Finite Group Databasebeta

← C61×#24469 #29527902

Subgroups — C61×#24469 #29527902

Order 15616.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3489C211yesmaximal, characteristic, complemented
2C61×#3055C211yesmaximal, characteristic, complemented
3C2×C61×#454C211yesmaximal, characteristic, complemented
4C61×#3006C211yesmaximal, characteristic, complemented
5C2×C61×#421C211yesmaximal, characteristic, complemented
6C61×#2620C211yesmaximal, characteristic, complemented
7C61×#2039C211yesmaximal, characteristic, complemented
8C61×#2038C211yesmaximal, characteristic, complemented
9C61×#2006C211yesmaximal, characteristic, complemented
10C61×#2003C211yesmaximal, characteristic, complemented
11C61×#1901C211yesmaximal, characteristic, complemented
12C61×#1897C211yesmaximal, characteristic, complemented
13C61×#1883C211yesmaximal, characteristic, complemented
14C61×#1859C211yesmaximal, characteristic, complemented
15C61×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C61C2211yescharacteristic
17C22×#41×C61C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C61C2211yescharacteristic, complemented
21C22×M16×C61C2211yescharacteristic
22D4×Q8×C61—21no—
23C61×#548—21no—
24C61×#547—21no—
25C61×#547—22no—
26C61×#546—21no—
27C61×#546—22no—
28C61×#537—21no—
29C61×#537C2211yescharacteristic
30C61×#536—21no—
31C61×#536C2211yescharacteristic
32C2×#124×C61C2211yescharacteristic, complemented
33C61×#525—21no—
34C61×#525C2211yescharacteristic
35C2×C22⋊Q8×C61—21no—
36C2×C22⋊Q8×C61C2211yescharacteristic
37C2×#121×C61C2211yescharacteristic
38C61×#520C2211yescharacteristic
39C2×#117×C61C2211yescharacteristic
40C61×#469—21no—
41C61×#468—21no—
42C61×#466—21no—
43C61×#465—21no—
44C61×#454—24no—
45C61×#449—21no—
46C61×#449—21no—
47C61×#448—21no—
48C61×#447—21no—
49C61×#428C2211yescharacteristic, complemented
50C61×#421—24no—
51C2×#104×C61C2211yescharacteristic
52C2×#104×C61C2211yescharacteristic
53C2×#104×C61C2211yescharacteristic
54C2×#104×C61C2211yescharacteristic
55C2×#104×C61C2211yescharacteristic, complemented
56C2×#104×C61C2211yescharacteristic, complemented
57C61×#418C2211yescharacteristic, complemented
58C61×#417C2211yescharacteristic
59C61×#417C2211yescharacteristic
60C61×#417C2211yescharacteristic, complemented
61C2×#101×C61C2211yescharacteristic, complemented
62C2×#101×C61C2211yescharacteristic, complemented
63C61×#407C2211yescharacteristic
64C61×#396—22no—
65C61×#394—22no—
66C61×#391C2211yescharacteristic, complemented
67C61×#390C2211yescharacteristic, complemented
68C61×#384C2211yescharacteristic, complemented
69C61×#343C2211yescharacteristic, complemented
70C61×#343C2211yescharacteristic, complemented
71C61×#339C2211yescharacteristic, complemented
72C61×#339C2211yescharacteristic, complemented
732−1+4×C61—22no—
742−1+4×C61—22no—
752−1+4×C61—41no—
762−1+4×C61—41no—
77C2×#41×C61—21no—
78C2×#41×C61—21no—
79C2×#41×C61—21no—
80C2×#41×C61—22no—
81C2×#41×C61—21no—
82C2×#41×C61—22no—
