Finite Group Databasebeta

← C61×#24882 #29528315

Subgroups — C61×#24882 #29528315

Order 15616.

1168 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#480C211yesmaximal, characteristic, complemented
2C2×C61×#418C211yesmaximal, characteristic, complemented
3C61×#2408C211yesmaximal, characteristic
4C61×#2352C211yesmaximal, characteristic, complemented
5C61×#2092C211yesmaximal, characteristic, complemented
6C61×#2073C211yesmaximal, characteristic, complemented
7C61×#2034C211yesmaximal, characteristic, complemented
8C61×#2034C211yesmaximal, characteristic, complemented
9C61×#1926C211yesmaximal, characteristic, complemented
10C61×#1925C211yesmaximal, characteristic, complemented
11C61×#1874C211yesmaximal, characteristic, complemented
12C61×#1870C211yesmaximal, characteristic, complemented
13C61×#1854C211yesmaximal, characteristic, complemented
14C61×#1809C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C61C2211yescharacteristic
17C22×M16×C61C2211yescharacteristic
18C2×#121×C61C2211yescharacteristic
19C2×#121×C61C2211yescharacteristic
20C2×#120×C61—21no—
21C2×C4×D4×C61C2211yescharacteristic
22C2×#117×C61C2211yescharacteristic
23C22×C4⋊C4×C61C2211yescharacteristic, complemented
24C61×#480—24no—
25C2×#107×C61C2211yescharacteristic, complemented
26C2×#107×C61C2211yescharacteristic, complemented
27C2×#106×C61C2211yescharacteristic, complemented
28C2×#106×C61C2211yescharacteristic, complemented
29C61×#418—24no—
30C2×#102×C61C2211yescharacteristic
31C2×#102×C61C2211yescharacteristic
32C2×#102×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×#102×C61C2211yescharacteristic
37C2×#102×C61C2211yescharacteristic
38C2×C22⋊C8×C61C2211yescharacteristic
39C2×C22⋊C8×C61C2211yescharacteristic, complemented
40C2×C22⋊C8×C61C2211yescharacteristic, complemented
41C61×#394—21no—
42C61×#392—21no—
43C61×#390C2211yescharacteristic
44C61×#390C2211yescharacteristic
45C61×#388—21no—
46C61×#387—21no—
47C61×#386—21no—
48C61×#382C2211yescharacteristic, complemented
49C61×#380C2211yescharacteristic
50C61×#380C2211yescharacteristic
51C61×#380C2211yescharacteristic, complemented
52C61×#379—21no—
53C4×C4⋊C4×C61C2211yescharacteristic, complemented
54C4×C22⋊C4×C61—21no—
55C61×#340C2211yescharacteristic, complemented
56C61×#340C2211yescharacteristic, complemented
57C61×#340C2211yescharacteristic, complemented
58C61×#340C2211yescharacteristic, complemented
59C61×#336C2211yescharacteristic, complemented
60C61×#336C2211yescharacteristic, complemented
61C25×C61—21no—
62C22×D4×C61—22no—
63C22×D4×C61—22no—
64C22×D4×C61—21no—
65C22×D4×C61—21no—
66C22×D4×C61—21no—
67C22×D4×C61—22no—
68C22×D4×C61—22no—
69C22×D4×C61—41no—
70C22×D4×C61—41no—
71C22×D4×C61D411yescharacteristic
72C22×D4×C61C2311yescharacteristic
73C22×D4×C61C2311yescharacteristic
74C23×C4×C61—21no—
75C23×C4×C61C2311yescharacteristic
76C23×C4×C61C2311yescharacteristic
77C2×M16×C61—22no—
78C2×M16×C61—22no—
79C2×M16×C61—41no—
80C22×C8×C61C2311yescharacteristic
81C22×C8×C61C2311yescharacteristic
82C22×C8×C61C2311yescharacteristic
83C22×C8×C61C2311yescharacteristic
84#121×C61—22no—
85#121×C61—22no—
86#121×C61—41no—
87#121×C61—41no—
88#120×C61—44no—
89C4×D4×C61—22no—
90C4×D4×C61—22no—
91#117×C61—22no—
92#117×C61—41no—
93C2×C4⋊C4×C61—22no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—41no—
