Finite Group Databasebeta

← C61×#29747 #29533180

Subgroups — C61×#29747 #29533180

Order 15616.

1024 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#468C211yesmaximal, characteristic, complemented
2C2×C61×#408C211yesmaximal, characteristic, complemented
3C61×#2616C211yesmaximal, characteristic, complemented
4C61×#2615C211yesmaximal, characteristic
5C61×#2076C211yesmaximal, characteristic, complemented
6C61×#2075C211yesmaximal, characteristic, complemented
7C61×#2036C211yesmaximal, characteristic, complemented
8C61×#2035C211yesmaximal, characteristic, complemented
9C61×#2034C211yesmaximal, characteristic, complemented
10C61×#2033C211yesmaximal, characteristic, complemented
11C61×#2000C211yesmaximal, characteristic, complemented
12C61×#2000C211yesmaximal, characteristic, complemented
13C61×#1893C211yesmaximal, characteristic, complemented
14C61×#1892C211yesmaximal, characteristic, complemented
15C61×#1809C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C22×M16×C61C2211yescharacteristic
19C23×C8×C61C2211yescharacteristic
20C2×C22⋊Q8×C61C2211yescharacteristic
21C2×C22⋊Q8×C61C2211yescharacteristic
22C2×C22⋊Q8×C61C2211yescharacteristic
23C2×#121×C61C2211yescharacteristic
24C2×#121×C61C2211yescharacteristic
25C2×#121×C61C2211yescharacteristic
26C61×#468—24no—
27C2×#107×C61C2211yescharacteristic
28C2×#107×C61C2211yescharacteristic
29C2×#106×C61C2211yescharacteristic
30C2×#103×C61C2211yescharacteristic
31C2×#103×C61C2211yescharacteristic
32C2×#103×C61C2211yescharacteristic
33C2×#102×C61C2211yescharacteristic
34C2×#102×C61C2211yescharacteristic
35C2×#102×C61C2211yescharacteristic
36C61×#408—24no—
37C2×C22⋊C8×C61C2211yescharacteristic
38C2×C22⋊C8×C61C2211yescharacteristic
39C2×C22⋊C8×C61C2211yescharacteristic
40C2×C22⋊C8×C61C2211yescharacteristic
41C61×#395—21no—
42C61×#394—21no—
43C61×#394—21no—
44C61×#394—21no—
45C61×#393—21no—
46C61×#392—21no—
47C61×#392—21no—
48C61×#392—21no—
49C61×#380C2211yescharacteristic
50C61×#380C2211yescharacteristic
51C61×#380C2211yescharacteristic
52C61×#380C2211yescharacteristic
53C61×#380C2211yescharacteristic
54C61×#380C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C2×#41×C61—22no—
62C2×#41×C61—22no—
63C2×#41×C61—41no—
64C2×#41×C61—41no—
65C2×#41×C61—41no—
66C2×#41×C61—41no—
67C22×Q8×C61D411yescharacteristic
68C22×Q8×C61C2311yescharacteristic
69C22×D4×C61—21no—
70C22×D4×C61—21no—
71C22×D4×C61—21no—
72C22×D4×C61D411yescharacteristic
73C22×D4×C61D411yescharacteristic
74C22×D4×C61D411yescharacteristic
75C22×D4×C61C2311yescharacteristic
76C23×C4×C61C2311yescharacteristic
77C23×C4×C61C2311yescharacteristic
78C23×C4×C61C2311yescharacteristic
79C2×SD16×C61—22no—
80C2×SD16×C61—41no—
81C2×SD16×C61—41no—
82C2×M16×C61—41no—
83C2×M16×C61—41no—
84C2×M16×C61D414yescomplemented
85C22×C8×C61—22no—
86C22×C8×C61—41no—
87C22×C8×C61—41no—
88C22×C8×C61C2311yescharacteristic
89C22×C8×C61C2311yescharacteristic
90C22×C8×C61C2311yescharacteristic
91C22×C8×C61C2311yescharacteristic
92C22⋊Q8×C61—22no—
93C22⋊Q8×C61—22no—
94C22⋊Q8×C61—41no—
95C22⋊Q8×C61—41no—
96C22⋊Q8×C61—41no—
97C22⋊Q8×C61—41no—
98#121×C61—22no—
99#121×C61—22no—
100#121×C61—41no—
101#121×C61—41no—
102#121×C61—41no—
103#121×C61—41no—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61C2311yescharacteristic
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C22⋊C4×C61—21no—
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—
125#107×C61—22no—
126#107×C61—41no—
127#106×C61—41no—
128#103×C61—22no—
129#103×C61—41no—
130#103×C61—41no—
131#102×C61—22no—
132#102×C61—41no—
133#102×C61—41no—
134C22⋊C8×C61—22no—
135C22⋊C8×C61—22no—
136C22⋊C8×C61—22no—
137C22⋊C8×C61—22no—
138#95×C61—21no—
139#95×C61—21no—
140#95×C61—21no—