83C2×#41×C61—22no—
84C2×#41×C61—41no—
85C2×#41×C61—41no—
86C2×#41×C61D411yescharacteristic
87C2×#41×C61D411yescharacteristic
88C2×#41×C61C2311yescharacteristic
89C2×#41×C61C2311yescharacteristic
90C2×#41×C61C2311yescharacteristic
91C22×Q8×C61—21no—
92C22×Q8×C61—21no—
93C22×Q8×C61D411yescharacteristic
94C22×Q8×C61C2311yescharacteristic
95C22×D4×C61—21no—
96C22×D4×C61—21no—
97C22×D4×C61D411yescharacteristic
98C22×D4×C61C2311yescharacteristic
99C23×C4×C61—21no—
100C23×C4×C61C2311yescharacteristic
101AGL(1,ℤ/8)×C61—22no—
102AGL(1,ℤ/8)×C61—22no—
103AGL(1,ℤ/8)×C61—22no—
104AGL(1,ℤ/8)×C61—41no—
105AGL(1,ℤ/8)×C61—41no—
106AGL(1,ℤ/8)×C61—41no—
107C2×SD16×C61—21no—
108C2×SD16×C61—21no—
109C2×SD16×C61—21no—
110C2×D8×C61—21no—
111C2×D8×C61—21no—
112C2×D8×C61—21no—
113C2×M16×C61—21no—
114C2×M16×C61—22no—
115C2×M16×C61—41no—
116C2×M16×C61C2311yescharacteristic
117C2×M16×C61C2311yescharacteristic
118C2×M16×C61C2311yescharacteristic
119C2×M16×C61C2311yescharacteristic
120C22×C8×C61—21no—
121C4⋊Q8×C61—22no—
122C4⋊Q8×C61—21no—
123#124×C61—22no—
124#124×C61—21no—
125#124×C61—22no—
126#124×C61—41no—
127#123×C61—22no—
128#123×C61—22no—
129#123×C61—22no—
130#123×C61—22no—
131#123×C61—21no—
132C22⋊Q8×C61—22no—
133C22⋊Q8×C61—22no—
134C22⋊Q8×C61—22no—
135C22⋊Q8×C61—21no—
136C22⋊Q8×C61—21no—
137C22⋊Q8×C61—21no—
138C22⋊Q8×C61—21no—
139C22⋊Q8×C61—21no—
140C22⋊Q8×C61—21no—
141C22⋊Q8×C61—21no—
142C22⋊Q8×C61—21no—
143C22⋊Q8×C61D411yescharacteristic
144C22⋊Q8×C61D411yescharacteristic
145#121×C61—22no—
146#121×C61—22no—
147#121×C61—22no—
148#121×C61—21no—
149#121×C61—21no—
150#121×C61—22no—
151#121×C61—21no—
152#121×C61—21no—
153#121×C61—21no—
154#121×C61—21no—
155#121×C61D411yescharacteristic
156#121×C61D411yescharacteristic
157#120×C61—22no—
158#120×C61—21no—
159C4×Q8×C61—21no—
160C4×D4×C61—22no—
161C4×D4×C61—22no—
162C4×D4×C61—21no—
163C4×D4×C61—22no—
164C4×D4×C61—21no—
165C4×D4×C61—21no—
166#117×C61—21no—
167#117×C61—22no—
168#117×C61—41no—
169#117×C61C2311yescharacteristic
170C2×C4⋊C4×C61—22no—
171C2×C4⋊C4×C61—21no—
172C2×C4⋊C4×C61—21no—
173C2×C4⋊C4×C61—22no—
174C2×C4⋊C4×C61D412yes—
175C2×C4⋊C4×C61C2311yescharacteristic
176C2×C4⋊C4×C61C2311yescharacteristic
177C2×C22⋊C4×C61—22no—
178C2×C22⋊C4×C61—21no—
179C2×C22⋊C4×C61—22no—
180C2×C22⋊C4×C61—21no—
181C2×C22⋊C4×C61—22no—
182C2×C22⋊C4×C61D412yes—
183C2×C42×C61C2311yescharacteristic
184C2×C42×C61C2311yescharacteristic
185#107×C61—21no—
186#106×C61—21no—
187#104×C61—22no—
188#104×C61—22no—
189#104×C61—22no—
190#104×C61—22no—
191#104×C61—41no—
192#104×C61D414yescomplemented
193#103×C61—21no—
194#103×C61—21no—
195#103×C61—21no—
196#102×C61—21no—
197#102×C61—21no—
198#102×C61—21no—
199#102×C61—21no—
200#102×C61—21no—
201#101×C61—22no—
202#101×C61—41no—
203C22⋊C8×C61—21no—
204C22⋊C8×C61—21no—
205#95×C61—22no—
206C24×C61—21no—
207C24×C61—21no—
208C24×C61C2×D411yescharacteristic
209#41×C61—21no—
210#41×C61—21no—
211#41×C61—22no—
212#41×C61—22no—
213#41×C61—21no—
