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—22no—
297C23×C61—48no—
298C23×C61—48no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—84no—
310C23×C61—84no—
311C23×C61—84no—
312C23×C61—84no—
313C23×C61—84no—
314C23×C61C2×C22⋊C412yes—
315C23×C61C2×C22⋊C412yes—
316C23×C61C22×D411yescharacteristic
317Q8×C61—22no—
318Q8×C61—22no—
319Q8×C61—41no—
320Q8×C61—41no—
321D4×C61—22no—
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—22no—
325D4×C61—22no—
326D4×C61—44no—
327D4×C61—48no—
328D4×C61—48no—
329D4×C61—41no—
330D4×C61—41no—
331D4×C61—84no—
332D4×C61C4×D414yes—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—48no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—84no—
369C2×C4×C61C2×C22⋊C412yes—
370C2×C4×C61C2×C22⋊C412yes—
371C2×C4×C61C2×C22⋊C412yes—
372C2×C4×C61C2×C22⋊C412yes—
373C2×C4×C61C23×C411yescharacteristic
374C2×C4×C61C22×D411yescharacteristic
375C2×C4×C61C22×D411yescharacteristic
376C2×C4×C61C2×#4111yescharacteristic
377C2×C4×C61H(5,𝔽2)11yescharacteristic
378C2×C4×C61H(5,𝔽2)11yescharacteristic
379C8×C61—22no—
380C8×C61—41no—
381C8×C61—41no—
382C8×C61—41no—
383#22424C6111yesmaximal, characteristic, direct product factor, Sylow
384C22×C61—22no—
385C22×C61—22no—
386C22×C61—24no—
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—22no—
391C22×C61—42no—
392C22×C61—42no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—42no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—42no—
399C22×C61—41no—
400C22×C61—41no—
401C22×C61—42no—
402C22×C61—41no—
403C22×C61—41no—
404C22×C61—42no—
405C22×C61—42no—
406C22×C61—42no—
407C22×C61—42no—
408C22×C61—816no—
409C22×C61—81no—
410C22×C61—81no—
411C22×C61—81no—
412C22×C61—81no—
413C22×C61C22×C22⋊C411yescharacteristic
414C22×C61D4211yescharacteristic
415C22×C61#54611yescharacteristic
416C22×C61#57511yescharacteristic
417C22×C61#57511yescharacteristic
418C22×C61#57611yescharacteristic
419C22×C61#57711yescharacteristic
420C4×C61—22no—
421C4×C61—22no—
422C4×C61—22no—
423C4×C61—22no—
424C4×C61—42no—
425C4×C61—42no—
426C4×C61—42no—
427C4×C61—81no—
428C4×C61—81no—
429C4×C61—81no—
430C4×C61C2×C4×D411yescharacteristic
431C4×C61#51811yescharacteristic
432C4×C61D4211yescharacteristic
433C4×C61#54611yescharacteristic
434C2×#546C2×C6111yescharacteristic
435C2×#435C2×C6111yescharacteristic, complemented
436C2×#418C2×C6111yescharacteristic, complemented
437C2×#416C2×C6111yescharacteristic, complemented
438#2354C2×C6111yescharacteristic, complemented
439#1983C2×C6111yescharacteristic, complemented
440#1959C2×C6111yescharacteristic, complemented
441#1894C2×C6111yescharacteristic, complemented
442#1893C2×C6111yescharacteristic, complemented
443#1875C2×C6111yescharacteristic, complemented
444#1873C2×C6111yescharacteristic, complemented
445#1802C2×C6111yescharacteristic, complemented
446#1788C2×C6111yescharacteristic, complemented
447#1786C2×C6111yescharacteristic, complemented
448#1762C2×C6111yescharacteristic, complemented
449C2×C61—42no—
450C2×C61—42no—
451C2×C61—44no—
452C2×C61—82no—
453C2×C61D4×C22⋊C411yescharacteristic
454C2×C61#289611yescharacteristic
455C2×C61#289711yescharacteristic
456C2×C61#326711yescharacteristic
457C2×C61#326811yescharacteristic
458C2×C61#331111yescharacteristic
459C2×C61#331911yescharacteristic
460C22×#41C22×C6111yescharacteristic
461C23×D4C22×C6111yescharacteristic
462C22×M16C22×C6111yescharacteristic
463C23×C8C22×C6111yescharacteristic, complemented
464#546—24no—
465#546C4×C6118yescomplemented
466C2×#124C22×C6111yescharacteristic
467C2×#123—21no—
468C2×C22⋊Q8C22×C6111yescharacteristic
469C2×#121—21no—
470C2×#121C22×C6111yescharacteristic
471C2×#120—21no—
472C2×C4×D4C22×C6111yescharacteristic
473C2×C4×D4C22×C6111yescharacteristic
474C2×#117C22×C6111yescharacteristic
475C2×#117C22×C6111yescharacteristic, complemented
476C22×C22⋊C4—21no—
477#435—24no—
478C2×C4⋊C8C22×C6111yescharacteristic, complemented
479#418—24no—
480#416—24no—