96C2×C4⋊C4×C61D411yescharacteristic
97C2×C4⋊C4×C61C2311yescharacteristic
98C2×C4⋊C4×C61C2311yescharacteristic
99C2×C4⋊C4×C61C2311yescharacteristic
100C2×C4⋊C4×C61C2311yescharacteristic
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C22⋊C4×C61—21no—
104C2×C22⋊C4×C61—21no—
105C2×C22⋊C4×C61—21no—
106C2×C22⋊C4×C61—21no—
107C2×C22⋊C4×C61—21no—
108C2×C22⋊C4×C61—21no—
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61—21no—
111C2×C22⋊C4×C61—21no—
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61D411yescharacteristic
114C2×C22⋊C4×C61D411yescharacteristic
115C2×C42×C61—21no—
116C2×C42×C61—21no—
117C2×C42×C61C2311yescharacteristic
118#107×C61—22no—
119#107×C61—22no—
120#106×C61—41no—
121#106×C61—41no—
122#102×C61—22no—
123#102×C61—22no—
124#102×C61—22no—
125#102×C61—22no—
126#102×C61—22no—
127#102×C61—41no—
128#102×C61—41no—
129#102×C61D414yescomplemented
130C22⋊C8×C61—22no—
131C22⋊C8×C61—22no—
132C22⋊C8×C61—41no—
133#95×C61—21no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61—21no—
137#95×C61—21no—
138#95×C61—21no—
139C24×C61—21no—
140C24×C61—21no—
141C24×C61—42no—
142C24×C61—42no—
143C24×C61—42no—
144C24×C61—42no—
145C24×C61—42no—
146C24×C61—81no—
147C24×C61—81no—
148C24×C61C2×D411yescharacteristic
149C24×C61C2×D411yescharacteristic
150C2×D4×C61—28no—
151C2×D4×C61—22no—
152C2×D4×C61—22no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—44no—
164C2×D4×C61—44no—
165C2×D4×C61—41no—
166C2×D4×C61—42no—
167C2×D4×C61—42no—
168C2×D4×C61—44no—
169C2×D4×C61—42no—
170C2×D4×C61—42no—
171C2×D4×C61—42no—
172C2×D4×C61—42no—
173C2×D4×C61—42no—
174C2×D4×C61—81no—
175C2×D4×C61—81no—
176C2×D4×C61C2×D412yes—
177C2×D4×C61#4112yes—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—42no—
195C22×C4×C61—42no—
196C22×C4×C61—81no—
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D411yescharacteristic
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61#4112yes—
202C22×C4×C61#4112yes—
203C22×C4×C61C2411yescharacteristic
204M16×C61—44no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61—21no—
210C2×C8×C61—21no—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61C2×D412yes—
217C4⋊C4×C61—22no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—42no—
230C4⋊C4×C61C2×D412yes—
231C22⋊C4×C61—22no—
232C22⋊C4×C61—22no—
233C22⋊C4×C61—42no—
234C22⋊C4×C61—42no—
235C22⋊C4×C61—42no—
236C22⋊C4×C61—42no—
237C22⋊C4×C61—42no—
238C22⋊C4×C61—42no—
239C22⋊C4×C61—42no—
240C22⋊C4×C61—81no—
241C22⋊C4×C61—81no—
242C22⋊C4×C61—81no—
243C42×C61—21no—
244C42×C61—21no—
245C42×C61—42no—
246C42×C61—81no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—48no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61—41no—
272C23×C61—41no—
273C23×C61—41no—
274C23×C61—84no—
275C23×C61—84no—
276C23×C61—84no—
277C23×C61—84no—
278C23×C61—84no—
279C23×C61—84no—
280C23×C61#12312yes—
281C23×C61AGL(1,ℤ/8)12yes—
282C23×C61C22×D411yescharacteristic
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—22no—
286D4×C61—22no—
287D4×C61—48no—
288D4×C61—44no—
289D4×C61—41no—
290D4×C61—41no—
291D4×C61—41no—
292D4×C61—41no—
293D4×C61—84no—
294D4×C61—84no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—22no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—84no—
333C2×C4×C61#12312yes—