214#41×C61—21no—
215#41×C61—21no—
216#41×C61—21no—
217#41×C61—21no—
218#41×C61—21no—
219#41×C61—21no—
220#41×C61—21no—
221#41×C61—42no—
222#41×C61—42no—
223#41×C61—41no—
224#41×C61—41no—
225#41×C61—42no—
226#41×C61—42no—
227#41×C61—42no—
228#41×C61—42no—
229#41×C61—44no—
230#41×C61—44no—
231#41×C61—42no—
232#41×C61—42no—
233#41×C61C2×D412yes—
234#41×C61#4112yes—
235C2×Q8×C61—22no—
236C2×Q8×C61—21no—
237C2×Q8×C61—21no—
238C2×Q8×C61—21no—
239C2×Q8×C61—21no—
240C2×Q8×C61—21no—
241C2×Q8×C61—21no—
242C2×Q8×C61—21no—
243C2×Q8×C61—22no—
244C2×Q8×C61—41no—
245C2×Q8×C61—42no—
246C2×Q8×C61—42no—
247C2×Q8×C61—42no—
248C2×Q8×C61—42no—
249C2×Q8×C61C2×D411yescharacteristic
250C2×Q8×C61C2×D411yescharacteristic
251C2×Q8×C61C2×D411yescharacteristic
252C2×D4×C61—21no—
253C2×D4×C61—22no—
254C2×D4×C61—22no—
255C2×D4×C61—21no—
256C2×D4×C61—21no—
257C2×D4×C61—21no—
258C2×D4×C61—21no—
259C2×D4×C61—21no—
260C2×D4×C61—22no—
261C2×D4×C61—21no—
262C2×D4×C61—21no—
263C2×D4×C61—21no—
264C2×D4×C61—21no—
265C2×D4×C61—21no—
266C2×D4×C61—21no—
267C2×D4×C61—21no—
268C2×D4×C61—21no—
269C2×D4×C61—41no—
270C2×D4×C61—42no—
271C2×D4×C61—42no—
272C2×D4×C61—41no—
273C2×D4×C61—41no—
274C2×D4×C61—82no—
275C2×D4×C61C2×D411yescharacteristic
276C2×D4×C61C2×D411yescharacteristic
277C2×D4×C61C2×D411yescharacteristic
278C22×C4×C61—21no—
279C22×C4×C61—21no—
280C22×C4×C61—21no—
281C22×C4×C61—21no—
282C22×C4×C61—21no—
283C22×C4×C61—22no—
284C22×C4×C61—22no—
285C22×C4×C61—21no—
286C22×C4×C61—21no—
287C22×C4×C61—22no—
288C22×C4×C61—21no—
289C22×C4×C61—21no—
290C22×C4×C61—21no—
291C22×C4×C61—21no—
292C22×C4×C61—21no—
293C22×C4×C61—21no—
294C22×C4×C61—42no—
295C22×C4×C61—42no—
296C22×C4×C61C2×D412yes—
297C22×C4×C61C2×D411yescharacteristic
298C22×C4×C61C2×D411yescharacteristic
299C22×C4×C61C2×D411yescharacteristic
300C22×C4×C61C2×D411yescharacteristic
301C22×C4×C61C2×D411yescharacteristic
302C22×C4×C61C2×D412yes—
303C22×C4×C61C2411yescharacteristic
304SD16×C61—42no—
305SD16×C61—42no—
306SD16×C61—42no—
307D8×C61—42no—
308D8×C61—42no—
309D8×C61—42no—
310M16×C61—21no—
311M16×C61—21no—
312M16×C61—21no—
313M16×C61—21no—
314M16×C61—21no—
315M16×C61—21no—
316M16×C61—21no—
317M16×C61—42no—
318M16×C61C2×D412yes—
319C2×C8×C61—21no—
320C2×C8×C61—21no—
321C2×C8×C61—21no—
322C2×C8×C61—21no—
323C2×C8×C61—42no—
324C4⋊C4×C61—22no—
325C4⋊C4×C61—22no—
326C4⋊C4×C61—22no—
327C4⋊C4×C61—22no—
328C4⋊C4×C61—21no—
329C4⋊C4×C61—22no—
330C4⋊C4×C61—22no—
331C4⋊C4×C61—21no—
332C4⋊C4×C61—21no—
333C4⋊C4×C61—21no—
334C4⋊C4×C61—21no—
335C4⋊C4×C61—21no—
336C4⋊C4×C61—42no—
337C4⋊C4×C61—82no—
338C4⋊C4×C61C2×D411yescharacteristic
339C4⋊C4×C61C2×D411yescharacteristic
340C22⋊C4×C61—22no—
341C22⋊C4×C61—22no—
342C22⋊C4×C61—22no—
343C22⋊C4×C61—22no—
344C22⋊C4×C61—22no—
345C22⋊C4×C61—21no—
346C22⋊C4×C61—22no—
347C22⋊C4×C61—22no—
348C22⋊C4×C61—21no—
349C22⋊C4×C61—21no—
350C22⋊C4×C61—21no—
351C22⋊C4×C61—21no—
352C22⋊C4×C61—44no—
353C22⋊C4×C61—42no—
354C22⋊C4×C61—41no—
