Finite Group Databasebeta

← C61×#25553 #29528986

Subgroups — C61×#25553 #29528986

Order 15616.

1200 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#553C211yesmaximal, characteristic, complemented
2C2×C61×#480C211yesmaximal, characteristic, complemented
3C2×C61×#469C211yesmaximal, characteristic, complemented
4C61×#2414C211yesmaximal, characteristic, complemented
5C61×#2059C211yesmaximal, characteristic, complemented
6C61×#2033C211yesmaximal, characteristic, complemented
7C61×#2025C211yesmaximal, characteristic, complemented
8C61×#1999C211yesmaximal, characteristic, complemented
9C61×#1879C211yesmaximal, characteristic, complemented
10C61×#1875C211yesmaximal, characteristic, complemented
11C61×#1875C211yesmaximal, characteristic, complemented
12C61×#1870C211yesmaximal, characteristic, complemented
13C61×#1862C211yesmaximal, characteristic, complemented
14C61×#1854C211yesmaximal, characteristic, complemented
15C61×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C61C2211yescharacteristic
17C22×M16×C61C2211yescharacteristic
18C61×#553—24no—
19C61×#553—24no—
20C2×#126×C61—21no—
21C2×#125×C61C2211yescharacteristic
22C2×#123×C61—21no—
23C2×#121×C61—21no—
24C2×#121×C61C2211yescharacteristic
25C2×#121×C61C2211yescharacteristic
26C2×#121×C61C2211yescharacteristic
27C2×#121×C61C2211yescharacteristic
28C2×C4×D4×C61—21no—
29C2×C4×D4×C61C2211yescharacteristic
30C2×C4×D4×C61C2211yescharacteristic
31C2×#117×C61C2211yescharacteristic
32C2×#117×C61C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C61×#480—24no—
35C61×#469—24no—
36C2×#107×C61C2211yescharacteristic
37C2×#107×C61C2211yescharacteristic
38C2×#106×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×C22⋊C8×C61C2211yescharacteristic
48C61×#394—21no—
49C61×#392—21no—
50C61×#390—21no—
51C61×#390C2211yescharacteristic
52C61×#389C2211yescharacteristic
53C61×#388—21no—
54C61×#380C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
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×C61D411yescharacteristic
68C22×D4×C61C2311yescharacteristic
69C22×D4×C61C2311yescharacteristic
70C23×C4×C61—21no—
71C23×C4×C61—21no—
72C23×C4×C61C2311yescharacteristic
73C23×C4×C61C2311yescharacteristic
74C2×D8×C61—22no—
75C2×D8×C61—22no—
76C2×D8×C61—41no—
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#126×C61—28no—
85#125×C61—22no—
86#125×C61—22no—
87#123×C61—28no—
88#121×C61—28no—
89#121×C61—22no—
90#121×C61—22no—
91#121×C61—22no—
92#121×C61—22no—
93#121×C61—22no—
94#121×C61—22no—
95#121×C61—41no—
96#121×C61D414yescomplemented
97C4×D4×C61—28no—
98C4×D4×C61—22no—
99C4×D4×C61—22no—
100C4×D4×C61—22no—
101C4×D4×C61—22no—
102#117×C61—22no—
103#117×C61—22no—
104#117×C61—22no—
105#117×C61—41no—
106C2×C4⋊C4×C61—22no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61D411yescharacteristic
112C2×C4⋊C4×C61D414yescomplemented
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
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×C61—21no—
129C2×C22⋊C4×C61D411yescharacteristic
130C2×C22⋊C4×C61D411yescharacteristic
131C2×C42×C61—21no—
132C2×C42×C61—21no—
133C2×C42×C61C2311yescharacteristic
134#107×C61—22no—
135#107×C61—22no—
136#106×C61—22no—
137#102×C61—22no—
138#102×C61—22no—
139#102×C61—22no—
140#102×C61—22no—
141#102×C61—22no—
142#102×C61—41no—
143C22⋊C8×C61—22no—
144C22⋊C8×C61—22no—
145C22⋊C8×C61—41no—
146#95×C61—21no—
147#95×C61—21no—
148C24×C61—21no—
149C24×C61—21no—
150C24×C61C2×D411yescharacteristic
151C24×C61C2×D411yescharacteristic
152C2×D4×C61—22no—
153C2×D4×C61—24no—
154C2×D4×C61—24no—
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—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—41no—
