Finite Group Databasebeta

← C61×#24395 #29527828

Subgroups — C61×#24395 #29527828

Order 15616.

1450 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#537C211yesmaximal, characteristic
2C2×C61×#470C211yesmaximal, characteristic, complemented
3C2×C61×#465C211yesmaximal, characteristic, complemented
4C2×C61×#452C211yesmaximal, characteristic, complemented
5C2×C61×#408C211yesmaximal, characteristic, complemented
6C61×#2616C211yesmaximal, characteristic, complemented
7C61×#2035C211yesmaximal, characteristic, complemented
8C61×#2034C211yesmaximal, characteristic, complemented
9C61×#2001C211yesmaximal, characteristic, complemented
10C61×#2000C211yesmaximal, characteristic, complemented
11C61×#1895C211yesmaximal, characteristic, complemented
12C61×#1892C211yesmaximal, characteristic, complemented
13C61×#1872C211yesmaximal, characteristic, complemented
14C61×#1853C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×#41×C61C2211yescharacteristic
18C22×Q16×C61C2211yescharacteristic
19C22×SD16×C61C2211yescharacteristic
20C22×M16×C61C2211yescharacteristic
21C23×C8×C61C2211yescharacteristic
22C61×#537—24no—
23C61×#537—24no—
24C2×C22⋊Q8×C61—21no—
25C2×C22⋊Q8×C61C2211yescharacteristic
26C2×C22⋊Q8×C61C2211yescharacteristic
27C2×C22⋊Q8×C61C2211yescharacteristic
28C2×C22⋊Q8×C61C2211yescharacteristic
29C2×C22⋊Q8×C61C2211yescharacteristic
30C2×#121×C61—21no—
31C2×#121×C61—21no—
32C2×#121×C61—21no—
33C2×#121×C61C2211yescharacteristic
34C2×#121×C61C2211yescharacteristic
35C22×C4⋊C4×C61C2211yescharacteristic
36C61×#470—24no—
37C61×#465—24no—
38C61×#452—24no—
39C2×#106×C61C2211yescharacteristic
40C2×#106×C61C2211yescharacteristic
41C2×#103×C61C2211yescharacteristic
42C2×#103×C61C2211yescharacteristic
43C2×#103×C61C2211yescharacteristic
44C2×#103×C61C2211yescharacteristic
45C2×#103×C61C2211yescharacteristic
46C2×#102×C61C2211yescharacteristic
47C2×#102×C61C2211yescharacteristic
48C2×#102×C61C2211yescharacteristic
49C61×#408—24no—
50C2×C22⋊C8×C61C2211yescharacteristic
51C2×C22⋊C8×C61C2211yescharacteristic
52C2×C22⋊C8×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic
54C61×#395—21no—
55C61×#394—21no—
56C61×#394—21no—
57C61×#394—21no—
58C61×#380C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#380C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C61×#340C2211yescharacteristic
65C2×#41×C61—22no—
66C2×#41×C61—22no—
67C2×#41×C61—22no—
68C2×#41×C61—22no—
69C2×#41×C61—22no—
70C2×#41×C61—22no—
71C2×#41×C61—22no—
72C2×#41×C61—22no—
73C2×#41×C61—41no—
74C2×#41×C61—41no—
75C2×#41×C61—41no—
76C2×#41×C61—41no—
77C22×Q8×C61D411yescharacteristic
78C22×Q8×C61C2311yescharacteristic
79C22×Q8×C61C2311yescharacteristic
80C22×D4×C61—21no—
81C22×D4×C61—21no—
82C22×D4×C61—21no—
83C22×D4×C61D411yescharacteristic
84C22×D4×C61D411yescharacteristic
85C22×D4×C61D411yescharacteristic
86C22×D4×C61C2311yescharacteristic
87C23×C4×C61—21no—
88C23×C4×C61—21no—
89C23×C4×C61C2311yescharacteristic
90C23×C4×C61C2311yescharacteristic
91C23×C4×C61C2311yescharacteristic
92C2×Q16×C61—22no—
93C2×Q16×C61—22no—
94C2×Q16×C61—41no—
95C2×SD16×C61—22no—
96C2×SD16×C61—22no—
97C2×SD16×C61—41no—
98C2×M16×C61—22no—
99C2×M16×C61—22no—
100C2×M16×C61—41no—
101C22×C8×C61—22no—
102C22×C8×C61—22no—
103C22×C8×C61—41no—
104C22×C8×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C22⋊Q8×C61—28no—
109C22⋊Q8×C61—22no—
110C22⋊Q8×C61—22no—
111C22⋊Q8×C61—22no—
112C22⋊Q8×C61—22no—