481C2×#103C22×C6111yescharacteristic, complemented
482C2×#103C22×C6111yescharacteristic, complemented
483C2×#103C22×C6111yescharacteristic, complemented
484C2×#103C22×C6111yescharacteristic, complemented
485C2×#102C22×C6111yescharacteristic
486C2×#102C22×C6111yescharacteristic
487C2×#102C22×C6111yescharacteristic
488C2×#102C22×C6111yescharacteristic
489C2×#102C22×C6111yescharacteristic
490C2×#102C22×C6111yescharacteristic
491C2×#102C22×C6111yescharacteristic
492C2×#102C22×C6111yescharacteristic
493C2×C22⋊C8C22×C6111yescharacteristic
494C2×C22⋊C8C22×C6111yescharacteristic, complemented
495C2×#97C22×C6111yescharacteristic, complemented
496#390—21no—
497#388—21no—
498#388—21no—
499#384C22×C6111yescharacteristic, complemented
500#380C22×C6111yescharacteristic
501#380C22×C6111yescharacteristic, complemented
502C4×C4⋊C4—21no—
503C4×C4⋊C4C22×C6111yescharacteristic, complemented
504#340C22×C6111yescharacteristic, complemented
505#340C22×C6111yescharacteristic, complemented
506#340C22×C6111yescharacteristic, complemented
507#340C22×C6111yescharacteristic, complemented
508C61#2242411yescharacteristic, direct product factor, Sylow
509C25—21no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×C4×C6114yes—
516C22×Q8C23×C6111yescharacteristic
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×C4×C6114yes—
526C22×D4D4×C6111yescharacteristic
527C22×D4C23×C6111yescharacteristic
528C22×D4C23×C6111yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C23×C6111yescharacteristic
532C23×C4C23×C6111yescharacteristic
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—41no—
536C22×C8—22no—
537C22×C8—22no—
538C22×C8—41no—
539C22×C8C23×C6111yescharacteristic
540C22×C8C23×C6111yescharacteristic
541C22×C8C23×C6111yescharacteristic
542C22×C8C23×C6111yescharacteristic
543#124—22no—
544#124C2×C4×C6114yes—
545#123—28no—
546C22⋊Q8—22no—
547C22⋊Q8C2×C4×C6114yes—
548#121—22no—
549#121—28no—
550#121C2×C4×C6114yes—
551#120—28no—
552C4×D4—22no—
553C4×D4C2×C4×C6114yes—
554C4×D4C2×C4×C6114yes—
555C4×D4D4×C6114yes—
556#117—22no—
557#117—22no—
558#117—41no—
559#117—41no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4D4×C6111yescharacteristic
564C2×C4⋊C4C23×C6111yescharacteristic
565C2×C4⋊C4C23×C6111yescharacteristic
566C2×C4⋊C4C23×C6111yescharacteristic
567C2×C4⋊C4C23×C6111yescharacteristic
568C2×C4⋊C4C23×C6111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4D4×C6111yescharacteristic
580C2×C22⋊C4D4×C6111yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42—21no—
584C2×C42C23×C6111yescharacteristic
585C4⋊C8—22no—
586#103—22no—
587#103—22no—
588#103—41no—
589#103—41no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—22no—
595#102—41no—
596#102—41no—
597#102D4×C6114yescomplemented
598C22⋊C8—22no—
599C22⋊C8—22no—
600#97—22no—
601#95—21no—
602#95—21no—
603#95—21no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24C2×D4×C6111yescharacteristic
614C24C2×D4×C6111yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C22×C4×C6112yes—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊C4×C6114yes—
649C2×D4C22×C4×C6112yes—
650C2×D4C22×C4×C6112yes—
651C2×D4C2×D4×C6112yes—
652C2×D4#41×C6112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—81no—
672C22×C4—81no—
673C22×C4C22×C4×C6112yes—
674C22×C4C22×C4×C6112yes—
675C22×C4C2×D4×C6111yescharacteristic
676C22×C4C2×D4×C6111yescharacteristic
677C22×C4C2×D4×C6111yescharacteristic
678C22×C4C2×D4×C6111yescharacteristic
679C22×C4C2×D4×C6112yes—
680C22×C4C2×D4×C6112yes—
681C22×C4C24×C6111yescharacteristic
682M16—44no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—44no—
695C2×C8C2×D4×C6112yes—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—42no—
706C4⋊C4—81no—
707C4⋊C4C22⋊C4×C6114yes—
708C4⋊C4C22×C4×C6112yes—
709C4⋊C4C2×D4×C6112yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—81no—
718C22⋊C4—81no—
719C22⋊C4C22⋊C4×C6114yes—
720C22⋊C4C22⋊C4×C6114yes—
721C42—42no—
722C42—42no—
723C42—42no—
724C42C22×C4×C6112yes—
