Finite Group Databasebeta

← C61×#25131 #29528564

Subgroups — C61×#25131 #29528564

Order 15616.

1158 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#468C211yesmaximal, characteristic, complemented
2C2×C61×#449C211yesmaximal, characteristic, complemented
3C2×C61×#435C211yesmaximal, characteristic, complemented
4C2×C61×#416C211yesmaximal, characteristic, complemented
5C61×#2414C211yesmaximal, characteristic, complemented
6C61×#2407C211yesmaximal, characteristic, complemented
7C61×#2067C211yesmaximal, characteristic, complemented
8C61×#2055C211yesmaximal, characteristic, complemented
9C61×#2035C211yesmaximal, characteristic, complemented
10C61×#1999C211yesmaximal, characteristic, complemented
11C61×#1972C211yesmaximal, characteristic, complemented
12C61×#1935C211yesmaximal, characteristic, complemented
13C61×#1895C211yesmaximal, characteristic, complemented
14C61×#1893C211yesmaximal, characteristic, complemented
15C61×#1854C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C22×SD16×C61C2211yescharacteristic
18C22×D8×C61C2211yescharacteristic
19C22×M16×C61C2211yescharacteristic
20C23×C8×C61C2211yescharacteristic
21C2×C22⋊Q8×C61C2211yescharacteristic
22C2×#121×C61C2211yescharacteristic
23C2×#121×C61C2211yescharacteristic
24C2×#121×C61C2211yescharacteristic
25C2×C4×D4×C61C2211yescharacteristic
26C2×#117×C61C2211yescharacteristic
27C61×#468—24no—
28C61×#449—24no—
29C61×#435—24no—
30C2×#107×C61C2211yescharacteristic
31C2×#106×C61C2211yescharacteristic
32C2×C4⋊C8×C61C2211yescharacteristic
33C61×#416—24no—
34C2×#103×C61C2211yescharacteristic
35C2×#103×C61C2211yescharacteristic
36C2×#103×C61C2211yescharacteristic
37C2×#102×C61C2211yescharacteristic
38C2×#102×C61C2211yescharacteristic
39C2×#102×C61C2211yescharacteristic
40C2×#102×C61C2211yescharacteristic
41C2×#102×C61C2211yescharacteristic
42C2×C22⋊C8×C61C2211yescharacteristic
43C2×C22⋊C8×C61C2211yescharacteristic
44C2×#97×C61C2211yescharacteristic
45C61×#394—21no—
46C61×#394—21no—
47C61×#392—21no—
48C61×#392—21no—
49C61×#391C2211yescharacteristic
50C61×#390—21no—
51C61×#390C2211yescharacteristic
52C61×#390C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C61×#388—21no—
55C61×#386—21no—
56C61×#385—21no—
57C61×#380C2211yescharacteristic
58C61×#380C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C2×#41×C61—22no—
64C2×#41×C61—22no—
65C2×#41×C61—22no—
66C2×#41×C61—22no—
67C2×#41×C61—41no—
68C2×#41×C61—41no—
69C22×Q8×C61C2311yescharacteristic
70C22×D4×C61—21no—
71C22×D4×C61—21no—
72C22×D4×C61—21no—
73C22×D4×C61—21no—
74C22×D4×C61D411yescharacteristic
75C22×D4×C61C2311yescharacteristic
76C22×D4×C61C2311yescharacteristic
77C23×C4×C61—21no—
78C23×C4×C61C2311yescharacteristic
79C23×C4×C61C2311yescharacteristic
80C2×SD16×C61—22no—
81C2×SD16×C61—22no—
82C2×SD16×C61—41no—
83C2×D8×C61—22no—
84C2×D8×C61—22no—
85C2×D8×C61—41no—
86C2×M16×C61—22no—
87C2×M16×C61—22no—
88C2×M16×C61—41no—
89C22×C8×C61—22no—
90C22×C8×C61—22no—
91C22×C8×C61—41no—
92C22×C8×C61C2311yescharacteristic
93C22×C8×C61C2311yescharacteristic
94C22×C8×C61C2311yescharacteristic
95C22×C8×C61C2311yescharacteristic
96C22⋊Q8×C61—22no—
97C22⋊Q8×C61—41no—
98#121×C61—22no—
99#121×C61—22no—
100#121×C61—22no—
101#121×C61—22no—