113C22⋊Q8×C61—22no—
114C22⋊Q8×C61—22no—
115C22⋊Q8×C61—22no—
116C22⋊Q8×C61—41no—
117C22⋊Q8×C61—41no—
118C22⋊Q8×C61D414yes—
119#121×C61—28no—
120#121×C61—28no—
121#121×C61—28no—
122#121×C61—22no—
123#121×C61—22no—
124#121×C61—22no—
125#121×C61D414yes—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—22no—
130C2×C4⋊C4×C61—22no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61—21no—
133C2×C4⋊C4×C61—21no—
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
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×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C22⋊C4×C61—21no—
149#106×C61—22no—
150#106×C61—22no—
151#103×C61—22no—
152#103×C61—22no—
153#103×C61—22no—
154#103×C61—22no—
155#103×C61—41no—
156#102×C61—22no—
157#102×C61—22no—
158#102×C61—41no—
159C22⋊C8×C61—22no—
160C22⋊C8×C61—22no—
161C22⋊C8×C61—22no—
162C22⋊C8×C61D414yescomplemented
163#95×C61—21no—
164#95×C61—21no—
165#95×C61—21no—
166C24×C61—21no—
167C24×C61C2×D411yescharacteristic
168C24×C61C2×D411yescharacteristic
169C24×C61C2×D411yescharacteristic
170#41×C61—44no—
171#41×C61—44no—
172#41×C61—44no—
173#41×C61—44no—
174#41×C61—44no—
175#41×C61—44no—
176#41×C61—44no—
177#41×C61—44no—
178C2×Q8×C61—22no—
179C2×Q8×C61—22no—
180C2×Q8×C61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61—21no—
187C2×Q8×C61—21no—
188C2×Q8×C61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—21no—
191C2×Q8×C61—41no—
192C2×Q8×C61C2×D412yes—
193C2×D4×C61—24no—
194C2×D4×C61—22no—
195C2×D4×C61—22no—
196C2×D4×C61—22no—
197C2×D4×C61—22no—
198C2×D4×C61—24no—
199C2×D4×C61—24no—
200C2×D4×C61—22no—
201C2×D4×C61—22no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—41no—
208C2×D4×C61—41no—
209C2×D4×C61—41no—
210C2×D4×C61—42no—
211C2×D4×C61—42no—
212C2×D4×C61—81no—
213C2×D4×C61—81no—
214C2×D4×C61—81no—
215C2×D4×C61—81no—
216C2×D4×C61C2×D412yes—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—24no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—24no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—42no—
241C22×C4×C61—42no—
242C22×C4×C61—81no—
243C22×C4×C61—81no—
244C22×C4×C61C2×D411yescharacteristic
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2×D412yes—
247C22×C4×C61C2×D412yes—
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D412yes—
250C22×C4×C61#4112yes—
251C22×C4×C61C2411yescharacteristic
252Q16×C61—44no—
253SD16×C61—44no—
254M16×C61—44no—
255C2×C8×C61—21no—
256C2×C8×C61—21no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—44no—
266C2×C8×C61C2×D412yes—
267C2×C8×C61C2×D412yes—
268C4⋊C4×C61—24no—
269C4⋊C4×C61—24no—
270C4⋊C4×C61—24no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—42no—
280C4⋊C4×C61—42no—
281C4⋊C4×C61—42no—
282C4⋊C4×C61C2×D412yes—
283C4⋊C4×C61C2×D412yes—
284C22⋊C4×C61—24no—
285C22⋊C4×C61—24no—
286C22⋊C4×C61—24no—
287C22⋊C4×C61—24no—
288C22⋊C4×C61—42no—
289C22⋊C4×C61—42no—
290C22⋊C4×C61—42no—
291C22⋊C4×C61—81no—
292C22⋊C4×C61—81no—
293C22⋊C4×C61—81no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—22no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—21no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61#12012yes—
321C23×C61#12112yes—
322C23×C61C22×D411yescharacteristic
323Q8×C61—22no—
324Q8×C61—22no—
325Q8×C61—44no—
326Q8×C61—41no—
327Q8×C61—41no—
328Q8×C61—41no—
329Q8×C61—41no—
330Q8×C61—41no—
331Q8×C61—41no—
332D4×C61—22no—
333D4×C61—22no—
334D4×C61—44no—
335D4×C61—44no—
336D4×C61—44no—
337D4×C61—48no—
