Finite Group Databasebeta

← C61×#24452 #29527885

Subgroups — C61×#24452 #29527885

Order 15616.

1592 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#546C211yesmaximal, characteristic
2C2×C61×#468C211yesmaximal, characteristic, complemented
3C2×C61×#452C211yesmaximal, characteristic, complemented
4C2×C61×#450C211yesmaximal, characteristic, complemented
5C2×C61×#417C211yesmaximal, characteristic, complemented
6C61×#2417C211yesmaximal, characteristic, complemented
7C61×#2042C211yesmaximal, characteristic, complemented
8C61×#2036C211yesmaximal, characteristic, complemented
9C61×#2015C211yesmaximal, characteristic, complemented
10C61×#2001C211yesmaximal, characteristic, complemented
11C61×#1877C211yesmaximal, characteristic, complemented
12C61×#1874C211yesmaximal, characteristic, complemented
13C61×#1870C211yesmaximal, characteristic, complemented
14C61×#1862C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C23×D4×C61C2211yescharacteristic
18C22×Q16×C61C2211yescharacteristic, complemented
19C22×SD16×C61C2211yescharacteristic
20C22×SD16×C61C2211yescharacteristic
21C22×M16×C61C2211yescharacteristic, complemented
22C61×#546—24no—
23C61×#546—24no—
24C2×#124×C61C2211yescharacteristic
25C2×#123×C61—21no—
26C2×C22⋊Q8×C61C2211yescharacteristic
27C2×C22⋊Q8×C61C2211yescharacteristic
28C2×C22⋊Q8×C61C2211yescharacteristic, complemented
29C2×#121×C61—21no—
30C2×#121×C61C2211yescharacteristic
31C2×#120×C61—21no—
32C2×C4×D4×C61C2211yescharacteristic
33C2×C4×D4×C61C2211yescharacteristic
34C22×C4⋊C4×C61C2211yescharacteristic, complemented
35C22×C22⋊C4×C61—21no—
36C61×#468—24no—
37C61×#452—24no—
38C61×#450—24no—
39C2×#107×C61C2211yescharacteristic, complemented
40C61×#417—24no—
41C2×#103×C61C2211yescharacteristic, complemented
42C2×#103×C61C2211yescharacteristic, complemented
43C2×#103×C61C2211yescharacteristic, complemented
44C2×#103×C61C2211yescharacteristic, complemented
45C2×#102×C61C2211yescharacteristic
46C2×#102×C61C2211yescharacteristic
47C2×#102×C61C2211yescharacteristic
48C2×#102×C61C2211yescharacteristic
49C2×#102×C61C2211yescharacteristic
50C2×#102×C61C2211yescharacteristic
51C2×C22⋊C8×C61C2211yescharacteristic
52C2×C22⋊C8×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic, complemented
54C61×#398—21no—
55C61×#396—21no—
56C61×#391C2211yescharacteristic, complemented
57C61×#389C2211yescharacteristic, complemented
58C61×#386—21no—
59C61×#380—21no—
60C61×#380C2211yescharacteristic
61C61×#340C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#336C2211yescharacteristic, complemented
64C61×#336C2211yescharacteristic, complemented
65C25×C61—21no—
66C2×#41×C61—22no—
67C2×#41×C61—22no—
68C2×#41×C61—22no—
69C2×#41×C61—41no—
70C2×#41×C61—41no—
71C2×#41×C61D414yes—
72C22×Q8×C61C2311yescharacteristic
73C22×Q8×C61C2311yescharacteristic
74C22×D4×C61—21no—
75C22×D4×C61—21no—
76C22×D4×C61—22no—
77C22×D4×C61—22no—
78C22×D4×C61—22no—
79C22×D4×C61—22no—
80C22×D4×C61—21no—
81C22×D4×C61—41no—
82C22×D4×C61—41no—
83C22×D4×C61D411yescharacteristic
84C22×D4×C61C2311yescharacteristic
85C22×D4×C61C2311yescharacteristic
86C23×C4×C61—21no—
87C23×C4×C61—21no—
88C23×C4×C61—21no—