102#121×C61—41no—
103#121×C61—41no—
104C4×D4×C61—22no—
105C4×D4×C61—22no—
106#117×C61—22no—
107#117×C61—41no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61D411yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
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—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61D411yescharacteristic
128C2×C22⋊C4×C61D411yescharacteristic
129C2×C42×C61—21no—
130C2×C42×C61C2311yescharacteristic
131#107×C61—22no—
132#106×C61—41no—
133C4⋊C8×C61—22no—
134#103×C61—22no—
135#103×C61—22no—
136#103×C61D414yescomplemented
137#102×C61—22no—
138#102×C61—22no—
139#102×C61—22no—
140#102×C61—22no—
141#102×C61—41no—
142C22⋊C8×C61—22no—
143C22⋊C8×C61D414yescomplemented
144#97×C61—22no—
145#95×C61—21no—
146#95×C61—21no—
147#95×C61—21no—
148#95×C61—21no—
149#95×C61—21no—
150C24×C61—21no—
151C24×C61—21no—
152C24×C61C2×D411yescharacteristic
153C24×C61C2×D411yescharacteristic
154#41×C61—28no—
155#41×C61—44no—
156#41×C61—44no—
157#41×C61—44no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×Q8×C61C2×D412yes—
164C2×D4×C61—22no—
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—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—41no—
177C2×D4×C61—41no—
178C2×D4×C61—42no—
179C2×D4×C61—42no—
180C2×D4×C61—42no—
181C2×D4×C61—42no—
182C2×D4×C61—42no—
183C2×D4×C61—42no—
184C2×D4×C61—42no—
185C2×D4×C61—42no—
186C2×D4×C61—81no—
187C2×D4×C61—81no—
188C2×D4×C61—81no—
189C2×D4×C61—81no—
190C2×D4×C61#4112yes—
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—42no—
208C22×C4×C61—42no—
209C22×C4×C61—42no—
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D412yes—
215C22×C4×C61#4112yes—
216C22×C4×C61C2411yescharacteristic
217SD16×C61—44no—
218D8×C61—44no—
219M16×C61—44no—
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—21no—
227C2×C8×C61—21no—
228C2×C8×C61—21no—
229C2×C8×C61—44no—
230C2×C8×C61C2×D412yes—
231C2×C8×C61C2×D412yes—
232C2×C8×C61C2×D412yes—
233C4⋊C4×C61—22no—
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—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—42no—
244C4⋊C4×C61—81no—
245C4⋊C4×C61C2×D412yes—
246C22⋊C4×C61—22no—
247C22⋊C4×C61—22no—
248C22⋊C4×C61—42no—
249C22⋊C4×C61—42no—
250C22⋊C4×C61—42no—
251C22⋊C4×C61—42no—
252C22⋊C4×C61—42no—
253C22⋊C4×C61—42no—
254C22⋊C4×C61—42no—
255C22⋊C4×C61—81no—
256C22⋊C4×C61—81no—
257C22⋊C4×C61—81no—
258C22⋊C4×C61—81no—
259C42×C61—21no—
260C42×C61—21no—
261C42×C61—42no—
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—22no—
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—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61—41no—
289C23×C61#12112yes—
290C23×C61C22×D411yescharacteristic
291Q8×C61—22no—
292Q8×C61—22no—
293Q8×C61—41no—
294Q8×C61—41no—
295D4×C61—22no—
296D4×C61—22no—
297D4×C61—44no—
298D4×C61—48no—
299D4×C61—41no—
300D4×C61—41no—
301D4×C61—41no—
302D4×C61—41no—
303D4×C61—41no—
304D4×C61—41no—
305D4×C61—84no—
306D4×C61—84no—
307D4×C61—84no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C2×C4×C61—22no—
318C2×C4×C61—21no—
319C2×C4×C61—22no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—48no—
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—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61#12112yes—