338D4×C61—41no—
339D4×C61—41no—
340D4×C61—84no—
341D4×C61—84no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
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—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—48no—
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—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—84no—
384C2×C4×C61#12012yes—
385C2×C4×C61#12112yes—
386C2×C4×C61C22×D411yescharacteristic
387C2×C4×C61C22×D411yescharacteristic
388C2×C4×C61C22×D411yescharacteristic
389C2×C4×C61C2×#4111yescharacteristic
390C2×C4×C61H(5,𝔽2)11yescharacteristic
391C2×C4×C61H(5,𝔽2)11yescharacteristic
392C8×C61—22no—
393C8×C61—22no—
394C8×C61—41no—
395C8×C61—41no—
396#24395C6111yesmaximal, characteristic, direct product factor, Sylow
397C22×C61—22no—
398C22×C61—22no—
399C22×C61—22no—
400C22×C61—22no—
401C22×C61—22no—
402C22×C61—22no—
403C22×C61—41no—
404C22×C61—41no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61—42no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61—41no—
415C22×C61—41no—
416C22×C61—42no—
417C22×C61—41no—
418C22×C61—42no—
419C22×C61—41no—
420C22×C61—41no—
421C22×C61—81no—
422C22×C61—81no—
423C22×C61—81no—
424C22×C61—81no—
425C22×C61C2×#12011yescharacteristic
426C22×C61C2×#12111yescharacteristic
427C22×C61#53411yescharacteristic
428C22×C61#57711yescharacteristic
429C22×C61#57711yescharacteristic
430C22×C61#57711yescharacteristic
431C22×C61#57811yescharacteristic
432C4×C61—22no—
433C4×C61—22no—
434C4×C61—41no—
435C4×C61—42no—
436C4×C61—42no—
437C4×C61—42no—
438C4×C61—81no—
439C4×C61—81no—
440C4×C61—81no—
441C4×C61—81no—
442C4×C61D4211yescharacteristic
443C4×C61D4211yescharacteristic
444C4×C61#54611yescharacteristic
445C4×C61#54611yescharacteristic
446C2×#537C2×C6111yescharacteristic
447C2×#470C2×C6111yescharacteristic, complemented
448C2×#465C2×C6111yescharacteristic, complemented
449C2×#452C2×C6111yescharacteristic, complemented
450C2×#408C2×C6111yescharacteristic, complemented
451#2616C2×C6111yescharacteristic, complemented
452#2035C2×C6111yescharacteristic, complemented
453#2034C2×C6111yescharacteristic, complemented
454#2001C2×C6111yescharacteristic, complemented
455#2000C2×C6111yescharacteristic, complemented
456#1895C2×C6111yescharacteristic, complemented
457#1892C2×C6111yescharacteristic, complemented
458#1872C2×C6111yescharacteristic, complemented
459#1853C2×C6111yescharacteristic, complemented
460#1788C2×C6111yescharacteristic, complemented
461C2×C61—42no—
462C2×C61—42no—
463C2×C61—81no—
464C2×C61—82no—
465C2×C61#241011yescharacteristic
466C2×C61#300911yescharacteristic
467C2×C61#301311yescharacteristic
468C2×C61#306011yescharacteristic
469C2×C61#306311yescharacteristic
470C2×C61#320111yescharacteristic
471C2×C61#320411yescharacteristic
472C22×#41C22×C6111yescharacteristic
473C22×#41C22×C6111yescharacteristic
474C22×Q16C22×C6111yescharacteristic
475C22×SD16C22×C6111yescharacteristic
476C22×M16C22×C6111yescharacteristic
477C23×C8C22×C6111yescharacteristic
478#537—24no—
479#537—24no—
480C2×C22⋊Q8—21no—
481C2×C22⋊Q8C22×C6111yescharacteristic
482C2×C22⋊Q8C22×C6111yescharacteristic
483C2×C22⋊Q8C22×C6111yescharacteristic
484C2×C22⋊Q8C22×C6111yescharacteristic
485C2×C22⋊Q8C22×C6111yescharacteristic
486C2×#121—21no—
487C2×#121—21no—
488C2×#121—21no—
489C2×#121C22×C6111yescharacteristic
490C2×#121C22×C6111yescharacteristic
491C22×C4⋊C4C22×C6111yescharacteristic
492#470—24no—