89C23×C4×C61C2311yescharacteristic
90C23×C4×C61C2311yescharacteristic
91C2×Q16×C61—22no—
92C2×Q16×C61—41no—
93C2×Q16×C61—41no—
94C2×SD16×C61—22no—
95C2×SD16×C61—22no—
96C2×SD16×C61—22no—
97C2×SD16×C61—22no—
98C2×SD16×C61—22no—
99C2×SD16×C61—41no—
100C2×M16×C61—22no—
101C2×M16×C61—22no—
102C2×M16×C61—41no—
103C22×C8×C61C2311yescharacteristic
104C22×C8×C61C2311yescharacteristic
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107#124×C61—22no—
108#124×C61—22no—
109#123×C61—28no—
110C22⋊Q8×C61—22no—
111C22⋊Q8×C61—22no—
112C22⋊Q8×C61—22no—
113C22⋊Q8×C61—22no—
114C22⋊Q8×C61—22no—
115C22⋊Q8×C61—41no—
116#121×C61—28no—
117#121×C61—22no—
118#121×C61D414yes—
119#120×C61—28no—
120C4×D4×C61—22no—
121C4×D4×C61—22no—
122C4×D4×C61—22no—
123C4×D4×C61—22no—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61—22no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—41no—
131C2×C4⋊C4×C61D411yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61C2311yescharacteristic
136C2×C22⋊C4×C61—28no—
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×C61D411yescharacteristic
146C2×C22⋊C4×C61D411yescharacteristic
147C2×C42×C61C2311yescharacteristic
148#107×C61—22no—
149#103×C61—22no—
150#103×C61—22no—
151#103×C61—22no—
152#103×C61—22no—
153#102×C61—22no—
154#102×C61—22no—
155#102×C61—22no—
156#102×C61—22no—
157#102×C61—41no—
158#102×C61D414yescomplemented
159C22⋊C8×C61—22no—
160C22⋊C8×C61—22no—
161C22⋊C8×C61—41no—
162#95×C61—21no—
163#95×C61—21no—
164#95×C61—21no—
165#95×C61—21no—
166C24×C61—21no—
167C24×C61—24no—
168C24×C61—21no—
169C24×C61—42no—
170C24×C61—42no—
171C24×C61—42no—
172C24×C61—42no—
173C24×C61—81no—
174C24×C61—81no—
175C24×C61C2×D411yescharacteristic
176C24×C61C2×D411yescharacteristic
177#41×C61—28no—
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—22no—
195C2×D4×C61—24no—
196C2×D4×C61—22no—
197C2×D4×C61—24no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—41no—
207C2×D4×C61—42no—
208C2×D4×C61—42no—
209C2×D4×C61—44no—
210C2×D4×C61—44no—
211C2×D4×C61—44no—
212C2×D4×C61—42no—
213C2×D4×C61—42no—
214C2×D4×C61—44no—
215C2×D4×C61—81no—
216C2×D4×C61—81no—
217C2×D4×C61C2×D412yes—
218C2×D4×C61C2×D412yes—
219C2×D4×C61C2×D412yes—
220C2×D4×C61#4112yes—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—24no—
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—42no—
240C22×C4×C61—42no—
241C22×C4×C61—42no—
242C22×C4×C61—42no—
243C22×C4×C61—81no—
244C22×C4×C61—81no—
245C22×C4×C61—81no—
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D412yes—
251C22×C4×C61C2×D412yes—
252C22×C4×C61C2411yescharacteristic
253Q16×C61—44no—
254SD16×C61—44no—
255SD16×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×C61—21no—
268C2×C8×C61C2×D412yes—
269C4⋊C4×C61—24no—
270C4⋊C4×C61—22no—
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—42no—
278C4⋊C4×C61—42no—
279C4⋊C4×C61—42no—
280C4⋊C4×C61—81no—
281C4⋊C4×C61C2×D412yes—
282C4⋊C4×C61C2×D412yes—
283C22⋊C4×C61—24no—
284C22⋊C4×C61—24no—
285C22⋊C4×C61—24no—
286C22⋊C4×C61—24no—
287C22⋊C4×C61—22no—
288C22⋊C4×C61—22no—
289C22⋊C4×C61—24no—
290C22⋊C4×C61—42no—
291C22⋊C4×C61—42no—
292C22⋊C4×C61—81no—
293C42×C61—21no—