334C2×C4×C61C22×D411yescharacteristic
335C2×C4×C61C2×#4111yescharacteristic
336C2×C4×C61C2×#4111yescharacteristic
337C2×C4×C61C2×#4111yescharacteristic
338C2×C4×C61H(5,𝔽2)11yescharacteristic
339C2×C4×C61H(5,𝔽2)11yescharacteristic
340C8×C61—22no—
341C8×C61—41no—
342C8×C61—41no—
343C8×C61—41no—
344#24882C6111yesmaximal, characteristic, direct product factor, Sylow
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—41no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—42no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—816no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61—81no—
371C22×C61—81no—
372C22×C61—81no—
373C22×C61—81no—
374C22×C61C2×#12311yescharacteristic
375C22×C61D4211yescharacteristic
376C22×C61#54611yescharacteristic
377C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
378C22×C61#57511yescharacteristic
379C22×C61#57611yescharacteristic
380C22×C61#57711yescharacteristic
381C4×C61—22no—
382C4×C61—41no—
383C4×C61—41no—
384C4×C61—41no—
385C4×C61—42no—
386C4×C61—81no—
387C4×C61—81no—
388C4×C61—81no—
389C4×C61—81no—
390C4×C61—81no—
391C4×C61#52511yescharacteristic
392C4×C61#53811yescharacteristic
393C4×C61#54611yescharacteristic
394C4×C61#55111yescharacteristic
395C2×#480C2×C6111yescharacteristic, complemented
396C2×#418C2×C6111yescharacteristic, complemented
397#2408C2×C6111yescharacteristic
398#2352C2×C6111yescharacteristic, complemented
399#2092C2×C6111yescharacteristic, complemented
400#2073C2×C6111yescharacteristic, complemented
401#2034C2×C6111yescharacteristic, complemented
402#2034C2×C6111yescharacteristic, complemented
403#1926C2×C6111yescharacteristic, complemented
404#1925C2×C6111yescharacteristic, complemented
405#1874C2×C6111yescharacteristic, complemented
406#1870C2×C6111yescharacteristic, complemented
407#1854C2×C6111yescharacteristic, complemented
408#1809C2×C6111yescharacteristic, complemented
409#1786C2×C6111yescharacteristic, complemented
410C2×C61—42no—
411C2×C61—42no—
412C2×C61—82no—
413C2×C61—82no—
414C2×C61#241811yescharacteristic
415C2×C61#309411yescharacteristic
416C2×C61#309611yescharacteristic
417C2×C61#326411yescharacteristic
418C2×C61#327511yescharacteristic
419C2×C61#331011yescharacteristic
420C2×C61#332211yescharacteristic
421C23×D4C22×C6111yescharacteristic
422C22×M16C22×C6111yescharacteristic
423C2×#121C22×C6111yescharacteristic
424C2×#121C22×C6111yescharacteristic
425C2×#120—21no—
426C2×C4×D4C22×C6111yescharacteristic
427C2×#117C22×C6111yescharacteristic
428C22×C4⋊C4C22×C6111yescharacteristic, complemented
429#480—24no—
430C2×#107C22×C6111yescharacteristic, complemented
431C2×#107C22×C6111yescharacteristic, complemented
432C2×#106C22×C6111yescharacteristic, complemented
433C2×#106C22×C6111yescharacteristic, complemented
434#418—24no—
435C2×#102C22×C6111yescharacteristic
436C2×#102C22×C6111yescharacteristic
437C2×#102C22×C6111yescharacteristic
438C2×#102C22×C6111yescharacteristic
439C2×#102C22×C6111yescharacteristic
440C2×#102C22×C6111yescharacteristic
441C2×#102C22×C6111yescharacteristic
442C2×#102C22×C6111yescharacteristic
443C2×C22⋊C8C22×C6111yescharacteristic
444C2×C22⋊C8C22×C6111yescharacteristic, complemented
445C2×C22⋊C8C22×C6111yescharacteristic, complemented
446#394—21no—
447#392—21no—
448#390C22×C6111yescharacteristic
