Finite Group Databasebeta

← C61×#24541 #29527974

Subgroups — C61×#24541 #29527974

Order 15616.

982 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#448C211yesmaximal, characteristic
2C2×C61×#419C211yesmaximal, characteristic, complemented
3C61×#2500C211yesmaximal, characteristic
4Q8×C22⋊C4×C61C211yesmaximal, characteristic, complemented
5C61×#2074C211yesmaximal, characteristic, complemented
6C61×#2072C211yesmaximal, characteristic, complemented
7C61×#2055C211yesmaximal, characteristic, complemented
8C61×#2055C211yesmaximal, characteristic, complemented
9C61×#1895C211yesmaximal, characteristic
10C61×#1880C211yesmaximal, characteristic, complemented
11C61×#1880C211yesmaximal, characteristic, complemented
12C61×#1851C211yesmaximal, characteristic, complemented
13C61×#1825C211yesmaximal, characteristic, complemented
14C61×#1805C211yesmaximal, characteristic, complemented
15C61×#1803C211yesmaximal, characteristic, complemented
16C23×Q8×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic
19C22×M16×C61C2211yescharacteristic
20C2×#121×C61C2211yescharacteristic
21C2×C4×Q8×C61C2211yescharacteristic
22C2×C4×Q8×C61C2211yescharacteristic
23C2×#117×C61C2211yescharacteristic
24C61×#448—24no—
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C61×#419—24no—
28C2×#103×C61C2211yescharacteristic
29C2×#103×C61C2211yescharacteristic
30C2×#103×C61C2211yescharacteristic
31C2×#103×C61C2211yescharacteristic
32C2×#103×C61C2211yescharacteristic
33C2×#103×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×C22⋊C8×C61C2211yescharacteristic
37C61×#394—21no—
38C61×#394—21no—
39C61×#391—21no—
40C61×#391—21no—
41C61×#391C2211yescharacteristic
42C61×#391C2211yescharacteristic
43C61×#390C2211yescharacteristic
44C61×#390C2211yescharacteristic
45C61×#388—21no—
46C61×#388—21no—
47C61×#384C2211yescharacteristic
48C61×#382C2211yescharacteristic
49C61×#380—21no—
50C61×#380C2211yescharacteristic
51C4×C22⋊C4×C61—21no—
52C4×C22⋊C4×C61C2211yescharacteristic
53C61×#340C2211yescharacteristic
54C61×#340C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×Q8×C61—21no—
62C22×Q8×C61—22no—
63C22×Q8×C61—22no—
64C22×Q8×C61—22no—
65C22×Q8×C61—41no—
66C22×Q8×C61—41no—
67C22×Q8×C61D414yes—
68C22×Q8×C61C2311yescharacteristic
69C22×Q8×C61C2311yescharacteristic
70C22×D4×C61—21no—
71C22×D4×C61C2311yescharacteristic
72C23×C4×C61—21no—
73C23×C4×C61C2311yescharacteristic
74C2×SD16×C61—22no—
75C2×SD16×C61—22no—
76C2×SD16×C61—22no—
77C2×SD16×C61—22no—
78C2×SD16×C61—41no—
79C2×SD16×C61—41no—
80C2×M16×C61—22no—
81C2×M16×C61—41no—
82C2×M16×C61—41no—
83C22×C8×C61C2311yescharacteristic
84C22×C8×C61C2311yescharacteristic
85C22×C8×C61C2311yescharacteristic
86C22×C8×C61C2311yescharacteristic
87#121×C61—22no—
88#121×C61—22no—
89C4×Q8×C61—22no—
90C4×Q8×C61—22no—
91C4×Q8×C61—41no—
92C4×Q8×C61—41no—
93#117×C61—22no—
94#117×C61—22no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C4⋊C4×C61—21no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61C2311yescharacteristic
100C2×C4⋊C4×C61C2311yescharacteristic
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
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×C61D411yescharacteristic
112C2×C22⋊C4×C61D411yescharacteristic
113C2×C42×C61—21no—
114C2×C42×C61—21no—
115C2×C42×C61—21no—
116C2×C42×C61C2311yescharacteristic
117C2×C42×C61C2311yescharacteristic
118C4⋊C8×C61—41no—
119C4⋊C8×C61—41no—
120#103×C61—22no—
121#103×C61—22no—
122#103×C61—22no—
123#103×C61—22no—
124#103×C61—22no—
125#103×C61—22no—
126#102×C61—41no—
127#102×C61—41no—