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61C2×#4111yescharacteristic
350C2×C4×C61C2×#4111yescharacteristic
351C2×C4×C61H(5,𝔽2)11yescharacteristic
352C2×C4×C61H(5,𝔽2)11yescharacteristic
353C8×C61—22no—
354C8×C61—22no—
355C8×C61—22no—
356C8×C61—41no—
357#25131C6111yesmaximal, characteristic, direct product factor, Sylow
358C22×C61—22no—
359C22×C61—22no—
360C22×C61—22no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—42no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—42no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—42no—
375C22×C61—81no—
376C22×C61—81no—
377C22×C61—81no—
378C22×C61—81no—
379C22×C61—81no—
380C22×C61—81no—
381C22×C61—81no—
382C22×C61—81no—
383C22×C61—81no—
384C22×C61—81no—
385C22×C61—81no—
386C22×C61C2×#12111yescharacteristic
387C22×C61D4211yescharacteristic
388C22×C61#54611yescharacteristic
389C22×C61#57511yescharacteristic
390C22×C61#57511yescharacteristic
391C22×C61#57611yescharacteristic
392C22×C61#57711yescharacteristic
393C4×C61—22no—
394C4×C61—41no—
395C4×C61—42no—
396C4×C61—42no—
397C4×C61—41no—
398C4×C61—41no—
399C4×C61—81no—
400C4×C61—81no—
401C4×C61—81no—
402C4×C61—81no—
403C4×C61#52511yescharacteristic
404C4×C61#53811yescharacteristic
405C4×C61D4211yescharacteristic
406C4×C61#54611yescharacteristic
407C2×#468C2×C6111yescharacteristic, complemented
408C2×#449C2×C6111yescharacteristic, complemented
409C2×#435C2×C6111yescharacteristic, complemented
410C2×#416C2×C6111yescharacteristic, complemented
411#2414C2×C6111yescharacteristic, complemented
412#2407C2×C6111yescharacteristic, complemented
413#2067C2×C6111yescharacteristic, complemented
414#2055C2×C6111yescharacteristic, complemented
415#2035C2×C6111yescharacteristic, complemented
416#1999C2×C6111yescharacteristic, complemented
417#1972C2×C6111yescharacteristic, complemented
418#1935C2×C6111yescharacteristic, complemented
419#1895C2×C6111yescharacteristic, complemented
420#1893C2×C6111yescharacteristic, complemented
421#1854C2×C6111yescharacteristic, complemented
422C2×C61—42no—
423C2×C61—81no—
424C2×C61—82no—
425C2×C61—161no—
426C2×C61#242411yescharacteristic
427C2×C61#305411yescharacteristic
428C2×C61#306211yescharacteristic
429C2×C61#326811yescharacteristic
430C2×C61#327111yescharacteristic
431C2×C61#330711yescharacteristic
432C2×C61#331911yescharacteristic
433C22×#41C22×C6111yescharacteristic
434C22×SD16C22×C6111yescharacteristic
435C22×D8C22×C6111yescharacteristic
436C22×M16C22×C6111yescharacteristic
437C23×C8C22×C6111yescharacteristic
438C2×C22⋊Q8C22×C6111yescharacteristic
439C2×#121C22×C6111yescharacteristic
440C2×#121C22×C6111yescharacteristic
441C2×#121C22×C6111yescharacteristic
442C2×C4×D4C22×C6111yescharacteristic
443C2×#117C22×C6111yescharacteristic
444#468—24no—
445#449—24no—
446#435—24no—
447C2×#107C22×C6111yescharacteristic
448C2×#106C22×C6111yescharacteristic
449C2×C4⋊C8C22×C6111yescharacteristic
450#416—24no—
451C2×#103C22×C6111yescharacteristic
452C2×#103C22×C6111yescharacteristic
453C2×#103C22×C6111yescharacteristic
454C2×#102C22×C6111yescharacteristic
455C2×#102C22×C6111yescharacteristic
456C2×#102C22×C6111yescharacteristic
457C2×#102C22×C6111yescharacteristic
458C2×#102C22×C6111yescharacteristic