355C22⋊C4×C61—41no—
356C22⋊C4×C61—82no—
357C42×C61—22no—
358C42×C61—21no—
359C42×C61—21no—
360C42×C61—21no—
361C42×C61—21no—
362C42×C61C2×D412yes—
363C23×C61—21no—
364C23×C61—21no—
365C23×C61—21no—
366C23×C61—21no—
367C23×C61—21no—
368C23×C61—41no—
369C23×C61—41no—
370C23×C61—42no—
371C23×C61—42no—
372C23×C61—42no—
373C23×C61—42no—
374C23×C61—41no—
375C23×C61—41no—
376C23×C61—41no—
377C23×C61—81no—
378C23×C61#12011yescharacteristic
379C23×C61#12011yescharacteristic
380C23×C61C22×D411yescharacteristic
381Q8×C61—21no—
382Q8×C61—21no—
383Q8×C61—21no—
384Q8×C61—21no—
385Q8×C61—21no—
386Q8×C61—42no—
387Q8×C61—44no—
388Q8×C61—41no—
389Q8×C61—41no—
390Q8×C61—41no—
391Q8×C61—41no—
392Q8×C61#12112yes—
393D4×C61—22no—
394D4×C61—22no—
395D4×C61—21no—
396D4×C61—21no—
397D4×C61—21no—
398D4×C61—21no—
399D4×C61—21no—
400D4×C61—42no—
401D4×C61—42no—
402D4×C61—42no—
403D4×C61—42no—
404D4×C61—44no—
405D4×C61—41no—
406D4×C61—41no—
407D4×C61—41no—
408D4×C61—41no—
409D4×C61—41no—
410D4×C61—41no—
411D4×C61—41no—
412D4×C61—41no—
413D4×C61—81no—
414D4×C61—82no—
415D4×C61—82no—
416D4×C61—82no—
417D4×C61#12112yes—
418C2×C4×C61—21no—
419C2×C4×C61—21no—
420C2×C4×C61—21no—
421C2×C4×C61—21no—
422C2×C4×C61—21no—
423C2×C4×C61—21no—
424C2×C4×C61—21no—
425C2×C4×C61—21no—
426C2×C4×C61—21no—
427C2×C4×C61—22no—
428C2×C4×C61—21no—
429C2×C4×C61—21no—
430C2×C4×C61—22no—
431C2×C4×C61—21no—
432C2×C4×C61—22no—
433C2×C4×C61—21no—
434C2×C4×C61—21no—
435C2×C4×C61—22no—
436C2×C4×C61—21no—
437C2×C4×C61—22no—
438C2×C4×C61—22no—
439C2×C4×C61—22no—
440C2×C4×C61—42no—
441C2×C4×C61—42no—
442C2×C4×C61—42no—
443C2×C4×C61—44no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—44no—
447C2×C4×C61—41no—
448C2×C4×C61—41no—
449C2×C4×C61—41no—
450C2×C4×C61—41no—
451C2×C4×C61—42no—
452C2×C4×C61—41no—
453C2×C4×C61—42no—
454C2×C4×C61—41no—
455C2×C4×C61—41no—
456C2×C4×C61—41no—
457C2×C4×C61—82no—
458C2×C4×C61#12011yescharacteristic
459C2×C4×C61#12011yescharacteristic
460C2×C4×C61C22×D411yescharacteristic
461C2×C4×C61C22×D411yescharacteristic
462C2×C4×C61C22×D411yescharacteristic
463C2×C4×C61C2×#4111yescharacteristic
464C2×C4×C61H(5,𝔽2)11yescharacteristic
465C2×C4×C61H(5,𝔽2)11yescharacteristic
466C8×C61—22no—
467C8×C61—41no—
468C8×C61—41no—
469C8×C61—41no—
470#24469C6111yesmaximal, characteristic, direct product factor, Sylow
471C22×C61—21no—
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—22no—
476C22×C61—21no—
477C22×C61—21no—
478C22×C61—21no—
479C22×C61—21no—
480C22×C61—41no—
481C22×C61—41no—
482C22×C61—41no—
483C22×C61—41no—
484C22×C61—41no—
485C22×C61—41no—
486C22×C61—41no—
487C22×C61—41no—
488C22×C61—81no—
489C22×C61—81no—
490C22×C61—82no—
491C22×C61—82no—
492C22×C61—84no—
493C22×C61—81no—
494C22×C61—81no—
495C22×C61—81no—
496C22×C61C2×#12011yescharacteristic
497C22×C61D4211yescharacteristic
498C22×C61#54611yescharacteristic
499C4×C61—21no—
500C4×C61—21no—
501C4×C61—22no—
502C4×C61—42no—
503C4×C61—42no—
504C4×C61—41no—