128C22⋊C8×C61—22no—
129#95×C61—21no—
130#95×C61—21no—
131#95×C61—21no—
132#95×C61—21no—
133#95×C61—21no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61D411yescharacteristic
137#95×C61D411yescharacteristic
138C24×C61—21no—
139C24×C61C2×D411yescharacteristic
140C2×Q8×C61—24no—
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—28no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—42no—
151C2×Q8×C61—42no—
152C2×Q8×C61—44no—
153C2×Q8×C61—44no—
154C2×Q8×C61—44no—
155C2×Q8×C61C2×D412yes—
156C2×Q8×C61C2×D412yes—
157C2×Q8×C61#4112yes—
158C2×Q8×C61#4112yes—
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—42no—
166C2×D4×C61—81no—
167C2×D4×C61—81no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—24no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—42no—
181C22×C4×C61—42no—
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D412yes—
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61#4112yes—
189C22×C4×C61C2411yescharacteristic
190SD16×C61—44no—
191SD16×C61—44no—
192M16×C61—44no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—21no—
215C4⋊C4×C61—42no—
216C4⋊C4×C61—42no—
217C4⋊C4×C61—81no—
218C4⋊C4×C61—81no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—41no—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—42no—
223C22⋊C4×C61—42no—
224C22⋊C4×C61—42no—
225C22⋊C4×C61—42no—
226C22⋊C4×C61—81no—
227C22⋊C4×C61—81no—
228C42×C61—21no—
229C42×C61—21no—
230C42×C61—21no—
231C42×C61—21no—
232C42×C61—42no—
233C42×C61—42no—
234C42×C61—42no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61#12112yes—
249C23×C61C22×D411yescharacteristic
250Q8×C61—22no—
251Q8×C61—22no—
252Q8×C61—22no—
253Q8×C61—22no—
254Q8×C61—22no—
255Q8×C61—48no—
256Q8×C61—41no—
257Q8×C61—41no—
258Q8×C61#12314yes—
259D4×C61—41no—
260D4×C61—41no—
261D4×C61—41no—
262D4×C61—41no—
263D4×C61—84no—
264C2×C4×C61—22no—
265C2×C4×C61—21no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—48no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61#12112yes—
304C2×C4×C61#13712yes—
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61C2×#4111yescharacteristic
309C2×C4×C61H(5,𝔽2)11yescharacteristic
310C2×C4×C61H(5,𝔽2)11yescharacteristic
311C8×C61—41no—
312C8×C61—41no—
313C8×C61—41no—
314C8×C61—41no—
315#24541C6111yesmaximal, characteristic, direct product factor, Sylow
316C22×C61—22no—
317C22×C61—22no—
318C22×C61—22no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61—81no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61—81no—
327C22×C61—81no—
328C22×C61—81no—
329C22×C61—81no—
330C22×C61C2×#12111yescharacteristic
331C22×C61#54611yescharacteristic
332C22×C61#54611yescharacteristic
333C22×C61C2×#13711yescharacteristic
334C22×C61#57511yescharacteristic
335C22×C61#57711yescharacteristic
336C22×C61#57711yescharacteristic
337C4×C61—22no—
338C4×C61—24no—
339C4×C61—22no—
340C4×C61—41no—
341C4×C61—42no—
342C4×C61—41no—
343C4×C61—41no—
344C4×C61—81no—
345C4×C61—81no—
346C4×C61—81no—
347C4×C61—81no—
348C4×C61—81no—
349C4×C61C2×#12311yescharacteristic
350C4×C61#53411yescharacteristic
351C4×C61#55111yescharacteristic
352C4×C61#55111yescharacteristic
353C2×#448C2×C6111yescharacteristic
354C2×#419C2×C6111yescharacteristic, complemented
355#2500C2×C6111yescharacteristic
356Q8×C22⋊C4C2×C6111yescharacteristic, complemented
357#2074C2×C6111yescharacteristic, complemented
358#2072C2×C6111yescharacteristic, complemented
359#2055C2×C6111yescharacteristic, complemented
360#2055C2×C6111yescharacteristic, complemented
361#1895C2×C6111yescharacteristic