493#465—24no—
494#452—24no—
495C2×#106C22×C6111yescharacteristic
496C2×#106C22×C6111yescharacteristic
497C2×#103C22×C6111yescharacteristic
498C2×#103C22×C6111yescharacteristic
499C2×#103C22×C6111yescharacteristic
500C2×#103C22×C6111yescharacteristic
501C2×#103C22×C6111yescharacteristic
502C2×#102C22×C6111yescharacteristic
503C2×#102C22×C6111yescharacteristic
504C2×#102C22×C6111yescharacteristic
505#408—24no—
506C2×C22⋊C8C22×C6111yescharacteristic
507C2×C22⋊C8C22×C6111yescharacteristic
508C2×C22⋊C8C22×C6111yescharacteristic
509C2×C22⋊C8C22×C6111yescharacteristic
510#395—21no—
511#394—21no—
512#394—21no—
513#394—21no—
514#380C22×C6111yescharacteristic
515#380C22×C6111yescharacteristic
516#380C22×C6111yescharacteristic
517#340C22×C6111yescharacteristic
518#340C22×C6111yescharacteristic
519#340C22×C6111yescharacteristic
520#340C22×C6111yescharacteristic
521C61#2439511yescharacteristic, direct product factor, Sylow
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—41no—
531C2×#41—41no—
532C2×#41—41no—
533C2×#41—41no—
534C22×Q8D4×C6111yescharacteristic
535C22×Q8C23×C6111yescharacteristic
536C22×Q8C23×C6111yescharacteristic
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4D4×C6111yescharacteristic
541C22×D4D4×C6111yescharacteristic
542C22×D4D4×C6111yescharacteristic
543C22×D4C23×C6111yescharacteristic
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C23×C6111yescharacteristic
547C23×C4C23×C6111yescharacteristic
548C23×C4C23×C6111yescharacteristic
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—41no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×M16—22no—
556C2×M16—22no—
557C2×M16—41no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—41no—
561C22×C8C23×C6111yescharacteristic
562C22×C8C23×C6111yescharacteristic
563C22×C8C23×C6111yescharacteristic
564C22×C8C23×C6111yescharacteristic
565C22⋊Q8—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8D4×C6114yes—
576#121—28no—
577#121—28no—
578#121—28no—
579#121—22no—
580#121—22no—
581#121—22no—
582#121D4×C6114yes—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4C23×C6111yescharacteristic
592C2×C4⋊C4C23×C6111yescharacteristic
593C2×C4⋊C4C23×C6111yescharacteristic
594C2×C4⋊C4C23×C6111yescharacteristic
595C2×C4⋊C4C23×C6111yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606#106—22no—
607#106—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—22no—
612#103—41no—
613#102—22no—
614#102—22no—
615#102—41no—
616C22⋊C8—22no—
617C22⋊C8—22no—
618C22⋊C8—22no—
619C22⋊C8D4×C6114yescomplemented
620#95—21no—
621#95—21no—
622#95—21no—
623C24—21no—
624C24C2×D4×C6111yescharacteristic
625C24C2×D4×C6111yescharacteristic
626C24C2×D4×C6111yescharacteristic
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—44no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—41no—
649C2×Q8C2×D4×C6112yes—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—41no—
665C2×D4—41no—
666C2×D4—41no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—81no—
670C2×D4—81no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4C2×D4×C6112yes—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—24no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—24no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—81no—
700C22×C4—81no—
701C22×C4C2×D4×C6111yescharacteristic
702C22×C4C2×D4×C6111yescharacteristic
703C22×C4C2×D4×C6112yes—
704C22×C4C2×D4×C6112yes—
705C22×C4C2×D4×C6111yescharacteristic
