Finite Group Databasebeta

← C61×#25136 #29528569

Subgroups — C61×#25136 #29528569

Order 15616.

1264 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#468C211yesmaximal, characteristic, complemented
2C2×C61×#450C211yesmaximal, characteristic, complemented
3C2×C61×#436C211yesmaximal, characteristic, complemented
4C2×C61×#418C211yesmaximal, characteristic, complemented
5C61×#2415C211yesmaximal, characteristic, complemented
6C61×#2408C211yesmaximal, characteristic
7C61×#2067C211yesmaximal, characteristic, complemented
8C61×#2055C211yesmaximal, characteristic, complemented
9C61×#2034C211yesmaximal, characteristic, complemented
10C61×#2000C211yesmaximal, characteristic, complemented
11C61×#1968C211yesmaximal, characteristic, complemented
12C61×#1934C211yesmaximal, characteristic, complemented
13C61×#1895C211yesmaximal, characteristic, complemented
14C61×#1894C211yesmaximal, characteristic, complemented
15C61×#1854C211yesmaximal, characteristic, complemented
16C23×D4×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic
19C22×M16×C61C2211yescharacteristic
20C22×M16×C61C2211yescharacteristic, complemented
21C2×C22⋊Q8×C61C2211yescharacteristic
22C2×C22⋊Q8×C61C2211yescharacteristic, complemented
23C2×#121×C61C2211yescharacteristic
24C2×#121×C61C2211yescharacteristic
25C2×#120×C61—21no—
26C2×C4×D4×C61C2211yescharacteristic
27C2×#117×C61C2211yescharacteristic
28C61×#468—24no—
29C61×#450—24no—
30C61×#436—24no—
31C2×#107×C61C2211yescharacteristic, complemented
32C2×#106×C61C2211yescharacteristic, complemented
33C2×C4⋊C8×C61C2211yescharacteristic, complemented
34C61×#418—24no—
35C2×#103×C61C2211yescharacteristic, complemented
36C2×#103×C61C2211yescharacteristic, complemented
37C2×#102×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×C22⋊C8×C61C2211yescharacteristic
44C2×C22⋊C8×C61C2211yescharacteristic, complemented
45C2×C4×C8×C61C2211yescharacteristic, complemented
46C61×#397—21no—
47C61×#394—21no—
48C61×#394—21no—
49C61×#392—21no—
50C61×#391C2211yescharacteristic, complemented
51C61×#390C2211yescharacteristic
52C61×#390C2211yescharacteristic
53C61×#389—21no—
54C61×#389C2211yescharacteristic, complemented
55C61×#388—21no—
56C61×#380C2211yescharacteristic
57C61×#380C2211yescharacteristic, complemented
58C61×#379—21no—
59C61×#340C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C25×C61—21no—
64C22×Q8×C61C2311yescharacteristic
65C22×D4×C61—22no—
66C22×D4×C61—22no—
67C22×D4×C61—21no—
68C22×D4×C61—21no—
69C22×D4×C61—22no—
70C22×D4×C61—21no—
71C22×D4×C61—22no—
72C22×D4×C61—41no—
73C22×D4×C61—41no—
74C22×D4×C61D411yescharacteristic
75C22×D4×C61C2311yescharacteristic
76C22×D4×C61C2311yescharacteristic
77C23×C4×C61C2311yescharacteristic
78C23×C4×C61C2311yescharacteristic
79C2×SD16×C61—22no—
80C2×SD16×C61—22no—
81C2×SD16×C61—22no—
82C2×SD16×C61—22no—
83C2×SD16×C61—41no—
84C2×SD16×C61—41no—
85C2×M16×C61—22no—
86C2×M16×C61—22no—
87C2×M16×C61—22no—
88C2×M16×C61—22no—
89C2×M16×C61—41no—
90C2×M16×C61—41no—
91C22×C8×C61C2311yescharacteristic
92C22×C8×C61C2311yescharacteristic
93C22×C8×C61C2311yescharacteristic
94C22×C8×C61C2311yescharacteristic
95C22⋊Q8×C61—22no—
96C22⋊Q8×C61—22no—
97C22⋊Q8×C61—22no—
98C22⋊Q8×C61—41no—
99#121×C61—22no—
100#121×C61—22no—
101#121×C61—41no—
102#121×C61—41no—
103#120×C61—44no—
104C4×D4×C61—22no—
105C4×D4×C61—22no—
106#117×C61—22no—
