Finite Group Databasebeta

← C61×#24389 #29527822

Subgroups — C61×#24389 #29527822

Order 15616.

1568 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#525C211yesmaximal, characteristic
2C2×C61×#470C211yesmaximal, characteristic, complemented
3C2×C61×#468C211yesmaximal, characteristic, complemented
4C2×C61×#452C211yesmaximal, characteristic, complemented
5C2×C61×#407C211yesmaximal, characteristic, complemented
6C61×#2848C211yesmaximal, characteristic, complemented
7C61×#2036C211yesmaximal, characteristic, complemented
8C61×#2034C211yesmaximal, characteristic, complemented
9C61×#2001C211yesmaximal, characteristic, complemented
10C61×#2000C211yesmaximal, characteristic, complemented
11C61×#1895C211yesmaximal, characteristic, complemented
12C61×#1894C211yesmaximal, characteristic, complemented
13C61×#1873C211yesmaximal, characteristic, complemented
14C61×#1854C211yesmaximal, characteristic, complemented
15C61×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C24×C4×C61C2211yescharacteristic
18C22×Q16×C61C2211yescharacteristic, complemented
19C22×SD16×C61C2211yescharacteristic, complemented
20C22×M16×C61C2211yescharacteristic
21C22×M16×C61C2211yescharacteristic
22C61×#525—24no—
23C61×#525—24no—
24C2×#123×C61—21no—
25C2×C22⋊Q8×C61C2211yescharacteristic
26C2×C22⋊Q8×C61C2211yescharacteristic
27C2×C22⋊Q8×C61C2211yescharacteristic
28C2×C22⋊Q8×C61C2211yescharacteristic
29C2×C22⋊Q8×C61C2211yescharacteristic
30C2×#121×C61C2211yescharacteristic
31C2×#121×C61C2211yescharacteristic
32C2×#120×C61—21no—
33C2×C4×D4×C61—21no—
34C2×C4×D4×C61—21no—
35C2×#117×C61C2211yescharacteristic
36C61×#470—24no—
37C61×#468—24no—
38C61×#452—24no—
39C2×#107×C61C2211yescharacteristic, complemented
40C2×#106×C61C2211yescharacteristic, complemented
41C2×#103×C61C2211yescharacteristic, complemented
42C2×#103×C61C2211yescharacteristic, complemented
43C2×#103×C61C2211yescharacteristic, complemented
44C2×#103×C61C2211yescharacteristic, complemented
45C2×#103×C61C2211yescharacteristic, complemented
46C2×#102×C61C2211yescharacteristic, complemented
47C2×#102×C61C2211yescharacteristic, complemented
48C2×#102×C61C2211yescharacteristic, complemented
49C61×#407—24no—
50C2×C22⋊C8×C61C2211yescharacteristic
51C2×C22⋊C8×C61C2211yescharacteristic
52C2×C22⋊C8×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic
54C61×#385—21no—
55C61×#385—21no—
56C61×#385—21no—
57C61×#380C2211yescharacteristic
58C61×#380C2211yescharacteristic
59C61×#380C2211yescharacteristic
60C61×#379—21no—
61C61×#340C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C61×#340C2211yescharacteristic, complemented
65C25×C61D411yescharacteristic
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×Q8×C61C2311yescharacteristic
74C22×D4×C61—21no—
75C22×D4×C61—21no—
76C22×D4×C61—21no—
77C22×D4×C61C2311yescharacteristic
78C23×C4×C61—22no—
79C23×C4×C61—22no—
80C23×C4×C61—22no—
81C23×C4×C61—21no—
82C23×C4×C61—22no—
83C23×C4×C61—41no—
84C23×C4×C61—41no—
85C23×C4×C61D411yescharacteristic
86C23×C4×C61D411yescharacteristic
87C23×C4×C61D411yescharacteristic
88C23×C4×C61C2311yescharacteristic
89C23×C4×C61C2311yescharacteristic
90C23×C4×C61C2311yescharacteristic
91C2×Q16×C61—22no—
92C2×Q16×C61—22no—
93C2×Q16×C61—41no—
94C2×SD16×C61—22no—
95C2×SD16×C61—22no—
96C2×SD16×C61—41no—
97C2×M16×C61—22no—
98C2×M16×C61—22no—
99C2×M16×C61—22no—
100C2×M16×C61—22no—
101C2×M16×C61—41no—
102C2×M16×C61—41no—
103C22×C8×C61C2311yescharacteristic
104C22×C8×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107#123×C61—28no—
108C22⋊Q8×C61—22no—
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—41no—
116C22⋊Q8×C61—41no—
117C22⋊Q8×C61D414yes—
