Finite Group Databasebeta

← C61×#25147 #29528580

Subgroups — C61×#25147 #29528580

Order 15616.

1022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#471C211yesmaximal, characteristic, complemented
2C61×#3055C211yesmaximal, characteristic, complemented
3C61×#3005C211yesmaximal, characteristic, complemented
4C2×C61×#449C211yesmaximal, characteristic, complemented
5C61×#2933C211yesmaximal, characteristic, complemented
6C2×C61×#413C211yesmaximal, characteristic, complemented
7C61×#2063C211yesmaximal, characteristic, complemented
8C61×#2052C211yesmaximal, characteristic, complemented
9C61×#2046C211yesmaximal, characteristic, complemented
10C61×#2018C211yesmaximal, characteristic, complemented
11C61×#1978C211yesmaximal, characteristic, complemented
12C61×#1930C211yesmaximal, characteristic, complemented
13C61×#1907C211yesmaximal, characteristic, complemented
14C61×#1900C211yesmaximal, characteristic, complemented
15C61×#1855C211yesmaximal, characteristic, complemented
16C22×#41×C61C2211yescharacteristic
17C2×#137×C61C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
20C22×SD16×C61C2211yescharacteristic
21C22×D8×C61C2211yescharacteristic
22C2×#131×C61C2211yescharacteristic
23C22×M16×C61C2211yescharacteristic
24C22×M16×C61C2211yescharacteristic
25C61×#525C2211yescharacteristic
26C2×#121×C61C2211yescharacteristic
27C61×#471—24no—
28C61×#469—21no—
29C61×#468—21no—
30C61×#466—21no—
31C61×#465—21no—
32C61×#452—21no—
33C61×#452—21no—
34C61×#449—21no—
35C61×#449—21no—
36C61×#449—21no—
37C61×#449—21no—
38C61×#449—21no—
39C61×#449—21no—
40C61×#436—21no—
41C61×#435—21no—
42C61×#435—21no—
43C8×D4×C61—21no—
44C2×#108×C61C2211yescharacteristic
45C2×#108×C61C2211yescharacteristic
46C61×#428C2211yescharacteristic
47C61×#424C2211yescharacteristic
48C61×#419C2211yescharacteristic
49C61×#418C2211yescharacteristic
50C61×#418C2211yescharacteristic
51C61×#417C2211yescharacteristic
52C2×#103×C61C2211yescharacteristic
53C2×#102×C61C2211yescharacteristic
54C61×#413—24no—
55C2×#101×C61C2211yescharacteristic
56C2×#101×C61C2211yescharacteristic
57C2×#100×C61C2211yescharacteristic
58C2×#100×C61C2211yescharacteristic
59C2×#100×C61C2211yescharacteristic
60C2×#100×C61C2211yescharacteristic
61C61×#408C2211yescharacteristic
62C61×#407C2211yescharacteristic
63C2×C22⋊C8×C61C2211yescharacteristic
64C61×#405C2211yescharacteristic
65C61×#343C2211yescharacteristic
66C61×#343C2211yescharacteristic
67C61×#341C2211yescharacteristic
68C61×#341C2211yescharacteristic
69C2×#41×C61—22no—
70C2×#41×C61—22no—
71C2×#41×C61—21no—
72C2×#41×C61—21no—
73C2×#41×C61—21no—
74C2×#41×C61—21no—
75C2×#41×C61—41no—
76C2×#41×C61—41no—
77C2×#41×C61C2311yescharacteristic
78C22×Q8×C61C2311yescharacteristic
79C22×D4×C61—21no—
80C22×D4×C61—21no—
81C22×D4×C61C2311yescharacteristic
82C22×D4×C61C2311yescharacteristic
83C23×C4×C61—21no—
84C23×C4×C61C2311yescharacteristic
85#137×C61—22no—
86#137×C61—41no—
87AGL(1,ℤ/8)×C61—22no—
88AGL(1,ℤ/8)×C61—22no—
89AGL(1,ℤ/8)×C61—41no—
90AGL(1,ℤ/8)×C61—41no—