107#117×C61—41no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61D411yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C22⋊C4×C61—21no—
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61D411yescharacteristic
129C2×C22⋊C4×C61D411yescharacteristic
130C2×C42×C61—21no—
131C2×C42×C61C2311yescharacteristic
132#107×C61—22no—
133#106×C61—41no—
134C4⋊C8×C61—22no—
135#103×C61—22no—
136#103×C61—41no—
137#102×C61—22no—
138#102×C61—22no—
139#102×C61—22no—
140#102×C61—22no—
141#102×C61—22no—
142#102×C61D414yescomplemented
143C22⋊C8×C61—22no—
144C22⋊C8×C61D414yescomplemented
145C4×C8×C61—22no—
146#95×C61—21no—
147#95×C61—21no—
148#95×C61—21no—
149#95×C61—21no—
150#95×C61—21no—
151C24×C61—21no—
152C24×C61—21no—
153C24×C61—42no—
154C24×C61—42no—
155C24×C61—42no—
156C24×C61—42no—
157C24×C61—42no—
158C24×C61—81no—
159C24×C61—81no—
160C24×C61C2×D411yescharacteristic
161C24×C61C2×D411yescharacteristic
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—21no—
165C2×Q8×C61—21no—
166C2×Q8×C61—21no—
167C2×Q8×C61—21no—
168C2×D4×C61—28no—
169C2×D4×C61—22no—
170C2×D4×C61—22no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—44no—
182C2×D4×C61—44no—
183C2×D4×C61—41no—
184C2×D4×C61—42no—
185C2×D4×C61—42no—
186C2×D4×C61—44no—
187C2×D4×C61—42no—
188C2×D4×C61—42no—
189C2×D4×C61—42no—
190C2×D4×C61—42no—
191C2×D4×C61—42no—
192C2×D4×C61—81no—
193C2×D4×C61—81no—
194C2×D4×C61C2×D412yes—
195C2×D4×C61#4112yes—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61—21no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D412yes—
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61#4112yes—
218C22×C4×C61C2411yescharacteristic
219SD16×C61—44no—
220SD16×C61—44no—
221M16×C61—44no—
222M16×C61—44no—
223C2×C8×C61—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—21no—
230C2×C8×C61—21no—
231C2×C8×C61—21no—
232C2×C8×C61C2×D412yes—
233C2×C8×C61C2×D412yes—
234C2×C8×C61C2×D412yes—
235C4⋊C4×C61—22no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—42no—
246C4⋊C4×C61—42no—
247C4⋊C4×C61—42no—
248C4⋊C4×C61C2×D412yes—
249C22⋊C4×C61—22no—
250C22⋊C4×C61—22no—
251C22⋊C4×C61—42no—
252C22⋊C4×C61—42no—
253C22⋊C4×C61—42no—
254C22⋊C4×C61—42no—
255C22⋊C4×C61—42no—
256C22⋊C4×C61—42no—
257C22⋊C4×C61—42no—
258C22⋊C4×C61—42no—
259C22⋊C4×C61—42no—
260C22⋊C4×C61—81no—
261C22⋊C4×C61—81no—
262C42×C61—21no—
263C42×C61—21no—
264C42×C61—42no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—48no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—84no—
294C23×C61—84no—
295C23×C61—84no—
296C23×C61—84no—
297C23×C61—84no—
298C23×C61—84no—
299C23×C61#12112yes—
300C23×C61C22×D411yescharacteristic
301Q8×C61—41no—
302Q8×C61—41no—
303Q8×C61—41no—
304Q8×C61—41no—
305D4×C61—22no—
306D4×C61—22no—
307D4×C61—22no—
308D4×C61—22no—
309D4×C61—44no—
310D4×C61—48no—
311D4×C61—41no—
312D4×C61—41no—
313D4×C61—41no—
314D4×C61—41no—
315D4×C61—84no—
316D4×C61—84no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—22no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61#12112yes—
354C2×C4×C61AGL(1,ℤ/8)12yes—
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C2×#4111yescharacteristic
358C2×C4×C61C2×#4111yescharacteristic
359C2×C4×C61H(5,𝔽2)11yescharacteristic
360C2×C4×C61H(5,𝔽2)11yescharacteristic
361C8×C61—22no—
362C8×C61—22no—
363C8×C61—22no—
364C8×C61—41no—
365#25136C6111yesmaximal, characteristic, direct product factor, Sylow