294C42×C61—21no—
295C23×C61—21no—
296C23×C61—22no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—22no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—22no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—22no—
311C23×C61—48no—
312C23×C61—48no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—41no—
322C23×C61—41no—
323C23×C61—84no—
324C23×C61—84no—
325C23×C61—84no—
326C23×C61—84no—
327C23×C61—84no—
328C23×C61#12012yes—
329C23×C61#13712yes—
330C23×C61C22×D411yescharacteristic
331Q8×C61—22no—
332Q8×C61—22no—
333Q8×C61—41no—
334Q8×C61—41no—
335Q8×C61—41no—
336Q8×C61—41no—
337Q8×C61—41no—
338Q8×C61—41no—
339D4×C61—22no—
340D4×C61—22no—
341D4×C61—22no—
342D4×C61—22no—
343D4×C61—22no—
344D4×C61—44no—
345D4×C61—48no—
346D4×C61—48no—
347D4×C61—41no—
348D4×C61—41no—
349D4×C61—84no—
350D4×C61#12114yes—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
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—22no—
360C2×C4×C61—22no—
361C2×C4×C61—21no—
362C2×C4×C61—22no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—48no—
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—84no—
390C2×C4×C61—84no—
391C2×C4×C61#12012yes—
392C2×C4×C61C22×D411yescharacteristic
393C2×C4×C61C22×D411yescharacteristic
394C2×C4×C61C22×D411yescharacteristic
395C2×C4×C61C2×#4111yescharacteristic
396C2×C4×C61H(5,𝔽2)11yescharacteristic
397C2×C4×C61H(5,𝔽2)11yescharacteristic
398C8×C61—22no—
399C8×C61—41no—
400C8×C61—41no—
401C8×C61—41no—
402#24452C6111yesmaximal, characteristic, direct product factor, Sylow
403C22×C61—22no—
404C22×C61—24no—
405C22×C61—22no—
406C22×C61—22no—
407C22×C61—22no—
408C22×C61—22no—
409C22×C61—22no—
410C22×C61—41no—
411C22×C61—42no—
412C22×C61—41no—
413C22×C61—42no—
414C22×C61—42no—
415C22×C61—41no—
416C22×C61—41no—
417C22×C61—41no—
418C22×C61—42no—
419C22×C61—41no—
420C22×C61—42no—
421C22×C61—41no—
422C22×C61—41no—
423C22×C61—42no—
424C22×C61—42no—
425C22×C61—42no—
426C22×C61—42no—
427C22×C61—816no—
428C22×C61—81no—
429C22×C61—81no—
430C22×C61—81no—
431C22×C61—81no—
432C22×C61C2×#12011yescharacteristic
433C22×C61D4211yescharacteristic
434C22×C61#54611yescharacteristic
435C22×C61C2×#13711yescharacteristic
436C22×C61#57511yescharacteristic
437C22×C61#57611yescharacteristic
438C22×C61#57711yescharacteristic
439C4×C61—22no—
440C4×C61—41no—
441C4×C61—42no—
442C4×C61—41no—
443C4×C61—41no—
444C4×C61—42no—
445C4×C61—42no—
446C4×C61—81no—
447C4×C61—81no—
448C4×C61—81no—
449C4×C61C2×#12111yescharacteristic
450C4×C61#53411yescharacteristic
451C4×C61D4211yescharacteristic
452C4×C61#54611yescharacteristic
453C2×#546C2×C6111yescharacteristic
454C2×#468C2×C6111yescharacteristic, complemented
455C2×#452C2×C6111yescharacteristic, complemented
456C2×#450C2×C6111yescharacteristic, complemented
457C2×#417C2×C6111yescharacteristic, complemented
458#2417C2×C6111yescharacteristic, complemented
459#2042C2×C6111yescharacteristic, complemented
460#2036C2×C6111yescharacteristic, complemented
461#2015C2×C6111yescharacteristic, complemented
462#2001C2×C6111yescharacteristic, complemented
463#1877C2×C6111yescharacteristic, complemented
464#1874C2×C6111yescharacteristic, complemented