505C4×C61—41no—
506C4×C61—41no—
507C4×C61—42no—
508C4×C61—41no—
509C4×C61—81no—
510C4×C61—81no—
511C4×C61C2×#12111yescharacteristic
512C4×C61#53411yescharacteristic
513C4×C61D4211yescharacteristic
514C4×C61#54611yescharacteristic
515#3489C2×C6111yescharacteristic, complemented
516#3055C2×C6111yescharacteristic, complemented
517C2×#454C2×C6111yescharacteristic, complemented
518#3006C2×C6111yescharacteristic, complemented
519C2×#421C2×C6111yescharacteristic, complemented
520#2620C2×C6111yescharacteristic, complemented
521#2039C2×C6111yescharacteristic, complemented
522#2038C2×C6111yescharacteristic, complemented
523#2006C2×C6111yescharacteristic, complemented
524#2003C2×C6111yescharacteristic, complemented
525#1901C2×C6111yescharacteristic, complemented
526#1897C2×C6111yescharacteristic, complemented
527#1883C2×C6111yescharacteristic, complemented
528#1859C2×C6111yescharacteristic, complemented
529#1793C2×C6111yescharacteristic, complemented
530C2×C61—21no—
531C2×C61—21no—
532C2×C61—41no—
533C2×C61—41no—
534C2×C61—42no—
535C2×C61—81no—
536C2×C61—81no—
537C2×C61—161no—
538C2×C61#241011yescharacteristic
539C2×C61#302011yescharacteristic
540C2×C61#302111yescharacteristic
541C2×2−1+4C22×C6111yescharacteristic
542C22×#41C22×C6111yescharacteristic
543C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
544C2×AGL(1,ℤ/8)C22×C6111yescharacteristic
545C2×AGL(1,ℤ/8)C22×C6111yescharacteristic, complemented
546C22×M16C22×C6111yescharacteristic
547D4×Q8—21no—
548#548—21no—
549#547—21no—
550#547—22no—
551#546—21no—
552#546—22no—
553#537—21no—
554#537C22×C6111yescharacteristic
555#536—21no—
556#536C22×C6111yescharacteristic
557C2×#124C22×C6111yescharacteristic, complemented
558#525—21no—
559#525C22×C6111yescharacteristic
560C2×C22⋊Q8—21no—
561C2×C22⋊Q8C22×C6111yescharacteristic
562C2×#121C22×C6111yescharacteristic
563#520C22×C6111yescharacteristic
564C2×#117C22×C6111yescharacteristic
565#469—21no—
566#468—21no—
567#466—21no—
568#465—21no—
569#454—24no—
570#449—21no—
571#449—21no—
572#448—21no—
573#447—21no—
574#428C22×C6111yescharacteristic, complemented
575#421—24no—
576C2×#104C22×C6111yescharacteristic
577C2×#104C22×C6111yescharacteristic
578C2×#104C22×C6111yescharacteristic
579C2×#104C22×C6111yescharacteristic
580C2×#104C22×C6111yescharacteristic, complemented
581C2×#104C22×C6111yescharacteristic, complemented
582#418C22×C6111yescharacteristic, complemented
583#417C22×C6111yescharacteristic
584#417C22×C6111yescharacteristic
585#417C22×C6111yescharacteristic, complemented
586C2×#101C22×C6111yescharacteristic, complemented
587C2×#101C22×C6111yescharacteristic, complemented
588#407C22×C6111yescharacteristic
589#396—22no—
590#394—22no—
591#391C22×C6111yescharacteristic, complemented
592#390C22×C6111yescharacteristic, complemented
593#384C22×C6111yescharacteristic, complemented
594#343C22×C6111yescharacteristic, complemented
595#343C22×C6111yescharacteristic, complemented