167C2×D4×C61—41no—
168C2×D4×C61—42no—
169C2×D4×C61—42no—
170C2×D4×C61—42no—
171C2×D4×C61—42no—
172C2×D4×C61—42no—
173C2×D4×C61—81no—
174C2×D4×C61—81no—
175C2×D4×C61—81no—
176C2×D4×C61—81no—
177C2×D4×C61—81no—
178C2×D4×C61C2×D412yes—
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—24no—
188C22×C4×C61—24no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—81no—
198C22×C4×C61—81no—
199C22×C4×C61—81no—
200C22×C4×C61—81no—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2×D412yes—
206C22×C4×C61C2×D412yes—
207C22×C4×C61C2411yescharacteristic
208D8×C61—44no—
209M16×C61—44no—
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×C61—21no—
217C2×C8×C61—21no—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61#4112yes—
222C4⋊C4×C61—24no—
223C4⋊C4×C61—24no—
224C4⋊C4×C61—24no—
225C4⋊C4×C61—22no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61—21no—
230C4⋊C4×C61—21no—
231C4⋊C4×C61—21no—
232C4⋊C4×C61—21no—
233C4⋊C4×C61—21no—
234C4⋊C4×C61—81no—
235C4⋊C4×C61C2×D412yes—
236C4⋊C4×C61C2×D412yes—
237C4⋊C4×C61C2×D412yes—
238C4⋊C4×C61#4112yes—
239C22⋊C4×C61—24no—
240C22⋊C4×C61—24no—
241C22⋊C4×C61—24no—
242C22⋊C4×C61—22no—
243C22⋊C4×C61—24no—
244C22⋊C4×C61—22no—
245C22⋊C4×C61—42no—
246C22⋊C4×C61—42no—
247C22⋊C4×C61—42no—
248C22⋊C4×C61—42no—
249C22⋊C4×C61—81no—
250C22⋊C4×C61—81no—
251C42×C61—24no—
252C42×C61—21no—
253C42×C61—21no—
254C42×C61—42no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—22no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
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#12012yes—
283C23×C61C22×D411yescharacteristic
284D4×C61—22no—
285D4×C61—22no—
286D4×C61—44no—
287D4×C61—48no—
288D4×C61—41no—
289D4×C61—41no—
290D4×C61—41no—
291D4×C61—41no—
292D4×C61—41no—
293D4×C61—41no—
294D4×C61—84no—
295D4×C61—84no—
296D4×C61—84no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—22no—
306C2×C4×C61—21no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
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—41no—
333C2×C4×C61—41no—
334C2×C4×C61—84no—
335C2×C4×C61—84no—
336C2×C4×C61#12012yes—
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C2×#4111yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C2×C4×C61H(5,𝔽2)11yescharacteristic
342C2×C4×C612−1+411yescharacteristic
343C8×C61—22no—
344C8×C61—41no—
345C8×C61—41no—
346C8×C61—41no—
347#25553C6111yesmaximal, characteristic, direct product factor, Sylow
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—42no—
359C22×C61—41no—
360C22×C61—42no—
361C22×C61—42no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—81no—
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×C61C2×#12011yescharacteristic
377C22×C61#54611yescharacteristic
378C22×C61#54711yescharacteristic
379C22×C61#57511yescharacteristic
380C22×C61#57511yescharacteristic
381C22×C61#57611yescharacteristic
382C22×C61#57611yescharacteristic
383C4×C61—22no—
384C4×C61—41no—
385C4×C61—41no—
386C4×C61—42no—
387C4×C61—41no—
388C4×C61—42no—
389C4×C61—42no—
390C4×C61—42no—
391C4×C61—81no—
392C4×C61—81no—
393C4×C61#53211yescharacteristic
394C4×C61#53711yescharacteristic
395C4×C61#54611yescharacteristic
396C4×C61#54711yescharacteristic
397C2×#553C2×C6111yescharacteristic, complemented
398C2×#480C2×C6111yescharacteristic, complemented
399C2×#469C2×C6111yescharacteristic, complemented
400#2414C2×C6111yescharacteristic, complemented
401#2059C2×C6111yescharacteristic, complemented
402#2033C2×C6111yescharacteristic, complemented
403#2025C2×C6111yescharacteristic, complemented
404#1999C2×C6111yescharacteristic, complemented
405#1879C2×C6111yescharacteristic, complemented