141#95×C61—21no—
142#95×C61—21no—
143#95×C61—21no—
144C24×C61—21no—
145C24×C61C2×D411yescharacteristic
146C24×C61C2×D411yescharacteristic
147C24×C61C2×D411yescharacteristic
148#41×C61—44no—
149#41×C61—44no—
150#41×C61—44no—
151#41×C61—44no—
152C2×Q8×C61—22no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—41no—
160C2×Q8×C61—41no—
161C2×D4×C61—22no—
162C2×D4×C61—22no—
163C2×D4×C61—22no—
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—41no—
171C2×D4×C61—41no—
172C2×D4×C61—41no—
173C2×D4×C61—41no—
174C2×D4×C61—41no—
175C2×D4×C61—41no—
176C2×D4×C61—42no—
177C2×D4×C61—42no—
178C2×D4×C61—42no—
179C2×D4×C61—81no—
180C2×D4×C61—81no—
181C2×D4×C61—81no—
182C2×D4×C61—81no—
183C2×D4×C61—81no—
184C2×D4×C61—81no—
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—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61—21no—
205C22×C4×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61C2×D411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D412yes—
212C22×C4×C61#4112yes—
213C22×C4×C61C2411yescharacteristic
214SD16×C61—44no—
215M16×C61—44no—
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—21no—
224C2×C8×C61—21no—
225C2×C8×C61—21no—
226C2×C8×C61—44no—
227C2×C8×C61C2×D412yes—
228C2×C8×C61C2×D412yes—
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—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—42no—
242C4⋊C4×C61—42no—
243C4⋊C4×C61—42no—
244C22⋊C4×C61—42no—
245C22⋊C4×C61—42no—
246C22⋊C4×C61—42no—
247C22⋊C4×C61—42no—
248C22⋊C4×C61—42no—
249C22⋊C4×C61—42no—
250C22⋊C4×C61—81no—
251C22⋊C4×C61—81no—
252C22⋊C4×C61—81no—
253C22⋊C4×C61—81no—
254C22⋊C4×C61—81no—
255C22⋊C4×C61—81no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—41no—
280C23×C61—41no—
281C23×C61—41no—
282C23×C61—41no—
283C23×C61#12112yes—
284C23×C61C22×D411yescharacteristic
285Q8×C61—44no—
286Q8×C61—41no—
287Q8×C61—41no—
288Q8×C61—41no—
289Q8×C61—41no—
290D4×C61—44no—
291D4×C61—44no—
292D4×C61—44no—
293D4×C61—41no—
294D4×C61—41no—
295D4×C61—41no—
296D4×C61—41no—
297D4×C61—84no—
298D4×C61—84no—
299D4×C61—84no—
300C2×C4×C61—21no—
301C2×C4×C61—21no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
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—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61#12112yes—
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C2×#4111yescharacteristic
344C2×C4×C61H(5,𝔽2)11yescharacteristic
345C2×C4×C61H(5,𝔽2)11yescharacteristic
346C2×C4×C61H(5,𝔽2)11yescharacteristic
347C2×C4×C61H(5,𝔽2)11yescharacteristic
348C8×C61—22no—
349C8×C61—22no—
350C8×C61—41no—
351C8×C61—41no—
352#29747C6111yesmaximal, characteristic, direct product factor, Sylow
353C22×C61—22no—
354C22×C61—22no—
355C22×C61—22no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—81no—
375C22×C61—81no—
376C22×C61—81no—
377C22×C61—81no—
378C22×C61—81no—
379C22×C61—81no—
380C22×C61—81no—
381C22×C61C2×#12111yescharacteristic
382C22×C61#53411yescharacteristic
383C22×C61#53411yescharacteristic
384C22×C61#57611yescharacteristic
385C22×C61#57711yescharacteristic
386C22×C61#57711yescharacteristic
387C22×C61#57811yescharacteristic
388C4×C61—22no—
389C4×C61—41no—
390C4×C61—41no—
391C4×C61—81no—
392C4×C61—81no—
393C4×C61—81no—
394C4×C61—81no—
395C4×C61—81no—
396C4×C61—81no—
397C4×C61—81no—
398C4×C61#53411yescharacteristic
399C4×C61#53511yescharacteristic
400C4×C61#53811yescharacteristic
401C4×C61#53811yescharacteristic
402C2×#468C2×C6111yescharacteristic, complemented
403C2×#408C2×C6111yescharacteristic, complemented
404#2616C2×C6111yescharacteristic, complemented
405#2615C2×C6111yescharacteristic
406#2076C2×C6111yescharacteristic, complemented
407#2075C2×C6111yescharacteristic, complemented
408#2036C2×C6111yescharacteristic, complemented