596#339C22×C6111yescharacteristic, complemented
597#339C22×C6111yescharacteristic, complemented
598C61#2446911yescharacteristic, direct product factor, Sylow
5992−1+4—22no—
6002−1+4—22no—
6012−1+4—41no—
6022−1+4—41no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—22no—
607C2×#41—21no—
608C2×#41—22no—
609C2×#41—22no—
610C2×#41—41no—
611C2×#41—41no—
612C2×#41D4×C6111yescharacteristic
613C2×#41D4×C6111yescharacteristic
614C2×#41C23×C6111yescharacteristic
615C2×#41C23×C6111yescharacteristic
616C2×#41C23×C6111yescharacteristic
617C22×Q8—21no—
618C22×Q8—21no—
619C22×Q8D4×C6111yescharacteristic
620C22×Q8C23×C6111yescharacteristic
621C22×D4—21no—
622C22×D4—21no—
623C22×D4D4×C6111yescharacteristic
624C22×D4C23×C6111yescharacteristic
625C23×C4—21no—
626C23×C4C23×C6111yescharacteristic
627AGL(1,ℤ/8)—22no—
628AGL(1,ℤ/8)—22no—
629AGL(1,ℤ/8)—22no—
630AGL(1,ℤ/8)—41no—
631AGL(1,ℤ/8)—41no—
632AGL(1,ℤ/8)—41no—
633C2×SD16—21no—
634C2×SD16—21no—
635C2×SD16—21no—
636C2×D8—21no—
637C2×D8—21no—
638C2×D8—21no—
639C2×M16—21no—
640C2×M16—22no—
641C2×M16—41no—
642C2×M16C23×C6111yescharacteristic
643C2×M16C23×C6111yescharacteristic
644C2×M16C23×C6111yescharacteristic
645C2×M16C23×C6111yescharacteristic
646C22×C8—21no—
647C4⋊Q8—22no—
648C4⋊Q8—21no—
649#124—22no—
650#124—21no—
651#124—22no—
652#124—41no—
653#123—22no—
654#123—22no—
655#123—22no—
656#123—21no—
657#123—22no—
658C22⋊Q8—22no—
659C22⋊Q8—22no—
660C22⋊Q8—22no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C6111yescharacteristic
670C22⋊Q8D4×C6111yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—21no—
675#121—21no—
676#121—22no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121D4×C6111yescharacteristic
682#121D4×C6111yescharacteristic
683#120—22no—
684#120—21no—
685C4×Q8—21no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—21no—
689C4×D4—22no—
690C4×D4—21no—
691C4×D4—21no—
692#117—21no—
693#117—22no—
694#117—41no—
695#117C23×C6111yescharacteristic
696C2×C4⋊C4—22no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4D4×C6112yes—
701C2×C4⋊C4C23×C6111yescharacteristic
702C2×C4⋊C4C23×C6111yescharacteristic
703C2×C22⋊C4—22no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4D4×C6112yes—
709C2×C42C23×C6111yescharacteristic
710C2×C42C23×C6111yescharacteristic
711#107—21no—
712#106—21no—
713#104—22no—
714#104—22no—
715#104—22no—
716#104—22no—
717#104—41no—
718#104D4×C6114yescomplemented
719#103—21no—
720#103—21no—
721#103—21no—
722#102—21no—
723#102—21no—
724#102—21no—
725#102—21no—
726#102—21no—
727#101—22no—
728#101—41no—
729C22⋊C8—21no—
730C22⋊C8—21no—
731#95—22no—
732C24—21no—
733C24—21no—
734C24C2×D4×C6111yescharacteristic
735#41—21no—
736#41—21no—
737#41—22no—
738#41—22no—
739#41—21no—
740#41—21no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—42no—
748#41—42no—
749#41—41no—
750#41—41no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—44no—
756#41—44no—
757#41—42no—
758#41—42no—
759#41C2×D4×C6112yes—
760#41#41×C6112yes—