465#1870C2×C6111yescharacteristic, complemented
466#1862C2×C6111yescharacteristic, complemented
467#1786C2×C6111yescharacteristic, complemented
468C2×C61—42no—
469C2×C61—42no—
470C2×C61—44no—
471C2×C61—82no—
472C2×C61#241011yescharacteristic
473C2×C61#300711yescharacteristic
474C2×C61#301211yescharacteristic
475C2×C61#326611yescharacteristic
476C2×C61#327311yescharacteristic
477C2×C61#331411yescharacteristic
478C2×C61#332311yescharacteristic
479C22×#41C22×C6111yescharacteristic
480C23×D4C22×C6111yescharacteristic
481C22×Q16C22×C6111yescharacteristic, complemented
482C22×SD16C22×C6111yescharacteristic
483C22×SD16C22×C6111yescharacteristic
484C22×M16C22×C6111yescharacteristic, complemented
485#546—24no—
486#546—24no—
487C2×#124C22×C6111yescharacteristic
488C2×#123—21no—
489C2×C22⋊Q8C22×C6111yescharacteristic
490C2×C22⋊Q8C22×C6111yescharacteristic
491C2×C22⋊Q8C22×C6111yescharacteristic, complemented
492C2×#121—21no—
493C2×#121C22×C6111yescharacteristic
494C2×#120—21no—
495C2×C4×D4C22×C6111yescharacteristic
496C2×C4×D4C22×C6111yescharacteristic
497C22×C4⋊C4C22×C6111yescharacteristic, complemented
498C22×C22⋊C4—21no—
499#468—24no—
500#452—24no—
501#450—24no—
502C2×#107C22×C6111yescharacteristic, complemented
503#417—24no—
504C2×#103C22×C6111yescharacteristic, complemented
505C2×#103C22×C6111yescharacteristic, complemented
506C2×#103C22×C6111yescharacteristic, complemented
507C2×#103C22×C6111yescharacteristic, complemented
508C2×#102C22×C6111yescharacteristic
509C2×#102C22×C6111yescharacteristic
510C2×#102C22×C6111yescharacteristic
511C2×#102C22×C6111yescharacteristic
512C2×#102C22×C6111yescharacteristic
513C2×#102C22×C6111yescharacteristic
514C2×C22⋊C8C22×C6111yescharacteristic
515C2×C22⋊C8C22×C6111yescharacteristic
516C2×C22⋊C8C22×C6111yescharacteristic, complemented
517#398—21no—
518#396—21no—
519#391C22×C6111yescharacteristic, complemented
520#389C22×C6111yescharacteristic, complemented
521#386—21no—
522#380—21no—
523#380C22×C6111yescharacteristic
524#340C22×C6111yescharacteristic, complemented
525#340C22×C6111yescharacteristic, complemented
526#336C22×C6111yescharacteristic, complemented
527#336C22×C6111yescharacteristic, complemented
528C61#2445211yescharacteristic, direct product factor, Sylow
529C25—21no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—41no—
534C2×#41—41no—
535C2×#41D4×C6114yes—
536C22×Q8C23×C6111yescharacteristic
537C22×Q8C23×C6111yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—21no—
545C22×D4—41no—
546C22×D4—41no—
547C22×D4D4×C6111yescharacteristic
548C22×D4C23×C6111yescharacteristic
549C22×D4C23×C6111yescharacteristic
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4C23×C6111yescharacteristic
554C23×C4C23×C6111yescharacteristic
555C2×Q16—22no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—41no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—41no—
567C22×C8C23×C6111yescharacteristic
568C22×C8C23×C6111yescharacteristic
569C22×C8C23×C6111yescharacteristic
570C22×C8C23×C6111yescharacteristic
571#124—22no—
572#124—22no—
573#123—28no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—41no—
