Finite Group Databasebeta

← C61×#24534 #29527967

Subgroups — C61×#24534 #29527967

Order 15616.

978 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#452C211yesmaximal, characteristic
2C2×C61×#416C211yesmaximal, characteristic
3C61×#2499C211yesmaximal, characteristic, complemented
4C61×#2341C211yesmaximal, characteristic
5C61×#2073C211yesmaximal, characteristic, complemented
6C61×#2071C211yesmaximal, characteristic, complemented
7C61×#2055C211yesmaximal, characteristic, complemented
8C61×#2055C211yesmaximal, characteristic, complemented
9C61×#1892C211yesmaximal, characteristic, complemented
10C61×#1878C211yesmaximal, characteristic, complemented
11C61×#1878C211yesmaximal, characteristic, complemented
12C61×#1850C211yesmaximal, characteristic, complemented
13C61×#1825C211yesmaximal, characteristic, complemented
14C61×#1805C211yesmaximal, characteristic, complemented
15C61×#1803C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×Q16×C61C2211yescharacteristic
18C22×SD16×C61C2211yescharacteristic
19C23×C8×C61C2211yescharacteristic
20C2×C22⋊Q8×C61C2211yescharacteristic
21C2×C4×Q8×C61C2211yescharacteristic
22C2×C4×Q8×C61C2211yescharacteristic
23C2×#117×C61C2211yescharacteristic
24C61×#452—24no—
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C61×#416—24no—
28C2×#103×C61C2211yescharacteristic
29C2×#103×C61C2211yescharacteristic
30C2×#103×C61C2211yescharacteristic
31C2×#103×C61C2211yescharacteristic
32C2×#103×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C2×C22⋊C8×C61C2211yescharacteristic
37C61×#397—21no—
38C61×#397—21no—
39C61×#391C2211yescharacteristic
40C61×#391C2211yescharacteristic
41C61×#390—21no—
42C61×#390—21no—
43C61×#390C2211yescharacteristic
44C61×#390C2211yescharacteristic
45C61×#387—21no—
46C61×#387—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
61C2×#41×C61—22no—
62C2×#41×C61—22no—
63C2×#41×C61—22no—
64C2×#41×C61—41no—
65C2×#41×C61—41no—
66C2×#41×C61D414yes—
67C22×Q8×C61C2311yescharacteristic
68C22×Q8×C61C2311yescharacteristic
69C22×D4×C61—21no—
70C22×D4×C61C2311yescharacteristic
71C23×C4×C61—21no—
72C23×C4×C61C2311yescharacteristic
73C2×Q16×C61—22no—
74C2×Q16×C61—22no—
75C2×Q16×C61—22no—
76C2×SD16×C61—22no—
77C2×SD16×C61—41no—
78C2×SD16×C61—41no—
79C22×C8×C61—22no—
80C22×C8×C61—41no—
81C22×C8×C61—41no—
82C22×C8×C61C2311yescharacteristic
83C22×C8×C61C2311yescharacteristic
84C22×C8×C61C2311yescharacteristic
85C22×C8×C61C2311yescharacteristic
86C22⋊Q8×C61—22no—
87C22⋊Q8×C61—22no—
88C4×Q8×C61—22no—
89C4×Q8×C61—22no—
90C4×Q8×C61—41no—
91C4×Q8×C61—41no—
92#117×C61—22no—
93#117×C61—22no—
94C2×C4⋊C4×C61—21no—
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—41no—
124#103×C61—41no—
125#102×C61—22no—
126#102×C61—22no—
127#102×C61—22no—
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
140#41×C61—28no—
141#41×C61—44no—
142#41×C61—44no—
143#41×C61—44no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61C2×D412yes—
154C2×Q8×C61#4112yes—
155C2×Q8×C61#4112yes—
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—42no—
163C2×D4×C61—42no—
164C2×D4×C61C2×D412yes—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—24no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—42no—
178C22×C4×C61—42no—
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D412yes—
