Finite Group Databasebeta

← C61×#23580 #29527013

Subgroups — C61×#23580 #29527013

Order 15616.

1242 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#540C211yesmaximal, characteristic, complemented
2C2×C61×#442C211yesmaximal, characteristic, complemented
3C2×C4×D8×C61C211yesmaximal, characteristic, complemented
4C61×#2324C211yesmaximal, characteristic, complemented
5C61×#2059C211yesmaximal, characteristic, complemented
6C61×#2041C211yesmaximal, characteristic, complemented
7C61×#2034C211yesmaximal, characteristic, complemented
8C61×#2033C211yesmaximal, characteristic, complemented
9C61×#2025C211yesmaximal, characteristic, complemented
10C61×#2011C211yesmaximal, characteristic, complemented
11C61×#1999C211yesmaximal, characteristic, complemented
12C61×#1999C211yesmaximal, characteristic, complemented
13C61×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C61C211yesmaximal, characteristic, complemented
15C61×#1750C211yesmaximal, characteristic, complemented
16C22×D8×C61C2211yescharacteristic
17C22×D8×C61C2211yescharacteristic
18C61×#540—24no—
19C61×#540—24no—
20C2×#127×C61C2211yescharacteristic
21C2×#125×C61C2211yescharacteristic
22C2×#123×C61—21no—
23C2×#123×C61—21no—
24C2×#121×C61—21no—
25C2×#121×C61—21no—
26C2×#121×C61C2211yescharacteristic
27C2×#121×C61C2211yescharacteristic
28C2×#121×C61C2211yescharacteristic
29C2×C4×D4×C61C2211yescharacteristic
30C2×C4×D4×C61C2211yescharacteristic
31C2×C4×D4×C61C2211yescharacteristic
32C2×#117×C61C2211yescharacteristic
33C61×#442—24no—
34C4×D8×C61—24no—
35C2×#107×C61C2211yescharacteristic
36C2×#106×C61C2211yescharacteristic
37C2×#102×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic
42C2×#102×C61C2211yescharacteristic
43C2×#102×C61C2211yescharacteristic
44C2×#102×C61C2211yescharacteristic
45C2×C22⋊C8×C61C2211yescharacteristic
46C2×C22⋊C8×C61C2211yescharacteristic
47C2×#97×C61C2211yescharacteristic
48C2×C4×C8×C61C2211yescharacteristic
49C61×#390—21no—
50C61×#390C2211yescharacteristic
51C61×#389C2211yescharacteristic
52C61×#388—21no—
53C61×#386—21no—
54C61×#385—21no—
55C61×#380C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×D4×C61—21no—
64C22×D4×C61—21no—
65C22×D4×C61—21no—
66C22×D4×C61—21no—
67C22×D4×C61—21no—
68C22×D4×C61C2311yescharacteristic
69C22×D4×C61C2311yescharacteristic
70C22×D4×C61C2311yescharacteristic
71C23×C4×C61—21no—
72C23×C4×C61—21no—
73C23×C4×C61—21no—
74C23×C4×C61C2311yescharacteristic
75C2×D8×C61—22no—
76C2×D8×C61—22no—
77C2×D8×C61—22no—
78C2×D8×C61—22no—
79C2×D8×C61—22no—
80C2×D8×C61—22no—
81C22×C8×C61C2311yescharacteristic
82C22×C8×C61C2311yescharacteristic
83C22×C8×C61C2311yescharacteristic
84C22×C8×C61C2311yescharacteristic
85#127×C61—22no—
86#127×C61—22no—
87#125×C61—22no—
88#125×C61—22no—
89#123×C61—28no—
90#123×C61—28no—
91#121×C61—28no—
92#121×C61—28no—
93#121×C61—22no—
94#121×C61—22no—
95#121×C61—22no—
96#121×C61—22no—
97#121×C61—22no—
98#121×C61—22no—
99C4×D4×C61—22no—
100C4×D4×C61—22no—
101C4×D4×C61—22no—
102C4×D4×C61—22no—
103C4×D4×C61D414yescomplemented
104C4×D4×C61D414yescomplemented
105#117×C61—22no—
106#117×C61—22no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61D411yescharacteristic
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×C61D411yescharacteristic
127C2×C22⋊C4×C61D411yescharacteristic
128C2×C42×C61—21no—
129C2×C42×C61C2311yescharacteristic
130C2×C42×C61C2311yescharacteristic
131#107×C61—22no—
132#106×C61—22no—
133#102×C61—22no—
134#102×C61—22no—
135#102×C61—22no—
136#102×C61—22no—
137#102×C61—22no—
138#102×C61—22no—
139#102×C61—22no—
140#102×C61—22no—
141C22⋊C8×C61—22no—
142C22⋊C8×C61—22no—
143#97×C61—22no—
144C4×C8×C61—22no—