366C22×C61—22no—
367C22×C61—22no—
368C22×C61—22no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—42no—
375C22×C61—42no—
376C22×C61—41no—
377C22×C61—42no—
378C22×C61—41no—
379C22×C61—42no—
380C22×C61—41no—
381C22×C61—41no—
382C22×C61—41no—
383C22×C61—42no—
384C22×C61—41no—
385C22×C61—42no—
386C22×C61—816no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61—81no—
391C22×C61—81no—
392C22×C61—81no—
393C22×C61—81no—
394C22×C61—81no—
395C22×C61C2×#12111yescharacteristic
396C22×C61D4211yescharacteristic
397C22×C61#54611yescharacteristic
398C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
399C22×C61#57511yescharacteristic
400C22×C61#57711yescharacteristic
401C22×C61#57711yescharacteristic
402C4×C61—22no—
403C4×C61—22no—
404C4×C61—41no—
405C4×C61—42no—
406C4×C61—41no—
407C4×C61—81no—
408C4×C61—81no—
409C4×C61—81no—
410C4×C61—81no—
411C4×C61—81no—
412C4×C61#52511yescharacteristic
413C4×C61#53811yescharacteristic
414C4×C61D4211yescharacteristic
415C4×C61#54611yescharacteristic
416C2×#468C2×C6111yescharacteristic, complemented
417C2×#450C2×C6111yescharacteristic, complemented
418C2×#436C2×C6111yescharacteristic, complemented
419C2×#418C2×C6111yescharacteristic, complemented
420#2415C2×C6111yescharacteristic, complemented
421#2408C2×C6111yescharacteristic
422#2067C2×C6111yescharacteristic, complemented
423#2055C2×C6111yescharacteristic, complemented
424#2034C2×C6111yescharacteristic, complemented
425#2000C2×C6111yescharacteristic, complemented
426#1968C2×C6111yescharacteristic, complemented
427#1934C2×C6111yescharacteristic, complemented
428#1895C2×C6111yescharacteristic, complemented
429#1894C2×C6111yescharacteristic, complemented
430#1854C2×C6111yescharacteristic, complemented
431C2×C61—42no—
432C2×C61—81no—
433C2×C61—82no—
434C2×C61—82no—
435C2×C61#242411yescharacteristic
436C2×C61#305511yescharacteristic
437C2×C61#305711yescharacteristic
438C2×C61#327211yescharacteristic
439C2×C61#327511yescharacteristic
440C2×C61#332311yescharacteristic
441C2×C61#332411yescharacteristic
442C23×D4C22×C6111yescharacteristic
443C22×SD16C22×C6111yescharacteristic
444C22×SD16C22×C6111yescharacteristic
445C22×M16C22×C6111yescharacteristic
446C22×M16C22×C6111yescharacteristic, complemented
447C2×C22⋊Q8C22×C6111yescharacteristic
448C2×C22⋊Q8C22×C6111yescharacteristic, complemented
449C2×#121C22×C6111yescharacteristic
450C2×#121C22×C6111yescharacteristic
451C2×#120—21no—
452C2×C4×D4C22×C6111yescharacteristic
453C2×#117C22×C6111yescharacteristic
454#468—24no—
455#450—24no—
456#436—24no—
457C2×#107C22×C6111yescharacteristic, complemented
458C2×#106C22×C6111yescharacteristic, complemented
459C2×C4⋊C8C22×C6111yescharacteristic, complemented
460#418—24no—
461C2×#103C22×C6111yescharacteristic, complemented
462C2×#103C22×C6111yescharacteristic, complemented
463C2×#102C22×C6111yescharacteristic
464C2×#102C22×C6111yescharacteristic
465C2×#102C22×C6111yescharacteristic
466C2×#102C22×C6111yescharacteristic
467C2×#102C22×C6111yescharacteristic
468C2×#102C22×C6111yescharacteristic
469C2×C22⋊C8C22×C6111yescharacteristic
470C2×C22⋊C8C22×C6111yescharacteristic, complemented
471C2×C4×C8C22×C6111yescharacteristic, complemented
472#397—21no—
473#394—21no—
474#394—21no—
475#392—21no—
476#391C22×C6111yescharacteristic, complemented
477#390C22×C6111yescharacteristic