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61#4112yes—
186C22×C4×C61C2411yescharacteristic
187Q16×C61—44no—
188SD16×C61—44no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
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—44no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C4⋊C4×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—42no—
213C4⋊C4×C61—42no—
214C4⋊C4×C61—42no—
215C4⋊C4×C61—42no—
216C4⋊C4×C61—42no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—41no—
219C22⋊C4×C61—42no—
220C22⋊C4×C61—42no—
221C22⋊C4×C61—42no—
222C22⋊C4×C61—42no—
223C22⋊C4×C61—81no—
224C22⋊C4×C61—81no—
225C22⋊C4×C61—81no—
226C42×C61—21no—
227C42×C61—21no—
228C42×C61—21no—
229C42×C61—21no—
230C42×C61—42no—
231C42×C61—42no—
232C42×C61—42no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—22no—
240C23×C61—41no—
241C23×C61—41no—
242C23×C61—41no—
243C23×C61—41no—
244C23×C61—41no—
245C23×C61—41no—
246C23×C61#12112yes—
247C23×C61C22×D411yescharacteristic
248Q8×C61—22no—
249Q8×C61—22no—
250Q8×C61—22no—
251Q8×C61—41no—
252Q8×C61—41no—
253Q8×C61—41no—
254Q8×C61—41no—
255Q8×C61#12314yes—
256D4×C61—22no—
257D4×C61—22no—
258D4×C61—48no—
259D4×C61—41no—
260D4×C61—41no—
261C2×C4×C61—22no—
262C2×C4×C61—21no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—48no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
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#12112yes—
301C2×C4×C61#13512yes—
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61H(5,𝔽2)11yescharacteristic
307C2×C4×C61H(5,𝔽2)11yescharacteristic
308C8×C61—41no—
309C8×C61—41no—
310C8×C61—41no—
311C8×C61—41no—
312#24534C6111yesmaximal, characteristic, direct product factor, Sylow
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—22no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—42no—
321C22×C61—42no—
322C22×C61—42no—
323C22×C61—81no—
324C22×C61—81no—
325C22×C61—81no—
326C22×C61—81no—
327C22×C61C2×#12111yescharacteristic
328C22×C61#54611yescharacteristic
329C22×C61#54611yescharacteristic
330C22×C61C2×#13511yescharacteristic
331C22×C61#57511yescharacteristic
332C22×C61#57711yescharacteristic
333C22×C61#57811yescharacteristic
334C4×C61—22no—
335C4×C61—24no—
336C4×C61—22no—
337C4×C61—41no—
338C4×C61—41no—
339C4×C61—41no—
340C4×C61—81no—
341C4×C61—81no—
342C4×C61—81no—
343C4×C61—81no—
344C4×C61—81no—
345C4×C61—81no—
346C4×C61C2×#12311yescharacteristic
347C4×C61#53411yescharacteristic
348C4×C61#55111yescharacteristic
349C4×C61#55111yescharacteristic
350C2×#452C2×C6111yescharacteristic
351C2×#416C2×C6111yescharacteristic
352#2499C2×C6111yescharacteristic, complemented
353#2341C2×C6111yescharacteristic
354#2073C2×C6111yescharacteristic, complemented
355#2071C2×C6111yescharacteristic, complemented
356#2055C2×C6111yescharacteristic, complemented
357#2055C2×C6111yescharacteristic, complemented
358#1892C2×C6111yescharacteristic, complemented
359#1878C2×C6111yescharacteristic, complemented
360#1878C2×C6111yescharacteristic, complemented
361#1850C2×C6111yescharacteristic, complemented
362#1825C2×C6111yescharacteristic, complemented
363#1805C2×C6111yescharacteristic, complemented
364#1803C2×C6111yescharacteristic, complemented
365C2×C61—42no—
366C2×C61—82no—
367C2×C61#241211yescharacteristic
368C2×C61#303511yescharacteristic
369C2×C61#304611yescharacteristic