91C2×Q16×C61—21no—
92C2×SD16×C61—22no—
93C2×SD16×C61—21no—
94C2×SD16×C61—21no—
95C2×SD16×C61—21no—
96C2×SD16×C61—21no—
97C2×SD16×C61—21no—
98C2×SD16×C61—41no—
99C2×D8×C61—21no—
100C2×D8×C61—21no—
101C2×D8×C61—22no—
102C2×D8×C61—21no—
103C2×D8×C61—21no—
104C2×D8×C61—41no—
105#131×C61—22no—
106#131×C61—41no—
107C2×M16×C61—21no—
108C2×M16×C61—21no—
109C2×M16×C61—21no—
110C2×M16×C61—22no—
111C2×M16×C61—22no—
112C2×M16×C61—41no—
113C2×M16×C61—41no—
114C2×M16×C61C2311yescharacteristic
115C2×M16×C61C2311yescharacteristic
116C2×M16×C61C2311yescharacteristic
117C2×M16×C61C2311yescharacteristic
118C2×M16×C61C2311yescharacteristic
119C2×M16×C61C2311yescharacteristic
120C22×C8×C61—21no—
121C22×C8×C61—21no—
122C22×C8×C61—21no—
123C22×C8×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125#123×C61—21no—
126C22⋊Q8×C61D411yescharacteristic
127C22⋊Q8×C61D411yescharacteristic
128#121×C61—21no—
129#121×C61—21no—
130#121×C61—21no—
131#121×C61—21no—
132#121×C61D411yescharacteristic
133#121×C61D411yescharacteristic
134#120×C61—21no—
135C4×D4×C61—21no—
136C4×D4×C61—21no—
137#117×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140#108×C61—22no—
141#108×C61—41no—
142#107×C61—21no—
143#106×C61—21no—
144C4⋊C8×C61—21no—
145C4⋊C8×C61—21no—
146#103×C61—21no—
147#103×C61—21no—
148#103×C61—21no—
149#103×C61—21no—
150#103×C61—21no—
151#102×C61—21no—
152#102×C61—21no—
153#102×C61—21no—
154#102×C61—21no—
155#102×C61—21no—
156#102×C61—21no—
157#102×C61—21no—
158#101×C61—22no—
159#101×C61D414yescomplemented
160#100×C61—22no—
161#100×C61—22no—
162#100×C61—22no—
163#100×C61—41no—
164C22⋊C8×C61—21no—
165C22⋊C8×C61—21no—
166C22⋊C8×C61—21no—
167C22⋊C8×C61—21no—
168C22⋊C8×C61D411yescharacteristic
169C22⋊C8×C61D411yescharacteristic
170C22⋊C8×C61D411yescharacteristic
171C22⋊C8×C61D411yescharacteristic
172#97×C61—21no—
173C4×C8×C61—21no—
174C24×C61—21no—
175C24×C61—21no—
176C24×C61#4111yescharacteristic
177#41×C61—21no—
178#41×C61—21no—
179#41×C61—21no—
180#41×C61—21no—
181#41×C61—42no—
182#41×C61—42no—
183#41×C61—42no—
184#41×C61—42no—
185#41×C61—42no—
186#41×C61—42no—
187#41×C61—42no—
188#41×C61—42no—
189C2×Q8×C61—21no—
190C2×Q8×C61—21no—
191C2×Q8×C61—21no—
192C2×Q8×C61—21no—
193C2×Q8×C61—21no—
194C2×Q8×C61C2×D412yes—
195C2×Q8×C61C2×D411yescharacteristic
196C2×D4×C61—24no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—21no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—21no—
206C2×D4×C61—21no—
207C2×D4×C61—21no—
208C2×D4×C61—21no—
209C2×D4×C61—21no—
210C2×D4×C61—21no—
211C2×D4×C61—42no—
212C2×D4×C61—41no—
213C2×D4×C61—41no—
214C2×D4×C61—41no—
215C2×D4×C61—41no—
216C2×D4×C61—82no—
217C2×D4×C61C2×D411yescharacteristic
218C2×D4×C61#4112yes—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—24no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—42no—
228C22×C4×C61—41no—
229C22×C4×C61—41no—
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61#4111yescharacteristic
235C22×C4×C61C2411yescharacteristic
236Q16×C61—42no—
237SD16×C61—42no—