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148C24×C61—21no—
149C24×C61—21no—
150C24×C61—21no—
151C24×C61C2×D411yescharacteristic
152C2×D4×C61—24no—
153C2×D4×C61—24no—
154C2×D4×C61—24no—
155C2×D4×C61—24no—
156C2×D4×C61—24no—
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—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—81no—
173C2×D4×C61—81no—
174C2×D4×C61—81no—
175C2×D4×C61—81no—
176C2×D4×C61—81no—
177C2×D4×C61—81no—
178C2×D4×C61—81no—
179C2×D4×C61—81no—
180C2×D4×C61—81no—
181C2×D4×C61—81no—
182C2×D4×C61C2×D412yes—
183C2×D4×C61C2×D412yes—
184C2×D4×C61#4112yes—
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—24no—
195C22×C4×C61—24no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—42no—
199C22×C4×C61—81no—
200C22×C4×C61—81no—
201C22×C4×C61—81no—
202C22×C4×C61—81no—
203C22×C4×C61—81no—
204C22×C4×C61—81no—
205C22×C4×C61C2×D411yescharacteristic
206C22×C4×C61C2×D411yescharacteristic
207C22×C4×C61C2×D411yescharacteristic
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2411yescharacteristic
211D8×C61—28no—
212D8×C61—28no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61#4112yes—
224C2×C8×C61#4112yes—
225C4⋊C4×C61—24no—
226C4⋊C4×C61—24no—
227C4⋊C4×C61—22no—
228C4⋊C4×C61—22no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—21no—
235C4⋊C4×C61—21no—
236C4⋊C4×C61—81no—
237C4⋊C4×C61C2×D412yes—
238C4⋊C4×C61C2×D412yes—
239C4⋊C4×C61#4112yes—
240C22⋊C4×C61—24no—
241C22⋊C4×C61—24no—
242C22⋊C4×C61—24no—
243C22⋊C4×C61—24no—
244C22⋊C4×C61—24no—
245C22⋊C4×C61—22no—
246C22⋊C4×C61—22no—
247C22⋊C4×C61—42no—
248C22⋊C4×C61—81no—
249C22⋊C4×C61—81no—
250C22⋊C4×C61—81no—
251C42×C61—21no—
252C42×C61—21no—
253C42×C61—81no—
254C42×C61C2×D412yes—
255C42×C61C2×D412yes—
256C23×C61—21no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
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—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61C22×D411yescharacteristic
285D4×C61—22no—
286D4×C61—22no—
287D4×C61—22no—
288D4×C61—22no—
289D4×C61—22no—
290D4×C61—22no—
291D4×C61—41no—
292D4×C61—41no—
293D4×C61—41no—
294D4×C61—41no—
295D4×C61—41no—
296D4×C61—41no—
297D4×C61—84no—
298D4×C61—84no—
299D4×C61—84no—
300D4×C61—84no—
301D4×C61—84no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—21no—
312C2×C4×C61—22no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
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—41no—
333C2×C4×C61—41no—
334C2×C4×C61—84no—
335C2×C4×C61—84no—
336C2×C4×C61—84no—
337C2×C4×C61#12012yes—
338C2×C4×C61#12012yes—
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C2×#4111yescharacteristic
342C2×C4×C61C2×#4111yescharacteristic
343C2×C4×C61C2×#4111yescharacteristic
344C2×C4×C61C2×#4111yescharacteristic
345C8×C61—22no—
346C8×C61—22no—
347C8×C61—41no—
348C8×C61—41no—
349#23580C6111yesmaximal, characteristic, direct product factor, Sylow
350C22×C61—41no—
351C22×C61—42no—
352C22×C61—41no—
353C22×C61—42no—
354C22×C61—41no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—42no—
361C22×C61—41no—
362C22×C61—42no—
363C22×C61—42no—
364C22×C61—41no—
365C22×C61—42no—
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×C61—81no—
375C22×C61—81no—
376C22×C61—81no—
377C22×C61—81no—
378C22×C61C2×#12011yescharacteristic
379C22×C61#52511yescharacteristic
380C22×C61#53211yescharacteristic
381C22×C61#57611yescharacteristic
382C22×C61#57611yescharacteristic
383C22×C61#57611yescharacteristic
384C22×C61#57711yescharacteristic
385C4×C61—22no—
386C4×C61—22no—
387C4×C61—42no—
388C4×C61—41no—
389C4×C61—41no—
390C4×C61—42no—
391C4×C61—41no—
392C4×C61—42no—
393C4×C61—81no—
394C4×C61—81no—
395C4×C61#52511yescharacteristic
396C4×C61#52511yescharacteristic
397C4×C61#53211yescharacteristic