706C22×C4C2×D4×C6112yes—
707C22×C4#41×C6112yes—
708C22×C4C24×C6111yescharacteristic
709Q16—44no—
710SD16—44no—
711M16—44no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—44no—
723C2×C8C2×D4×C6112yes—
724C2×C8C2×D4×C6112yes—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4—42no—
739C4⋊C4C2×D4×C6112yes—
740C4⋊C4C2×D4×C6112yes—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—81no—
749C22⋊C4—81no—
750C22⋊C4—81no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—21no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23#120×C6112yes—
778C23#121×C6112yes—
779C23C22×D4×C6111yescharacteristic
780Q8—22no—
781Q8—22no—
782Q8—44no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789D4—22no—
790D4—22no—
791D4—44no—
792D4—44no—
793D4—44no—
794D4—48no—
795D4—41no—
796D4—41no—
797D4—84no—
798D4—84no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—48no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—84no—
841C2×C4#120×C6112yes—
842C2×C4#121×C6112yes—
843C2×C4C22×D4×C6111yescharacteristic
844C2×C4C22×D4×C6111yescharacteristic
845C2×C4C22×D4×C6111yescharacteristic
846C2×C4C2×#41×C6111yescharacteristic
847C2×C4H(5,𝔽2)×C6111yescharacteristic
848C2×C4H(5,𝔽2)×C6111yescharacteristic
849C8—22no—
850C8—22no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—42no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—42no—
875C22—41no—
876C22—42no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22C2×#120×C6111yescharacteristic
882C22C2×#121×C6111yescharacteristic
883C22C61×#53411yescharacteristic
884C22C61×#57711yescharacteristic
885C22C61×#57711yescharacteristic
886C22C61×#57711yescharacteristic
887C22C61×#57811yescharacteristic
888C4—22no—
889C4—22no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4D42×C6111yescharacteristic
899C4D42×C6111yescharacteristic
900C4C61×#54611yescharacteristic
901C4C61×#54611yescharacteristic
902C2—42no—
903C2—42no—
904C2—81no—
905C2—82no—
906C2C61×#241011yescharacteristic
907C2C61×#300911yescharacteristic
908C2C61×#301311yescharacteristic
909C2C61×#306011yescharacteristic
910C2C61×#306311yescharacteristic
911C2C61×#320111yescharacteristic
912C2C61×#320411yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×C61×#537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C22×#41×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#470C2semidirect
3. C2×C61×#465C2semidirect
4. C2×C61×#452C2semidirect
5. C2×C61×#408C2semidirect
6. C61×#2616C2semidirect
7. C61×#2035C2semidirect
8. C61×#2034C2semidirect
9. C61×#2001C2semidirect
10. C61×#2000C2semidirect
11. C61×#1895C2semidirect
12. C61×#1892C2semidirect
13. C61×#1872C2semidirect
14. C61×#1853C2semidirect
15. C61×#1788C2semidirect
162. C22⋊C8×C61D4semidirect
396. #24395C61direct (N × H)
447. C2×#470C2×C61semidirect
448. C2×#465C2×C61semidirect
449. C2×#452C2×C61semidirect
450. C2×#408C2×C61semidirect
451. #2616C2×C61semidirect
452. #2035C2×C61semidirect
453. #2034C2×C61semidirect
454. #2001C2×C61semidirect
455. #2000C2×C61semidirect
456. #1895C2×C61semidirect
457. #1892C2×C61semidirect
458. #1872C2×C61semidirect
459. #1853C2×C61semidirect
460. #1788C2×C61semidirect
521. C61#24395direct (N × H)
619. C22⋊C8D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5372
C2×C61×#4702
C2×C61×#4652
C2×C61×#4522
C2×C61×#4082
C61×#26162
C61×#20352
C61×#20342
C61×#20012
C61×#20002
C61×#18952
C61×#18922
C61×#18722
C61×#18532
C61×#17882
#2439561