406#1875C2×C6111yescharacteristic, complemented
407#1875C2×C6111yescharacteristic, complemented
408#1870C2×C6111yescharacteristic, complemented
409#1862C2×C6111yescharacteristic, complemented
410#1854C2×C6111yescharacteristic, complemented
411#1736C2×C6111yescharacteristic, complemented
412C2×C61—42no—
413C2×C61—81no—
414C2×C61—82no—
415C2×C61—161no—
416C2×C61#243011yescharacteristic
417C2×C61#300511yescharacteristic
418C2×C61#300811yescharacteristic
419C2×C61#330911yescharacteristic
420C2×C61#332211yescharacteristic
421C2×C61#334711yescharacteristic
422C2×C61#335511yescharacteristic
423C22×D8C22×C6111yescharacteristic
424C22×M16C22×C6111yescharacteristic
425#553—24no—
426#553—24no—
427C2×#126—21no—
428C2×#125C22×C6111yescharacteristic
429C2×#123—21no—
430C2×#121—21no—
431C2×#121C22×C6111yescharacteristic
432C2×#121C22×C6111yescharacteristic
433C2×#121C22×C6111yescharacteristic
434C2×#121C22×C6111yescharacteristic
435C2×C4×D4—21no—
436C2×C4×D4C22×C6111yescharacteristic
437C2×C4×D4C22×C6111yescharacteristic
438C2×#117C22×C6111yescharacteristic
439C2×#117C22×C6111yescharacteristic
440C22×C4⋊C4C22×C6111yescharacteristic
441#480—24no—
442#469—24no—
443C2×#107C22×C6111yescharacteristic
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×C22⋊C8C22×C6111yescharacteristic
453C2×C22⋊C8C22×C6111yescharacteristic
454C2×C22⋊C8C22×C6111yescharacteristic
455#394—21no—
456#392—21no—
457#390—21no—
458#390C22×C6111yescharacteristic
459#389C22×C6111yescharacteristic
460#388—21no—
461#380C22×C6111yescharacteristic
462#340C22×C6111yescharacteristic
463#340C22×C6111yescharacteristic
464#340C22×C6111yescharacteristic
465#340C22×C6111yescharacteristic
466#340C22×C6111yescharacteristic
467#340C22×C6111yescharacteristic
468#336C22×C6111yescharacteristic
469#336C22×C6111yescharacteristic
470C61#2555311yescharacteristic, direct product factor, Sylow
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4D4×C6111yescharacteristic
476C22×D4C23×C6111yescharacteristic
477C22×D4C23×C6111yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4C23×C6111yescharacteristic
481C23×C4C23×C6111yescharacteristic
482C2×D8—22no—
483C2×D8—22no—
484C2×D8—41no—
485C2×M16—22no—
486C2×M16—22no—
487C2×M16—41no—
488C22×C8C23×C6111yescharacteristic
489C22×C8C23×C6111yescharacteristic
490C22×C8C23×C6111yescharacteristic
491C22×C8C23×C6111yescharacteristic
492#126—28no—
493#125—22no—
494#125—22no—
495#123—28no—
496#121—28no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—22no—
503#121—41no—
504#121D4×C6114yescomplemented
505C4×D4—28no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510#117—22no—
511#117—22no—
512#117—22no—
513#117—41no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4D4×C6111yescharacteristic
520C2×C4⋊C4D4×C6114yescomplemented
521C2×C4⋊C4C23×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⋊C4—21no—
537C2×C22⋊C4D4×C6111yescharacteristic
538C2×C22⋊C4D4×C6111yescharacteristic
539C2×C42—21no—
540C2×C42—21no—
541C2×C42C23×C6111yescharacteristic
542#107—22no—
543#107—22no—
544#106—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—41no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—41no—
554#95—21no—
555#95—21no—
556C24—21no—
557C24—21no—
558C24C2×D4×C6111yescharacteristic
559C24C2×D4×C6111yescharacteristic
560C2×D4—22no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—81no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4C2×D4×C6112yes—
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—24no—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4C2×D4×C6111yescharacteristic
610C22×C4C2×D4×C6111yescharacteristic