478#390C22×C6111yescharacteristic
479#389—21no—
480#389C22×C6111yescharacteristic, complemented
481#388—21no—
482#380C22×C6111yescharacteristic
483#380C22×C6111yescharacteristic, complemented
484#379—21no—
485#340C22×C6111yescharacteristic, complemented
486#340C22×C6111yescharacteristic, complemented
487#340C22×C6111yescharacteristic, complemented
488#340C22×C6111yescharacteristic, complemented
489C61#2513611yescharacteristic, direct product factor, Sylow
490C25—21no—
491C22×Q8C23×C6111yescharacteristic
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4D4×C6111yescharacteristic
502C22×D4C23×C6111yescharacteristic
503C22×D4C23×C6111yescharacteristic
504C23×C4C23×C6111yescharacteristic
505C23×C4C23×C6111yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—41no—
511C2×SD16—41no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—41no—
517C2×M16—41no—
518C22×C8C23×C6111yescharacteristic
519C22×C8C23×C6111yescharacteristic
520C22×C8C23×C6111yescharacteristic
521C22×C8C23×C6111yescharacteristic
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8—22no—
525C22⋊Q8—41no—
526#121—22no—
527#121—22no—
528#121—41no—
529#121—41no—
530#120—44no—
531C4×D4—22no—
532C4×D4—22no—
533#117—22no—
534#117—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4D4×C6111yescharacteristic
539C2×C4⋊C4C23×C6111yescharacteristic
540C2×C4⋊C4C23×C6111yescharacteristic
541C2×C4⋊C4C23×C6111yescharacteristic
542C2×C4⋊C4C23×C6111yescharacteristic
543C2×C4⋊C4C23×C6111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4D4×C6111yescharacteristic
556C2×C22⋊C4D4×C6111yescharacteristic
557C2×C42—21no—
558C2×C42C23×C6111yescharacteristic
559#107—22no—
560#106—41no—
561C4⋊C8—22no—
562#103—22no—
563#103—41no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102D4×C6114yescomplemented
570C22⋊C8—22no—
571C22⋊C8D4×C6114yescomplemented
572C4×C8—22no—
573#95—21no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578C24—21no—
579C24—21no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—81no—
586C24—81no—
587C24C2×D4×C6111yescharacteristic
588C24C2×D4×C6111yescharacteristic
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×D4—28no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—41no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4C2×D4×C6112yes—
622C2×D4#41×C6112yes—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4C2×D4×C6111yescharacteristic
640C22×C4C2×D4×C6111yescharacteristic
641C22×C4C2×D4×C6111yescharacteristic
642C22×C4C2×D4×C6112yes—
643C22×C4C2×D4×C6111yescharacteristic
644C22×C4#41×C6112yes—
645C22×C4C24×C6111yescharacteristic
646SD16—44no—
647SD16—44no—
648M16—44no—
649M16—44no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8C2×D4×C6112yes—
660C2×C8C2×D4×C6112yes—
661C2×C8C2×D4×C6112yes—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4C2×D4×C6112yes—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—42no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—22no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23#121×C6112yes—
727C23C22×D4×C6111yescharacteristic
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—44no—
737D4—48no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—84no—
743D4—84no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4#121×C6112yes—
781C2×C4AGL(1,ℤ/8)×C6112yes—
782C2×C4C22×D4×C6111yescharacteristic