370C2×C61#330011yescharacteristic
371C2×C61#330411yescharacteristic
372C2×C61#331311yescharacteristic
373C2×C61#331711yescharacteristic
374C22×#41C22×C6111yescharacteristic
375C22×Q16C22×C6111yescharacteristic
376C22×SD16C22×C6111yescharacteristic
377C23×C8C22×C6111yescharacteristic
378C2×C22⋊Q8C22×C6111yescharacteristic
379C2×C4×Q8C22×C6111yescharacteristic
380C2×C4×Q8C22×C6111yescharacteristic
381C2×#117C22×C6111yescharacteristic
382#452—24no—
383C2×C4⋊C8C22×C6111yescharacteristic
384C2×C4⋊C8C22×C6111yescharacteristic
385#416—24no—
386C2×#103C22×C6111yescharacteristic
387C2×#103C22×C6111yescharacteristic
388C2×#103C22×C6111yescharacteristic
389C2×#103C22×C6111yescharacteristic
390C2×#103C22×C6111yescharacteristic
391C2×#102C22×C6111yescharacteristic
392C2×#102C22×C6111yescharacteristic
393C2×#102C22×C6111yescharacteristic
394C2×C22⋊C8C22×C6111yescharacteristic
395#397—21no—
396#397—21no—
397#391C22×C6111yescharacteristic
398#391C22×C6111yescharacteristic
399#390—21no—
400#390—21no—
401#390C22×C6111yescharacteristic
402#390C22×C6111yescharacteristic
403#387—21no—
404#387—21no—
405#384C22×C6111yescharacteristic
406#382C22×C6111yescharacteristic
407#380—21no—
408#380C22×C6111yescharacteristic
409C4×C22⋊C4—21no—
410C4×C22⋊C4C22×C6111yescharacteristic
411#340C22×C6111yescharacteristic
412#340C22×C6111yescharacteristic
413#340C22×C6111yescharacteristic
414#340C22×C6111yescharacteristic
415#340C22×C6111yescharacteristic
416#340C22×C6111yescharacteristic
417#336C22×C6111yescharacteristic
418#336C22×C6111yescharacteristic
419C61#2453411yescharacteristic, direct product factor, Sylow
420C2×#41—22no—
421C2×#41—22no—
422C2×#41—22no—
423C2×#41—41no—
424C2×#41—41no—
425C2×#41D4×C6114yes—
426C22×Q8C23×C6111yescharacteristic
427C22×Q8C23×C6111yescharacteristic
428C22×D4—21no—
429C22×D4C23×C6111yescharacteristic
430C23×C4—21no—
431C23×C4C23×C6111yescharacteristic
432C2×Q16—22no—
433C2×Q16—22no—
434C2×Q16—22no—
435C2×SD16—22no—
436C2×SD16—41no—
437C2×SD16—41no—
438C22×C8—22no—
439C22×C8—41no—
440C22×C8—41no—
441C22×C8C23×C6111yescharacteristic
442C22×C8C23×C6111yescharacteristic
443C22×C8C23×C6111yescharacteristic
444C22×C8C23×C6111yescharacteristic
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C4×Q8—22no—
448C4×Q8—22no—
449C4×Q8—41no—
450C4×Q8—41no—
451#117—22no—
452#117—22no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4C23×C6111yescharacteristic
459C2×C4⋊C4C23×C6111yescharacteristic
460C2×C4⋊C4C23×C6111yescharacteristic
461C2×C4⋊C4C23×C6111yescharacteristic
462C2×C4⋊C4C23×C6111yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4D4×C6111yescharacteristic
471C2×C22⋊C4D4×C6111yescharacteristic
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42C23×C6111yescharacteristic
476C2×C42C23×C6111yescharacteristic
477C4⋊C8—41no—
478C4⋊C8—41no—
479#103—22no—
480#103—22no—
481#103—22no—
482#103—41no—
483#103—41no—
484#102—22no—
485#102—22no—
486#102—22no—
487C22⋊C8—22no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95D4×C6111yescharacteristic
496#95D4×C6111yescharacteristic
497C24—21no—
498C24C2×D4×C6111yescharacteristic
499#41—28no—
500#41—44no—
501#41—44no—
502#41—44no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8C2×D4×C6112yes—
513C2×Q8#41×C6112yes—