725C42C2×D4×C6112yes—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—22no—
741C23—22no—
742C23—48no—
743C23—48no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23C2×C22⋊C4×C6112yes—
760C23C2×C22⋊C4×C6112yes—
761C23C22×D4×C6111yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—44no—
772D4—48no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4C4×D4×C6114yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—48no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—84no—
814C2×C4C2×C22⋊C4×C6112yes—
815C2×C4C2×C22⋊C4×C6112yes—
816C2×C4C2×C22⋊C4×C6112yes—
817C2×C4C2×C22⋊C4×C6112yes—
818C2×C4C23×C4×C6111yescharacteristic
819C2×C4C22×D4×C6111yescharacteristic
820C2×C4C22×D4×C6111yescharacteristic
821C2×C4C2×#41×C6111yescharacteristic
822C2×C4H(5,𝔽2)×C6111yescharacteristic
823C2×C4H(5,𝔽2)×C6111yescharacteristic
824C8—22no—
825C8—41no—
826C8—41no—
827C8—41no—
828C22—22no—
829C22—22no—
830C22—24no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—41no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22C22×C22⋊C4×C6111yescharacteristic
858C22D42×C6111yescharacteristic
859C22C61×#54611yescharacteristic
860C22C61×#57511yescharacteristic
861C22C61×#57511yescharacteristic
862C22C61×#57611yescharacteristic
863C22C61×#57711yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4C2×C4×D4×C6111yescharacteristic
875C4C61×#51811yescharacteristic
876C4D42×C6111yescharacteristic
877C4C61×#54611yescharacteristic
878C2—42no—
879C2—42no—
880C2—44no—
881C2—82no—
882C2D4×C22⋊C4×C6111yescharacteristic
883C2C61×#289611yescharacteristic
884C2C61×#289711yescharacteristic
885C2C61×#326711yescharacteristic
886C2C61×#326811yescharacteristic
887C2C61×#331111yescharacteristic
888C2C61×#331911yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutatorC2×C4C23×C4×C61
Frattini, cosocleC22×C4C24×C61
prime radicalC2×C61×#546C2
LCSG ▷ C2×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
2. C2×C61×#435C2semidirect
3. C2×C61×#418C2semidirect
4. C2×C61×#416C2semidirect
5. C61×#2354C2semidirect
6. C61×#1983C2semidirect
7. C61×#1959C2semidirect
8. C61×#1894C2semidirect
9. C61×#1893C2semidirect
10. C61×#1875C2semidirect
11. C61×#1873C2semidirect
12. C61×#1802C2semidirect
13. C61×#1788C2semidirect
14. C61×#1786C2semidirect
15. C61×#1762C2semidirect
19. C23×C8×C61C22semidirect
21. C61×#546C4semidirect
31. C2×#117×C61C22semidirect
34. C2×C4⋊C8×C61C22semidirect
37. C2×#103×C61C22semidirect
38. C2×#103×C61C22semidirect
39. C2×#103×C61C22semidirect
40. C2×#103×C61C22semidirect
50. C2×C22⋊C8×C61C22semidirect
51. C2×#97×C61C22semidirect
55. C61×#384C22semidirect
57. C61×#380C22semidirect
59. C4×C4⋊C4×C61C22semidirect
60. C61×#340C22semidirect
61. C61×#340C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
152. #102×C61D4semidirect
383. #22424C61direct (N × H)
435. C2×#435C2×C61semidirect
436. C2×#418C2×C61semidirect
437. C2×#416C2×C61semidirect
438. #2354C2×C61semidirect
439. #1983C2×C61semidirect
440. #1959C2×C61semidirect
441. #1894C2×C61semidirect
442. #1893C2×C61semidirect
443. #1875C2×C61semidirect
444. #1873C2×C61semidirect
445. #1802C2×C61semidirect
446. #1788C2×C61semidirect
447. #1786C2×C61semidirect
448. #1762C2×C61semidirect
463. C23×C8C22×C61semidirect
465. #546C4×C61semidirect
475. C2×#117C22×C61semidirect
478. C2×C4⋊C8C22×C61semidirect
481. C2×#103C22×C61semidirect
482. C2×#103C22×C61semidirect
483. C2×#103C22×C61semidirect
484. C2×#103C22×C61semidirect
494. C2×C22⋊C8C22×C61semidirect
495. C2×#97C22×C61semidirect
499. #384C22×C61semidirect
501. #380C22×C61semidirect
503. C4×C4⋊C4C22×C61semidirect
504. #340C22×C61semidirect
505. #340C22×C61semidirect
506. #340C22×C61semidirect
507. #340C22×C61semidirect
508. C61#22424direct (N × H)
597. #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×#4352
C2×C61×#4182
C2×C61×#4162
C61×#23542
C61×#19832
C61×#19592
C61×#18942
C61×#18932
C61×#18752
C61×#18732
C61×#18022
C61×#17882
C61×#17862
C61×#17622
#2242461