362#1880C2×C6111yescharacteristic, complemented
363#1880C2×C6111yescharacteristic, complemented
364#1851C2×C6111yescharacteristic, complemented
365#1825C2×C6111yescharacteristic, complemented
366#1805C2×C6111yescharacteristic, complemented
367#1803C2×C6111yescharacteristic, complemented
368C2×C61—42no—
369C2×C61—161no—
370C2×C61#241211yescharacteristic
371C2×C61#303711yescharacteristic
372C2×C61#304311yescharacteristic
373C2×C61#332011yescharacteristic
374C2×C61#332111yescharacteristic
375C2×C61#332611yescharacteristic
376C2×C61#332911yescharacteristic
377C23×Q8C22×C6111yescharacteristic
378C22×SD16C22×C6111yescharacteristic
379C22×SD16C22×C6111yescharacteristic
380C22×M16C22×C6111yescharacteristic
381C2×#121C22×C6111yescharacteristic
382C2×C4×Q8C22×C6111yescharacteristic
383C2×C4×Q8C22×C6111yescharacteristic
384C2×#117C22×C6111yescharacteristic
385#448—24no—
386C2×C4⋊C8C22×C6111yescharacteristic
387C2×C4⋊C8C22×C6111yescharacteristic
388#419—24no—
389C2×#103C22×C6111yescharacteristic
390C2×#103C22×C6111yescharacteristic
391C2×#103C22×C6111yescharacteristic
392C2×#103C22×C6111yescharacteristic
393C2×#103C22×C6111yescharacteristic
394C2×#103C22×C6111yescharacteristic
395C2×#102C22×C6111yescharacteristic
396C2×#102C22×C6111yescharacteristic
397C2×C22⋊C8C22×C6111yescharacteristic
398#394—21no—
399#394—21no—
400#391—21no—
401#391—21no—
402#391C22×C6111yescharacteristic
403#391C22×C6111yescharacteristic
404#390C22×C6111yescharacteristic
405#390C22×C6111yescharacteristic
406#388—21no—
407#388—21no—
408#384C22×C6111yescharacteristic
409#382C22×C6111yescharacteristic
410#380—21no—
411#380C22×C6111yescharacteristic
412C4×C22⋊C4—21no—
413C4×C22⋊C4C22×C6111yescharacteristic
414#340C22×C6111yescharacteristic
415#340C22×C6111yescharacteristic
416#340C22×C6111yescharacteristic
417#340C22×C6111yescharacteristic
418#340C22×C6111yescharacteristic
419#340C22×C6111yescharacteristic
420#336C22×C6111yescharacteristic
421#336C22×C6111yescharacteristic
422C61#2454111yescharacteristic, direct product factor, Sylow
423C22×Q8—21no—
424C22×Q8—22no—
425C22×Q8—22no—
426C22×Q8—22no—
427C22×Q8—41no—
428C22×Q8—41no—
429C22×Q8D4×C6114yes—
430C22×Q8C23×C6111yescharacteristic
431C22×Q8C23×C6111yescharacteristic
432C22×D4—21no—
433C22×D4C23×C6111yescharacteristic
434C23×C4—21no—
435C23×C4C23×C6111yescharacteristic
436C2×SD16—22no—
437C2×SD16—22no—
438C2×SD16—22no—
439C2×SD16—22no—
440C2×SD16—41no—
441C2×SD16—41no—
442C2×M16—22no—
443C2×M16—41no—
444C2×M16—41no—
445C22×C8C23×C6111yescharacteristic
446C22×C8C23×C6111yescharacteristic
447C22×C8C23×C6111yescharacteristic
448C22×C8C23×C6111yescharacteristic
449#121—22no—
450#121—22no—
451C4×Q8—22no—
452C4×Q8—22no—
453C4×Q8—41no—
454C4×Q8—41no—
455#117—22no—
456#117—22no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4C23×C6111yescharacteristic
462C2×C4⋊C4C23×C6111yescharacteristic
463C2×C4⋊C4C23×C6111yescharacteristic
464C2×C4⋊C4C23×C6111yescharacteristic
465C2×C4⋊C4C23×C6111yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4D4×C6111yescharacteristic
474C2×C22⋊C4D4×C6111yescharacteristic
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42C23×C6111yescharacteristic
479C2×C42C23×C6111yescharacteristic
480C4⋊C8—41no—
481C4⋊C8—41no—
482#103—22no—
483#103—22no—
484#103—22no—
485#103—22no—
486#103—22no—
487#103—22no—
488#102—41no—
489#102—41no—
490C22⋊C8—22no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95D4×C6111yescharacteristic
499#95D4×C6111yescharacteristic
500C24—21no—
501C24C2×D4×C6111yescharacteristic