514C2×Q8#41×C6112yes—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4C2×D4×C6112yes—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—24no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4C2×D4×C6111yescharacteristic
539C22×C4C2×D4×C6111yescharacteristic
540C22×C4C2×D4×C6111yescharacteristic
541C22×C4C2×D4×C6111yescharacteristic
542C22×C4C2×D4×C6112yes—
543C22×C4C2×D4×C6111yescharacteristic
544C22×C4#41×C6112yes—
545C22×C4C24×C6111yescharacteristic
546Q16—44no—
547SD16—44no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—44no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C22⋊C4—22no—
577C22⋊C4—41no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—42no—
590C42—42no—
591C42—42no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—22no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23#121×C6112yes—
606C23C22×D4×C6111yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—22no—
610Q8—41no—
611Q8—41no—
612Q8—41no—
613Q8—41no—
614Q8#123×C6114yes—
615D4—22no—
616D4—22no—
617D4—48no—
618D4—41no—
619D4—41no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—48no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
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#121×C6112yes—
660C2×C4#135×C6112yes—
661C2×C4C22×D4×C6111yescharacteristic
662C2×C4C2×#41×C6111yescharacteristic
663C2×C4C2×#41×C6111yescharacteristic
664C2×C4C2×#41×C6111yescharacteristic
665C2×C4H(5,𝔽2)×C6111yescharacteristic
666C2×C4H(5,𝔽2)×C6111yescharacteristic
667C8—41no—
668C8—41no—
669C8—41no—
670C8—41no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22C2×#121×C6111yescharacteristic
686C22C61×#54611yescharacteristic
687C22C61×#54611yescharacteristic
688C22C2×#135×C6111yescharacteristic
689C22C61×#57511yescharacteristic
690C22C61×#57711yescharacteristic
691C22C61×#57811yescharacteristic
692C4—22no—
693C4—22no—
694C4—24no—
695C4—41no—
696C4—41no—
697C4—41no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4—81no—
704C4C2×#123×C6111yescharacteristic
705C4C61×#53411yescharacteristic
706C4C61×#55111yescharacteristic
707C4C61×#55111yescharacteristic
708C2—42no—
709C2—82no—
710C2C61×#241211yescharacteristic
711C2C61×#303511yescharacteristic
712C2C61×#304611yescharacteristic
713C2C61×#330011yescharacteristic
714C2C61×#330411yescharacteristic
715C2C61×#331311yescharacteristic
716C2C61×#331711yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC22×#41×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
3. C61×#2499C2semidirect
5. C61×#2073C2semidirect
6. C61×#2071C2semidirect
7. C61×#2055C2semidirect
8. C61×#2055C2semidirect
9. C61×#1892C2semidirect
10. C61×#1878C2semidirect
11. C61×#1878C2semidirect
12. C61×#1850C2semidirect
13. C61×#1825C2semidirect
14. C61×#1805C2semidirect
15. C61×#1803C2semidirect
312. #24534C61direct (N × H)
352. #2499C2×C61semidirect
354. #2073C2×C61semidirect
355. #2071C2×C61semidirect
356. #2055C2×C61semidirect
357. #2055C2×C61semidirect
358. #1892C2×C61semidirect
359. #1878C2×C61semidirect
360. #1878C2×C61semidirect
361. #1850C2×C61semidirect
362. #1825C2×C61semidirect
363. #1805C2×C61semidirect
364. #1803C2×C61semidirect
419. C61#24534direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#4522
C2×C61×#4162
C61×#24992
C61×#23412
C61×#20732
C61×#20712
C61×#20552
C61×#18922
C61×#18782
C61×#18502
C61×#18252
C61×#18052
C61×#18032
#2453461