409#2035C2×C6111yescharacteristic, complemented
410#2034C2×C6111yescharacteristic, complemented
411#2033C2×C6111yescharacteristic, complemented
412#2000C2×C6111yescharacteristic, complemented
413#2000C2×C6111yescharacteristic, complemented
414#1893C2×C6111yescharacteristic, complemented
415#1892C2×C6111yescharacteristic, complemented
416#1809C2×C6111yescharacteristic, complemented
417C2×C61—42no—
418C2×C61—81no—
419C2×C61—81no—
420C2×C61—161no—
421C2×C61#261711yescharacteristic
422C2×C61#306211yescharacteristic
423C2×C61#306311yescharacteristic
424C2×C61#319811yescharacteristic
425C2×C61#320011yescharacteristic
426C2×C61#320111yescharacteristic
427C2×C61#320311yescharacteristic
428C22×#41C22×C6111yescharacteristic
429C22×SD16C22×C6111yescharacteristic
430C22×M16C22×C6111yescharacteristic
431C23×C8C22×C6111yescharacteristic
432C2×C22⋊Q8C22×C6111yescharacteristic
433C2×C22⋊Q8C22×C6111yescharacteristic
434C2×C22⋊Q8C22×C6111yescharacteristic
435C2×#121C22×C6111yescharacteristic
436C2×#121C22×C6111yescharacteristic
437C2×#121C22×C6111yescharacteristic
438#468—24no—
439C2×#107C22×C6111yescharacteristic
440C2×#107C22×C6111yescharacteristic
441C2×#106C22×C6111yescharacteristic
442C2×#103C22×C6111yescharacteristic
443C2×#103C22×C6111yescharacteristic
444C2×#103C22×C6111yescharacteristic
445C2×#102C22×C6111yescharacteristic
446C2×#102C22×C6111yescharacteristic
447C2×#102C22×C6111yescharacteristic
448#408—24no—
449C2×C22⋊C8C22×C6111yescharacteristic
450C2×C22⋊C8C22×C6111yescharacteristic
451C2×C22⋊C8C22×C6111yescharacteristic
452C2×C22⋊C8C22×C6111yescharacteristic
453#395—21no—
454#394—21no—
455#394—21no—
456#394—21no—
457#393—21no—
458#392—21no—
459#392—21no—
460#392—21no—
461#380C22×C6111yescharacteristic
462#380C22×C6111yescharacteristic
463#380C22×C6111yescharacteristic
464#380C22×C6111yescharacteristic
465#380C22×C6111yescharacteristic
466#380C22×C6111yescharacteristic
467#340C22×C6111yescharacteristic
468#340C22×C6111yescharacteristic
469#340C22×C6111yescharacteristic
470#340C22×C6111yescharacteristic
471#340C22×C6111yescharacteristic
472#340C22×C6111yescharacteristic
473C61#2974711yescharacteristic, direct product factor, Sylow
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—41no—
477C2×#41—41no—
478C2×#41—41no—
479C2×#41—41no—
480C22×Q8D4×C6111yescharacteristic
481C22×Q8C23×C6111yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4D4×C6111yescharacteristic
486C22×D4D4×C6111yescharacteristic
487C22×D4D4×C6111yescharacteristic
488C22×D4C23×C6111yescharacteristic
489C23×C4C23×C6111yescharacteristic
490C23×C4C23×C6111yescharacteristic
491C23×C4C23×C6111yescharacteristic
492C2×SD16—22no—
493C2×SD16—41no—
494C2×SD16—41no—
495C2×M16—41no—
496C2×M16—41no—
497C2×M16D4×C6114yescomplemented
498C22×C8—22no—
499C22×C8—41no—
500C22×C8—41no—
501C22×C8C23×C6111yescharacteristic
502C22×C8C23×C6111yescharacteristic
503C22×C8C23×C6111yescharacteristic
504C22×C8C23×C6111yescharacteristic
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—41no—
508C22⋊Q8—41no—
509C22⋊Q8—41no—
510C22⋊Q8—41no—
511#121—22no—
512#121—22no—
513#121—41no—
514#121—41no—
515#121—41no—
516#121—41no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4C23×C6111yescharacteristic
521C2×C4⋊C4C23×C6111yescharacteristic
522C2×C4⋊C4C23×C6111yescharacteristic
523C2×C4⋊C4C23×C6111yescharacteristic
524C2×C4⋊C4C23×C6111yescharacteristic
525C2×C4⋊C4C23×C6111yescharacteristic
526C2×C22⋊C4—21no—
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⋊C4—21no—
538#107—22no—
539#107—41no—
540#106—41no—
541#103—22no—
542#103—41no—
543#103—41no—
544#102—22no—
545#102—41no—
546#102—41no—