238SD16×C61—42no—
239SD16×C61—42no—
240SD16×C61—42no—
241SD16×C61—42no—
242D8×C61—42no—
243D8×C61—42no—
244D8×C61—42no—
245D8×C61—42no—
246M16×C61—21no—
247M16×C61—21no—
248M16×C61—21no—
249M16×C61—21no—
250M16×C61—21no—
251M16×C61—21no—
252M16×C61—21no—
253M16×C61—21no—
254M16×C61—21no—
255M16×C61—21no—
256M16×C61—42no—
257M16×C61—42no—
258M16×C61—42no—
259M16×C61C2×D412yes—
260M16×C61C2×D412yes—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61—21no—
270C2×C8×C61—21no—
271C2×C8×C61—42no—
272C2×C8×C61—42no—
273C2×C8×C61—42no—
274C2×C8×C61C2×D411yescharacteristic
275C2×C8×C61C2×D411yescharacteristic
276C2×C8×C61C2×D411yescharacteristic
277C2×C8×C61C2×D411yescharacteristic
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—21no—
281C4⋊C4×C61—21no—
282C4⋊C4×C61C2×D411yescharacteristic
283C4⋊C4×C61C2×D411yescharacteristic
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61—41no—
290C22⋊C4×C61—41no—
291C42×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—22no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—81no—
304C23×C61—81no—
305C23×C61—81no—
306C23×C61—81no—
307C23×C61#12111yescharacteristic
308C23×C61#12111yescharacteristic
309C23×C61C2×#4111yescharacteristic
310Q8×C61—21no—
311Q8×C61—22no—
312Q8×C61—22no—
313Q8×C61—21no—
314Q8×C61—41no—
315Q8×C61—41no—
316D4×C61—21no—
317D4×C61—22no—
318D4×C61—21no—
319D4×C61—22no—
320D4×C61—42no—
321D4×C61—44no—
322D4×C61—44no—
323D4×C61—41no—
324D4×C61—41no—
325D4×C61—41no—
326D4×C61—41no—
327D4×C61—41no—
328D4×C61—41no—
329D4×C61—41no—
330D4×C61—41no—
331D4×C61—81no—
332D4×C61—82no—
333D4×C61—82no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—22no—
348C2×C4×C61—44no—
349C2×C4×C61—44no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—81no—
356C2×C4×C61#12111yescharacteristic
357C2×C4×C61#12111yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C22×D411yescharacteristic
361C2×C4×C61C2×#4111yescharacteristic
362C2×C4×C61H(5,𝔽2)11yescharacteristic
363C2×C4×C61H(5,𝔽2)11yescharacteristic
364C8×C61—21no—
365C8×C61—21no—
366C8×C61—22no—
367C8×C61—22no—
368C8×C61—21no—
369C8×C61—21no—
370C8×C61—41no—
371C8×C61—41no—
372C8×C61—41no—
373C8×C61—41no—
374#25147C6111yesmaximal, characteristic, direct product factor, Sylow
375C22×C61—21no—
376C22×C61—21no—
377C22×C61—21no—
378C22×C61—21no—
379C22×C61—21no—
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—21no—
383C22×C61—42no—
384C22×C61—41no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—81no—
388C22×C61—81no—
389C22×C61—82no—
390C22×C61—82no—
391C22×C61—81no—
392C22×C61—81no—
393C22×C61—81no—
394C22×C61—81no—
395C22×C61—81no—
396C22×C61—161no—
397C22×C61—161no—
398C22×C61C2×#12111yescharacteristic
399C22×C61#52511yescharacteristic
400C22×C61#53811yescharacteristic
401C4×C61—21no—
402C4×C61—21no—
403C4×C61—42no—
404C4×C61—41no—
405C4×C61—41no—
406C4×C61—41no—
407C4×C61—81no—
408C4×C61D4211yescharacteristic
409C4×C61D4211yescharacteristic
410C4×C61#54611yescharacteristic
411C4×C61#54611yescharacteristic