459C2×C22⋊C8C22×C6111yescharacteristic
460C2×C22⋊C8C22×C6111yescharacteristic
461C2×#97C22×C6111yescharacteristic
462#394—21no—
463#394—21no—
464#392—21no—
465#392—21no—
466#391C22×C6111yescharacteristic
467#390—21no—
468#390C22×C6111yescharacteristic
469#390C22×C6111yescharacteristic
470#389C22×C6111yescharacteristic
471#388—21no—
472#386—21no—
473#385—21no—
474#380C22×C6111yescharacteristic
475#380C22×C6111yescharacteristic
476#340C22×C6111yescharacteristic
477#340C22×C6111yescharacteristic
478#340C22×C6111yescharacteristic
479#340C22×C6111yescharacteristic
480C61#2513111yescharacteristic, direct product factor, Sylow
481C2×#41—22no—
482C2×#41—22no—
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—41no—
486C2×#41—41no—
487C22×Q8C23×C6111yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4D4×C6111yescharacteristic
493C22×D4C23×C6111yescharacteristic
494C22×D4C23×C6111yescharacteristic
495C23×C4—21no—
496C23×C4C23×C6111yescharacteristic
497C23×C4C23×C6111yescharacteristic
498C2×SD16—22no—
499C2×SD16—22no—
500C2×SD16—41no—
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—41no—
504C2×M16—22no—
505C2×M16—22no—
506C2×M16—41no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—41no—
510C22×C8C23×C6111yescharacteristic
511C22×C8C23×C6111yescharacteristic
512C22×C8C23×C6111yescharacteristic
513C22×C8C23×C6111yescharacteristic
514C22⋊Q8—22no—
515C22⋊Q8—41no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—41no—
521#121—41no—
522C4×D4—22no—
523C4×D4—22no—
524#117—22no—
525#117—41no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4D4×C6111yescharacteristic
529C2×C4⋊C4C23×C6111yescharacteristic
530C2×C4⋊C4C23×C6111yescharacteristic
531C2×C4⋊C4C23×C6111yescharacteristic
532C2×C4⋊C4C23×C6111yescharacteristic
533C2×C4⋊C4C23×C6111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4D4×C6111yescharacteristic
546C2×C22⋊C4D4×C6111yescharacteristic
547C2×C42—21no—
548C2×C42C23×C6111yescharacteristic
549#107—22no—
550#106—41no—
551C4⋊C8—22no—
552#103—22no—
553#103—22no—
554#103D4×C6114yescomplemented
555#102—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—41no—
560C22⋊C8—22no—
561C22⋊C8D4×C6114yescomplemented
562#97—22no—
563#95—21no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568C24—21no—
569C24—21no—
570C24C2×D4×C6111yescharacteristic
571C24C2×D4×C6111yescharacteristic
572#41—28no—
573#41—44no—
574#41—44no—
575#41—44no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8C2×D4×C6112yes—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—81no—
605C2×D4—81no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4#41×C6112yes—
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×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4C2×D4×C6111yescharacteristic
629C22×C4C2×D4×C6111yescharacteristic
630C22×C4C2×D4×C6111yescharacteristic
631C22×C4C2×D4×C6111yescharacteristic
632C22×C4C2×D4×C6112yes—
633C22×C4#41×C6112yes—
634C22×C4C24×C6111yescharacteristic
635SD16—44no—
636D8—44no—
637M16—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—44no—
648C2×C8C2×D4×C6112yes—
649C2×C8C2×D4×C6112yes—
650C2×C8C2×D4×C6112yes—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—42no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C6112yes—