547C22⋊C8—22no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8—22no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—21no—
557C24—21no—
558C24C2×D4×C6111yescharacteristic
559C24C2×D4×C6111yescharacteristic
560C24C2×D4×C6111yescharacteristic
561#41—44no—
562#41—44no—
563#41—44no—
564#41—44no—
565C2×Q8—22no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—41no—
573C2×Q8—41no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4—81no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4C2×D4×C6111yescharacteristic
622C22×C4C2×D4×C6111yescharacteristic
623C22×C4C2×D4×C6111yescharacteristic
624C22×C4C2×D4×C6112yes—
625C22×C4#41×C6112yes—
626C22×C4C24×C6111yescharacteristic
627SD16—44no—
628M16—44no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—44no—
640C2×C8C2×D4×C6112yes—
641C2×C8C2×D4×C6112yes—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—81no—
664C22⋊C4—81no—
665C22⋊C4—81no—
666C22⋊C4—81no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23#121×C6112yes—
697C23C22×D4×C6111yescharacteristic
698Q8—44no—
699Q8—41no—
700Q8—41no—
701Q8—41no—
702Q8—41no—
703D4—44no—
704D4—44no—
705D4—44no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—84no—
711D4—84no—
712D4—84no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
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—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4#121×C6112yes—
755C2×C4C22×D4×C6111yescharacteristic
756C2×C4C2×#41×C6111yescharacteristic
757C2×C4H(5,𝔽2)×C6111yescharacteristic
758C2×C4H(5,𝔽2)×C6111yescharacteristic
759C2×C4H(5,𝔽2)×C6111yescharacteristic
760C2×C4H(5,𝔽2)×C6111yescharacteristic
761C8—22no—
762C8—22no—
763C8—41no—
764C8—41no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22C2×#121×C6111yescharacteristic
794C22C61×#53411yescharacteristic
795C22C61×#53411yescharacteristic
796C22C61×#57611yescharacteristic
797C22C61×#57711yescharacteristic
798C22C61×#57711yescharacteristic
799C22C61×#57811yescharacteristic
800C4—22no—
801C4—41no—
802C4—41no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4—81no—
810C4C61×#53411yescharacteristic
811C4C61×#53511yescharacteristic
812C4C61×#53811yescharacteristic
813C4C61×#53811yescharacteristic
814C2—42no—
815C2—81no—
816C2—81no—
817C2—161no—
818C2C61×#261711yescharacteristic
819C2C61×#306211yescharacteristic
820C2C61×#306311yescharacteristic
821C2C61×#319811yescharacteristic
822C2C61×#320011yescharacteristic
823C2C61×#320111yescharacteristic
824C2C61×#320311yescharacteristic
subgroupG/H
center, socleC23×C61C22×D4
commutator, Frattini, cosocleC22×C4C24×C61
prime radicalC61×#2615C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C61 ◁ C22×#41×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#468C2semidirect
2. C2×C61×#408C2semidirect
3. C61×#2616C2semidirect
5. C61×#2076C2semidirect
6. C61×#2075C2semidirect
7. C61×#2036C2semidirect
8. C61×#2035C2semidirect
9. C61×#2034C2semidirect
10. C61×#2033C2semidirect
11. C61×#2000C2semidirect
12. C61×#2000C2semidirect
13. C61×#1893C2semidirect
14. C61×#1892C2semidirect
15. C61×#1809C2semidirect
84. C2×M16×C61D4semidirect
352. #29747C61direct (N × H)
402. C2×#468C2×C61semidirect
403. C2×#408C2×C61semidirect
404. #2616C2×C61semidirect
406. #2076C2×C61semidirect
407. #2075C2×C61semidirect
408. #2036C2×C61semidirect
409. #2035C2×C61semidirect
410. #2034C2×C61semidirect
411. #2033C2×C61semidirect
412. #2000C2×C61semidirect
413. #2000C2×C61semidirect
414. #1893C2×C61semidirect
415. #1892C2×C61semidirect
416. #1809C2×C61semidirect
473. C61#29747direct (N × H)
497. C2×M16D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4682
C2×C61×#4082
C61×#26162
C61×#26152
C61×#20762
C61×#20752
C61×#20362
C61×#20352
C61×#20342
C61×#20332
C61×#20002
C61×#18932
C61×#18922
C61×#18092
#2974761