412C2×#471C2×C6111yescharacteristic, complemented
413#3055C2×C6111yescharacteristic, complemented
414#3005C2×C6111yescharacteristic, complemented
415C2×#449C2×C6111yescharacteristic, complemented
416#2933C2×C6111yescharacteristic, complemented
417C2×#413C2×C6111yescharacteristic, complemented
418#2063C2×C6111yescharacteristic, complemented
419#2052C2×C6111yescharacteristic, complemented
420#2046C2×C6111yescharacteristic, complemented
421#2018C2×C6111yescharacteristic, complemented
422#1978C2×C6111yescharacteristic, complemented
423#1930C2×C6111yescharacteristic, complemented
424#1907C2×C6111yescharacteristic, complemented
425#1900C2×C6111yescharacteristic, complemented
426#1855C2×C6111yescharacteristic, complemented
427C2×C61—21no—
428C2×C61—21no—
429C2×C61—41no—
430C2×C61—41no—
431C2×C61—81no—
432C2×C61—82no—
433C2×C61—161no—
434C2×C61#242411yescharacteristic
435C2×C61#306711yescharacteristic
436C2×C61#306811yescharacteristic
437C22×#41C22×C6111yescharacteristic
438C2×#137C22×C6111yescharacteristic
439C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
440C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
441C22×SD16C22×C6111yescharacteristic
442C22×D8C22×C6111yescharacteristic
443C2×#131C22×C6111yescharacteristic
444C22×M16C22×C6111yescharacteristic
445C22×M16C22×C6111yescharacteristic
446#525C22×C6111yescharacteristic
447C2×#121C22×C6111yescharacteristic
448#471—24no—
449#469—21no—
450#468—21no—
451#466—21no—
452#465—21no—
453#452—21no—
454#452—21no—
455#449—21no—
456#449—21no—
457#449—21no—
458#449—21no—
459#449—21no—
460#449—21no—
461#436—21no—
462#435—21no—
463#435—21no—
464C8×D4—21no—
465C2×#108C22×C6111yescharacteristic
466C2×#108C22×C6111yescharacteristic
467#428C22×C6111yescharacteristic
468#424C22×C6111yescharacteristic
469#419C22×C6111yescharacteristic
470#418C22×C6111yescharacteristic
471#418C22×C6111yescharacteristic
472#417C22×C6111yescharacteristic
473C2×#103C22×C6111yescharacteristic
474C2×#102C22×C6111yescharacteristic
475#413—24no—
476C2×#101C22×C6111yescharacteristic
477C2×#101C22×C6111yescharacteristic
478C2×#100C22×C6111yescharacteristic
479C2×#100C22×C6111yescharacteristic
480C2×#100C22×C6111yescharacteristic
481C2×#100C22×C6111yescharacteristic
482#408C22×C6111yescharacteristic
483#407C22×C6111yescharacteristic
484C2×C22⋊C8C22×C6111yescharacteristic
485#405C22×C6111yescharacteristic
486#343C22×C6111yescharacteristic
487#343C22×C6111yescharacteristic
488#341C22×C6111yescharacteristic
489#341C22×C6111yescharacteristic
490C61#2514711yescharacteristic, direct product factor, Sylow
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—21no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41C23×C6111yescharacteristic
500C22×Q8C23×C6111yescharacteristic
501C22×D4—21no—
502C22×D4—21no—
503C22×D4C23×C6111yescharacteristic
504C22×D4C23×C6111yescharacteristic
505C23×C4—21no—
506C23×C4C23×C6111yescharacteristic
507#137—22no—
508#137—41no—
509AGL(1,ℤ/8)—22no—
510AGL(1,ℤ/8)—22no—
511AGL(1,ℤ/8)—41no—
512AGL(1,ℤ/8)—41no—