118#121×C61—22no—
119#121×C61—22no—
120#121×C61—22no—
121#121×C61D414yes—
122#120×C61—28no—
123C4×D4×C61—28no—
124C4×D4×C61—28no—
125#117×C61—22no—
126#117×C61—22no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131C2×C4⋊C4×C61—21no—
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61C2311yescharacteristic
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×C61—21no—
147C2×C22⋊C4×C61—21no—
148C2×C42×C61—21no—
149#107×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—22no—
167C24×C61—22no—
168C24×C61—22no—
169C24×C61—21no—
170C24×C61—41no—
171C24×C61—41no—
172C24×C61—41no—
173C24×C61—41no—
174C24×C61C2×D411yescharacteristic
175C24×C61C2×D411yescharacteristic
176C24×C61C2×D411yescharacteristic
177#41×C61—44no—
178#41×C61—44no—
179#41×C61—44no—
180#41×C61—44no—
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—21no—
192C2×Q8×C61C2×D412yes—
193C2×D4×C61—24no—
194C2×D4×C61—24no—
195C2×D4×C61—24no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—42no—
202C2×D4×C61—42no—
203C2×D4×C61—42no—
204C2×D4×C61—42no—
205C2×D4×C61—42no—
206C2×D4×C61—42no—
207C2×D4×C61C2×D412yes—
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—24no—
217C22×C4×C61—22no—
218C22×C4×C61—22no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—22no—
223C22×C4×C61—22no—
224C22×C4×C61—22no—
225C22×C4×C61—22no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
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—41no—
237C22×C4×C61—41no—
238C22×C4×C61—41no—
239C22×C4×C61—44no—
240C22×C4×C61—44no—
241C22×C4×C61—44no—
242C22×C4×C61—44no—
243C22×C4×C61—42no—
244C22×C4×C61—42no—
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D412yes—
248C22×C4×C61C2×D412yes—
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D412yes—
251C22×C4×C61#4112yes—
252C22×C4×C61C2411yescharacteristic
253Q16×C61—44no—
254SD16×C61—44no—
255M16×C61—44no—
256M16×C61—44no—
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—21no—
266C2×C8×C61—21no—
267C2×C8×C61C2×D412yes—
268C2×C8×C61C2×D412yes—
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—24no—
289C22⋊C4×C61—42no—
290C22⋊C4×C61—42no—
291C22⋊C4×C61—42no—
292C22⋊C4×C61—42no—
293C22⋊C4×C61—42no—
294C22⋊C4×C61—42no—
295C42×C61—24no—
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—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—21no—
313C23×C61—21no—
314C23×C61—22no—
315C23×C61—44no—
316C23×C61—44no—
317C23×C61—44no—
318C23×C61—44no—
319C23×C61—44no—
320C23×C61—44no—
321C23×C61—44no—
322C23×C61—41no—
323C23×C61—41no—
324C23×C61—41no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—41no—
328C23×C61#12012yes—
329C23×C61#12112yes—
330C23×C61#13712yes—
331C23×C61C22×D411yescharacteristic
332Q8×C61—22no—
333Q8×C61—22no—
334Q8×C61—41no—
335Q8×C61—41no—
336Q8×C61—41no—
337Q8×C61—41no—
338Q8×C61—41no—
339Q8×C61—41no—
340D4×C61—22no—
341D4×C61—22no—
342D4×C61—48no—
343D4×C61—48no—
344D4×C61—48no—
345D4×C61—41no—
346D4×C61—41no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—21no—
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—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—21no—
362C2×C4×C61—22no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—44no—
366C2×C4×C61—44no—
367C2×C4×C61—44no—
368C2×C4×C61—48no—
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—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#12012yes—
392C2×C4×C61#12112yes—
393C2×C4×C61C22×D411yescharacteristic
394C2×C4×C61C22×D411yescharacteristic
395C2×C4×C61C22×D411yescharacteristic
396C2×C4×C61C2×#4111yescharacteristic
397C2×C4×C61H(5,𝔽2)11yescharacteristic
398C2×C4×C61H(5,𝔽2)11yescharacteristic
399C8×C61—22no—