761C2×Q8—22no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—41no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8C2×D4×C6111yescharacteristic
776C2×Q8C2×D4×C6111yescharacteristic
777C2×Q8C2×D4×C6111yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—41no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—82no—
801C2×D4C2×D4×C6111yescharacteristic
802C2×D4C2×D4×C6111yescharacteristic
803C2×D4C2×D4×C6111yescharacteristic
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4C2×D4×C6112yes—
823C22×C4C2×D4×C6111yescharacteristic
824C22×C4C2×D4×C6111yescharacteristic
825C22×C4C2×D4×C6111yescharacteristic
826C22×C4C2×D4×C6111yescharacteristic
827C22×C4C2×D4×C6111yescharacteristic
828C22×C4C2×D4×C6112yes—
829C22×C4C24×C6111yescharacteristic
830SD16—42no—
831SD16—42no—
832SD16—42no—
833D8—42no—
834D8—42no—
835D8—42no—
836M16—21no—
837M16—21no—
838M16—21no—
839M16—21no—
840M16—21no—
841M16—21no—
842M16—21no—
843M16—42no—
844M16C2×D4×C6112yes—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—42no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—21no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—42no—
863C4⋊C4—82no—
864C4⋊C4C2×D4×C6111yescharacteristic
865C4⋊C4C2×D4×C6111yescharacteristic
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—21no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—44no—
879C22⋊C4—42no—
880C22⋊C4—41no—
881C22⋊C4—41no—
882C22⋊C4—82no—
883C42—22no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42C2×D4×C6112yes—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—41no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—81no—
904C23#120×C6111yescharacteristic
905C23#120×C6111yescharacteristic
906C23C22×D4×C6111yescharacteristic
907Q8—21no—
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—42no—
913Q8—44no—
914Q8—41no—
915Q8—41no—
916Q8—41no—
917Q8—41no—
918Q8#121×C6112yes—
919D4—22no—
920D4—22no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—21no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—42no—
930D4—44no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—81no—
940D4—82no—
941D4—82no—
942D4—82no—
943D4#121×C6112yes—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—22no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—22no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—22no—
965C2×C4—21no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—44no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—44no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—41no—
979C2×C4—42no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—82no—
984C2×C4#120×C6111yescharacteristic
985C2×C4#120×C6111yescharacteristic
986C2×C4C22×D4×C6111yescharacteristic
987C2×C4C22×D4×C6111yescharacteristic
988C2×C4C22×D4×C6111yescharacteristic
989C2×C4C2×#41×C6111yescharacteristic
990C2×C4H(5,𝔽2)×C6111yescharacteristic
991C2×C4H(5,𝔽2)×C6111yescharacteristic
992C8—22no—
993C8—41no—
994C8—41no—