513C2×Q16—21no—
514C2×SD16—22no—
515C2×SD16—21no—
516C2×SD16—21no—
517C2×SD16—21no—
518C2×SD16—21no—
519C2×SD16—21no—
520C2×SD16—41no—
521C2×D8—21no—
522C2×D8—21no—
523C2×D8—22no—
524C2×D8—21no—
525C2×D8—21no—
526C2×D8—41no—
527#131—22no—
528#131—41no—
529C2×M16—21no—
530C2×M16—21no—
531C2×M16—21no—
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—41no—
535C2×M16—41no—
536C2×M16C23×C6111yescharacteristic
537C2×M16C23×C6111yescharacteristic
538C2×M16C23×C6111yescharacteristic
539C2×M16C23×C6111yescharacteristic
540C2×M16C23×C6111yescharacteristic
541C2×M16C23×C6111yescharacteristic
542C22×C8—21no—
543C22×C8—21no—
544C22×C8—21no—
545C22×C8C23×C6111yescharacteristic
546C22×C8C23×C6111yescharacteristic
547#123—21no—
548C22⋊Q8D4×C6111yescharacteristic
549C22⋊Q8D4×C6111yescharacteristic
550#121—21no—
551#121—21no—
552#121—21no—
553#121—21no—
554#121D4×C6111yescharacteristic
555#121D4×C6111yescharacteristic
556#120—21no—
557C4×D4—21no—
558C4×D4—21no—
559#117C23×C6111yescharacteristic
560C2×C4⋊C4C23×C6111yescharacteristic
561C2×C22⋊C4—21no—
562#108—22no—
563#108—41no—
564#107—21no—
565#106—21no—
566C4⋊C8—21no—
567C4⋊C8—21no—
568#103—21no—
569#103—21no—
570#103—21no—
571#103—21no—
572#103—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#101—22no—
581#101D4×C6114yescomplemented
582#100—22no—
583#100—22no—
584#100—22no—
585#100—41no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8D4×C6111yescharacteristic
591C22⋊C8D4×C6111yescharacteristic
592C22⋊C8D4×C6111yescharacteristic
593C22⋊C8D4×C6111yescharacteristic
594#97—21no—
595C4×C8—21no—
596C24—21no—
597C24—21no—
598C24#41×C6111yescharacteristic
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—42no—
607#41—42no—
608#41—42no—
609#41—42no—
610#41—42no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8C2×D4×C6112yes—
617C2×Q8C2×D4×C6111yescharacteristic
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—42no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—41no—
637C2×D4—41no—
638C2×D4—82no—
639C2×D4C2×D4×C6111yescharacteristic
640C2×D4#41×C6112yes—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—42no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4C2×D4×C6111yescharacteristic
653C22×C4C2×D4×C6111yescharacteristic
654C22×C4C2×D4×C6111yescharacteristic
655C22×C4C2×D4×C6111yescharacteristic
656C22×C4#41×C6111yescharacteristic
657C22×C4C24×C6111yescharacteristic
658Q16—42no—
659SD16—42no—
660SD16—42no—
661SD16—42no—
662SD16—42no—
663SD16—42no—
664D8—42no—
665D8—42no—
666D8—42no—
667D8—42no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—21no—
672M16—21no—
673M16—21no—
674M16—21no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—42no—
679M16—42no—
680M16—42no—
681M16C2×D4×C6112yes—
682M16C2×D4×C6112yes—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8C2×D4×C6111yescharacteristic
697C2×C8C2×D4×C6111yescharacteristic
698C2×C8C2×D4×C6111yescharacteristic
699C2×C8C2×D4×C6111yescharacteristic
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4C2×D4×C6111yescharacteristic