783C2×C4C22×D4×C6111yescharacteristic
784C2×C4C2×#41×C6111yescharacteristic
785C2×C4C2×#41×C6111yescharacteristic
786C2×C4H(5,𝔽2)×C6111yescharacteristic
787C2×C4H(5,𝔽2)×C6111yescharacteristic
788C8—22no—
789C8—22no—
790C8—22no—
791C8—41no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—41no—
811C22—42no—
812C22—816no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22C2×#121×C6111yescharacteristic
822C22D42×C6111yescharacteristic
823C22C61×#54611yescharacteristic
824C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
825C22C61×#57511yescharacteristic
826C22C61×#57711yescharacteristic
827C22C61×#57711yescharacteristic
828C4—22no—
829C4—22no—
830C4—41no—
831C4—41no—
832C4—42no—
833C4—81no—
834C4—81no—
835C4—81no—
836C4—81no—
837C4—81no—
838C4C61×#52511yescharacteristic
839C4C61×#53811yescharacteristic
840C4D42×C6111yescharacteristic
841C4C61×#54611yescharacteristic
842C2—42no—
843C2—81no—
844C2—82no—
845C2—82no—
846C2C61×#242411yescharacteristic
847C2C61×#305511yescharacteristic
848C2C61×#305711yescharacteristic
849C2C61×#327211yescharacteristic
850C2C61×#327511yescharacteristic
851C2C61×#332311yescharacteristic
852C2C61×#332411yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#2408C2
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×#468C2semidirect
2. C2×C61×#450C2semidirect
3. C2×C61×#436C2semidirect
4. C2×C61×#418C2semidirect
5. C61×#2415C2semidirect
7. C61×#2067C2semidirect
8. C61×#2055C2semidirect
9. C61×#2034C2semidirect
10. C61×#2000C2semidirect
11. C61×#1968C2semidirect
12. C61×#1934C2semidirect
13. C61×#1895C2semidirect
14. C61×#1894C2semidirect
15. C61×#1854C2semidirect
20. C22×M16×C61C22semidirect
22. C2×C22⋊Q8×C61C22semidirect
31. C2×#107×C61C22semidirect
32. C2×#106×C61C22semidirect
33. C2×C4⋊C8×C61C22semidirect
35. C2×#103×C61C22semidirect
36. C2×#103×C61C22semidirect
44. C2×C22⋊C8×C61C22semidirect
45. C2×C4×C8×C61C22semidirect
50. C61×#391C22semidirect
54. C61×#389C22semidirect
57. C61×#380C22semidirect
59. C61×#340C22semidirect
60. C61×#340C22semidirect
61. C61×#340C22semidirect
62. C61×#340C22semidirect
142. #102×C61D4semidirect
144. C22⋊C8×C61D4semidirect
365. #25136C61direct (N × H)
416. C2×#468C2×C61semidirect
417. C2×#450C2×C61semidirect
418. C2×#436C2×C61semidirect
419. C2×#418C2×C61semidirect
420. #2415C2×C61semidirect
422. #2067C2×C61semidirect
423. #2055C2×C61semidirect
424. #2034C2×C61semidirect
425. #2000C2×C61semidirect
426. #1968C2×C61semidirect
427. #1934C2×C61semidirect
428. #1895C2×C61semidirect
429. #1894C2×C61semidirect
430. #1854C2×C61semidirect
446. C22×M16C22×C61semidirect
448. C2×C22⋊Q8C22×C61semidirect
457. C2×#107C22×C61semidirect
458. C2×#106C22×C61semidirect
459. C2×C4⋊C8C22×C61semidirect
461. C2×#103C22×C61semidirect
462. C2×#103C22×C61semidirect
470. C2×C22⋊C8C22×C61semidirect
471. C2×C4×C8C22×C61semidirect
476. #391C22×C61semidirect
480. #389C22×C61semidirect
483. #380C22×C61semidirect
485. #340C22×C61semidirect
486. #340C22×C61semidirect
487. #340C22×C61semidirect
488. #340C22×C61semidirect
489. C61#25136direct (N × H)
569. #102D4×C61semidirect
571. 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×#4682
C2×C61×#4502
C2×C61×#4362
C2×C61×#4182
C61×#24152
C61×#24082
C61×#20672
C61×#20552
C61×#20342
C61×#20002
C61×#19682
C61×#19342
C61×#18952
C61×#18942
C61×#18542
#2513661