398C4×C61#53211yescharacteristic
399C2×#540C2×C6111yescharacteristic, complemented
400C2×#442C2×C6111yescharacteristic, complemented
401C2×C4×D8C2×C6111yescharacteristic, complemented
402#2324C2×C6111yescharacteristic, complemented
403#2059C2×C6111yescharacteristic, complemented
404#2041C2×C6111yescharacteristic, complemented
405#2034C2×C6111yescharacteristic, complemented
406#2033C2×C6111yescharacteristic, complemented
407#2025C2×C6111yescharacteristic, complemented
408#2011C2×C6111yescharacteristic, complemented
409#1999C2×C6111yescharacteristic, complemented
410#1999C2×C6111yescharacteristic, complemented
411#1762C2×C6111yescharacteristic, complemented
412C4×#102C2×C6111yescharacteristic, complemented
413#1750C2×C6111yescharacteristic, complemented
414C2×C61—81no—
415C2×C61—82no—
416C2×C61—82no—
417C2×C61—82no—
418C2×C61#238811yescharacteristic
419C2×C61#300811yescharacteristic
420C2×C61#301211yescharacteristic
421C2×C61#311911yescharacteristic
422C2×C61#312211yescharacteristic
423C2×C61#317611yescharacteristic
424C2×C61#317911yescharacteristic
425C22×D8C22×C6111yescharacteristic
426C22×D8C22×C6111yescharacteristic
427#540—24no—
428#540—24no—
429C2×#127C22×C6111yescharacteristic
430C2×#125C22×C6111yescharacteristic
431C2×#123—21no—
432C2×#123—21no—
433C2×#121—21no—
434C2×#121—21no—
435C2×#121C22×C6111yescharacteristic
436C2×#121C22×C6111yescharacteristic
437C2×#121C22×C6111yescharacteristic
438C2×C4×D4C22×C6111yescharacteristic
439C2×C4×D4C22×C6111yescharacteristic
440C2×C4×D4C22×C6111yescharacteristic
441C2×#117C22×C6111yescharacteristic
442#442—24no—
443C4×D8—24no—
444C2×#107C22×C6111yescharacteristic
445C2×#106C22×C6111yescharacteristic
446C2×#102C22×C6111yescharacteristic
447C2×#102C22×C6111yescharacteristic
448C2×#102C22×C6111yescharacteristic
449C2×#102C22×C6111yescharacteristic
450C2×#102C22×C6111yescharacteristic
451C2×#102C22×C6111yescharacteristic
452C2×#102C22×C6111yescharacteristic
453C2×#102C22×C6111yescharacteristic
454C2×C22⋊C8C22×C6111yescharacteristic
455C2×C22⋊C8C22×C6111yescharacteristic
456C2×#97C22×C6111yescharacteristic
457C2×C4×C8C22×C6111yescharacteristic
458#390—21no—
459#390C22×C6111yescharacteristic
460#389C22×C6111yescharacteristic
461#388—21no—
462#386—21no—
463#385—21no—
464#380C22×C6111yescharacteristic
465C4×C4⋊C4C22×C6111yescharacteristic
466#340C22×C6111yescharacteristic
467#340C22×C6111yescharacteristic
468#340C22×C6111yescharacteristic
469#340C22×C6111yescharacteristic
470#336C22×C6111yescharacteristic
471#336C22×C6111yescharacteristic
472C61#2358011yescharacteristic, direct product factor, Sylow
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4C23×C6111yescharacteristic
479C22×D4C23×C6111yescharacteristic
480C22×D4C23×C6111yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C6111yescharacteristic
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—22no—
491C22×C8C23×C6111yescharacteristic
492C22×C8C23×C6111yescharacteristic
493C22×C8C23×C6111yescharacteristic
494C22×C8C23×C6111yescharacteristic
495#127—22no—
496#127—22no—
497#125—22no—
498#125—22no—
499#123—28no—
500#123—28no—
501#121—28no—
502#121—28no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C6114yescomplemented
514C4×D4D4×C6114yescomplemented
515#117—22no—
516#117—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4D4×C6111yescharacteristic
521C2×C4⋊C4D4×C6111yescharacteristic
522C2×C4⋊C4C23×C6111yescharacteristic
523C2×C4⋊C4C23×C6111yescharacteristic
524C2×C4⋊C4C23×C6111yescharacteristic
525C2×C4⋊C4C23×C6111yescharacteristic
526C2×C4⋊C4C23×C6111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4D4×C6111yescharacteristic
537C2×C22⋊C4D4×C6111yescharacteristic