580#121—28no—
581#121—22no—
582#121D4×C6114yes—
583#120—28no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4D4×C6111yescharacteristic
596C2×C4⋊C4C23×C6111yescharacteristic
597C2×C4⋊C4C23×C6111yescharacteristic
598C2×C4⋊C4C23×C6111yescharacteristic
599C2×C4⋊C4C23×C6111yescharacteristic
600C2×C22⋊C4—28no—
601C2×C22⋊C4—21no—
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⋊C4D4×C6111yescharacteristic
610C2×C22⋊C4D4×C6111yescharacteristic
611C2×C42C23×C6111yescharacteristic
612#107—22no—
613#103—22no—
614#103—22no—
615#103—22no—
616#103—22no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102—22no—
621#102—41no—
622#102D4×C6114yescomplemented
623C22⋊C8—22no—
624C22⋊C8—22no—
625C22⋊C8—41no—
626#95—21no—
627#95—21no—
628#95—21no—
629#95—21no—
630C24—21no—
631C24—24no—
632C24—21no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—81no—
638C24—81no—
639C24C2×D4×C6111yescharacteristic
640C24C2×D4×C6111yescharacteristic
641#41—28no—
642#41—44no—
643#41—44no—
644#41—44no—
645C2×Q8—21no—
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×Q8C2×D4×C6112yes—
657C2×D4—24no—
658C2×D4—22no—
659C2×D4—24no—
660C2×D4—22no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—41no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—44no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—44no—
679C2×D4—81no—
680C2×D4—81no—
681C2×D4C2×D4×C6112yes—
682C2×D4C2×D4×C6112yes—
683C2×D4C2×D4×C6112yes—
684C2×D4#41×C6112yes—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—81no—
708C22×C4—81no—
709C22×C4—81no—
710C22×C4C2×D4×C6111yescharacteristic
711C22×C4C2×D4×C6111yescharacteristic
712C22×C4C2×D4×C6111yescharacteristic
713C22×C4C2×D4×C6111yescharacteristic
714C22×C4C2×D4×C6112yes—
715C22×C4C2×D4×C6112yes—
716C22×C4C24×C6111yescharacteristic
717Q16—44no—
718SD16—44no—
719SD16—44no—
720M16—44no—
721C2×C8—21no—
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—
733C4⋊C4—24no—
734C4⋊C4—22no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—42no—
742C4⋊C4—42no—
743C4⋊C4—42no—
744C4⋊C4—81no—
745C4⋊C4C2×D4×C6112yes—
746C4⋊C4C2×D4×C6112yes—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—24no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—81no—
757C42—21no—
758C42—21no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—22no—
774C23—22no—
775C23—48no—
776C23—48no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23—84no—
792C23#120×C6112yes—
793C23#137×C6112yes—
794C23C22×D4×C6111yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—44no—
809D4—48no—
810D4—48no—
811D4—41no—
812D4—41no—
813D4—84no—
814D4#121×C6114yes—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—21no—
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—84no—
854C2×C4—84no—
855C2×C4#120×C6112yes—
856C2×C4C22×D4×C6111yescharacteristic
857C2×C4C22×D4×C6111yescharacteristic
858C2×C4C22×D4×C6111yescharacteristic
859C2×C4C2×#41×C6111yescharacteristic
860C2×C4H(5,𝔽2)×C6111yescharacteristic
861C2×C4H(5,𝔽2)×C6111yescharacteristic
862C8—22no—
863C8—41no—
864C8—41no—
865C8—41no—
866C22—22no—
867C22—22no—
868C22—24no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—41no—