664C22⋊C4—22no—
665C22⋊C4—22no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—81no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C22⋊C4—81no—
677C42—21no—
678C42—21no—
679C42—42no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—22no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23#121×C6112yes—
708C23C22×D4×C6111yescharacteristic
709Q8—22no—
710Q8—22no—
711Q8—41no—
712Q8—41no—
713D4—22no—
714D4—22no—
715D4—44no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—84no—
724D4—84no—
725D4—84no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—48no—
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—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4#121×C6112yes—
765C2×C4C22×D4×C6111yescharacteristic
766C2×C4C22×D4×C6111yescharacteristic
767C2×C4C2×#41×C6111yescharacteristic
768C2×C4C2×#41×C6111yescharacteristic
769C2×C4H(5,𝔽2)×C6111yescharacteristic
770C2×C4H(5,𝔽2)×C6111yescharacteristic
771C8—22no—
772C8—22no—
773C8—22no—
774C8—41no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—42no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—42no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22C2×#121×C6111yescharacteristic
804C22D42×C6111yescharacteristic
805C22C61×#54611yescharacteristic
806C22C61×#57511yescharacteristic
807C22C61×#57511yescharacteristic
808C22C61×#57611yescharacteristic
809C22C61×#57711yescharacteristic
810C4—22no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—42no—
815C4—42no—
816C4—81no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4C61×#52511yescharacteristic
821C4C61×#53811yescharacteristic
822C4D42×C6111yescharacteristic
823C4C61×#54611yescharacteristic
824C2—42no—
825C2—81no—
826C2—82no—
827C2—161no—
828C2C61×#242411yescharacteristic
829C2C61×#305411yescharacteristic
830C2C61×#306211yescharacteristic
831C2C61×#326811yescharacteristic
832C2C61×#327111yescharacteristic
833C2C61×#330711yescharacteristic
834C2C61×#331911yescharacteristic
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×#468C2semidirect
2. C2×C61×#449C2semidirect
3. C2×C61×#435C2semidirect
4. C2×C61×#416C2semidirect
5. C61×#2414C2semidirect
6. C61×#2407C2semidirect
7. C61×#2067C2semidirect
8. C61×#2055C2semidirect
9. C61×#2035C2semidirect
10. C61×#1999C2semidirect
11. C61×#1972C2semidirect
12. C61×#1935C2semidirect
13. C61×#1895C2semidirect
14. C61×#1893C2semidirect
15. C61×#1854C2semidirect
136. #103×C61D4semidirect
143. C22⋊C8×C61D4semidirect
357. #25131C61direct (N × H)
407. C2×#468C2×C61semidirect
408. C2×#449C2×C61semidirect
409. C2×#435C2×C61semidirect
410. C2×#416C2×C61semidirect
411. #2414C2×C61semidirect
412. #2407C2×C61semidirect
413. #2067C2×C61semidirect
414. #2055C2×C61semidirect
415. #2035C2×C61semidirect
416. #1999C2×C61semidirect
417. #1972C2×C61semidirect
418. #1935C2×C61semidirect
419. #1895C2×C61semidirect
420. #1893C2×C61semidirect
421. #1854C2×C61semidirect
480. C61#25131direct (N × H)
554. #103D4×C61semidirect
561. C22⋊C8D4×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×#4492
C2×C61×#4352
C2×C61×#4162
C61×#24142
C61×#24072
C61×#20672
C61×#20552
C61×#20352
C61×#19992
C61×#19722
C61×#19352
C61×#18952
C61×#18932
C61×#18542
#2513161