538C2×C42—21no—
539C2×C42C23×C6111yescharacteristic
540C2×C42C23×C6111yescharacteristic
541#107—22no—
542#106—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553#97—22no—
554C4×C8—22no—
555#95—21no—
556#95—21no—
557#95—21no—
558C24—21no—
559C24—21no—
560C24—21no—
561C24C2×D4×C6111yescharacteristic
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C6112yes—
593C2×D4C2×D4×C6112yes—
594C2×D4#41×C6112yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C2×D4×C6111yescharacteristic
616C22×C4C2×D4×C6111yescharacteristic
617C22×C4C2×D4×C6111yescharacteristic
618C22×C4C2×D4×C6111yescharacteristic
619C22×C4C2×D4×C6111yescharacteristic
620C22×C4C24×C6111yescharacteristic
621D8—28no—
622D8—28no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8#41×C6112yes—
634C2×C8#41×C6112yes—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C6112yes—
648C4⋊C4C2×D4×C6112yes—
649C4⋊C4#41×C6112yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—81no—
664C42C2×D4×C6112yes—
665C42C2×D4×C6112yes—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23C22×D4×C6111yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
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—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4#120×C6112yes—
748C2×C4#120×C6112yes—
749C2×C4C22×D4×C6111yescharacteristic
750C2×C4C22×D4×C6111yescharacteristic
751C2×C4C2×#41×C6111yescharacteristic
752C2×C4C2×#41×C6111yescharacteristic
753C2×C4C2×#41×C6111yescharacteristic
754C2×C4C2×#41×C6111yescharacteristic
755C8—22no—
756C8—22no—
757C8—41no—
758C8—41no—
759C22—41no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22C2×#120×C6111yescharacteristic
788C22C61×#52511yescharacteristic
789C22C61×#53211yescharacteristic
790C22C61×#57611yescharacteristic
791C22C61×#57611yescharacteristic
792C22C61×#57611yescharacteristic
793C22C61×#57711yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—41no—
798C4—41no—
799C4—42no—
800C4—41no—
801C4—42no—
802C4—81no—
803C4—81no—
804C4C61×#52511yescharacteristic
805C4C61×#52511yescharacteristic
806C4C61×#53211yescharacteristic
807C4C61×#53211yescharacteristic
808C2—81no—
809C2—82no—
810C2—82no—
811C2—82no—
812C2C61×#238811yescharacteristic
813C2C61×#300811yescharacteristic
814C2C61×#301211yescharacteristic
815C2C61×#311911yescharacteristic
816C2C61×#312211yescharacteristic
817C2C61×#317611yescharacteristic
818C2C61×#317911yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C2×#117×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#540C2semidirect
2. C2×C61×#442C2semidirect
3. C2×C4×D8×C61C2semidirect
4. C61×#2324C2semidirect
5. C61×#2059C2semidirect
6. C61×#2041C2semidirect
7. C61×#2034C2semidirect
8. C61×#2033C2semidirect
9. C61×#2025C2semidirect
10. C61×#2011C2semidirect
11. C61×#1999C2semidirect
12. C61×#1999C2semidirect
13. C61×#1762C2semidirect
14. C4×#102×C61C2semidirect
15. C61×#1750C2semidirect
103. C4×D4×C61D4semidirect
104. C4×D4×C61D4semidirect
349. #23580C61direct (N × H)
399. C2×#540C2×C61semidirect
400. C2×#442C2×C61semidirect
401. C2×C4×D8C2×C61semidirect
402. #2324C2×C61semidirect
403. #2059C2×C61semidirect
404. #2041C2×C61semidirect
405. #2034C2×C61semidirect
406. #2033C2×C61semidirect
407. #2025C2×C61semidirect
408. #2011C2×C61semidirect
409. #1999C2×C61semidirect
410. #1999C2×C61semidirect
411. #1762C2×C61semidirect
412. C4×#102C2×C61semidirect
413. #1750C2×C61semidirect
472. C61#23580direct (N × H)
513. C4×D4D4×C61semidirect
514. C4×D4D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5402
C2×C61×#4422
C2×C4×D8×C612
C61×#23242
C61×#20592
C61×#20412
C61×#20342
C61×#20332
C61×#20252
C61×#20112
C61×#19992
C61×#17622
C4×#102×C612
C61×#17502
#2358061