611C22×C4C2×D4×C6111yescharacteristic
612C22×C4C2×D4×C6111yescharacteristic
613C22×C4C2×D4×C6112yes—
614C22×C4C2×D4×C6112yes—
615C22×C4C24×C6111yescharacteristic
616D8—44no—
617M16—44no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8#41×C6112yes—
630C4⋊C4—24no—
631C4⋊C4—24no—
632C4⋊C4—24no—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—81no—
643C4⋊C4C2×D4×C6112yes—
644C4⋊C4C2×D4×C6112yes—
645C4⋊C4C2×D4×C6112yes—
646C4⋊C4#41×C6112yes—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—24no—
652C22⋊C4—22no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—81no—
658C22⋊C4—81no—
659C42—24no—
660C42—21no—
661C42—21no—
662C42—42no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—22no—
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#120×C6112yes—
691C23C22×D4×C6111yescharacteristic
692D4—22no—
693D4—22no—
694D4—44no—
695D4—48no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—41no—
702D4—84no—
703D4—84no—
704D4—84no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
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—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
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—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4#120×C6112yes—
745C2×C4C22×D4×C6111yescharacteristic
746C2×C4C22×D4×C6111yescharacteristic
747C2×C4C2×#41×C6111yescharacteristic
748C2×C4C2×#41×C6111yescharacteristic
749C2×C4H(5,𝔽2)×C6111yescharacteristic
750C2×C42−1+4×C6111yescharacteristic
751C8—22no—
752C8—41no—
753C8—41no—
754C8—41no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22C2×#120×C6111yescharacteristic
784C22C61×#54611yescharacteristic
785C22C61×#54711yescharacteristic
786C22C61×#57511yescharacteristic
787C22C61×#57511yescharacteristic
788C22C61×#57611yescharacteristic
789C22C61×#57611yescharacteristic
790C4—22no—
791C4—42no—
792C4—41no—
793C4—41no—
794C4—42no—
795C4—41no—
796C4—42no—
797C4—42no—
798C4—81no—
799C4—81no—
800C4C61×#53211yescharacteristic
801C4C61×#53711yescharacteristic
802C4C61×#54611yescharacteristic
803C4C61×#54711yescharacteristic
804C2—42no—
805C2—81no—
806C2—82no—
807C2—161no—
808C2C61×#243011yescharacteristic
809C2C61×#300511yescharacteristic
810C2C61×#300811yescharacteristic
811C2C61×#330911yescharacteristic
812C2C61×#332211yescharacteristic
813C2C61×#334711yescharacteristic
814C2C61×#335511yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
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×#553C2semidirect
2. C2×C61×#480C2semidirect
3. C2×C61×#469C2semidirect
4. C61×#2414C2semidirect
5. C61×#2059C2semidirect
6. C61×#2033C2semidirect
7. C61×#2025C2semidirect
8. C61×#1999C2semidirect
9. C61×#1879C2semidirect
10. C61×#1875C2semidirect
11. C61×#1875C2semidirect
12. C61×#1870C2semidirect
13. C61×#1862C2semidirect
14. C61×#1854C2semidirect
15. C61×#1736C2semidirect
96. #121×C61D4semidirect
112. C2×C4⋊C4×C61D4semidirect
347. #25553C61direct (N × H)
397. C2×#553C2×C61semidirect
398. C2×#480C2×C61semidirect
399. C2×#469C2×C61semidirect
400. #2414C2×C61semidirect
401. #2059C2×C61semidirect
402. #2033C2×C61semidirect
403. #2025C2×C61semidirect
404. #1999C2×C61semidirect
405. #1879C2×C61semidirect
406. #1875C2×C61semidirect
407. #1875C2×C61semidirect
408. #1870C2×C61semidirect
409. #1862C2×C61semidirect
410. #1854C2×C61semidirect
411. #1736C2×C61semidirect
470. C61#25553direct (N × H)
504. #121D4×C61semidirect
520. C2×C4⋊C4D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#5532
C2×C61×#4802
C2×C61×#4692
C61×#24142
C61×#20592
C61×#20332
C61×#20252
C61×#19992
C61×#18792
C61×#18752
C61×#18702
C61×#18622
C61×#18542
C61×#17362
#2555361