995C8—41no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—22no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—81no—
1014C22—81no—
1015C22—82no—
1016C22—82no—
1017C22—84no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22C2×#120×C6111yescharacteristic
1022C22D42×C6111yescharacteristic
1023C22C61×#54611yescharacteristic
1024C4—21no—
1025C4—21no—
1026C4—22no—
1027C4—42no—
1028C4—42no—
1029C4—41no—
1030C4—41no—
1031C4—41no—
1032C4—42no—
1033C4—41no—
1034C4—81no—
1035C4—81no—
1036C4C2×#121×C6111yescharacteristic
1037C4C61×#53411yescharacteristic
1038C4D42×C6111yescharacteristic
1039C4C61×#54611yescharacteristic
1040C2—21no—
1041C2—21no—
1042C2—41no—
1043C2—41no—
1044C2—42no—
1045C2—81no—
1046C2—81no—
1047C2—161no—
1048C2C61×#241011yescharacteristic
1049C2C61×#302011yescharacteristic
1050C2C61×#302111yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
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. C61×#3489C2semidirect
2. C61×#3055C2semidirect
3. C2×C61×#454C2semidirect
4. C61×#3006C2semidirect
5. C2×C61×#421C2semidirect
6. C61×#2620C2semidirect
7. C61×#2039C2semidirect
8. C61×#2038C2semidirect
9. C61×#2006C2semidirect
10. C61×#2003C2semidirect
11. C61×#1901C2semidirect
12. C61×#1897C2semidirect
13. C61×#1883C2semidirect
14. C61×#1859C2semidirect
15. C61×#1793C2semidirect
20. C2×AGL(1,ℤ/8)×C61C22semidirect
32. C2×#124×C61C22semidirect
49. C61×#428C22semidirect
55. C2×#104×C61C22semidirect
56. C2×#104×C61C22semidirect
57. C61×#418C22semidirect
60. C61×#417C22semidirect
61. C2×#101×C61C22semidirect
62. C2×#101×C61C22semidirect
66. C61×#391C22semidirect
67. C61×#390C22semidirect
68. C61×#384C22semidirect
69. C61×#343C22semidirect
70. C61×#343C22semidirect
71. C61×#339C22semidirect
72. C61×#339C22semidirect
192. #104×C61D4semidirect
470. #24469C61direct (N × H)
515. #3489C2×C61semidirect
516. #3055C2×C61semidirect
517. C2×#454C2×C61semidirect
518. #3006C2×C61semidirect
519. C2×#421C2×C61semidirect
520. #2620C2×C61semidirect
521. #2039C2×C61semidirect
522. #2038C2×C61semidirect
523. #2006C2×C61semidirect
524. #2003C2×C61semidirect
525. #1901C2×C61semidirect
526. #1897C2×C61semidirect
527. #1883C2×C61semidirect
528. #1859C2×C61semidirect
529. #1793C2×C61semidirect
545. C2×AGL(1,ℤ/8)C22×C61semidirect
557. C2×#124C22×C61semidirect
574. #428C22×C61semidirect
580. C2×#104C22×C61semidirect
581. C2×#104C22×C61semidirect
582. #418C22×C61semidirect
585. #417C22×C61semidirect
586. C2×#101C22×C61semidirect
587. C2×#101C22×C61semidirect
591. #391C22×C61semidirect
592. #390C22×C61semidirect
593. #384C22×C61semidirect
594. #343C22×C61semidirect
595. #343C22×C61semidirect
596. #339C22×C61semidirect
597. #339C22×C61semidirect
598. C61#24469direct (N × H)
718. #104D4×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#34892
C61×#30552
C2×C61×#4542
C61×#30062
C2×C61×#4212
C61×#26202
C61×#20392
C61×#20382
C61×#20062
C61×#20032
C61×#19012
C61×#18972
C61×#18832
C61×#18592
C61×#17932
#2446961