400C8×C61—22no—
401C8×C61—41no—
402C8×C61—41no—
403#24389C6111yesmaximal, characteristic, direct product factor, Sylow
404C22×C61—22no—
405C22×C61—22no—
406C22×C61—22no—
407C22×C61—22no—
408C22×C61—22no—
409C22×C61—22no—
410C22×C61—22no—
411C22×C61—22no—
412C22×C61—22no—
413C22×C61—416no—
414C22×C61—41no—
415C22×C61—41no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—41no—
420C22×C61—41no—
421C22×C61—41no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—42no—
427C22×C61—42no—
428C22×C61—42no—
429C22×C61—81no—
430C22×C61—81no—
431C22×C61—81no—
432C22×C61—81no—
433C22×C61C2×#12011yescharacteristic
434C22×C61C2×#12111yescharacteristic
435C22×C61#53411yescharacteristic
436C22×C61C2×#13711yescharacteristic
437C22×C61#57511yescharacteristic
438C22×C61#57511yescharacteristic
439C22×C61#57511yescharacteristic
440C4×C61—22no—
441C4×C61—22no—
442C4×C61—41no—
443C4×C61—42no—
444C4×C61—42no—
445C4×C61—42no—
446C4×C61—81no—
447C4×C61—81no—
448C4×C61—81no—
449C4×C61—81no—
450C4×C61D4211yescharacteristic
451C4×C61D4211yescharacteristic
452C4×C61#54611yescharacteristic
453C4×C61#54611yescharacteristic
454C2×#525C2×C6111yescharacteristic
455C2×#470C2×C6111yescharacteristic, complemented
456C2×#468C2×C6111yescharacteristic, complemented
457C2×#452C2×C6111yescharacteristic, complemented
458C2×#407C2×C6111yescharacteristic, complemented
459#2848C2×C6111yescharacteristic, complemented
460#2036C2×C6111yescharacteristic, complemented
461#2034C2×C6111yescharacteristic, complemented
462#2001C2×C6111yescharacteristic, complemented
463#2000C2×C6111yescharacteristic, complemented
464#1895C2×C6111yescharacteristic, complemented
465#1894C2×C6111yescharacteristic, complemented
466#1873C2×C6111yescharacteristic, complemented
467#1854C2×C6111yescharacteristic, complemented
468#1788C2×C6111yescharacteristic, complemented
469C2×C61—42no—
470C2×C61—42no—
471C2×C61—42no—
472C2×C61—82no—
473C2×C61#241011yescharacteristic
474C2×C61#300511yescharacteristic
475C2×C61#300711yescharacteristic
476C2×C61#305411yescharacteristic
477C2×C61#305611yescharacteristic
478C2×C61#319611yescharacteristic
479C2×C61#319711yescharacteristic
480C22×#41C22×C6111yescharacteristic
481C24×C4C22×C6111yescharacteristic
482C22×Q16C22×C6111yescharacteristic, complemented
483C22×SD16C22×C6111yescharacteristic, complemented
484C22×M16C22×C6111yescharacteristic
485C22×M16C22×C6111yescharacteristic
486#525—24no—
487#525—24no—
488C2×#123—21no—
489C2×C22⋊Q8C22×C6111yescharacteristic
490C2×C22⋊Q8C22×C6111yescharacteristic
491C2×C22⋊Q8C22×C6111yescharacteristic
492C2×C22⋊Q8C22×C6111yescharacteristic
493C2×C22⋊Q8C22×C6111yescharacteristic
494C2×#121C22×C6111yescharacteristic
495C2×#121C22×C6111yescharacteristic
496C2×#120—21no—
497C2×C4×D4—21no—
498C2×C4×D4—21no—
499C2×#117C22×C6111yescharacteristic
500#470—24no—
501#468—24no—
502#452—24no—
503C2×#107C22×C6111yescharacteristic, complemented
504C2×#106C22×C6111yescharacteristic, complemented
505C2×#103C22×C6111yescharacteristic, complemented
506C2×#103C22×C6111yescharacteristic, complemented
507C2×#103C22×C6111yescharacteristic, complemented
508C2×#103C22×C6111yescharacteristic, complemented
509C2×#103C22×C6111yescharacteristic, complemented
510C2×#102C22×C6111yescharacteristic, complemented
511C2×#102C22×C6111yescharacteristic, complemented
512C2×#102C22×C6111yescharacteristic, complemented
513#407—24no—
514C2×C22⋊C8C22×C6111yescharacteristic
515C2×C22⋊C8C22×C6111yescharacteristic
516C2×C22⋊C8C22×C6111yescharacteristic
517C2×C22⋊C8C22×C6111yescharacteristic
518#385—21no—
519#385—21no—
520#385—21no—
521#380C22×C6111yescharacteristic