502C2×Q8—24no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—28no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8C2×D4×C6112yes—
518C2×Q8C2×D4×C6112yes—
519C2×Q8#41×C6112yes—
520C2×Q8#41×C6112yes—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—42no—
528C2×D4—81no—
529C2×D4—81no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4C2×D4×C6111yescharacteristic
545C22×C4C2×D4×C6111yescharacteristic
546C22×C4C2×D4×C6111yescharacteristic
547C22×C4C2×D4×C6111yescharacteristic
548C22×C4C2×D4×C6112yes—
549C22×C4C2×D4×C6111yescharacteristic
550C22×C4#41×C6112yes—
551C22×C4C24×C6111yescharacteristic
552SD16—44no—
553SD16—44no—
554M16—44no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—81no—
580C4⋊C4—81no—
581C22⋊C4—22no—
582C22⋊C4—41no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—81no—
589C22⋊C4—81no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—42no—
595C42—42no—
596C42—42no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23#121×C6112yes—
611C23C22×D4×C6111yescharacteristic
612Q8—22no—
613Q8—22no—
614Q8—22no—
615Q8—22no—
616Q8—22no—
617Q8—48no—
618Q8—41no—
619Q8—41no—
620Q8#123×C6114yes—
621D4—41no—
622D4—41no—
623D4—41no—
624D4—41no—
625D4—84no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—48no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4#121×C6112yes—
666C2×C4#137×C6112yes—
667C2×C4C22×D4×C6111yescharacteristic
668C2×C4C2×#41×C6111yescharacteristic
669C2×C4C2×#41×C6111yescharacteristic
670C2×C4C2×#41×C6111yescharacteristic
671C2×C4H(5,𝔽2)×C6111yescharacteristic
672C2×C4H(5,𝔽2)×C6111yescharacteristic
673C8—41no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22C2×#121×C6111yescharacteristic
692C22C61×#54611yescharacteristic
693C22C61×#54611yescharacteristic
694C22C2×#137×C6111yescharacteristic
695C22C61×#57511yescharacteristic
696C22C61×#57711yescharacteristic
697C22C61×#57711yescharacteristic
698C4—22no—
699C4—22no—
700C4—24no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—42no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4C2×#123×C6111yescharacteristic
711C4C61×#53411yescharacteristic
712C4C61×#55111yescharacteristic
713C4C61×#55111yescharacteristic
714C2—42no—
715C2—161no—
716C2C61×#241211yescharacteristic
717C2C61×#303711yescharacteristic
718C2C61×#304311yescharacteristic
719C2C61×#332011yescharacteristic
720C2C61×#332111yescharacteristic
721C2C61×#332611yescharacteristic
722C2C61×#332911yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC2×#121×C61C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C4×C22⋊C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C61×#419C2semidirect
4. Q8×C22⋊C4×C61C2semidirect
5. C61×#2074C2semidirect
6. C61×#2072C2semidirect
7. C61×#2055C2semidirect
8. C61×#2055C2semidirect
10. C61×#1880C2semidirect
11. C61×#1880C2semidirect
12. C61×#1851C2semidirect
13. C61×#1825C2semidirect
14. C61×#1805C2semidirect
15. C61×#1803C2semidirect
315. #24541C61direct (N × H)
354. C2×#419C2×C61semidirect
356. Q8×C22⋊C4C2×C61semidirect
357. #2074C2×C61semidirect
358. #2072C2×C61semidirect
359. #2055C2×C61semidirect
360. #2055C2×C61semidirect
362. #1880C2×C61semidirect
363. #1880C2×C61semidirect
364. #1851C2×C61semidirect
365. #1825C2×C61semidirect
366. #1805C2×C61semidirect
367. #1803C2×C61semidirect
422. C61#24541direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#4482
C2×C61×#4192
C61×#25002
Q8×C22⋊C4×C612
C61×#20742
C61×#20722
C61×#20552
C61×#18952
C61×#18802
C61×#18512
C61×#18252
C61×#18052
C61×#18032
#2454161