705C4⋊C4C2×D4×C6111yescharacteristic
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—41no—
712C22⋊C4—41no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—81no—
729C23#121×C6111yescharacteristic
730C23#121×C6111yescharacteristic
731C23C2×#41×C6111yescharacteristic
732Q8—21no—
733Q8—22no—
734Q8—22no—
735Q8—21no—
736Q8—41no—
737Q8—41no—
738D4—21no—
739D4—22no—
740D4—21no—
741D4—22no—
742D4—42no—
743D4—44no—
744D4—44no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—81no—
754D4—82no—
755D4—82no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—81no—
778C2×C4#121×C6111yescharacteristic
779C2×C4#121×C6111yescharacteristic
780C2×C4C22×D4×C6111yescharacteristic
781C2×C4C22×D4×C6111yescharacteristic
782C2×C4C22×D4×C6111yescharacteristic
783C2×C4C2×#41×C6111yescharacteristic
784C2×C4H(5,𝔽2)×C6111yescharacteristic
785C2×C4H(5,𝔽2)×C6111yescharacteristic
786C8—21no—
787C8—21no—
788C8—22no—
789C8—22no—
790C8—21no—
791C8—21no—
792C8—41no—
793C8—41no—
794C8—41no—
795C8—41no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—41no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—81no—
809C22—81no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—161no—
818C22—161no—
819C22C2×#121×C6111yescharacteristic
820C22C61×#52511yescharacteristic
821C22C61×#53811yescharacteristic
822C4—21no—
823C4—21no—
824C4—41no—
825C4—41no—
826C4—42no—
827C4—41no—
828C4—81no—
829C4D42×C6111yescharacteristic
830C4D42×C6111yescharacteristic
831C4C61×#54611yescharacteristic
832C4C61×#54611yescharacteristic
833C2—21no—
834C2—21no—
835C2—41no—
836C2—41no—
837C2—81no—
838C2—82no—
839C2—161no—
840C2C61×#242411yescharacteristic
841C2C61×#306711yescharacteristic
842C2C61×#306811yescharacteristic
subgroupG/H
center, socleC22×C61C2×#121
commutator, Frattini, cosocleC22×C4C24×C61
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C61×#471C2semidirect
2. C61×#3055C2semidirect
3. C61×#3005C2semidirect
4. C2×C61×#449C2semidirect
5. C61×#2933C2semidirect
6. C2×C61×#413C2semidirect
7. C61×#2063C2semidirect
8. C61×#2052C2semidirect
9. C61×#2046C2semidirect
10. C61×#2018C2semidirect
11. C61×#1978C2semidirect
12. C61×#1930C2semidirect
13. C61×#1907C2semidirect
14. C61×#1900C2semidirect
15. C61×#1855C2semidirect
159. #101×C61D4semidirect
374. #25147C61direct (N × H)
412. C2×#471C2×C61semidirect
413. #3055C2×C61semidirect
414. #3005C2×C61semidirect
415. C2×#449C2×C61semidirect
416. #2933C2×C61semidirect
417. C2×#413C2×C61semidirect
418. #2063C2×C61semidirect
419. #2052C2×C61semidirect
420. #2046C2×C61semidirect
421. #2018C2×C61semidirect
422. #1978C2×C61semidirect
423. #1930C2×C61semidirect
424. #1907C2×C61semidirect
425. #1900C2×C61semidirect
426. #1855C2×C61semidirect
490. C61#25147direct (N × H)
581. #101D4×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#4712
C61×#30552
C61×#30052
C2×C61×#4492
C61×#29332
C2×C61×#4132
C61×#20632
C61×#20522
C61×#20462
C61×#20182
C61×#19782
C61×#19302
C61×#19072
C61×#19002
C61×#18552
#2514761