449#390C22×C6111yescharacteristic
450#388—21no—
451#387—21no—
452#386—21no—
453#382C22×C6111yescharacteristic, complemented
454#380C22×C6111yescharacteristic
455#380C22×C6111yescharacteristic
456#380C22×C6111yescharacteristic, complemented
457#379—21no—
458C4×C4⋊C4C22×C6111yescharacteristic, complemented
459C4×C22⋊C4—21no—
460#340C22×C6111yescharacteristic, complemented
461#340C22×C6111yescharacteristic, complemented
462#340C22×C6111yescharacteristic, complemented
463#340C22×C6111yescharacteristic, complemented
464#336C22×C6111yescharacteristic, complemented
465#336C22×C6111yescharacteristic, complemented
466C61#2488211yescharacteristic, direct product factor, Sylow
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—41no—
476C22×D4—41no—
477C22×D4D4×C6111yescharacteristic
478C22×D4C23×C6111yescharacteristic
479C22×D4C23×C6111yescharacteristic
480C23×C4—21no—
481C23×C4C23×C6111yescharacteristic
482C23×C4C23×C6111yescharacteristic
483C2×M16—22no—
484C2×M16—22no—
485C2×M16—41no—
486C22×C8C23×C6111yescharacteristic
487C22×C8C23×C6111yescharacteristic
488C22×C8C23×C6111yescharacteristic
489C22×C8C23×C6111yescharacteristic
490#121—22no—
491#121—22no—
492#121—41no—
493#121—41no—
494#120—44no—
495C4×D4—22no—
496C4×D4—22no—
497#117—22no—
498#117—41no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4D4×C6111yescharacteristic
503C2×C4⋊C4C23×C6111yescharacteristic
504C2×C4⋊C4C23×C6111yescharacteristic
505C2×C4⋊C4C23×C6111yescharacteristic
506C2×C4⋊C4C23×C6111yescharacteristic
507C2×C4⋊C4C23×C6111yescharacteristic
508C2×C4⋊C4C23×C6111yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4D4×C6111yescharacteristic
520C2×C22⋊C4D4×C6111yescharacteristic
521C2×C42—21no—
522C2×C42—21no—
523C2×C42C23×C6111yescharacteristic
524#107—22no—
525#107—22no—
526#106—41no—
527#106—41no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—41no—
534#102—41no—
535#102D4×C6114yescomplemented
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—41no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545C24—21no—
546C24—21no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—81no—
553C24—81no—
554C24C2×D4×C6111yescharacteristic
555C24C2×D4×C6111yescharacteristic
556C2×D4—28no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—41no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—44no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—81no—
581C2×D4—81no—
582C2×D4C2×D4×C6112yes—
583C2×D4#41×C6112yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—81no—
603C22×C4C2×D4×C6111yescharacteristic
604C22×C4C2×D4×C6111yescharacteristic
605C22×C4C2×D4×C6111yescharacteristic
606C22×C4C2×D4×C6111yescharacteristic
607C22×C4#41×C6112yes—
608C22×C4#41×C6112yes—
609C22×C4C24×C6111yescharacteristic
610M16—44no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8C2×D4×C6112yes—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—42no—
636C4⋊C4C2×D4×C6112yes—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—42no—
652C42—81no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—22no—
666C23—22no—
667C23—48no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23#123×C6112yes—
687C23AGL(1,ℤ/8)×C6112yes—
688C23C22×D4×C6111yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—48no—
694D4—44no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—84no—