874C22—42no—
875C22—41no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—42no—
880C22—41no—
881C22—42no—
882C22—42no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—816no—
891C22—81no—
892C22—81no—
893C22—81no—
894C22—81no—
895C22C2×#120×C6111yescharacteristic
896C22D42×C6111yescharacteristic
897C22C61×#54611yescharacteristic
898C22C2×#137×C6111yescharacteristic
899C22C61×#57511yescharacteristic
900C22C61×#57611yescharacteristic
901C22C61×#57711yescharacteristic
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—42no—
908C4—42no—
909C4—81no—
910C4—81no—
911C4—81no—
912C4C2×#121×C6111yescharacteristic
913C4C61×#53411yescharacteristic
914C4D42×C6111yescharacteristic
915C4C61×#54611yescharacteristic
916C2—42no—
917C2—42no—
918C2—44no—
919C2—82no—
920C2C61×#241011yescharacteristic
921C2C61×#300711yescharacteristic
922C2C61×#301211yescharacteristic
923C2C61×#326611yescharacteristic
924C2C61×#327311yescharacteristic
925C2C61×#331411yescharacteristic
926C2C61×#332311yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×C61×#546C2
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
2. C2×C61×#468C2semidirect
3. C2×C61×#452C2semidirect
4. C2×C61×#450C2semidirect
5. C2×C61×#417C2semidirect
6. C61×#2417C2semidirect
7. C61×#2042C2semidirect
8. C61×#2036C2semidirect
9. C61×#2015C2semidirect
10. C61×#2001C2semidirect
11. C61×#1877C2semidirect
12. C61×#1874C2semidirect
13. C61×#1870C2semidirect
14. C61×#1862C2semidirect
15. C61×#1786C2semidirect
18. C22×Q16×C61C22semidirect
21. C22×M16×C61C22semidirect
28. C2×C22⋊Q8×C61C22semidirect
34. C22×C4⋊C4×C61C22semidirect
39. C2×#107×C61C22semidirect
41. C2×#103×C61C22semidirect
42. C2×#103×C61C22semidirect
43. C2×#103×C61C22semidirect
44. C2×#103×C61C22semidirect
53. C2×C22⋊C8×C61C22semidirect
56. C61×#391C22semidirect
57. C61×#389C22semidirect
61. C61×#340C22semidirect
62. C61×#340C22semidirect
63. C61×#336C22semidirect
64. C61×#336C22semidirect
158. #102×C61D4semidirect
402. #24452C61direct (N × H)
454. C2×#468C2×C61semidirect
455. C2×#452C2×C61semidirect
456. C2×#450C2×C61semidirect
457. C2×#417C2×C61semidirect
458. #2417C2×C61semidirect
459. #2042C2×C61semidirect
460. #2036C2×C61semidirect
461. #2015C2×C61semidirect
462. #2001C2×C61semidirect
463. #1877C2×C61semidirect
464. #1874C2×C61semidirect
465. #1870C2×C61semidirect
466. #1862C2×C61semidirect
467. #1786C2×C61semidirect
481. C22×Q16C22×C61semidirect
484. C22×M16C22×C61semidirect
491. C2×C22⋊Q8C22×C61semidirect
497. C22×C4⋊C4C22×C61semidirect
502. C2×#107C22×C61semidirect
504. C2×#103C22×C61semidirect
505. C2×#103C22×C61semidirect
506. C2×#103C22×C61semidirect
507. C2×#103C22×C61semidirect
516. C2×C22⋊C8C22×C61semidirect
519. #391C22×C61semidirect
520. #389C22×C61semidirect
524. #340C22×C61semidirect
525. #340C22×C61semidirect
526. #336C22×C61semidirect
527. #336C22×C61semidirect
528. C61#24452direct (N × H)
622. #102D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5462
C2×C61×#4682
C2×C61×#4522
C2×C61×#4502
C2×C61×#4172
C61×#24172
C61×#20422
C61×#20362
C61×#20152
C61×#20012
C61×#18772
C61×#18742
C61×#18702
C61×#18622
C61×#17862
#2445261