522#380C22×C6111yescharacteristic
523#380C22×C6111yescharacteristic
524#379—21no—
525#340C22×C6111yescharacteristic, complemented
526#340C22×C6111yescharacteristic, complemented
527#340C22×C6111yescharacteristic, complemented
528#340C22×C6111yescharacteristic, complemented
529C61#2438911yescharacteristic, direct product factor, Sylow
530C25D4×C6111yescharacteristic
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—22no—
535C2×#41—41no—
536C2×#41—41no—
537C22×Q8C23×C6111yescharacteristic
538C22×Q8C23×C6111yescharacteristic
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4C23×C6111yescharacteristic
543C23×C4—21no—
544C23×C4—22no—
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—41no—
549C23×C4—41no—
550C23×C4D4×C6111yescharacteristic
551C23×C4D4×C6111yescharacteristic
552C23×C4D4×C6111yescharacteristic
553C23×C4C23×C6111yescharacteristic
554C23×C4C23×C6111yescharacteristic
555C23×C4C23×C6111yescharacteristic
556C2×Q16—22no—
557C2×Q16—22no—
558C2×Q16—41no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—41no—
562C2×M16—22no—
563C2×M16—22no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—41no—
567C2×M16—41no—
568C22×C8C23×C6111yescharacteristic
569C22×C8C23×C6111yescharacteristic
570C22×C8C23×C6111yescharacteristic
571C22×C8C23×C6111yescharacteristic
572#123—28no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8D4×C6114yes—
583#121—22no—
584#121—22no—
585#121—22no—
586#121D4×C6114yes—
587#120—28no—
588C4×D4—28no—
589C4×D4—28no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4C23×C6111yescharacteristic
598C2×C4⋊C4C23×C6111yescharacteristic
599C2×C4⋊C4C23×C6111yescharacteristic
600C2×C4⋊C4C23×C6111yescharacteristic
601C2×C4⋊C4C23×C6111yescharacteristic
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C42—21no—
614#107—22no—
615#106—22no—
616#103—22no—
617#103—22no—
618#103—22no—
619#103—22no—
620#103—41no—
621#102—22no—
622#102—22no—
623#102—41no—
624C22⋊C8—22no—
625C22⋊C8—22no—
626C22⋊C8—22no—
627C22⋊C8D4×C6114yescomplemented
628#95—21no—
629#95—21no—
630#95—21no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—21no—
635C24—41no—
636C24—41no—
637C24—41no—
638C24—41no—
639C24C2×D4×C6111yescharacteristic
640C24C2×D4×C6111yescharacteristic
641C24C2×D4×C6111yescharacteristic
642#41—44no—
643#41—44no—
644#41—44no—
645#41—44no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8C2×D4×C6112yes—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4C2×D4×C6112yes—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—41no—
702C22×C4—41no—
703C22×C4—41no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4C2×D4×C6111yescharacteristic
711C22×C4C2×D4×C6111yescharacteristic
712C22×C4C2×D4×C6112yes—
713C22×C4C2×D4×C6112yes—
714C22×C4C2×D4×C6111yescharacteristic
715C22×C4C2×D4×C6112yes—
716C22×C4#41×C6112yes—
717C22×C4C24×C6111yescharacteristic
718Q16—44no—
719SD16—44no—
720M16—44no—
721M16—44no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8C2×D4×C6112yes—
733C2×C8C2×D4×C6112yes—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—42no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4C2×D4×C6112yes—
748C4⋊C4C2×D4×C6112yes—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—24no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C22⋊C4—42no—
760C42—24no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23—44no—
786C23—44no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23#120×C6112yes—
794C23#121×C6112yes—
795C23#137×C6112yes—
796C23C22×D4×C6111yescharacteristic
797Q8—22no—
798Q8—22no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803Q8—41no—
804Q8—41no—
805D4—22no—
806D4—22no—
807D4—48no—
808D4—48no—