700D4—84no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4#123×C6112yes—
740C2×C4C22×D4×C6111yescharacteristic
741C2×C4C2×#41×C6111yescharacteristic
742C2×C4C2×#41×C6111yescharacteristic
743C2×C4C2×#41×C6111yescharacteristic
744C2×C4H(5,𝔽2)×C6111yescharacteristic
745C2×C4H(5,𝔽2)×C6111yescharacteristic
746C8—22no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—816no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22C2×#123×C6111yescharacteristic
780C22D42×C6111yescharacteristic
781C22C61×#54611yescharacteristic
782C22C2×AGL(1,ℤ/8)×C6111yescharacteristic
783C22C61×#57511yescharacteristic
784C22C61×#57611yescharacteristic
785C22C61×#57711yescharacteristic
786C4—22no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—42no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C61×#52511yescharacteristic
797C4C61×#53811yescharacteristic
798C4C61×#54611yescharacteristic
799C4C61×#55111yescharacteristic
800C2—42no—
801C2—42no—
802C2—82no—
803C2—82no—
804C2C61×#241811yescharacteristic
805C2C61×#309411yescharacteristic
806C2C61×#309611yescharacteristic
807C2C61×#326411yescharacteristic
808C2C61×#327511yescharacteristic
809C2C61×#331011yescharacteristic
810C2C61×#332211yescharacteristic
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×#480C2semidirect
2. C2×C61×#418C2semidirect
4. C61×#2352C2semidirect
5. C61×#2092C2semidirect
6. C61×#2073C2semidirect
7. C61×#2034C2semidirect
8. C61×#2034C2semidirect
9. C61×#1926C2semidirect
10. C61×#1925C2semidirect
11. C61×#1874C2semidirect
12. C61×#1870C2semidirect
13. C61×#1854C2semidirect
14. C61×#1809C2semidirect
15. C61×#1786C2semidirect
23. C22×C4⋊C4×C61C22semidirect
25. C2×#107×C61C22semidirect
26. C2×#107×C61C22semidirect
27. C2×#106×C61C22semidirect
28. C2×#106×C61C22semidirect
39. C2×C22⋊C8×C61C22semidirect
40. C2×C22⋊C8×C61C22semidirect
48. C61×#382C22semidirect
51. C61×#380C22semidirect
53. C4×C4⋊C4×C61C22semidirect
55. C61×#340C22semidirect
56. C61×#340C22semidirect
57. C61×#340C22semidirect
58. C61×#340C22semidirect
59. C61×#336C22semidirect
60. C61×#336C22semidirect
129. #102×C61D4semidirect
344. #24882C61direct (N × H)
395. C2×#480C2×C61semidirect
396. C2×#418C2×C61semidirect
398. #2352C2×C61semidirect
399. #2092C2×C61semidirect
400. #2073C2×C61semidirect
401. #2034C2×C61semidirect
402. #2034C2×C61semidirect
403. #1926C2×C61semidirect
404. #1925C2×C61semidirect
405. #1874C2×C61semidirect
406. #1870C2×C61semidirect
407. #1854C2×C61semidirect
408. #1809C2×C61semidirect
409. #1786C2×C61semidirect
428. C22×C4⋊C4C22×C61semidirect
430. C2×#107C22×C61semidirect
431. C2×#107C22×C61semidirect
432. C2×#106C22×C61semidirect
433. C2×#106C22×C61semidirect
444. C2×C22⋊C8C22×C61semidirect
445. C2×C22⋊C8C22×C61semidirect
453. #382C22×C61semidirect
456. #380C22×C61semidirect
458. C4×C4⋊C4C22×C61semidirect
460. #340C22×C61semidirect
461. #340C22×C61semidirect
462. #340C22×C61semidirect
463. #340C22×C61semidirect
464. #336C22×C61semidirect
465. #336C22×C61semidirect
466. C61#24882direct (N × H)
535. #102D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4802
C2×C61×#4182
C61×#24082
C61×#23522
C61×#20922
C61×#20732
C61×#20342
C61×#19262
C61×#19252
C61×#18742
C61×#18702
C61×#18542
C61×#18092
C61×#17862
#2488261