809D4—48no—
810D4—41no—
811D4—41no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—22no—
829C2×C4—21no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—48no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4#120×C6112yes—
857C2×C4#121×C6112yes—
858C2×C4C22×D4×C6111yescharacteristic
859C2×C4C22×D4×C6111yescharacteristic
860C2×C4C22×D4×C6111yescharacteristic
861C2×C4C2×#41×C6111yescharacteristic
862C2×C4H(5,𝔽2)×C6111yescharacteristic
863C2×C4H(5,𝔽2)×C6111yescharacteristic
864C8—22no—
865C8—22no—
866C8—41no—
867C8—41no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—416no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—81no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22C2×#120×C6111yescharacteristic
898C22C2×#121×C6111yescharacteristic
899C22C61×#53411yescharacteristic
900C22C2×#137×C6111yescharacteristic
901C22C61×#57511yescharacteristic
902C22C61×#57511yescharacteristic
903C22C61×#57511yescharacteristic
904C4—22no—
905C4—22no—
906C4—41no—
907C4—42no—
908C4—42no—
909C4—42no—
910C4—81no—
911C4—81no—
912C4—81no—
913C4—81no—
914C4D42×C6111yescharacteristic
915C4D42×C6111yescharacteristic
916C4C61×#54611yescharacteristic
917C4C61×#54611yescharacteristic
918C2—42no—
919C2—42no—
920C2—42no—
921C2—82no—
922C2C61×#241011yescharacteristic
923C2C61×#300511yescharacteristic
924C2C61×#300711yescharacteristic
925C2C61×#305411yescharacteristic
926C2C61×#305611yescharacteristic
927C2C61×#319611yescharacteristic
928C2C61×#319711yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×C61×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C24×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#470C2semidirect
3. C2×C61×#468C2semidirect
4. C2×C61×#452C2semidirect
5. C2×C61×#407C2semidirect
6. C61×#2848C2semidirect
7. C61×#2036C2semidirect
8. C61×#2034C2semidirect
9. C61×#2001C2semidirect
10. C61×#2000C2semidirect
11. C61×#1895C2semidirect
12. C61×#1894C2semidirect
13. C61×#1873C2semidirect
14. C61×#1854C2semidirect
15. C61×#1788C2semidirect
18. C22×Q16×C61C22semidirect
19. C22×SD16×C61C22semidirect
39. C2×#107×C61C22semidirect
40. C2×#106×C61C22semidirect
41. C2×#103×C61C22semidirect
42. C2×#103×C61C22semidirect
43. C2×#103×C61C22semidirect
44. C2×#103×C61C22semidirect
45. C2×#103×C61C22semidirect
46. C2×#102×C61C22semidirect
47. C2×#102×C61C22semidirect
48. C2×#102×C61C22semidirect
61. C61×#340C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
64. C61×#340C22semidirect
162. C22⋊C8×C61D4semidirect
403. #24389C61direct (N × H)
455. C2×#470C2×C61semidirect
456. C2×#468C2×C61semidirect
457. C2×#452C2×C61semidirect
458. C2×#407C2×C61semidirect
459. #2848C2×C61semidirect
460. #2036C2×C61semidirect
461. #2034C2×C61semidirect
462. #2001C2×C61semidirect
463. #2000C2×C61semidirect
464. #1895C2×C61semidirect
465. #1894C2×C61semidirect
466. #1873C2×C61semidirect
467. #1854C2×C61semidirect
468. #1788C2×C61semidirect
482. C22×Q16C22×C61semidirect
483. C22×SD16C22×C61semidirect
503. C2×#107C22×C61semidirect
504. C2×#106C22×C61semidirect
505. C2×#103C22×C61semidirect
506. C2×#103C22×C61semidirect
507. C2×#103C22×C61semidirect
508. C2×#103C22×C61semidirect
509. C2×#103C22×C61semidirect
510. C2×#102C22×C61semidirect
511. C2×#102C22×C61semidirect
512. C2×#102C22×C61semidirect
525. #340C22×C61semidirect
526. #340C22×C61semidirect
527. #340C22×C61semidirect
528. #340C22×C61semidirect
529. C61#24389direct (N × H)
627. 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×#5252
C2×C61×#4702
C2×C61×#4682
C2×C61×#4522
C2×C61×#4072
C61×#28482
C61×#20362
C61×#20342
C61×#20012
C61×#20002
C61×#18952
C61×#18942
C61×#18732
C61×#18542
C61×#17882
#2438961